Physical properties of the ambient medium and of dense cores in the Perseus star-forming region derived from Herschel Gould Belt Survey observations
S. Pezzuto, M. Benedettini, J. Di Francesco, P. Palmeirim, S. Sadavoy, E. Schisano, G. Li Causi, Ph. André, D. Arzoumanian, J.-Ph. Bernard, S. Bontemps, D. Elia, E. Fiorellino, J.M. Kirk, V. Könyves, B. Ladjelate, A. Menshchikov, F. Motte, L. Piccotti, N. Schneider, L. Spinoglio, D. Ward-Thompson, C. D. Wilson
aa r X i v : . [ a s t r o - ph . GA ] N ov Astronomy & Astrophysicsmanuscript no. perseus © ESO 2020November 5, 2020
Physical properties of the ambient medium and of dense cores inthe Perseus star-forming region derived from Herschel ⋆ Gould BeltSurvey observations
S. Pezzuto , M. Benedettini , J. Di Francesco , , P. Palmeirim , S. Sadavoy , E. Schisano , G. Li Causi , Ph. André ,D. Arzoumanian , J.-Ph. Bernard , S. Bontemps , D. Elia , E. Fiorellino , , , , J.M. Kirk , V. Könyves , B.Ladjelate , A. Men’shchikov , F. Motte , , L. Piccotti , , , N. Schneider , L. Spinoglio , D. Ward-Thompson ,and C. D. Wilson (A ffi liations can be found after the references) ABSTRACT
The complex of star-forming regions in Perseus is one of the most studied due to its proximity (about 300 pc). In addition, its regions showdi ff erent activity of star formation and ages, with low-mass and intermediate-mass stars forming. In this paper, we present analyses of imagestaken with the Herschel
ESA satellite from 70 µ m to 500 µ m. From these images, we first constructed column density and dust temperature maps.Next, we identified compact cores in the maps at each wavelength, and characterise the cores using modified blackbody fits to their spectral energydistributions (SEDs): we identified 684 starless cores, of which 199 are bound and potential prestellar cores, and 132 protostars. We also matchedthe Herschel -identified young stars with
GAIA sources to model distance variations across the Perseus cloud. We measure a linear gradient functionwith right ascension and declination for the entire cloud. This function is the first quantitative attempt to derive in an analytical form the gradientin distances going from West to East Perseus. From the SED fits, mass and temperature of cores were derived. The core mass function can bemodelled with a log-normal distribution that peaks at 0.82 M ⊙ suggesting a star formation e ffi ciency of 0.30 for a peak in the system initial massfunction of stars at 0.25 M ⊙ . The high-mass tail can be modelled with a power law of slope ∼ − .
32, close to the Salpeter’s value. We also identifythe filamentary structure of Perseus and discuss the relation between filaments and star formation, confirming that stars form preferentially infilaments. We find that the majority of filaments where star formation is ongoing are transcritical against their own internal gravity because theirlinear masses are below the critical limit of 16 M ⊙ pc − above which we expect filaments to collapse. We find a possible explanation for thisresult, showing that a filament with a linear mass as low as 8 M ⊙ pc − can be already unstable. We confirm a linear relation between star formatione ffi ciency and slope of dust probability density function and a similar relation is also seen with the core formation e ffi ciency. We derive a lifetimefor the prestellar core phase of 1 . ± .
52 Myr for the whole Perseus but di ff erent regions have a wide range in prestellar core fractions, hint thatstar-formation has started only recently in some clumps. We also derive a free-fall time for prestellar cores of 0.16 Myr. Key words. circumstellar matter - Stars: protostars
1. Introduction
The aim of this paper is to derive a catalogue of cold com-pact cores, dust and gas condensations of < ∼ . Herschel observations andis part of the “Herschel Gould Belt Survey” (HGBS, Andréet al. 2010), which aims at probing the origin of the stellar ini-tial mass function (IMF) by finding the physical mechanisms in-fluencing star formation at its earliest stages. The HGBS teamhas already published core catalogues for many clouds: Aquila(Könyves et al. 2015, the reference paper for HGBS); L1495in Taurus (Marsh et al. 2016); Lupus (Benedettini et al. 2018);Corona Australis (Bresnahan et al. 2018); Orion B (Könyveset al. 2020), Ophiuchus (Ladjelate et al. 2020, in press); Cepheus(Di Francesco et al., ApJ, in press).The analysis of these data have led to the idea that grav-itational fragmentation of the cloud filaments is the dominantphysical mechanism generating prestellar cores within interstel-lar filaments (see André et al. 2014, and references therein). It ⋆ Herschel is an ESA space observatory with science instruments pro-vided by European-led Principal Investigator consortia and with impor-tant participation from NASA. was already suggested in the past that the filamentary structureof the interstellar medium is fragmenting to form cores (see,e.g., Román-Zúñiga et al. 2009), but only with
Herschel it be-came clear that filament fragmentation is the dominant mode of(solar-type) star formation, because the physical properties andthe spatial distribution of both the di ff use dust and of the com-pact cold cores in the clouds can be derived simultaneously, withsu ffi ciently high spatial resolution, 36 ′′ . Moreover, the large ar-eas observed combined with the high sensitivity of Herschel in-struments, allow to construct catalogues containing a factor 2–9more cores than in previously ground-based surveys (e.g., John-stone et al. 2000; Stanke et al. 2006; Enoch et al. 2006; Nutter &Ward-Thompson 2007; Alves et al. 2007).The first prestellar core mass functions (CMFs) in star-forming regions, (e.g., Motte et al. 1998; Testi & Sargent 1998)revealed a similarity between the shape of the CMF and the ini-tial mass function (IMF) of the stars. The system
IMF shows(Chabrier 2005) a log-normal distribution with a peak at 0 . M ⊙ ,and a high-mass tail for M ≥ M ⊙ modelled with a power-lawfunction d N / dlog( M ) ∝ M − . , also known as the Salpeter slope(Salpeter 1955).A quantitative assessment of the similarity between CMFand IMF was derived for the Pipe nebula by Alves et al. (2007) Article number, page 1 of 52 & Aproofs: manuscript no. perseus who found that the peak of the CMF was about 3 times higherthan the peak of the IMF. Assuming a one-to-one correspon-dence between cores and stars, the shift in the peaks of CMFand IMF was interpreted by Alves et al. (2007) as an indicationof a star formation e ffi ciency (SFE) per single core of about 0.3,meaning that 30% of the core mass eventually ends in the starmass. Later studies have confirmed that values around 0.3–0.4are typical in many other star-forming regions even if di ff erentvalues are also reported (see Section 5.1).The similarity between CMF and IMF led to the hypothesisthat the IMF is a consequence of the physical mechanisms thatproduce the prestellar core population. Testing this hypothesisrequires to derive the CMF in many star-forming regions in themost possible uniform way with respect to how observations areexecuted as well as to how cores are detected and their intensitiesare measured. Only in this way di ff erent CMFs can be comparedconsistently (see, e.g., Swift & Beaumont 2010).Another issue on a proper CMF derivation is that it is veryimportant to assign each core its temperature rather than using aconstant temperature for all the cores in a cloud, assumption thatbrings to ill-determined core masses. Unless we determine bothmass and temperature at same time, the stability of cores cannotbe investigated on a purely photometric basis, and the derivedCMF can contain collapsing cores and transient structures thatare not forming stars, as pointed out already 20 years ago byJohnstone et al. (2000).Deriving the CMF for the most important nearby star-forming regions in a robust and uniform way is the main aimof the HGBS.The Gould Belt is a complex of neutral gas and star-formingmolecular clouds covering an area of ∼ . × pc (e.g.,Bobylev 2016); the molecular clouds are located within dis-tances d < ∼
500 pc from the Sun, close enough to observe in-dividual cores. Among them, the system of clouds in Perseus(Fig. 1) are at distances in the range ∼
230 pc – 320 pc (Hirotaet al. 2008, 2011; Strom et al. 1974) with many sites of activelow-mass as well as intermediate-mass star formation. The re-view by Bally et al. (2008) gives a complete presentation of theregion, including its surrounding, with a long list of references;here we limit the literature references to papers that are pertinentto our work or when their results are used in this study.Perseus was observed as part of the
Spitzer “Cores to Disks”(c2d) program (Evans et al. 2009) with the InfraRed Array Cam-era (IRAC, Jørgensen et al. 2006) and the Multiband ImagingPhotometer (MIPS, Rebull et al. 2007). The analysis of bothdatasets was later presented by Young et al. (2015). Perseus wasalso mapped in the sub-mm with SCUBA (Hatchell et al. 2005)and later with SCUBA-2 (Chen et al. 2016), and at 1.1 mm withBOLOCAM (Enoch et al. 2006).Previous publications related to HGBS data are the study ofB1-E (Sadavoy et al. 2012) and of the relation between
Spitzer
Class 0 and the distribution of dense gas (Sadavoy et al. 2014, seealso Sect. 3.2.4 of this work); Pezzuto et al. (2012) discussed theproperties of two sources, B1-bN and B1-bS, that were proposedto be first hydrostatic cores candidates (see Sect. 4.3).The paper is organised as follows. In Sect. 2, we give anoverview of the observations of Perseus and present our data re-duction and analysis. In Sect. 3, we derive a first quantitativeestimate of the distance gradient across the cloud using using
Gaia
Data Release 2 (DR2) results. Then, we derive and discussthe column density and temperature maps, and the filamentarystructure of the region. In Sect. 4, we present the source extrac-tion and the physical properties of the cores derived via SEDfitting. We also discuss the core stability against their internal gravity. In Sect. 5, we present the CMF and link the cores tothe filaments. We also analyse the core and star formation e ffi -ciencies and estimate the lifetimes of the di ff erent phases of starformation. In Sect. 6, we summarise our conclusions.We include several appendices with the full source catalogue,completeness testing, region definitions, and the catalogue ofsources found in our maps that are not related to star formationlike, e.g., galaxies. In this paper, we present a catalogue of protostars and starlesscores. We define a core as a compact over density of gas and dustthat is round in shape and exceeds the density of its local di ff usebackground emission appearing as a local maximum in an inten-sity image or in a column density map. Cores are most easilyidentified using mid-infrared to mm wavelengths (di Francescoet al. 2007; Ward-Thompson et al. 2007; André et al. 2014).A core is defined starless if there is no internal source ofenergy (e.g., a protostar). Starless cores are instead warmed bythe interstellar radiation field and their spectral energy distri-bution (SED) can be modelled as a single modified blackbody I ν ∝ ν β B ν ( T ) at temperature T . We use our source extractiontechnique and the modified blackbody fits to derive the radius, R ,mass, M , and temperature T of the cores, and we use these physi-cal properties to determine the dynamical state of the cores. If thecore self-gravity exceeds its pressure support, we consider thesource to be bound. We define bound, starless cores as prestel-lar cores. These objects can collapse, or are collapsing, and willlikely form one or more stars. If the core’s self-gravity is insuf-ficient to balance its internal pressure, the core is classified asunbound and may be a transient structure that will dissipate inthe future unless it is confined by another mechanism (e.g., pres-sure confined).Once a star forms, it warms up the surrounding envelopewhose emission, in the first phases, is still resembling a mod-ified blackbody for λ > ∼ µ m while at shorter wavelengthsthe SED is no longer compatible with a such a model. For thisreason, a core with compact 70 µ m emission is considered pro-tostellar because a central source in the centre must be presentto warm the dust. Note, however, that in principle a starless corecan be detected at 70 µ m if it is su ffi ciently warm ( T > ∼
20 K),so the shape of the SED at short wavelengths determines if theobject is already a protostar. On the other hand, an object unde-tected at 70 µ m is always considered a starless core even if thelack of detection in the PACS band(s) may be just a matter ofsensitivity.The focus of this paper is on starless cores. Protostars aretouched upon in the text when necessary, for instance to derivestar formation e ffi cency in Sect. 5.3, but a fully discussion on theprotostars in Perseus is postponed to a forthcoming paper.
2. Observations and data reduction
Perseus was observed with
Herschel (Pilbratt et al. 2010) as partof the HGBS (André et al. 2010) in two overlapping mosaics:the Western field (mainly NGC1333, B1, L1448, L1455) andthe Eastern field (L1468, IC348, B5). Results from these obser-vations were initially presented in Sadavoy et al. (2012, 2014),Pezzuto et al. (2012), and Zari et al. (2016).Both fields were observed with PACS (Poglitsch et al. 2010)at 70 µ m (blue) and 160 µ m (red), and with SPIRE (Gri ffi n et al.2010), at 250 µ m (PSW), 350 µ m (PMW) and 500 µ m (PLW), Article number, page 2 of 52. Pezzuto et al.: The Perseus population of dense cores
Table 1.
The log of the observations. OBSID: identifier in the HerschelScience Archive; Date: start of the observation; Centre: the J2000 cen-tral coordinates of each field; Size: requested size.
West Perseus East PerseusOBSID 1342190326 13422145041342190327 1342214505Date 09 / / / / h m s + d ′ ′′ h m s + d ′ ′′ Size 135 ′ × ′ ′ × ′ in parallel mode with the telescope scanning at a speed of 60 ′′ / s.The total area common to both instruments is about 13 squaredegrees. Table 1 gives the observation log.A composite RGB image using PACS bands and SPIREPSW band is shown in Fig. 1. All the maps have been reportedto the same spatial resolution of the 70 µ m map by using themethod presented in Li Causi et al. (2016).Each field was observed twice along two almost orthogonaldirections to remove better instrumental 1 / f noise. The Herschel raw data were reduced with HIPE (Ott 2010) version 10. ForPACS, we reduced the data to Level 1 with HIPE, using ver-sion 45 of the set of calibration files. Level 1 data consist of thecalibrated timelines of the detectors to which the celestial co-ordinates were added. Afterwards, the data were exported out-side HIPE and maps were generated with Unimap (Piazzo et al.2015) version 6.5.3. The adopted spatial grid is 3 ′′ and 4 ′′ for theblue and red bands, respectively.For SPIRE, we used the calibration files version 10.1 andmaps were generated with the destriper module in HIPE. Weadopted the default values for the spatial grids: 6 ′′ , 10 ′′ and 14 ′′ for PSW, PMW and PLW bands, respectively. The SPIRE mapsare given in Jy / beam that we converted into MJy / sr using thenominal beamsizes of 426 arcsec , 771 arcsec and 1626 arcsec ,respectively. Additional details on the PACS and SPIRE dataprocessing can be found in Könyves et al. (2015).The alignment of each image was checked by comparing the Herschel position at 70 µ m of 22 bright and isolated sources,with their corresponding positions reported in the Spitzer cat-alogue at 24 µ m (Evans et al. 2009), 11 each for the Westernand Eastern part. For the Western field we found a shift in RAof ∆ α = ′′ . ± ′′ .
56 that was added to our coordinates. We alsoapplied a similar shift to the red map. SPIRE maps required nocorrection. The final residuals in the five maps run from − / + / /
10 of a pixel in the PSW map to 1 / ff set was applied to each map, obtained by cor-relating the Herschel data with
Planck and
IRAS data (Bernardet al. 2010). All five maps, shown in the Appendix D, are avail-able on the HGBS archive .
3. Data analysis
Given that physical parameters, like mass and radius, depend onthe distance to the sources, we start this section with a discussionon the distance to Perseus. http://gouldbelt-herschel.cea.fr/archives For IC 348, in the Eastern part of the complex, Herbig (1998)discussed a variety of distance measurements in literature andconcluded that the value 316 ±
22 pc derived by Strom et al.(1974) is the most reliable. This distance was later confirmedindirectly by Ripepi et al. (2002) who detected δ -Scuti oscilla-tions in one star of IC 348, and concluded that the derived starproperties were not compatible with distances < ∼
260 pc, but werecompatible with 316 pc. On the other hand, the Western halfof Perseus regions is known to be closer, which led to the con-clusions that the molecular clouds in Perseus form a chain withincreasing distance from West to East (see ˇCernis 1993). Thisconjecture was definitively confirmed with the measure of maserparallaxes for a couple of sources in NGC1333 and L1448 (Hi-rota et al. 2008, 2011) giving a distance of ∼
240 pc.To gain some insight on this gradient in distance, we ex-ploited the
GAIA archive second data release (DR2) of astromet-ric data (Gaia Collaboration et al. 2016). We looked for sourcesin our protostar catalogue (see Appendix A) spatially close to asource in the
GAIA archive with an angular separation of lessthan 10 ′′ . Objects with negative parallax were excluded. Allsources had spatial correspondences of < ′′ , with only two hav-ing separations > ′′ (6.5 ′′ and 7.4 ′′ ). Conversely, 18 are spa-tially separated by < ′′ and 7 are separated by < ′′ . Parallaxeswere converted into distances following Luri et al. (2018). Inparticular, we used the DistanceEstimatorApplication.py tool with the median of the Exponentially Decreasing SpaceDensity Prior distribution option. The tool returns also the 5%and 95% quantiles that are not symmetrical around the median(this reflects the obvious prior that the distance must be positive).Since the di ff erence between (median-5% quantile) and (95%quantile-median) is negligible, we adopted the larger (95%-median), for the distance uncertainty. No attempt was made toexclude projection e ff ects. Hence, some associations betweenour sources and GAIA stars may not be physical. On the otherhand, it is unlikely that a proximity of few arcseconds between a
GAIA source at the distance expected for Perseus and a protostaris only due to projection.In Table 2 we show distances and uncertainties for the 28sources possibly associated with our protostars. We also reportthe distances for the maser sources in L1448 (Hirota et al. 2011,h1 in the table) and NGC1333 (Hirota et al. 2008, h2) derivedusing the python tool reported above to convert the parallax todistance.In Fig. 2 the 30 distances are plotted as a function of theirright ascension. Starting from the observational finding that adistance gradient exist going from West to East, and noting thata gradient also exists going from South to North, see the di ff erentsymbols of the points in the figure, we made a multivariate linearfit to the data and we found the following relation d (pc) = . ± . + (5 . ± . × ( α − α ) + (5 . ± . × ( δ − δ )(1) α = ◦ . δ = ◦ . d ≡ d ( α, δ ) is the first quantitativeestimate of the distance gradient in Perseus even if the large scat-ter in distances could be due to false associations between ourprotostars and GAIA sources. In particular, if all the associationsin NGC1333 are physical, an exceptional depth of more than https://repos.cosmos.esa.int/socci/projects/GAIA/repos/astrometry-inference-tutorials/browse/single-source/tutorial Article number, page 3 of 52 & Aproofs: manuscript no. perseus
Fig. 1.
An RGB composite of the star-forming region in Perseus. Blue is PACS 70 µ m; green is PACS 160 µ m; red is SPIRE 250 µ m; North is up,East is to the left. The latter two maps have been processed to simulate having the highest resolution of the 70 µ m. The resulting image is thennot meant to be used for science analysis. Labels identify on the map the approximate position of main sub-regions. Monochromatic Herschel intensity maps are reproduced in Appendix D with coordinate grids.
Table 2.
