Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores II. Simulated ALMA dust emission maps
Benoît Commerçon, François Levrier, Anaëlle J. Maury, Thomas Henning, Ralf Launhardt
aa r X i v : . [ a s t r o - ph . S R ] O c t Astronomy&Astrophysicsmanuscript no. paper2-v4 c (cid:13)
ESO 2018November 10, 2018
Synthetic observations of first hydrostatic cores in collapsinglow-mass dense cores.
II. Simulated ALMA dust emission maps
B. Commerc¸on , F. Levrier , A.J. Maury , Th. Henning , and R. Launhardt Laboratoire de radioastronomie, UMR 8112 du CNRS, ´Ecole Normale Sup´erieure et Observatoire de Paris, 24 rue Lhomond, 75231Paris Cedex 05, France ESO, Karl Schwarzschild Strasse 2, 85748, Garching bei M¨unchen, Germany Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, 69117 Heidelberg, GermanyReceived 20 july 2012; accepted 3 october 2012
ABSTRACT
Context.
First hydrostatic cores are predicted by theories of star formation, but their existence has never been demonstrated con-vincingly by (sub)millimeter observations. Furthermore, the multiplicity at the early phases of the star formation process is poorlyconstrained.
Aims.
The purpose of this paper is twofold. First, we seek to provide predictions of ALMA dust continuum emission maps from earlyClass 0 objects. Second, we show to what extent ALMA will be able to probe the fragmentation scale in these objects.
Methods.
Following our previous paper (Commerc¸on et al. 2012, hereafter paper I), we post-process three state-of-the-art radiation-magneto-hydrodynamic 3D adaptive mesh refinement calculations to compute the emanating dust emission maps. We then producesynthetic ALMA observations of the dust thermal continuum from first hydrostatic cores.
Results.
We present the first synthetic ALMA observations of dust continuum emission from first hydrostatic cores. We analyze theresults given by the di ff erent bands and configurations and we discuss for which combinations of the two the first hydrostatic coreswould most likely be observed. We also show that observing dust continuum emission with ALMA will help in identifying the physi-cal processes occurring within collapsing dense cores. If the magnetic field is playing a role, the emission pattern will show evidenceof a pseudo-disk and even of a magnetically driven outflow, which pure hydrodynamical calculations cannot reproduce. Conclusions.
The capabilities of ALMA will enable us to make significant progress towards understanding fragmentation at the earlyClass 0 stage and discovering first hydrostatic cores.
Key words.
Stars: low mass, formation - Magnetohydrodynamics (MHD), radiative transfer - Methods: numerical - Techniques:interferometric
1. Introduction
It is established that most stars form in multiple systems(Duquennoy & Mayor 1991; Janson et al. 2012). This indicatesa fragmentation process during star formation, which can be ex-plained by several mechanisms (e.g., Bodenheimer et al. 2000;McKee & Ostriker 2007). The first picture is to consider the in-terplay between turbulence and gravity within molecular clouds,which can lead to an initial fragmentation prior to the col-lapse (Hennebelle & Chabrier 2008). In this picture, the stel-lar Initial Mass Function (IMF) is mainly determined at thedense core formation stage, the latter undergoing collapse with-out fragmenting into individual objects (e.g., Price & Bate 2007;Hennebelle & Teyssier 2008; Commerc¸on et al. 2010). On theother hand, fragmentation may also occur during the collapseof molecular clouds (e.g Bate & Bonnell 2005; Bate 2012)or within disks that are formed because of the conservationof angular momentum (e.g., Whitworth & Stamatellos 2006;Commerc¸on et al. 2008). The fragmentation process thus re-mains a matter of intense debate, and in particular, the disk for-mation and early fragmentation (i.e., during the early phase of
Send o ff print requests to : B. Commerc¸on [email protected] the collapse) issues appear to be critical to better constrain thestar formation mechanism (e.g., Li et al. 2011; Joos et al. 2012;Seifried et al. 2012).The tremendous combined developments of observationaland supercomputing capabilities allow to study astrophysicalprocesses on scales which were until today unresolved. In par-ticular, great advances in understanding the star formation pro-cess have been achieved during the past ten years. On the onehand, thanks to various (sub)millimeter interferometric facili-ties (e.g., the IRAM Plateau de Bure Interferometer, PdBI, andthe Submillimeter Array, SMA) and to the Spitzer and
