The Plateau de Bure + 30m Arcsecond Whirlpool Survey reveals a thick disk of diffuse molecular gas in the M51 galaxy
J. Pety, E. Schinnerer, A. K. Leroy, A. Hughes, S. E. Meidt, D. Colombo, G. Dumas, S. Garcia-Burillo, K. F. Schuster, C. Kramer, C. L. Dobbs, T. A. Thompson
DD RAFT VERSION A PRIL
5, 2013
Preprint typeset using L A TEX style emulateapj v. 12/16/11
THE PLATEAU DE BURE + 30 M ARCSECOND WHIRLPOOL SURVEYREVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE M51 GALAXY J ÉRÔME P ETY , E VA S CHINNERER , A DAM
K. L
EROY , A NNIE H UGHES , S HARON
E. M
EIDT , D ARIO C OLOMBO , G AELLE D UMAS , S ANTIAGO G ARCÍA -B URILLO , K ARL
F. S
CHUSTER , C ARSTEN K RAMER , C LARE
L. D
OBBS , AND T ODD
A. T
HOMPSON
Draft version April 5, 2013
ABSTRACTWe present the data of the Plateau de Bure Arcsecond Whirlpool Survey (PAWS), a high spatial and spectralresolution CO (1–0) line survey of the inner ∼ × . (cid:48)(cid:48) -resolution over the ∼ (cid:48)(cid:48) × (cid:48)(cid:48) field of view, with sensitivity to all spatial scales from the combination of PdBI and IRAM-30m data,and brightness sensitivity of 0 . σ ) in each 5 km s − -wide channel map. We find a CO-luminosity of 9 × K km s − pc , corresponding to a molecular gas mass of 4 × M (cid:12) for a standard CO-to-H conversionfactor. Unexpectedly, we find that a large fraction, (50 ± (cid:48)(cid:48) (cid:39) . CO / COratio, and the difference between the kinematics and structure of the PdBI-only and hybrid synthesis (PdBI +IRAM-30m) images. The extended emission is consistent with a thick, diffuse disk of molecular gas with atypical scale height of ∼
200 pc, substructured in unresolved filaments which fills ∼ .
1% of the volume.
Keywords: galaxies: individual (M51) INTRODUCTIONAlong the path leading from the accretion of hot ionized gasonto galaxies to the birth of stars, the formation and evolutionof Giant Molecular Clouds (GMCs) is the least well under-stood step. For example, the dependence of their mass distri-butions, lifetimes, and star formation efficiencies on galacticenvironment ( e.g. arm, interarm, nuclear region) is largely un-known (for a review, see McKee & Ostriker 2007). Becausethe Sun’s position within the Milky Way disk makes GMCstudies difficult within our own Galaxy, observations of GMCpopulations in nearby face-on galaxies offer the best way toaddress many of these unknowns.Complete CO maps that resolve individual GMCs havebeen carried out across the Local Group, allowing for the con-struction of mass functions and an estimation of GMC life-times via comparison with maps at other wavelengths (Kawa-mura et al. 2009). To date, these observations have probed [email protected] Institut de Radioastronomie Millimétrique, 300 Rue de la Piscine, F-38406 Saint Martin d’Hères, France Observatoire de Paris, 61 Avenue de l’Observatoire, F-75014 Paris,France. Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidel-berg, Germany National Radio Astronomy Observatory, 520 Edgemont Road, Char-lottesville, VA 22903, USA Observatorio Astronómico Nacional - OAN, Observatorio de MadridAlfonso XII, 3, 28014 - Madrid, Spain Instituto Radioastronomía Milimétrica, Av. Divina Pastora 7, NucleoCentral, 18012 Granada, Spain School of Physics and Astronomy, University of Exeter, Stocker Road,Exeter EX4 4QL, UK Department of Astronomy, The Ohio State University, 140 W. 18thAve., Columbus, OH 43210, USA Center for Cosmology and AstroParticle Physics, The Ohio State Uni-versity, 191 W. Woodruff Ave., Columbus, OH 43210, USA mostly low mass galaxies where H I dominates the interstellarmedium ( e.g. , Blitz et al. 2007). The main reason is that theangular resolution required to identify individual GMCs (typ-ical size ∼
40 pc, e.g. , Solomon et al. 1987) in any galaxy out-side the Local Group is extremely difficult to achieve. Reach-ing such resolutions with single dish telescopes remains im-possible in all but the very closest galaxies. This presents amajor obstacle in linking our understanding of star formationand galactic evolution. Even for M31, the closest massive spi-ral galaxy to the Milky Way, the CO (1–0) IRAM-30m mapachieves a spatial resolution of only 85 pc and it suffers fromprojection effects (Nieten et al. 2006). This is an importantproblem because these massive star forming spirals dominatethe mass and light budget of blue galaxies and they host mostof the star formation in the present-day universe ( e.g.
Schimi-novich et al. 2007).To remedy this situation, we used the Plateau de Bure Inter-ferometer (PdBI) to carry out the PdBI Arcsecond WhirlpoolSurvey (PAWS, Schinnerer et al. 2013). The high quality re-ceivers and good weather conditions allowed PAWS to mapthe central, molecule-bright part of M51 at a resolution of ∼ . (cid:48)(cid:48) ( ∼
40 pc) while still maintaining good brightness sen-sitivity (RMS ∼ . D ∼ . i ∼ ◦ ) grand design spirals, and it has been exten-sively studied at essentially all wavelengths. In contrast toLocal Group galaxies with a resolved GMC population, themolecular gas clearly dominates the interstellar medium in-side the mapped region ( e.g. , Garcia-Burillo et al. 1993; Aaltoet al. 1999; Schuster et al. 2007; Hitschfeld et al. 2009; Leroyet al. 2009; Koda et al. 2011). M51 thus offers the opportu-nity to relate the physical properties of molecular gas to spiralstructure. We complemented the interferometric data with asensitive (RMS ∼
16 mK) map of the whole M51 system with a r X i v : . [ a s t r o - ph . GA ] A p r P ETY ET AL . Figure 1. CO (1–0) integrated emission of the inner ∼ × CO (1–0) integrated emission of the full M51 system ( i.e. , NGC 5194 + NGC 5195) as observed by the IRAM-30m telescope.The white horizontal rectangle shows the PAWS field of view. The images were scaled such that the angular resolution of both data sets occupies the same sizeon paper. In other words, the PAWS image shows the center of the small image zoomed by a factor of 21.
Table 1
Parameters for NGC 5194.Parameter NGC 5194 Notes Ref.Morphological type SA(s)bc pec de Vaucouleurs et al. (1991)Activity type Seyfert 2 Véron-Cetty & Véron (2006)Kinematic center 13 h m . s ; + ◦ (cid:48) . (cid:48)(cid:48) α , δ J2000 Hagiwara (2007)1 . (cid:48)(cid:48) , . (cid:48)(cid:48) Offset from phase centerDistance 7 . ± (cid:48)(cid:48) = 37 ± . ± . − LSR, radio convention Shetty et al. (2007)Mean CO inclination 21 ± ◦ Colombo et al. (2013b)Mean position angle 173 ± ◦ Colombo et al. (2013b)Emitting surface 1 . × pc W CO ≥ σ This work, Appendix ATotal CO luminosity a . × Kkms − pc in [LSR − + − This work, Appendix ATotal molecular mass a . × M (cid:12) Helium included This work, Appendix AMean brightness b . − This work, Appendix AMean mass surface density b (cid:12) pc This work, Appendix A a Using the IRAM-30m data. b The mean brightness and mass surface density are computed using the area with significant emission, i.e. , W CO ≥ σ . AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 2.
Pointing pattern of the two observed PdBI mosaics overlaid on theintegrated emission of the CO (1–0) line observed with the IRAM-30m.The 30 fields of each mosaic are displayed as red and blue circles, respec-tively. The diameter of each circle is λ / d prim , where λ is the observationwavelength and d prim is the diameter of an interferometer antenna, i.e. , 15mfor the PdBI. In our case, we have λ / d prim ∼ (cid:48)(cid:48) . the IRAM-30m single-dish telescope. This allowed us to pro-duce a hybrid synthesis map — a joint deconvolution of thePdBI and IRAM-30m data sets — that is sensitive to all spa-tial scales between our synthesized beam and the PAWS fieldof view (see Fig. 1).In Section 2, we detail the observing strategy and the datareduction. In Section 3, we show that a large portion ( ∼ ± PAWS DATA ACQUISITION AND REDUCTIONThis section presents the observing strategy, the data reduc-tion and the resulting data set. Sects. 2.1 and 2.2 focus on thePdBI and IRAM-30m data, respectively. Sect. 2.3 explainshow we combined these data to produce a final set of hybridmaps sensitive to all spatial scales.2.1.
IRAM Plateau de Bure Interferometer data
After a discussion of the observing setup, we describe thecalibration of the interferometric data.2.1.1.
Observations
PdBI observations dedicated to this project were carried outwith either 5 or 6 antennas in the A, B, C, and D configura-tions (baseline lengths from 24 m to 760 m) from August 2009to March 2010. The two polarizations of the single-sidebandreceivers were tuned at 115.090 GHz, i.e. , the CO (1–0)rest frequency redshifted to the LSR velocity (471.7 km s − )of M51. Four correlator bands of 160 MHz per polariza-tion were concatenated to cover a bandwidth of ∼
550 MHz or ∼ − at a spectral resolution of 1 .
25 MHz or3 .
25 km s − .We observed two 30-field mosaics, as described in Table 2and shown in Fig. 2. Both mosaics were centered such thattheir combination covers the inner part of M51. The totalfield of view is approximately 270 (cid:48)(cid:48) × (cid:48)(cid:48) . Each pointingwas observed during 3 ×
15 seconds in turn. This allowedus 1) to observe one mosaic between two calibrations, whichwere taken every 22.5 minutes and 2) to minimize the dead-times due to moves from one field position to the next, whileensuring that the integration time per visibility (15 seconds) isshort enough to avoid mixing independent uv plane informa-tion in all the configurations (see, e.g. , Appendix C.1 of Pety& Rodríguez-Fernández 2010, for detailed calculations). Aninconvenient aspect of such an observing strategy is that weobtained two data sets, observed in slightly different condi-tions, implying slightly different noise properties and uv cov-erage ( i.e. slightly different dirty/synthesized beams).The field positions followed an hexagonal pattern, eachfield pointing being separated from its nearest neighbors bythe primary beam full width at half maximum (FWHM), θ fwhm . Nyquist sampling requires a distance between twoconsecutive pointings of λ/ d prim along two orthogonal axes,where λ is the observation wavelength and d prim is the diame-ter of the interferometer antennas. At PdBI, we typically have θ fwhm = 1 . λ/ d prim . The hexagonal pattern used here thus en-sures Nyquist sampling along the Declination axis but a slightundersampling along the Right Ascension axis.The field-of-view was observed for about 169 hours of tele-scope time with 5 antennas in configuration D (19 hours) and6 antennas in configuration C (18 hours), B (57 hours) and A(75 hours). Taking into account the time for calibration andthe data filtering applied, this translated into final on–source integration times (computed for a 6-antenna array) of usefuldata of 8.3 hours in D configuration, 15.2 hours in C config-uration, 43 hours in B configuration and 60 hours in A con-figuration. In each configuration, the time was approximatelyequally distributed between both mosaics.2.1.2. Calibration
Standard calibration methods implemented inside the
GILDAS / CLIC software were used for the PdBI data. Theradio-frequency bandpass was calibrated using observationsof two bright ( ∼
10 Jy) quasars, 0851 +
202 and 3C279, lead-ing to an excellent bandpass accuracy (phase rms (cid:46) ◦ , am-plitude rms (cid:46) + + + ∼ ◦ , an amplitude losslarger than 22%, a pointing error larger than 30% of the pri-mary beamwidth and/or a focus error larger than 30% of thewavelength. Finally, the data were also flagged when thetracking error was larger than 10% of the field of view. Thisreduces the amount of usable data to 39% , 70%, 71%, and This number takes into account visibilities that were flagged because ofshadowing. P ETY ET AL . Table 2
Parameters of the PdBI observations.Molecule Transition Frequencies [GHz] Velocity [kms − ]Rest Tuned LSR Tuned Resolution CO (1–0) 115.271202 115.090 471.7 0 5Mosaic N fields Beam PAR.A Dec. (cid:48)(cid:48) × (cid:48)(cid:48) degTop 13 h m . s ◦ (cid:48) . (cid:48)(cid:48)
30 1 . × .
92 61.5Bottom 13 h m . s ◦ (cid:48) . (cid:48)(cid:48)
30 1 . × .
01 84.0Full 13 h m . s ◦ (cid:48) . (cid:48)(cid:48)
60 1 . × .
97 73.0
Table 3
Parameters of the 30m observations.Molecule Frequency F eff B eff Resol. a Resol. b Map Size Time c T sys σ & Transition GHz kms − arcsec arcmin hours K [ T ∗ A ] mK [ T mb ] CO (1–0) 115.271202 0.95 0.75 5.20/5.00 21.3/22.5 53 ( ∼ ×
10) 17.3/41 285 16 CO (1–0) 110.201354 0.95 0.76 5.44/5.00 22.3/23.6 53 ( ∼ ×
10) 17.3/41 140 7.5 a The two values correspond to the backend natural channel spacing and to the channel spacing used to match the PdBI channel spacing. b The two values correspond to the natural FWHM of the beam and to the map resolution after gridding through convolution with a Gaussian. c Two values are given for the integration time: the on-source time and the telescope time.
Table 4
Median noise levels of the different CO (1–0) cubes.Cube type Resolution 1 σ Noise levelsarcsec (mK[ T mb ]) (Kkms − ) (M (cid:12) pc − )5kms − − − − − − − − IRAM-30m 22.5 16 0.08 0.18 0.25 0.36 0.35 0.78 1.11 1.57Hybrid synthesis 6.0 35 0.17 0.39 0.55 0.78 0.76 1.70 2.40 3.40Hybrid synthesis 3.0 106 0.53 1.18 1.67 2.37 2.30 5.15 7.28 10.30Hybrid synthesis 1.1 394 1.97 4.40 6.23 8.81 8.56 19.15 27.08 38.30PdBI-only 6.0 38 0.19 0.43 0.60 0.85 0.83 1.85 2.62 3.71PdBI-only 3.0 95 0.47 1.06 1.50 2.11 2.06 4.60 6.50 9.19PdBI-only 1.1 396 1.98 4.43 6.27 8.86 8.62 19.26 27.24 38.53Hybrid synthesis - PdBI-only 6.0 14 0.07 0.15 0.22 0.31 0.30 0.66 0.94 1.33Hybrid synthesis - PdBI-only 3.0 25 0.12 0.27 0.39 0.55 0.53 1.19 1.69 2.39Hybrid synthesis - PdBI-only 1.1 33 0.17 0.37 0.52 0.74 0.72 1.61 2.27 3.22
71% of the data obtained in the D, C, B, and A configurations,respectively. 2.2.
IRAM-30m single-dish data
A multiplicative interferometer filters out the low spatialfrequencies, i.e. , spatially extended emission. We thus ob-served M51 with the IRAM-30m single dish telescope onMay 18-22, 2010 in order to recover the low spatial frequency(“short- and zero-spacing”) information filtered out by thePdBI. We describe here the observing strategy and the cali-bration, baselining and gridding methods we used to obtainsingle-dish data whose quality matches the interferometricdata. 2.2.1.
Observations
Table 3 summarizes the IRAM-30m observations. We usedthe EMIR receivers to map the CO (1–0) and CO (1–0)lines over a ∼
60 square arcminute field-of-view covering theM51 system, i.e. , NGC 5194 and its companion NGC 5195.The upper sideband of the 3 mm separated sideband EMIRmixers (E090) was tuned at the CO (1–0) frequency. Thefull 8 GHz bandwidth of the upper sideband was then con-nected to the WILMA autocorrelator backend. This allowedus to simultaneously measure the CO and CO lines (at 115.271 and 110.201 GHz, respectively). The backend chan-nel spacing is 2 MHz, which translates into a velocity chan-nel spacing of 5.4 and 5.2 km s − at 110 and 115 GHz, respec-tively.We observed the galaxy in seven different patches. Four ofthese covered the central 400 (cid:48)(cid:48) × (cid:48)(cid:48) part of the galaxy indifferent ways. Three additional patches extended the cover-age to include the ends of the spiral arms and the companion.Conditions during the observations varied from “good” sum-mer weather ( ∼ ∼ ≈ (cid:48)(cid:48) /sec and we dumped data to disk every 0.5 seconds,yielding about 5.5 integrations per beam in the scanning di-rection (the HPBW of the IRAM-30m telescope at the fre-quency of the CO (1–0) line is ∼ (cid:48)(cid:48) ). The scan legs wereseparated by 8 (cid:48)(cid:48) , yielding Nyquist sampling transverse to thescan direction at 2.6 mm. Each position in the central part wasobserved 34 times on average, with observations split evenlybetween right ascension- and declination-oriented scanning tosuppress scan artifacts. The sky positions at the far end of theAWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 3.
