Gas infalling motions in the envelopes of Very Low Luminosity Objects
Mi-Ryang Kim, Chang Won Lee, Maheswar, Philip C. Myers, Gwanjeong Kim
DD RAFT VERSION F EBRUARY
23, 2021Typeset using L A TEX twocolumn style in AASTeX63
Gas infalling motions in the envelopes of Very Low Luminosity Objects M I -R YANG K IM , C HANG W ON L EE ,
1, 2 M AHESWAR , G, P HILIP
C. M
YERS , AND G WANJEONG K IM Korea Astronomy and Space Science Institute, 776, Daedeokdae-ro, Yuseong-gu, Daejeon 34055, Korea University of Science and Technology, Korea (UST), 217 Gajeong-ro, Yuseong-gu, Daejeon 34113, Korea Indian Institute of Astrophysics, II Block, Koramangala, Bengaluru 560 034, INDIA Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA Nobeyama Radio Observatory, National Astronomical Observatory of Japan, National Institutes of Natural Sciences, Nobeyama, Minamimaki, Minamisaku,Nagano 384-1305, Japan (Received; Revised; Accepted; Published)
Submitted toABSTRACTWe present the results of a single dish survey toward 95 VeLLOs in optically thick (HCN 1-0) and thin ( N H + δV HCN ) between thepeak velocities of the two lines were derived for 41 VeLLOs detected in both lines. The δV distribution ofthese VeLLOs is found to be significantly skewed to the blue, indicating the dominance of infalling motions intheir envelopes. The infall speeds were derived for 15 infall candidates by using the HILL5 radiative transfermodel. The speeds were in the range of 0.03 km s − to 0.3 km s − , with a median value of 0.16 km s − ,being consistent with the gravitational free-fall speeds from pressure-free envelopes. The mass infall ratescalculated from the infall speeds are mostly of the order of − M (cid:12) yr − with a median value of . ± . × − M (cid:12) yr − . These are found to be also consistent with the values predicted with the inside-out collapsemodel and show a fairly good correlation with the internal luminosities of the VeLLOs. This again indicatesthat the infall motions observed toward the VeLLOs are likely to be due to the gravitational infall motions intheir envelopes. Our study suggests that most of the VeLLOs are potentially faint protostars while two of theVeLLOs could possibly be proto-brown dwarf candidates. Keywords:
ISM: kinematics — stars: formation INTRODUCTIONDense molecular cores that are bright in submillimetercontinuum emission but are soon to form a protostar aregenerally classified as starless (or prestellar) cores and coreswith a detectable infrared source are classified as protostellarcores. The evolution of a starless core depends on the in-terplay between the inward force of gravity and the outwardpush of the internal pressure inside the core. Thus, the in-ternal dynamics of the core may determine whether the corebecomes static, oscillatory, expand or undergo gravitationalcollapse (Lada et al. 2003; Broderick & Keto 2010; Lee &Myers 2011; Keto et al. 2015).
Corresponding author: Chang Won [email protected]
When the inward force of gravity wins over the outwardpush of the internal pressure, the starless core begins grav-itational contraction resulting in the movement of materialtowards its center. Thus, the cores that show infall motionsare most likely to form a star in the future. The presence ofsuch infalling motions can be inferred by conducting spec-troscopic observations of optically thick and thin molecularlines and by looking for what is known as the “the spectralinfall asymmetry” (e.g., Mardones et al. 1997; Tafalla et al.1998; Lee & Myers 1999). The infall asymmetry is identifiedwith a combination of a double-peaked feature in an opticallythick line where the blue peak is brighter than the red peak(such as HCN 1-0 and CS 2-1) and a single-peaked feature inan optically thin line (such as N H + a r X i v : . [ a s t r o - ph . GA ] F e b M. K
IM ET AL .et al. 1997; Park et al. 1999; Wu et al. 2005; Keown et al.2016) have shown that the inward motions are a fundamentalphysical process that occurs in the formation of the cores andprotostars.Observations with the
Spitzer
Space Telescope have led tothe discovery of a new class of objects called the very lowluminosity objects (VeLLOs) in dense cores previously clas-sified as “starless” based on the non-detection of any pointsource by the Infrared Astronomical Satellite (IRAS). TheVeLLOs are defined as objects having a very similar spec-tral energy distribution (SED) to that of a protostar, but avery faint internal luminosity of (cid:46) . (cid:12) considering itsuncertainty(Young et al. 2004). Their luminosities are foundto be much fainter than those expected by the least mas-sive protostar from the standard star formation theory byShu et al. (1987). They may be extremely young protostarswith very small central mass and mass accretion that hasjust begun, or normal protostars in a quiescent state betweenepisodic accretion events during the normal mass accretionphase, or proto-brown dwarfs with very small mass accretionrates (Kenyon et al. 1990; Myers 2011; Dunham & Vorobyov2012; Myers 2014; Hartmann et al. 2016).Several VeLLOs, including L1014-IRS ( L int ∼ .