Herschel space telescopes, much progress has been achieved towards un-derstanding the formation and structure of prestellar dense cores,and constraining the evolutionary stages of star-forming regions(e.g., Kennicutt & Evans 2012). On the other hand, numericalmodels of star formation integrate more and more physical pro-cesses. Among the most important ones, magnetic fields andradiative transfer appear to shape the collapse and fragmenta-tion of prestellar dense cores (e.g., Hennebelle & Teyssier 2008;Bate 2009), while their combined feedback dramatically inhibitsfragmentation in low- and high-mass collapsing dense cores(Commerc¸on et al. 2010, 2011b). Unfortunately, there is cur-rently no direct evidence of these mechanisms, since observa-
B. Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. tions are not yet able to probe the fragmentation scale in nearbystar-forming regions. While wide > ∼ . −
1” (e.g., using the IRAM PdBI or the SMA) show alack of close < ∼ / Submillimeter Array (ALMA) obser-vations are definitely needed.First hydrostatic cores (FHSC), i.e., first Larson cores(Larson 1969) are the first protostellar objects formed during thestar formation process with typical sizes of a few AU. Althoughtheir existence is predicted by theory (e.g., Larson 1969;Masunaga et al. 1998; Tomida et al. 2010b; Commerc¸on et al.2011a), there still is no strong observational evidence for suchobjects, because FHSCs are deeply embedded within collaps-ing cores and their lifetimes are relatively short (at most afew thousand years, e.g., Tomida et al. 2010a; Commerc¸on et al.2012, hereafter Paper I) compared to the Class 0 phase duration(0 . − . ff ner et al. (2012) presented synthetic ALMA observations ofdust continuum or line emission. In this paper, we present thefirst predictive dust emission maps of embedded FHSCs as theyshould be observable with ALMA. This study focusing on dustcontinuum is considered as a first step towards FHSC character-ization in combination with the results of Paper I.The paper is organized as follows. Section 2 presents thephysical models and the method we use to derive syntheticALMA dust emission maps. Section 3 reports on the results weobtain to select the best ALMA configuration and the best re-ceiver band in order to observe FHSCs. We discuss the limita-tion of our work in Sec. 4. Section 5 presents our conclusionsand perspectives concerning the future work needed to confirmthe results obtained as a first step with dust continuum observa-tions.
2. Method
In this study, we restrict our work to the early stages of thestar formation process, i.e., the first collapse and FHSC forma-tion. As mentioned in the introduction, a lot of progress has beenachieved in theory and observations to characterize what wewould expect at those early stages. In the following, we combinestate-of-the-art tools to produce synthetic ALMA dust emissionobservations.
We performed 3D full radiation-magneto-hydrodynamic(RMHD) calculations using the adaptive mesh refinement code
RAMSES (Teyssier 2002), which integrates the equations of idealmagneto-hydrodynamics (Fromang et al. 2006) and uses thegrey flux-limited-di ff usion approximation for the radiative trans-fer (Commerc¸on et al. 2011c). We used the same RMHD calcu-lations presented in Paper I, which consisted in letting rotating(in solid-body rotation) 1 M ⊙ dense cores collapse, with initiallyuniform temperature, density and magnetic field. The ratio ofthe initial thermal and rotational energies to the gravitational en-ergy are respectively α = .
35 and β = . ff erent models with the same initial conditions except for theinitial magnetization, which is parametrized by the mass-to-fluxto critical mass-to-flux ratio µ = ( M / Φ ) / ( M / Φ ) c . The threemodels are depicted as follows : MU2 model (strong magneticfield, µ = µ = µ = ff erent physical structures and FHSC life-times found in the three models are summarized in Table 1.In the MU2 model, only one FHSC is formed, surrounded bya pseudo-disk, and an outflow has been launched. The MU10model does not fragment either and results in a system composedof a disk, a pseudo-disk and an outflow. The MU200 modelhas classical features of hydrodynamical models, in which rel-atively large disks ( ∼
150 AU) are formed and subsequentlyfragment. Readers are referred to Paper I for a thorough de-scription of the di ff erent models and their limitations. Note thatthe MU2 and MU10 models are more representative of the ob-served magnetization level in star forming regions (i.e., µ ≈ − t + .
78 kyr for theMU2 model, t + .