Sources from our protostar catalogue with
GAIA counterpart within 10 ′′ ; we listed also h1 (L1448 C) and h2 (SVS13 in NGC1333) whichhost masers from which an astrometric distance was obtained (Hirota et al. 2008, 2011). For all the sources, the distance in parsec was derivedfrom parallax according to Luri et al. (2018). ID RA Dec Distance ID RA Dec Distance ID RA Dec Distance1) 51.27800 31.11428 299 ±
10 10) 52.23893 31.23733 291 ±
10 19) 55.41336 31.60310 300 ± ±
65 h2) 52.26552 31.26772 240 ±
36 20) 55.49376 31.81556 312 ± ±
26 11) 52.37169 31.30924 315 ±
24 21) 55.72903 31.72932 330 ± ±
11 12) 52.47598 31.34729 296 ±
17 22) 55.73202 31.97893 313 ± ±
14 13) 52.71848 30.90509 327 ±
66 23) 56.11088 32.07526 330 ± ±
29 14) 52.82618 30.82677 302 ±
12 24) 56.14806 32.15777 333 ± ±
60 15) 52.87012 30.51453 295.1 ± ± ±
36 16) 53.14148 31.01549 307 ±
19 26) 56.33484 32.10952 310 ± ±
31 17) 55.19518 32.53161 308 ±
13 27) 56.45099 32.40305 311 ± ±
40 18) 55.28775 31.74389 326 ±
28 28) 56.94595 33.06746 343 ± ff er-ent clouds, is implied (see also Appendix C). Further, there areno data points (no associations) in the range 53 ◦ . ≤ α ≤ ◦ . GAIA , from younger sources, Class 0 objects, thatare more obscured in the visible light and, for this reason, moredi ffi cult to be present in the GAIA archive. An association be-tween a Class 0 source and a
GAIA object may be due to a pro-jection e ff ect.Recent distance measurements to the main Perseus cloudshave been reported by Zucker et al. (2018) and Ortiz-León et al.(2018). Table 3 compares these distances: Col. P gives the dis-tance based on our Equation (1) using right ascension and decli-nation from Zucker et al. (2018), Col. Z gives the Zucker et al. (2018) distances, and Col. O gives the Ortiz-León et al. (2018)values. The distances from Zucker et al. (2018) are derived bycombining data from PAN-STARRS1, 2MASS, Gaia and the CO data from the COMPLETE survey (Ridge et al. 2006a)(we use the CO data in Sect. 3.2.2 and Appendix C). Ortiz-León et al. (2018) measure distances using VLBA and
Gaia data.Uncertainties in Col. P, derived through error propagation fromEquation (1), can be misleading. They are small because theygive the (estimated) distance of each point in the sky assuminga 2D geometry for Perseus. These uncertainties do not catch thedispersion in distance caused by the depth of each cloud, andthey do not take into account that in the region with right as-cension between ∼ ◦ and ∼ ◦ , there are no protostars, andthen we do not have indications on the distance. Uncertainties inCol. Z are the sum in quadrature of the random and sistematicerrors given by Zucker et al. (2018). Article number, page 4 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 2.
Relation between distance and Right Ascension for the 30sources in Table 2.
Table 3.
Comparison between distances, in pc, derived by di ff erent au-thor: RA and Dec are in degrees as quoted by Zucker et al. (2018);P distance based on our Equation (1); Z distance from Zucker et al.(2018); O distance from Ortiz-León et al. (2018). Name RA Dec P Z OL1451 51.0 30.5 282.3 ± ± ± ± ± ±
14 293 + − B1 53.4 31.1 297.9 ± ± ± ±
15 320 + − B5 56.9 32.9 325.7 ± ± Table 4.
Comparison between the distance, in pc, derived in this paper(column P) and that derived by Zucker et al. (2019) (column Z) for thefour lines of sight reported in their Table 3 for the Perseus cloud.
RA Dec P Z51.5455 30.6747 285.7 ± ± ± ± ± + − ± + − We find excellent agreement ( <
3% di ff erences) between ourmeasurements and those of Zucker et al. (2018) and Ortiz-Leónet al. (2018). Only IC 348 and B5 show more significant di ff er-ences but still <
10% and, in any case, within the uncertainties.Zucker et al. (2019) derived a distance map of Perseus andother molecular clouds through per-star distance–extinction esti-mates improved with
GAIA parallaxes. The result for a small setof lines of sight is reported in Table 4 where we compare theirdistances with ours: the agreement is very good, better than 5%in all cases.The full set of distances derived by Zucker et al. (2019) isshown in Fig. 3 where we give a graphical representation ofEquation (1): our distance was computed for each point of thecolumn density map (see Sect. 3.2) and coded in colour accord-ing to the bar on the right of the figure. Dashed black lines con-nect points at the same distance, reported at the top of each line.The coordinates grid, in blue, is in step of 2 ◦ . Zucker et al. (2019)give the distance averaged over boxes of 0.84 deg : they areshown in green at the position of the centre of each box. While, on one hand, Zucker et al. (2019) computed accuratedistances to Perseus that are more precise than those given byour Equation (1), it is not easy, on the other hand, to extract adistance for a given point in space from their map; for instance,B5 is put at 302 pc in Zucker et al. (2018), distance that canbe hardly derived from the grid of distances shown in Fig. 3.Conversely, our Equation (1) has been derived in a less rigorousway, but it gives immediately a reference distance at any point( α, δ ) in space, distance that captures the distance gradient in thecomplex, and matches very well with the distances derived byother authors.For the rest of the paper, we adopted the mean of the 30sources, 300 pc, as a representative value of the distance for thewhole Perseus complex (294 pc in Zucker et al. 2019). We will,however, show how the physical description of the whole regionchanges when distances are varied according to our formula. Dust emission in the far-infrared can be modelled as a modifiedblackbody I ν = κ ν Σ B ν ( T d ), where κ ν is the dust opacity per unitmass expressed as a power law normalised to the value κ at areference frequency ν so κ ν = κ ( ν/ν ) β cm g − . Σ is the gassurface-density distribution µ H m H N (H ) with µ H the molecu-lar weight, m H the mass of the hydrogen atom and N (H ) thecolumn density assuming the gas is fully molecular hydrogen.Finally, B ν ( T d ) is the Planck function at the dust temperature T d . Following the GBS conventions (Könyves et al. 2015), weadopted an opacity of 0.1 cm g − at 300 µ m (gas-to-dust ratio of100), a dust opacity index β =
2, and µ H = . ff mann et al. 2008).We used the four intensity maps from 160 µ m to 500 µ m toderive N (H ) and T d maps. The 70 µ m map was not includedbecause emission at this wavelength may include contributionsfrom very small grains (VSGs), which can not be modelled witha simple single-temperature modified blackbody. Indeed, Schneeet al. (2008) found that in Perseus contribution from VSGs mayelevate the 70 µ m emission by 70% at 17 K and by 90% below14 K. Contribution from VSGs is not expected for λ > µ m(Li & Draine 2001).The three intensity maps shortwards of 500 µ m were de-graded to the spatial resolution of the PLW band (36 ′′ . ′′ pixels at all wavelengths.The SED fitting procedure was executed pixel by pixel witha code that takes as input the four images in FITS format. Thecode creates a grid of models, as in Pezzuto et al. (2012), byvarying only the temperature, in the range 5 ≤ T d (K) ≤
50, instep of 0.01 K. For each temperature T j , the code computes theintensity at far-infrared wavelengths for a fixed column densityof 1 cm − .Since I ν is linear with N (H ), we can compute the columndensity at each pixel using a straightforward application of theleast-squares technique N (H ) j = P i f i q i ( T j ) /σ i P i q i ( T j ) /σ i (2)where f i is the observed SED I ν at each frequency i and q i ( T j ) isthe synthetic SED model at frequency i and temperature T j . Theuncertainty σ i is 10% and 20% for SPIRE and PACS respectively(Könyves et al. 2015). Index i runs from 1 to 4, index j runs from1 to 4501, the number of models in the grid. Article number, page 5 of 52 & Aproofs: manuscript no. perseus
Fig. 3.
Color-coded 2D visualisationof Equation (1). Color bar is in par-sec, coordinates grid in degrees. Blackdashed lines connect points at the samedistance, shown in the labels. Green la-bels are the distances derived by Zuckeret al. (2019) in boxes of 0.84 ◦ , the la-bels are at the centre of the boxes. At each pixel of the intensities maps, the model j with thesmallest residuals is kept as best-fit model. To be consistent withthe other HGBS papers, we run the code without applying colourcorrections but in Sect. 3.3 we show how much the results de-pend on this assumption and on the choice of β = N (H ).Another column density map at higher spatial resolution (i.e.,18 ′′ . µ m band) was also ob-tained using the method described in Palmeirim et al. (2013).The procedure is based on a multi-scale decomposition tech-nique. The high-resolution column density map, used to opti-mise the source extraction described in Sect. 4.1, is available fordownloading on the HGBS website. This map, shown in Ap-pendix D, has an higher spatial resolution than those previouslyobtained with the same Herschel data at 36 ′′ . × cm − and 10 cm − . The first levelfollows quite well the border of the known main regions, even ifB3 and B4 form a single complex with IC348, while the othermarks the densest part of the clouds.The histogram of T d is shown in Fig. 5. There are two peaksseen at 16.4 K and 17.1 K, and a third, very broad one, a plateauindeed, at 19.2 K. The first two peaks correspond to the temper-atures of the di ff use medium in West and East Perseus, respec-tively. In other words, the dust temperature is slightly lower inthe Western half of Perseus than in the East. The peak at 19.2 Kreflects the inner parts of NGC1333 and IC348, and a few otherregions that we discuss below.To check our results, we compared the Herschel N (H ) mapwith the all-sky Planck map of the optical depth τ P at 850 µ m(Planck Collaboration et al. 2014) . First we convolved our map HFI_CompMap_ThermalDustModel_2048_R1.20.fits availableat http://pla.esac.esa.int/pla to the
Planck resolution of 5 ′ and projected the result onto the Planck grid. We then computed the ratio r = τ H /τ P where τ H = . / . µ m H N (H ). Because of the convolution, the Herschel column density and, as a consequence, the optical depth, havevery low values close to map borders, with τ H as low as 6 × − .To exclude these points, we made the comparison in the regionwhere τ H ≥ . × − = min( τ P ).In Figure 6 we show in grey the ratios r vs. τ P ; with greenpoints we highlight the values corresponding to τ H < . × − . The blue histogram shows the mean ratios, averaged inbins of 10 − , excluding the green points. The weighed mean ofthe histogram values is ¯ r = . ± .
040 (shown as dark greenline in Figure 6, with the two red dashed lines giving r ± σ )and all the blue points fall in the red-lines region. This impliesthat the histogram is compatible with a constant ratio for r . Onthe other hand, an increasing trend of r with τ P seems present inthe figure, with r < ∼ .
05 for τ P < × − , and increasing upto 1.30 when τ P ∼ × − . In particular, 98% of the points ofthe optical depth map have 1 . × − ≤ τ P ≤ × − , andfor them the ratio r is 1 . ± .
15. A change in r might witness achange in opacity at high column density. As written, the 70 µ m map was not used to derive the columndensity map, because of possible VSG emission at this wave-length. We can, however, estimate this contribution by comput-ing the intensity map at 70 µ m from the column density and tem-perature maps obtained for λ ≥ µ m. Fig. 7 compares theextrapolated 70 µ m map with the di ff erence map between theextrapolated and observed data. All maps have been convolvedto 36 ′′ . ff use background emission if given su ffi cient sensitiv-ity. Such 70 µ m dark clouds are typically classified as infrareddark clouds (IRDCs, Carey et al. 1998). The observed data (seeAppendix D), however, do not show the subregions as silhou-ettes.The right panel of Fig. 7 shows the di ff erence between theobserved 70 µ m map, degraded in spatial resolution and pro- Article number, page 6 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 4.
Top panel: column density mapwith contours at 3 × cm − and10 cm − . Bottom panel: dust tempera-ture map. In both panels the magenta linein the bottom left corner shows the angu-lar scale corresponding to 1 pc at 300 pc;J2000.0 coordinates grid is shown. Bothmaps have a spatial resolution of 36 ′′ .
1. Theanticorrelation between N (H ) and T d isevident: regions at high / low column den-sity are cold / warm, with few exceptions inIC348 and NGC1333. jected onto the 500 µ m spatial grid, and the computed 70 µ mmap. If the far-infrared dust emission can be extrapolated bya modified blackbody distribution, then the di ff erence mapshould approach zero everywhere. This is indeed true for most of Perseus with the exception of NGC1333 and the complexIC348 / B3 / B4 / L1468, with di ff erences as high as 10 MJy sr − in NGC1333. Article number, page 7 of 52 & Aproofs: manuscript no. perseus
Fig. 5.
Histogram of dust temperature in the range 11 – 21 K (minimumis 10.1 K, maximum is 28.3 K).
Fig. 6.
With the grey points we show here the ratio of τ H , the opti-cal depth derived from our Herschel observations, over τ P , the opti-cal depth derived from Planck observations (Planck Collaboration et al.2014), both τ ’s computed at 850 µ m. The ratio is against τ P . Greenpoints correspond to low values of τ H due to the convolution applied tothe Herschel column density map (see text). Mean values ± one stan-dard deviation of the grey points, excluding the green ones, are shownwith the blue histogram. The dark green and the two red lines show theweighed mean of the ratio: 1 . ± . As first hypothesis we can suppose that there is not a popula-tion of VSG and that the di ff erences in observed and computed70 µ m flux, are due to a poor estimation of T d . In fact, for a mod-ified blackbody, T , β and the wavelength where the SED peaks λ peak are related through the relation (Elia & Pezzuto 2016) λ peak = . T ( K )(3 + β ) cm (3)If T = . λ peak = µ m if β =
2. Athigher temperatures, λ peak moves shortwards of 160 µ m so thatthe peak wavelength, and then T , is poorly determined from ourdataset built for λ ≥ µ m. To quantify this e ff ect, we derivedthe column density and temperature maps using only PACS data.To this aim we used an additional PACS intensity map at 100 µ m, also observed as part of the HGBS and that will be the subject ofa future paper focused on Class 0 objects.The 70 µ m and 100 µ m maps were degraded to the red bandspatial resolution, projected onto the spatial grid of the latter im-age, and then fitted following the same pixel-by-pixel techniquedescribed previously. Since the 100 µ m observation covered asmaller area than the PACS / SPIRE parallel-mode observations,and because the PACS intensities have larger uncertainties inthe zero-level of the di ff use emission, the resulting N (H ) and T maps have small coverage and higher noise when compared tothe “nominal” maps obtained for λ ≥ µ m.The new temperature map, T PACSonly , was then degraded tothe 500 µ m spatial resolution and projected onto the spatial gridof the nominal T map, T + SPIRE .In Fig. 8, we show, as a function of T PACSonly , the mean of theratio T PACSonly / T + SPIRE in bins of 1 ◦ K. At low temperatures T PACSonly is a poor estimate of T , as expected. More interesting,however, is the trend for T PACSonly >
20 K. In this regime, cor-responding to λ peak < ∼ µ m, the peak of the SED falls outsidethe range of wavelengths used to derive T + SPIRE . On the otherhand, the PACS bands span the SED peak, making T PACSonly amore reliable measurement of the dust temperature, at least aslong as T < ∼
43 K (above this temperature the SED peak movesat λ < µ m). From the figure, we see that T + SPIRE starts be-ing colder than T PACSonly for T >
20 K (for T PACSonly >
28 K,the value of the mean is likely a ff ected by the small number ofpoints).The blue contours in the right panel of Fig. 7 show the re-gions where T PACSonly ≥
20 K. These regions are confined tothe inner parts of IC348 and NGC 1333. Clearly, underestima-tion of T d cannot explain the large di ff erence where the observedemission at 70 µ m is higher than that computed from the 160 + SPIRE column density and temperature maps. The VSG popula-tion in Perseus may be the cause of this excess. If so, however, itis clear that VSGs are detected primarily in the Eastern field. Wealso note that the bubble CP5 (Arce et al. 2011) for which Ridgeet al. (2006b) derived T ∼
29 K with IRAS 60 µ m and 100 µ mdata, is not visible in the right panel of Fig. 7, suggesting that its70 µ m emission seen by Herschel is actually compatible with amodified blackbody at lower temperatures, i.e., less than ∼
20 K.HD 278942, thought to be the driving source of the bubble, hasa distance of ∼
520 pc (Gaia Collaboration et al. 2016) excludingthat this star can be indeed related to the shell.The fact that T can be underestimated when T >
20 K couldhave, in principle, an impact on the core temperature derivedfrom SED fits when a source is not visible in the PACS blueband. For the starless cores, however, almost all of their tem-peratures are <
20 K with only a few exceptions. Sources withtemperature >
20 K are detected at 70 µ m so that the observedSED covers the region of the peak intensity. From the intensity maps at the di ff erent wavelengths or the col-umn density map, it is not clear how to define the borders ofindividual subregions of Perseus. The contour at 3 × cm − shown in Fig. 4 provides a good first order estimate of the densematerial, but it does not separate the individual subregions well.Further, our choice of 3 × cm − does not have a physicalmeaning and one could adopt another level of N (H ) and mea-sure a di ff erent mass.To find a solution for the border definition, we started draw-ing a polygon enclosing each 3 × cm − contour. Indeed, apolygon is much easier to handle in a computer code given the Article number, page 8 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 7.
Left panel: the inferred 70 µ m intensity map extrapolated from the column density and temperature maps obtained for λ ≥ µ m. Thegreen circle shows the bubble found by Ridge et al. (2006b) (CP5 in the list by Arce et al. 2011). Right panel: di ff erence between the observed70 µ m map and the extrapolated map. Green contours are 20 MJy sr − and 200 MJy sr − ; blue contours show the region where T PACSonly ≥
20 K(see text). Colourbars are in MJy sr − . M e a n ( T ( P A C S o n l y ) / T ( + S P I R E )) Fig. 8.
Change in dust temperature when PACS data only are used(70 µ m, 100 µ m and 160 µ m) instead of PACS 160 µ m plus SPIREbands. Error bars are one standard deviation. The point at T ∼
30 K isnot reliable because mean of few values. fact that it is defined with much fewer vertices. Hence, we usedsuch polygons to get a first guess for the borders. Then we visual-ized the CO 1–0 (Ridge et al. 2006a) spectrum inside each areawhose perimeter was varied by eye to find locations with one ve-locity component. This approach, however, was possible only ina few cases because most of regions have multiple CO compo-nents. So, in the end, we defined the di ff erent subclouds trying tohave one bright line with few contaminants . The areas so definedare shown in Fig. 9 while in Figs. C.1 to C.2 of Appendix C theyare overplotted onto the CO intensity maps at di ff erent veloc-ity components to make it clear why a certain region was definedwith that border. We introduced additional zones not associatedwith already known subregions, naming them HPZ N (H ) > × cm − . The last two Cols. showthe e ff ect of assigning to each point of the column densitymap a di ff erent distance, following Equation (1). Specifically, M d ( α,δ ) shows how the total mass of the cloud is a ff ected, andCol. ¯ d gives the distance at which M d ( α,δ ) = M ¯ d , where ¯ d = pP N i (H ) d ( α i , δ i ) / P N i (H ), with i running over all the pix-els of each subregion. The total mass, area, median temperature,and the mean distance for the entire cloud within specific col-umn density ranges are given in Table 6. From the values of ¯ d inthis table we conclude that our choice of 300 pc as representativedistance is reasonable.The mass for N (H ) > × cm − is 954 M ⊙ at 300 pc.With the same set of data Sadavoy et al. (2014) found 1171 M ⊙ when adopting 235 pc, that translates into 1908 M ⊙ at our dis-tance of 300 pc, a factor 2 higher than our value. The main dif-ference between the two analyses is that we adopted a newer ver-sion of the calibration files with slightly di ff erent SPIRE beam-sizes. Since the mass enclosed within a certain contour scaleswith the area defined by that contour, small variations in columndensity can cause large variations in mass. In particular, scalingby 30% the column density derived by Sadavoy et al. (2014), thearea decreases from 600 arcmin to 303 arcmin and the massreduces to 944 M ⊙ , in agreement with the values derived by us.We also compare the Herschel -derived column density mapswith the near-infrared extinction maps based on star counts (see,e.g., Cambrésy 1999; Schneider et al. 2011). Such a compari-son, however, is not immediate. Benedettini et al. (2015) foundlarge discrepancies between the masses derived with these twomethods in Lupus, due to the uncertainties on the opacity lawused to compute the
Herschel column density map. The situationis more di ffi cult for Perseus because of the known variability of R ≡ A V / E(B − V). Foster et al. (2013) found a strong correlation
Article number, page 9 of 52 & Aproofs: manuscript no. perseus
Fig. 9.