Spatial distributions of the rms noise, peak intensity, integrated intensity and centroid velocity of the CO (upper panels) and CO (lower panels)(1–0) emission as observed with the IRAM-30m telescope. The angular resolution is displayed as a circle in the bottom left corner of each panel. The intensityscale is shown on the right side of each panel with units indicated in the caption title. The major and minor kinematic axes are displayed as perpendicular dottedlines. The dotted circles show the two inner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the dashed circle marks the start of the material arms at aradius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013).
CO spiral arms were observed 12 times so that the final ef-fective integration time on the extensions is somewhat shorterthan on the main field (see Fig. 3).We observed the hot and cold loads plus the sky contribu-tion every 12 minutes to establish the temperature scale andchecked the pointing and focus every ∼ ∼ ∼ (cid:48)(cid:48) .2.2.2. Calibration and gridding
We reduced the IRAM-30m data using a combination of the
GILDAS software suite (Pety 2005) and an IDL pipelinedeveloped for the IRAM HERACLES Large Program (Leroyet al. 2009).First, we calibrated the temperature scale of the data in
GILDAS/MIRA based on the hot and cold loads plus sky ob-servations (Penzias & Burrus 1973). The resulting flux ac-curacy is better than 10% (Kramer et al. 2008). We thensubtracted the “OFF” spectrum from each on-source spec-trum. We used
GILDAS/CLASS to write these calibrated,off-subtracted spectra to
FITS tables which we read into
IDL for further processing.In
IDL , visual inspection indicated the presence of signalin the [ − ,
300 km s − ] velocity range around the systemicvelocity of the galaxy. About 1/16th of the 8 GHz bandwidth( i.e. about 1000 km s − ) centered on the line rest frequencywere thus extracted from the calibrated spectra to reduce thecomputation load of the next data reduction steps. We thenfit and subtracted a third-order baseline from each spectrum. See for more informa-tion about the
GILDAS softwares.
When conducting these fits, we use an outlier-resistant ap-proach and exclude regions of the spectrum that we know tocontain bright emission based on previous reduction or otherobservations. We experimented with higher and lower orderbaselines and found a third-degree fit to yield the best results.After fitting, we compared the rms noise about the baseline fitin signal-free regions of each spectrum to the expected theo-retical noise and used this to reject a few pathological spectra.For the most part the data are very well behaved and this is aminor step.We gridded the calibrated, off-subtracted, baseline-subtracted spectra into a data cube whose pixel size is 4 (cid:48)(cid:48) .Doing so, we weighted each spectrum by the inverse of theassociated rms noise. We employed a gaussian convolution(gridding) kernel with FWHM 7 . (cid:48)(cid:48) , ∼ / ∼ . (cid:48)(cid:48) to ∼ . (cid:48)(cid:48) at115 GHz.After gridding, we fit a second set of third-order polyno-mial baselines to each line of sight through the cube. The pro-cess of the initial fitting and gridding is linear, so that thesefits represent refinements to our initial fits after the averag-ing involved in gridding. We experimented with several moreadvanced processing options such as PLAITing (Emerson &Graeve 1988) and flagging of standing waves. However thedata were very clean and none of these algorithms improvedthe quality.Figure 3 presents the reduced, calibrated, gridded IRAM-30m maps of the CO (1–0) and CO (1–0) line emis-sion. The figure displays the spatial distributions of noise, P
ETY ET AL . Figure 4. Top, left:
Area of the
CLEAN mask, normalized to its maximumvalue, as a function of the channel velocity.
Top, right:
Ellipses representingthe mean Gaussian beams for the top (red) and bottom (blue) mosaics. Theblack ellipse represents the Gaussian beam used for the restoration of the
CLEAN component list.
Middle: uv coverages for the fields of the top (leftpanel) and bottom (right panel) mosaics. Bottom:
Zoom of the dirty beamsfor the top (left panel) and bottom (right panel) mosaics. peak temperature, integrated emission and centroid velocity.Fig. 26 and 27 (available in the electronic version only) dis-play the channel maps of these lines.2.3.
Combination, imaging and deconvolution
The interferometric and single-dish data provide us withtwo data sets, which sample the high and low spatial frequen-cies, respectively. It is thus possible to produce two differentdeconvolved results: 1) one obtained from the interferomet-ric data set alone, and 2) one obtained from the combinationof the interferometric and single-dish data. While the latteris the desired final product, as it is sensitive to all measuredspatial scales, the former is often produced because no single-dish measurements will be available or because they have notyet been acquired. In this paper, we will present both datacubes to emphasize the amount of flux which is recovered inthe interferometric-only data set. Moreover, the angular res-olution of the interferometric data is not uniquely defined. Itdepends on the weighting scheme chosen. For instance, itis sometimes useful to produce data cubes at lower angularresolutions to improve the brightness sensitivity, i.e. , the sen-sitivity to extended emission. We exploit this here in additionto producing the full resolution cube.This section explains 1) the generic imaging and deconvo-lution methods used to produce all these data cubes, 2) howthese methods influence the amount of flux recovered in theinterferometric-only data, and 3) the additional steps required to image jointly the single-dish and interferometric data.2.3.1.
Generic methods
Each interferometric pointing was imaged and a single dirtyimage was built by linear combination of the 60 individualdirty images. The dirty image was then deconvolved us-ing an adaption of the Högbom
CLEAN algorithm. A de-tailed account of the
GILDAS / MAPPING implementation ofthe imaging and deconvolution processing of mosaics can befound in Pety & Rodríguez-Fernández (2010). To help thedeconvolution, masks indicating the region where to searchfor
CLEAN components were defined on individual channelsfrom the short-spacing data cube. This cube was convolvedwith a Gaussian kernel to a final angular resolution of 30 (cid:48)(cid:48) .The
CLEAN masks were then defined by all the pixels whosesignal-to-noise ratio was larger than 6. This method was de-signed to avoid biasing the deconvolution by defining maskswide enough to encompass all the detected signal from M51.The deconvolution of each channel was stopped when afraction of the maximum number of clean components werefound. This fraction was defined as the ratio of the area of thecurrent channel mask to the area of the wider channel mask(see left panel of Fig. 4). The deconvolution was assumed tohave converged under three conditions. First, the cumulativeflux as a function of the number of clean components con-verged in each channel. Second, the residual channel imageslooked like noise. Both criteria indicated a satisfying conver-gence of the deconvolution. Finally, we deconvolved againthe data using exactly the same method except that we dou-bled the maximum number of clean components. The sub-traction of both cubes looks like noise.The list of clean components was regularized with a Gaus-sian beam and the residual image was added to obtain the finalcube. As all the 30 fields of the top and bottom mosaics wereregularly observed in short cycles of 22.5 minutes, the synthe-sized beams do not vary inside each mosaic. However, the twomosaics were observed at different times implying a slight dif-ference of the synthesized beam between both mosaics (seeTable 2). We used the same averaged Gaussian restorationbeam for the northern and southern mosaic. This process isvalid because 1) the Gaussian fits of the synthesized beamsare similar as shown in the top right panel of Fig. 4 and 2)the remaining flux in the residual image is negligible or unde-tectable ( i.e. , below the noise limit). The resulting data cubewas then scaled from Jy/beam to T mb temperature scale usingthe restoration beam size.While the natural velocity channel spacing of the inter-ferometer backend is 3.25 km s − at 2.6 mm, we smoothedthe data to a velocity resolution of 5 km s − . This decreasesthe effect of correlation between adjacent frequency channelsoutput by the correlator. This also increases the signal-to-noise ratio per channel (an important factor for the deconvo-lution) and speeds up the processing. Signal is present be-tween −
110 and +
110 km s − , relative to NGC 5194’s LSRsystemic velocity of 471.7 km s − . We thus imaged anddeconvolved 120 channels producing a velocity range of[ − . , + . − ], implying that about two-thirds of thechannels are devoid of signal. On a machine with 2 octa-core processors and 72 GB of total RAM memory, the de-convolution of the 120 channels up to a maximum number of320 000 clean components typically took 38.5 hours (humantime). The deconvolution duration increases linearly with themaximum number of clean components per channel.AWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 5.
Deconvolved flux as a function of velocity for the hybrid synthesis(top) and the PdBI only (bottom) data sets. Yellow, red, and black curvescorrespond to cubes imaged at an angular resolution of 1 (cid:48)(cid:48) , 3 (cid:48)(cid:48) , and 6 (cid:48)(cid:48) , re-spectively. The percentage of total flux recovered compared to the 6 (cid:48)(cid:48) cube isindicated in the top right corner using the same color coding.
PdBI only
To start, we imaged and deconvolved the PdBI data with-out the short-spacings from the IRAM-30m observations.Achieving the convergence of the deconvolution algorithm ata given angular resolution is insufficient to prove that all theflux was recovered in PdBI-only data sets. Indeed, the ab-sence of zero spacing implies that the total flux of the dirtyimage is zero valued, and it is the deconvolution algorithmwhich tries to recover the correct flux of the source. Thisworks only when the source is small compared to the primarybeam and the signal-to-noise is large enough. No deconvo-lution algorithm will succeed in recovering the exact flux ofeven a point source at low signal-to-noise. Indeed, the algo-rithm recovers only the flux which is above a few times thenoise rms. Adding the deconvolution residuals will not helpbecause the dirty beam ( i.e. , the interferometer response) hasa zero valued integral, i.e. , the residuals always contain zeroflux.Moreover, a given interferometer needs 2 as much observ-ing time to keep the same brightness sensitivity when justdoubling the angular resolution (assuming similar observingconditions). Such an increase in observing time is impracti-cal. The brightness sensitivity thus decreases quickly whenthe angular resolution improves. In the PAWS case, we ap-proximately doubled the observing time every time we wentto the next wider interferometer configuration, which typi-cally doubled the angular resolution. This allowed us to reacha median noise of 0.4 K at full resolution, i.e. . (cid:48)(cid:48) × . (cid:48)(cid:48) ata position angle (PA) of 73 deg (when using natural weightingof the visibilities). While this is the best (pre-ALMA) sensivi-tivity reachable for such a large mosaic, it is also much higherthan the sensitivity of 16 mK we reached with the IRAM-30mat an angular resolution of 22 . (cid:48)(cid:48) . This may mean that faint in-tensities may be hidden in the noise of the 1 (cid:48)(cid:48) -resolution cube.Multi-resolution CLEAN algorithms (only available for single-field observations in
GILDAS and thus not used for thePAWS mosaic) partly solve this problem of brightness signal-to-noise ratio because the deconvolution simultaneously hap-pens on dirty images at different resolutions and thus differ-ent brightness noise levels. Interferometric brightness noiseis a compromise between the synthesized angular resolutionand the time spent in the different configurations. To checkwhat happens with our deconvolution algorithm, we taperedthe visibility weights to increase the brightness sensitivity atthe cost of losing angular resolution, as this method is to firstorder similar to a Gaussian smoothing in the image plane.We choose Gaussian tapering functions such that we obtainedsynthesized resolutions of 3 (cid:48)(cid:48) and 6 (cid:48)(cid:48) . Table 4 lists the typicalrms noise values for the 3 different resolutions, i.e. , 0.4, 0.1and 0.03 K at respectively 1 (cid:48)(cid:48) , 3 (cid:48)(cid:48) , and 6 (cid:48)(cid:48) .The lower panel of Fig. 5 visualizes the flux found by the
CLEAN algorithm at the 3 different resolutions as a functionof velocity. The Högbom
CLEAN algorithm finds 40% moreflux at 3 (cid:48)(cid:48) than at 1 (cid:48)(cid:48) . On the other hand, only 4% more flux isrecovered at 6 (cid:48)(cid:48) than at 3 (cid:48)(cid:48) even though the brightness sensitiv-ity increases by a factor of ∼ .
5. Since the typical resolutionof PdBI at 3 mm in its most compact configuration is 6 (cid:48)(cid:48) , itmeans that PdBI reaches its maximum brightness sensitivityin this configuration. Hence, further tapering the data would not recover more flux. Recovering only a marginal additionalamount of flux when going from 3 (cid:48)(cid:48) to 6 (cid:48)(cid:48) thus implies that werecovered at these resolution all the flux present in the inter-ferometric data.2.3.3.
Hybrid synthesis (PdBI + IRAM-30m)
The hybrid synthesis is a joint deconvolution of the PdBIand IRAM-30m data sets. The IRAM-30m and PdBI datasets were first made consistent using the following 4 steps. 1)We converted the IRAM-30m spectra to main beam tempera-tures ( T mb ) using the forward and main beam efficiencies ( F eff & B eff ) given in Table 3. 2) These spectra were reprojectedon the projection center used for the interferometric data set.3) The LSR systemic velocity was set to zero to mimic ob-servations at the redshifted frequency. 4) The velocity axiswas resampled to 5 km s − channel spacing. The last transfor-mation introduced some correlation between channels as theautocorrelator natural channel spacing is only 5.2 km s − at the CO (1–0) frequency.Following Rodriguez-Fernandez et al. (2008), the
GILDAS / MAPPING software and the single-dish mapfrom the IRAM-30m were used to create the short-spacingvisibilities not sampled by the Plateau de Bure interferometer.In short, the maps were deconvolved from the IRAM-30mbeam in the Fourier plane before multiplication by the PdBIprimary beam in the image plane. After a last Fouriertransform, pseudo-visibilities were sampled between 0 and15 m (the diameter of the PdBI antenna). These visibilitieswere then merged with the interferometric observations. Therelative weight of the single-dish versus interferometric datawas computed in order to get a combined weight density inthe uv plane close to Gaussian. Since the Fourier transformof a Gaussian is a Gaussian, and the dirty beam is the Fouriertransform of the weight density, this ensures that the dirtybeam is as close as possible to a Gaussian, making thiscriterion optimum from the deconvolution point-of-view. Ingeneral, the short spacing frequencies are small compared tothe largest spatial frequency measured by an interferometer.This implies we can use the linear approximation of a P ETY ET AL . Figure 6.
Spectra, averaged over the field of view, of the hybrid synthesis(blue), PdBI-only (red) and filtered (= hybrid-PdBI, white) emission. Thepercentage of flux recovered in each spectrum is written in the top right cor-ners with the same color code. The computations were done at the angularresolution displayed at the top left corner of each panel.
Gaussian in the vicinity of its maximum, i.e. , one can assumethe Gaussian is constant in the range of frequencies used forthe processing of the short spacings. We thus need to matchthe single-dish and interferometric densities of weights in theinner region of the uv plane.In practice, we compute the density of weights from thesingle-dish in a uv circle of radius 1 . d prim and we match itto the averaged density of weights from the interferometer ina uv ring between 1.25 and 2 . d prim . Experience shows thatthis gives the right order of magnitude for the relative weightand that a large range of relative weight around this valuegives very similar final results (see e.g. Fig. 5 of Rodriguez-Fernandez et al. 2008). In our case, this computation wasindependently done for each interferometric pointing to takeinto account the fact that the two mosaics used to producethe final image were observed in slightly different conditions.The relative weight varies typically by 1% from pointing topointing in each mosaic, and by ∼ −
7% between both mo-saics.Contrary to interferometric-only data sets, the upper panelof Fig. 5 shows that the deconvolved flux in a hybrid synthe-sis is the same for the 3 different angular resolutions. In otherwords, the deconvolved flux is independent of the brightnesssensitivity reached, as it is fully constrained by the zero spac-ing amplitude. Having high signal-to-noise zero spacing datathus ensures that the total flux inside the deconvolved cube will be the total flux of the single-dish data in the same fieldof view. Section 3.1.3 checks this for the PAWS data set.This is linked to the fact that the dirty beam integral is nownormalized to unity. Both the dirty image and the residualfluxes are meaningful in this case. This enables an additionalcheck of the convergence of the deconvolution algorithm forthe hybrid synthesis deconvolution: We checked that less than1.2% of the clean flux remains in the residual cube in the[ − , + − velocity range, even at 1 (cid:48)(cid:48) angular reso-lution.Fig. 28 and 29 (available in the electronic versiononly) display the channel maps of the 1 (cid:48)(cid:48) -resolution hybrid(30m+PdBI) synthesis cube at negative and positive veloci-ties (relative to the systemic velocity), respectively. A LUMINOUS COMPONENT OF EXTENDEDEMISSIONThis section presents the unexpected finding that about halfthe CO luminosity in the hybrid map arises from a faint, ex-tended component. Sect. 3.1 and 3.1.5 demonstrate that thisresult is unlikely to reflect an artifact in the data. Sect. 3.2 ex-plores how the emission in the hybrid map breaks apart into abright, compact and a faint, extended component. It also com-pares the structures of these distributions. Sect. 3.3 and 3.4consider the nature of the CO emission components in light of1) calculations of vertical disk structure, and 2) the observed CO/ CO ratio. Sect. 3.5 discusses our interpretation of thisemission component.3.1.
