Multi-wavelength observations and modelling of a quiescent cloud LDN1512
AAstronomy & Astrophysics manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512©ESO 2021January 29, 2021
Multi-wavelength observations and modelling of a quiescentcloud LDN1512
Mika Saajasto , Mika Juvela , Charlène Lefèvre , Laurent Pagani , and Nathalie Ysard Department of Physics, P.O.Box 64, FI-00014, University of Helsinki, Finland Institut de Radioastronomie Millimétrique (IRAM), 300 rue de la Piscine, 38406 Saint-Martin d’Hères, France LERMA & UMR 8112 du CNRS, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités,UPMC Univ. Paris 06, 75014 Paris, France Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, B ˆ a t. 121, 91405 Orsay cedex,FranceReceived day month year / Accepted day month year ABSTRACT
Context.
Light scattering at near-infrared wavelengths has been used to study the optical properties of the interstellardust grains, but these studies are limited by the assumptions on the strength of the radiation field. On the other hand,thermal dust emission can be used to constrain the properties of the radiation field, although this is hampered byuncertainty about the dust emissivity.
Aims.
Combining light scattering and emission studies allows us to probe the properties of the dust grains in detail. Wewish to study if current dust models allow us to model a molecular cloud simultaneously in the near infrared (NIR)and far infrared (FIR) wavelengths and compare the results with observations. Our aim is to place constraints on theproperties of the dust grains and the strength of the radiation field.
Methods.
We present computations of dust emission and scattered light of a quiescent molecular cloud LDN1512. We useNIR observations covering the J, H, and K S bands, and FIR observations between 250 µ m and 500 µ m from Herschelspace telescope. We construct radiative transfer models for LDN1512 that include an anisotropic radiation field and athree-dimensional cloud model. Results.
We are able to reproduce the observed FIR observations, with a radiation field derived from the DIRBEobservations, with all of the tested dust models. However, with the same density distribution and the assumed radiationfield, the models fail to reproduce the observed NIR scattering in all cases except for models that take into accountdust evolution via coagulation and mantle formation. The intensity from the diffuse interstellar medium (ISM) like,dust models can be increased to match the observed one by reducing the derived density, increasing the intensity of thebackground sky and the strength of the radiation field between factors from 2 to 3. We find that the column densitiesderived from our radiative transfer modelling can differ by a factor of up to two, compared to the column densitiesderived from the observations with modified blackbody fits. The discrepancy in the column densities is likely causedbecause of temperature difference between a modified blackbody fit and the real spectra. The difference between thefitted temperature and the true temperature could be as high as ∆ T = +1 . K. Conclusions.
We show that the observed dust emission can be reproduced with several different assumptions about theproperties of the dust grains. However, in order to reproduce the observed scattered surface brightness dust evolutionmust be taken into account.
Key words.
Interstellar medium (ISM): Clouds – Physical processes: Emission – Physical processes: Scattering –Methods: Radiative Transfer – Stars: Formation
1. Introduction
Understanding how stars are formed is one of the cru-cial questions in astronomy. The Herschel space observa-tory has provided us with detailed observations of nearbymolecular clouds and shown that star forming regions havevastly diverse morphologies, from dynamically active fila-mentary fields to more quiescent clouds with simple geome-tries (Molinari et al. 2010; Men’shchikov et al. 2010; Juvelaet al. 2012). These far infrared (FIR) observations can beused to derive column density estimates and to study pos-sible variations in dust properties. However, these studiesare limited by our understanding of the emission propertiesof the grains, in particular the dust opacity and to a lesserdegree the dust opacity spectral index. The light scattered by dust grains at near-infrared(NIR) and mid-infrared (MIR) wavelengths can be stud-ied and analysed without explicit assumptions of the FIRthermal emission properties of the grains, thus the scat-tering observations can be used to place additional con-straints on dust properties and the density distribution.Lehtinen & Mattila (1996) were the first to study the ex-tended surface brightness of dense interstellar cores at NIRwavelengths and later Foster & Goodman (2006) showedthat it is possible to make large-scale maps of this extendedsurface brightness, naming it ’Cloudshine’, and attributedit to scattered light. Padoan et al. (2006) used radiativetransfer modelling to show that the observed Cloudshinewas consistent with the hypothesis of light scattering and
Article number, page 1 of 35 a r X i v : . [ a s t r o - ph . GA ] J a n &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 could be used for studies of cloud structure. Star-formingclouds, but not the cores, are usually only moderately op-tically thick in the NIR and therefore there is a near-lineardependence between the surface brightness and the columndensity, assuming that the dust properties do not changewith column density.At MIR wavelengths, especially in the Spitzer 3.6 and4.5 µ m bands, a surprisingly high surface brightness was de-tected towards several cloud cores (Steinacker et al. 2010;Pagani et al. 2010; Juvela et al. 2012). Explaining thehigher-than-expected surface brightnesses with the classi-cal grain size distributions (Mathis et al. 1977) proved dif-ficult, implying the presence of larger grains with sizes ofthe order of ∼ µ m (Steinacker et al. 2010; Pagani et al.2010; Andersen et al. 2013; Lefèvre et al. 2014; Steinackeret al. 2015). The high surface brightness towards cloud cen-tres was named ’Coreshine’ and is considered to be a directevidence of dust growth in dense clouds.The comparison of thermal dust emission and light scat-tering provides crucial information on the dust properties.On the other hand, because of limited resolution, or issuescaused by anisotropic illumination and line-of-sight confu-sion, careful radiative transfer modelling is often needed toplace constraints on theoretical models of dust.We have chosen the cloud LDN1512 (hereafter L1512)to study and model NIR light scattering and thermaldust emission at FIR wavelengths. The cloud has a simplecometary morphology, is nearby (140 ± pc, Launhardtet al. 2013), and based on the reported small line width of N H + (Caselli et al. 1995, 2002; Lin et al. 2020), appearsto be quiescent.The cloud has been previously mapped with the Her-schel space observatory using both the photodetecting ar-ray camera and spectrometer (PACS) (Poglitsch et al. 2010)and the spectral and photometric imaging receiver (SPIRE)(Griffin et al. 2010) instruments. As discussed by Laun-hardt et al. (2013) and Lippok et al. (2013) the
Herschel observations show a single starless core surrounded by adiffuse envelope. Based on the fitting of the CO line, Lip-pok et al. (2013) showed that the envelope of the core hasa higher gas temperature compared to the central regionsand their stability analysis shows that the core is thermallysupercritical. The N H + observations of Lin et al. (2020)show a low kinetic temperature of ∼ ± K within theinnermost ∼ . pc of the core, and based on their chem-ical modelling, the cloud is sufficiently evolved that the N chemistry has reached a steady state. Their results suggestthat L1512 is likely older than 1.4 Myr and that ambipolardiffusion has led to the formation of the core.We use J, H, and K S bands images, shown as a three-colour image in Fig. 1, from the Wide InfraRed CAM-era (WIRCAM) on the Canada-France-Hawaii Telescope(CFHT). The observations are presented in Lin et al.(2020), where only the stellar content of the images hasbeen exploited. in this paper we concentrate on the ex-tended emission. After background subtraction, all threebands show a clear extended surface brightness component.In this study, we will simultaneously model the cloud atNIR and FIR wavelengths using an anisotropic radiationfield and a cloud model derived from the Herschel observa-tions together with dust models for the diffuse ISM dust,based on the model described by Compiègne et al. (2011)and three models that take into account the evolution ofdust grains in shape and size. The aim of our study is to find a solution, or place constraints, for the cloud, the radi-ation field and the properties of the dust grains, that wouldgive a consistent explanation for the observed extinction,NIR scattering, and dust emission.This paper is organised as follows. In section 2, we givean overview of the archival observations used in the paperand describe our NIR observations. In section 3, we de-scribe our radiative transfer methodology and explain ourradiation field and cloud models. In section 4 we presentour results and discuss our findings in section 5. Finally,in section 6, we summarise our findings and provide ourconclusions.
2. Observations
The
Herschel observations were downloaded from the Her-schel science archive and are a part of the
Herschel keyproject The Earliest Phases of Star Formation (EPoS, PI:O. Krause). The EPoS project used both the PACS andthe SPIRE instruments to cover a total of 12 differentfields between wavelengths from 100 µ m to 500 µ m. In theprojects source list, the source CB 27 corresponds to thecloud L1512. The nominal scanning speeds for the PACSand SPIRE instruments were set to 20 (cid:48)(cid:48) s − and 30 (cid:48)(cid:48) s − ,respectively. The general noise level in the EPoS projectsmaps is ∼ mJy/beam, but for the L1512 the noise levelsare slightly higher ∼ mJy/beam. A more detailed de-scription on the data reduction is given by Launhardt et al.(2013).The NIR observations cover the wide filters J (1.25 µ m),H (1.6 µ m), and K S (2.15 µ m) (see Fig. D.1) and wereobtained in 2013 using the WIRCAM instrument on theCFHT. The observations were carried out using the Sky-Target-Sky (STS) dithering mode, to subtract the atmo-spheric IR-emission and to preserve any extended scatteredlight from the source. The seeing conditions during the ob-servations were good, with typical values less than (cid:48)(cid:48) . Datareduction was performed at the TERAPIX center using aspecific reduction method to recover the extended emission.
3. Methods
Our aim is to simultaneously model the cloud in NIR andFIR and to compare our modelling results with observa-tions. In this section we describe our model of the densitydistribution within the cloud and our radiation field model.
We use a three-dimensional model cloud discretised ontoa grid of 225 cells with a Gaussian density distributionalong the line-of-sight (LOS). The angular cell size of ourmodel cloud is 6 (cid:48)(cid:48) which corresponds to the pixel size ofthe Herschel
SPIRE 250 µ m map. Thus, the total angularextent of our model is . (cid:48) × . (cid:48) , which at a distanceof 140 pc corresponds to a physical size of ∼ . × . pc.The density distribution is based on the Herschel
SPIRE350 µ m surface brightness (determining the column densitydistribution on the plane of the sky) and scaled along theLOS (z-coordinate) by a Gaussian distribution ρ ( z ) = 1 σ √ π exp (cid:18) − ( z − µ ) σ (cid:19) , (1) Article number, page 2 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512
RA (J2000) +32°39'42'45'48'51' D e c ( J ) Fig. 1.