The regions identified in Perseus overplotted on the column density map. The magenta line in the bottom left corner shows the angularscale corresponding to 1 pc at 300 pc; J2000.0 coordinates grid is shown. Coordinates of the regions are given in Appendix C.
Table 5.
The properties of the sub-regions of the Perseus molecular cloud. Coordinates give the position of the peak in column density reportedunder Peak. The next six Cols. give the mass, area, and median temperature, with two values for each parameter. The first value refers to the entiresubregion within the boundaries shown in Fig. 9. The second value applies only for the data with N (H ) > × cm − . Column labeled M d ( α,δ ) gives the mass of each subregion using a modified distance according to Equation (1), with ¯ d being the mean distance for the entire region. Thelast three Cols. are the number of cores detected: Pro(tostars), Pre(stellar cores) and U(n)B(ound) cores. Name RA Dec Peak M Area Med( T ) M d ( α,δ ) ¯ d Pro Pre UBJ2000 (10 cm − ) ( M ⊙ ) (arcmin ) (K) ( M ⊙ ) (pc)L1451 51.32 30.32 16.9 276 125 746 140 15.1 13.3 246 283 0 19 8L1448 51.40 30.76 106 313 194 610 122 15.2 13.2 285 285 4 18 7L1455 51.92 30.20 37.0 740 375 1897 420 15.0 13.3 677 286 8 36 17NGC1333 52.29 31.23 138 1060 727 1661 538 15.2 13.8 1021 294 44 23 23Perseus6 52.64 30.44 19.1 203 74 579 93 15.5 13.6 191 290 5 4 2B1 53.34 31.13 112 1443 780 3444 657 15.8 14.2 1423 297 15 31 38B1E 53.98 31.24 9.65 389 157 887 215 15.6 14.7 395 301 0 8 9L1468 54.91 31.53 7.87 455 49 1391 79 17.4 15.7 479 307 0 4 18IC348 a b Notes. ( a ) Includes regions B3 and B4; ( b ) coordinates of the geometrical centre. between R and A V in Perseus, with the former increasing from ∼ ∼ R = R ( A V ), it is not possibleto translate N (H ) to A V . Moreover, A V maps are also subject toa zero-level uncertainty, in the sense that stars must be counted relative to a fiducial zone where A V = ffi cult to find such a clean region.To investigate further, we derived the mass enclosed withina certain contour of A V using both our column density mapand a 2MASS-based extinction map (Cambrésy 2015, privatecommunication), taking into account the di ff erent spatial reso- Article number, page 10 of 52. Pezzuto et al.: The Perseus population of dense cores
Table 6.
The properties of the Perseus molecular cloud as a whole inthree di ff erent regimes of column density; mass M , area and mediantemperature Med( T ); column labeled M d ( α,δ ) gives the mass as in Table 5using Equation (1) for the distance; ¯ d is the mean distance. N (H ) M Area Med( T ) M d ( α,δ ) ¯ d (10 cm − ) ( M ⊙ ) (degrees ) (K) ( M ⊙ ) (pc) ≤ a > >
10 954 303 b Notes. ( a ) Minimum value in our map is 2 . × cm − ; ( b ) area is inarcmin . lution and pixel size. We use the nominal conversion N (H ) = . × A V mag − cm − from Bohlin et al. (1978), which as-sumes fully ionised hydrogen and R = .
1. The mass foundfor A V > M ⊙ in our map and 9980 M ⊙ in theextinction map, a factor 2.76 higher. For A V > M ⊙ and 4290 M ⊙ ). Thecomparison improves if we derive the mass enclosed within thesame area instead of the same A V . The area is found projectingthe A V contour derived on the extinction map onto our columndensity map. In this way we measure in our map 5523 M ⊙ and2548 M ⊙ for A V > / mass(column density map) of 1.81 and1.68 for the two contours. A qualitative similar trend is foundin Orion B (Könyves et al. 2020). All in all, the masses derivedfrom our Herschel-based column density map are accurate towithin a factor of ∼ . − A V > A V < ∼ − R can play a role in causingcolumn density discrepancies, we varied R until a good agree-ment was found between the extinction map and thermal dustmap. We chose a fiducial extinction level of A V = R that equalises the masses found from the two maps.We find a best match for R = .
95 which implies N (H ) = . × A V mag − cm − . With this conversion, the cloud massfor A V > M ⊙ from both maps. Assumingthe nominal value R = .
1, the thermal dust map gives a mass of1213 M ⊙ and the extinction map gives 2046 M ⊙ .Another study of the extinction in the Perseus molecularcloud has been done by Zari et al. (2016) using the same setof Herschel images. They give the mass enclosed within a set of A K contours based on the relation A K = . × [2 N (H ) + N (H)] mag cm − that becomes A K = . × N (H ) mag cm − assuming fully molecular hydrogen. To take into account the dif-ferent mean molecular weight (1 . × ff erent adopted distance (240 pc instead of 300 pc), weincreased their masses by 1.53.Finally, we had to consider the di ff erent dust opacity, whichwas more tricky. By combining their relation between A K and N (H ) with their Equation (4) that relates A K with the opticaldepth at 850 µ m, we derived κ = A K − δ . × µ H m H A K (4)The fact that their zero-point δ is not zero, makes κ a functionof A K ; on the other hand, if A K ≫ k δ k = .
05 mag, then κ → Table 7.
Mass cloud derived with two dust emissivity indices β , with-out and with colour corrections applied, and with a di ff erent spatial sam-pling of the column density map. The value β = β = . β in the Perseus region (PlanckCollaboration et al. 2014). Masses in Cols. (2), (3) and (5) were derivedwithout applying colour corrections, while in Cols. (4) and (6) the re-ported masses were computed with colour corrections. In all cases butCol. (3), the column density map was created on a grid of size 14 ′′ andspatial resolution of 36 ′′ , default values for HGBS. In Col. (3) the col-umn density map was projected onto the grid used for Planck data: 90 ′′ pixels and 5 ′ resolution. The 7 mag contour has been drawn assuming R = . β = β = . M ⊙ )(1) (2) (3) (4) (5) (6) N (H ) ≤ × N (H ) > × N (H ) > A V > . g − . Since we have assumed a dust opacity index β = κ = .
052 cm g − ; and because I ν ∝ κ ν Σ , lowering κ ν by a factor 0 . /. = .
52, implies increasing our values of N (H ) by the factor 1 / . = . τ map from CDS andconverted it in A K following their prescription. Our N (H ) wasprojected onto theirs, to take into account the di ff erent pixel size,and then we computed the mass enclosed within the A K contoursused by Zari et al. (2016). For A K > . M Z , derived by Zari et al. (2016), and M P , the mass es-timated from our column density map, is 1.72 instead of the ex-pected value of 1.92. This small di ff erence, 10% in mass, can bedue to the di ff erent way to derive the zero-level of the intensitymaps, combined with the fact that for 0.6 mag, the zero-point δ in Equation (4) is not yet negligible. The ratio of the massesincreases with increasing A K until, for A K > . β fixed to 2 and onneglecting colour corrections. In Table 7 we report the massesenclosed within di ff erent N (H ) levels and for A V > R = .
1. The first set ofCols. show the masses from our data for β = β = .
7, which is the the peak ofthe distribution of β in the Perseus region (Planck Collaborationet al. 2014). For each β case, we measure masses first without ap-plying a colour correction (No CC) and then with applying thecolour correction (see below for details). Finally, in the middleCol. for the β = ′ ) with 90 ′′ pixel size.In general, smoothing the map decreases the column den-sity in the densest parts and increases the column density inthe more di ff use regions surrounding the denser material. Forexample, at N (H ) > cm − , we recover only 62% of themass measured in the smoothed Herschel map at 5 ′ resolutioncompared to the original map at 36 ′′ resolution, whereas for N (H ) < × cm − , we find a slightly higher mass in the5 ′ resolution map. Article number, page 11 of 52 & Aproofs: manuscript no. perseus
With β = .
7, the column density and cloud mass decreasessubstantially. We find values that are roughly 75–80% what wasobtained with β = ν F ν spectrum . For all other kinds of SEDs, the derived fluxes mustbe colour-corrected according to the intrinsic source spectrum.To compute the column density with color corrections applied,our fitting code integrates the synthetic SEDs over the PACS andSPIRE response filters during the generation of the grid. In thisway, each model has its own CC built-in.In the rest of this paper we used the maps at the spatial res-olution of 500 µ m derived as in the other HGBS works: no CCapplied and β fixed to 2. One of the main results of
Herschel in the field of star forma-tion is the discovery of the deep link between the filamentarystructure of molecular clouds and the sites where stars form. Inparticular, star-forming cores are found preferentially in denserfilaments (André et al. 2010; Molinari et al. 2010; Rayner et al.2017).Based on
Herschel data, Polychroni et al. (2013) derived twodistinct core mass functions in L1641, part of the Orion A com-plex, for sources inside and outside of filaments. The mass dis-tribution of the sources on the filaments was found to peak at4 M ⊙ with a CMF at higher masses modelled with a power lawd N / dlog M ∝ M − . . The mass distribution of the sources o ff thefilaments has the peak at 0.8 M ⊙ and a flat CMF at masses lowerthan ∼ M ⊙ .Roy et al. (2015) found a possible link between the 1D powerspectrum of filaments and the origin of the high-mass tail inthe core mass function (very close to Salpeter’s law d N / d M ∝ M − . ).A complete study of the filaments in Perseus is not in thescope of this paper, nevertheless, given the aforementioned re-sults, it is important to give here at least a short summary of thefilaments main properties that will be later discussed in Sect. 5where the relation with the core population will be addressed.We used the filament detection algorithm of Schisano et al.(2020, 2014) to identify filamentary structures and their proper-ties across our column density map. Here we summarise how thealgorithm works adopting the nomenclature described in thosepapers.By thresholding the minimum eigenvalue of the Hessian ofthe column density map, the code is able to find and encompassregions where there are maximum variations of the contrast, i.e.,the bright features on the map. Filamentary structures are pickedamong these features through selection criteria on the elongationand coverage of the region of interests.Once the regions of interest are identified, the IDL morpho-logical operator THIN is applied to them. The result of the oper-ator is the region “skeleton”. Because of the nested morphologyof filamentary features, the skeleton in each region is composedby one or more “branches”. The spine of the filament is defined This is a common assumption when calibrating a photometer. The code is freely available at the following URL http://vialactea.iaps.inaf.it/vialactea/eng/tools.php IDL is registered trademark of Harris Corporation. as the group of consecutive branches, connected each other, trac-ing the longest possible path over the filamentary region.Schisano et al. (2014) found that the area of the filament isunderestimated by a mere thresholding of the eigenvalue, thatonly traces where the emission is concave downwards. They alsofound that by enlarging the border by three pixels on both direc-tion perpendicular to the spine gives a better estimate of the po-sition where filaments merge with the background. We verifiedthat such approach is valid also for our case and we applied it toour filament sample.The code was run on the 36 ′′ -resolution column density map.Among the identified features, we selected as filaments the elon-gated regions having a spine longer than 12 pixels, correspond-ing to 0.24 pc at 300 pc, or about 4 times the spatial resolutionat 500 µ m.The result of the extraction is shown in Fig. 10 where thefilaments are overlapped on the column density map. Green linesshow the filament borders, red and white lines are the spines andthe branches, respectively.In the left panel of Fig. 11 we show in details all the fea-tures previously defined: the filament border (thin grey line), themain spine (white line) and the system of branches (short blacklines), for the case of the L1448 cloud. The identified filamentruns along almost all the cloud. The thick black line defines anarbitrary region R used in the right panel of Fig. 11 to show theradial profile of the filament, averaged along the filament itself,and the to assess, at least in one case, the validity of the 3-pixelsborder expansion.As written, in fact, the filament-detection code expands radi-ally the filament border by three pixels to identify the positionwhere the filament merges with the surroundings. The averageradial profile inside R is shown in the right panel of Fig. 11. Theerror bars are the standard deviation of the column density foreach bin of distance from the spine. Due to the irregular shapeof expansion, that reflects the irregular filament profile, the bor-der does not have a constant o ff set from the spine. The minimumand the maximum radial distance from the spine reached by thefilament border over R , r and r , respectively, are shown withthin black lines, running parallel to the spine, in the left panelof Fig. 11. For distances | r | ≤ r , within the two vertical dashedblack lines in the right panel of Fig. 11, all the pixel of the mapbelong to the filament area, while for distances | r | ≥ r , markedwith the two dotted black lines, all the pixel are external to thefilament and contains only background pixel. At intermediatedistances r ≤ | r | ≤ r , to be or to be not part of the filamentbecomes a local property, depending on the position along thespine.The background is estimated from linear interpolation of thepixels that are outside the filament area, where | r | ≥ r , or, lo-cally, where r ≤ | r | ≤ r . The background so estimated is shownwith a thick grey line in the right panel of Fig. 11. The blue linein the same figure is the Gaussian fit to the radial profile. The fil-ament width is estimated as the FWHM of the fit. The Gaussianfit gives another estimate of the background, but we prefer to usethe linear interpolation because the Gaussian fit is less suited tocatch possible asymmetries, as is visible in our example. Theseasymmetries are stronger in the wings of the profile rather than inthe inner part, so that it is reasonable to use the Gaussian FWHMto estimate the width.In Fig. 12 we show the filament widths averaged over thespine and deconvolved by the FWHM at 500 µ m, 36 ′′ . The widthis given in pc assuming a distance of 300 pc. The peak of thedistribution is ∼ .
08 pc, consistent with the finding of Arzou-
Article number, page 12 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 10.
Network of filaments overplotted on the column density map. Red lines show the spine of the filaments, white lines show the branches,and the green contours show the width of the filaments and branches. Map has been rotated by 28 ◦ . The magenta line in the centre shows theangular scale corresponding to 1 pc at 300 pc; J2000.0 coordinates grid is shown. -200 -100 0 100 200Offset (arcsec)4.0 × × × × × × C o l u m n D en s i t y ( c m - ) Fig. 11.
Left panel: zoom-in of the filament in the region of L1448. The white line is the spine, while the grey line is the border of the filament.The short black lines are branches. To explain how the radial profile of the filament is derived, we defined, with the thick black line, an arbitraryregion. Right panel: the radial profile of the filament averaged longitudinally within the black region shown in the left panel. The error bars are thestandard deviation of the column density averaged within 10 pixels. The blue line is the Gaussian fit, and the grey line the estimated background.The dashed and dotted vertical lines are explained in the text. manian et al. (2019) of a characteristic width of 0 . ± .
03 pcfor the filaments in 8 HGBS regions.An important physical parameter for filaments is the massper unit length. Theoretical models of isothermal infinite cylin-drical filaments confined by the external pressure of the ambientmedium predict the existence of a maximum equilibrium valueto the mass per unit length (Ostriker 1964): M line , max = kT µ m H G = . (cid:18) T
10 K (cid:19) M ⊙ pc − (5) Above this value the filament is unstable and can fragment toform cores.In our case, M line = M / L where the mass M of the filamentis µ m H P i n i (H ) A with A the area of one pixel in cm , and thesum is over all the pixel in the filament area, while L is the spinelength. Note that A depends on the distance as d while L on d ,so M / L increases with d and, for a constant d =
300 pc, is likelyoverestimated in the Western half of Perseus, and underestimatedin the Eastern half.In Fig. 13 we show with the green line, the distribution ofthe mass per unit length for all the filaments we find in Perseus,
Article number, page 13 of 52 & Aproofs: manuscript no. perseus
Fig. 12.
Histogram of the filament widths, averaged over the spine (binsize 1 pixel or 0.02 pc at d =
300 pc).
Fig. 13.
Histograms of mass per unit length for filaments with cores(green line) and prestellar cores (blue and red lines, see text). that contain at least one core of any type (for core definitionand extraction, see Sect. 4.1 below). The mass per unit lengthdistribution peaks at ∼ . M ⊙ pc − , well below the typical valueof 16 M ⊙ pc − of Equation (5).If we consider that 10 K is notrepresentative of the dust temperature and that we should adopt T > ∼
12 K (see Fig. 5; see also Arzoumanian et al. 2019, where arange between 11 K and 30 K is found for the dust temperatureof filaments in many HGBS regions) the peak in the distributionis more than a factor 10 smaller than the maximum linear mass.An important issue here is the background subtraction be-cause, if the background is overestimated, the linear mass of thefilament is underestimated. To address this problem we madeuse of the results found by Hacar et al. (2017). They derive 14kinematically-coherent structures in NGC1333 through observa-tions of the N H + (1–0) line. These structures, named fibres, aresimilar to what we call branches. The comparison between fi-bres and branches, however, is not easy because of the di ff erenttracers used, molecular gas vs. dust emission, and because of thedi ff erent algorithm used to derive the structures. Only in one casewe found a fibre and a branch that have a reasonable spatial over-lap with a similar length. This happens for fibre number 9: Hacar et al. (2017) derived a length of 0.47 pc and M lin = . M ⊙ pc − ,while we found a length of 0.50 pc and M lin = . M ⊙ pc − , so,at least for this case, the background estimate looks reliable.Since only prestellar cores are likely star-forming in nature(see Sect. 4.3), it is perhaps more reasonable to consider thefilaments that contain prestellar cores instead of the filamentsthat contain only unbound cores. In this case (blue histogram inFig. 13), the peak of the distribution increases to ∼ M ⊙ pc − .This value is still less than the value M lin / M lin , max . Adding the candidate prestellar cores (see again Sect. 4.3) to enlarge thesamples of bound cores, changes the shape of the histogram(dashed red line), but only in the region of smaller masses. In anycase, the majority of filaments are below M lin , max . Note, however,that Fischera & Martin (2012) found that fragmentation and coreformation can occur in filaments when M lin / M lin , max > .
5, closeto our value.Similarly, Benedettini et al. (2018) found that the majority offilaments with bound cores in Lupus have M lin < M lin , max . Theauthors suggest that in a filament the mass per unit length shouldbe considered locally instead of giving one value for a whole fil-ament. In fact, if we compute M lin for the single branches insteadof considering the entire filament, we derive a much broader dis-tribution toward high values, > ∼ M ⊙ pc − , of M lin . Nonethe-less, the median of the distribution is ∼ . M ⊙ pc − with a peakat less than 1 M ⊙ pc − .Note, however, that the formula given in Equation (5) givesthe maximum line-mass for isothermal equilibrium when thenon-dimensional radius ξ of an infinite length filament goes toinfinity. In the more general case of finite ξ , however, Equa-tion (5) reads (Ostriker 1964) M ( ξ ) = kT µ m H G + /ξ ≤ . (cid:18) T
10 K (cid:19) M ⊙ pc − (6)where the equality holds only for ξ → ∞ . So, in the more generalcase of finite ξ , the mass M ( ξ ) of a self-gravitating cylinder inthermal equilibrium is smaller than the asymptotic M lin , max forthe same temperature.The non-dimensional radius ξ can be transformed back to aphysical radius once we know T and ρ , i.e., the temperatureand central density of the filament, respectively. Alternatively,one can estimate ρ from the observed values. For example, ifwe assume T =
16 K and M lin , max = M ⊙ pc − , Equation (6)solved for ξ gives ξ ∼ .
15. Then, if we assume 0.08 pc to be thetypical filament radius, solving Equation (45) in Ostriker (1964)for the central density yields ρ ∼ . × − g cm − or n ∼ × cm − for µ = .