Verifying the existence of an extended component
This section shows that (50 ± (cid:48)(cid:48) , i.e. , 1 . D / . D is the assumed distance of M51.3.1.1. Flux recovered in the PdBI-only data cubes
Fig. 6 compares the spectra averaged over the field of viewof 1) the hybrid synthesis data set (in blue) and 2) the PdBI-only data set (in red) for the 1, 3, and 6 (cid:48)(cid:48) data cubes from topto bottom. These spectra were obtained as a mean over thePAWS field of view contracted by about 1 primary beamwidthto decrease the influence of increasing noise at the map edges.The differences between the hybrid synthesis and PdBI-onlyspectra are displayed in white.The main result is that only half of the total flux is recov-ered in the PdBI-only data set. Indeed, only 37% of the to-tal flux is recovered at 1 (cid:48)(cid:48) but this is attributed to the rela-tively “low” brightness sensitivity reached at this resolution(see Section 2.3.2). Approximately 50% of the total flux isrecovered both at 3 (cid:48)(cid:48) and 6 (cid:48)(cid:48) , while the brightness sensitivitydiffers by a factor of 2.5 between them. We stress that al-though the deconvolution recovers 44% more flux at 6 (cid:48)(cid:48) thanat 1 (cid:48)(cid:48) , the difference amounts to only 13% of the total fluxpresent in the PAWS field of view.3.1.2.
Coordinate registration
We checked the overall registration of the IRAM-30mmoment-0 images against the PdBI-only data. We convolvedthese “reference” maps to the resolution of the IRAM-30mdata. We then repeatedly shifted the images relative to one an-other and recorded the cross-correlation between the IRAM-30m data and the other images. The overall registration ofAWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY −100 0 1000.00.20.4−20 0 20 40 Velocity [km/s] M ea n T C O [ K ] D i ff e r e n ce [ % ] CARMA+45mPdBI+30m BIMA+12mIRAM 30m
Figure 7.
Channel by channel flux comparison of the PdBI+30m, IRAM-30m, CARMA and BIMA data cubes over the PAWS field of view. Thebottom panel shows the mean CO temperature as a function of the velocityand the top panel shows the relative difference with respect to the PdBI+30mdata set. The dotted horizontal line indicates perfect agreement.
Table 5
Comparison of registration and total flux within different CO (1–0)datasets.Data set Offset Integrated flux Flux differencearcsec 10 Kkms − pc % of PdBI+30m fluxIRAM-30m 0 7.82 − . < + . < − . < − . the IRAM-30m with the PdBI data appears to agree within ∼ (cid:48)(cid:48) . In addition, we obtained the same agreement withthe BIMA SoNG (Helfer et al. 2003) and CARMA (Kodaet al. 2011) data. This good agreement is expected becauseradio-observatories check the coordinate registration directlyagainst the radio-quasars used to define the equatorial coordi-nate frame. 3.1.3. Flux calibration
As a test of our calibration strategy, we compared the fluxwithin the hybrid synthesis data cube with recent CO surveysof M51 by BIMA (Helfer et al. 2003) and CARMA (Kodaet al. 2011). Although conceptually straightforward, this com-parison must be done with care since each dataset has dif-ferent angular resolution, channel width, noise characteristicsand field of view. To obtain the most meaningful comparison,we smoothed the BIMA, CARMA and hybrid synthesis datacubes to the same angular resolution as the IRAM-30m data(22 . (cid:48)(cid:48)
5) and interpolated them onto a common ( l , m , v ) gridwith square pixels of 4 (cid:48)(cid:48) size, and a velocity channel spacingof 5 km s − . The grid uses a global sinusoid (GLS) projection,and is centered at RA 13:29:54.09, Dec + σ of all the pixels whose intensity is above 5 σ . TheIRAM-30m σ ’s were estimated for each sightline using themedian absolute deviation. The resulting mask was applied toall four data cubes. The total integrated flux within a spatialregion corresponding to the PAWS field of view contracted by ∼ i.e. , there is ∼
10% (5%) less flux ineach channel of the BIMA+12m (CARMA+45m) data cubecompared to PdBI+30m.These tests confirm the IRAM-30m flux calibration accu-racy and its correct transmission to the hybrid synthesis dataset. As a test of the flux accuracy of the PdBI-only data set,we compared the efficiencies resulting from the interferomet-ric flux calibration to the well-known PdBI antenna efficien-cies as measured through regular holographies. These agreewithin ∼ Amplitude of the brightness Fourier transform as a functionof the uv distance
It is important to test how well the hybrid synthesis and thePdBI-only data cubes agree with each other at high spatial fre-quencies. To do this, Fig. 8 compares the azimuthal average ofthe amplitude of the Fourier transform of the PdBI-only andthe hybrid synthesis data cubes at 6 (cid:48)(cid:48) resolution as a functionof the uv distance for every third velocity channel between[ − . , + .
5] km s − . In such a representation, the ampli-tude at the zero uv radius is equal to the total flux presentin the channel map. We thus normalized all the curves in-side each panel so that their zero-spacing values represent thefraction of the total flux available in the hybrid synthesis cubeat this velocity channel. For reference, 1) the power spec-trum would be computed as the square of these curves, 2)the dashed vertical lines indicate the minimum radius directlymeasured by the interferometer, i.e. , r min (cid:39) . e.g. , signal-free channels atthe edges of the velocity range in the figure) will give a shapeconsistent with the Fourier transform of the Gaussian restora-tion beam (see Chapter 17 of Bracewell 2000). On the otherhand, signal channels display the product of Fourier transformof the true source brightness and the Fourier transform of theGaussian restoration beam as a function of the uv spacing.Hence, channels with significant line signal fall more quickly0 P ETY ET AL . Figure 8.
Variations of the azimuthal average of the Fourier transform am-plitude as a function of uv radius for every third velocity channel between − . + . − . On the y-axis, we plot the percentage of the maxi-mum flux at the zero uv radius. The pink dashed curve displays the theoreticalshape for a signal-free channel, i.e. , the Fourier Transform of the hybrid syn-thesis beam. The pink and blue solid curves show, respectively, the hybridsynthesis and PdBI-only data imaged at 6 (cid:48)(cid:48) resolution. The dotted verticalline indicates the minimum uv radius measured by the interferometer ( i.e. ∼ Figure 9.
Zoom of the variations of the azimuthal average of the Fouriertransform amplitude as a function of uv radius for every third velocity channelbetween − . + . − . The y-axis shows the percentage of themaximum flux at zero uv radius. The dashed pink and green curves displaythe Fourier Transforms of the hybrid synthesis and the IRAM-30m beams,respectively. The solid pink curve shows the hybrid synthesis data imaged at6 (cid:48)(cid:48) resolution. The solid green and cyan curves represent, respectively, theIRAM-30m data before and after deconvolution from the 22 . (cid:48)(cid:48)
30m beamand convolution with a 6 (cid:48)(cid:48) beam. The dashed vertical line indicates the mini-mum uv radius measured by the interferometer ( i.e. , ∼ than the Gaussian restoration beam.The good agreement between the amplitudes from the hy-brid and PdBI-only data at radii larger than r min provides con-fidence in the deconvolution results of the compact sources(whose angular extent is smaller than λ/ r min ∼ (cid:48)(cid:48) ) in the PdBI-only data set even though the short-spacings are miss-ing. Below r min , the two curves diverge because the decon-volution can only “extrapolate” up to the zero uv radius forthe PdBI-only data set, while it “interpolates” for the hybridsynthesis data set. As the amplitude at zero spacing is propor-tional to the total flux, these plots clearly indicate that PdBI-only data miss a large fraction of the flux even for the 6 (cid:48)(cid:48) res-olution cube, whose deconvolution is immune to low signal-to-noise effects.Moreover, the change of slope visible in Fig. 8 for the hy-brid synthesis amplitude between ∼ not a pro-cessing artifact. Indeed, Fig. 9 displays a zoom of the az-imuthal average of the amplitude of the Fourier Transform ofthe IRAM-30m and the hybrid synthesis data cubes at 22 . (cid:48)(cid:48) and 6 (cid:48)(cid:48) resolution (green and pink curves, respectively). Thesecurves cannot be directly compared because they result fromtwo different measurement equations (the single-dish and theinterferometric ones). The solution is well-known: We justhave to apply to the IRAM-30m curve the standard process-ing steps needed to produce short-spacing visibilities (seeSect. 2.3.3). Indeed, after deconvolution of the single-dishbrightness by the 22 . (cid:48)(cid:48) single-dish beam and multiplicationwith the 6 (cid:48)(cid:48) interferometric primary beam, the amplitudes ofthe Fourier transform of both data sets agree well. Since aGaussian of 22 . (cid:48)(cid:48) FWHM has a flux equal to 77, 45, and 21%of its maximum at 5, 10, and 15 m, the observed change ofslope of the deconvolved 30m data cannot be attributed to im-precision in the deconvolution of the IRAM-30m beam. Thischange of slope in flux is responsible for the failure of the de-convolution to extrapolate the correct total flux at the zero uv radius for the PdBI-only data set.3.1.5. Impact of the IRAM-30m error beam
The beam efficiency of the IRAM-30m telescope at the fre-quency of the CO (1–0) line is predicted to be 0.78, basedon the interpolation of the measured efficiencies at 86, 145,210, 260, and 340 GHz using the Ruze formula . Moreover,the forward efficiency is 0.95 at the same frequency. Thisimplies that about 22% of the measured flux in a given di-rection results from beam pick-up from solid angles outsidethe main beam. Of this amount, 5% originates from the rearlobes, which mainly collects diffuse emission from the tele-scope backside. Hence, about 17% of the measured flux ispicked up by the rings of the telescope diffraction pattern andthe error beams due to the limited surface accuracy of the tele-scope. In Appendix C, we assess in-depth how much theseeffects contribute to the extended emission. Here, we summa-rize the main results.We estimate that the peak brightness due to the error beamcontribution is at most 55 mK, i.e. , about 3.5 times the me-dian noise level of the IRAM-30m observations. The medianvalue of the error beam contribution is 19 mK, while pixelsbrighter than 5 times the noise level have a median of 140 mKin the extended emission measured at 6 (cid:48)(cid:48) (see Sect. 3.2.1). Theemission associated with the error beams has a very differ-ent signature from that of extended emission both in spaceand velocity. In particular, the putative error beam contribu-tion translates into much wider lines than actually observed.Moreover, the typical angular scales of the error beams arelarge, implying that the flux is scattered at low brightness levelover wide regions of the sky. Finally, we estimate that at most For details, see
AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 10.
Same as Fig. 8 but the pink dot-dashed curve displays the averagenoise level as a function of the uv radius. The red curve shows the differencebetween the hybrid synthesis and the PdBI-only at 6 (cid:48)(cid:48) resolution. The 3 dot-ted vertical lines indicate d prim , 2 d prim , and 3 d prim , where d prim is the primarybeam diameter of the interferometer.
10% of the total flux in the PAWS field of view can be due toerror beam scattering.Taken together, these arguments lead us to the conclusionthat the IRAM-30m error beam cannot explain the presenceand properties of the extended emission.3.1.6.
About half the CO luminosity arises from an extendedemission component
We now consider why (50 ± ∼
15 m, i.e. thewell-known short-spacing problem. We now wish to quantifythe spatial scales at which the emission filtered by the PdBI isstructured. To do this, Fig. 10 compares as a function of the uv distance 1) the amplitude of the difference of the Fouriertransforms between the hybrid synthesis and the PdBI-onlydata cubes (red plain curve), with 2) the noise of the hybridsynthesis Fourier transform (pink dashed curve), computedby averaging the signal-free channels. For all the velocitychannels showing some signal, the amplitude of PdBI-filteredemission is (much) larger than the noise level only up to aradius of ∼
15 m. This implies that a very large fraction ofthe missing flux is structured only at spatial scales larger than ∼ λ/ r min = 36 (cid:48)(cid:48) . However, the difference and noise curves stayclose to each others up to 35 m for a few velocity channels( e.g. , v = − . + . − ). This indicates there is prob-ably a small fraction of the missing flux which is structuredat spatial scales between 15 (cid:48)(cid:48) and 36 (cid:48)(cid:48) . In the following, wewill thus state that the missing flux is structured mostly at spa-tial scales larger than ∼ λ/
15 m = 36 (cid:48)(cid:48) or 1 . D / . D is the distance of M51. Conversely, this also meansthat the flux recovered in the PdBI-only cubes is structuredmostly at spatial scales smaller than 36 (cid:48)(cid:48) .3.2. Structure of compact and extended emissions
In order to investigate the nature of the emission filtered bythe PdBI interferometer, we need to image it. To do this, we subtracted at each angular resolution (1, 3 and 6 (cid:48)(cid:48) ) the PdBI-only from the hybrid synthesis data cubes to determine theproperties of the emission filtered by the PdBI. We were care-ful to image both data sets on the same spatial and spectralgrid. We also used the same weighting scheme, deconvolu-tion method, stopping criterion and restoration beam.In the following, we will refer to the 3 cubes as hybridsynthesis (PdBI+30m), PdBI-only, and subtracted ( i.e. , hy-brid synthesis minus PdBI-only) cubes. The PdBI-only andsubtracted cubes are equivalent to a decomposition of the hy-brid synthesis signal into two kinds of source morphology:Compact (angular scales (cid:46) (cid:48)(cid:48) ) and extended (angular scales (cid:38) (cid:48)(cid:48) ) sources. This decomposition is a convenient instru-mental side effect. As such, it is arbitrary and only a multi-scale analysis would deliver the full spatial distribution ofthe emission. However, Fig. 8 and 9 show that the Fouriertransform amplitude changes its slope between ∼ (cid:48)(cid:48) cubes. While this gives a taste of multi-scale ap-proaches, two of these cubes stand out. The PdBI-only 1 (cid:48)(cid:48) datacube is the one where the “compact” sources are best resolvedwhile the subtracted 6 (cid:48)(cid:48) data cube is the one which gives themost accurate description of the extended component. Finally,we smoothed the PdBI-only 6 (cid:48)(cid:48) cube to the resolution of theIRAM-30m data cube (22 . (cid:48)(cid:48) ) and we subtracted them fromthe 30m data. This allows us to obtain an idea of the relativecontribution of both emission components at the typical reso-lution of single-dish observations as discussed in Sect. 3.4.3.In the rest of this section, we first describe the statisticaldistributions of noise and signal for the different data cubes,as this allows us to discuss how beam dilutions and signal-to-noise ratios evolve with angular scale. We then comment onthe 2-dimensional spatial distributions of the line moments.We also present their azimuthal averages, which we will lateruse to analyse the vertical structure of both components. Fi-nally, we show the kinematics of the two components alongthe M51 major axis.3.2.1. Noise and signal distributions
In order to quantify the ( l , m , v )-volume filling factors andthe beam dilution properties of the compact and extendedemission, we now describe the distribution of the noise andbrightness values.Figure 11 displays the cumulative histograms of the rmsnoise for the 4 different resolutions (1, 3, 6, and 22 . (cid:48)(cid:48) ), andfor the 3 kind of cubes: Hybrid synthesis (top), PdBI-only(middle) and subtracted (bottom). The left column displaysthe raw histograms while the right column presents the his-tograms normalized by their median value, as this eases thecomparison of shapes. The histograms show that the noisedistributions are well centered on the median value, implyingrelatively uniform noise properties. The IRAM-30m single-dish data display an increase of the histogram population athigh noise values because the noise distributions are homo-geneous over the inner 400 (cid:48)(cid:48) × (cid:48)(cid:48) field of view but theyincrease on the northern and southern patch. A similar effectis seen for the interferometric data, which is directly linked toa noise increase at the edges of the field because of the cor-rection of primary beam attenuation. Moreover, in the single-dish data, the CO median noise level (16 mK) is about twiceas high as the CO one (7.5 mK) because the CO (1–0) lineis closer to an oxygen atmospheric line.2 P
ETY ET AL . Figure 11.
Cumulative histograms of the rms noise for the CO (1–0)(dashed line) and CO (1–0) (solid lines) cubes. The IRAM-30m cubesare displayed in black, the interferometric cubes at 1, 3, and 6 (cid:48)(cid:48) are displayedin blue, green, and red, respectively.
Top:
Hybrid synthesis or IRAM-30mdata cubes.
Middle:
PdBI-only data cubes or the 6 (cid:48)(cid:48) extended data cubesmoothed to 22 . (cid:48)(cid:48) and subtracted from the IRAM-30m cube. Bottom:
PdBI-only cubes subtracted from the hybrid synthesis cubes or the 6 (cid:48)(cid:48)
PdBI-onlydata cube smoothed to 22 . (cid:48)(cid:48) and subtracted from the IRAM-30m cube. Left:
Histograms of absolute noise values.