Three colour image of the field L1512.The colours correspond to the NIR surfacebrightness at J (blue colour), H (green), andK S bands (red). All point sources have beenmasked. where µ = 0 . pc and with either σ = 0 . pc, labeledNarrow, or with σ = 0 . pc, labeled Wide. The columndensity distribution is optimised during the model fitting,taking into account the temperature structure of the modelcloud. The radiation field used in our modelling is based on theDiffuse Infrared Background Experiment (DIRBE ) Zodi-Subtracted Mission Average (ZSMA) maps (Hauser et al.1998) at 1.2 - 240 µ m. Outside the DIRBE wavelengths wefollow the Mathis et al. (1983) model, scaling the valuesbelow 1 µ m by 1.4 to match the level of the DIRBE data.Similarly, we use linear interpolation in the range from 240 µ m to 650 µ m, to avoid a discontinuity in our model (Fig.2). The intensity is distributed over the map pixels follow-ing the surface brightness distribution of the DIRBE maps.The spatial distribution at wavelengths shorter than 1 µ mfollows the distribution of the DIRBE J band (Fig. 3). Atwavelengths longer than 240 µ m, we assume the spatialdistribution of the DIRBE 240 µ m band. Compared to theMathis et al. (1983) model, our radiation field has signifi-cantly higher intensity in the range [10, 240] µ m, but thecontribution from these wavelengths to the heating of thedust particles is not significant. However, the increased ra-diation field strength at NIR and MIR wavelengths willaffect our light scattering modelling. http://lambda.gsfc.nasa.gov/product/cobe/dirbe_exsup.cfm Wavelength ( m)10 I n t e n s i t y ( M J y / s r ) Mathis et al.ISRF modelDIRBE
Fig. 2.
Intensity of the radiation field, green line, as a functionof wavelength. The purple line shows the Mathis et al. (1983)model. The black dots show the intensity of the DIRBE obser-vations averaged over the HEALPIX map.
To solve the dust emission and the surface brightness ofthe scattered radiation, we use the Monte Carlo radiativetransfer program SOC (Juvela 2019). A schematic overviewof our modelling is shown in Fig E.12.The dust grain properties are defined by the absorp-tion and scattering efficiencies, Q abs and Q sca , and a scat-tering function described using the asymmetry parametersof the Henyey–Greenstein scattering functions, g , summedover the individual dust components. The default parame-ters are taken from the Compiègne et al. (2011) model for Article number, page 3 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512
Intensity (MJysr ) Fig. 3.
Model for the all-sky sky brightness distribution in theJ band. The map has been rotated so that the direction towardsL1512 is in the centre. The intensity of the model has beentruncated at 20 MJy sr − for plotting and the image has beensmoothed by a Gaussian with FWHM = 2 ◦ . Frequency (Hz)10 H ( c m H ) DefaultLGMTHEMIS
AMMI
SIGMA dense
Fig. 4.
Comparison between the optical depth per H as a func-tion of frequency for the Default, LGM, SIGMA, and THEMISmodels. The yellow shaded regions show the frequency rangefrom 250 to 500 µ m and from 1.2 to 2.5 µ m. the diffuse ISM. Variations in these parameters, as well asthree models including dust evolution, are also considered.A more detailed description of the dust models is providedin Appendix A. The absorption and scattering propertiesof the dust grains vary significantly between the models,an example of the optical properties of selected models isshown in Fig. 4.As a first step, the dust properties, the radiation field,and cloud model are used to compute the dust emission atthe Herschel
SPIRE wavelengths of 250, 350, and 500 µ m.We fit our model to the observed dust emission by an iter-ative process where the density of the model cloud and thestrength of the radiation field are fitted to the observations.For each iteration step, we compare the difference betweenthe observed and simulated surface brightness at 350 µ m, I obs (350) − I sim (350) and, for each map pixel, scale the den-sity of each model cloud cell along the corresponding LOSby K ρ = I obs (350) I sim (350) . (2) Similarly, we scale the radiation field by an average scalarfactor K ISRF = (cid:28) I obs (250 µ m) / I obs (500 µ m) I sim (250 µ m) / I sim (500 µ m) (cid:29) . (3)In the K ISRF computation, we use only the pixels in thecentral part of the map, within the red circle shown in Fig.5. The scaled radiation field and cloud model are then usedto compute a new estimate for the dust emission.Once the emission fit has converged, we use the finalscaled cloud model and radiation field in a separate radia-tive transfer calculation to predict the scattered light atNIR wavelengths.The observed surface brightness excess is relative to thebackground sky I ∆ ν = I sca + I bg × ( e − τ − , (4)where I sca is the intensity of the scattered light, I bg is theabsolute value of the background radiation seen towardsthe cloud and τ is the optical depth of the cloud. To com-pare the observations and simulations a background needsto be subtracted from the simulated maps. For the J andK S bands, the background is estimated from the DIRBEZSMA maps as an average over the four closest pixels toL1512 and for the H band we estimate the value from theJ and K S band values following the Mathis et al. (1983)model. However, the DIRBE observations include the con-tribution from point sources which for Eq. 4 needs to beremoved. We estimate this contribution from the 2MASSpoint source catalogue by integrating the intensity of allpoint sources that are within the DIRBE pixels (see Lefèvreet al. (2014) for details). The integrated intensity values arethen subtracted from the average DIRBE values resulting inbackground levels of 0.059, 0.061, and 0.040 MJy / sr for theJ, H, and K S bands, respectively. The pixel-to-pixel varia-tions in the DIRBE observations are at most ∼
15 % for theJ and K S bands. Because of the relative proximity of thecloud, D = 140 pc, we assume that all of the backgroundradiation is emitted from behind the cloud (i.e. there is noforeground emission).
4. Results
In this section we report the main results of our study. InSection 4.1, we analyse the NIR and
Herschel observationsand describe the results of our modelling in Section 4.2.
Figure 5 shows the column density map obtained with mod-ified blackbody (MBB) fits of the
Herschel
SPIRE data.We assume a spectral index β = 1 . , which corresponds tothe average in nearby molecular clouds (Planck Collabora-tion XXV 2011). The SPIRE observations were convolvedto a common resolution of 40 (cid:48)(cid:48) and colour corrected usingthe factors of Sadavoy et al. (2013). The J band surfacebrightness has a local minimum at the location of the col-umn density maximum, showing that the J-band scatter-ing has saturated because of high optical depth. The dustemission peaks south of the column density peak in all the Article number, page 4 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512
SPIRE channels, indicating stronger heating from that di-rection.The Gaia data release 2 (DR2, Gaia Collaboration et al.2018) provides the parallaxes and magnitudes of over 1.6billion sources, a catalogue that can be used to estimatedistances within the Galaxy. To locate stars that could pro-duce additional illumination, we select all stars that arewithin two degrees of the cloud centre and brighter than15 mag in the Gaia G band. We convert the parallaxes todistance estimates assuming r = 1 / ¯ ω , where ¯ ω is given inseconds of arc (see discussion by Bailer-Jones (2015) andLuri et al. (2018) for the accuracy of this method). We findnine stars that are likely to be closer than 100 pc to thecloud and have Gaia G band magnitude brighter than 10magnitudes. Only three of these stars are on the southernside of the cloud (Fig. 5). However, their estimated G bandillumination compared to the observed NIR surface bright-ness is I stars /I SB = 0 . , with I stars = 5 . × − MJy/srand assuming an average surface brightness of 0.07 MJy/sr.Thus, compared to the illumination from the ISRF, the con-tribution from these stars to the illumination of the cloudis minimal.We derive the J band optical depth from the WIRCamobservations using the Near-Infrared Color Excess Revis-ited (
NICER;
Lombardi & Alves 2001) method and assumea standard extinction curve (Cardelli et al. 1989). The sub-millimetre optical depth was obtained by fitting the spectralenergy distribution (SED) of the
Herschel
SPIRE observa-tions with MBB curves, assuming an opacity spectral in-dex β = 1 . and a dust opacity of κ ν = 0 . ν/ β cm g − (Beckwith et al. 1990), thus τ = I B ( T ) , (5)where I is the fitted 250 µ m intensity, B is the Planckfunction at 250 µ m, and T is the colour temperature fromthe SED fit.The maps for J-band extinction and τ are shown inFig. 6 and the correlation between the two quantities in Fig.7. In Fig. 7, we have excluded the central region where theextinction estimates are uncertain due to the low numberof background stars (the region within the contours in Fig6). A linear least squares fit gives τ /A J = (4 . ± . × − mag − . Masking the high values above τ > . ,reduces the ratio to τ /A J = (2 . ± . × − mag − .The ratio of τ /A J = 4 . × − mag − is slightly higherthan what one would expect for diffuse clouds (Bohlin et al.1978; Planck Collaboration XI 2014), but is lower than theaverage value in dense clumps found in Juvela et al. (2015). In this section we describe the results of our emission andscattering modelling. We use the Compiègne et al. (2011)dust model as the default model, but will also test varia-tions, for example the effects of different size distributionsand grain optical properties. We will refer to these as ’COMmodels’.Table 1 lists the dust models used, and a more detailedexplanations are provided in Appendix A. We computedfor each model the column density, background-subtractedintensity in the J, H, and K S bands, the J band and 250 µ m optical depths ( τ J , em and τ ), and the scaling factor of theradiation field K ISRF . The values in Table 1 are averagesover × map pixels centred on point 1. The temperatureof the core is computed as an average value over cells,centred at the core. The values derived from observationsare all averages over 5 × N H + observations byLin et al. (2020). In addition to the models in Table 1, wetested three further modifications to the dust properties.The differences to the Default model were minor, and theseresults are presented only in Appendix C.Our radiative transfer computations do not includestochastically heated grains (SHG), as the emission fromthese grains is minimal in the SPIRE bands and includ-ing the stochastic heating would increase the computationstimes significantly. We computed stochastic heating onlyfor two test cases, for models that were previously fittedassuming dust at an equilibrium temperature. The resultsare shown in Appendix B (Figs. B.1 and B.2). Includingthe stochastic heating decreases the emission in the SPIREbands by ∼ −