09 L (cid:12) ;Young et al. 2004), L1521F-IRS ( L int ∼ .
06 L (cid:12) ; Bourkeet al. 2006), IRAM 04191+1522 ( L int ∼ .
08 L (cid:12) ; Dunhamet al. 2006), L328-IRS ( L int ∼ .
05 L (cid:12) ; Lee et al. 2009),L673-7-IRS ( L int ∼ .
04 L (cid:12) ; Dunham et al. 2010), L1148-IRS ( L int ∼ .
10 L (cid:12) ; Kauffmann et al. 2011), IC348-SMM2E ( L int ∼ .
06 L (cid:12) ; Palau et al. 2014), and IRAS16253-2429 ( L int ∼ .
08 L (cid:12) ; Hsieh et al. 2016), have beenstudied in detail. Irrespective of the basic nature of theseVeLLOs, it is possible that they are formed as a result ofinfall motions of material inside their parent core, whichmight have occurred due to mainly gravity-driven kinemat-ics. Therefore, observations to look for the infall motions inthe cores that harbor VeLLOs is important to understand theinitial processes that lead to the formation of protostars orproto-brown dwarfs.The physical and kinematic states of cores with VeLLOsremain poorly understood. So far, there are only a few caseswhere infalling motions in dense cores with VeLLOs havebeen detected (e.g., L328-IRS and L1521F-IRS). Lee et al.(2013) detected extended infalling motions in a core withthe VeLLO, L328-IRS. The infall speeds calculated using atwo-layer fitting analysis of HCN 1-0 F=2-1 are found to be . − .
08 km s − . Also, the recent study of L1521F-IRSshows an infall speed of about 0.1 km s − calculated from DCO + lines and the HILL5 model (Keown et al. 2016). Theinfall speeds of the cores with VeLLOs seem to be similar tothose of starless cores having velocities ≤ . − (Leeet al. 2001). Based on the shape of the SEDs from the near-IR to thesubmillimeter wavelengths using photometric data from the Spitzer and the
Herschel telescopes, and from the detectabil-ity in a high density tracer, N H + line, Kim et al. (2016)recently produced a catalog of VeLLOs. In this paper, wepresent the results of a systematic study conducted on a sta-tistically significant sample of VeLLOs selected from theabove-mentioned catalog. The cores harboring VeLLOs wereobserved using HCN (J = 1-0) and N H + (J = 1-0) molecu-lar lines to characterize the infall motions in the envelopesand compare them with those of the dense starless and proto-stellar cores. This study would provide useful insights tounderstand the fundamental physics associated with inwardmotions in the envelopes where VeLLOs are currently form-ing and discuss their properties which would in turn help usto identify their nature.This paper is organized as follows. In Section 2, we de-scribe our observations and data reduction procedure. Ourresults and discussion are presented in Sections 3 and 4, re-spectively. In Section 5, we conclude the paper with a sum-mary of the results. OBSERVATIONS AND DATA REDUCTION2.1.