81 kyr for the MU10 model, and t + . t corresponds to the FHSCsformation in each model, i.e. 50.4 kyr for MU2, 35.7 kyr forMU10 , and 35.4 kyr for MU200). RAMDC-3D
We used the same interface as that presented in Paper I,which couples the outputs of the RMHD calculations, donewithin
RAMSES , to the 3D radiative transfer code
RADMC-3D .In this interface, we assumed that gas and dust are thermallycoupled ( T dust = T gas ), which is a valid approximation giventhe high density within the dense cores (e.g, Galli et al. 2002).We also assumed that the gas temperature T gas computed inthe RMHD calculations is correct (Commerc¸on et al. 2011a;Vaytet et al. 2012). We used the low temperature opacities ofSemenov et al. (2003) for a model in which dust is made of ho-mogeneous spheres with a ”normal” (Fe / Fe + Mg = .
3) silicatecomposition.The dust thermal continuum emission maps were computedon a square box with physical size ∆ x = δ x = .
54 AU. Since models were assumed to be ata distance D =
150 pc, this translates into an angular extent ∆ ϑ = .
67” and an angular resolution δϑ = . ff er- ∼ dullemond/software/radmc-3d/ . Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. 3 Table 1.
Summary of the physical structures and FHSC lifetimes found in the three models. The last four columns indicate whetherthese structures are observed (cross) or not (dash) in the synthetic ALMA observations presented in Fig. 3 to 6.
Model Physical structures FHSC lifetime Structures in synthetic observations θ = ◦ θ = ◦ θ = ◦ θ = ◦ MU2 one object 1.2 kyr x x x xpseudo-disk x x x xoutflow - - - -MU10 one object 1.8 kyr x x x xpseudo-disk x x x xcompact disk x x x -outflow - - - xMU200 five fragments > Table 2.
Characteristics of the ALMA bands used, denoted B .Listed are the central frequency ν , full bandwith ∆ ν (not tobe confused with the bandwidth ∆ ν = B ν [GHz] ∆ ν [GHz] FoV [”] Early Science3 100 32 63 Yes4 144 38 44 No6 243 64 26 Yes7 324 98 19 Yes8 442.5 115 14 No9 661 118 9.5 Yes Table 3.
Characteristics of the full ALMA configurations used,denoted C . Listed are the minimum and maximum baselines, andsynthesized beam major and minor axes for bands 3 and 9. C b min [m] b maj [m] θ [”] θ [”]5 15 390 2 . × .
12 0 . × . . × .
99 0 . × . . × .
43 0 . × . . × .
22 0 . × . ent viewing angles are used in the following : θ = ◦ (equatorialplane seen face-on), θ = ◦ , θ = ◦ , and θ = ◦ (edge-on view, perpendicular to the rotational axis). These model dustemission maps were computed for six ALMA bands (3, 4, 6, 7,8 and 9), including the four that are in use in the Early Sciencestage (see table 2), over a total bandwidth ∆ ν = ν . This was done by computinga set of ten emission maps, one for each of ten 800 MHz sub-bands, and averaging them. The resulting map gives the meanspecific intensity h I ν i of the thermal dust emission over the band,in erg cm − s − Hz − sr − , and is then converted to a brightnesstemperature map in K via T B = − × c h I ν i k B ν . The
GILDAS software package , developed and maintainedby IRAM, is primarily intended for the reduction and analysis of The factor 10 − comes from the CGS to SI conversion of the specificintensity, as the ALMA simulator assumes input brightness distributionsto be in K. iram.fr/IRAMFR/GILDAS/ observational data acquired via the IRAM instruments (single-dish 30-m radiotelescope at Pico Veleta and 6-antenna array atIRAM PdBI). It also includes a full ALMA simulator, with up-to-date array configurations , which was primarily developed toassess the impact of the ALMA compact array (ACA) on theimaging capabilities of ALMA (Pety et al. 2001; Tsutsumi et al.2004).To produce synthetic ALMA observations from our dustemission models, maps are converted to the GILDAS data format(GDF) and projected on a fixed sky position ( α , δ ) = (0 ◦ , − ◦ )such that sources transit at the zenith of the array. The field-of-view in each band (see table 2), given by 1 . λ / d with d =
12 mthe antenna diameter and λ the central wavelength of the band,shows that a single pointing su ffi ces to map the emission in allcases.ALMA consists of two sub-arrays, the fifty 12-m antennasand the twelve 7-m antennas of the ACA. The array operationwill consist in constantly moving antennas around, so that notwo observations may be obtained with exactly the same con-figuration. We do not consider the compact array and focus onimaging the cores’ thermal emission with ALMA only. To keepthe number of simulations down to a manageable number, weselect four ”typical” configurations (out of the 28 representativeconfigurations implemented in GILDAS), whose properties arelisted in table 3. Since we make one simulation per model, perconfiguration, per inclination angle, and per band, the total num-ber of simulations is thus 3 × × × =
3. Results
In our models, thermal dust emission at millimeter and sub-millimeter wavelengths mostly comes from structures that arelarger than the FHSC (i.e., from the disk and the pseudo-disk).Yet, to discriminate between di ff erent magnetization levels µ ,one needs to resolve the fragmentation scale of a few AU. Thislatter constraint means that only extended configurations of thearray will be able to provide a su ffi cient angular resolution, inthe few tens of milliarcseconds range. However, this comes with We used release apr11h of GILDAS . The latest releases also containEarly Science Cycle 1 configurations of the array. B. Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. UV radius [m] P D F o f U V - c o v e r [ . G H z ][ . G H z ][ . G H z ][ . G H z ][ . G H z ][ . G H z ] UV radius [m] -1 P o w e r Sp e c t r u m B =3 ; MU2B =3 ; MU10B =3 ; MU200B =9 ; MU2B =9 ; MU10B =9 ; MU200
Fig. 1.