15 % , because some of the energy is nowemitted in the MIR wavelengths. The emission is at 100 µ m30-45 % and at 160 µ m 15 % above the observed values.For the Default model, the morphology of the simulated 100and 160 µ m maps agrees with the observed maps. For theTHEMIS model, the bright rim in both maps is up to 40MJy sr − brighter than observed. For these two cases, wealso computed the predicted SEDs for the full wavelengthrange 3.6-500 µ m (Fig. B.3). Figure 8 compares the dust emission in the Default modelwith the observations. The fit residuals (observed value mi-nus the model prediction) of the simulated 350 µ m emissionare ± . . For the 250 and 500 µ m bands, the residuals areon average ± , but increase up to −
10 % in the densestregion.The fitted radiation field strength is lower than our ref-erence model for all test cases, but on average, the observa-tions can be fitted with a scaling factor of K ISRF = 0 . . Thelowest value is K ISRF ∼ . for the model LGM, while thehighest value is K ISRF ∼ . for the Scaled4 model. Thus,increasing the emissivity of the grains, models Scaled2 andScaled4, increases the required K ISRF to compensate forthe grains being colder for a given radiation field. The τ values of the models are within higher but within
15 % ofthe values derived from the observations with SED fits. Inmodels with larger grain sizes, such as LG and LGM, thedifference increases to ∼
30 % .The column density of the simulated Default case has amaximum of ∼ . × cm − , whereas the maximumvalue derived from the Herschel observations via MBBanalysis is . × cm − . Changes in the assumed emis-sivity of the dust grains naturally affect the derived columndensity, see also the discussion by Malinen et al. (2011) andYsard et al. (2012) on the uncertainties of the MBB analy-sis. A low kinetic temperature of ∼ ± K within the inner-most ∼ . pc of the core was derived by Lin et al. (2020)using N H + line observations. We computed for each modelan average temperature T core over a cube of cells centredon the core. For the Default model T core = 9 . K, whichis ∼ K higher than the N H + estimate. The other models Article number, page 5 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 T a b l e . Su mm a r y o f t h e r a d i a t i v e t r a n s f e r m o d e l s ,i n c l ud i n g t h e c o l u m nd e n s i t i e s , N I R i n t e n s i t i e s , J b a nd o p t i c a l d e p t h , µ m o p t i c a l d e p t h , r a d i a t i o nfi e l d s c a li n g , a nd t h e c o r e t e m p e r a t u r e . M o d e l n a m e D e s c r i p t i o n N ( H ) ( ) J ( ) H ( ) K S ( ) τ J , e m ( ) τ ( ) K I S R F T c o r e ( ) ( c m − )( M J y / s r )( M J y / s r )( M J y / s r ) ( × − ) ( K ) O B S V a l u e s d e r i v e d f r o m o b s e r v a t i o n s . × . . . . . - . C O M m o d e l s D e f a u l t C o m p i è g n ee t a l. ( ) . × . . . . . . . S c a l e d E m i ss i v i t y o f λ > µ m s c a l e db y . × . . . . . . . S c a l e d E m i ss i v i t y o f λ > µ m s c a l e db y . × . . . . . . . L G I n c l ud e d g r a i n s up t oa s i ze o f µ m . × . . . . . . . L G MM a ss o f l a r g e g r a i n s × , P AH m a ss × . . × . . . . . . . M o d e l s w i t hdu s t e v o l u t i o n S I G M A Tw o c o m p o n e n t s , d i ff u s e a ndd e n s ec o m p o n e n t s ( ) . × . . . . . . . T H E M I S D u s t m o d e l u s i n g t h e T H E M I S f r a m e w o r k ( ) . × . . . . . . . DD u s t Tw o du s t c o m p o n e n t s , D e f a u l t a nd L G . × . . . . . . . N o t e s . ( ) T h e c o l u m nd e n s i t y , b a c k g r o und s ub t r a c t e d i n t e n s i t y , a nd t h e o p t i c a l d e p t h s o f J b a nd a nd µ m b a ndh a v e b ee n c o m pu t e d a s a v e r ag e v a l u e s o v e r × m a pp i x e l s c e n t r e d o np o i n t ( s ee l e f t p a n e l o f F i g . ) . ( ) T h e v a l u e d e r i v e d f r o m o b s e r v a t i o n s b a s e d o n t h e N H + li n e o b s e r v a t i o n s b y L i n e t a l. ( ) . T h e m o d e ll e d v a l u e s a r e c o m pu t e d a s a v e r ag e s o v e r c e ll s c e n t r e d a tt h e c o r e . ( ) T h e d i ff u s e c o m p o n e n t i s t h e D e f a u l t m o d e l a nd t h e d e n s e c o m p o n e n t i s bu il t w i t hS I G M A ( L e f è v r ee t a l,i np r e p . ) . ( ) F o r d e t a il ss ee K ö h l e r e t a l. ( ) ; Y s a r d e t a l. ( ) Article number, page 6 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 D e c ( J ) mag mag mag N ( H ) ( c m ) Fig. 5.
Contours of J-band surface brightness on
Herschel column density map. The plus signs show the locations of the 250 µ m,350 µ m, and 500 µ m emission maxima (red, green, and black, respectively). The white arrows indicate the projected direction ofthe three brightest nearby stars and the numbers next to the arrows indicate the 3D distance to the star and the Gaia G bandaverage magnitude. The red circle shows the area that is used to compute the K ISRF scaling factor. also show temperatures 1-2.5 K above the N H + estimate.The models with higher emissivity, Scaled2 and Scaled4,and with larger grains, LG and LGM, are . − . K warmerthan the Default model. This is caused by the higher sub-millimetre emissivity leading to lower column density andlower cloud optical depth at the short wavelengths respon-sible for dust heating. This, in turn, results in higher dusttemperatures in the core. On the other hand, the increasedLOS illumination, model Wide, only increases the core tem-perature marginally to 9.7 K.
We calculated the scattered surface brightness for the J,H, and K S bands using the density distribution and theradiation field obtained from the fits to the dust emissionand by adding net effect of the background I BG × ( e − τ − ,resulting in simulated surface brightness maps. The computed surface brightness maps are shown in Fig.9 and the individual components of the signal in Fig. E.5.The modelled surface brightnesses are up to a factor of fourlower compared to the observed surface brightness. Further-more, the general morphology of the simulated maps doesnot match the observed maps. The faint striations (see Fig.9 E) are more pronounced and the morphology of the brightrim is narrower in the simulated maps. The central part ofthe cloud has a low intensity, ∼ .
01 MJy sr − , but the low-surface-brightness area is more extended. In the simulatedH and K S band maps, the rim and the striations are clearlyvisible, unlike in the observations. As in the case of the Jband, the morphology of the core does not match the obser-vations. In all simulated maps, the Veil is considerably moreprominent than in the observations. Since the Veil cannotbe seen in the WIRCam observations but is clearly seen inthe Herschel observations, it is possibly not connected tothe L1512 but is further away on the same line-of-sight.The increase in emissivity, and thus lower column den-sity, of the Scaled2 and Scaled4 models has increased the
Article number, page 7 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 D e c ( J ) A J (WIRCam) A J ( m a g ) Fig. 6.
J band extinction map and the optical depth at 250 µ m. The white contours in the J band extinction map show theestimated uncertainties of . , . , . mag, from lowest to highest contour level J (mag)0.0000.0010.0020.0030.0040.005 / A J = 4.91 × 10 (1/mag) Fig. 7.
Correlation between the optical depth at 250 µ m andthe J band extinction. The purple line is a least squares fit tothe data and the Pearson correlation coefficient is 0.65 (p << surface brightness by up to
40 % in the J band. In the Hand K S bands the intensity has decreased by
10 % in thediffuse regions and increased by up to
30 % in the denseregions. This produces a more compact core and the Veil isless prominent. However, the intensities are still a factor of2-3 below the observed values. For the models that includelarger grains, LG and LGM, the surface brightness valuesare only ∼
30 % lower in the H and K s bands and ∼
20 % higher in the J band than the observed values. However,the morphology of the maps does not match the observa-tions: the core is less compact and the Striations and theVeil more prominent.The values of τ J , em are on average three times higherthan the NICER estimates (see Table 1). The model Scaled4is an exception, the optical depth τ J , em = 1 . being within of the value derived from observations. The Default model is designed for diffuse lines of sight,but in dense cores dust grains are expected to grow due tocoagulation and mantle formation. Thus, we also test dustmodels that take into account the evolution of dust grains.A comparison between the optical properties of the modelsis shown in Fig. 4.We test three cases where the dust evolution is modelledby changing the properties of the dust grains with increas-ing density. A more detailed explanation of the models isprovided in the Appendix A. As a summary: the modelDDust is a combination of models Default and LG, wherethe relative abundance of the LG component increases withincreasing density. The SIGMA model uses the Defaultmodel for diffuse gas and a combination of aggregate sil-icate and carbon grains with ice mantles in the dense re-gions. Finally, the THEMIS model uses a diffuse componentwith core-mantle (CM) grains, an intermediate componentwith core-mantle-mantle grains (CMM), and a dense dustcomponent with amorphous core-mantle-mantle aggregatesthat have ice mantles (AMMI) (Köhler et al. 2015; Ysardet al. 2016). The evolution of the dust grains, with increas-ing density, will affect all dust parameters. Thus, one cannotidentify a single parameter or parameters that change, asnot only the physical parameters, emissivity absorption andscattering properties, and size distribution, but also chem-ical properties evolve due to formation of aggregate grainsand formation of (ice)mantles. Furthermore, the changes inthe chemical composition are also expected to effect theoptical properties, thus the affect of dust evolution is intri-cate.In the fits of the dust emission, the 250 and 500 µ mresiduals in the central region are smaller for SIGMA (Fig.E.10) than for the default dust model (e.g. Fig. 8). Theresiduals are slightly larger in the case of the THEMISmodel (Fig. E.10) and in the case of the DDust (Fig. E.10)model are similar to the Default model.Compared to the Default case, the SIGMA and DDustmodels have higher K ISRF factor, 0.67 and 0.75 respectively,while the K ISRF factor of the THEMIS model is 0.47. As
Article number, page 8 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS 250 m A M J y s r y ( p c ) SIM 250 m D M J y s r y ( p c ) (OBS SIM) 250 m G I O B S I S I M ( M J y s r ) y ( p c ) OBS 350 m B M J y s r y ( p c ) SIM 350 m E M J y s r y ( p c ) (OBS SIM) 350 m H I O B S I S I M ( M J y s r ) y ( p c ) OBS 500 m C M J y s r y ( p c ) SIM 500 m F M J y s r y ( p c ) (OBS SIM) 500 m I I O B S I S I M ( M J y s r ) Fig. 8.