Observing targets and lines
The samples of VeLLOs studied here are listed in Table1. The targets were selected from the catalog of the VeL-LOs produced by Kim et al. (2016). Distances to the targetsources are adopted from the recent catalogs (Zucker et al.2018; Kuhn et al. 2019; Zucker et al. 2019, 2020) where thedistances to the local molecular clouds associated with theGould Belt regions were estimated employing the Gaia DR2parallax measurements. The internal luminosities estimatedbased on these new, more reliable, distances for some of thesources in our sample are found to be (cid:38) . (cid:12) . Though thisis not in accordance with the original definition of VeLLOs,we retained them in our sample list as they were not detectedpreviously by the IRAS and hence not studied in depth.We conducted survey observations of 66 out of 95 VeL-LOs cataloged by Kim et al. (2016) in N H + and HCN. Wecould not observe all the 95 VeLLOs due to the limited tele-scope time that was available to us. Thus, although we couldobserve only 70 % of the sources from Kim et al. (2016) cat-alog, the number is still significant to conduct any statisticalstudy on the infall motions in the VeLLOs. The molecularlines HCN (J = 1-0) and N H + (J = 1-0) are used as opticallythick and thin tracers, respectively, for the detection of theinward motions. The HCN 1-0 line is usually observed witha self-absorbed feature, in other words, a double-peaked or askewed profile, toward dense cores when this line becomesoptically thick. However, this seemingly absorbed featurecan be formed by the presence of two slightly different ve-locity components along the line of sight. The optically thin NFALL N H + was observed to discriminate these two scenar-ios.The HCN emission is easily detected in low-mass star-forming regions (Afonso et al. 1998; Sohn et al. 2007; Danielet al. 2013; Hsieh et al. 2015). Its high critical density( n cr ∼ cm − at T=10 K; Krumholz 2017) is expectedto be useful to probe a dense gas envelope region. HCNhas three hyperfine lines with different intensities of F(0-1): F(2-1) : F(1-1) = 1 : 5 : 3 under optically thin conditions.These lines are expected to trace different regions depend-ing on their optical depths. Therefore, the HCN 1-0 line isthought to be one of the best appropriate tracers to study in-ward motions of gaseous material around the VeLLOs, whichare deeply embedded in the dense cores. The second tracer, N H + , is an ion-molecule less sensitive to the chemical evo-lution of dense cores. This line has been detected in variousenvironments such as infrared dark clouds, starless cores, andprotostellar cores (Lee & Myers 1999; Bergin et al. 2002; Ra-gan et al. 2006; Busquet et al. 2011; Storm et al. 2016). Thismolecule has seven hyperfine structures that can characterizea dense inner region and estimate the systematic velocities ofdense cores with better accuracy (Mardones et al. 1997).In order to trace the infall motions based on the spectralasymmetry, it is very important to exactly measure even avery small velocity shift between the two tracers that areused for comparing the motions. Hence, the setting of ac-curate frequencies of HCN 1-0 and N H + N H + N H + Observations with KVN telescopes
The observations were carried out using one of the threesingle dishes of the Korean VLBI Network (KVN) 21 m ra-dio telescopes during September 2013 and May 2016. Weobserved 60 sources in the HCN 1-0 line, 64 sources in the N H + km s − at 88 GHz (for the HCNline) and 0.025 km s − at 93 GHz (for the N H + line). Thepointing and the focus were checked every 3-4 hours using nearby known strong SiO maser sources and the pointing ac-curacy was within 4 (cid:48)(cid:48) during the observations. The data werecalibrated by the standard chopper wheel method and the lineintensity was obtained in the T ∗ A scale. The beam size andmain beam efficiency of the KVN are 32 (cid:48)(cid:48) and 0.4 at 86 GHz,respectively (Lee et al. 2011). The spectral data are reducedwith CLASS software.2.3. Observations with the Mopra telescope
We observed two southern hemisphere sources in the 3 mmband using the Mopra 22 m telescope located in Australiaduring May 2014. Unfortunately, these sources were not de-tected at observations with the HCN and N H + mainly be-cause of their low observing sensitivity level of 1 σ T ∼ km s − . The observations were conducted bya position switching mode with a total (ON+OFF) integra-tion time of 30 minutes with two polarized feeds. The Mopraspectrometer, MOPS, can cover 8 GHz bandwidth simulta-neously in both the wide-band and zoom modes. The zoommode with high resolution was tuned at 89.190 GHz with 16windows of 137 MHz. The telescope pointing correction wasperformed by SiO maser sources every hour, giving a point-ing accuracy better than 3 (cid:48)(cid:48) . The measured beam size andmain beam efficiency of the Mopra are 38 (cid:48)(cid:48) and 0.49 at 86GHz, respectively (Ladd et al. 2005). The spectral lines werereduced by the Australia Telescope National Facility (ATNF)Spectral Analysis Package (ASAP) and CLASS software. RESULTS3.1.