Left :
Probability density function from the distribution of samples in the u − v plane for the 4 configurations used here(numbers 5, 10, 15 and 20, indicated next to each curve) as a function of u − v radius d uv = √ u + v . The relevant parameters arethe source position and duration of observation, which are described in section 2.3. The small vertical lines indicate the minimumbaseline for each configuration. Also marked, with dashed lines, are characteristic baselines d uv = cD / (2 πν d ) corresponding to aphysical size d =
10 AU at a distance D =
150 pc, for the six frequencies ν . Right :
Power spectra of the input maps at 100 GHz(solid lines) and 661 GHz (dashed lines) for θ = ◦ . The wavenumber axis has been rescaled to match the u − v radius of the leftplot. The vertical black lines mark the positions of the 10 AU scale at 150 pc at these frequencies (solid for 100 GHz, dashed for661 GHz, reported from left plot).an increase of the minimum baseline length, so that large-scaleemission is lost due to the central hole in the visibility (Fourier)space, also called u − v plane.To make this idea more quantitative, Fig. 1 ( left ) shows thedistribution of visibility samples as a function of radius in the u − v plane for the four configurations. Marked on this graphare the baselines d uv = cD / (2 πν d ) corresponding to a physicalsize d =
10 AU (roughly equal to the size of fragments in theMU200 models) at a distance D =
150 pc, for the six centralfrequencies ν . On the right plot of Fig. 1 we display the powerspectra of the face-on input maps at 100 GHz (band 3) and 661GHz (band 9), with the wavenumber axis k rescaled to matchthat of the u − v radius on the left plot. This is done by noticingthat the largest wavenumber in the power spectrum correspondsto the pixel physical size δ x .The fragmentation in the MU200 model appears as the ex-cess power at intermediate scales compared to MU2 and MU10.This excess is clearly seen for 300 m . d uv . d uv = C = C =
15 and C =
20. However, both ofthese configurations have a larger central hole than C = C =
10, and therefore should lose a larger amount of flux. Thisflux loss becomes larger at higher frequencies, since d uv ∝ /ν implies a global compression of the sources’ power spectra to-wards smaller baselines.For a global view on the emission loss at large scales, Fig. 2shows the ratio between the observed flux to the model flux asa function of frequency and array configuration. As expected,the most compact configurations ( C = C =
10) allow torecover essentially all of the flux in bands 3 to 7. Only in band8 and 9 we see a ∼
50% drop in the received flux for the non-fragmenting models MU2 and MU10. Figure 2 also confirmsthat flux loss increases with frequency in configurations 15 and20, most ( ∼ We show, in Fig. 3 to 6, the brightness distribution maps out-put by the ALMA simulator in bands 3 and 4, for configurations15 and 20. In each figure, four inclination angles are shown,i.e., θ = ◦ , ◦ , ◦ , and 90 ◦ . Also shown are the sensitivitylimits 3 σ S in these two bands, given by the ALMA SensitivityCalculator . The most extended configuration and the largest fre-quency best probe the fragmentation scales ( C = B = C =
15 and B =