8. Strictly speaking, 0.08 pc is the widthof the filament, defined as the FWHM of the Gaussian fit. If wedefine, instead, the radius as 1.29 × FWHM (Pezzuto et al. 2012),then the typical filament radius becomes ∼ .
10 pc and n ∼ . × cm − . In any case, we conclude that as long as n > ∼ n ,a filament with radius 0.08 pc and T =
16 K has M lin , max = M ⊙ pc − , similar to the peak value we find in the histogram ofFig. 13. The probability density function (PDF) derived from the columndensity map has been used to probe the physics governing thedi ff use medium (see Schneider et al. 2015, for a review on PDF).Briefly, the PDF shows a log-normal behaviour at low densitiesdue to the turbulence in the cloud, while a power-law tail de-velops at higher densities as a consequence of self-gravity andstar-formation activity. Article number, page 14 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 14.
The column density PDF for the whole Perseus molecularcloud: s is the slope of the power-law fit, shown in red, over the interval x – x , both in 10 cm − . As shown with the green line, the fit can beextended down to ∼ × cm − . The brown line is a log-normal fit tothe low-density PDF whose parameters are given in the text. Note that N (H ) ∼ . × cm − is the smallest column density having a closedcontour in our map. In Fig. 14, we present the PDF for the whole molecularcloud. We model the observed distribution with a log-normal anda power-law functions, fitting each curve independently.The brown line shows the best log-normal fit to the low-column density part of the distribution. The peak is at N (H ) = (9 . ± . × cm − . The significance of this fit is, how-ever, limited by the fact that the smallest value of column densityhaving a closed contour in our map is N (H ) ∼ . × cm − .As a consequence, the shape of the PDF in the region where thelog-normal fit is derived, can be distorted by data incomplete-ness (Alves et al. 2017, argued that the overall log-normal shapeis actually created rather than distorted by incompleteness).Moving now to the high column density tail in the PDF, Fed-errath & Klessen (2013) showed that the following relation existsbetween s , the power-law slope in the PDF, and q , the power-lawslope ρ ( r ) ∝ r − q of the volume density for cores: q = − s (7)so that if s is derived, hints on how the star-formation process ina cloud is proceeding can be obtained.To find the exponent of a power-law, the easiest and oftenused solution is to linearise the problem in log-log space, gettingan equation of the kind log y = log c − γ log x . The unknowns c and γ are immediately found by fitting a straight-line to thedataset. This procedure, however, should be avoided for manyreasons (Bauke 2007; Clauset et al. 2009), for instance it vio-lates the assumption that uncertainties on the dependent variablefollow a Gaussian distribution. This assumption is the base forleast-square fit.Our strategy instead was to fit directly a function y = cx γ using non-linear fitting routine. We used the linearisation schemedescribed above to obtain only a first estimate of the parameters.Since we do not know the extent of the interval over which the fitshould be done, we treated the interval extremes, N (H ) min and N (H ) max , as free parameters.In this way, it is not possible to compare directly the χ cor-responding to each model, because the number of data points is not constant. Furthermore, the use of the reduced χ with non-linear models is questionable because the degrees of freedomin this case are generally not known . To derive the best modelwe adopted the cross-validation method (Andrae et al. 2010).Namely, for a given N (H ) min and N (H ) max , we computed thebest c , γ excluding one point of the dataset and from the derivedbest-fit model we computed the di ff erence between the expectedvalue and the model-derived value. This procedure is repeatedfor all the points in the dataset and the product of all the di ff er-ences gives an estimate of the likelihood for that model. Then,we looked for the maximum likelihood value among all the mod-els ( N (H ) min , N (H ) max , c , γ ).The validity of this strategy is limited by the fact that of-ten the PDF does not show a clear power-law trend. As aconsequence, the fit procedure tends to minimize the interval N (H ) min – N (H ) max . To impose physical constraints to the fit,we varied N (H ) min around the value reported in Col. N (H )of Table 10, discussed later on in the paper. This value in col-umn density is the smallest background column density foundfor prestellar cores in each sub-cloud. Since the power-law tailshould trace the region where gravity is strong enough for coresto form, it looks reasonable to impose that N (H ) min is not muchdi ff erent from the minimum background column density.To derive an uncertainty for N (H ) min and N (H ) max , dubbed x and x in Fig. 14, we created the PDF histogram with fivedi ff erent binsizes from 0.8 to 1.2, in steps of 0.1, in units of10 cm − (the one shown in the figure corresponds to the choice1 × cm − ). The power-law slopes and limits were found forthe five histograms and similar solutions were sought. The redline in Fig. 14 shows the power-law whose slope is the weighedaverage of the five slopes and is measured over an interval of7 . × cm − and 1 . × cm − . These intervals arethe mean of the five starting and end points over which the fitextends.For the whole Perseus cloud, the minimum background col-umn density for prestellar cores is 9 . × cm − (see Table 10).We could not find any good power-law fit starting from suchsmall values. Indeed, the best fit we found (slope –3.190) is lim-ited to 7 . × cm − but it is nonetheless a good solution downto ∼ × cm − , as it can be seen from the green line that ex-tends the best fit to smaller column densities.Our slope − . ± .
033 is in good agreement with thevalue –3 found by Zari et al. (2016), and translates into q = . ± . ffi ciency. We will discussthis topic later on in the paper. Here, we show the results forthe individual subregions defined in Fig. 9. Fig. 15 shows thePDFs for each of the subregions that hosts at least one protostar.In many cases, the low-density portion cannot be fit with a log-normal function, while the high density tail shows a wide rangeof values (labels s in Fig. 15). The slopes s for the single cloudsare di ff erent from the one found for the whole Perseus region,as predicted by Chen et al. (2018). Through Equation (7), theinterval in slopes translates into an interval for q limited by 1.5, The usual assumption of N − n degrees of freedom if N is the numberof data and n is the number of parameters may be valid, but in generalis not. The background column density is computed by getsources at theposition of each core in the high-resolution column density map, andreported in the catalogue, see Table A.1. Article number, page 15 of 52 & Aproofs: manuscript no. perseus
Table 8.
Comparison of the PDF power-law slopes found by Sadavoyet al. (2014) (Col. S) and in this paper (Col. P). Column P S reports theslope found with our data following Sadavoy et al.’s procedure. Region S P S PL1448 − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . − . ± . ff erent strategyadopted. To make the comparison, we derived the slope of thepower law following their method: first, we fixed N (H ) min to7 × cm − , 30% (see Sect. 3.2.2) of 1 × cm − , the valueadopted in Sadavoy et al. Second, we made a linear fit in thelog-log plane. The slopes are compared in Table 8.In this table we report both the slopes found with our dataaccording to the procedure written above (Col. P) and the theslopes found still with our data but following the same procedureas in Sadavoy et al. (Col. P S ). Naming s ± σ s and p ± σ p the valuesreported in Col. S and Col. P S , respectively, we see that s > p always. In three cases s − σ s < p < s and in other three case theintervals s − σ s and p + σ p overlap. Only for L1448 we find adi ff erence slightly larger than 1 σ s : p = s − . σ s . We concludethat the slopes reported in Fig. 15 di ff er from those reported inSadavoy et al. (2014) because of the di ff erent strategy adoptedto fit the power-law tail in the PDF. When used in the rest of thispaper, the slopes of the PDFs are those reported in Fig. 15.
4. Physical properties of the cores
Sources were extracted from the intensity images using re-lease 1.140127 of getsources (Men’shchikov et al. 2012;Men’shchikov 2013), a multi-scale, multi-wavelength source ex-traction algorithm. Its application to the fields of the HGBS isdescribed in Könyves et al. (2015). We followed their strategy todetect starless cores and protostars by running twice getsourceswith two separate set of parameters to optimize the extraction. Inthe following we summarize the extraction procedure.For starless cores, we extracted sources on the SPIRE inten-sity maps and the high spatial-resolution column density map(Palmeirim et al. 2013, see also Sect. 3.2). We also use the160 µ m data via a temperature-corrected map, which is ob-tained by convolving the PACS red image to the resolution ofthe SPIRE 250 µ m band and then combining them to derive atwo-colour column density map (Könyves et al. 2015). The pur-pose of this approach is to avoid strong gradients of intensity thatcan be found in proximity to photon-dominated regions (PDRs)or hot sources. For protostars, only the 70 µ m band was used fordetection.After source detection is completed, flux intensity, or simplyflux, is measured for each source by getsources at all Herschel wavelengths. In particular, at 160 µ m we use the intensity map,and not the colour-corrected map, used only for detection. To both catalogues, we applied the selection criteria used for Aquila(Könyves et al. 2015). For the starless cores: – Column density detection significance greater than 5; – Global detection significance over all wavelengths greaterthan 10; – Global “goodness” ≥ – Column density measurement with signal-to-noise ratio(SNR) greater than 1 in the high-resolution column densitymap; – Monochromatic detection significance greater than 5 in atleast two bands between 160 µ m and 500 µ m; – Flux measurement with SNR > µ m and 500 µ m for which the monochromatic detectionsignificance is simultaneously greater than 5.For prostostars, the criteria are: – Monochromatic detection significance greater than 5 in the70 µ m band; – Positive peak and integrated flux densities at 70 µ m; – Global “goodness” ≥ – Flux measurement with SNR > µ m band; – FWHM source size at 70 µ m smaller than 1.5 times the70 µ m beam size (i.e., < ′′ . – Estimated source elongation < µ m.The two catalogues were cross-matched to look for associa-tions within 6 ′′ . We found 60 sources present in both catalogues.These sources were removed from the cores analysis being con-sidered as candidate protostars. In Appendix A we explain inmore detail how the SEDs were built for the objects detected inboth catalogues. Sources with no counterpart at 70 µ m were clas-sified as tentative starless cores. We then visually inspected theintensity maps and column density map toward each candidateto be sure that the source is not an artefact. This step removesnon-existent sources due to local fluctuations in the maps andalso finds candidate protostars present only in the starless corescatalogue (e.g., protostars that are not well detected at 70 µ m).The reason for this depends on the slightly di ff erent criteria usedto build the catalogues (see Appendix A for details).To remove known galaxies we queried the NED and SIM-BAD archives.Starless cores not visible at 70 µ m but with a SIMBAD coun-terpart at shorter wavelengths were removed from the cataloguebecause starless cores are not expected to be detected < ∼ µ m.We use a distance criterion of 6 ′′ . Since the association with aSIMBAD source may be only spatial and not physical, whena starless core with no detection at 70 µ m has also a (sub)mmcounterpart within 6 ′′ beside a counterpart at short wavelengths,the source was left in our catalogue.We also scanned the WISE (Wright et al. 2010) archivewithin a radius of 6 ′′ from our objects, imposing to have SNRgreater than 0 in bands 3 and 4. This approach is quite conserva-tive because the threshold of SNR is very low. Moreover, thereremains the possibility that two di ff erent sources appear closeeach other in projection. In any case, sources with a WISE coun-terpart were removed.All the starless cores removed from our catalogue are re-ported in Appendix E. http://ned.ipac.caltech.edu/ http://simbad.u-strasbg.fr/simbad/ https://irsa.ipac.caltech.edu/cgi-bin/Gator/nph-scan?mission=irsa&submit=Select&projshort=WISE Article number, page 16 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 15.
The PDF’s for the subregionsidentified in Perseus where protostarswere detected. In each panel s givesthe slope of the power-law fit, shown inred, in the interval delimited by x and x , both in 10 cm − ; the fitting proce-dure is detailed in the text. The x -axis is N (H ) in cm − . Green lines extend thebest-fit over the interval of column den-sities where protostars were found (seeCol. N (H ) in Table 9). In the end, we were left with 816 candidates: 684 starlesscores and 132 protostars. A search for counterparts within 6 ′′ in the c2d archive (Evans et al. 2009) shows no associationsfor the starless cores, while about 70% of our prostostars hasa possible counterpart. The catalogue, presented in Appendix Aand available as on-line material, reports data for all 816 sources,both starless cores and protostars. In the following we discuss the http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=J/ApJS/181/321 physical properties of the starless cores while the protostars willbe the subject of a forthcoming paper.As an additional check on the reliability of the detectedsources, we made a second extraction with a completely di ff erentsource identification algorithm, namely CuTEx (Molinari et al.2011). This method identifies sources via the second-order dif-ferentiation of the signal image in four di ff erent directions, look-ing for minima of the curvature. Since CuTEx makes detectionand measurements on single band images, it is not straightfor-ward to make comparisons with extractions by getsources, which Article number, page 17 of 52 & Aproofs: manuscript no. perseus builds its catalogue by combining the results of monochromaticdetections. Given that the peak of the SED of cold cores is ex-pected around 250 µ m, we looked for agreement from both get-sources and PSW CuTEx catalogues. Indeed, we find that 467(68%) of getsourcescores have a CuTEx-detected object locatedwithin the 250 µ m elliptical extent measured by getsources.We find excellent agreement (98%) between the protostarcatalogues derived with getsources and CuTEx. Since to extractthe candidate protostars both algorithms use only the 70 µ m data,where di ff use emission is less intense, it is not surprising that thetwo methods found similar objects. Once the source catalogue has been produced, we fitted the mea-sured SEDs using a grid of theoretical models. This approach,already used in Benedettini et al. (2018) and equivalent to thatused in Sect. 3.2, consists of generating a number of modifiedblackbodies F ν = κ ν M B ν ( T ) d ; κ ν = κ (cid:18) λ λ (cid:19) β (8)where M is the mass of the isothermal emitting dusty envelopeat temperature T and distance d . For the dust opacity, we usedthe same parametrisation as for the column density map: κ = . g − at λ = µ m with β = M = M ⊙ and d = T was varied in the range 5–50 K in steps of0.01 K (4501 models). The distance is scaled to the requiredvalue, 300 pc for Perseus, during the fitting procedure.Using a grid instead of a non-linear fitting procedure has twoadvantages. First, it is not necessary to give initial guesses of theparameters, which are more or less arbitrary. Second, as long asthe grid is large and dense, we can be sure to find the globalminimum and not a local one.Since Equation (8) is linear in M , the mass can be foundwith a straightforward application of the least squares methodwhen comparing a given SED to the grid of models, as shown inEquation (2). Among the 4501 models, the best fit corresponds tothe pair ( T , M ) with the minimum χ . Uncertainty in T is derivedfrom the range in temperatures whose models have χ ≤ χ + T and T are minimum andmaximum temperatures of these models then we give T + ( T − T ) − ( T − T ) .Uncertainty in M was derived both according to the leastsquares method, and from the variation in mass correspondingto T and T . Clearly, if T < T then M < M . The larger ofthe two uncertainties was then adopted.For SEDs with less than three significant flux measurements(see Appendix A), the fitting procedure was not applied. Wealso did not look for the best fit in cases where F ν (350 µ m) < F ν (500 µ m). For all these cases, we adopted a fiducial temper-ature equal to 10 . ± . ∆ T / T for reliable sourcesis ∼ T = . As explained in Sect. 4.1, we classify a core as protostellar if itis in emission at 70 µ m. This approach is physically plausiblebecause in general cold cores are not visible at this wavelength,often not even at 160 µ m. On the contrary, once the source isvisible at 70 µ m, a star has already formed, warming up its sur-rounding envelope. This rule, however, is not always valid. Inprinciple, any core emits in the PACS bands, and its detectionat 70 µ m depends on its physical properties combined with thesensitivity of the instrument. Indeed, we find seven objects (ID µ memission that is either uncertain or at a level compatible with, orbelow, the best-fit SED found with Equation (8). These sourceswere classified post facto as starless cores.First Hydrostatic Cores (FHSC) are expected to have excess70 µ m with respect to a modified blackbody, even if they can notbe considered genuine Class 0 objects. They have masses com-parable to a giant planet and radii are only few astronomical units(Larson 1969). Source µ m emission was an upper limit. From visual inspect, how-ever, this source is visible at 70 µ m but since the uncertainty onthe flux is higher than the flux itself, the code used to make theSED fitting classified it as a starless, putting an upper limit in theblue band. We re-defined this source as protostar.Among the starless sources, we want to identify cores thatare not stable against their own gravity. As a result, they arelikely to be collapsing or on the verge of collapse, forming inthe near future one or more stars. As done in other HGBS papers(e.g., Könyves et al. 2015), we adopted the Bonnor-Ebert (BE)critical mass as an indicator of the maximum mass a core canhave to be stable against gravitational collapse. For an isother-mal sphere consisting of particles of mass m , the BE mass is(Bonnor 1956): M BE , crit = . R BE KT µ m H G (9)where µ = .
33 is the mean molecular weight per free particle(Kau ff mann et al. 2008), R BE is the BE radius estimated as thedeconvolved geometrical mean radius of each source measuredin the high-resolution column density map, K is the Boltzmannconstant and G is the gravitational constant. We imposed a de-convolved radius of 6 ′′ .
1, one third of the FWHM at 250 µ m,to sources that are unresolved. Note that in the above equation,non-thermal e ff ects like turbulence or magnetic fields are nottaken into account. If the source mass is M , we define an ob-ject as bound (or prestellar) if it has M BE , crit / M ≡ α BE ≤ prestellar for boundcores and starless for unbound cores, even if both are starless, tobe consistent with the other HGBS catalogues.Since for unresolved cores the deconvolved radius tends tozero causing M BE , crit →
0, Könyves et al. (2015) used a setof simulated bound cores to find that bound, unresolved corescan be identified if α BE ≤ / FWHM) . , where FWHMis the non-deconvolved source radius estimated in the high-resolution column density map and HPBW is the linear map res-olution, 18 ′′ .
2. Sources that fulfilled this criterion were named candidate bound cores while cores having α BE ≤ robust . In this paper we adopt the same nomenclature. Article number, page 18 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 16.
Relation between mass and radius for all the 519 detected cores:vertical dashed line corresponds to 0.026 pc, the linear distance corre-sponding to the FWHM (18 ′′ .
2) of the high-resolution column densitymap at 300 pc. The three power laws are fit to our data. Black trianglesare hot starless cores discussed in the text; also the blue dashed line isdiscussed in the text.
We simulated bound cores as in Könyves et al. (2015) to de-rive the completeness limit in mass of our survey. In Appendix Bwe present our simulations. We find that for sources with massabove ∼ . M ⊙ we are complete at > ∼
90% in general, but thislimit depends on the contrast between source intensity and back-ground level. We used the simulations also to verify that theabove formula for candidate bound cores works in our case too.
In Fig. 16 we show the relation between mass and radius for thewhole population of 519 cores. The bound sources are in blue,unbound sources in green, and candidate bound sources in red.At any radius, bound cores are more massive than unboundcores: this is not a consequence of using Equation (9) as stabil-ity criterion. A massive starless core can be unbound if warmenough and, conversely, a low-mass starless core can be boundif cold enough. The fact that bound cores are more massive im-plies some relation between M and T , an anticorrelation that isin fact present in our data (see below Fig. 18).For the population of unbound cores, we find M ∝ R . ,shown with the red line in Fig. 16, while for candidate boundcores, we find M ∝ R . , the solid black line in the same fig-ure. Bound cores do not show a clear relation between mass andradius: indeed, the best-fit slope is M ∝ R . . The lack of cor-relation is not surprising given that: 1) Equation (9) is a relationbetween mass, temperature and radius: when, as in our case, T isnot assumed constant, as it was in general before Herschel , thereis not an obvious relation between M and R ; 2) if a bound coreis collapsing, it is not even expected to be described by Equa-tion (9). In fact, our stability criterion is not M = M BE , but rather M greater than M BE by some factor. Coming back to the origi-nal paper by Bonnor, in particular Fig. 1 in Bonnor (1956), inthe plot p − V bound cores should populate the curve on the leftof point A, where instability is dominating. Equation (9), on thecontrary, describes the condition of a core that is found exactlyon point A. Fig. 17.