Observing statistics
We observed a total of 62 sources in HCN 1-0 and N H + N H + N H + ∼ ∼ T MB ) scale.3.2. Line profile shapes
Towards all our targets, the N H + line being an opticallythin tracer showed a single peaked Gaussian profile. How-ever, HCN line profiles showed a variety of shapes; some-times double peaked with a brighter blue peak or a brighterred peak, or single peaked with red or blue shoulder, similar M. K IM ET AL .to the line profiles typically observed for the starless densecores (Sohn et al. 2007). It is very interesting to note that ofthese various shapes seen in HCN profile, the double peakedone where the blue peak is brighter than the red peak, so called infall asymmetric profile (as shown in Figure 1), isfound to be dominant ( ∼ ) compared with profiles ofother shapes. The various other HCN line profiles seen inour targets are shown in Figure 2. Table 1 . Observing targets and basic results of their observations in the HCN and N H + lines Name Coordinate (J2000) L int Distance V N H + T N H + MB T HCNMB (hh:mm:ss.s dd:mm:ss) ( L (cid:12) ) (pc) (km s − ) (K) (K) (1) (2) (3) (4) (5) (6) (7)J0328325 03:28:32.5 +31:11:05 0.062 ± ±
16 7.21 ± ± ± ± ±
16 7.07 ± ± ± ± ±
20 6.14 ± ± ± ± ±
15 8.70 ± ± ± ± ±
24 -7.22 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± · · · < . < . J0428151 04:28:15.1 +36:30:28 0.051 ± ± · · · < . < . J0430149 04:30:14.9 +36:00:08 0.013 ± ± ± ± ± ± ± · · · · · · ± ± ± · · · < . ± ± ± · · · < . < . J0440224 04:40:22.4 +25:58:32 0.002 ± ± · · · < . < . J1542169 15:42:16.9 -52:48:02 0.042 ± ± · · · < . < . J1601155 16:01:15.5 -41:52:35 0.151 ± ± · · · < . < . J1626484 16:26:48.4 -24:28:38 0.056 ± ± ± ± ± ± ± ± ± ± ± ± · · · < . < . J1804493 18:04:49.3 -04:36:39 0.062 ± ± · · · < . < . J1809419 18:09:41.9 -03:31:26 0.020 ± ± · · · < . · · · CB130-1 18:16:16.3 -02:32:37 0.072 ± ±
17 7.60 ± ± ± ± ±
30 6.72 ± ± ± ± ±
96 7.44 ± ± ± ± ±
96 5.34 ± ± ± ± ±
96 6.90 ± ± ± ± ±
96 6.87 ± ± · · · J1829209 18:29:20.9 -01:37:14 0.653 ± ±
96 7.70 ± ± ± ± ±
96 7.52 ± ± ± ± ±
96 7.64 ± ± ± ± ± · · · < . < . J1829439 18:29:43.9 -02:12:55 1.104 ± ±
96 7.71 ± ± · · · J1829529 18:29:52.9 -01:58:05 0.235 ± ±
96 7.59 ± ± ± ± ±
96 7.71 ± ± < . J1830144 18:30:14.4 -01:33:33 0.250 ± ±
96 8.13 ± ± ± ± ±
96 6.74 ± ± ± Table 1 continued
NFALL Table 1 (continued)
Name Coordinate (J2000) L int Distance V N H + T N H + MB T HCNMB (hh:mm:ss.s dd:mm:ss) ( L (cid:12) ) (pc) (km s − ) (K) (K) (1) (2) (3) (4) (5) (6) (7)J1830162 18:30:16.2 -01:52:52 0.519 ± ±
96 6.74 ± ± ± ± ±
96 6.93 ± ± ± ± ±
96 7.20 ± ± ± ± ±
96 7.38 ± ± ± ± ±
96 7.84 ± ± · · · J1830476 18:30:47.6 -02:43:56 0.253 ± ± · · · < . < . J1832374 18:32:37.4 -02:50:45 0.738 ± ±
96 6.24 ± ± < . J1832424 18:32:42.4 -02:47:56 0.677 ± ±
96 6.30 ± ± ± ± ±
96 6.33 ± ± ± ± ±
96 7.36 ± ± < . J1839298 18:39:29.8 +00:37:40 0.187 ± ±
96 8.22 ± ± ± ± ±
100 7.22 ± ± ± ± ±
18 2.62 ± ± ± ± ±
18 2.88 ± ± ± ± ±
18 2.80 ± ± ± ± ±
50 4.20 ± ± ± ± ± · · · · · · ± ± ±
36 1.63 ± ± ± ± ±
36 3.86 ± ± ± ± ± · · · < . ± ± ±
41 4.05 ± ± ± ± ±
36 4.32 ± ± ± ± ± · · · · · · ± ± ± · · · · · · < . J2156073 21:56:07.3 +76:42:29 0.022 ± ± · · · < . < . J2229333 22:29:33.3 +75:13:16 0.074 ± ±
18 -3.68 ± ± ± ± ±
18 -4.00 ± ± ± ± ±