Observed (first row) and simulated (second row) emission maps using the Default model at 250, 350, and 500 µ m. Thethird row shows the difference between the observations and simulations. with the models that include larger grains, LG and LGM, τ of the SIGMA, THEMIS, and DDust models are higherby ∼
30 % compared to the Default model. The NIR opticaldepths are τ J =3.4, 1.05, and 14.4 for the SIGMA, THEMIS,and DDust models, respectively. The corresponding coretemperatures read from the 3D models are 10.6 K, 7.6 K,and 9.3 K. Thus, in spite of the lowest τ J value (even belowthe NICER measurement), THEMIS results in the lowestdust temperatures, some 0.5 K below the estimate derivedfrom N H + line observations.The THEMIS, and DDust models produce column den-sities close to the Default model with N (H ) = 1 . × cm − and . × cm − , respectively. The column densityof the SIGMA model is lower, with N (H ) = 9 . × cm − . The model column density profiles (Fig. 10) agreewith the profile derived from the Herschel observations viaMBB fits, but are narrower than the FWHM=2.0 (cid:48) esti-mated from the
Herschel estimate. The profile of the De-fault model, FWHM = 1 . (cid:48) , is close to the modelled N H + profile with FWHM = 1 . (cid:48) (Lin et al. 2020).THEMIS produces two to three times higher NIR sur-face brightness than the Default model (Fig. E.4), but theSED shape and the morphology still do not match the ob-servations. Although the central region of the cloud in Hand K S bands has surface brightness values within 0.02 MJy sr − of the observed value, the more diffuse regions arebrighter than observed regions. The striations are clearlyvisible in the THEMIS maps (H and K S bands), whereasin observations no extended surface brightness is seen. Themodel SIGMA has the highest surface brightness of all ourtest cases, the intensities in the diffuse regions are in ex-cess of 0.1 MJy sr − for the H and K S bands and even forthe J band the values are in range [0.04,0.12] MJy sr − . The morphology is close to the observed morphology, witha compact core in the H and K S bands and the surfacebrightness of the Veil is lower. The model DDust shows aclear dip in the core, even in the K S band map, a factor of 2to 3 lower surface brightness compared to the observationsand the model clearly overestimates the surface brightnessof the diffuse regions. Figure 11 shows NIR spectra for observations and the De-fault model, for the four positions indicated in the figure.Point 1 corresponds to the brightest part of the J bandmap and the three other points trace density variationsacross the densest part of the cloud. In addition to thelow intensities, the general shapes of the simulated spectrado not match the observations, the relative brightness ofthe K S and J bands being too high. A factor of three in-crease in the scattered light would increase the net surfacebrightness by a larger factor but would not improve thematch with the SED shape. However, the observed H-bandvalue has somewhat higher uncertainty because of the lackof a direct background sky brightness measurements at thatwavelength.Figure 12 shows the NIR spectra for all test cases andpoints 1, 3, and 4. Point 2 is similar to point 4 and itsspectra are shown in the appendix (Fig. E.11).The error bars assume an uncertainty in the backgroundsky brightness that is
30 % in the H and
20 % in the otherbands. The Default-case simulated intensities are a factortwo to three lower than the observed values. The models LG(Default model with grains up to 5 µ m in size) and LGM Article number, page 9 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512
Fig. 9.
Observed (first row) and estimated surface brightness maps from the Default model at the J, H, and K S bands (secondrow). All maps have been background substracted. Fig. 10.
Column density of H derived from Herschel observations and the comparison between column density profiles for selectedmodels. The profiles have been computed as average values over × pixels along the arrow in the left panel. (As LG but relative amount of large grains increased) pro-duce higher intensities, but the intensity of the H band is ∼
30 % lower than the observed value while the J and K S bands are 30 to
40 % brighter. The SIGMA model (two dustcomponents, Default for diffuse and a component derivedwith SIGMA for dense LOS) is clearly overestimating theintensity of the scattered light in all three channels. In point1, the THEMIS model (three dust component based on theTHEMIS framework) is closest to the observations, but theintensity of the K S band is 0.05 MJy sr − too bright. How-ever, in the point 3, the intensity and the shape of the spec-tra of the THEMIS model is within
10 % of the observed intensity. In general the spectra from point 3 is more eas-ily reproduced and the models LG, LGM, and DDust allproduce approximately the correct SED shape but do notmatch the level of intensity. Like in the point 1, the SIGMAmodel is overestimating the intensity, but the shape of thespectra is correct.For point 4, the COM models tend to underestimate theNIR intensities, with the exception of the LG and LGMmodels that overestimate the J and K S bands, but under-estimate the H band. However, models Scaled2 and Albedogive very similar results. Article number, page 10 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c )
12 3 4
OBS J I n t e n s i t y ( M J y s r ) I n t e n s i t y ( M J y s r ) Fig. 11.
Observed map of the J band scattered light (left panel), the red numbers from one to four indicate the locations fromwhere we have extracted NIR spectra, shown in the panel on the right. The solid lines show the observed spectra and the dashedlines show the spectra derived from the Default model. The dotted lines show the simulated spectra derived from the Defaultmodel, but the intensity of the scattered light has been multiplied by a factor of three before background subtraction.
The increased FIR/submillimetre emissivity in the casesScaled2 (emissivity for λ > scaled by a factor of 2) andScaled4 (as Scaled 2 but scaled by a factor of 4) decreasesthe column density, thus, the higher intensity of the H bandcompared to the K S band can be understood as a saturationeffect. However, increasing the emissivity further does notimprove the match as the column density becomes too lowand the intensity of the scattered light is reduced. The in-creased emissivity of the grains decreases the J band opticaldepth, which for model Scaled4 is close to the NICER es-timate, but the morphology of the surface brightness mapsand the shape of the NIR spectra are further away fromthe observations. Thus, emissivity alone can not reconcileobservations and simulations.
5. Discussion
Based on our modelling of the LDN1512 observations, itsthermal dust emission can be fitted with many different as-sumptions on dust properties. However, we can not simulta-neously fit both the dust emission and NIR scattered lightwith the COM models. The Default model was designedfor high-latitude diffuse lines of sight, while the L1512 cloudhas a dense central core. The disparity between the observa-tions and our radiative transfer models based on the Defaultmodel is a clear indication for the need of evolution of thedust grains and we thus tested additional models, DDust,SIGMA, and THEMIS. We are able to reproduce the ob-served intensity of dust emission and scattered light at NIRwavelengths with the THEMIS model. However, the mor-phology of the surface brightness maps shows considerabledeviation from the observations. In this section we discussthese results in more detail.
The ISRF used in our simulations is based on the DIRBEobservations and the shape of the Mathis et al. (1977)model. We did not test changes in the anisotropy of the external field. However, based on Gaia point sources, thecontribution from the nearby stars is minimal.Based on the intensity variation between the DIRBEpixels, the background uncertainty is of the order of ∼
20 % ,but for the H band, for which there are no direct DIRBEmeasurements, we have assumed a value of
30 % . With theexception of the model SIGMA (model with two dust com-ponents, Default dust for diffuse regions and dust createdwith SIGMA for dense LOS), the spectra derived from bothpoints 1 and 3 are systematically underestimating the in-tensity of the H band. For the THEMIS model (model withthree dust components based on the THEMIS framework),the intensity of the J and K S bands from point 3 are compa-rable with the observed values. However, the H band inten-sity from both points is still significantly below the observedvalues. For point 4, the J and H band intensities of theTHEMIS model are comparable with the observed values,but the K S band is over-estimated by a factor of 2. Further-more, the shape of the spectra of the model SIGMA agreewith the observed spectra, although the intensity is clearlyoverestimated. Thus, the discrepancy between the observedand simulated values can be explained to a certain degreewith uncertainties in the background sky estimate, but sincethe shape of the simulated spectra also depends on the op-tical depth of the cloud, uncertainties in the optical depthof the model or variations in the relative abundances of thedust components will also affect the estimated intensity. In the models fitted to dust emission observations, the NIRextinction is typically three times higher than the directNICER estimate of τ J . In addition to NICER estimatesusing the Cardelli et al. (1989) extinction curve, we alsocalculated estimates for the extinction curves of the re-spective dust models. The values are computed as averagesover a × pixel region around point 1 (the resolution ofthe optical depth maps was set to 40 (cid:48)(cid:48) ). For the Defaultmodel τ J , ext = 1 . , which is lower compared to the value Article number, page 11 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512
Fig. 12.
J, H, and K S band intensitiesfrom observations (horizontal lines) anddifferent models (symbols) for the mappoint 1 (lower panel), point 3 (middlepanel), and point 4 (upper panel). Thecolours correspond to the J (purple), H(red), and K S (black) bands. All intensityvalues have been background subtracted.We assume a
20 % uncertainty in back-ground sky estimates for the J and K S bands and an uncertainty of
30 % for theH band. derived using the Cardelli et al. (1989) extinction curve, τ J , Card . = 1 . . For the models LG (model with grains upto 5 µ m in size), LGM (as the LG model but the relativeamount of large grains increased), and SIGMA, the opticaldepths are τ J , ext = 2 . − . . For the model THEMIS the τ J , ext = 1 . , which is within ∼
10 % of the Cardelli et al.(1989) estimate.The ratio for the Default model is τ J , em /τ J , ext ∼ . ,while it is lower, τ J , em /τ J , ext = 1 . − . , for the modelsLG and LGM (Table 2). For the models with dust evolu-tion, the ratios are smaller, 0.74 and 1.56 for THEMIS and Article number, page 12 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512
Table 2.
Comparison of τ J values derived from the dust-emission models and from the observations of background stars.The values are computed as averages over a × region centredon point 1. Model τ J , em τ J , ext τ J , em /τ J , ext Default 5.80 1.32 4.39LG 4.50 2.90 1.55LGM 5.00 3.00 1.66SIGMA 3.42 2.19 1.56THEMIS 1.05 1.42 0.74SIGMA, respectively. Thus the models with larger grains,or some form of dust evolution, are more consistent betweenthe sub-millimetre emission and NIR extinction.
We derived the cloud density distribution and strength ofthe external radiation field by fitting the observations ofFIR dust emission. The estimated column density is sensi-tive to the dust temperature which in turn is sensitive tothe strength of the radiation field. In this section, we quan-tify the dependences between the radiation field, the dusttemperatures, and the optical depth of the cloud.The effects of scaling and attenuation of the radiationfield on the dust temperature can be solved from the equi-librium equation (cid:90) ∞ Q abs ( ν ) × I ISRF dν = (cid:90) ∞ Q abs ( ν ) × B ν ( T ) dν, (6)where Q( ν ) are the dust absorption efficiencies, I ISRF is theintensity of the radiation field, and B ν ( T ) is a black-bodyfunction at temperature T . Figure 13 shows the dependenceof the temperature of the Default and LGM dust grains onthe energy density of the radiation field. Results are calcu-lated for grains at an equilibrium temperature and usingthe Mathis et al. (1983) radiation field with a linear scalingfactor (cid:15) and an attenuation by by e − τ . We use values in therange of [0.1,10] for both (cid:15) and τ /τ J .Compared to the Default model, the LGM model hasmore large grains and to reach similar temperature, a higherradiation field is required. Because of the higher emissivity,larger grains will have a lower temperature for a given radi-ation field and a lower column density is required to reachsimilar temperature as with the Default model.Dust emission spectra are typically analysed as modi-fied black-body radiation. However, the spectra will alwaysdeviate from this model, because of temperature variationsin the sources and because the spectral index of dust opac-ity is not constant over the examined wavelength range.Figure 14 shows emission spectra obtained by multiplyingthe absorption cross sections of the Default and LGM mod-els with a T = 15
K black-body function. The figure alsoshows the MBB fits using three points at 250, 350, and500 µ m and keeping both T and β as free parameters. Thefitted temperatures T c = 16 . K and T c = 15 . K forthe Default model and LGM model, respectively, are higherthan the true temperature of 15 K. The fitted β values are U/U T e m p e r a t u r e ( K ) (Default) e (Default) (LGM) e (LGM) Fig. 13.