Right:
Histograms of noise normalizedby the median noise value.
The brightness noise levels of the hybrid synthesis datacubes are mostly set by the interferometric radiometric noisebecause the increase of integration time from the IRAM-30mto the PdBI does not match the gain in angular resolution (seeSect. 2.3.2). Hence, the median rms noise (see Table 4) andthe noise cumulative histograms (see Fig. 11) are almost iden-tical for the PdBI-only and hybrid synthesis data cubes. Onthe other hand, the brightness noise levels for the subtracteddata cubes are mostly set by the single-dish data. Indeed, wesubtracted two data sets whose noise is partially correlated:The noise coming from the PdBI visibilities is common. Sub-tracting both data cubes result in noise properties close to theIRAM-30m noise properties. In particular, the median rmsnoise in the subtracted data cube is more than one order ofmagnitude smaller than the median rms noise of the hybridsynthesis cube at 1 (cid:48)(cid:48) resolution.Figure 12 shows the cumulative histograms of the cubebrightness using a similar layout as Fig. 11. In the right col-umn, the histograms are normalized by the maximum bright-
Figure 12.
Cumulative histograms of the signal above the 5 σ -level for the CO (1–0) (dashed line) and CO (1–0) (solid lines) cubes. The IRAM-30m cubes are displayed in black, the interferometric cubes at 1, 3, and 6 (cid:48)(cid:48) are displayed in blue, green, and red, respectively.
Top:
Hybrid synthesis orIRAM-30m data cubes.
Middle:
PdBI-only data cubes or the 6 (cid:48)(cid:48) extendeddata cube smoothed to 22 . (cid:48)(cid:48) and subtracted from the IRAM-30m cube. Bot-tom:
PdBI-only cubes subtracted from the hybrid synthesis cubes or the 6 (cid:48)(cid:48)
PdBI-only data cube smoothed to 22 . (cid:48)(cid:48) and subtracted from the IRAM-30mcube. Left:
Histograms of raw brightnesses.
Right:
Histograms of bright-nesses normalized to the maximum brightness. ness. The histograms were computed using the full PAWSfield of view but only the parts above the 5 σ brightness noiselevel are displayed. The hybrid synthesis and PdBI-only his-tograms are similar both qualitatively and quantitatively. Thehistograms are displaced towards higher brightness valueswhen the angular resolution increases, implying that all thestructures above the 5 σ noise levels experience large beamdilution effects. For example, the maximum brightness in-creases by more than one order of magnitude from 1.3 to16 K, when increasing the resolution from 22.5 to 1 (cid:48)(cid:48) . On theother hand, the histograms of the subtracted cubes are identi-cal within the noise constraints (even for the normalized his-togram of the 1 (cid:48)(cid:48) cube as the value of the maximum bright-ness is relatively uncertain). Indeed, the maximum brightnessof the extended component evolves only from 0 . ± .
07 to1 . ± .
07 K from 22 . (cid:48)(cid:48) (the IRAM-30m resolution) to 6 (cid:48)(cid:48) (the PAWS resolution for which the extended emission is bestdefined). This implies that beam dilution is negligible for thesubtracted emission. This is consistent with this emission be-AWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY (cid:48)(cid:48) .The ( l , m , v )-volume filling factors and the median bright-ness values were computed on all the cube pixels with de-tected signal, i.e. their brightness is larger than 5 times theirnoise. Using this definition, the brightness of the compactcomponent (measured on the 1 (cid:48)(cid:48) PdBI-only cube) ranges from2.0 to 16.0 K, with a median value of 2.5 K and it fills less than2% of the ( l , m , v )-volume. The brightness of the extendedcomponent (measured on the 6 (cid:48)(cid:48) subtracted cube) ranges from0.07 to 1.36 K, with a median value of 0.14 K and it fills ∼
30% of the ( l , m , v )-volume.The comparison of the noise and signal distributions of thecubes at different angular resolutions makes it clear why thedeconvolution of the PdBI-only data recovers more flux at 3 (cid:48)(cid:48) than 1 (cid:48)(cid:48) but almost the same flux at 6 (cid:48)(cid:48) and 3 (cid:48)(cid:48) . Indeed, thesubtracted emission has a median brightness of 0.14 K, whichis ∼ .
35 times the hybrid synthesis brightness noise level at1 (cid:48)(cid:48) but ∼ . (cid:48)(cid:48) and 6 (cid:48)(cid:48) , respectively. In other words, any emission present inthe PdBI-only data is only recovered when its signal-to-noiseis large enough (typically ≥ Spatial distribution of the line moments
Figure 13 summarizes the properties of the decompositionof the total emission into the compact and the extended emis-sion. The spatial distributions of the peak temperature, lineintegrated emission (the 0th order moment), centroid veloc-ity (the 1st order moment), line full width at half maximum(computed as 2.35 times the line 2nd order moment), and thenoise are presented from top to bottom. The total and compactemissions are presented at the best possible PAWS resolution(1 (cid:48)(cid:48) ), while the extended emission is displayed at the resolu-tion where it is best measured, i.e. , 6 (cid:48)(cid:48) . Figures 32, 33, 34,and 35 (available in the electronic version only) show thesame decomposition at fixed angular resolutions from 1, 3, 6,and 22 . (cid:48)(cid:48) , respectively. This demonstrates how the differentmoments of each component of the emission vary with spatialresolution.The deconvolved intensity distribution is corrected for pri-mary beam attenuation, which makes the noise level spatiallyinhomogeneous. In particular, the noise strongly increasesnear the edges of the field of view (see, e.g. , panels [m] to[o] of Fig. 13). To limit this effect, the deconvolved mosaicis truncated at its edge, giving an almost parallelogram fieldof view of ∼ . (cid:48)(cid:48) subtracted cube, whichshows the extended component. First, a moire effect due tothe undersampling of the field pointings in the mosaic appearsas a slight modulation of the intensity at a typical spatial scaleof ∼ (cid:48)(cid:48) (see Fig. 32[f]). This is due to power aliasing in the uv plane (Pety & Rodríguez-Fernández 2010). Second, thechicken-pox aspect at a spatial scale close to the synthesizedresolution is a known artifact of the deconvolution methodthat we used (see Fig. 32[c]). The overall spatial repartition ofthe extended component is nevertheless correct as evidencedby the comparison with the spatial distributions of the mo- ments at 3 (cid:48)(cid:48) and 6 (cid:48)(cid:48) , where the impact of these artifacts be-comes negligible.The subtracted cube reveals extended emission whose peaktemperature distribution is barely detected in the 1 (cid:48)(cid:48) hybridsynthesis cube, as the signal-to-noise ratio of this emissionranges between 0.2 and 3.5 (see Fig. 13[a-c]). This is why arelatively complex dedicated masking technique was devisedto compute meaningful 1st and 2nd order moments for the 1 (cid:48)(cid:48) hybrid synthesis cube (see Section B for a detailed descrip-tion). The peak temperature (Fig. 13[c]) and integrated emis-sion (Fig. 13[f]) maps are maximum along the major axis ofthe galaxy. This is expected because emission in a given ve-locity channel extends over a large 2D area near the majoraxis, while is mostly extended in one spatial dimension alongthe minor axis. Hence, the interferometer will recover “ex-tended” emission along the minor axis much better than alongthe major axis. This projection effect thus minimizes emis-sion along the minor axis in the subtracted cube. However,there is more than a major axis trend in the subtracted cube.Indeed, Figure 30 and 31 (available in the electronic versiononly) show an overlay of the signal-to-noise contours of the1 (cid:48)(cid:48) PdBI-only data cube onto the signal of the 6 (cid:48)(cid:48) subtractedcube for a set of channels at negative and positive velocities.These figures suggest that the extended emission fills the cen-tral 55 (cid:48)(cid:48) , bounded by the inner edge of the spiral arms, andthen falls on the convex side of the arms at larger radii (out to ∼ (cid:48)(cid:48) ).While the peak temperature map exhibits a symmetric spa-tial distribution relative to the galaxy center, the integratedemission peaks in the southern part. Extended emission iscompletely absent in the 1 (cid:48) × (cid:48) -areas located roughly south-west ( − (cid:48)(cid:48) , − (cid:48)(cid:48) ) and northeast ( + (cid:48)(cid:48) , + (cid:48)(cid:48) ) of the center.The maps of centroid velocity indicate differences betweenthe kinematics of the compact and extended emission. This isbest seen when following the 0 km s − -isovelocity line, i.e. ,NGC 5194’s systemic velocity, on Fig. 34[h and i] or onFig. 35[h and i]. The linewidth of the extended component(Fig. 13[l]) is largest inside a central circle of ∼ (cid:48)(cid:48) radius.Linewidths are on average much larger for the extended thanfor the compact emission. The clearest exception is at thegalaxy center, i.e. , at radii smaller than 2 . (cid:48)(cid:48) , where the com-pact emission has high peak temperature, large linewidth, andlarge integrated emission. This is reminiscent of the proper-ties of molecular gas in the inner 180 pc of our Galaxy (Morris& Serabyn 1996). Alternatively, Kohno et al. (1996) and Mat-sushita et al. (2004) interpret these as gas being entrained bythe AGN radio jet.We verified that the large linewidth of the extended compo-nent is not caused by the contribution from the error beams.Details are provided in the Appendix C.3.3.2.3. Azimuthal averages
Figure 14 shows the azimuthal average (and the associateddispersion) around the kinematic center of the deprojected im-ages of the peak temperature, the integrated emission, the ro-tational velocity, the modulus of the centroid velocity gradi-ent, and the line full width at half maximum computed for the1 (cid:48)(cid:48)
PdBI-only (blue curves), the 1 (cid:48)(cid:48) subtracted (red curves),and the 22 . (cid:48)(cid:48) IRAM-30m (green curves) cubes.For the compact emission (PdBI-only cube), the inner 5 (cid:48)(cid:48) clearly display high peak temperatures and large FWHMs,implying large integrated line emissions. The molecular ringdominates from ∼
10 to 40 (cid:48)(cid:48) , where the integrated emissionand the peak temperatures are larger than in the disk (radii4 P
ETY ET AL . Figure 13.
Comparison of the spatial distribution (from top to bottom) of the peak intensity, integrated intensity, centroid velocity, the line full width at halfmaximum ( i.e. , 2.35 times the standard deviation in velocity), and rms noise of the CO (1–0) emission for the hybrid synthesis (PdBI + 30m, left column) andthe PdBI-only (middle column) cubes at ∼ (cid:48)(cid:48) resolution, and the 6 (cid:48)(cid:48) -resolution subtracted cube (right column). The angular resolution is indicated by a circle inthe bottom left corner of each panel. The intensity scale is shown on the right-hand side of each panel. The major and minor axes are displayed as perpendiculardotted lines. The dotted circles show the two inner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the dashed circle indicates the start of the materialarms at a radius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013). larger than ∼ (cid:48)(cid:48) ). The peak temperature seems to increasefrom the ring to the outer disk, while the integrated emissionstays mostly constant outside r ∼ (cid:48)(cid:48) . On the other hand,the velocity FWHM decreases slightly from ∼
25 km s − at aradius of ∼ (cid:48)(cid:48) to 20 km s − at radii larger than ∼ (cid:48)(cid:48) .The extended emission (subtracted cube) has a typicalpeak temperature of 0.75 K in the central region and 0.5 Kin the disk. The FWHM decreases by a factor of 2 from ∼
100 km s − at 0 (cid:48)(cid:48) to ∼
45 km s − at 50 (cid:48)(cid:48) and it then variesbetween 40 and 50 km s − in the outer disk. Both propertiesresult in a regular decrease of the integrated emission from ∼
45 K km s − at the center to ∼
15 K km s − at 50 (cid:48)(cid:48) . It thenvaries between 10 and 15 K km s − .The compact emission has on average a peak temperaturetwice as large as the extended emission. In contrast, the ex- tended emission has a velocity FWHM at least twice as largeas the compact emission (except near the center). Both effectsalmost compensate to yield similar integrated line emissionsfor both components.The dispersion of the peak temperature and of the integratedemission is larger for the compact emission than for the ex-tended one. This is a consequence of the fact that the compactemission is structured at all scales down to or below the an-gular resolution while the filtered flux is structured mostly atscales larger than 36 (cid:48)(cid:48) . The dispersion of the FWHM measure-ment is similar in both the compact and extended emissions.Indeed, its azimuthal average is computed only where there isenough signal to define it ( i.e. , on a small fraction of 360 ◦ ),while the peak temperature and integrated emission are aver-aged over 360 ◦ (at least up to a radius of 85 (cid:48)(cid:48) ).AWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 14.
Deprojected azimuthal averages around the kinematic center forthe IRAM-30m (green curves), the PdBI-only (blue curves) and the subtrac-tion of the PdBI-only from the hybrid synthesis (red curves) cubes. The solidlines display the averages while the dashed lines give the azimuthal averagesplus/minus the azimuthal standard deviations. From top to bottom, the panelspresent the peak temperature, line integrated emission, the rotational velocity,the modulus of the centroid velocity gradient, and 2.35 times the line 2nd or-der moment as a function of radius. The vertical dashed lines indicate the twoinner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the verticaldotted line show the start of the material arms at a radius equal to 85 (cid:48)(cid:48) (Meidtet al. 2013). The radial zone where the averages are affected by edge effects(see Sect. 3.2.3) is highlighted in grey.
The rotation velocity of each component was measured byfitting tilted rings with fixed systemic velocity to the line-of-sight velocity field using the
GIPSY task
ROTCUR . In bothcases, we assume the kinematic center listed in Table 1, andwe adopt a constant position angle (173 ◦ ) and inclination(21 ◦ ), as estimated from the more radially extended H I emis-sion mapped at lower resolution by the THINGS project (seeColombo et al. 2013b, for more details). The middle blackcurve, labeled “Model”, is a 3-parameter fit of the measuredrotation curve. The inner part of this fit (inside 100 (cid:48)(cid:48) ) com-pares well with what we would expect if the stars (traced at3.6 µ m) dominate the baryonic mass (Meidt et al. 2013).The rotational velocity of the extended emission (red curve)is increasing almost monotonically with radius, while it oscil-lates twice for the compact emission (blue curve) as an ef-fect of the streaming motions and corotation resonances (andnot the bulge). Moreover, the centroid velocity of the ex-tended emission is typically closer to NGC 5194’s systemicvelocity by 50 km s − at radii smaller than 35 (cid:48)(cid:48) where an innerstellar bar dominates the dynamics. At larger radii, it over-laps the rotational velocity curve of the compact emission.The modulus of the centroid velocity gradient is around 6and 10 km s − / (cid:48)(cid:48) for the extended and compact components,respectively. Hence, the kinematics of the extended emis-sion vary much more smoothly on the plane of the sky thanthe kinematics of the compact emission, which is very muchaffected by streaming motions (This is further discussed inSect. 3.3.3).Any intrinsic behavior beyond a radius of 85 (cid:48)(cid:48) must be inter-preted with caution as the azimuthal averages reach the edgesof the field of view in its smallest dimension. Two effects hap-pen: 1) The noise increases sharply at the mosaic edges (seethe bottom left panel of Fig. 13), and 2) the azimuthal aver-ages miss the outside interarm regions, which occupy a largerand larger fraction of the area as the distance from the centerincreases. However, the comparison of the averages of the ex-tended and compact emission at each radius is meaningful asthe averages are made on the same ellipse portions.3.2.4. Kinematics along the major axis
Figure 15 compares the position-velocity diagrams alongthe major axis of the compact emission (PdBI-only, greencontours) and the extended (grey image) emission. The redcurve is the measured rotation curve. It matches well the over-all velocity variation along the major axis. The middle bluecurve is the 3-parameter fit of the measured rotation curve, im-plying an overall inclination of the galaxy on the plane of skyof 21 ± ◦ (see Sect. 3.2.3). The two other blue curves showthe same velocity model for inclinations of 15 ◦ and 27 ◦ , inorder to give an indication of the effect of inclination on thekinematics.This diagram confirms that the linewidth is much largerfor the extended than for the compact emission (with thepossible exception of the molecular gas at the center of thegalaxy). The extended emission has a parallelogram shapewith gas emitting at forbidden velocity in the [ − (cid:48)(cid:48) , + (cid:48)(cid:48) ] ra-dius range. This is a typical signature of nuclear bar kinemat-ics ( e.g. , Binney et al. 1991; Garcia-Burillo & Guelin 1995;Garcia-Burillo et al. 1999). The distribution of the extendedemission in PV-space might in addition or otherwise indicatethat it lags the compact emission. The parallelogram shapeis not symmetric, and emission is absent in the region near( + (cid:48)(cid:48) , −
25 km s − ). At and inside this position (and its mirror,6 P ETY ET AL . Figure 15.