18 -4.19 ± ± ± OTE —The source names and coordinates in Col.(1) and (2) are from Kim et al. (2016). Col.(3): The internal luminosities ofthe sources. These were re-calculated using the new distances given in Col.(4), which are from Zucker et al. (2018); Kuhnet al. (2019); Zucker et al. (2019, 2020). Col.(5): The Gaussian fit velocities for N H + lines. These were obtained from asimultaneous Gaussian fit for seven hyperfine components of the N H + spectrum. Col.(6) and (7): The peak temperaturesfor the main components in the N H + N H + and HCN are given by their 3 σ T upper limit. The ellipsis symbols ( · · · ) are meant to indicate “no observations”. Based on the characteristic shapes of HCN line profiles,we classified the sources observed by us into the followingcategories:1. Sources showing blue asymmetry profiles inthe main component – J0328325, J0328391,J0330326, IC348-SMM2E, J0418402,L1521F-IRS, J0430149, L328-IRS,J1828558, J1829054, J1830144, J1830156,J1830162, J1830174, J1832424, L1148-IRS, J2102212, J2102273, J2144570,J2229594, and L1251A-IRS4. 2. Sources showing red asymmetry pro-files in the main component – J0401343,IRAS04111+2800G, IRAM04191, CB130-1, J1829209, and L673-7-IRS.3. Sources showing a mixture of blue and redasymmetry in the hyperfine profiles. Thisprofile may be due to the presence of bothexpanding and infalling motions and HCNhyperfine line may be tracing these mo-tions selectively due to their different opticaldepth. The sources are J0330326, J0401343, M. K
IM ET AL . T M B ( K ) J0330326HCN 1 0N H + Figure 1.
Observed line profiles of HCN (J=1-0 F=2-1) and N H + (J=1-0 F F =01-12) of J0330326. The green profile and the dot-ted line indicate the Gaussian profile and velocity obtained from asimultaneous Gaussian fit for N H + seven hyperfine components,respectively. IRAM04191, J0430149, J1829121, andJ2102212.4. Sources with wide wing features. Wefound several sources (J0328325, J0328391,IC348-SMM2E, IRAS04111+2800G,L1521F-IRS, IRAS16253-2429, J1829054,J1829336, J1830174, J2102212, J2147060,and L1251A-IRS4) that showed wide wingfeatures in HCN profiles, probably implyingthe existence of outflows.5. Sources showing anomalous intensity ra-tios among the hyperfine components. Inour survey, we found a number of sourcesthat are very peculiar as they show anoma-lous intensity ratios among HCN hyperfinetransitions. In local thermodynamic equi-librium (LTE) and optically thin conditions,the relative intensity ratios are expected tobe 1:5:3 for the hyperfine lines of F=0-1:2-1:1-1, respectively. However, more thanhalf of our samples (24) show very differ-ent ratios from the LTE values. One ex-treme case is J1833294, where the F=0-1component only is seen while two other hy-perfine components are completely absent.A number of factors such as turbulent over-lap, radiative scattering, line opacity effects, and line overlap have been suggested as thepossible cause for this observed phenom-ena (Guilloteau & Baudry 1981; Cernicharo& Guelin 1987; Gonzalez-Alfonso & Cer-nicharo 1993; Turner et al. 1997; Loughnaneet al. 2012). At this moment, any further dis-cussion on the observed anomalous ratio isout of the scope of this work and thus weleave it for further study in the future.The number of sources in each category is counted as 21( ∼ ) in category 1, 6 ( ∼ ) in category 