Comparison between the dust temperature and theenergy density of the radiation field for the Default and LGMmodels. The strength of the radiation field has been normalisedby the Mathis et al. (1983) model. β = 1 . and β = 1 . , for the Default and LGM modelsrespectively, lower than the β values of the dust models inthe − and − µ m intervals, β ∼ . and β ∼ . for the Default and LGM models, respectively.Thus, an observer relying on MBB fits would underesti-mate the column density (see also Fig. 10). Similar resultsof dust models containing only bare astrosilicates (Draine &Lee 1984; Draine & Li 2001, 2007) failing to reproduce theSED of the observed dust emission, have been discussed byFanciullo et al. (2015); Planck Collaboration XXII (2015);Planck Collaboration XXIX (2016).The errors in column density and radiation field willalso affect the predictions of NIR scattering. However, thelow intensity of our modelled NIR surface brightness is notcaused by the uncertainties in the column density, but isrelated to the scattering efficiency of the dust models, orin the case of the evolved dust models (e.g. SIGMA andTHEMIS) the chosen relative abundances of the differentgrain populations. Furthermore, MBB results are sensitiveto temperature variations that can lead to a severe underes-timation of dust column densities (Shetty et al. 2009; Juvela& Ysard 2012). For example, Pagani et al. (2015), who stud-ied the cloud LDN 183, showed that Herschel observationscan not be used to set strong constraints on the amount ofvery cold dust. Additional methods may be needed, such asobservations of molecular lines and NIR/MIR extinction.The column densities based on the Default model varywithin a factor of 2, while the variation in the radiationfield strengths is within a factor of ∼ . . The column den-sity differences are not much larger between the SIGMA,THEMIS, and DDust models, but the the differences in theradiation field strength reach a factor of two. However, therelationships between the true Q ( ν ) B ( T d ) of the dust, theemission predicted by RT models, and the results of MBBfits are complex (Fig. 15). The emission from the dust grainsmight not follow any MBB curve, T d and T c differ and thefitted spectral index β differs from the opacity spectral in-dex of the dust grains. These problems are acerbated whentemperatures also vary within the beam.We further quantify the discussion above by comput-ing H band surface brightness maps using the Default Article number, page 13 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 I ( e r g s c m H z s r H ) Q × B(T) DefaultQ × B(T) LGMSim Default10 Frequency (Hz)0.020.000.02
Fig. 14.
Comparison of dust emissionspectra and their MBB fits. The blackand purple lines show the emission spectrafor Default and LGM models with grainsat 15 K temperature. The dashed linesshow MBB spectra fitted to the 250, 350,and 500 µ m points. The resulting fit pa-rameters are T c = 16 . , β = 1 . and T c = 15 . , β = 1 . , for the Defaultand LGM models, respectively. The redcurve (scaled by a factor of . × − tofit the figure) is from a simulated Defaultmodel map pixel where the fitted temper-ature is similar to that of the black curve.The blue vertical lines show the 250, 350,and 500 µ m frequencies. The relative dif-ferences between the black-bodies and theMBB fits near the 250, 350, and 500 µ mpoints are shown in the plot below theemission spectra curves. Fig. 15.
Schematic overview between the assumptions that aremade during a MBB fit and their comparison to the simulatedspectra and a real cloud. model, with the assumption that we have underestimatedthe strength of the radiation field and overestimated thecolumn density. Our aim is to see if by modifying theseparameters, the Default model can be made to agree withthe observations. We use a radiation field that is 1, 2, or3 times and a column density that is 1, 0.6, or 0.3 timesthe value previously obtained for the Default model. An-other component affecting the shape and strength of theNIR scattered light is the sky background behind the cloud,we assume that this is 1.0, 2.0, or 3.0 times the value de-rived from the DIRBE observations. The resulting H bandsurface brightness maps are shown in Fig. 16 and in Figs.E.6, E.7. Increasing the strength of the radiation field willincrease the surface brightness excess, but increasing thebackground sky brightness will decrease the surface bright-ness. The two values can be used to fix the level of themodelled surface brightness, but they are not enough to re- produce the observed surface brightness morphology (Fig.E.6). For that, also the cloud column density needs to bedecreased.Increasing the strength of the radiation field by a factorof 2 and simultaneously decreasing the column density by ∼
30 % , (e.g. Fig. 16 panel G), the intensity of the simu-lated H band surface brightness is within
15 % of the ob-served one. This can also be achieved by increasing thestrength of the radiation field and the assumed backgroundsky brightness by a factor of 3 and decreasing the columndensity by ∼
30 % (e.g. Fig. 16 panel L)). In both cases,the morphology of the surface brightness map in the cen-tral part is comparable with the observations, with a brightrim towards the south and decreasing surface brightness to-wards the core. However, the Veil (Fig. 9) is still prominent.Decreasing the density of the cloud further (Fig. E.7) thecentral region of the cloud becomes excessively compact, al-though the correct intensity can be reached by scaling theradiation field or the assumed intensity of the backgroundsky brightness (e.g. Fig. 16 panels G, K, and L).Although suitable parameters can be found to correctthe H band intensity of the Default model, the requiredchanges are substantial. Thus, it is evident that dust evo-lution needs to be taken into account, since the modelsSIGMA and THEMIS produce results closer to the obser-vations without the need to fine tune other parameters.
Launhardt et al. (2013) showed that L1512 is a cold( T ≈ K) core with high column density ( N (H ) ≈∼ . × cm − ) and in the study by Lippok et al. (2013), theenvelope of the core was better fitted by assuming a highertemperature compared to the core, which is consistent withthe absence of internal heating. However, to explain the ob-served molecular abundances, Lippok et al. (2013) had toincrease the hydrogen density derived by Launhardt et al.(2013) and the abundances of all modelled chemical species Article number, page 14 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS H A 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 1.0K BG = 1.0 D 0.000.010.020.030.04 I n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 2.0K BG = 1.0 G 0.000.020.040.060.080.100.120.14 I n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 3.0K BG = 1.0 J 0.000.050.100.150.200.25 I n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) ISRF = 1.0K BG = 2.0 E 0.030.020.010.000.010.02 I n t e n s i t y ( M J y s r ) ISRF = 2.0K BG = 2.0 H 0.000.020.040.060.08 I n t e n s i t y ( M J y s r ) ISRF = 3.0K BG = 2.0 K 0.0000.0250.0500.0750.1000.1250.1500.1750.200 I n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) ISRF = 1.0K BG = 3.0 F 0.080.060.040.020.000.02 I n t e n s i t y ( M J y s r ) ISRF = 2.0K BG = 3.0 I 0.030.020.010.000.010.020.030.04 I n t e n s i t y ( M J y s r ) ISRF = 3.0K BG = 3.0 L 0.000.020.040.060.080.100.120.14 I n t e n s i t y ( M J y s r ) Fig. 16.
Simulated H band surface brightness maps for the Default model with density scaled by a factor of 0.6 during thescattering computations and with different assumptions on the strength of the radiation field and on the sky brightness behindthe cloud. Shown on the first row is the observed H band surface brightness map. Shown on the rows 2 to 4 are the simulated Hband maps, for which the strength of the radiation field has been scaled with a factor between 1 and 3, and the intensity of thebackground has been scaled between factors 1 and 3.0. between a factor of 2 to 3. In their chemical models Lip-pok et al. (2013) used a slightly coagulated grain modelfor the whole cloud with a coagulation time of yr ata gas density of cm − (Ossenkopf & Henning 1994).Lippok et al. (2013) discuss that by using a model of non-coagulated grains, they would have increased the hydrogendensity by a factor of ∼ . .Larger grains lead to stronger scattering as discussed bySteinacker et al. (2010) and Ysard et al. (2018), but the in-crease in grain size also increases the absorption coefficient.On the other hand, more complex or ’fluffy’ grains can havea larger surface area, and have higher scattering efficiencywith respect to their absorption efficiency (Lefèvre et al.2016). This can be seen with the dense dust components ofthe models SIGMA and DDust (Fig. E.4), where the denseregions of the model have higher intensity and their mor-phology agrees better with the observations. Our Default model consists of only PAH, silicate, andcarbon grains, however, in dense regions of the ISM, gasphase freeze-out can create mantles on the grains. The ini-tial studies trying to explain the detected coreshine requireda high fraction of dust mass in large grains (Pagani et al.2010; Steinacker et al. 2010; Andersen et al. 2013), withmaximum grain size of the order of ∼ µ m. However, toreach such large grain size through coagulation is difficultwith respect to the time-scales, cloud densities, and tur-bulence (Steinacker et al. 2014). On the other hand, asdiscussed by Ysard et al. (2016), a dust model includingmantle formation and low-level coagulation is able to re-produce the observed cloudshine levels without the need ofvery large grains. Our results using the THEMIS modelshow that the model can fit the observed emission, theintensity of the scattered light is within
15 % of the ob-served values, and the morphology of the central region ofthe surface brightness maps is comparable to the observed
Article number, page 15 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 surface brightness (Fig. 12. However, the intensity of thediffuse region surrounding the cloud is a factor of 3 to 5higher than observed. Furthermore, as discussed by Bazell& Dwek (1990) and Ossenkopf (1991), porosity increasesthe absorption efficiencies at FIR and sub-millimetre wave-lengths while the compositional inhomogeneities will havean effect upon the shape and strength of broadband fea-tures. Thus, these structural differences of the grains willaffect both the true temperature and color temperature de-rived from sub-millimetre flux ratios (Kruegel & Sieben-morgen 1994).Thus it is evident that a larger maximum grain sizeor the relative amount of large grains in the dust mix-ture is not sufficient to reproduce the observed NIR sur-face brightness. Evolution of dust grains, in the form ofaggregates and mantle formation, appears necessary. Thisis supported by our core temperature estimates that tendto overestimate the core temperature by ∼ . K. However,the THEMIS model, with three different dust populationsproduces a colder core, with T core = 7 . K, similar to theestimated temperature of 8 K derived from line observa-tions. However, even for the evolved grain models, the dif-fuse regions are still problematic as they are systematicallybrighter compared to the observations. The high surfacebrightness is likely related to the relative abundances ofthe dust populations, as for example, the THEMIS modelshas a relatively high abundance of the CMM population inthe Veil and Striation regions, and similarly, the SIGMAmodel has a high abundance of the dense component inthe Veil and Striations (Figs. A.1 and A.3). Decreasing therelative abundances of the dense dust components in theseregions would decrease the surface brightness and improvethe match with the observed surface-brightness morphol-ogy.