Position-velocity diagrams of the extended emission (hybrid synthesis minus PdBI-only) imaged at 6 (cid:48)(cid:48) along 3 axes at PA = 173 ◦ (major axis, centralpanel), and 173 ± ◦ (left and right panels) shown in grey-scale. The scale is shown in the right-hand side (K [ T mb ]). The green contours (at levels 2, 4, 6, 8, 10K [ T mb ]) display the hybrid synthesis emission at 1 (cid:48)(cid:48) resolution. The red curve is the azimuthally averaged rotational velocity profile and the central blue curveis a smooth 3-parameters fit of the red curve with a fixed inclination of 21 ◦ . The two other blue curves diplay the same model but for an inclination of 15 ◦ and27 ◦ . The vertical lines show the two inner corotation resonances at a radius of 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) (Meidt et al. 2013). near − (cid:48)(cid:48) ), emission in the extended component that falls be-low the rotational velocities exhibited by the compact emis-sion (red curve) might arise with a genuine lag.3.3. Interpretation 1: Two CO disks – Thin and thick
After an intermediate summary of the main observationalproperties of the two CO emission components, we will trans-late them into physical properties of the gas traced by the CO (1–0) emission. To do this, we will first summarize theexpressions for the gas scale height, mid-plane pressure andgas density as a function of the gas and stellar surface den-sities and vertical velocity dispersions (Koyama & Ostriker2009). We will then discuss how to apply these expressionsto M51. In particular, we will show how the contribution ofthe streaming motions to the CO linewidth can be estimatedto derive an accurate vertical gas velocity dispersion.3.3.1.
Intermediate summary and consistency checks
The emission filtered out by the PdBI interferometer ac-counts for about half of the total flux imaged in the hy-brid (PdBI+30m) synthesis. The subtraction of the PdBI-only from the hybrid synthesis cubes shows CO (1–0) emis-sion mostly structured at angular scales larger than 36 (cid:48)(cid:48) , i.e. , ∼ . − near the major axis in the south-western galaxyquadrant, the peak brightness along the major axis rangesfrom 0.7 to 1.4 K in the northeast and 0.5 to 0.8 K in thesouth-western quadrant. This emission is thus faint and ex-tended. In contrast, the emission observed by the interferom-eter is compact and bright. Indeed, its brightness temperatureranges from 2 to 16 K with a median value of 2.5 K and itcovers less than 2% of the PAWS field of view. Rotationalvelocities estimated from the centroid velocity map of the ex-tended component are closer by 50 −
100 km s − to the sys-temic velocity than the ones of the compact component insidea circle of 35 (cid:48)(cid:48) radius. Outside this radius, the rotational ve-locities of both components have the same order of magni- Figure 16.
Dual Gaussian decomposition of the THINGS HI spectrum aver-aged over the PAWS field of view after having aligned all the individual spec-tra along the velocity axis according to their centroid velocity value.
Top:
Brightness of the average spectra as a black histogram. The dual Gaussianfit is displayed as the green line and the two individual Gaussians are shownin red and blue.
Bottom:
Residual brightness after subtraction of the dualGaussian fit.
Table 6
Results of the dual Gaussian fit (see Fig. 16).Gaussian T peak Velocity Width Area T mb ]) (kms − ) (kms − ) (Kkms − )1 5.7 − . ± . ± ±
132 7.2 + . ± . ± ± tude. But, the rotational velocity curve of the compact com-ponent oscillates around the modeled velocities, while the ro-tational velocity curve of the extended component smoothlyincreases and mostly lies below the modeled velocities. Theline FWHM of the extended component is twice as large asthat of the compact component.We made two additional consistency checks. First, CPROPS decomposes the 1 (cid:48)(cid:48) hybrid synthesis cube into twodifferent components: 1) “Clouds” which account for 55% ofthe total flux, and 2) “Intercloud” gas which “surrounds” theGMCs and accounts for the remaining flux (Colombo et al.2013a). These numbers remain stable when the analysis isAWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY (cid:48)(cid:48) hybrid synthesis cube. This decompositionresult reflects the fact that we have a faint extended compo-nent in addition to the bright compact CO emission. Second,we checked whether existing H I observations are consistentwith the possibility of having a narrow and broad linewidthcomponent. We started from the THINGS H I cube imaged at11 . (cid:48)(cid:48) × . (cid:48)(cid:48) resolution with natural weighting (Walter et al.2008), as it maximizes the signal-to-noise ratio. We appliedthe shuffle method of Schruba et al. (2011), i.e. , we shiftedeach spectrum of the H I cube to a common velocity scaleby removing the systematic velocity field structure as mea-sured from the centroid velocity. The spectra were then aver-aged over the PAWS field of view. Only a dual Gaussian canaccurately fit the H I spectrum. Figure 16 displays the shuf-fled, averaged spectrum, its Gaussian decomposition and theresiduals. Table 6 presents the quantitative results of the dualGaussian fit. The total flux is divided approximately equallyin both components while the FWHM is approximately twiceas large in one of the components. This is consistent with aseparation into two emission components with very differentlinewidths.3.3.2. Expressions for the gas scale heights, mid-plane pressures,and gas densities
Using the vertical momentum and Poisson equations aver-aged over the horizontal plane of the galaxy, Koyama & Os-triker (2009) obtained a second-order differential equation forthe averaged vertical density profile. Solving it, they showedthe averaged gas density ( ρ ) and pressure ( P ) are approxi-mately given by Gaussian profiles of the height z , i.e. , ρ ( z ) = ρ exp (cid:18) − z H (cid:19) and P ( z ) = P exp (cid:18) − z H (cid:19) . (1)In these equations, the gas scale height H is given by H = σ z √ π G ρ (cid:63) A + √ A + , (2)where σ z is the thermal plus turbulent velocity dispersion per-pendicular to the galactic disk, ρ (cid:63) is the stellar density, G isthe gravitational constant, and A is a dimensionless factor thatmeasures the relative densities of the gaseous and stellar disks.It can be expressed as A = (cid:115) G Σ ρ (cid:63) σ z , (3)where Σ gas is the gas surface density. Once the gas verticalscale height is known, the gas mid-plane density and pressurecan easily be derived with ρ = Σ gas √ π H and P = σ z ρ . (4)These expressions for the gas scale height, mid-plane pres-sure, and mid-plane density take into account 1) gravity forcesthat both the stars and gas exert, and 2) turbulent and thermalhydrodynamic pressures. However, they still are lower limitsas they neglect any contribution from the magnetic field.Finally, for an isothermal, self-gravitating stellar disk, thestellar surface density, the stellar volume density, the stellarvertical scale height, H (cid:63) , and the stellar vertical velocity dis-persion, σ (cid:63) , are linked via ρ (cid:63) = Σ (cid:63) H (cid:63) , and H (cid:63) = σ (cid:63) π G Σ (cid:63) . (5) The A factor can then be rewritten as A ∼ Q (cid:63) Q gas , (6)where Q (cid:63) and Q gas are the Toomre’s gravitational stability pa-rameters for the stellar and gas disks.3.3.3. Application to M51
Figure 17 displays how the previous expressions are ap-plied to the case of M51 as a function of galactocentric radiusfor the total gas at 22 . (cid:48)(cid:48) resolution (green curves), the ex-tended component at 6 (cid:48)(cid:48) resolution (red curves) and the com-pact component at 1 (cid:48)(cid:48) resolution (blue curves). Radial zoneswhere the results should be interpreted with caution are high-lighted in grey: 1) at radii larger than 85 (cid:48)(cid:48) , the azimuthal av-erages start to reach the edges of the observed field of view;and 2) from 0 to ∼ (cid:48)(cid:48) , the assumption that the stars are dis-tributed in a disk breaks down, so that the stellar scale heightand volume density are not well constrained (see below).The gas mass surface densities for each component arecomputed from the azimuthal averages of the CO (1–0) in-tegrated emission using the Galactic value of the X CO factorand taking into account the presence of helium. The stellarsurface density is derived from the 3.6 µ m emission (Meidtet al. 2012). The stellar velocity is computed following Bot-tema (1993) and Boissier et al. (2003) who showed that, for aflat exponential disk, it falls off from the central dispersion σ according to σ (cid:63) = σ exp (cid:18) − r H B (cid:19) , (7)where r is the galaxy radius and H B is the disk scale length ofthe B -band. McElroy (1995) estimates the central stellar ve-locity dispersion in M51 to be σ = 113 km s − and Trewhellaet al. (2000) estimates that H B = 2 .
82 kpc. This gives us an es-timate for the stellar scale height and volume density, accord-ing to Eq. 5. We emphasize that this assumes an isothermal,self-gravitating stellar disk. This assumption clearly breaksdown in the center of M51, where the bulge and nuclear bardominate, i.e. , at radii less than ∼ (cid:48)(cid:48) where the 3.6 µ m sur-face brightness profile exhibits steepening, and near the lo-cation of the bar corotation radius as estimated from gravi-tational torques (Meidt et al. 2013). In fact, the applicationof Eq. 5 results in a stellar scale height that decreases withradius from ∼ (cid:48)(cid:48) to the galaxy center. We therefore optedto adopt a constant, lower limit to the scale height inside thiszone by extrapolating the value given by Eq. 5 at a radius of45 (cid:48)(cid:48) inward.The vertical velocity dispersion of the gas can be estimatedas the line 2nd order moment for a face-on galaxy. The in-clination of M51 onto the line of sight is small but non-zero,implying that the line 2nd order moment is only a first orderapproximation. Indeed, the systematic motions averaged in-side the beam of the observations contribute to the line 2ndorder moment. This is more problematic in the case of M51because the streaming motions are known to be large for thisgalaxy. Appendix D shows that the vertical velocity disper-sion can be estimated as σ z ∼ (cid:10) ( v obs − v cent ) (cid:11) − (cid:20) | grad( v cent ) | θ . (cid:21) , (8)where (cid:104)(cid:105) symbolizes the brightness-weighted average over theline profile, v obs is the velocity projected along the line of8 P ETY ET AL . Figure 17.
Azimuthal averages around the kinematic center, from top to bottom:
Mass surface densities, vertical velocity standard deviations ( i.e. , line fullwidth at half maximum divided by 2.35), gas-to-stellar density ratios (A factor), gas thermal + turbulent mid-plane pressures, gas mid-plane densities, verticalscale heights for the stars (pink curves), the IRAM-30m (green curves), the PdBI-only (blue curves) and the subtracted (red curves) cubes. The bottom paneldisplays the ratios of the scale heights (black) and mid-plane densities (cyan) computed from the PdBI-only and subtracted data sets. The horizontal lines indicatestypical values of the different parameters for the compact and extended components. The vertical dashed lines indicate the two inner corotation resonances atradii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the vertical dotted line show the start of the material arms at a radius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013). The radial zones wherethe results should be interpreted with caution (see Sect. 3.3.3) are highlighted in grey.
AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 18.
Joint distributions of the line 2nd order moment as a function ofthe centroid velocity gradient modulus times the half primary beam width forthe 30m (left), PdBI-only (middle) and subtracted (right) cubes. The lineshave a slope of 0.2 (green, solid), 0.5 (green, dashed), 1 (black, solid), 2 (red,dashed), and 5 (red, solid). sight, v cent the line centroid velocity, | grad( v cent ) | the modu-lus of the gradient of the centroid velocity, and θ the resolu-tion beamwidth of the observations. In this equation, the firstterm is the square of the second moment and the second termestimates the contribution of unresolved systematic motions.Figure 18 diplays the joint distributions of these two quan-tities for the IRAM-30m cube and the 1 (cid:48)(cid:48) PdBI-only and sub-tracted cubes. At the resolution of the IRAM-30m data, theunresolved systematic motions contribute significantly to thevalue of the second moment. This behavior is clearly splitin the decomposition between compact and extended com-ponents at 1 (cid:48)(cid:48) . The unresolved systematic motions are neg-ligible for the extended component. For the compact com-ponent, they contribute to less than 34% of the linewidth for50% of the data. Hence, the streaming motions are seen inthe compact component but they are not seen in the extendedcomponent. We stress that the subtracted cube measures theextended component at an angular resolution of 1 (cid:48)(cid:48) becauseit results from the subtraction of two cubes whose resolutionis 1 (cid:48)(cid:48) , namely the hybrid synthesis and the PdBI-only cubes.Beam smearing of unresolved systematic motions must there-fore be considered only at angular scales lower than 1 (cid:48)(cid:48) . As acorollary, if the large linewidths are due to beam smearing ofunresolved streaming motions, then the linewidths should de-crease when increasing the imaging angular resolution. Thiseffect is observed in both the hybrid synthesis and PdBI-onlycubes (panels [j] and [k] of Fig. 32 to 34), while the sec-ond moment of the subtracted cube (panels [l] of the samefigures) stays basically constant when increasing the angularresolution from 22 . (cid:48)(cid:48) to 1 (cid:48)(cid:48) . We thus deduced that the largelinewidths of the extended component are not caused by un-resolved streaming motions.As the unresolved systematic motion can be larger than thesecond moment for the compact component, we only usedthe second moments to compute the vertical velocity disper-sion, implying that the scale heights and mid-plane pressuresderived are slightly more robust for the extended componentthan for the compact component and the IRAM-30m data.3.3.4. Results
Using these inputs, we computed the stellar vertical scaleheight, and volume density. We also computed the gas-to-stellar density ratio ( A factor), the gas mid-plane pressures,densities, and scale heights for all the molecular gas (using theIRAM-30m data), the compact component (using the PdBI-only data), and the extended component (using the subtractedcube). We neglect the contribution from atomic gas traced byH I emission, as this gas represents only between 2.5 and 30%of the molecular gas mass for radii from 0 to 130 (cid:48)(cid:48) (see Fig. 42 of Leroy et al. 2008; Schuster et al. 2007).Our estimates agree very well with expectations. For ex-ample, the A factor is less than 1 for the extended compo-nent, while it is equal to ∼ . Q compact ∼ . Q extended , where Q compact and Q extended are theToomre factors for the compact and extended components,respectively. Said otherwise, the compact component is morelikely to form stars than the extended component. The gasmid-plane pressure is about the same for both components andfor the total gas. This probably reflects pressure equilibrium.From the mid-plane pressure, we estimate a molecular frac-tion Σ H / Σ H I close to what is observed: Using the empiricalformula which relates the molecular fraction Σ H / Σ H I to themid-plane pressure (Blitz & Rosolowsky 2006) Σ H / Σ H I = (cid:18) P . × K cm − (cid:19) . , (9)we find a molecular fraction of ∼
26 and ∼ ∼
40 pc between ∼ . ∼
20 and 40 pc beyond ∼ . ∼
10 pc at ∼ . ∼ . . ∼ cm − , respectively. Forreference, the distribution of the molecular gas density in theSolar Neighborhood is (Ferrière 2001; Cox 2005) n H cm − = 0 .
29 exp (cid:2) − ( z / (cid:3) , (10) i.e. , a scale height of 57 pc(= 81 pc / √
2) and a mid-plane gasdensity of 0.29 H cm − . The volume density is several ordersof magnitude smaller than the expected densities of moleculargas. This is due to the fact that the molecular gas fills a smallfraction of the galactic volume.3.4. Interpretation 2: A mixture of dense and diffuse gas
The averaged volume density of the compact component istypically one order of magnitude larger than the one of the ex-tended component, pointing toward different kinds of molec-ular gas. In this section, we recall that 1) bright CO (1–0)emission traces diffuse as well as dense gas, and 2) the valueof the T ( CO) / T ( CO) ratio may be used to discriminatebetween dense and diffuse gas. We will then check this ratiofor M51.3.4.1.
Bright CO (1–0) emission also traces diffuse gas
Bright CO (1–0) emission is generally associated withdense cold (typically n ∼ − cm − and T ∼ −
20 K)0 P
ETY ET AL . Figure 19.
Joint distributions of the CO (1–0) emission as a function of the CO (1–0) emission.
Top row:
Brightness integrated over the line profile.
Bottomrow:
Brightness in 5kms − channels. Contour levels are set to 2, 4, 8, ... 2048 and 8, 16, 32, ... 2048 points per pixel respectively for the top and bottom rows. First column:
Full field-of-view (black contours).
Second column:
Radii below 35 (cid:48)(cid:48) (red contours).
Third column:
Radii between 35 (cid:48)(cid:48) and 150 (cid:48)(cid:48) (greencontours).