2 and 3, and12 ( ∼ ) in category 4. We noticed that a considerablenumber of sources are found to be belonging to more thanone category. DISCUSSION4.1. δV distribution of HCN spectra As shown in Figure 2, the HCN line profiles can have vari-ous shapes. This can be quantitatively discussed by introduc-ing the velocity differences ( δV ) between two intensity peaksin optically thick and thin tracers. We estimated the δV HCN from our observed HCN 1-0 (optically thick) and N H + δV HCN = V HCN − V N H + ∆ V N H + , (1)where V HCN is the peak velocity of the HCN line profile, V N H + is the Gaussian fit velocity of the N H + line pro-file, and ∆ V N H + is the FWHM of the N H + spectrum. The V HCN was obtained for each hyperfine line of HCN by creat-ing a Gaussian fit to the brightest peak part of the asymmetricline profile. The V N H + and ∆ V N H + were derived by mak-ing a simultaneous Gaussian fit to the seven hyperfine com-ponents of the N H + line whose line parameters are givenby Caselli et al. (1995) .The shapes of the HCN line profiles can be due to variousfactors such as optical depth, infall/expanding motions, andoutflow motions. Therefore, understanding the distributionof the normalized velocity difference ( δV ) would be usefulto recognize the dominant gas motion present around the en-velopes in a quantitative way and compare them with thosefor the starless and other protostellar cores.We estimated the values of δV using the three hyperfinecomponents of HCN. The values are listed in Table 2 and J1626484 has an unusually wide line width, as shown in Figure 2. Bar-sony et al. (2005) reported that J1626484 consists of multiple cores fromthe mid-infrared observation. We have confirmed that the three cores aredistributed within the KVN beam size in the
Spitzer µ m image, which cannot be resolved by our HCN observations. We exclude J1626484 in further δV discussions, even though J1626484 has a distinct blue asymmetric lineprofile.NFALL Table 2.
The velocity information for 41 VeLLOs by HCN and N H + lines Name V N H + ∆ V N H + V HCN δV HCNF =0 − δV HCNF =2 − δV HCNF =1 − (km s − ) (km s − ) (km s − ) (1) (2) (3) (4) (5) (6) (7)J0328325 7.21 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± · · · -0.30 ± · · · J1839298 8.22 ± ± ± · · · ± · · · L673-7-IRS 7.22 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± OTE —Col.(1) lists the source names. Col.(2) and (3) indicate the Gaussian fit velocities and FWHMs of N H + (1-0). The intensity-peak velocity of HCN (1-0) line given in Col.(4) was obtained by a Gaussianfit for its brighter peak component after masking the other fainter component. The normalized velocitydifferences in Cols.(5)-(7) are calculated using equation (1) in the text. The uncertainties are propagationerrors in δV . Line information is measured from the spectra with a channel width of 15.63 kHz (0.05 km s − ). The ellipsis symbols ( · · · ) are to indicate no-determination of δV HCN due to the noisy profile.
M. K
IM ET AL . V V N H + (km/s) T M B ( K ) J0328325J0328391J0330326IC348-SMM2EJ0401343X2 IRAS04111+2800GJ0418402X2 IRAM04191X2 L1521F-IRSJ0430149J1626484
V V N H + (km/s) T M B ( K ) IRAS16253-2429CB130-1L328-IRSJ1828558J1829054X2 J1829121J1829209J1829251J1829336J1829529X2 J1830144
Figure 2.