6. Conclusions
We have studied the cloud L1512 and modelled simultane-ously the scattered NIR light at J, H, and K S bands andthe FIR emission at 250, 350, and 500 µ m. We have usedseveral dust models based on the Compiègne et al. (2011)dust and three separate dust models taking into accountdust evolution. The radiation field used in the modellingis derived from the DIRBE observations. The NIR surfacebrightness is estimated using a density field and radiationfield strength that are obtained from first fitting the FIRdust emission. The key result of our study are: – The morphologies of the observed NIR surface bright-ness maps are in good agreement with the column den-sity map derived from the
Herschel observations. How-ever, the low-column-density Veil seen above the cloudin the
Herschel observations is not visible in scatteredlight. – In the radiative transfer modelling, we can fit the ob-served emission with any of the tested dust models. Theaverage fit residual in the 350 µ m band are ± . andfor the 250 and 500 µ m bands at most −
15 % . Depend-ing on the model, the estimated H column density atthe cloud centre (point 1) ranges from . × cm − to . × cm − , and the relative radiation field strengthfrom 0.3 to 0.75. – The core temperature of the radiative transfer modelsis on average ∼ . K higher than the value ∼ ± K, suggested by N H + line observations. With T core = 7 . K, the THEMIS dust model gives the core temperatureclosest to the gas inferred value. – The radiative transfer models matching the dust emis-sion predict a J band optical depth that is on aver-age three times higher than the value measured withthe background stars. The exceptions are Scaled4 andTHEMIS, with τ J , em = 1 . and τ J , em = 1 . , respec-tively, in agreement with the value τ J , Card = 1 . derivedusing the Cardelli et al. (1989) extinction curve. – The NICER estimates of τ J , ext obtained with the NIRextinction curves of the tested dust models are mostlywithin
15 % of the values obtained with the Cardelliet al. (1989) extinction curve. However, dust modelscontaining larger grains (e.g. LG and LGM) increase τ J , ext by a factor of two. – For the models based on the Compiègne et al. (2011)model, the predicted surface brightness excess I ∆ ν in thecentral region of the cloud is a factor of 2 to 4 below theobserved values and the morphology of the simulatedscattered light maps does not match the observations.Increasing the maximum grain size of the dust grains orextending the width of the cloud along the line-of-sightwill increase the intensity of the scattered light, but notenough. Thus, dust grain evolution (e.g. aggregates) isneeded. – Increasing the FIR emissivity by a factor of two (modelScaled2), increases the predicted NIR surface brightnessby up to a factor of two. It also decreases the columndensity and produces more compact scattered NIR sur-face brightness maps. However, further increase of emis-sivity (model Scaled4) again decreases the NIR signal. – The observed H-band surface brightness and its mor-phology could only be matched with the Default modelby making substantial modifications to the values de-rived from the emission fitting and observations, indi-cating the need of changes in the dust properties. – The observed thermal emission and scattered NIR sur-face brightness can be reasonably reproduced only byusing dust models that take into account grain evolu-tion. However, the J-band intensity and the H- and K S -band intensities of the diffuse regions are far above theobserved values.It is easy to fit the dust emission alone but the simul-taneous fitting of emission and scattering is challenging.The dust evolution must be taken into account, to producesufficient amounts of scattered light and with the correctmorphology. The uncertainty of the sky brightness behindthe studied cloud can have a significant effect on both theintensity and morphology and should be constrained with ahigh precision before drawing conclusions on the dust prop-erties. Acknowledgements.
This work has made use of data from the Eu-ropean Space Agency (ESA) mission
Gaia ( ), processed by the Gaia
Data Processing and AnalysisConsortium (DPAC, ). Funding for the DPAC has been provided by nationalinstitutions, in particular the institutions participating in the
Gaia
Multilateral Agreement.
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Appendix A: Summary of dust models
A more detailed description of all dust models used in ourradiative transfer modelling is provided in this section. Un-less otherwise noted, the different dust models are based onthe Compiègne et al. (2011) model. We use the size distri-butions and optical properties as included in the DustEM (Compiègne et al. 2011).The changes that we have made to the Compiègne et al.(2011) model do not take into account any limits placedby the mineralogy or constraints placed by chemical abun-dances available in the ISM. The changes to for examplethe albedo or emissivity of the grains, are meant to be rela-tively small, but still large enough that differences betweenthe models can be distinguished. – Default: The Compiègne et al. (2011) model. Containstwo populations of PAH grains with log-normal size dis-tributions, a single component of small carbon grainswith a log-normal distribution, and two components oflarge grains following power-law size distributions. Thelarge grains consist of a population of carbon grains anda population of silicate grains. The average opacity spec-tral index in the range [ , ] µ m is β / = 1 . . – Albedo: The albedo of the grains at NIR wavelengthshas been increased by
20 % without changing the extinc-tion cross sections during the scattering computations. – Disttest: Compiègne et al. (2011) assumed a power-lawsize distribution for the large silicate and carbon grains.For this model the exponent factor of the power-law γ has been increased by
20 % for both the silicate (original γ = − . ) and carbon grains(original γ = − . ) and β / = 1 . . – Gtest: The asymmetry parameter g of the grains hasbeen increased by
15 % . – Scaled2: The emissivity of all wavelengths longer than60 µ m has been multiplied by a factor of 2. – Scaled4: As Scaled2, but the emissivity has been multi-plied by a factor of 4. – Wide: The FWHM of the Gaussian distribution describ-ing the line-of-sight density distribution has been in-creased from σ = 1 . to σ = 1 . . – LG: Extended the maximum grain size of the Com-piègne et al. (2011) model to 5 µ m. The value of β / is 1.903. – LGM: As LG, but in addition increased the relativeabundance of the large grains by a factor of 2 anddecreased the relative abundance of the small carbongrains and PAH components by a factor of 2. The valueof β / is 1.948. – Ddust: Combination of Default and LG dust models, therelative abundance of the latter increasing with densityas S LG = 12 + 12 tanh( 2 . × log( ρ ) ρ ) , (A.1)where ρ is the density of the modelled cloud and ρ de-fines the limit where the relative abundances of the twodust components are equal. An example of the abun-dances is shown in Fig. A.1. In our model we have set ρ = 1 . . For the average of the Default and LG models β / = 1 . . Article number, page 17 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) R e l a t i v e a b un d a n c e y ( p c ) R e l a t i v e a b un d a n c e Fig. A.1.
Relative abundances of the diffuse and dense components for the DDust and SIGMA models across the innermost cellsof the model cloud. Left panel: the relative abundance of the diffuse component. Right panel: relative abundance of the densecomponent. – SIGMA: A model with two dust components, for thediffuse component we use our Default model, and thedense component is built using SIGMA (Simple IcyGrain Model for Aggregates, Lefèvre et al. 2019). Thedense component consists of aggregate silicate and car-bon grains from the Min et al. (2016) model (note thatwe do not use the iron sulphide component) with addedices (Pollack et al. 1994). The final mixture consists of . silicates, . carbons, and . ices. Thesize distribution has a maximum grain size of 10.0 µ m(see Fig. A.2), however for this work we have truncatedthe maximum grain size at 5 µ m, and use a porosityfactor of 0.7 for the grains. The porosity was chosen ac-cordingly to the size distribution obtained from coagu-lation computation. Such a high porosity was necessaryto obtain favourable conditions to stick dust grains to-gether (Ormel et al. 2011; Hirashita & Nozawa 2013;Hirashita & Voshchinnikov 2014, Pagani et al. in prep).In practice, there is a significant fraction of fluffy icyaggregates with a fractal degree close to 2. The dustdistribution is representative of a coagulation at a con-stant density of × cm with a constant porosityof 0.7 for 0.436 My. The simplification of dust distri-bution evolving at constant density and porosity will bediscussed in a forthcoming paper (Pagani et al. in prep.)The relative abundances of the dense and diffuse dustcomponents are set according to Eq. A.1, with ρ =1 . . The threshold was so that the diffuse dust com-ponent would have a relative abundance of less than ∼
10 % in the core of the model. For the average of thetwo dust components β / = 2 . . – THEMIS: A dust model as discussed by Köhler et al.(2015) and Ysard et al. (2016). The model consists ofdifferent dust population mixtures, that have a varyingrelative abundance based on the density of the model.In the following we adopt the naming convention as de-fined by Köhler et al. (2015). The diffuse regions of themodel consist of mostly core-mantle (CM) grains whichgradually evolve to core-mantle-mantle grains (CMM)as density increases. In the densest regions of the model, Grain size ( m)10 a n ( a ) n H ( g r a i n s H c m ) Fig. A.2.
Size distribution of of the dust grains used for thedense component of the SIGMA model. For the emission fittingand scattering computations, the size distribution was truncatedat 5 µ m, as indicated by the purple line. we assume that the grains have further evolved and aregradually replaced by aggregate CMM grains with ad-ditional ice mantles (AMMI). The relative abundancesof the CM and CMM populations are set according toEq. A.1, with ρ = 1 . . The relative abundance of theAMMI grains is then defined by taking all cells where ρ > . , setting the relative abundance of these cellsto 1.0 and smoothing the cells with a × Gaussianbeam. We then reduce the relative abundance of theCMM population in these cells so that for each cell, thesum
CM + CMM + AMMI = 1 . . An example of therelative abundances of the three components across thedensest part of the cloud is shown in Fig. A.3. The sizedistributions of the different dust components are dis-cussed by Köhler et al. (2015) and Ysard et al. (2016)(Figs. 1 and 2, respectively). The average β / overthe three dust components is 2.011. Article number, page 18 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) R e l a t i v e a b un d a n c e y ( p c ) R e l a t i v e a b un d a n c e y ( p c ) R e l a t i v e a b un d a n c e Fig. A.3.
Relative abundances of the CM, CMM, and AMMI dust populations of the THEMIS model across the innermost cellsof the model cloud. Left panel: the relative abundance of the diffuse CM component. Centre: relative abundance of the CMMcomponent. Right panel: relative abundance of the dense AMMI component.