Fourth column:
Radii larger than 150 (cid:48)(cid:48) (blue contours). The 3 same straight lines display 3 different CO/ CO emission ratios on each panel: 7(red), 8.3 (green) and, 11 (blue). molecular gas, where all hydrogen is molecular and all car-bon is locked in CO. However, Pety et al. (2008) and Lisztet al. (2009) found surprisingly bright CO (1–0) lines (up to ∼
10 K) in the nearby environment of Galactic diffuse linesof sight (A v ∼ i.e. , C + . Liszt et al. (2010) explain such large CObrightnesses in diffuse warm gas (typically n ∼ −
500 cm − and T ∼ −
100 K) by the fact that the gas is subthermallyexcited gas. Indeed, large velocity gradient radiative trans-fer methods (Goldreich & Kwan 1974; Scoville & Solomon1974) show that 1) W CO / N CO is large because of weak COexcitation in warm gas (50-100 K), and 2) W CO ∝ N CO untilthe opacity is so large that the transition approaches thermal-ization. Hence, relatively bright CO lines may at least traceeither diffuse warm or dense cold molecular gas.This is surprising because it is often argued that CO can-not survive outside dense molecular gas since chemical mod-els predict that several magnitude of visual extinction arerequired so that CO survives photo-dissociation. However,many absorption measures in the UV and millimeter domainsshow that CO is present in gas whose hydrogen column den-sity is as low as 10 cm − (Liszt 2008; Sheffer et al. 2008;Sonnentrucker et al. 2007). The key point here is that theCO chemistry in diffuse gas is still far from being under-stood. Sonnentrucker et al. (2007) found that a plot of thelog( N CO ) as a function of the log( N H ) can only be cor-rectly fitted by two power-law relationships, with a break at( N CO = 1 . × cm − , N H = 2 . × cm − ), correspond-ing to a change in the production route for CO. The produc-tion routes of CO are well understood only in the regime of higher density gas. In diffuse gas, Liszt & Lucas (2000) andLiszt (2007) showed that if the amount of HCO + observed inthe diffuse gas is fixed as a model parameter, it is easy to getlarge amount of CO in UV illuminated gas through electronrecombination of HCO + HCO + + e − → CO + H . (11)Visser et al. (2009) later confirmed this result. The next (stillunsolved) question is how large quantities of HCO + form inthe diffuse gas.3.4.2. The value of the T ( CO ) / T ( CO ) ratio may discriminatebetween dense and diffuse gas As bright CO (1–0) lines may be associated with diffuse ordense gas, this line alone cannot be used to differentiate bothscenarios. Liszt et al. (2010) argue that the T ( CO) / T ( CO)ratio can discriminate diffuse and dense gas. Indeed, fromwide ( ∼ . ◦ ) CO and CO (1–0) maps of the Galacticplane, Polk et al. (1988) measured an average ratio of line in-tensities R = T ( CO) / T ( CO) of 6 . ± .
7. Matching thebeam areas at the two frequencies introduces an upward cor-rection factor of 1.1, i.e. , R = 7 . ± .
8. This value is higherthan the typical factor measured for the core of Giant Molec-ular Clouds, i.e. , ∼ − e.g. Frerking et al. 1982). Us-ing the observational fact that T ( CO) / T ( CO) ∼ − e.g. Knapp & Bowers 1988),Polk et al. (1988) deduced that this diffuse gas componentsignificantly contributes to the large-scale CO emission ofthe Galaxy. More recently, Goldsmith et al. (2008) deducedfrom CO and CO wide-field mapping of the Taurus giantmolecular cloud that about half the mass of the gas traced byAWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY CO (1–0) emission comes from diffuse gas.The radiative and chemical properties of CO explain thelarge values of this ratio in diffuse molecular gas. From mea-surements of CO absorption lines against extra-galactic con-tinuum background sources, Liszt & Lucas (1998) showedthat in local diffuse clouds, the ratio of CO and CO col-umn densities is in the range 15 ≤ N ( CO) / N ( CO) ≤ N ( CO). Hence, thisratio usually differs strongly from the local interstellar ratioof the C elemental abundances, typically C / C = 60. Thevalue of the N ( CO) / N ( CO) ratio is due to the competi-tion between the fractionation of CO with C + and selectivephoto-dissociation of the two CO isotopologues (Liszt 2007).Fractionation of CO with C + , i.e. , CO + C + ↔ CO + C + , (12)enriches CO in CO. But selective photodissociation ( i.e. , thefact that CO better self-shields from UV illumination than CO) more than counters this effect in diffuse gas.3.4.3.
In M51
Figure 3 indicates that the morphology of the CO and CO moments are strikingly similar where both tracers aredetected. To quantify this, Fig. 19 shows bi-dimensional his-tograms of the integrated intensity (top row) and brightness(bottom row) of the CO (1–0) versus CO (1–0) emission.Both sets of histograms display similar linear relationshipswhose width is typically related to the noise levels of bothtracers. The left column displays the histogram computed forthe full field of view, while the three other columns show howthis histogram decomposes as a function of radius. For ref-erence, we drew the same three lines on all histograms. Theslope of these lines were chosen to follow the ridges of thebrightness histograms in the different radial ranges.While the typical value for the CO / CO ratios is about8, there is a slight but significant increase of this ratio fromthe inside to the outside of the galaxy: This ratio is typically7 (blue lines and histograms) for radii below 35 (cid:48)(cid:48) , 8.3 (greenlines and histograms) for radii between 35 and 150 (cid:48)(cid:48) and 11(red lines and histograms) for radii beyond 150 (cid:48)(cid:48) . For com-parison, this ratio increases from 4.6 to 10.0 across the Milky-way molecular ring, i.e. from 0.5 R (cid:12) to R (cid:12) (Liszt et al. 1984).This was an early indication that molecular gas near the SolarCircle has a high proportion of diffuse material.At the angular resolution of the IRAM-30m (22 . (cid:48)(cid:48) ), the T ( CO) / T ( CO) increases from 6 to 11 with a typical valueof ∼ C]/[ C] elementalratio, the comparison with our Galaxy points towards the in-terpretation that a significant fraction of the CO emitting gasis diffuse. Is this visible in the emission of C + ? Nikola et al.(2001) published the first map of the 158 µ m [C II ] emissionat 55 (cid:48)(cid:48) resolution for M51 obtained with the Kuiper AirborneObservatory. The interpretation of this emission is difficultbecause it originates mostly from the warm ionized medium,though the cold neutral medium contributes significantly tothe [C II ] emission. In the cold neutral medium, the density so-lution is degenerate, i.e. , the medium could have either a low( ∼ −
300 cm − ) or a high (10 − cm − ) density. Theyconclude that “A large fraction of the overall [C II ] emissionin M51 can originate in an underlying extended medium.”A 12 (cid:48)(cid:48) -resolution [C II ] maps was observed as part of a Her-schel/PACS guaranted time project (PI: C. Wilson, Parkin et al., in prep.). The comparison of this map with the 22 . (cid:48)(cid:48) decomposition between compact and extended sources (seeFig. 35) will probably shed light on the origin of the [C II ].3.5. Discussion
Here we discuss the structure of the gas that emits the ex-tended component — in particular the fact that it could besubstructured like drops in fog — and the amount of gas thatis extra-planar. We then summarize results about extra-planargas traced in H I and CO. We finish with a discussion of thepossible origin of extra-planar CO emission.3.5.1. Structure of the extended component
Giant molecular clouds are often thought to be composed ofsmall clumps that are unresolved, i.e. a set of point sources.Hence, the interferometer should recover all the flux of thisset of point sources and short-spacings should not be neededfor extra-galactic observations. This argument is incorrect fortwo reasons. The first reason is that the limited sensitivityof the interferometers limits the power of deconvolution torecover the flux of point sources at low signal-to-noise ratio(See Sect. 2.3.2 and 2.3.3).The second reason why the PdBI-only data may not recoverthe full flux of the source is more fundamental. We first as-sume that the source is a set of unresolved components fillinga volume that projects onto a plane-of-sky area larger thanthe interferometer primary beam. If the unresolved compo-nents are typically separated by an angular distance largerthan the synthesized beamwidth, the interferometer will in-deed recover all the flux because the GMC is observed as aset of separated point sources. In contrast, the interferometerwill filter out most of the source flux when the typical angu-lar separation between the unresolved components is smallerthan the synthesized beamwidth because the source emissionappears like a flat source. Well known examples of this ef-fect are 1) fog which appears flat while made of water drops,and 2) a XIXth century pointilliste painting which appears flatwhen unresolved by the eye. For this reason, it is not possibleto know before the observation of large complex sources likenearby galaxies whether the short-spacings will be needed,and multi-resolution
CLEAN algorithms cannot help to solvethis ambiguity.To explore this further, we speculate that the CO extendedcomponent is made of diffuse gas as found in the envelopesof giant molecular clouds. This gas would have a typicalmid-plane density (cid:46) − , and a temperature (cid:46)
200 K.In such conditions, the CO (1–0) is subthermally excited.Moreover, Sect. 3.3.4 indicates that the average volume den-sity is 1 cm − , implying a typical volume filling factor of0.1%. The structure of this gas is probably filamentary, asobserved in our Galaxy.3.5.2. Vertical mass distribution and extra-planar gas
Figure 20 displays the vertical distribution of the moleculargas volume density, its decomposition into two componentsof different scale heights, and the percentage of mass above agiven galactic height | z | . In order to sample a large fraction ofthe sensible parameter space, we computed 4 different cases:Two fractions of flux in the extended component (either 30or 50%) and two scale height ratios (5 and 10) between thecompact and extended components. We see that the fractionof flux in both components has a significant impact on thegas distribution close to the galatic mid-plane. However, the2 P ETY ET AL . Figure 20. First and third columns:
Vertical distributions of the total volume density (green), decomposed into the sum of two Gaussian of different scaleheight. The broad and narrow Gaussian are respectively called diffuse (red) and dense (blue).
Second and fourth columns:
Percentage of the vertical mass abovea given altitude in scale height unit of the dense Gaussian for the total distributions plotted in the first and third columns. The vertical lines indicate the altitudesabove which 1% (red), 3% (green), 10% (blue), 33% (cyan), and 100% (yellow) of the mass is located. The ratio of the integrated masses of the diffuse over thetotal (diffuse+dense) are 0.3 for the top row and 0.5 for the bottom row. The two right (respectively left) columns are for a diffuse scale height 5 (respectively 10)times higher than the dense scale height. This allows us to quantify the mass of molecular gas which is extra-planar in different scenarii. percentage of the total mass above a given height z is onlymarginally affected. In contrast, doubling the ratio of the scaleheight doubles the galaxy height above which a given mass islocated. For instance, if we assume that the smallest scaleheight is 40 pc and a scale height ratio of 5, only 2% of thetotal mass is above 400 pc while this proportion increases to20% when the scale height ratio is 10. We thus estimate thatbetween 2 and 20% of the molecular gas is extra-planar, i.e. itlies at a galactic height at least 10 times larger than the scaleheight of the dense molecular gas.3.5.3. H I thick disk Lagging, thick H I layers have long been detected in externalgalaxies (see, e.g. , Boomsma et al. 2005; Barbieri et al. 2005;Oosterloo et al. 2007; Boomsma et al. 2008, in NGC 253,NGC 4559, NGC 891 and NGC 6946). The H I gas in thesegalaxy halos amounts to 3-30% of the total H I mass. For edge-on galaxies, the H I emission extends up to 12-22 kpc from thegalactic mid-planes.Miller et al. (2009) studied the prototypical face-on spi-ral galaxy M83. They found a spatially extended compo-nent rotating in the same sense but 40-50 km s − more slowlyin projection, with a line-of-sight velocity dispersion of 10 −
15 km s − . The spatially extended structures are coincidentwith the optical spiral arms. They interpreted this compo-nent as a vertically extended disk rotating in the same sensebut about 100 km s − more slowly than the kinematically cold,thin disk. It contains 5.5% of the total H I mass within thestellar disk of the galaxy.3.5.4. A CO thick disk in the edge-on NGC 891 galaxy
Among the previous galaxies, NGC 891 is particularly in-teresting. Its characteristics are very similar to the Milky Wayand Garcia-Burillo et al. (1992) found in this system the firstevidence for extra-planar CO emission in an edge-on galaxy.They detected molecular emission 1-1.4 kpc above the disk, wide-spread along the major axis. The associated Gaussianscale height is ≥
600 pc, i.e. typically 2 to 3 times larger thanthat deduced here for M51. This CO scale height is confirmedby a new IRAM/HERA map, which now images most of thethick disk of the galaxy (Garcia-Burillo et al., in prep.), andit is consistent with the scale height derived from the PAHemission (Rand et al. 2008).Garcia-Burillo et al. (1992) estimate this halo emission rep-resents less than 20% of the molecular mass in the disk. How-ever, they also state that 40 to 60% of the thin disk emissionmust be in a low density component (diffuse gas) to explainthe typical value (8.5) of the ratio of the CO (1–0) to CO(1–0) brightnesses. Hence, the halo molecular emission couldbe the tip of an independent component mixed with the densemolecular thin disk. In this case, the extended componentwould amount for a much larger fraction of the entire molec-ular gas. Indeed, in a follow-up study Sofue & Nakai (1993)mapped the molecular gas at a distance of 3.5 kpc from NGC891’s galaxy center, i.e. , at the ring northern side. Using a dualGaussian fit through the emission profile extracted perpendic-ular to the galaxy plane, they estimate 1) that the extendedcomponent has a typical scale height of 2.1 kpc and 2) that itcould account for 50% of the entire molecular gas.3.5.5.
A diffuse CO thick disk in our Galaxy?