3. A better compromise betweenhigh resolution imaging and flux recovering is found using ei-ther C =
15 and B = C =
20 and B =
3. Overall, there is aclear distinction between the two magnetized models (MU2 andMU10) and the quasi-hydro MU200 model. As expected theo-retically, as soon as a magnetic field is taken into account, withfield strengths in the range of what is actually observed (e.g.,Falgarone et al. 2008; Crutcher et al. 2010; Maury et al. 2012),the picture changes dramatically.Interestingly, many features that are directly probing thephysical conditions can be observed with the dust emission al-ready (see Table 1). In the MU200 model, the fragmentation isresolved for inclination angles θ < ◦ , and only the compactemission of the disk is observed in the edge-on view. In con-trast to that, the dust emission is much more extended in themagnetized MU2 and MU10 models, and corresponds to den-sity features that are typical of magnetized collapse: the pseudo-disk and the outflow. In both cases, the most powerful emission The weather conditions used are that of the first octile, i.e., 0.47mmof precipitable water vapor above the instrument.. Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. 5 -2 -1 F o b s e r v e d / F t r u e MU2 - (cid:0) =0 (cid:1) -2 -1 MU10 - (cid:2) =0 (cid:3) MU200 - (cid:4) =0 (cid:5) -2 -1 F o b s e r v e d / F t r u e MU2 - (cid:6) =45 (cid:7) -2 -1 MU10 - (cid:8) =45 (cid:9)
MU200 - (cid:10) =45 (cid:11) -2 -1 F o b s e r v e d / F t r u e MU2 - (cid:12) =60 (cid:13) -2 -1 MU10 - (cid:14) =60 (cid:15)
MU200 - (cid:16) =60 (cid:17)
100 200 300 400 500 600 700
Frequency [GHz] -2 -1 F o b s e r v e d / F t r u e MU2 - (cid:18) =90 (cid:19)
100 200 300 400 500 600 700
Frequency [GHz] -2 -1 MU10 - (cid:20) =90 (cid:21)
100 200 300 400 500 600 700
Frequency [GHz]
MU200 - (cid:22) =90 (cid:23)
Fig. 2.
Ratio F obs / F model of the observed flux to the model flux as a function of frequency, for the three di ff erent models (MU2,MU10, and MU200), four array configurations ( C = , , , θ = ◦ , ◦ , ◦ , ◦ ). Magnetization level µ increases from left to right, and inclination angle θ increases from top to bottom.comes from the central FHSC (point-like source,yellow area). Inthe MU10 model, the disk emission is observed (blue regions)for inclination angles θ < ◦ , but it remains relatively small incomparison to the pseudo-disk one. The pseudo-disk emissionfeatures are very similar in the MU2 and MU10 models for in-clination angles θ < ◦ . In the edge-on view ( θ = ◦ ), theemission from the pseudo-disk is clearly observed in the MU2and MU10 models, and is much more extended than that of thedisk in the MU200 model. The pattern of the pseudo-disk ob-served with C =
20 and B = ∼ ′′ along the polar axis, corresponding to ∼
300 AU. This isnot surprising since the outflow tends to transport more mass inthe case of a lower magnetization (Hennebelle & Fromang 2008,and see Fig. 2 in Commerc¸on et al. 2012).We investigate thoroughly in appendix A the e ff ects of noise(thermal and atmospheric phase) and pointing errors on the syn-thetic observations. The main conclusions draw from the noise-free case remain unchanged, except that more flux is lost in noisyobservations. We refer interested readers to appendix A.