Relation between T and mean column density of the sources,where symbols are defined as in the previous figure. The two lines arelinear fits of the form T = s log N (H ) + b . The slopes s are given inthe legend and in the text where we also report the uncertainties. Blacktriangles are hot starless cores discussed in the text. In Fig. 16 the dashed blue line shows the M − R relation forcores at T = . α BE =
2. This temperature is thelowest we derived for prestellar cores. We consider this line tobe the lower-limit for bound cores in our sample. Note, how-ever, that for T = . β =
2, the modified black bodydistribution peaks at λ > µ m, which means that we maylack colder, bound cores in our data because we imposed that F ν (350 µ m) > F ν (500 µ m) in Sect. 4.2.The smallest radius in our sample, 0.0089 pc or 6 ′′ . ′′ .
1, i.e., one third of the FWHM at 250 µ m, to sourcesthat are unresolved. The largest observed radius is 0.11 pcfor bound cores. During the detection and measurement of thesources with getsources, we imposed a maximum radius of 220 ′′ (0.32 pc), which is 3–4 times larger than the largest core sizethat we detect. Thus, this size constraint does not a ff ect our re-sults. Instead, we find that the cores in Perseus have a maximumsize of ∼ . ffi cult to detect.In Fig. 17 we show the relation between cores temperature T and their mean column density N (H ) (defined as M /π R ,where T , M and R were derived from source SED fitting). Wemodelled the trend seen with the equation T = s log N (H ) + b .Two di ff erent slopes are found for prestellar and unbound cores: − . ± .
21 and − . ± .
41 for bound and unbound, respec-tively. This result is in contrast with what was found by Marshet al. (2016) in L1495. They found there that the trend fromthe unbound populations continues smoothly when entering thebound region, with a single slope indeed enough to describe theoverall trend. Their slope itself, − .
6, is di ff erent from the valueof − .
32 we find for unbound cores. Such a di ff erence could bedue to the di ff erent environments in which cores are embedded.In deriving the M − T slope for the unbound cores, we ex-cluded seven objects that are clearly warmer than other cores,i.e., with T >
20 K. Including these points the result is s = − . ± .
67. These sources are the seven starless cores that showemission at 70 µ m (see Sect. 4.3). As noted earlier, detection in Article number, page 19 of 52 & Aproofs: manuscript no. perseus
Fig. 18.
Relation between T and M of the sources. The warmest un-bound source at ∼
40 K is not shown to limit the extension of the x-axis.The three lines are explained in the text. the PACS blue band does not necessarily mean that a source hasevolved into protostar, but it requires the object to be warm. Forthese sources the peak of the SED moves toward shorter λ (for T >
20 K the peak moves at λ < µ m for β =
2, Elia &Pezzuto 2016) while at low T the peak moves at longer wave-lengths so that the emission in the PACS blue band becomes toofaint to be detected. Moreover, the SED increases at higher T as L ∝ T + β (see Elia & Pezzuto 2016). In principle, one could havebright enough starless core emission at 70 µ m by also increasingthe mass, but the intensity depends only linearly with M so thathuge masses are required to make an unbound, and cold, corevisible at short λ . In fact, these seven sources are warm and havesmall masses (see black triangles in Fig. 17).In principle, there is no reason why warm unbound coresshould not exist. Their position in Fig. 17 seems, however, todefine a class of sources independent from the other unboundcores. It is possible that these sources have poorly-determinedintensities so that T was not estimated correctly. For example,they could be objects falling very close to strong sources, so thattheir envelope is unusually warm. Alternatively, these sourcescould have some intrinsic properties that make them di ff erentfrom the others. Since our goal here is a statistical description ofthe cold core population in Perseus, we do not investigate furtherthis small sample.Finally, in Fig. 18 we show the relation M vs. T , which showssimilar distinctions between the populations that were seen inFig. 17. The anticorrelation between M and T is evident (see thediscussion about Fig. 16).For any given temperature, there is a mass below which coresare not detected. To investigate from a quantitative point of viewthis relation, we studied if, and to what extent, the sensitivity ofthe Herschel instruments plays any role. First we constructed aSED with the SPIRE-PACS Parallel Mode 1- σ instrument sen-sitivity for a point source , divided by √ http://herschel.esac.esa.int/Docs/PMODE/html/ch02s03.html . We adopted the sensitivity when scanning in thenominal direction that were slightly worse than those in the orthogonaldirection. tected cores, and the same distance of 300 pc. The best fit modelhas T = . M = . × − M ⊙ . Then, we derived foreach T , the mass that scales the model to the SED of sensitivi-ties. For instance, at 20 K the mass is M = . × − M ⊙ , at 10 K M = . × − M ⊙ and so on. To first approximation, withoutconsidering measurements uncertainties, these values give an es-timate of the smallest detectable mass for a given T compatiblewith Herschel sensitivities; clearly, the match between modelsand sensitivities-based SED is worse and worse as T decreases.All these values give the magenta line in Fig. 18, well de-scribed as M ∝ T − . This line, derived from Herschel sensitiv-ities for a point source, can be considered as the locus of thesmallest detectable mass of a compact source, as a function oftemperature. The line is well below the detected masses: indeed,in star forming regions it is well known that the
Herschel de-tection of cores is not driven by the sensitivity but by the con-trast between core and di ff use medium emission. Interestingly, asimple scaling by the arbitrary factor of 15, found by eye, givesthe black line that reproduces well the smallest detected mass ofstarless cores for T > ∼ T < ∼ M BE decreases while the smallest detectablemass of a source increases. So, an unbound cold core must havehigh mass to be detected, and then large radius not to be un-bound, but low T and high R means a faint and di ff use objectthat could remain undetected.The magenta line does not work with bound cores for T < ∼ T − . , shown inFig. 18 with a red line. This slope was found by choosing by eyetwo arbitrary bound cores, with T = . M = . M ⊙ ,and with T = . M = . M ⊙ . A possible explanation forthis behaviour is based on the finding that more massive prestel-lar cores are found in regions of high column density (see Fig. 21in Section 5.2). As a consequence, a bound core is detected ifmassive enough to show up against the bright di ff use medium,and the minimum mass does no longer reflect the law M ∝ T − that is more related to the instrument sensitivity. This conclusionis consistent with the result shown in Appendix B.2 where wediscuss the completeness in mass.
5. Discussion
In Fig. 19 the histograms shows the core mass functions (CMF)for robust prestellar cores (blue line), and for robust plus candi-date prestellar cores (red line) in Perseus in the form d N / dlog M .The histograms use logarithmic bin sizes of 0.1. The most mas-sive candidate prestellar core has M = . M ⊙ , so that at highmass blue and red lines overlap.The results found by Swift & Beaumont (2010) show thatwith 199 sources it is di ffi cult to discern between a power-lawtail or a log-normal function to model the CMF shape. Thus, wefit to the CMF shown in Fig. 19 both a power-law and a log-normal separately.The high-mass tail was fit with a power-law for M > M ⊙ .Given the limited number of sources, the size of the bin of thehistogram may play a role. Hence, we followed the prescriptionof Maíz Apellániz & Úbeda (2005) and used a variable bin sizewith a fixed number of values in each bin. In this procedure, N values, here the core masses, are arranged in m bins whose size ischosen such that each bin contains n = N / m values. This means Article number, page 20 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 19.
The core mass function (d N / dlog M ) for the 199 robust prestel-lar cores (blue histogram), and for the 299 robust and candidate prestel-lar cores (red histogram) in Perseus. Above M ∼ . M = .
1. Green anddashed gray lines show a log normal fit, orange line a power-law fit (seetext for details). The dashed black line shows the completeness limit at ∼ . M ⊙ . that each bin will have its own di ff erent size. Maíz Apellániz& Úbeda (2005) have shown that this procedure is robust evenwhen n =
1, i.e., when each bin contains one single value, or thenumber m of bins is as low as 3.There are 96 prestellar cores with M > M ⊙ . We constructeddi ff erent histograms having 4, 6, 8, 12, 16 and 24 sources per bin.For the fit we adopted the functional form d N / d M ∝ M α for theCMF and we find α = − . ± . σ level with Salpeter’s slope of − N / dlog M ∝ M α + so the power-law best-fit, orange line, has a slope − . ′′ . They fit the high-mass part of theirCMF with two power laws merging at 2.5 M ⊙ . They also trieda fit with only one slope for M > . M ⊙ . Although they find asingle power-law slope for d N / d M of − . ± .
1, which is closeto the Salpeter value, they note that the CMF is better fit withtwo power laws. In this respect, it is worth mentioning that thethree most massive cores in their survey, namely Bolo 48, Bolo 8and Bolo 43 with masses of 25.6 M ⊙ , 11.3 M ⊙ and 10.8 M ⊙ (foran assumed dust temperature of 10 K, distance of 250 pc, anda di ff erent opacity law), respectively, were detected by PACSin its blue band (ID 330, 68 and 303 in our catalogue, see Ap-pendix A). For this reason, we classified them as protostars, anddid not include them in our CMF. It is possible that removingthese sources would have made the BOLOCAM-derived CMFbetter described with a single slope.Sadavoy et al. (2010) also produced CMFs of Perseus usingSCUBA observations at 850 µ m from the SCUBA Legacy Sur-vey. They found a d N / dlog M slope of − . ± .
20, which iswithin 2- σ of Salpeter. Like Enoch et al. (2006), Sadavoy et al.(2010) also assumed a fixed dust temperature (11 K based onNH observations of cores in Perseus).The SCUBA Legacy catalogue was incomplete, however.The sample did not include B5 and also missed several otherhigh density regions. To account for the missing areas, Sadavoy et al. (2010) produced predicted CMFs. The predicted CMF wasstill consistent with Salpeter, and they estimated the number ofpredicted starless cores to be 232, which isn’t far o ff from thenumber of prestellar cores we found. Even if the predicted num-ber of 232 will include some unbound cores, SCUBA 850 µ mdata are most sensitive to dense cores that are likely to be boundrather than flu ff y unbound objects.Our CMF in Fig. 19 for robust prestellar cores (blue his-togram) can be fit with a log-normal function (green line) withpeak at − . ± .
028 (or M peak = . ± . M ⊙ and width0 . ± . M ⊙ and σ = .
55. If we assumethat the IMF of Perseus will resemble that of field stars, we de-rive ǫ core , the star formation e ffi ciency per single core, of 0.30.Adding the 199 candidate prestellar cores give the CMF shownas red histogram in Fig. 19. Since these cores have M < . M ⊙ ,the e ff ect is that of enlarging the distribution and shifting thepeak to a smaller value. The log-normal function (dashed grayline) has peak at − . ± .
033 (or M peak = . ± . M ⊙ )and width 0 . ± . ǫ core increases to 0.52. In case not all199 candidate prestellar cores are indeed bound, especially atlow masses, we can reasonably estimate ǫ core in the range 0.3– 0.4. A similar value, 0.4, was found in Aquila (Könyves et al.2015), but higher values are also reported in HGBS regions (e.g.,Marsh et al. 2016; Benedettini et al. 2018, with ǫ core ∼ ǫ core in Perseus was derived by Mer-cimek et al. (2017) using data from literature. They found ǫ core ∼ .
16, about half of what we find, but using a di ff erent method:they estimated ǫ core as the ratio between the total mass of proto-stars (Class 0 and Class I objects) over the total mass of starlesscores. To compare these two values for ǫ core is not easy becausethe two methods depend on di ff erent assumptions. Here we limitto note that, on one side, Mercimek et al. (2017) considered theirvalue a lower limit; on the other side, our value can be loweredif the peak of the IMF is chosen di ff erently.In fact, instead of using the peak of the IMF for field stars, wecan compare the peak of our CMF with the IMF derived in tworegions in Perseus: Alves de Oliveira et al. (2013) fit the IMF ofIC348 with a log-normal function finding M peak = . ± . M ⊙ and σ = . ± .
03; Scholz et al. (2013) derived instead themedian mass of the IMF for IC348 and NGC1333, finding forboth clouds the value ¯ M = . M ⊙ . Since the IMF has a high-mass tail, clearly ¯ M > M peak , but even assuming M peak = ¯ M weconclude that 0 . < ∼ ǫ core < ∼ . M > . M ⊙ . They could not estimate fromtheir data the dust temperature as we did, however, so theygave two values for M peak : 0.9 M ⊙ and 0.3 M ⊙ , assuming T d =
10 K and 20 K, respectively. If we want to compare their re-sults with ours, we have to take into account both the di ff er-ent opacities (0.0074 cm g − following our opacity law insteadof 0.0114 cm g − ) and the di ff erent distance (300 pc here vs.250 pc). Considering both di ff erences, the two values for M peak become ∼ M ⊙ and ∼ . M ⊙ for T d =
10 K and 20 K, respec-tively. Our M peak is closer to the value corresponding to 20 Keven if our range in T d (see Fig. 18) suggests that T d =
10 Kshould be more appropriate.In Sect. 3.1, we derived a relation between distance andsource coordinates. In Fig. 20, we show the resulting CMF forprestellar cores when each source is assigned a di ff erent dis-tance. Note that physical radius increases with d while massincreases as d , so, in general, α BE ∝ d − . As a consequence,objects that are closer will have in general lower α BE and ob- Article number, page 21 of 52 & Aproofs: manuscript no. perseus
Fig. 20.
The prestellar core mass function (d N / dlog M ) for sources inPerseus when each core is assigned a di ff erent distance based on Equa-tion (1). Lines as in Fig. 19. jects that are further will have higher α BE . Anyway, we find thatchanging the distance a ff ects our prestellar core counts only min-imally as the number of robust prestellar sources stays at 199while candidate bound cores increases by 1, from 100 to 101.Including a varying distance, the log-normal fits do notchange significantly: the peak for the robust prestellar cores is M peak = . ± . M ⊙ while that for all the bound cores,roubust and candidate, is M peak = . ± . M ⊙ . Within theuncertainties the two sets of values (with fixed and varying dis-tance) are equivalent. The slope of the high-mass power law, onthe contrary, changes: for M > . M ⊙ there are 92 sourcesand the average of the slopes found with 4 and 23 bins becomes − . ± . ff erent from Salpeter’s value at 1.8 σ . Even ifEquation (1) is only an approximation, nonetheless it highlightsthe importance of assuming a non uniform distance for a com-plex like Perseus. One of the key result from
Herschel observations is the deep linkbetween filamentary structures and the star formation in clouds.Numerous studies have shown that star formation preferentiallyoccurs within filaments, with dense prestellar cores primarily indenser filaments (e.g, André et al. 2014, and references therein).This correlation has led to a possible paradigm, where filamentsfragment into prestellar cores by gravitational instability (Andréet al. 2019).We derived the number of robust prestellar cores inside a fil-ament in two ways: in the most conservative approach, a core isconsidered internal to the filament if its distance from the spineis less than the filament width, actually 1.29 × FWHM. In the re-laxed approach, we simply require that the core is inside the fil-ament border (refer to Sect. 3.2.3 and Fig. 11). The first, con-servative sample consists of 167 bound cores (84% of the total)with a median mass of 1.0 M ⊙ . The second, relaxed sample con-tains an additional 23 (12%) bound cores, with a median massof 0.96 M ⊙ . The remaining 9 (4%) prestellar cores have medianmass of 0.47 M ⊙ . So, bound cores are preferentially found withinfilaments, where the more massive cores are.For the unbound cores, the percentages for the three samples(conservative, relaxed and out of filaments) are 47%, 14% and 39%, respectively, with median mass of 0.10 M ⊙ , 0.15 M ⊙ , and0.073 M ⊙ .Figure 21 compares the background column density, mea-sured by getsources, for the 519 starless cores (blue line) and199 robust prestellar cores (green line, adding the 100 candi-date prestellar cores shifts the distribution upwards but does notchange the conclusions). The low number of cores at high den-sity reflects to some extent the fact that regions with high N (H )have an intrinsically smaller area than regions at low density. Tocheck for this geometrical bias, we also plot in the same figurethe cumulative distribution of bound cores normalised to area.For those histograms, for each N (H ) bin we computed the num-ber of cores found at this level or below, and divided by the totalarea in the image where the density is below that value. The redcurve shows the distribution for all 199 robust prestellar coresand the black curve shows the distribution for the 9 o ff -filamentprestellar cores.This cumulative distribution shows a few interesting fea-tures. First, about 90% of prestellar cores are found above ∼ × cm − , in line with the value of ∼ ∼ × cm − belowwhich ∼
60% of bound sources are found, followed by a flatterdistribution.The distribution of the o ff -filament prestellar cores showsa di ff erent trend (clearly, the on-filament distribution overlapsalmost perfectly with the cumulative distribution for all boundcores). For the o ff -filament cores, all but one sources are foundat N (H ) < . × cm − .One might speculate that o ff -filament sources are less mas-sive than on-filament sources because the former are found atlower background column density than the latter. This is not,however, the case, because if we consider the median of the massfor sources that have N (H ) < . × cm − , we find for on-filament sources ∼ . M ⊙ . For o ff -filament sources, the medianof the mass is only 0.24 M ⊙ .The right panel of Fig. 21 shows the mass of prestellar coresas a function of the background column density. We find a rela-tively flat mass distribution up to a threshold of 15 × cm − .Above this threshold, sources are found only on-filament (ac-tually, 8 out of 9 o ff -filament bound cores are below 5 . × cm − ) and their masses grow with the background columndensity with a slope 1 . ± . M ⊙ − cm , if a linear trendis assumed (red line in figure).The distributions shown in Fig. 21 raise the question of whywe do not detect prestellar cores below 0 . × cm − . Forexample, the prestellar core with the smallest level of columndensity has a mass of 0.87 M ⊙ , 2.7 times above the completenesslimit. The area of the map at column densities lower than thislimit is 40% of the total map. If cores were distributed randomly,we would expect 90 prestellar cores of any mass to be found atlow column density values . The fact that we do not find boundcores at such low column densities implies that column densities N (H ) > ∼ cm − or A V > ∼ A V threshold for star forma-tion in Perseus was already investigated in the past with con- Strictly speaking, background column density and column densityare not the same thing in the sense that the former is estimated, thelatter is measured; on the other hand, the column density is exactly thebackground column density if a source would be put at that position.Article number, page 22 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 21.
Left panel: comparison of robust bound cores and starless cores. Histograms, left y − axis, show the distributions of all starless cores (blue)and all bound cores (green). The red and black lines, right y − axis, show cumulative surface density distributions for all bound cores and theo ff -filament bound cores, respectively. Right panel: prestellar core mass vs. background N (H ). Triangles are the mean mass averaged over bins of10 cm − . Fig. 22.