HCN (J=1-0) line profiles detected toward the sources. The dashed lines in the profiles indicate the N H + velocities of the sourceswhich are derived with the simultaneous Gaussian fit of the seven hyperfine components of N H + line. The HCN profiles were shifted forthe velocities of N H + in comparison with the main component of HCN to be zero km s − . The spectra for IRAM04191, IRAS16253-2429,J1832456, J1839298, J2147030, and J2229333 were Hanning-smoothed. NFALL V V N H + (km/s) T M B ( K ) J1830156J1830162X2 J1830174J1830218X2 J1830275J1832424J1832456X2 J1839298X2 L673-7-IRSL1148-IRSX2
V V N H + (km/s) T M B ( K ) J2102212J2102273L1014-IRSJ2144570X2 J2145312J2147030X2 J2147060J2229333X2 J2229594L1251A-IRS4
Figure 2. (Continued.) displayed as histograms in Figure 3. The distribution shownin the figure suggests that the hyperfine component with the higher optical depth has a more skewed δV distribution to-wards the blue side. Among the three hyperfine components,0 M. K IM ET AL .the δV values estimated for the main component of HCN(HCN 1-0, F=2-1) shows the largest negative shift implyingthat the main component may be the best tracer of inwardmotions in the envelope of the VeLLOs as was found truefor the δV distribution of the starless dense cores also (Sohnet al. 2007).Using the HCN main component and N H + lines, thus,we calculated the δV values for the 41 cores with VeLLOsand compared them with those for the protostars (Park et al.1999) and the starless cores (Sohn et al. 2007) as shown inFigure 4. The targets in the two surveys used here for com-parison were selected to include as many sources as possiblewhich are observable in the northern sky using the TRAO14-m telescope to avoid any likely selection bias. Note thatmost of the targets in these surveys are as distant as our tar-gets and thus our KVN survey traces a slightly ( ∼ percent)smaller size scale than that by TRAO telescope for the othertwo surveys. The results in the figure indicate that the δV distribution of the cores with VeLLOs is more similar to thatof the starless cores than that of the protostellar cores. Themean values of the δV distributions for the starless cores,the cores with VeLLOs, and the protostellar cores are − . , − . , and − . , respectively. This may indicate that theVeLLOs are deeply embedded in gaseous envelopes, whichare dominated by infalling motions, while other kinematiceffects such as outflow are minimal in comparison to the nor-mal protostars whose envelopes are highly affected by theoutflow motions as well as the infalling motions.4.2. Infall Kinematics toward VeLLOs
To investigate the kinematics of the infall motionin the envelopes that harbor the VeLLOs, we havecalculated the full width at half maximum (FWHM)for thermal and non-thermal motions by using N H + line profiles for the sources showing the infall asym-metry, ∆ V T = (cid:112) k B T k / (cid:104) m (cid:105) and ∆ V NT = (cid:113) ∆ V H + − (8ln(2) k B T k / (cid:104) m N H + (cid:105) ) , where k B is theBoltzmann constant, T k is the gas kinetic temperature, (cid:104) m (cid:105) is the mean molecular weight (2.3 amu), and (cid:104) m N H + (cid:105) isthe molecular weight of N H + (29 amu). If the dust andgas are well-mixed, then the gas kinetic temperature wouldfollow the dust temperature. With this assumption, we usedthe dust temperatures in the calculation of the thermal linewidth which are obtained from the Herschel
Gould Belt sur-vey archive . The dust temperatures in the archive were givenfor each pixel which size is about 3 (cid:48)(cid:48) and thus the dust tem-perature for each source was re-calculated as the mean valuewithin our observing beam size of 32 (cid:48)(cid:48) . The temperature was found to range between 11 and 16 K with the uncertaintyof ∼ in its value. This gives the thermal line widths(FWHMs) of 0.47 - 0.58 km s − for our targets with theirpropagation uncertainty of ∼ .