Mapping 3 strips at constant longitude within a latituderange of [ − . ◦ , + . ◦ ], Dame & Thaddeus (1994) detecteda thick molecular disk in the inner Galaxy about 3 times aswide as that of the dense central CO layer, and comparable inwidth to the thin H I layer, i.e. the height profile can be fittedwith a Gaussian FWHM of ∼
230 pc. This data also suggeststhat the high latitude gas lies mainly above the spiral arms.The mass of this gas would be 15% of the total if it belongs toa distinct molecular component.Combining E B − V reddening, H I absorption and CO emis-sion measurements along many diffuse lines of sight in theMilky Way, Liszt et al. (2010) recently found that the COAWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY molecule for diffuse gas is standard, i.e.X CO = 2 . × cm − / (K km s − ). This standard value wasintroduced by Polk et al. (1988) to take into account the con-tribution of the diffuse gas to the X CO factor. Liszt et al.(2010) and Liszt & Pety (2012) then deduced that the dif-fuse gas contribution to the total CO luminosity seen lookingdown on the Milky Way is 0.47 K km s − to be compared to0.75 K km s − , the result from Galactic surveys. Hence, thecontribution of diffuse gas to the total CO luminosity in ourGalaxy would be between 39% (= 100 × . / (0 . + . × . / . − . In addition, they have been mostly observed be-fore the advent of wide bandwidth receivers/spectrometers,which were installed in current facilities from ∼ ∼
300 km s − . Fi-nally, the extension of the diffuse component we detect inM51 is large, several hundred of parsecs. Hence, such a com-ponent in our Galaxy could have been confused with low levelbaselines in wide-field CO surveys.3.5.6. Possible origin of the extra-planar CO emission
The following three scenarios are typically evoked to ex-plain gas outside the disk (e.g. Putman et al. 2012): expelledgas from the disk via galactic fountains or chimneys, accre-tion from the inter-galactic medium and/or tidal debris fromgalaxy interactions. Except for the first scenario, it is expectedthat the involved component reaches very large (more than afew kpc) scale heights.Therefore we focus in the following discussion on observa-tional and theoretical evidence for a potential flow of densecold material from the disk to the halo caused by massive starformation. The most extreme case to be considered might bemolecular outflows driven by stellar winds or nuclear AGN,as seen, e.g., in CO in the nearby starburst galaxy M82 (Wal-ter et al. 2002), and recently by Herschel in several nearby(U)LIRGs (Sturm et al. 2011). However, typically these phe-nomena are restricted to the centers of galaxies.Evidence for dense material outside the thin disk comesfrom observations of distinct optical extinction features inedge-on galaxies that trace extra-planar dust. Howk (2005)summarizes the findings on extra-planar dust in nearby galax-ies: extra-planar dust is found out to scale heights of z ≤ n (H) >
25 cm − . Inthis context the detection of abundant extra-planar PAH emis-sion is interesting. Rand et al. (2011) find PAH emission outto ∼ . − µ m H line out to distances of 2 kpc intheir targets. They speculate that massive star formation in thedisk is the cause for the extra-planar cold interstellar mediumdetected.The resolved CO emission in M51 is preferentially foundalong the convex side of the spiral arms where massive starformation is ongoing and has an inferred scale height of z ∼
200 pc. These two findings are very similar to resultsof the studies of extra-planar dust and PAH emission. Thuswe speculate that indeed star formation via galactic fountains or chimneys has transported some of the molecular materialaway from the disk.Several simulations of disk galaxies with star formationalso suggest that this explanation might be valid. The simula-tions have shown that cold ( T (cid:46)
200 K), dense gas can reachheights of 100 −
200 pc above the plane, but only when stellarfeedback is included (Wada 2008; Koyama & Ostriker 2009;Dobbs et al. 2011; Acreman et al. 2012; Hill et al. 2012).Dobbs et al. (2011) find the scale height of the cold gas is ∼ −
100 pc, depending on the level of feedback in the simu-lation. From the top panel of Figure 9 of Dobbs et al. (2011),it is seen that gas at heights of a few 100 parsecs is around10 − − − g cm − or 20 −
200 H cm − ). Gas at these den-sities is not typically molecular. However, the top of Figure14 of Dobbs et al. (2008) shows that gas which has alreadybeen dense and molecular can retain a high molecular frac-tion down to densities of ∼ cm − before the H is pho-todissociated. Thus the simulations indicate that a possibleexplanation of an extended diffuse component is that stellarfeedback pushes gas out to large distances above the plane,but this gas remains molecular. The likelihood of this de-pends on the gravitational contribution from the stars/gas inthe vertical direction, the local chemistry of H formation anddestruction, the effects of the stellar feedback and the surfacedensity of the gas. SUMMARY AND CONCLUSIONSWe described in detail the calibration and construction ofthe PAWS CO (1–0) imaging of the central ∼ × ∼ (cid:48)(cid:48) × (cid:48)(cid:48) ) in M51, using observations from both thePdBI and 30m telescope. The achieved spatial resolution of40 pc (1 . (cid:48)(cid:48) ) is close to the typical size of galactic GMCs,and at least 10 times smaller in area than previous interfer-ometric maps obtained at OVRO, BIMA and CARMA (Aaltoet al. 1999; Helfer et al. 2003; Koda et al. 2011). Themedian brightness sensitivity of 0.4 K in 5 km s − channelspacing corresponds to 8 . (cid:12) pc − . The total flux in thePAWS field of view and in a velocity range of ±
120 km s − around the LSR systemic velocity is 64% of the total M51flux of 1 . × K km s − pc , i.e. , a molecular gas mass of6 . × M (cid:12) (helium included). The mean CO integrated in-tensity and molecular mass surface density inside the PAWSfield of view are 18 K km s − and 77 M (cid:12) pc − , respectively.The interferometer recovers only (50 ± (cid:48)(cid:48) ). Hence, the flux is about equally distributedinto a spatially extended and a spatially compact component.Using the hybrid synthesis (PdBI+30m) and the PdBI-onlydeconvolved results, we established that the extended compo-nent has the following properties: 1) It has a median bright-ness temperature of 0.14 K, about 18 times fainter than thecompact component. 2) It covers about 30% of the PAWSfield of view, about 15 times as much as the compact compo-nent. 3) Its plane-of-sky kinematics evolves smoothly, whileplane-of-sky kinematics of the compact component are moreaffected by streaming motions. 4) Its linewidth is typicallytwice as large as that of the compact component. 5) Outsidethe region dominated by the galaxy bulge and inner nuclearbar, its typical scale height is ∼
200 pc, or five times the com-pact component scale height. 6) Its typical gas mid-planepressure is ∼ (2 − × K cm − , in approximate pressureequilibrium with the compact component. 7) Its typical av-erage mid-plane gas volume density is ∼ cm − , 10 times4 P ETY ET AL .less dense than the compact component.We estimated between 2 and 20% of the total molecularmass to be extra-planar, i.e. at galactic heights larger than400 pc. We emphasized that, while the emission of the ex-tended component is mostly structured at spatial scale largerthan 36 (cid:48)(cid:48) , it is probably made of unresolved filamentary struc-tures, which could typically fill 0.1% of the volume of theextended component. The T ( CO) / T ( CO) ratio at 23 . (cid:48)(cid:48) resolution ranges from ∼ ∼
11 when going from the in-ner to the outer part of the galaxy, in agreement with a mixtureof dense and diffuse gas evolving from completely molecularin the inner galaxy to half atomic in the outer galaxy.Atomic thick disks are very common. Evidence for amolecular thick disk exists in at least the edge-on NGC 891galaxy. A thick molecular disk about 3 times as wide as thedense central CO layer was detected in the inner part of ourGalaxy. We thus interpret the extended component of M51as a diffuse CO thick disk. The underlying physical inter-pretation of the CO (1–0) emission is different. If the gasis dense, it fills a small fraction of the interstellar volume; itis confined by ram or turbulent pressure (if not gravitation-ally bound); and it is on the verge of forming stars. If thegas is diffuse, it is a warmer, low pressure medium filling alarge fraction of the interstellar volume; it contributes morethe mid-IR or PAH emission; and it is probably not gravition-ally bound or about to form stars.We thank the IRAM staff for their support during the ob-servations with the Plateau de Bure interferometer and the30m telescope. DC and AH acknowledge funding fromthe Deutsche Forschungsgemeinschaft (DFG) via grant SCHI536/5-1 and SCHI 536/7-1 as part of the priority program SPP1573 ’ISM-SPP: Physics of the Interstellar Medium’. CLDacknowledges funding from the European Research Councilfor the FP7 ERC starting grant project LOCALSTAR. TATacknowledges support from NASA grant
Agence Nationalede la Recherche as part of the SCHISM project ( http://schism.ens.fr/ ). ES, AH and DC thank NRAO for theirsupport and hospitality during their visits in Charlottesville.ES thanks the Aspen Center for Physics and the NSF Grant
Facilities:
IRAM:Interferometer, IRAM:30m.APPENDIX A. CO LUMINOSITY AND MOLECULAR GASMASSESA.1.
Computations
The CO luminosity, L CO , is estimated from the main beamtemperature, T mb , as L CO = (cid:88) l , m , v T mb ( l , m , v ) ∆ lmv , (A1)where ( l , m , v ) are the indices of the position, position, veloc-ity data cube and ∆ lmv is the volume of one pixel of this cube computed as ∆ lmv = ∆ v (cid:34) ∆ l (cid:48)(cid:48) ∆ m (cid:48)(cid:48) (cid:18)
37 pc D . (cid:19) (cid:35) . (A2)The uncertainty on this luminosity is computed as δ L CO = (cid:115)(cid:88) l , m , v η ( l , m , v ) δ T ( l , m , v ) ∆ lmv , (A3)where δ T mb ( l , m , v ) is the noise level for the pixel ( l , m , v ) and η ( l , m , v ) is the factor which reflects the correlations betweenpixels. If we assume that the noise level is independent of thevelocity channel and that the velocity channels are uncorre-lated, we obtain δ L CO = (cid:115)(cid:88) l , m n v ( l , m ) η ( l , m ) δ T ( l , m ) ∆ lmv , (A4)where n v ( l , m ) is the number of velocity channels for the po-sition (l,m). The correlation between spatial pixels can beapproximated as the inverse of the number of pixels in theresolution area, i.e. , η ( l , m ) = 8 log(2) ∆ l ∆ m π Θ θ , (A5)where Θ and θ are respectively the FWHM major and minoraxes of the Gaussian beam. It is independent of the pixel po-sition ( l , m ).The mass of the associated molecular gas, M H , is then M H ± δ M H = X CO ( L CO ± δ L CO ) , (A6)where X CO is the CO-to-H conversion factor. We will use thestandard Galactic conversion factor X CO = 2 . × H cm − / (K km s − ) (A7)= 4 .
35 M (cid:12) pc − / ( K km s − ) . (A8)The last value includes a factor of 1.36 by mass for the pres-ence of helium. A.2. Applications to M51
The direct sum of the pixel brightness over the fieldof view observed with the IRAM-30m map and betweenthe [ − , + − velocity range indicates that the to-tal CO luminosity of M51 (including the companion) is1 . × ± × K km s − pc . The same computation inthe [ − , + − velocity range (where mainly M51aemits) gives 1 . × ± × K km s − pc . Finally, thedirect sum of the pixel brightness over the field of view wherethe line integrated emission is measured with a signal to noiseratio larger than 3 gives 1 . × ± × K km s − pc .It is clear that the uncertainty on the result decreases whenthe summed volume of the cube is reduced because most ofthe original volume is devoid of signal. But reducing the vol-ume introduces some kind of bias. However, the total lumi-nosity does not vary significantly in both three results. Wethus assume that most of the signal is contained within thesmallest volume probed here. This in particular implies thatthe luminosity associated with the companion but outside the[ − , + − velocity range is negligible. The uncer-tainties are small compared to the absolute flux uncertaintyAWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Table 7
Total CO flux measured within the PdBI+30m data cube, as measured fromintegrated intensity images constructed using different techniques to isolatesignificant emission (see text).Method Parameters Total CO luminosity[ × Kkms − pc ]Direct sum [ − , + ]kms − Sigma-clipping T mb > σ T mb > σ T mb > σ T mb > σ T mb > σ t , p ) = (3 , .
2) 10( t , p ) = (3 ,
2) 6.9( t , p ) = (4 , .
2) 7.6( t , p ) = (4 ,
2) 5.8( t , p ) = ( , . ) ( t , p ) = (5 ,
2) 5.6Smooth & mask ( θ , m ) = (2 . ,
3) 8.7( θ , m ) = (2 . ,
5) 5.6( θ , m ) = (2 . ,
3) 8.7( θ , m ) = (2 . ,
5) 6.0( θ , m ) = (3 . ,
3) 8.7( θ , m ) = (3 . ,
5) 6.4( θ , m ) = (3 . ,
3) 8.6( θ , m ) = ( . , ) H I prior 10kms − window 3.220kms − window 5.0 kms − window 8.0 Combined ( (cid:46) i.e. , 1 . × pc . The associated total mass,mean brightness, and mass surface density are respectively6 . × M (cid:12) , 7 . − , and 33 M (cid:12) pc − . These values aresummarized in Table 1.The direct sum of the pixel brightness over the PAWS fieldof view and between the [ − , + − velocity rangeindicates that the final hybrid synthesis data cube containsa total CO luminosity of 9 . × K km s − pc . This corre-sponds to a molecular gas mass of 4 . × M (cid:12) . The to-tal surface covered was 10.5 square arcminutes, i.e. . × pc . The mean brightness and mean surface density arerespectively 18 K km s − and 77 M (cid:12) pc − . B. MASKING TECHNIQUESIn the previous section, we have seen that the line 0th or-der moment is much noisier when the velocity range used forintegration includes a large number of channels devoid of sig-nal. This effect is amplified when computing the line 1st and2nd order moments. It is thus desirable to limit the velocityrange of integration to channels where signal is detected. Asthe systematic motions are large for a galaxy, using a singlevelocity range for all the sky positions unavoidably impliesmoving the velocity range of integration from position to po-sition. Defining such moving velocity ranges is never straight-forward. In the case of the PAWS hybrid synthesis data set, itis even more complex because a large fraction of the flux liesat brightnesses barely detected (1 to 3 σ ).Moreover, masking out noisy channels always implies the risk to bias the result. We therefore explored several alterna-tive masking methods. In order to quantify the benefit overcost of different techniques, we compare the noise and signalaspects of 0th order moments images (Fig. 21) and the totalluminosity found inside the kept velocity channels (Table 7).Direct sum over a given velocity range produces an integratedintensity map that is dominated by noise (see Fig. 21[a]) be-cause CO emission is typically only detected in a few velocitychannels along each line-of-sight. But it produces a robust es-timate for the total CO luminosity.The first alternative we tried is a simple sigma-clipping method, whereby pixels containing emission with low signif-icance were excluded. We tested various brightness thresh-olds between 1 and 5 σ , where σ is the standard deviationof the noise fluctuations estimated using ∼
25 emission-free channels for each line-of-sight. The integrated inten-sity images were constructed by summing all unmasked (i.e.‘good’) pixels across the observed LSR velocity range, i.e.[ − . , + .
5] km s − . As expected, lower thresholds pro-duce maps that are dominated by noise peaks, especially inthe interarm region. Higher thresholds produce maps with acleaner appearance, but also do a poorer job of recovering thetotal luminosity (see Table 7). For thresholds above ∼ σ ,it is evident that genuine low surface brightness emission inthe interarm region is omitted. A map constructed using a 3 σ threshold is shown as an example in Fig. 21[b].For the second method, which we call the dilated mask method, we defined islands of significant emission in the hy-brid synthesis data cube by selecting peaks above a thresh-old of t σ across two contiguous velocity channels. This pre-liminary mask was expanded to include all connected pix-els with emission greater than p σ . Several combinationsof t and p values were tested, using t ∈ [3 ,
7] and p ∈ [1 . , − . , + .
5] km s − . We consider the map obtained for( t , p ) = (5 , . t values tended to omit genuine lowsurface brightness emission, whereas lower t values include alarger number of spurious noise peaks, especially in the in-terarm region and at the edges of the survey field. Setting p = 1 . . × K km s − pc ,however, indicating that a significant fraction of the CO emis-sion within the survey field is not recovered in this image.For the third method, which we call the smooth-and-mask method (e.g. Helfer et al. 2003), we generated a mask by con-volving the original hybrid synthesis cube to a coarser spatialresolution using a Gaussian smoothing kernel with FWHM θ .The RMS noise for each sightline within the smoothed cubewas estimated from ∼
25 emission-free channels, then pix-els in the smoothed cube with emission below a significancethreshold m σ were blanked. After transferring this mask backto the original data cube, the integrated intensity image wasconstructed by summing unmasked pixels across the LSRvelocity range [ − . , + .
5] km s − . As for the previousmethods, we experimented with different combinations of the θ and m parameters. We consider the map obtained using a3 . (cid:48)(cid:48) σ threshold to be the best produced using6 P ETY ET AL . Figure 21.
Integrated intensity images constructed from the hybrid synthesis cube using different techniques: [a] direct sum of all pixels; [b] sigma-clippingmethod with a threshold of 5 σ ; [c] dilated mask method with ( t , p ) = (5 , . θ , m ) = (3 . , I prior method, with a50kms − integration window; [f] the combined method (see text). All images are presented on the same intensity scale, which is displayed near the bottom rightimage. this method. The total CO luminosity within this map, whichis shown in Fig. 21[d], is 6 . × K km s − pc .For the fourth method, we integrated the PdBI+30m datacube over a narrow velocity range (which we refer to as the‘integration window’), centered on the radial velocity at thepeak of the H I line profile for each line-of-sight. We callthis method the ‘H I prior method’. The H I velocity templatewas constructed using the H I data cube from THINGS (Wal-ter et al. 2008), which covers the entire disk of M51 at ∼ (cid:48)(cid:48) resolution. Integration windows with velocity widths between10 and 100 km s − were tested. The rationale behind this ap-proach is that CO emission in nearby galaxies is mostly as-sociated with high brightness H I emission (e.g. Schruba et al.2011; Engargiola et al. 2003). Comparison with maps in theother panels of Fig. 21 suggests that CO emission in the nu-clear region of M51 is not well-recovered by this method. One advantage of this approach, however, is that it yields anupper limit on the CO integrated intensity for pixels withoutdetectable emission, and may therefore be more suitable forsome types of quantitative analysis. The map for a 50 km s − integration window is shown in Fig. 21[e]. The total luminos-ity in this map is 8 . × K km s − pc .Finally, we used the strengths of two of these methods tobuild our best mask. We started by building two 2D masksbased on the second ( dilated mask ) and fourth ( H I prior ) ap-proaches. In each case, we constructed a 3D dilated maskfrom the hybrid synthesis datacube. However, this techniquealso catches noise patches at “wrong” velocities. To removethese, we computed the associated centroid velocity map, andwe then produced a 2D mask where the CO velocity centroidsdiffered by less than 30 km s − from a map of the H I velocityfield. Using this 2D mask, we could build a 3D filtered mask.AWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
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GALAXY t , p ) = (4 , t , p ) = (10 , . . × K km s − pc , is shown in Fig. 21[f]. This map con-tains 93% of the total luminosity computed from direct sum-mation. The comparison of these maps with the ones of theother methods shows that it is the most successful at recover-ing all genuine emission within the data cube. This mask wasthus used to compute the 1st and 2nd order moments of thehybrid synthesis cube at 1 (cid:48)(cid:48) resolution. C. MODELING THE IMPACT OF THE IRAM-30MERROR BEAMIn this appendix, we assess how much the error beams ofthe IRAM-30m contribute to the extended emission. To dothis, we first convolved a model of the source emission in thePAWS field of view 1) with the ideal 30m beam and 2) witha model of the true 30m beam, including the diffraction pat-tern and the error beams. We then subtracted the convolvedmaps to estimate the contribution of the diffraction patternand error beams to the extended emission. We first describethe 30m beam and the source models used, before discussingthe results. C.1.
Beam model
After measuring the 30m beam pattern at 3.4, 2, 1.3 and0.8 mm from total power scans across the Moon around fullMoon and new Moon, Greve et al. (1998) modelled the beamusing antenna tolerance theory. They deduced that the beamconsists of the diffracted beam, two underlying error beams,which can be explained by the panel dimensions, and a beamdeformation mostly due to large-scale transient residual defor-mations of the telescope structure. We scaled their results tothe frequency of the CO (1–0) line to model the error beamswe use. The diffraction pattern was computed for an antennailluminated by a Gaussian beam of 12.5 dB edge taper and aratio of the secondary-to-primary diameter (blockage factor)of 0.067, using the prescription of Goldsmith (1998). Fig-ure 22 shows the properties of the resulting beam and Table 8lists the typical scales, amplitudes, and contributions to thetotal power of the different beam components.The diffraction pattern and two of the three error beams arelinked to the structure of the primary mirror of the 30m, whichhave not changed since the study of Greve et al. (1998). Hencethe typical angular scales of the different error beams stayconstant over time. However, the 30m primary surface ac-curacy improved in 2000 after several holography campaigns.Moreover, the thermal balance of the telescope primary sur-face was also improved around this time. Both effects ex-plain why the beam efficiencies of the 30m are significantly
Figure 22.