Minimum distance between bound cores (blue), unbound cores(green), and tentative bound cores (red). trasting results. Hatchell et al. (2005) found no column den-sity cuto ff for dense cores based on C O (1-0) observations,whereas Kirk et al. (2006) found that submillimetre clumpswere detected only at A V > N (H ) > × cm − . Above the same level of column den-sity, we find 63% of our sources.In Fig. 22 we show the histogram of the minimum distancebetween cores. For robust bound cores, the distribution has amedian value of 0.29 pc with a broad peak in the range 0.15–0.37 pc. For unbound cores, however, the distribution has a me-dian of 0.47 pc with a broad peak shifted to slightly larger sepa-rations than in the previous case, between 0.23–0.73 pc. For thetentative bound cores the median is 0.74 pc.If cores were distributed uniformly across the observed re-gion, one would expect a mean distance among bound cores of0.69 pc, a factor 2.4 larger than the observed value of 0.29 pc.For starless cores, the mean distance is 0.65 pc, a factor 1.4 largerthan 0.47 pc. This di ff erence implies that prestellar cores cluster to some extent. This clustering is evident in Fig. 23, which showsthe position of all the prestellar cores (red crosses) and of the un-bound cores (green crosses). We find that sources do not appearuniformly distributed, but with few exceptions they are confinedinside the regions defined in Fig. 9. The star formation rate (SFR) and star formation e ffi ciency(SFE) are two fundamental properties derived from observationsthat any star-formation theory has to address, explain and pre-dict. SFR is usually estimated as the total mass of young stellarobjects (YSOs) divided by the mean duration for star formation(e.g., 2 Myr, Evans et al. 2009).The total mass of YSOs is usually computed as the number N of YSOs multiplied by the representative value of 0.5 M ⊙ .Clearly, it is necessary to determine as precisely as possible N .Indeed, Herschel observations aimed to achieve better complete-ness for starless cores rather than YSOs, so from our data alonewe cannot derive a reliable SFR for Perseus.The SFE is defined as the total mass of YSOs divided bythe total mass M cloud of the cloud, i.e., the mass of protostarsplus gas. For each subcloud, the SFE depends on how the borderis defined. As we have already discussed in Sect. 3.2.2, defin-ing such borders is not obvious. Sadavoy et al. (2014) computeddense cloud masses for the Perseus subclouds using a columndensity threshold of N (H ) = cm − , chosen to select mate-rial primarily found in the high column density power-law tail.Here we follow another approach based on the local properties ofeach subcloud. Namely, we find for each subcloud the minimumbackground column density at the positions of the protostars ineach region and compute M cloud for N (H ) > min. In Table 9,we report for each zone the number of protostars, the minimumbackground column density where a protostar is found, the massof the subcloud within this minimum value, the exponent s of thepower-law fit to the associated PDF (see Sect. 3.2.4) and the re-spective SFE(%) = P M YSO / ( P M YSO + M cloud ). The number ofprotostars associated to the whole Perseus cloud is 126 instead of132 because five sources fall in the region observed with PACSonly, and one source is in a region masked out for 250 µ m extrac- Article number, page 23 of 52 & Aproofs: manuscript no. perseus
Fig. 23.
Column density map overlaid with the positions of the 299 prestellar cores (yellow crosses and red crosses are robust and tentative cores,respectively), 220 unbound cores (blue hashes), and 132 protostars (cyan asterisks, note that these sources were detected on the 70 µ m map thatdoes not overlap completely with the SPIRE field of view, so five cores are found outside the map). Blue regions are from Fig. 9. The map isrotated by 28 ◦ , with the top and bottom corners cut out. The magenta line in the centre shows the angular scale corresponding to 1 pc at 300 pc;J2000.0 coordinates grid is shown. Region N N (H ) M s
SFEL1448 4 17.1 87 − . ± .
035 2.2L1455 8 2.14 477 − . ± .
024 0.8NGC1333 44 4.26 613 − . ± .
011 3.5Per6 5 1.68 146 − . ± .
41 1.4B1 15 0.99 1336 − . ± .
058 0.6IC348 26 2.06 1241 − . ± .
033 1.0B5 3 2.96 108 − . ± .
019 1.4HPZ6 2 2.71 20 − . ± .
24 4.8Perseus 126 0.64 11229 − . ± .
033 0.6
Table 9. N : number of protostars (126 instead of 132 for whole Perseusbecause for six protostars the column density could not be computed,see text); N (H ): minimum background column density in 10 cm − ; M : mass in M ⊙ for N (H ) > min; s slope of PDF; SFE in %. tion because close to the border of the SPIRE map. In both casesthe column density was not computed. L1451, B1E and L1468were not included because no protostars were found.For the whole Perseus cloud the minimum column densityassociated with a protostar is 0 . × cm − , below the limitof 1 . × cm − that defines the last closed contour in thedensity column map. For this reason, the total mass of the cloudfor N (H ) > min is likely underestimated. If we consider onlyprotostars above the last closed column density contour, we find113 protostars whose minimum N (H ) is 1 . × cm − . Thetotal mass is now 6198 M ⊙ and the SFE becomes 0.9%.Sadavoy et al. (2014) found a linear correlation between SFEand slope s of the PDF, SFE ∝ . s , and they discussed the im-plications of such correlation. They identified candidate Class 0sources through their detectability at 70 µ m, excluding objects that could be more evolved, Class I and Class II sources. Sinceour column density map and slopes s are di ff erent from thosederived by Sadavoy et al. (2014), as discussed in Sections 3.2.2and 3.2.4, one may wonder if their result still holds with ourdata. A complete answer to this question cannot be addressed inthis paper because in our work we used the criterion of 70 µ mvisibility to pick up potential protostars in our catalogue, withoutseparating sources in Class 0, I or II (see Sect. 4.1). Nonetheless,to give at least an indication that Sadavoy et al. (2014)’s linearcorrelation is present also in our data, we made a linear fit us-ing fifth and sixth columns of Table 9, finding SFE ∝ . s , seeFig. 24. So, even with the caveat on the used sample, we confirmthe correlation between SFE and s .Since the Herschel -based catalogue is more complete in star-less cores than in YSOs, it is more reliable to derive from oursample the core mass e ffi ciency (CFE) than the SFE. Similarly tothe latter, the former is computed as CFE(%) = P M pre / ( P M pre + M cloud ) where we use only prestellar cores because unboundcores are less likely to form stars. For the CFE we used the coremasses computed during SED fitting instead of assuming a con-stant 0.5 M ⊙ value as done for SFE. The results are reportedin Table 10. Column N gives the number of prestellar cores persubcloud. In a few cases there is also an uncertainty for N thatwill be explained below. N II is the number of Class II objectsgiven by Young et al. (2015). They counted N II also for the restof the cloud (RC) defined as whole Perseus without IC348 andNGC1333. In Table 10 we define RC as whole Perseus with-out the 4 subregions for which the number of Class II objectswas found. Column N (H ) has the same meaning as in Table 9:the minimum background column density at the position of theprestellar cores in each region. Mass M , CFE and Area are thencomputed for N (H ) > min. The ratio M / Area gives the surface
Article number, page 24 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. 24.
Star formation e ffi ciency as a function of the PDF slope for thedi ff erent subclouds in Perseus, and for the whole cloud. The red pointis an alternative SFE for Perseus (see text). The cyan line is a linear fitwithout taking into account uncertainties on the x -axis. density reported in Col. Σ (gas). Finally, t pre is the estimated life-time of the prestellar core phase, derived by scaling the numberof bound cores to the number of Class II objects, and assuminga constant SFR, i.e., t pre = N pre / N II × t II . As before we fixed t II to the usually adopted value of 2 Myr for the duration of theClass II.The uncertainty in t pre was derived based on α BE , the crite-rion to define bound a core (see Sect. 4.3). We first derived theuncertainty ∆ α BE from the uncertainties in mass and tempera-ture of each source. Then, amoung the bound cores we countedthe number of sources having α BE + ∆ α BE >
2: within the un-certainty these sources could be unbound cores. Let’s call thisnumber N − . Similarly, unbound or candidate bound sources withreliable SED having α BE − ∆ α BE ≤ N + the number of these sources. In Table 10 wereport the number of prestellar cores as N N + N − for the subcloudswith N II estimated. For the other soubclouds, which do not havean estimate of N II , t pre was not computed. The uncertainty in N is assumed as max( N + , N − ). This uncertainty is then propagatedto t pre .The resulting lifetime for the whole Perseus cloud is t pre = . ± .
52 Myr that overlaps, within 1 σ , with the value 1 . ± . t pre is much higher than forthe other regions. This can be explained as if both clouds arevery young such that star formation started very recently. Inthis case, in fact, the number of Class II objects is less than ex-pected assuming a constant SFR (for a similar case reported inLupus I and Lupus IV, see Rygl et al. 2013). On the contrary,in NGC1333 and IC348 we observe a deficit of prestellar corescompared to Class II objects. This can be interpreted as a decel-erating SFR in these two regions, with IC348 having the shortestlifetime, in line with the known fact that this cloud is the oldestof the Perseus complex. We do not have the number of Class IIstars for the other regions, but the relative high t pre for RC mightsuggest that star formation started recently also in the other sub-clouds.In Fig. 25 we show the CFE as a function of the PDF power-law exponent. Similarly to the case of SFE, also for CFE we canconsider the threshold in column density of 1 . × cm − . In Fig. 25.
Core formation e ffi ciency as a function of the power-law slopeof the PDFs for the di ff erent subclouds in Perseus, and for the wholecloud. doing so, N decreases to 196 with a CFE of 4.5%, this is thevalue used in figure. The red line is a linear fit to all the datawith a slope of 2.4. If the value of HPZ6, looking like an outlier,is not used, the result is the black line with a slope 1.22.The mean value of all the subclouds excluding Perseus as awhole is 8 . ± .
8% or 7 . ± .
8% if we exclude also the HPZ σ from these values.Another time scale important to compare with our estimateof the prestellar phase duration is the free-fall time, i.e., the timerequired for a uniform sphere of density ρ and pressureless gas,i.e., gas at zero temperature, to collapse to infinite density (e.g.,Krumholz 2015) t ff = s π G ρ (10)where G is the gravitational constant and ρ is the uniform den-sity.In Fig. 26 we show the distribution of t ff for the 199 robustbound cores. The Gaussian fit to the distribution, plotted in red,has peak at 0 . ± .
01 Myr, and σ = . ± .
01 Myr, where weassigned and uncertainty of 0.1 Myr, half size of the histogrambin, to both parameters. For a star of 0.25 M ⊙ , peak of the IMF,this implies a mean mass accretion rate ˙ M ∼ . × − M ⊙ yr − .Our peak of 0.16 Myr is close to the value of 0.10 Myr de-rived by Mercimek et al. (2017) using the sample of 69 coresdefined by Sadavoy et al. (2010).
6. Conclusions
In this paper, we analysed photometric observations of thePerseus complex executed with PACS at 70 µ m and 160 µ m,and SPIRE at 250 µ m, 350 µ m and 500 µ m.We summarize our main conclusions here:1. using distances to protostars from GAIA
DR2, we find a lin-ear correlation between coordinates ( α, δ ) in the cloud anddistance across whole Perseus. This correlation is the first
Article number, page 25 of 52 & Aproofs: manuscript no. perseus
Region N N II N (H ) M CFE Area Σ (gas) t pre (10 cm − ) ( M ⊙ ) (%) (pc ) ( M ⊙ pc − ) (Myr)L1451 19 2.15 165 13 1.77 93L1448 18 2.37 213 10 1.24 172L1455 36 + − . ± + −
59 3.18 708 7.4 3.82 186 0 . ± . + − ± . + −
104 3.62 660 8.5 5.25 126 0 . ± . + −
231 1.67 5960 4.5 76 77 1 . ± . + −
56 2.4 ± . Table 10. N : number of prestellar cores; N II : number of Class II objects from Young et al. (2015); N (H ): minimum background column density; M : mass for N (H ) larger than minimum; CFE: core formation e ffi ciency; Area: area for N (H ) larger than minimum; Σ (gas): surface density; t pre :lifetime of prestellar phase. RC (rest of cloud) refers to Perseus without the 4 regions with independent lifetime estimates (note that Young et al.2015, define RC whole Perseus excluding only IC348 and NGC1333). Fig. 26.
Distribution of free-fall time for robust prestellar cores. Top-axis is the uniform density for spherical cores (3 M / π R ). The red lineis a Gaussian fit. estimate of such a trend that, qualitatively, was already sus-pected. Distances estimated from our relation do not takeinto account the depth of the region at any point and aremeant to give representative values; but they are not limitedto a few lines of sigths and are in very good agreement withother recent estimates reported in literature found with morerobust ways. We confirm that 300 pc is a good mean distancevalue for Perseus;2. we produce dust temperature and column density maps. Thedust temperature is in the range 10–28 K. Two main peaksin T d distribution are present at 16.4 K and 17.1 K, corre-sponding to the average temperature of the di ff use mediumin West and East Perseus, respectively. A small bump ispresent at 19.2 K associated with the inner part of NGC1333and IC348. The column density range is 2 . × –1 . × cm − with the smallest closed contour at 1 . × cm − . T d and N (H ) are anticorrelated throughout the complex, with the exception of the inner part of NGC1333 and IC348that are both warm and dense. We also show that a lack ofdata at λ < µ m makes T d underestimated by more than10% for T d >
22 K;3. extrapolating the column density and temperature maps to70 µ m shows that most of the cloud would appear as in-frared dark clouds if observed with enough sensitivity. Wealso find excess emission at 70 µ m above the extrapolatedfluxes, which we attribute to very small dust grains;4. we find that the optical depth derived from our column den-sity map, and extrapolated at 850 µ m, agrees with that mea-sured with Planck for τ P < × − , where τ P is the opti-cal depth measured by Planck . At higher τ P , the Herschel optical depth is higher than
Planck ’s. This can be due toa change in the dust opacity. Our column density map, onthe contrary, disagrees with the column density maps de-rived from near-infrared extinction maps if masses within thesame A V contour are compared; a better agreement is foundwhen masses are derived from same areas in the two maps.The comparison is, in any case, not easy, either because ofthe varying dust opacity, or because in star-forming regions R ≡ A V / E (B − V) > . M ⊙ pc − ,above which an isothermal filament at 10 K and infinite ra-dius becomes unstable to radial collapse. But we suggest thatwith a proper internal volume density a filament with a linemass as low as 8 M ⊙ pc − , i.e., half the critical line mass, canfragment.We extracted compact cores from the intensity maps andused SED fitting to determine their masses and temperatures.We find:7. 199 starless cores have masses larger than their correspond-ing Bonnor-Ebert masses, above which an isothermal sphere Article number, page 26 of 52. Pezzuto et al.: The Perseus population of dense cores of gas cannot provide su ffi cient support against gravity.These cores are thus thought to be collapsing, or close tocollapse, and forming stars. We name these sources robustbound or prestellar cores. Other 100 cores may be also col-lapsing and we name these candidate prestellar cores. Onthe other hand, 220 sources have masses below their cor-responding Bonnor-Ebert threshold so they are thought tobe not dominated by gravity. We name these objects un-bound cores. Next, we name 132 cores protostars becausethey show, through emission at 70 µ m, that an internal sourceof energy should be already present. Finally, the remaining165 sources cannot be fit satisfactorily with a modified black-body because their SEDs are too uncertain;8. on the plane M − R starless cores do not trace a clear path butshow a large scatter with a faint hint of a correlation between M and R . Ignoring the scatter and fitting anyway a power-law, for unbound sources we find M ∝ R . . A similar rela-tion is found for candidate prestellar cores: M ∝ R . . Forbound sources, however, we find M ∝ R . , a relation that isshallower than expected for Bonnor-Ebert spheres ( M ∝ R ).We suggest that our slope 0.25 likely reflects the lack of acorrelation for the prestellar cores as a whole, probably ahint that these sources are indeed collapsing. From M and R ,we derived a mean column density for sources that appearsanticorrelated with the temperature, with di ff erent exponentsfor bound and unbound sources;9. M and T are also anticorrelated. We have shown that the,for a given T , the smallest detectable mass of an unboundcore is given by a combination of the Herschel instrumentssensitivity, that gives a relation M ∝ T − , scaled by an empir-ical factor that is likely due to the presence of the bright dif-fuse medium in which cores are embedded. For bound cores,however, the relation is much steeper M ∝ T − , probably aconsequence of the fact that more massive, and colder, boundcores are found in brighter regions of the clouds;10. the prestellar core mass function (CMF) can be modelledwith a log-normal curve having a peak at M ∼ . M ⊙ ,above the completeness limit in mass estimated at 0.32 M ⊙ .Assuming a one-to-one mapping of the CMF over the IMF,this peak implies a core mass e ffi ciency of 0.30. The high-mass tail of the CMF can be modelled with a power law ofslope − . ± .
035 in agreement, at 1 σ , with Salpeter’sIMF value of –2.35. The two distributions, log-normal andpower-law, were modelled separately because the number ofbound cores is not large enough to make a combined fit; forthe same reason, we cannot conclude if one distribution alonecan fit the whole dataset;11. more than 84% of robust bound cores are found within fil-aments versus 47% for unbound cores. On-filament boundsources are on average more massive than the o ff -filamentones. No bound cores are found below 0 . × cm − .Should sources be distributed uniformly on the map, 90prestellar cores of any mass should have been found at col-umn densities lower than that value. We propose that a limitof ∼ × cm − in column density is required to formbound cores;12. we find a correlation between the star formation e ffi ciencyand slope of the column density PDF for di ff erent Perseussubclouds. The correlation has a slope of 1.3%. We also finda correlation with the core formation e ffi ciency, with a slopebetween 1.2% and 2.4%, depending on wether we use all thesubclouds or we exclude from the sample one extreme value;13. assuming a constant star formation rate we derived a lifetimefor the prestellar phase t pre of 1.69 Myr for Perseus but withsignificant scatter for the individual subclouds; 14. we find a typical free fall time of 0.16 Myr that implies amean mass accretion rate of ˙ M ∼ . × − M ⊙ yr − to forma star of 0.25 M ⊙ , peak of the IMF.The catalogue of all 816 detected sources is given in the Ap-pendix A. We also list in Appendix E sources that were excludedfrom our analysis, e.g, galaxies. Acknowledgements.
We thank the anonymous referee for the valuable com-ments that improved the readability of the paper. SB and NS ackowledgesupport by the french ANR and the german DFG through the project "GEN-ESIS" (ANR-16-CE92-0035-01 / DFG1591 / / MCTES through national funds (PIDDAC) by this grantUID / FIS / / / BPD / / / FSE (EC).PACS has been developed by a consortium of institutes led by MPE (Germany)and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA,LAM (France); MPIA (Germany); INAF-IFSI / OAA / OAP / OAT, LENS, SISSA(Italy); IAC (Spain). This development has been supported by the fundingagencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA / CNES (France),DLR (Germany), ASI / INAF (Italy), and CICYT / MCYT (Spain). SPIRE hasbeen developed by a consortium of institutes led by Cardi ff University (UK) andincluding Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France);IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden);Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK);and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has beensupported by national funding agencies: CSA (Canada); NAOC (China);CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden);STFC (UK); and NASA (USA). HIPE are joint developments by the HerschelScience Ground Segment Consortium, consisting of ESA, the NASA HerschelScience Center, and the HIFI, PACS and SPIRE consortia. Part of this work hasreceived support from the European Research Council (ERC Advanced GrantAgreement no. 291294 – ORISTARS) and from the French national programs ofCNRS / INSU on stellar and ISM physics (PNPS and PCMI). This research hasmade use of: the SIMBAD database, operated at CDS, Strasbourg, France; theNASA / IPAC Extragalactic Database (NED) and Infrared Science Archive whichare operated by the Jet Propulsion Laboratory, California Institute of Technol-ogy, under contract with the National Aeronautics and Space Administration;data from the ESA mission
Gaia ( ),processed by the Gaia
Data Processing and Analysis Consortium (DPAC, ). Fundingfor the DPAC has been provided by national institutions, in particular theinstitutions participating in the
Gaia
Multilateral Agreement. Figures showingthe column density and temperature maps were done with DS9 (Joye & Mandel2003).