4. Discussion
One limitation of this work is that we used a unique dustopacity model from Semenov et al. (2003), in which dust grainscan grow, so that we do not predict the variation of the dustemission with di ff erent dust grain properties. The dust properties (size, composition, and morphology) within dense cores are stillvery uncertain, but there is nevertheless theoretical and observa-tional evidence of dust grain growth within dense cores (e.g.,Ormel et al. 2009; Steinacker et al. 2010). Ormel et al. (2011)compared the dust grain opacities they got from the various grainmodels of Ormel et al. (2009) with the Ossenkopf & Henning(1994) opacities model and found that the opacity, in the sub-millimeter wavelength range, only varies by a factor of a fewbetween all the di ff erent models. We also checked that theSemenov et al. (2003) opacities we used are similar to the fromthe Ossenkopf & Henning (1994) ones by factors close 1, so thatthe choice in the opacity will not change the picture. In addition,we show in Paper I (Fig. 4) that the radius at which the opticaldepth equals unity does not depend strongly on the opacity for(sub)millimeter wavelengths. We thus speculate that our predic-tions are relatively robust given the small variations in opticaldepth and in opacity in the (sub)millimeter wavelength range.The second main limitation comes from our idealized initialand boundary conditions, which do not account for the densecore environment (e.g., eventual mass accretion on the corewhile it collapses) and initial turbulence, whereas the latter canpotentially modify the magnetic braking and thus the fragmen-tation properties during the collapse (e.g., for higher mass densecores, Seifried et al. 2012). Turbulence, however, is observed tobe sub- to trans-sonic in low mass dense cores (Goodman et al.1998; Andr´e et al. 2007), so that it will not change dramaticallythe outcome of the magnetized dense core collapse. In addition,magnetic fields dominate the dynamics and inhibit the fragmen-tation even more when combined with radiative transfer becauseof the energy released from the accretion shock at the FHSC bor- B. Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. (cid:24) (cid:25) (cid:26) (cid:27) Y [ a r c s e c ] (cid:28) =0 (cid:29) MU2 (cid:30) =0 (cid:31) MU10 =0 ! MU200 " $ % Y [ a r c s e c ] & =45 ’ ( =45 ) * =45 + , - . / Y [ a r c s e c ] =60 =60 =60 X [arcsec] : ; < = Y [ a r c s e c ] > =90 ? @ A B C X [arcsec] D =90 E F G H I X [arcsec] J =90 K Fig. 3.
Brightness distribution maps, in Jy / beam, output by the ALMA simulator in band B = C =
15. Magnetization level µ increases from left to right, and inclination angle θ increases from top to bottom. Contours show the3 σ S sensitivity limit in this band, as given by the ALMA Sensitivity Calculator. Here σ S = . µ Jy. The synthesized beam isshown in the bottom left corner of each plot. For a given θ , color scales are identical across all columns. . Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. 7 L M N O Y [ a r c s e c ] P =0 Q MU2 R =0 S MU10 T =0 U MU200 V W X Y Y [ a r c s e c ] Z =45 [ \ =45 ] ^ =45 _ ‘ a b c Y [ a r c s e c ] d =60 e f =60 g h =60 i j k l m X [arcsec] n o p q Y [ a r c s e c ] r =90 s t u v w X [arcsec] x =90 y z { | } X [arcsec] ~ =90 (cid:127) Fig. 4.
Same as Fig. 3 but for B = C =
15. Here, σ S = . µ Jy.
B. Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. (cid:128) (cid:129) (cid:130) (cid:131) Y [ a r c s e c ] (cid:132) =0 (cid:133) MU2 (cid:134) =0 (cid:135) MU10 (cid:136) =0 (cid:137) MU200 (cid:138) (cid:139) (cid:140) (cid:141) Y [ a r c s e c ] (cid:142) =45 (cid:143) (cid:144) =45 (cid:145) (cid:146) =45 (cid:147) (cid:148) (cid:149) (cid:150) (cid:151) Y [ a r c s e c ] (cid:152) =60 (cid:153) (cid:154) =60 (cid:155) (cid:156) =60 (cid:157) (cid:158) (cid:159) (cid:160) ¡ X [arcsec] ¢ £ ⁄ ¥ Y [ a r c s e c ] ƒ =90 § ¤ ' “ « X [arcsec] ‹ =90 › fi fl (cid:176) – X [arcsec] † =90 ‡ Fig. 5.
Same as Fig. 3 but for B = C =
20. Here, σ S = . µ Jy. . Commerc¸on et al.: Synthetic observations of first hydrostatic cores in collapsing low-mass dense cores. 9 · (cid:181) ¶ • Y [ a r c s e c ] ‚ =0 „ MU2 ” =0 » MU10 … =0 ‰ MU200 (cid:190) ¿ (cid:192) ` Y [ a r c s e c ] ´ =45 ˆ ˜ =45 ¯ ˘ =45 ˙ ¨ (cid:201) ˚ ¸ Y [ a r c s e c ] (cid:204) =60 ˝ ˛ =60 ˇ — =60 (cid:209) (cid:210) (cid:211) (cid:212) (cid:213) X [arcsec] (cid:214) (cid:215) (cid:216) (cid:217) Y [ a r c s e c ] (cid:218) =90 (cid:219) (cid:220) (cid:221) (cid:222) (cid:223) X [arcsec] (cid:224) =90
Æ (cid:226) ª (cid:228) (cid:229) X [arcsec] (cid:230) =90 (cid:231)
Fig. 6.