Appendix B: Stochastically heated grains
The effects of stochastic heating of small grains was notincluded in our modelling, because they are not directlyconnected to the submm emission and NIR scattering. How-ever, in order to study how well our best-fit models agreewith the observed emission in the MIR wavelengths, wecomputed two test cases using the models Default andTHEMIS, including the stochastic heating. We did not fitthe model to the observed emission, but rather used thebest-fit parameters from the computations without SHGsand re-computed the emission including the SHGs.The results of these computations are shown in Figs. B.1and B.2. For both models, the emission in the SPIRE bandshas decreased, by ∼ −
15 % , because some of the energy isnow emitted in the MIR wavelengths. The emission is at 100 µ m 30-45 % and at 160 µ m 15 % above the observed values.For the Default model, the morphology of the simulated100 and 160 µ m maps agrees with the observed maps. Forthe THEMIS model, the bright rim in both maps is upto 40 MJy sr − brighter than observed. The region wherethe CMM grains transition to the AMMI grains is clearlyvisible, especially in the 250 µ m map.An SED from the observations, computed as averagesover a region corresponding to the red circle in Fig. 5 isshown in Fig. B.3 (the orange line). The observations be-tween 3.6 µ m and 8 µ m are from the Spitzer IRAC in-strument and the 24 µ m data are from the Spitzer MIPSinstrument. The MIPS data are corrected with a aperturecorrection of 2 MJy sr − . For the 60 µ m observations, weuse the improved reprocessing of the IRAS survey (IRIS)data (Miville-Deschênes & Lagache 2005) and the 100 to500 µ m observations are from the Herschel
PACS (100 and160 µ m) and SPIRE (250, 350, and 500 µ m) instruments.An SED from the Default and THEMIS models withthe SHGs included are shown in Fig. B.3. The backgroundlevels of the IRAC observations have not been calibrated toan absolute level. Thus, we assume an uncertainty of ±
30 % for the simulated surface brightness at IRAC wavelengthsand because of the uncertainty of the colour corrections, weassume an uncertainty of ±
30 % for the 24 µ m data. As dis-cussed by Launhardt et al. (2013), the nominal calibrationuncertainties for PACS and SPIRE are ∼ and ∼ ,respectively, thus for the simulated MIR and FIR maps weassume a flat uncertainty of 10 % . These uncertainties arehighlighted with red and blue shading in Fig. B.3. It is clear that the simulations do not precisely matchthe observations, although the shapes of the SEDs are inagreement. The THEMIS model is closer to the observa-tions both in the NIR and FIR, although the Default modelat 60 and 160 µ m is closer to the observed values. Appendix C: Analysis of dust models based on thedefault model
In addition to the models discussed in the main part of thetext, we have tested dust models that are modifications ofthe Default model, increased albedo (model Albedo), in-creased the value of the g parameter (model Gtest), andchanges to the size distribution of the grains (Disttest). Wehave also tested a case where the LOS density of the cloudis wider compared to our assumed ’compact core’ model(model Wide). A description of these models is provided inAppendix A, and the results are summarised in Table C.1.The resulting dust emission and scattered surface bright-ness maps are shown in Appendix E. The scaling of theradiation field is similar to all models with K ISRF ∼ . ,expect for the model Wide which has a lower scaling factorof K ISRF ∼ . .Compared to the Default model the scattered surfacebrightness maps (see Figs. E.1, E.2, and E.3) of modelsAlbedo, Disttest, Gtest and Wide, show only minor differ-ences. The most notable difference is for the model Albedo,which produces ∼
20 % more surface brightness in all threebands compared to the Default model.Increasing the line-of-sight extent of the cloud can pro-duce more scattered light as the amount of illuminationalong the line-of-sight increases. We test a case, with theDefault model, where the line-of-sight density distributionis extended, case Wide. The results indicate that the sur-face brightness is increased but only by ∼
10 % (see Fig.E.3 second row).
Appendix D: NIR and MIR observations
The MIR Spitzer observations were acquired from theSpitzer Heritage Archive. The cloud L1512 has been coveredby three programs, Program id. 94 (PI Charles Lawrence)and Program id. 90109 (PI Roberta Paladini), both us-ing the InfraRed Array Camera (IRAC) (see Fig. D.2) andin Program id. 53 (PI George Rieke) with the Multiband
Article number, page 19 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 T a b l e C . . Su mm a r y o f t h e a dd i t i o n a l r a d i a t i v e t r a n s f e r m o d e l s ,i n c l ud i n g t h e c o l u m nd e n s i t i e s , N I R i n t e n s i t i e s , J b a nd o p t i c a l d e p t h , µ m o p t i c a l d e p t h , r a d i a t i o nfi e l d s c a li n g , a nd t h e c o r e t e m p e r a t u r e . M o d e l n a m e D e s c r i p t i o n N ( H ) ( ) J ( ) H ( ) K S ( ) τ J , e m ( ) τ ( ) K I S R F T c o r e ( ) ( c m − )( M J y / s r )( M J y / s r )( M J y / s r ) ( × − ) ( K ) O B S V a l u e s d e r i v e d f r o m o b s e r v a t i o n s . × . . . . . - . C O M m o d e l s D e f a u l t C o m p i è g n ee t a l. ( ) . × . . . . . . . A l b e d o A l b e d oo f t h e du s t g r a i n s i n c r e a s e db y % . × . . . . . . . G t e s t g p a r a m e t e r o f t h e du s t g r a i n s i n c r e a s e db y % . × . . . . . . . D i s tt e s t γ o f t h e du s t s i ze d i s t r i bu t i o n i n c r e a s e db y % . × . . . . . . . W i d e M o d e l c l o ud w i t h a w i d e r L O Sd e n s i t y d i s t r i bu t i o n . × . . . . . . . N o t e s . ( ) T h e c o l u m nd e n s i t y , b a c k g r o und s ub t r a c t e d i n t e n s i t y , a nd t h e o p t i c a l d e p t h s o f J b a nd a nd µ m b a ndh a v e b ee n c o m pu t e d a s a v e r ag e v a l u e s o v e r × m a pp i x e l s c e n t r e d o np o i n t ( s ee l e f t p a n e l o f F i g . ) . ( ) T h e v a l u e d e r i v e d f r o m o b s e r v a t i o n s b a s e d o n t h e N H + li n e o b s e r v a t i o n s b y L i n e t a l. ( ) . T h e m o d e ll e d v a l u e s a r e c o m pu t e d a s a v e r ag e s o v e r c e ll s c e n t r e d a tt h e c o r e . Article number, page 20 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS 100 m A M J y s r y ( p c ) SIM 100 m D M J y s r y ( p c ) (OBS SIM) 100 m G I O B S I S I M ( M J y s r ) y ( p c ) OBS 160 m B M J y s r y ( p c ) SIM 160 m E M J y s r y ( p c ) (OBS SIM) 160 m H I O B S I S I M ( M J y s r ) y ( p c ) OBS 250 m C M J y s r y ( p c ) SIM 250 m F M J y s r y ( p c ) (OBS SIM) 250 m I I O B S I S I M ( M J y s r ) Fig. B.1.
Observed (first row) and simulated (second row) emission maps using the Default model at 100, 160, and 250 µ m. Thethird row shows the difference between the observed and simulated maps. The simulated emission has been computed from thebest fit parameters of the Default model and with taking into account stochastically heated grains. Imaging Photometer for Spitzer (MIPS). However, the pro-gram 90109 was carried out during the warm mission, thusonly the 3.6 and 4.5 µ m channels were available. The IRACobservations are discussed in more detail by Stutz et al.(2009) and Steinacker et al. (2015), for the cold and warmmissions, respectively. The MIPS observations are describedby (Rieke & Keene 2004) and Stutz et al. (2007).The Spitzer 3.6 µ m and 4.5 µ m maps show extendedsurface brightness towards the central region of the cloud,but in both 5.8 µ m and 8.0 µ m maps the region is seenin absorption (see Fig. D.2). The surface brightness in the3.6 and 4.5 µ m maps can be caused by thermal emission bysmall grains, but the surface brightness is only seen from thedense central regions. If the surface brightness is caused bythermal emission because of the high optical depth for theradiation heating the dust grains, one would expect it to bebright in the more extended region, not in the cloud centre.On the other hand, as discussed by Steinacker et al. (2010),in the current PAH emission models, the emission shouldincrease towards the longer wavelengths and the Spitzer 4.5and 5.8 µ m bands, but in the Spitzer images the opposite isseen as the cloud in seen in absorption towards the longerwavelengths. Thus, we can conclude that the extended sur-face brightness seen in the 3.6 µ m band, and at shorterwavelengths, is scattered light.Shown in Figs. D.1 and D.2 are the observations fromthe WIRCam instrument and Spitzer space telescope. Tostudy the diffuse signal, we have used the Source-Extractor(Bertin & Arnouts 1996, SExtractor) and Point SpreadFunction Extractor (Bertin 2011, PSFEx) to remove pointsources. The extraction was carried out in three steps, in the first step, we use SExtractor to detect only the bright-est point sources in each image. The detected bright sourcesare then analysed by PSFEx to construct a PSF for eachdetected source. The PSFs are then used in a second runwith SExtractor to detect all point sources in the images.This second run produces an image of objects which wesubtract from the original observations resulting in an im-age in which stars appear as smooth holes. The NIR imagesare further smoothed over × map pixels to better showthe morphology of the scattered light. Appendix E: Additional figures
The Figs. E.1 to E.4 show all of our surface brightness mapsfor the different dust models. Shown in Fig. E.5 are theindividual components of the simulations.Figs. E.6 to E.7 are the simulated surface brightnessmaps of the H band using the Default dust model. Therows and columns of the figures corresponding to differentassumptions on the strength of the radiation field and thesky brightness behind the cloud. The model cloud columndensity is scaled by 1, 0.6, and 0.3 for the three figures,respectively.Shown in Figs. E.8 to E.10 are the residuals between ourmodels and the observed emission (observed value minusthe model prediction) for all dust models. Each row in thefigures corresponds to a single model and the column showthe reiduals in the 250, 350, and 500 µ m bands.Additional NIR spectra extracted from point 2, see Fig.11, is shown in Fig. E.11 and a schematic overview of ourmodelling process is shown in Fig. E.12. Article number, page 21 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) OBS 100 m A M J y s r y ( p c ) SIM 100 m D M J y s r y ( p c ) (OBS SIM) 100 m G I O B S I S I M ( M J y s r ) y ( p c ) OBS 160 m B M J y s r y ( p c ) SIM 160 m E M J y s r y ( p c ) (OBS SIM) 160 m H I O B S I S I M ( M J y s r ) y ( p c ) OBS 250 m C M J y s r y ( p c ) SIM 250 m F M J y s r y ( p c ) (OBS SIM) 250 m I I O B S I S I M ( M J y s r ) Fig. B.2.
As Fig. B.1, but for the THEMIS model.Article number, page 22 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 Wavelength ( m)10 I n t e n s i t y ( M J y / s r ) ObservedDefaultTHEMIS
Fig. B.3.
Spectral energy distributions for the observations (orange line), the Default model (star symbols), and the THEMISmodel (diamond symbols). The red and blue highlights show the assumed uncertainty in the modelled results for the Default andTHEMIS models, respectively. The data points of the models are a sum of scattered surface brightness seen over the backgroundlevel, estimated emission, and subtracting the background seen trough the cloud. D e c ( J ) J ) ) S ) Fig. D.1.