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Bordeaux, CNRS,B18N, allée G. Saint-Hilaire, 33615 Pessac, France INAF - Osservatorio Astronomico di Roma, via di Frascati 33,00078, Monte Porzio Catone, Italy Dipartimento di Fisica, Università di Roma Tor Vergata, via dellaRicerca Scientifica 1, 00133, Roma, Italy ESO / European Southern Observatory, Karl-Schwarzschild-Str. 2,D-85748 Garching bei Munchen, Germany Jeremiah Horrocks Institute, University of Central Lancashire, Pre-ston, Lancashire PR1 2HE, UK Université Grenoble Alpes, CNRS, Institut de Planétologie etd’Astrophysique de Grenoble, 38000 Grenoble, France Observatorio Astronómico Ramón María Aller, Universidade deSantiago de Compostela, Santiago de Compostela, E-15782, Galiza,Spain Instituto de Matemáticas and Departamento de Matemática Apli-cada, Universidade de Santiago de Compostela, Santiago de Com-postela, E-15782, Galiza, Spain I. Physik. Institut, University of Cologne, Germany Department of Physics and Astronomy, McMaster University,Hamilton Ontario L8S 4H7 CanadaArticle number, page 28 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. A.1.
An example of the atlas of the Perseus cores showing theprestellar core
Appendix A: The catalogue
The online material gives data for all 816 candidates cores, in theform of an atlas, one page per object. For each core we provide: – a figure showing a 2 ′ × ′ cutout around each source at 70 µ m(top left), 160 µ m (top middle), 250 µ m (top right), 350 µ m(bottom left), 500 µ m (bottom middle), and from the high-resolution column density map (bottom right). If the sourceis detected by getsources, a green ellipse shows the sourcesize from the extraction. We note that some sources were notobserved at all wavelengths, because PACS and SPIRE haveslightly di ff erent fields of view; – the observed SED (black points) and its best-fit modifiedblack body function (blue curve). We also give the best-fitvalues for dust temperature ( T ) and mass ( M ) from the SEDfit. The source radius ( R ), geometrical mean of major andminor FWHMs, is measured from the high-resolution col-umn density map and is given in arcsec, first two rows, andin parsec, third row. The size in arcsec are before and afterthe deconvolution with the instrumental FWHM (18 ′′ ). If asource is unresolved, we use a source size of < ′′ . / R = ′′ . µ m intensity map only.Since a residual misalignment may remain among the maps (seeSect. 2), the 70 µ m coordinates of the centre may appear o ff setin the SPIRE intensity maps. The misalignment is smaller thanthe instrument spatial resolution, but before running getsourcesall the maps are reprojected onto a grid with pixel size 3 ′′ , sothe displacement, if present, seems enhanced. Adopting the co-ordinates derived during the starless cores detection the protostarwould appear well centred at the SPIRE wavelengths, but o ff set Fig. A.2.
An example of the atlas of the Perseus cores showing the pro-tostar core in the PACS bands. To show this e ff ect we use Fig. A.3 wherethe background image in both panels is the 250 µ m cutout. In theupper panel, we show the ellipse and centre from the protostarcatalogue (obtained from the PACS extraction), whereas in thebottom panel, we show the ellipse and centre from the starlesscore catalogue (obtained from the SPIRE extraction). Clearly,at 250 µ m the source is better centred in the SPIRE extraction.So, for protostars, data in the PACS bands were taken from theprostostars catalogue, while data in the SPIRE bands were takenfrom the starless catalogue.A similar problem occurs at 160 µ m for starless cores. Inthis case, the detection is done in the SPIRE maps, in the high-resolution column density map and in the 160 µ m temperature-corrected map, but not in the 160 µ m intensity map that is usedfor photometry extraction at the position found in the other maps.This strategy could be the reason why many sources have onlyan upper limit at 160 µ m and in some cases the upper limit posesa problem when fitting the SED. In Fig. A.4 we show such anexample. The top-left panel shows the cutout in the PACS redband where getsources could not detect any source. However,already by eye it is possible to see that some emission is presentat the position of the source that was not recognised as a realobject. The bottom-left panel shows the corresponding SED withthe 3 σ upper limit estimated with getsources.We test our strategy by performing an alternative extractionusing all 5 Herschel intensity maps simultaneously. The bene-fit of this approach, is that the direct detection at 160 µ m mayhelp to extract photometry at this wavelength for weak sources.This alternative catalogue was used only to see if we could as-sign a measurement to sources having a stringent upper limit at160 µ m, like the one in Fig. A.4, with the conventional strategy.We found measurements for 12 sources using the alternative ex-traction. The top-right panel of Fig. A.4 shows that now the star-less core is detected also at 160 µ m. In the bottom-right panelwe show how the SED fitting benefits of this measurement.The new 160 µ m measurement has a large impact on thesource physical parameters, with the temperature increasing Article number, page 29 of 52 & Aproofs: manuscript no. perseus
Fig. A.3.
Coordinates of source µ m as derived in the proto-stars (top) and starless cores (bottom) catalogues, respectively. Fig. A.4. E ff ects on the SED when using an alternative extraction strat-egy (see text). Top panels: undetected and detected source at 160 µ m;bottom panels: SEDs with an upper limit and measure at 160 µ m. from 10.42 K to 16.14 K and the mass decreasing from 0.627 M ⊙ to 0.073 M ⊙ . Since there are 22 sources in the final cataloguewith masses 0 . ≤ M / M ⊙ < .
7, two of which have no reliableSED fit, it is clear that removing even one single source mayhave some impact on the CMF.Another approach we tried to solve the problem of the upperlimits at 160 µ m was to exclude this value during the fitting pro-cedure. When getsources can not detect at a certain wavelengtha source found in other images, it sets the so-called monochro-matic significance to the special value . When wefound evident that the upper limit at 160 µ m was influencing theSED fit much more than the SPIRE measures, we changed this Fig. A.5. E ff ects on the SED when the measurement at 160 µ m is usedinstead of the upper limit for undetected sources (see text). Left panel:best-fit with upper limit; right panel: best-fit with a measure. value to . In this case the fitting code uses the “ex-tracted” 160 um intensity as if it is reliable, but assigns it a verylow weight such that this band is not used to constrain the fit.This strategy was already used in the paper on Lupus (Benedet-tini et al., submitted). We show in Fig. A.5 the result of this pro-cedure applied to source T = . ± .
02 K and M = . ± . M ⊙ , a large mass indeed. On the other hand, us-ing the total flux density at 160 µ m that getsources measured atthe position of the core in the other bands gives the SED shownin the right panel of the figure. The 160 µ m value has a verylow weight so the best-fit is now determined by the SPIRE in-tensities only and the parameters become T = . + . − . K and M = . ± . M ⊙ , much reasonable values for Perseus.We corrected in this way the SED of 139 unbound cores withreliable SED fitting, 51 prestellar and 5 likely bound sources.A much more simple approach would be that of ignoring com-pletely the upper limit, but we found that in some cases the best-fit model agrees well with the 160 µ m measurement even if itwas not relevant during the fitting procedure. This means that inthis case getsourceswas able to make a reasonable measure evenwithout detecting directly the source. The reader will recognizethe corrected sources because in this case the ellipse showing thesize of the core (see Figs. A.1 and A.2) are drawn in red insteadthan in green.In the next section on the completeness limit, we will makea precise assessment about the validity of these two approachesto the 160 µ m upper limit problem, because in that case we dealwith simulated sources for which we know the true values of thephysical parameters.The master catalogue listing the observed properties of allthe cores is available in the online version of this paper. A tem-plate is provided in Table A.1 to illustrate its form and contentwhich follows Könyves et al. (2015). There are cases in whichtwo Spitzer sources can be associated with one
Herschel proto-star. In this case we chose the
Spitzer source detected at 70 µ m,exploiting the fact that in no case both sources had detectionsat 70 µ m. If none was revealed in this band, we associated thesource with the higher 24 µ m detection.The derived properties (physical radius, mass, SED dust tem-perature, peak column density at the resolution of the 500 µ mdata, average column density, peak volume density, and aver-age density) are given in another table also available online. Ta-ble A.2 gives an example. Note that for protostars the derivedproperties refer to the external envelope. A more detailed SEDfitting will be object of a forthcoming paper.We give in a third table, see the sample in Table A.3, addi-tional data for each source. Columns (2) and (3) give the source Article number, page 30 of 52. Pezzuto et al.: The Perseus population of dense cores luminosity in two ways. First, for a modified blackbody the bolo-metric luminosity L bol , can be computed analytically as shownby Elia & Pezzuto (2016). For β = L bol = π R π kh ν ! σ T where σ is the Stefan-Boltzmann constant, k and h are the Boltz-mann and Planck constants, T is the dust temperature, ν = c /λ where λ is the wavelength above which the model becomes op-tically thin. For a given dust opacity parametrized with a powerlaw of parameters ( λ ref , κ ref , β ) λ is (Pezzuto et al. 2012) λ = λ ref (cid:18) κ ref M π R (cid:19) /β = . R ! − s M ⊙ µ m (A.1)with R and M radius and mass of the (spherical) source.The bolometric luminosity then becomes L bol = κ ref M π k λ ref ch ! σ T = . × − M ⊙ ! T L ⊙ (A.2)Equation (A.2) implies an integration of the whole SED,even at λ < λ where the modified blackbody becomes opti-cally thick. Elia & Pezzuto (2016) have, however, shown that forEquation (A.2) to be valid, it is not necessary that the SED isoptically thin at all wavelengths, it is enough that optical depthis less than 1 for λ = λ ⋆ where λ ⋆ is defined by the condition Z ∞ x + β e x − x ≈ Z x ⋆ x + β e x − x with x ⋆ = hc / k λ ⋆ T . For β = < .
01) at x ⋆ =
15. This implies that the dusty envelope shouldbe already optically thin at λ ⋆ = / T µ m.Columns (4) and (5) in Table A.3 report for each model λ and λ ⋆ , while Col. (3) gives the luminosity obtained by numeri-cal integration of the SED at Herschel wavelengths. For the firstsource in the table, the model becomes optically thin at 82 µ m,while λ ⋆ is 131 µ m. In other words, the analitical formula for L bol does a good job as long as the model is optically thin at131 µ m which is correct given that λ = µ m.The second source is a protostar. In this case L bol cannot becomputed with Equation (A.2) so that Col. (2) is not correct andone can use Col. (3) as a measure of the FIR luminosity. Thethird source does not have a reliable SED fit so that M and T were not derived from the SED. In this case Cols. (2), (4) and (5)report a zero while Col. (3) gives a more precise FIR luminosity.Column (6) reports the kind of core: 0 is unbound, 1 prestel-lar, 2 protostellar and 3 candidate. Column (7) gives the reli-ability of the SED fitting: 1 means that the SED could be fitwith a modified blackbody, 0 otherwise. Column (8) gives theregion to which each source is associated, the numerical corre-spondence is given in the caption. These last three Cols. allowto make selections on the sample of cores easily: for instance,to select prestellar cores in IC348 one can look for sources with(1,1,9) in these Cols. Article number, page 31 of 52 & A p r oo f s : m a nu s c r i p t no . p e r s e u s Table A.1.
Catalogue of dense cores identified in the HGBS maps of Perseus molecular complex (full catalogue is at CDS).
No. Name RA
Dec
Sig S peak070 S peak070 / S bg S conv500070 S tot070 r a070 r b070 PA HGBS_J (h m s) ( ◦ ′ ′′ ) (Jy / beam) (Jy / beam ) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (2) (3) (4) (5) (6) ± (7) (8) (9) (10) ± (11) (12) (13) (14)49 032510.2 + + + + +
01 2.2e–02 227.14 1.61e +
01 2.42e +
01 3.7e–02 8 8 4960 032529.2 + + S peak160 S peak160 / S bg S conv500160 S tot160 r a160 r b160 PA Sig S peak250 S peak250 / S bg S conv500250 S tot250 r a250 r b250 PA (Jy / beam) (Jy / beam ) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy / beam ) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(15) (16) ± (17) (18) (19) (20) ± (21) (22) (23) (24) (25) (26) ± (27) (28) (29) (30) ± (31) (32) (33) (34)6.897 2.02e–01 4.2e–02 0.52 4.80e–01 3.70e–01 7.7e–02 25 20 53 23.880 8.09e–01 4.8e–02 1.01 8.93e–01 1.59e +
00 9.4e–02 21 19 –181673 5.44e +
01 1.5e–01 43.22 5.92e +
01 6.20e +
01 1.7e–01 14 14 0 1426 3.20e +
01 6.9e–01 7.22 3.16e +
01 3.36e +
01 7.2e–01 19 18 –290.000 3.82e–02 3.2e–02 0.11 1.45e–01 8.45e–02 7.1e–02 35 30 –89 6.138 1.64e–01 3.5e–02 0.31 2.17e–01 2.55e–01 5.5e–02 30 18 83Sig S peak350 S peak350 / S bg S conv500350 S tot350 r a350 r b350 PA Sig S peak500 S peak500 / S bg S tot500 r a500 r b500 PA (Jy / beam) (Jy / beam ) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(35) (36) ± (37) (38) (39) (40) ± (41) (42) (43) (44) (45) (46) ± (47) (48) (49) ± (50) (51) (52) (53)54.300 1.49e +
00 7.1e–02 1.50 1.56e +
00 2.02e +
00 9.6e–02 28 25 –32 66.400 1.67e +
00 7.9e–02 1.66 1.95e +
00 9.1e–02 47 36 –43849.200 2.02e +
01 4.8e–01 4.87 2.00e +
01 2.27e +
01 5.4e–01 25 25 –10 407.900 1.17e +
01 6.4e–01 4.82 1.26e +
01 6.9e–01 36 36 –86.427 1.05e–01 3.4e–02 0.19 1.29e–01 1.46e–01 4.8e–02 43 25 78 0.000 6.68e–02 2.5e–02 0.11 4.95e–02 1.8e–02 40 36 74Sig N H N peak H N peak H / N bg N conv500 H N bg H r a H r b H PA H N SED
CuTEx Core type SIMBAD
Spitzer
Comments(10 cm − ) (10 cm − ) (10 cm − ) ( ′′ ) ( ′′ ) ( ◦ )(54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64) (65) (66) (67)166.200 14.190 3.32 4.591 4.272 24 20 –41 4 1 prestellar [KJT2007] SMM J032516 + + Notes.
Cols.: (1) core running number; (2) name = HGBS_J followed by J2000 source coordinates in sexagesimal format; (3) and (4) J2000 RA and Dec of source centre; (5), (15), (25), (35) and(45): detection significance from monochromatic single scales in the
Herschel bands (0.0 when the core is not visible in clean single scales); (6) ± (7), (16) ± (17), (26) ± (27), (36) ± (37) and (46) ± (47):peak flux density and its uncertainty estimated by getsources; (8), (18), (28), (38) and (48): contrast over the local background, defined as the ratio of the background-subtracted peak intensityto the local background intensity; (9), (19), (29) and (39): peak flux density smoothed to a 36 ′′ . ± (11), (20) ± (21), (30) ± (31), (40) ± (41) and (49) ± (50): integrated flux density and itsuncertainty estimated by getsources; (12)-(13), (22)-(23), (32)-(33), (42)-(43) and (51)-(52): major & minor FWHM of the core, respectively, estimated by getsources; (14), (24), (34), (44) and (53):position angle, measured east of north, of the core major axis; (54): detection significance in the high-resolution column density map; (55) peak H column density as estimated by getsources in thehigh-resolution column density map;(56) column density contrast over the local background estimated by getsources in the high-resolution column density map; (57) peak column density smoothedto a 36 ′′ . column density estimated by getsources in the high-resolution column density map; (59)-(60)-(61): major & minor FWHM and position angle of the core,respectively, estimated by getsources in the high-resolution column density map; (62): number of Herschel bands in which the core is significant (Sig λ >
5) and has a positive flux density, excludingthe column density plane; (63): 2 means that CuTEx (Molinari et al. 2011) found a source whose position falls within the ellipse defined by the FWHMs estimated on the high-resolution columndensity map, if the distance between the two peaks is less than 6 ′′ the flag is 1, while 0 means that no counterpart was found by CuTEx; (64): core classification, starless means unbound core; (65)closest counterpart found in SIMBAD, if any, up to 6 ′′ from the Herschel peak position (the identifier is copied as is in the SIMBAD archive); (66) closest Spitzer -identified YSO from the c2dsurvey (Evans et al. 2009) within 6 ′′ from the Herschel peak position, if any. When present, the leading part of the name (SSTc2d) has been removed; (67) comments. A r ti c l e nu m b e r , p a g e f . P ezz u t o e t a l . : T h e P e r s e u s popu l a ti ono f d e n s ec o r e s Table A.2.
Catalogue of dense cores identified in the HGBS maps of Perseus molecular complex (full catalogue is at CDS).
No. Name RA
Dec R core M core T dust N peak H N ave H n peak H n ave H α BE Core type CommentsHGBS_J (h m s) ( ◦ ′ ′′ ) (pc) ( M ⊙ ) (K) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − )(1) (2) (3) (4) (5) (6) (7) ± (8) (9) ± (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)49 032510.2 + + + + + + Notes.
Cols.: (1) core running number; (2) name = HGBS_J followed by J2000 source coordinates in sexagesimal format; (3) and (4) J2000 RA and Dec of source centre; (5) and (6) geometricalaverage of the two FWHMs measured in the high-resolution column density map, after and before deconvolution with HPBW of 18 ′′ .
2, respectively (NB: both values provide estimates of theobject’s outer radius when the core can be approximately described by a Gaussian distribution, as is the case for the critical Bonnor-Ebert spheroid); (7) ± (8) estimated core mass; (9) ± (10) SED dusttemperature; (11) peak H column density, at the resolution of 500 µ m intensity map, derived from a modified blackbody SED fit to the core peak flux densities measured in a common 36 ′′ . M core / ( µ m H π R ), where M core is the estimated core mass (Col. 7), R core the estimated core radius before deconvolution (Col. 6), µ = µ m intensity map,derived from the peak column density (Col. 11) assuming a Gaussian spherical distribution: n peakH = q π N peakH2 FWHM ; (15) average volume density, calculated as n aveH = M core / π R µ m H using the estimatedcore radius before deconvolution; (16) average volume density calculated as previous Col. but using the deconvolved core radius; (17) Bonnor-Ebert mass ratio α BE = M BE , crit / M obs ; (18) core type:starless, prestellar or protostellar; (19) comments. A r ti c l e nu m b e r , p a g e f & Aproofs: manuscript no. perseus
Table A.3.
Catalogue of dense cores identified in the HGBS maps ofPerseus molecular complex (full catalogue is at CDS).
No. L bol , ana L SED λ λ ∗ Core SED Region( L ⊙ ) ( L ⊙ ) ( µ m) ( µ m) type fit(1) (2) (3) (4) (5) (6) (7) (8)49 0.052 0.049 82.307 131 1 1 155 3.722 4.152 89.583 53 2 1 260 0.000 0.002 0.000 0 0 0 2 Notes.