Same as Fig. 3 but for B = C =
20. Here, σ S = . µ Jy. der (Commerc¸on et al. 2010, 2011b). We thus conclude that thethree models presented here are representative of the variety ofFHSCs that can be formed with various initial conditions.Finally, all the analysis and the ALMA synthetic map calcu-lations have been done for objects placed at a distance of 150pc. The best compromise between flux loss and angular reso-lution may thus be altered for objects at significantly di ff erentdistances, but the method remains unchanged.
5. Summary and perspectives
We present synthetic dust emission maps of FHSCs as theywill be observed by the ALMA interferometer, using state-of-the-art radiation-magneto-hydrodynamic models of collapsingdense cores with di ff erent levels of magnetic intensity. We post-process the RMHD calculations performed with the RAMSES code using the 3D radiative transfer code
RADMC-3D to producedust emission maps. The synthetic observations are then com-puted using the ALMA simulator within the
GILDAS softwarepackage.We show that ALMA will shed light on the fragmentationprocess during star formation and will help in discriminatingnot only between the di ff erent physical conditions, but also be-tween the di ff erent models of star formation and fragmentation.The forthcoming facility will yield interferometric observationsof FHSC candidates (selected using SED data, see Paper I) innearby star-forming regions with su ffi cient angular resolution toprobe the fragmentation scale. We also show that the intensityof the magnetic field in this early phase of protostellar collapsewill also be assessed, since we do see clear morphological di ff er-ences between the magnetized and non-magnetized models, i.e.,pseudo-disk and outflow in the former case versus disk and frag-mentation features in the latter case. We stress that due to the un-precedented sensitivity and coverage of the instrument, this willbe achievable in a very short time (18 minutes), so that manyFHSC candidates may be observed in a single observing run.Reaching good enough angular resolution to probe the frag-mentation scales and limiting the loss of large-scale emission re-quires a compromise, which is achieved using frequency bands3 and 4 and the relatively extended configurations 15 and 20.We also investigate the e ff ect of noise on the interferometric ob-servations and show that in typical conditions (see Fig. A.1),ALMA will still be able to reveal fragmentation. We note thatthe e ff ect of atmospheric phase noise can be e ffi ciently reducedusing water vapor radiometers on the ALMA antennas.We do not discuss the impact of the ALMA Compact Array(ACA) on our simulated observations. Its purpose is to pro-vide measurements for the large-scale emission and improve thewide-field imaging capabilities of ALMA (Pety et al. 2001), butit is not meant to resolve fragmented molecular cores. In ourmodels, this requires a 0.5” angular resolution (see e.g., the case B = C =
15 on Figs. 1 and 3), but the longest baselinesaccessible to ACA are ∼
100 m, so that the best angular resolu-tion available, at the high-frequency end of band 10 (950 GHz),is 0.8”. However, ACA could help in recovering some of the lostflux from the disk, pseudo-disk and outflow.Our work is currently limited to the dust continuum emis-sion, which cannot yet provide robust means to discriminate be-tween FHSC and second hydrostatic cores (SHSC) and to con-clude on the nature of VeLLOs. Further work including molec-ular line emission calculations is thus warranted to better probethe physical conditions (density, temperature, etc...) in observedcollapsing cores, for instance to disentangle between the disk and the pseudo-disk, which should harbour di ff erent line pro-files (rotation dominated versus infall dominated). Line emissionpredictions are thus the obvious next step towards FHSCs char-acterization. Acknowledgements. We thank the anonymous referee for his / her comments.F.L. wishes to thank J´erˆome Pety, Alwyn Wootten and Ian Heywood for theircollaboration in including the final ALMA configurations in the GILDAS simula-tor. The research of B.C. is supported by the postdoctoral fellowships from theCNES and by the french ANR Retour Postdoc program.