Colour maps show the NIR surface brightness at J band (left frame), H band (centre), and K S band (right). The surfacebrightness maps have been smoothed over 6 × N (H ) column density derived from the Herschel observations. The contour levels are 15 % , 45 % , and 75 % of the peak column density of . × cm − .Article number, page 23 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 D e c ( J ) ) 5h03m44.80s44.90s45.00s45.10s45.20s+32°39'34.0"35.0"36.0"37.0"38.0" )5h03m44.80s44.90s45.00s45.10s45.20s RA (J2000)+32°39'34.0"35.0"36.0"37.0"38.0" D e c ( J ) ) 5h03m41.90s42.00s42.10s42.20s42.30s RA (J2000)+32°38'57.0"58.0"59.0"39'00.0"01.0"02.0"03.0" ) Fig. D.2.
Spitzer observations covering the 3.6, 4.5, 5.8, and 8.0 µ m bands. The surface brightness maps have been smoothedover 6 × N (H ) column density derived from the Herschel observations. The contourlevels are 15 % , 45 % , and 75 % of the peak column density of . × cm − .Article number, page 24 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS J A 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J D 0.000.010.020.030.040.050.060.070.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J G 0.000.020.040.060.080.100.12 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J J 0.000.010.020.030.040.050.060.07 i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) S C 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) S F 0.000.010.020.030.040.05 i n t e n s i t y ( M J y s r ) S I 0.000.010.020.030.040.050.060.07 i n t e n s i t y ( M J y s r ) S L 0.000.010.020.030.040.05 i n t e n s i t y ( M J y s r ) Fig. E.1.
Observed NIR surface brightness (first row) compared to model predictions with the Default (second row), Albedo (thirdrow), and Disttest (fourth row) models. Article number, page 25 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) OBS J A 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J D 0.000.020.040.060.080.10 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J G 0.000.010.020.030.040.050.060.070.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J J 0.000.010.020.030.040.050.060.070.08 i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) S C 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) S F 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) S I 0.000.010.020.030.040.050.06 i n t e n s i t y ( M J y s r ) S L 0.000.010.020.030.040.05 i n t e n s i t y ( M J y s r ) Fig. E.2.
As Fig. E.1, but for models Gtest (second row), Scaled2 (third row), and scaled4 (Fourth row).Article number, page 26 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS J A 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J D 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J G 0.000.020.040.060.080.100.12 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J J 0.000.020.040.060.080.100.12 i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) S C 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) S F 0.000.010.020.030.040.050.06 i n t e n s i t y ( M J y s r ) S I 0.000.020.040.060.080.100.12 i n t e n s i t y ( M J y s r ) S L 0.000.020.040.060.080.100.12 i n t e n s i t y ( M J y s r ) Fig. E.3.
As Fig. E.1, but for models Wide (second row), LG (third row), and LGM (Fourth row).Article number, page 27 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) OBS J A 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J D 0.0000.0250.0500.0750.1000.1250.1500.175 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J G 0.000.020.040.060.080.100.120.14 i n t e n s i t y ( M J y s r ) y ( p c ) SIM J J 0.000.020.040.060.08 i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) S C 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) S F 0.000.050.100.150.200.25 i n t e n s i t y ( M J y s r ) S I 0.0000.0250.0500.0750.1000.1250.1500.175 i n t e n s i t y ( M J y s r ) S L 0.000.020.040.060.080.10 i n t e n s i t y ( M J y s r ) Fig. E.4.
As Fig. E.1, but for models SIGMA (second row), THEMIS (third row), and DDust (Fourth row).Article number, page 28 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS J A 0.000.020.040.060.08 I n t e n s i t y ( M J y s r ) y ( p c ) Sca J D 0.0000.0250.0500.0750.1000.1250.1500.175 I n t e n s i t y ( M J y s r ) y ( p c ) BG J G 0.050.040.030.020.010.00 I n t e n s i t y ( M J y s r ) y ( p c ) SIM J J 0.150.100.050.000.05 I n t e n s i t y ( M J y s r ) y ( p c ) OBS SIM J M 0.050.000.050.100.150.20 I n t e n s i t y ( M J y s r ) I n t e n s i t y ( M J y s r ) I n t e n s i t y ( M J y s r ) I n t e n s i t y ( M J y s r ) I n t e n s i t y ( M J y s r ) I n t e n s i t y ( M J y s r ) S C 0.000.020.040.060.080.100.120.140.16 I n t e n s i t y ( M J y s r ) S F 0.000.020.040.060.080.100.120.140.16 I n t e n s i t y ( M J y s r ) S I 0.0350.0300.0250.0200.0150.0100.0050.000 I n t e n s i t y ( M J y s r ) S L 0.000.010.020.030.040.050.060.07 I n t e n s i t y ( M J y s r ) S O 0.0500.0250.0000.0250.0500.0750.100 I n t e n s i t y ( M J y s r ) Fig. E.5.
Different components in the surface brightness maps for the Default model. Shown on the first row are the backgroundsubtracted observed surface brightnesses and the second row shows the simulated scattered light without the background subtrac-tion. Shown on the third row is the component of the background that is seen trough the cloud (attenuated by a factor of e − τ )and the fourth row shows the background subtracted simulated surface brightness. The last row shows the difference between theobserved and simulated background subtracted surface brightness. Article number, page 29 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) OBS H A 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 1.0K BG = 1.0 D 0.000.010.020.030.040.05 I n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 2.0K BG = 1.0 G 0.000.020.040.060.080.100.120.14 I n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 3.0K BG = 1.0 J 0.000.050.100.150.200.25 I n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) ISRF = 1.0K BG = 2.0 E 0.040.030.020.010.000.010.020.03 I n t e n s i t y ( M J y s r ) ISRF = 2.0K BG = 2.0 H 0.000.020.040.060.080.10 I n t e n s i t y ( M J y s r ) ISRF = 3.0K BG = 2.0 K 0.0000.0250.0500.0750.1000.1250.1500.1750.200 I n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) ISRF = 1.0K BG = 3.0 F 0.100.080.060.040.020.000.02 I n t e n s i t y ( M J y s r ) ISRF = 2.0K BG = 3.0 I 0.020.000.020.040.06 I n t e n s i t y ( M J y s r ) ISRF = 3.0K BG = 3.0 L 0.000.020.040.060.080.100.120.14 I n t e n s i t y ( M J y s r ) Fig. E.6.
Simulated H band surface brightness maps for the Default model with different assumptions on the strength of theradiation field and on the sky brightness behind the cloud. Shown on the first row are the observed surface brightness maps. Shownon the rows 2 to 4 are the simulated H band maps, for which the strength of the radiation field has been scaled with a factorbetween 1 and 3, and the intensity of the background has been scaled between factors 1 and 0.3. The density of the cloud is thesame as in the Default model.Article number, page 30 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) OBS H A 0.000.020.040.060.080.100.120.140.16 i n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 1.0K BG = 1.0 D 0.010.000.010.020.030.040.05 I n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 2.0K BG = 1.0 G 0.000.020.040.060.080.100.120.140.16 I n t e n s i t y ( M J y s r ) y ( p c ) K ISRF = 3.0K BG = 1.0 J 0.000.050.100.150.200.25 I n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) ISRF = 1.0K BG = 2.0 E 0.040.030.020.010.000.01 I n t e n s i t y ( M J y s r ) ISRF = 2.0K BG = 2.0 H 0.020.000.020.040.060.080.10 I n t e n s i t y ( M J y s r ) ISRF = 3.0K BG = 2.0 K 0.000.050.100.150.20 I n t e n s i t y ( M J y s r ) i n t e n s i t y ( M J y s r ) ISRF = 1.0K BG = 3.0 F 0.080.060.040.020.00 I n t e n s i t y ( M J y s r ) ISRF = 2.0K BG = 3.0 I 0.040.020.000.020.04 I n t e n s i t y ( M J y s r ) ISRF = 3.0K BG = 3.0 L 0.0250.0000.0250.0500.0750.1000.1250.150 I n t e n s i t y ( M J y s r ) Fig. E.7.
As Fig. E.6, but the cloud model has a
70 % lower column density compared to the Default model.Article number, page 31 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) SIM 250 m D 0.0250.0000.0250.0500.0750.1000.1250.150 R e l a t i v e e rr o r y ( p c ) SIM 250 m G 0.0250.0000.0250.0500.0750.1000.1250.150 R e l a t i v e e rr o r y ( p c ) SIM 250 m G 0.0250.0000.0250.0500.0750.1000.125 R e l a t i v e e rr o r y ( p c ) SIM 250 m J 0.0250.0000.0250.0500.0750.1000.1250.150 R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r Fig. E.8.
Relative errors between the observed emission and our model predictions for 250, 350, and 500 µ m bands. Each rowcorresponds to a different dust model. The rows from top to bottom correspond to models Default, Albedo, Disttest, and Gtest.Article number, page 32 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 y ( p c ) SIM 250 m D 0.060.040.020.000.020.040.060.080.10 R e l a t i v e e rr o r y ( p c ) SIM 250 m G 0.050.000.050.10 R e l a t i v e e rr o r y ( p c ) SIM 250 m G 0.040.020.000.020.040.060.080.10 R e l a t i v e e rr o r y ( p c ) SIM 250 m J 0.0500.0250.0000.0250.0500.0750.100 R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r Fig. E.9.
As Fig. E.8, but for models Scaled2, Scaled4, Wide, and LG. Article number, page 33 of 35 &A proofs: manuscript no. Multi-wavelength_observations_and_modelling_of_a_quiescent_cloud_LDN1512 y ( p c ) SIM 250 m D 0.0750.0500.0250.0000.0250.0500.0750.100 R e l a t i v e e rr o r y ( p c ) SIM 250 m G 0.000.050.100.150.20 R e l a t i v e e rr o r y ( p c ) SIM 250 m G 0.050.000.050.100.150.200.25 R e l a t i v e e rr o r y ( p c ) SIM 250 m J 0.0250.0000.0250.0500.0750.1000.125 R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r R e l a t i v e e rr o r Fig. E.10.
As Fig. E.8, but for models LGM, SIGMA, THEMIS, and DDust.Article number, page 34 of 35ika Saajasto et al.: Multi-wavelength observations and modelling of a quiescent cloud LDN1512 D e f a u l t A l b e d o G t e s t D i s tt e s t s c a l e d s c a l e d w i d e L G L G M S I G M A T H E M I S D D u s t Model0.050.000.050.100.150.200.25 I n t e n s i t y ( M J y / s r ) JHK S Fig. E.11.
J, H, and K S band intensities from observations (horizontal lines) and different models (symbols) for the map position2. The colours correspond to the J (purple), H (red), and K S (black) bands. All intensity values have been background subtracted.We assume a
20 % uncertainty in background sky estimates for the J and K S bands and an uncertainty of
30 % for the H band.