Characteristics of the IRAM-30m beam at the frequency of the CO (1–0) line as a function of the opening angle in linear (left column) andlogarithmic (right column) scales. Top: Cut of the beam profile, normalizedto unity at θ = 0 (cid:48)(cid:48) . The black curve is a combination of the diffraction patternand the three Gaussian error beams. The green, blue, and red curves displaysthe three error beams. Middle: Beam power contained in circular annuli,normalized so that the integral is unity. Bottom: Beam power integrated overthe solid angle sustained by the opening angle, normalized to 100%. higher today than the values provided by Greve et al. (1998): e.g. , 0.78 instead of 0.72 at the CO (1–0) frequency. Weused slightly different values of the 30m beam efficiency inour analysis for historical reason. As no newer detailed mea-surements of the error beams are available, we used 0.72 forconsistency with the work by Greve et al. (1998) to model thebeam here, while we applied 0.75 to the data. As the cur-rent best estimate of the beam efficiency is 0.78, both valuespresent only variations of a few percent and do not alter ourconclusions. In particular, our estimates of the error beamcontribution can be seen as a firm upper limit.C.2.
Source model
The best proxy for the source model is the result of thisproject, i.e. the distribution of the emission measured in thePAWS field of view. We made two different source models.First, we want to check whether the error beam contributionof the compact sources alone can account for the extendedemission. We started with the 1 (cid:48)(cid:48)
PdBI-only data cube, and weset to zero all pixels whose brightness was below 3 times thenoise level in order to avoid spurious sources. We multipliedall pixel brightnesses by a factor of about 2, needed to recoverthe total flux in the PAWS field of view. This assumes thatall extended emission is spurious and that any flux associatedwith it should indeed belong to compact sources. We willrefer to this cube as the compact model.In contrast, we assume for the second model that the ex-tended emission is genuine. To model the extended compo-nent, we start with the 6 (cid:48)(cid:48) subtracted cube, in which we set tozero all pixels whose brightness was below 3 times the noiselevel. We then added all the brightness of the 1 (cid:48)(cid:48)
PdBI-onlydata cube whose brightness is above 3 times the noise level.The flux contained in this model is then 3% larger than the8 P
ETY ET AL . Table 8
Parameters used to model the IRAM-30m beam at 115.271202GHz. Adapted from Greve et al. (1998).Main beam 1st error beam 2nd error beam 3rd error beamOrigin Diffraction Large scale Panel Frame Panelpattern deformations misalignments deformationsCorrelation length — 2 . − .
5m 1 . − .
0m 0 . − . (cid:46) . . . . (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) (cid:48)(cid:48) Power amplitude 1.00 9 . × − . × − . × − Relative power 71.8% 7.4% 4.7% 16.1%
Figure 23.
Comparison of the spatial distribution (from top to bottom) of the peak intensity, integrated intensity, centroid velocity, and the line full width athalf maximum ( i.e. , 2.35 times the standard deviation in velocity) of the CO (1–0) emission from the actual observations (left column), and the two modelsconvolved with the modeled 30m beam (middle and right column). The angular resolution is indicated by a circle in the bottom left corner of each panel. Theintensity scale is shown on the right-hand side of each panel. The 3 images of each row share the same intensity scale to facilitate a meaningful visual comparison.The crosses on the images show the positions of the spectra displayed in Fig. 24. Other plot annotations are the same as in Fig. 13. flux measured in the PAWS field of view. We will refer to thiscube as the summed model.C.3.
Modeling results
We convolved each model with the true 30m beam model.We normalized the result by the main beam efficiency to getto the main beam temperature scale. Fig. 23 compares themoments of both modeled 30m emission with the measuredemission. All the moments were computed using the sameposition-position-velocity mask (the one of the data) to en-sure a meaningful comparison. The compact model producesmuch higher peak temperatures and integrated emission in thearms, while it understimates the flux in the inter-arm region. The summed model provides a much better match to the ob-servations.We subtracted from the previous cubes the associatedbrightness model convolved with the ideal 30m beam. Thisyields the contribution of the error beams to the signal mea-sured with the 30m. In particular, it allows us to estimatethe error beam contribution to the extended emission, as weshowed in Section 3.1.4 that the flux of the extended emissionis mostly structured at scales larger than 36 (cid:48)(cid:48) , i.e. at scaleslarger than the ideal 30m beam FWHM. For both source mod-els, the flux scattered into the error beams is less than 20% thetotal flux in the PAWS field of view but the peak brightnessdue to the error beam contribution is only 55 mK, i.e. , aboutAWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 24.
Comparison of the spectra of our summed model (in black), the extended emission as measured in the 6 (cid:48)(cid:48) subtracted cube (in red), and the error beamcontribution (in green), at six positions where the extended emission shows different characteristics. These positions are displayed as crosses on the images ofthe extended emission moments in Fig. 13. The bottom row shows a brightness zoom of the top row.
Figure 25.
Comparison of the spatial distribution of the line full width at halfmaximum ( i.e. , 2.35 times the standard deviation in velocity) of the CO(1–0) extended emission measured at 6 (cid:48)(cid:48) . Different masking techniques wereused to test the impact of the error beams on the computation of the linewidth (see text). The angular resolution is indicated by a circle in the bottomleft corner of each panel. The intensity scale is shown on the right-handside of each panel. The images share the same intensity scale to facilitatecomparison. The major and minor axes are displayed as perpendicular dottedlines. The dotted circles show the two inner corotation resonances at radiiequal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the dashed circle shows the start of the materialarms at a radius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013). (cid:48)(cid:48) (see Sect. 3.2.1). Moreover, flux above 0.1 K inthe extended emission cube represents 79% of the flux in thiscube (we subtracted the flux contributed by the error beams inthe same mask to compute this value). We deduce that the er-ror beams contribute less than 20% of the flux in the extendedemission, i.e. , less than 10% of the total flux in the PAWS fieldof view. We speculate that the baselining of the 30m spectraremoved a large fraction of the flux associated with the errorbeams.Fig. 24 compares the spectra of our summed model, the ex-tended emission, and the contribution from the error beamsat six positions, which sample different ratios of compact toextended brightness as well as different characteristics of theextended emission. These spectra illustrate that the emission associated with the error beams has a very different signaturein space and velocity from the extended emission distribu-tion. In particular, the spectra resulting from the error beamshave much wider linewidths than the observed spectra of theextended emission. We finally investigate the impact of theerror beams on the moments of the extended emission. Werecomputed the moments of the 6 (cid:48)(cid:48) extended emission cube intwo different ways. First, we only include the pixels brighterthan two times the peak brightness ( i.e. , 0.1 K) due to the errorbeams. In the second test, we include only the pixels brighterthan four times the contribution of the error beam for eachsource model. The three resulting moment maps are similarto the original one. This is also true for the second momentor linewidth displayed in Fig. 25. We thus conclude that thelarge linewidths of the extended emission are genuine. D. ESTIMATING THE VERTICAL VELOCITYDISPERSIONThe velocity of a parcel of gas in the galaxy frame is v gal = ( v p , v z ) , (D1)where ( v p , v z ) respectively are the in-plane and perpendicularto the galactic plane velocity components. In the observingframe, the Doppler effect allows us to infer an observed ve-locity, v obs , which is the projection of v gal along the line ofsight. If u p is the projection of v p on the galaxy major axisand ı is the inclination of the galaxy plane onto the line ofsight, we get v obs = u p sin ß + v z cos ß . (D2)In the optically thin limit, a line is an histogram of all the v obs values along each line of sight. For a resolved perfectlyface-on galaxy, v obs = v z . (D3)The centroid velocity would thus be constant and thelinewidth would give the dispersion of the velocity distribu-tion along the vertical axis under the condition that the veloc-ity has a symmetric distribution of velocity along any line ofsight. For a resolved edge-on galaxy, v obs = u p . (D4)If the velocity is only rotational and the density is much higherin the spiral arm, the centroid velocity is then biased towards0 P ETY ET AL .the velocities in the spiral arm and the velocity dispersiongives an idea of the velocity content along the line of sight.This is why we still have some information about the rotationcurve of the galaxy.For any other inclination, the centroid velocity, v cent , is v cent = (cid:104) v obs (cid:105) = (cid:104) u p (cid:105) sin ß , (D5)as long as the galaxy disk is not warped and the distribution ofthe velocity perpendicular to the galactic plane is symmetric, i.e. (cid:104) v z (cid:105) = 0. Now, the velocity dispersion is computed as (cid:10) ( v obs − v cent ) (cid:11) = (cid:68)(cid:2) v z cos ß + (cid:0) u p − (cid:104) u p (cid:105) (cid:1) sin ß (cid:3) (cid:69) . (D6)Assuming that there are no correlations between vertical andhorizontal motion, we obtain (cid:10) ( v obs − v cent ) (cid:11) = (cid:10) v z (cid:11) cos ß + (cid:68)(cid:0) u p − (cid:104) u p (cid:105) (cid:1) (cid:69) sin ß . (D7)If we also assume that the velocity field is only made of asystematic motion ( u sys ) parallel to the galaxy plane plus anisotropic 3D turbulent motion of typical dispersion ( σ turb ),then (cid:10) v z (cid:11) = σ and (D8) (cid:68)(cid:0) u p − (cid:104) u p (cid:105) (cid:1) (cid:69) = σ + (cid:68)(cid:0) u sys − (cid:104) u sys (cid:105) (cid:1) (cid:69) . (D9)Note that (cid:104) u sys (cid:105) = (cid:104) u p (cid:105) and the turbulent component yield onlyone time σ turb because u p is an unidimensional velocity com-ponent. Hence, (cid:10) ( v obs − v cent ) (cid:11) = σ + (cid:68)(cid:2)(cid:0) u sys − (cid:104) u sys (cid:105) (cid:1) sin ß (cid:3) (cid:69) , (D10)where (cid:68)(cid:2)(cid:0) u sys − (cid:104) u sys (cid:105) sin ß (cid:1)(cid:3) (cid:69) is the contribution of the sys-tematic in-plane motions inside the beam to the line 2nd ordermoment. We can estimate this contribution as (cid:68)(cid:2)(cid:0) u sys − (cid:104) u sys (cid:105) (cid:1) sin ß (cid:3) (cid:69) ∼ (cid:20) | grad( v cent ) | θ √ (cid:21) , (D11)where θ is the resolution beamwidth of the observationsand | grad( v cent ) | is the modulus of the centroid velocity 2D-gradient. In our case, these last two quantities can be mea-sured. This thus yields an estimation of the galaxy verticalvelocity dispersion as the square root of (cid:10) v z (cid:11) = σ ∼ (cid:10) ( v obs − v cent ) (cid:11) − (cid:20) | grad( v cent ) | θ . (cid:21) . (D12) E. ADDITIONAL MATERIALThis section displays additional material that completes thedescription of the observations and the presentation of the datacubes. All these tables and figures are only made availableonline.Table 9 presents the weather conditions during the IRAM-30m observing run. Table 10 exhaustively lists the interfer-ometric sessions observed during the IRAM large programPAWS. Table 11 gives the evolution of the calibrator fluxes asa function of time, a key intermediate in the absolute ampli-tude calibration of the data.Figures 26 and 27 present the channel maps of the IRAM-30m single-dish data for the CO and CO (1–0) lines. Fig-ures 28 and 28 show the channel maps of the hybrid synthe-sis data cube at 1 (cid:48)(cid:48) angular resolution, the main data product
Table 9
Detailed parameters for the IRAM-30m observationsObserving date Time a T sys b Water vaporhours K [ T ∗ A ] mm18/05/2010 3.8/8.0 279 4.3-8.819/05/2010 2.9/8.0 275 3.6-6.120/05/2010 3.4/8.0 273 2.6-8.521/05/2010 3.6/9.0 287 5.8-9.022/05/2010 3.6/8.0 297 6.5-9.4 a Two values are given for the integration time: the on-source time and thetelescope time. b The T sys values are given for the CO (1–0) frequency.
Table 10
Detailed parameters for the PdBI observations.Config. N ant Mosaic Int. Time a T sys Seeing Obs. date a Two values are given for the integration time: the good on-source time (asif observed with 6 antennas) and the telescope time. of the PAWS large program. Figures 30 and 31 overlay thechannel maps of the bright compact emission as contours overthe channel maps of the faint extended emission displayed incolor.Finally, Figures 32, 33, 34, and 35 summarize the propertiesof the decomposition of the hybrid synthesis emission into thePdBI-only and the subtracted emissions, respectively at 1, 3,6, and 22 . (cid:48)(cid:48) .AWS REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
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GALAXY Table 11
Flux (in Jy) of the amplitude and phase calibrators used during the PdBIcalibration.Date 1418 +
546 1308 +
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AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 26.
Channel maps of the CO (1–0) emission obtained with the IRAM-30m telescope. The velocity in kms − of each channel is displayed in the top leftcorner of each panel. The intensity scale (in T mb ) is shared by all the panels and it is displayed in the bottom right corner of the figure. The major and minor axesare displayed as perpendicular dotted lines. The dotted circles show the two inner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the dashed circleshows the start of the material arms at a radius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013). ETY ET AL . Figure 27.
Channel maps of the CO (1–0) emission obtained with the IRAM-30m telescope. The figure layout is the same as for Fig. 26.
AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
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GALAXY Figure 28.
Channel maps of the CO (1–0) emission obtained from the combination of IRAM-30m and IRAM-PdBI observations. The velocity of each channelin kms − is displayed in the top left corner of each panel. Only the negative velocity channels are shown here. The intensity scale (in T mb ) is shared by all thepanels and it is displayed in the bottom right corner of the figure. This intensity scale is saturated to emphasize the pixels with significant emission. The majorand minor axes are displayed as perpendicular dotted lines. The dotted circles show the two inner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while thedashed circle shows the start of the material arms at a radius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013). ETY ET AL . Figure 29.
Same as Fig. 28 but for the positive velocity channels.
AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
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GALAXY Figure 30.
Contours of the channel maps of the signal-to-noise ratio of the combined PdBI+30m cube laid over the channel maps of the resolved emission. Thecontour levels start at a signel-to-noise ratio of 8. The figure layout is as in Fig. 28.
ETY ET AL . Figure 31.
Same as Fig. 30 but for the positive velocity channels.
AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
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GALAXY Figure 32.
Comparison of the spatial distribution at ∼ (cid:48)(cid:48) -resolution (from top to bottom) of the peak intensity, integrated intensity, centroid velocity, the linefull width at half maximum ( i.e. , 2.35 times the standard deviation in velocity) and, rms noise of the CO (1–0) emission for the hybrid synthesis (PdBI + 30m,left column), the PdBI-only (middle column) and the subtraction of the PdBI-only from the hybrid synthesis cubes (right column). The angular resolution isshown as a circle in the bottom left corner of each panel. The intensity scale is shown on the right of each panel. The major and minor axes are displayed asperpendicular dotted lines. The dotted circles show the two inner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the dashed circle shows the start ofthe material arms at a radius equal to 85 (cid:48)(cid:48) (Meidt et al. 2013).
ETY ET AL . Figure 33.
Same as Fig. 32 but the comparison is done here at an angular resolution of 3 (cid:48)(cid:48) . AWS
REVEALS A THICK DISK OF DIFFUSE MOLECULAR GAS IN THE
M51
GALAXY Figure 34.
Same as Fig. 32 but the comparison is done here at an angular resolution of 6 (cid:48)(cid:48) . ETY ET AL . Figure 35.
Comparison of the spatial distributions at 22 . (cid:48)(cid:48) -resolution of the peak intensity (top), integrated intensity, centroid velocity, 2.35 times the standarddeviation and rms noise (bottom) of the CO (1–0) emission for IRAM-30m cube (left column), the 6 (cid:48)(cid:48)
PdBI-only data cube smoothed at 22 . (cid:48)(cid:48) (right column),and the subtraction of the two previous cubes (middle column). The angular resolution is displayed as a circle in the bottom left corner of each panel. Theintensity scale is shown on the right side of each panel. The major and minor axes are displayed as perpendicular dotted lines. The dotted circles show the twoinner corotation resonances at radii equal to 23 (cid:48)(cid:48) and 55 (cid:48)(cid:48) , while the dashed circle shows the start of the material arms at a radius equal to 85 (cid:48)(cid:48)(cid:48)(cid:48)