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The simulations presented in the main body of the paperwere performed in the unrealistic case of noiseless observations.To truly assess ALMA’s ability to resolve fragmented cores, anextension of this study to noisy observations is required, takinginto account the di ff erent causes of noise : pointing errors, ther-mal noise and phase noise.We start with an error-free simulation of the MU200 modelviewed face-on ( θ = ◦ ), in band B =
4, with configuration C =
20. All parameters are identical to those of the general setof simulations, but we add zero-spacing with a single-dish ob-servation, so that in this case all of the flux is recovered (0.1090Jy) instead of 96% of it (0.1046 Jy) with ALMA only.The following errors, whose results are summarized inTable A.1, may then be added, separately or simultaneously, tothe simulated observations : ◮ σ α , which correspond to ∼ Table A.1. E ff ect of the di ff erent noise types. The error-free sim-ulation is that of a combined B = C =
20 andwith a single-dish. Pointing errors ( σ α ) and thermal noise ( σ T )may be applied to neither instrument (” No ”), to the interferom-eter only (” ALMA ”), or to both interferometer and single-dish(”
Both ”). Phase noise is specified via the rms atmospheric phaseon a 300-m baseline, which can take the values 30 ◦ or 45 ◦ , andcan be corrected via water-vapor radiometers (” WVR ”). Shownare the fluxes S of the output maps and the median fidelities F . , F , F and F , on pixels whose intensities in the model imageare higher than 0.3%, 1%, 3% and 10% of the peak, respectively(see section A). σ α σ T σ φ WVR S [Jy] F . F F F No No No No 0.1090 107 208 279 418ALMA No No No 0.1089 119 200 245 309Both No No No 0.1088 114 202 241 312Both ALMA No No 0.1046 45 75 114 143Both Both No No 0.1035 44 75 112 141Both Both 30 ◦ No 0.0908 4 5 5 5Both Both 30 ◦ Yes 0.0987 13 15 16 16Both Both 45 ◦ No 0.0736 2 3 3 3Both Both 45 ◦ Yes 0.0947 7 7 8 8 ◮ Thermal noise σ T . In band 4, the ALMA SensitivityCalculator suggests using the 6 th octile for the atmospheric con-ditions, which corresponds to 2.75 mm of precipitable watervapor and a zenith opacity τ = . T =
40 K following Asayama et al. (2008).Regarding the single-dish measurements, we use a system tem-perature T sys =
100 K. The simulator allows for setting none,either or both ALMA and single-dish thermal noises. ◮ Atmospheric phase noise σ φ . The ALMA simulator allowsfor a turbulent atmospheric screen to pass over the interferome-ter, distorting the waveplanes and causing phase errors. This 2Dphase screen is characterized by a second-order structure func-tion that is the combination of three power-laws in three spa-tial ranges, scaled so that the rms phase di ff erence for a 300-mbaseline takes a specific value. In our case, we chose this valueto be either 30 ◦ or 45 ◦ (Pety et al. 2001). Situated at an altitude z = w =
10 m . s − . Calibration, which is done every 26 seconds usinga calibrator 2 degrees away from the source perpendicularly tothe wind direction, may include the use of water vapor radiome-ters (WVR), which directly measure the amount of precipitablewater vapor along the line of sight in the atmosphere above eachantenna.Table A.1 gives simulation results associated to the variousnoise situations considered : fluxes in the output (deconvolved)maps, and median fidelities on pixels whose intensities in themodel image are higher than 0.3%, 1%, 3% and 10% of thepeak. The fidelity is basically the inverse of the relative errorbetween the output map and the model (Pety et al. 2001), so thatthe higher the fidelity, the better the reconstruction. What is ap-parent is that atmospheric phase noise has the strongest impacton the reconstruction process, with a third of the flux being lostin the worst-case scenario, and fidelities dropping to a few (30%-50% relative error on the output maps). The use of WVR is a def-inite plus in this situation, as relative errors then drop to a littleover 10%. However, even in the worst possible situation consid-ered here, and without WVR correction, ALMA still is able touncover fragmentation, as Fig. A.1 shows that all five fragments Ł Ø Œ º X [arcsec] (cid:236) (cid:237) (cid:238) (cid:239) Y [ a r c s e c ] (cid:240) æ (cid:242) (cid:243) X [arcsec] (cid:244) ı (cid:246) (cid:247) Y [ a r c s e c ] Fig. A.1.
Brightness distribution maps, in Jy / beam, for two casesconsidered in section A. The top plot shows the case of an error-free observation at 144 GHz with ALMA in configuration C =
20, combined with single-dish. The bottom plot shows the caseof an observation with the same combination of instruments, butwith 0.6” pointing errors on all antennas, thermal noise as de-scribed in the text, and uncorrected atmospheric phase noise witha 45 ◦ rms phase di ff erence on 300-m baselines. Contours on bothplots correspond to the 3 σ S sensitivity limit given by the ALMASensitivity Calculator, where σ S = . µ Jy for the typical at-mospheric conditions in band B ==