Cols.: (1) core running number; (2) bolometric luminosity foundfrom Equation (A.2); (3) bolometric luminosity found by numerical in-tegration of the SED; (4) λ as given by Equation (A.1); (5) λ ∗ seetext; (6) core type: 0 = starless; 1 = prestellar; 2 = protostellar; 3 = candidatebound; (7) SED fit: 0 = no reliable SED fit; 1 = reliable SED fit; (8) re-gion: 1 = L1451; 2 = L1448; 3 = L1455; 4 = NGC1333; 5 = Perseus6; 6 = B1;7 = B1E; 8 = L1468; 9 = IC348; 10 = B5; 11 = HPZ1; 12 = HPZ2; 13 = HPZ3;14 = HPZ4; 15 = HPZ5; 16 = HPZ6; 0 = outside all the regions. Appendix B: Simulation of prestellar cores
Simulated 432 prestellar cores with Bonnor-Ebert density pro-file and mass between 0.05 M ⊙ and 0.96 M ⊙ were injectedin the source-free intensity maps to verify the correctness ofour extraction procedure and to derive the mass completenesslimit. The simulations were performed as in previous HGBSworks (Könyves et al. 2015; Marsh et al. 2016; Benedettini et al.2018). The extraction of the simulated sources was performednominally and the post-selection checks for cores described inSect. 4.1 were executed. This catalogue was then cross-checkedagainst the truth table of the synthetic cores and 315 sources outof the 432 were recovered. AppendixB.1: Restoring the160 µ m intensity As discussed in the previous section, we found some problemwhen dealing with the 160 µ m upper limit often found in thestandard extraction. To avoid that the upper limit forces the SEDfitting to too low temperatures, we adopted two di ff erent strate-gies previously described and here we discuss their validity.First, we made an alternative extraction using all five of the Herschel bands simultaneously. Compared to the nominal ex-traction, two sources with only upper limits at 160 µ m endedup with intensity measurements in the alternative extraction. Forone source, the mass derived from the SED fitting using the up-per limit at 160 µ m is 1.46 times the true mass. Using the mea-surement from the alternative catalogue the derived mass is 1.36the true mass, slightly better. For the second source, using theupper limit causes the derived mass to be overestimated by morethan a factor 3. Using the measured flux density in the alterna-tive catalogue the ratio is 0.75, which means that the mass inonly underestimated by 25%, in any case a better result.The second approach was to pretend that the upper limit inthe nominal extraction is indeed a real measurement but with anegligible weight during the SED fitting so that it does not forcethe fitting. For 96 sources out of 147 simulated cores with anupper limit, nothing changed either because the best-fit modelfullfilled the upper limit, or because the SED could not be fitanyway. For the remaining 51 sources, the mean ratio between(SED-fitting derived mass) / (true mass) is 1.5 ± ± µ m intensity isweighted down in the SED fit. The large standard deviation ofthe means shows that the results are valid for the whole sam-ple and not applicable to the single sources. Nevertheless, theupper limit causes, on average, an overestimation of the mass by Fig. B.1.
Number of detected sources over number of simulated sourcesvs. true core mass. The completeness limit is defined as the mass atwhich completeness is 90%: in our case this happens at 0.323 M ⊙ , limitshown as intersection between the two dashed lines. The decreasing ofdetected sources at high mass is discussed in the text (see also nextfigure).
50% while weighing down the 160 µ m intensity generally agreeswith the input mass, on average, of about 8%. We concluded thenthat the result of the SED fitting improves when using both ap-proaches. AppendixB.2: Completenesslimitinmass
In Fig. B.1 we show the fraction of detected sources with re-spect to the number of simulated sources as a function of thetrue core mass. To improve the statistics we summed the numberof detected sources in three adjacent bins having similar masses,while the mass of each bin was the average of the three masses.The last two points are the sum / average of four bins.The horizontal dashed lines shows the 90% level of com-pleteness while the vertical line corresponds to a mass of0.323 M ⊙ , found by linear interpolation of the two bins at0.290 M ⊙ and 0.420 M ⊙ .Very interesting is also the trend at high-mass in Fig. B.1where the number of detected sources decreases. As shown byKönyves et al. (2015), the likelihood of detecting a sources doesnot depend only on its intensity, but also on the contrast, i.e.,how well the source stands out above the emission of the di ff usemedium. In general, high-mass cores are found in high columndensity regions which are very bright. To estimate the contrastwe used the signal-to-noise ratio (SNR) expressed as the peakintensity of the simulated sources over the standard deviation ofthe local background, both in MJy sr − . This ratio, for the fiducialwavelength of 250 µ m, is shown in Fig. B.2: blue and red trian-gles refer to detected / undetected sources, respectively. We cansee that for SNR ≥ ∼
98% of the sources independenton their mass. The percentage is as low as 31% for SNR ≤
1. Athigh mass we explored low levels of SNR that resulted in a smallfraction of detected sources. This figure shows that not necessar-ily high-mass cores are found easier than low-mass cores. Inter-ested reader are invited to read the in-depth discussion on thistopic in Könyves et al. (2015).
Article number, page 34 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. B.2.
Contrast level (see text) for detected sources (blue triangles)and undetected sources (red triangles).
Appendix C: Definition of Perseus sub-regionsborders through C O observations
The Perseus molecular complex is known to host di ff erent re-gions with distances varying between > ∼
200 pc and < ∼
350 pc.From our intensity maps, because the dust emission is opticallythin, it is not possible to estimate which regions are closer orfurther. Also, their borders are arbitrary defined.To get some insight in these problems, especially for tracingthe borders, we combined our column density map (Sect. 3.2)with the CO map of Perseus (COMPLETE team 2012). In par-ticular, we started from the N (H ) contour at 3 × cm − andmodified it in order to maximise, wherever possible, one singlevelocity component in each region. The result of this exerciseis visualised in Figs. C.1–C.2, where we show how the bordershave been defined to accomodate the observed velocity compo-nents, and in Fig. C.3 that shows the CO spectra within theseborders. The regions are shown over the column density map inFig. 9.From these figures it is clear that only in a few cases a re-gion is associated to one single CO component. In general,two or even three components are present, often in the form ofbroad bump. The most complex case is NGC1333 which appearsbright from 6 to 10 km s − . It is not possible to assess if these dif-ferent velocity components are associated to di ff erent distancesor simply reflect the presence of complex motions of gas at thesame distance.Border coordinates are here reported in DS9 format. Article number, page 35 of 52 & Aproofs: manuscript no. perseus
Fig. C.1.
Maps of CO in three velocity channels: 1.1 Km s − (top), 4.35 Km s − (centre), 6.0 Km s − (bottom); colour bars are uncorrectedantenna temperature in K. Green labels mark the position of GAIA sources (see Table 2); h labels show the position of Hirota et al. (2008)and Hirota et al. (2011) sources (SVS13 is in the cloud of sources 6-10). The magenta lines at the centre of each map shows the angular scalecorresponding to 1 pc at 300 pc; J2000.0 coordinates grid is shown.Article number, page 36 of 52. Pezzuto et al.: The Perseus population of dense cores Fig. C.2.
Maps of CO in three velocity channels: 7.9 Km s − (top), 8.8 Km s − (centre), 10.0 Km s − (bottom). In the latter panel, north of B5and slightly covered by label 28, the bubble CPS12 (Arce et al. 2011) is evident. The magenta lines at the centre of each map shows the angularscale corresponding to 1 pc at 300 pc; J2000.0 coordinates grid is shown. Labels as in Fig. C.1. Article number, page 37 of 52 & Aproofs: manuscript no. perseus
Appendix D: Herschel intensity maps
In this appendix we show the PACS intensity maps at 70 µ m and160 µ m in Figure D.1; SPIRE intensity map at 250 µ m and thehigh resolution column density map with a resolution of 18 ′′ . ′′ . µ m and 500 µ m inFigure D.3. To help to localise the region of Perseus in othersurveys, we give a grid of coordinates in di ff erent systems: FK5(equatorial) for 70 µ m and 250 µ m, galactic for 160 µ m, 350 µ mand for the high resolution column density map, ecliptic for500 µ m.Maps centres, as given in FITS header and converted tothe specific coordinate system are: (3 h m s , + ◦ ′ ′′ ), or(54 ◦ . + ◦ . h m s , + ◦ ′ ′′ ), or (53 ◦ . + ◦ . ◦ . + ◦ . ff use emissionintensity increases at longer wavelengths, being marginally visi-ble at λ = µ m.The zero-level intensities for the di ff use emission were foundthrough comparison with the predicted Planck + IRAS emission(Bernard et al. 2010) for the same region. For each map andwavelength, the zero-level intensity was found separately forWest and East Perseus and the o ff set added to the map. Finally,the two maps were combined with a simple pixel-by-pixel mean(the two maps were created onto the same spatial grid). The o ff -sets are reported in Table D.1. Appendix E: Additional catalogue of sources
Here we report basic data for sources eliminated from the maincatalogue; since these data are not part of the o ffi cial HGBS de-livered products they are reported here. The Cols. in the follow-ing tables are a subset of the Cols. in Table A.1, of which theykeep the numbering: so, for instance, meaning of Col. (12) in Ta-ble E.1 is the same of Col. (12) in Table A.1. The only di ff erenceis units in Col. (55): 10 cm − in Table A.1 and 10 cm − here. Table D.1.
The zero-levels of the di ff use emission for each map. λ East West( µ m) (MJy sr − ) (MJy sr − )70 3.320 − ff erence is Col. (2) in this table: here an identi-fier is given that explains why source was removed (acronymsas in Simbad database): G – galaxy; W – counterpart in WISEcatalogue; 2 – counterpart in 2MASS; HH – Herbig-Haro ob-ject; M – star from catalogue MBO; HL – candidate YSO from[HL2013]; DS – source in [DS95]; LRL – source in “Cl* IC 348LRL”; PSZ – source in [PSZ2003]; NTC – source in “Cl* IC 348NTC”; U – W UMa star; δ – δ Scuti star.In particular, W and 2 means that an infrared sources wasfound in WISE or 2MASS catalogues within 6 ′′ from an Her-schel source not detected at 70 µ m nor in the millimetre band.No attempt was made to distinguish between physical and pro-jected associations. Article number, page 38 of 52. Pezzuto et al.: The Perseus population of dense cores
Fig. C.3. CO spectra for all the subregions we defined in Perseus. Whenever possible we made a Gaussian fit to one or two profiles; for thebroad bumps we just derived the position of the maximum and assigned it an uncertainty of 0.066 km s − , the step in the velocity grid.Article number, page 39 of 52 & Aproofs: manuscript no. perseus
Fig. D.1.
The combined maps of Perseus at 70 µ m (top, grid of equatorial J2000.0 coordinates, HPBW 8 ′′ .
4) and 160 µ m (bottom, grid of Galacticcoordinates, HPBW 13 ′′ . / sr.Article number, page 40 of 52. Pezzuto et al.: The Perseus population of dense cores Fig. D.2.
SPIRE intensity map of Perseus at 250 µ m (top, grid of equatorial J2000.0 coordinates) and the high resolution column density map(bottom, grid of Galactic coordinates). For both maps the HPBW is 18 ′′ .
2. Colorbars in MJy / sr (top) and cm − (bottom).Article number, page 41 of 52 & Aproofs: manuscript no. perseus
Fig. D.3.
SPIRE intensity maps of Perseus at 350 µ m (top, grid of Galactic coordinates, HPBW 24 ′′ .
9) and 500 µ m (bottom, grid of eclipticcoordinates, HPBW 36 ′′ . / sr.Article number, page 42 of 52 . P ezz u t o e t a l . : T h e P e r s e u s popu l a ti ono f d e n s ec o r e s Table E.1.
Catalogue of additional sources excluded from the main catalogue: Cols. have the same meaning as in Table A.1.
No. Type RA
Dec
Sig S peak070 S tot070 r a070 r b070 PA Sig S peak160 S tot160 r a160 r b160 PA (degree) (degree) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (2) (3) (4) (5) (6) ± (7) (10) ± (11) (12) (13) (14) (15) (16) ± (17) (20) ± (21) (22) (23) (24)1 W 51.03003 30.27615 0.000 2.02e–2 1.3e–2 –1.58e–2 5.6e–2 60.8 47.2 133.5 0.000 1.81e–1 4.1e–2 1.30e + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . p e r s e u s Table E.1. continued
No. Type RA
Dec
Sig S peak070 S tot070 r a070 r b070 PA Sig S peak160 S tot160 r a160 r b160 PA (degree) (degree) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (2) (3) (4) (5) (6) ± (7) (10) ± (11) (12) (13) (14) (15) (16) ± (17) (20) ± (21) (22) (23) (24)54 W 52.29768 31.31080 195.7 7.57e–3 1.1e–1 4.33e–1 1.5e–1 19.2 8.4 6.9 378.4 9.66e + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f . P ezz u t o e t a l . : T h e P e r s e u s popu l a ti ono f d e n s ec o r e s Table E.1. continued
No. Type RA
Dec
Sig S peak070 S tot070 r a070 r b070 PA Sig S peak160 S tot160 r a160 r b160 PA (degree) (degree) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (2) (3) (4) (5) (6) ± (7) (10) ± (11) (12) (13) (14) (15) (16) ± (17) (20) ± (21) (22) (23) (24)107 W 53.36533 31.37536 0.000 5.93e–2 1.8e–2 6.52e–1 8.1e–2 50.9 47.9 44.6 7.039 1.73e–1 4.1e–2 7.67e–1 1.0e–1 38.9 31.3 75.2108 2 53.42230 31.22838 9.578 1.37e–1 1.9e–2 1.94e–1 3.2e–2 29.6 8.4 68.1 6.864 2.02e–1 3.5e–2 2.36e–1 5.5e–2 21.6 13.5 76.7109 W 53.44435 30.46080 0.000 2.54e–3 7.6e–3 1.71e- + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + δ + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . p e r s e u s Table E.1. continued
No. Type RA
Dec
Sig S peak070 S tot070 r a070 r b070 PA Sig S peak160 S tot160 r a160 r b160 PA (degree) (degree) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (2) (3) (4) (5) (6) ± (7) (10) ± (11) (12) (13) (14) (15) (16) ± (17) (20) ± (21) (22) (23) (24)160 LRL 56.28257 32.00969 13.66 –5.20e–2 3.8e–3 –8.86e–2 7.8e–3 57.4 10.8 64.8 13.42 2.63e–1 4.2e–2 1.53e + + + Table E.2.
Same as Table E.1 for 250 µ m and 350 µ m. No. Sig S peak250 S tot250 r a250 r b250 PA Sig S peak350 S tot350 r a350 r b350 PA (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (25) (26) ± (27) (30) ± (31) (32) (33) (34) (35) (36) ± (37) (40) ± (41) (42) (43) (44)1 9.220 2.64e–1 3.9e–2 1.05e + + + + + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f . P ezz u t o e t a l . : T h e P e r s e u s popu l a ti ono f d e n s ec o r e s Table E.2. continued
No. Sig S peak250 S tot250 r a250 r b250 PA Sig S peak350 S tot350 r a350 r b350 PA (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (25) (26) ± (27) (30) ± (31) (32) (33) (34) (35) (36) ± (37) (40) ± (41) (42) (43) (44)35 80.78 2.13e + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f & A p r oo f s : m a nu s c r i p t no . p e r s e u s Table E.2. continued
No. Sig S peak250 S tot250 r a250 r b250 PA Sig S peak350 S tot350 r a350 r b350 PA (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (25) (26) ± (27) (30) ± (31) (32) (33) (34) (35) (36) ± (37) (40) ± (41) (42) (43) (44)87 6.218 3.12e–1 7.9e–2 3.15e + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f . P ezz u t o e t a l . : T h e P e r s e u s popu l a ti ono f d e n s ec o r e s Table E.2. continued
No. Sig S peak250 S tot250 r a250 r b250 PA Sig S peak350 S tot350 r a350 r b350 PA (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ )(1) (25) (26) ± (27) (30) ± (31) (32) (33) (34) (35) (36) ± (37) (40) ± (41) (42) (43) (44)140 8.379 2.22e–1 4.4e–2 5.87e–1 5.1e–2 43.2 19.2 159.4 11.49 2.94e–1 5.9e–2 4.81e–1 6.1e–2 42.8 24.9 153.7141 10.23 3.00e–1 6.8e–2 7.67e–1 8.8e–2 40.0 18.4 32.2 7.819 2.59e–1 6.4e–2 5.17e–1 7.3e–2 42.3 24.9 33.0142 12.96 3.10e–1 6.4e–2 2.84e–1 5.6e–2 18.2 18.2 135.0 6.493 1.44e–1 6.0e–2 1.62e–1 5.4e–2 27.1 24.9 129.3143 7.395 2.08e–1 6.8e–2 1.18e + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + A r ti c l e nu m b e r , p a g e f & Aproofs: manuscript no. perseus
Table E.3.
Same as Table E.1 for 500 µ m and high-resolution column density map. No. Sig S peak500 S tot500 r a500 r b500 PA Sig N H N peak H r a H r b H PA H (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (10 cm − ) ( ′′ ) ( ′′ ) ( ◦ )(1) (45) (46) ± (47) (49) ± (50) (51) (52) (53) (54) (55) (59) (60) (61)1 8.059 1.77e–1 4.8e–2 2.49e–1 4.7e–2 44.3 37.6 131.8 12.36 8.45e–2 37.2 31.0 88.22 7.044 1.38e–1 2.2e–2 1.63e–1 2.0e–2 49.4 36.3 78.7 10.68 6.56e–2 41.0 32.8 87.73 24.31 8.16e–1 2.0e–1 8.29e–1 1.8e–1 38.6 36.3 106.4 61.64 4.17e–1 34.5 18.2 113.34 13.34 4.69e–1 1.2e–1 5.12e–1 1.1e–1 38.2 36.3 3.0 24.97 1.34e–1 22.6 18.2 49.75 14.81 4.36e–1 7.0e–2 1.10e + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Article number, page 50 of 52. Pezzuto et al.: The Perseus population of dense cores
Table E.3. continued
No. Sig S peak500 S tot500 r a500 r b500 PA Sig N H N peak H r a H r b H PA H (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) ( ′′ ) ( ′′ ) ( ◦ )(38) (39) (40) ± (41) (42) ± (43) (44) (45) (46) (47) (48) ± (49) (50) (51) (52)73 19.81 5.04e–1 5.4e–2 1.05e + + + + + + + + + + + + + + Article number, page 51 of 52 & Aproofs: manuscript no. perseus
Table E.3. continued
No. Sig S peak500 S tot500 r a500 r b500 PA Sig N H N peak H r a H r b H PA H (Jy / beam) (Jy) ( ′′ ) ( ′′ ) ( ◦ ) (Jy / beam) ( ′′ ) ( ′′ ) ( ◦ )(38) (39) (40) ± (41) (42) ± (43) (44) (45) (46) (47) (48) ± (49) (50) (51) (52)145 0.000 5.39e–2 4.8e–2 3.18e–2 4.4e–2 36.3 36.3 69.3 6.051 3.48e–2 1.4e–2 37.0 18.2 157.4146 0.000 1.45e–1 6.8e–2 1.05e–1 6.2e–2 36.3 36.3 36.0 6.769 4.29e–2 1.7e–2 25.7 18.2 71.5147 7.163 1.83e–1 2.3e–2 3.08e–1 2.5e–2 51.9 36.3 149.0 6.210 4.19e–2 5.0e–3 49.2 21.3 130.7148 0.000 8.19e–2 5.3e–2 5.81e–2 4.8e–2 36.9 36.3 113.4 6.691 4.03e–2 6.9e–3 27.0 18.2 120.1149 30.61 1.05e + + + + + + + + + +0 3.3e–1 46.2 37.9 126.4 59.11 3.93e–1 8.4e–2 48.7 31.6 104.6170 0.000 1.03e–1 4.6e–2 7.03e–2 4.2e–2 38.2 36.3 112.0 8.611 5.87e–2 1.5e–2 21.1 18.2 77.7