01 km s − .Figure 5 illustrates the distribution of the ratios of thermaland non-thermal motion components as a function of the nor-malized velocity differences for HCN main hyperfine com-ponent for the starless cores, cores with VeLLOs, and pro-tostellar cores. For the majority (85%) of the starless cores,this ratio is less than 1, indicating that most of the starlesscores are in a state of thermal infall (Lee & Myers 1999;Sohn et al. 2007), while the ratio in half ( ∼ ) of the pro-tostellar cores is greater than 1 (Mardones et al. 1997; Parket al. 1999), indicating that in some of the protostellar coresthe non-thermal rather than the thermal infalling motions aredominant. In the case of cores with VeLLOs, the distribu-tion of ∆ V NT / ∆ V T is similar to or slightly higher than thatof the starless cores. Protostellar cores appear to have a largeinfluence on the non-thermal components. However, the non-thermal effect in the cores with VeLLOs is weaker, beingsimilar to that found in the starless cores. This is probablybecause although they have some star-forming activities suchas the presence of outflows, the energetics involved may besmaller when compared to those in the protostellar cores.4.3. Infall speeds in the envelopes of the VeLLOs and theirimplication
We derived the infall speed for the cores with VeLLOsshowing infall signatures using the HILL5 model (De Vries& Myers 2005). The HILL5 is a radiative transfer model inwhich two layers are approaching each other with a speed V infall . The excitation temperature in the layers is assumedto be peaked at a temperature T p at the center of the layerwhile it decreases at their near and far edges. In other words,the excitation temperature profile has a Λ -shaped distributionto the optical depths (i.e., T ex increases linearly with τ r fromedge to center in the rear section of the cloud and T ex de-creases with τ f from the center to edge in the front section ofthe cloud). The brightness temperature of the model is givenby: ∆ T B = [ J ( T p ) − J ( T )] (cid:20) (1 − e − τ f ) τ f − e − τ f (1 − e − τ r ) /τ r (cid:21) +[ J ( T ) − J ( T b )][1 − e − τ f − τ r ] , (2)where J ( T ) ≡ T / (exp( T /T ) − , T = hν/k B , h isPlanck’s constant, ν is the frequency of the transition, k B is Boltzmann’s constant, and T b is the background temper-ature, respectively. The optical depths are given by τ f = τ exp[ − ( v − v sys − V infall ) / σ v ] in the front section and τ r = τ exp[ − ( v − v sys + V infall ) / σ v ] in the rear section,where V infall is the infall speed, σ v is the velocity disper-sion, and τ is the total optical depth. The above equation NFALL -2 -1 0 1 2 V HCN N u m b e r o f s o u r c e s F = 0 1-0.19±0.07N=39 -2 -1 0 1 2 V HCN F = 2 1-0.36±0.10N=41 -2 -1 0 1 2 V HCN F = 1 1-0.37±0.09N=39 Figure 3.
Histograms of the normalized velocity difference between HCN (1-0) three hyperfine lines and N H + (1-0) line for cores harboringVeLLOs. The legend in the right-top corners in each panel indicates a transition of three hyperfine lines of HCN (1-0), the mean δV HCN foreach hyperfine component and the standard error of the mean (SEM), and the number of sources considered. is composed of five free parameters namely T p , τ , V infall , v sys , and σ v (De Vries & Myers 2005).We fitted 15 sources for which the HCN 1-0 spectra showclear double peaks or red shoulder, using HILL5 via thePySpecKit python module (Ginsburg & Mirocha 2011). Thefits require an input guess as a starting point for the fitting al-gorithm. The guesses for v sys and σ v were set based on theobservational values obtained from N H + lines. The best fitparameter for v sys was obtained within the range of ± km s − from the observational value of V N H + while σ v was fixed by the line width of N H + . We performed HILL5model fits for 1000 spectra, which are simulated with the bestfit parameters, with random noise equivalent to the observingrms for every spectrum to calculate 1 σ uncertainties on theparameters. The result of HILL5 fitting for the HCN (J=1-0F=2-1) spectrum of J0330326 as a fitting example is shownin Figure 6, indicating that the asymmetric shape of the ob-served HCN (J=1-0 F=2-1) line is well fitted with the HILL5model within a precision of 1 σ = 0 .
05 km s − .The infall speeds of the 15 VeLLOs obtained from theHILL5 model fits are listed in Table 3. Figure 7 displaysthe distribution of these infall speeds, showing that the de-rived infall speed ranges mostly from 0.03 km s − to 0.3 http://pyspeckit.bitbucket.org km s − , with a median value of 0.16 km s − . The in-fall speeds derived using similar models towards the starlesscores and protostellar cores are found to be V infall ∼ . − .
09 km s − (Lee et al. 2001) and V infall ∼ . − . − (Di Francesco et al. 2001; Mottram et al. 2013), respec-tively, suggesting that the infall speed of the envelope ofthe VeLLOs is slightly larger than that of the starless coresbut smaller than that of the protostellar cores. Here theinfall speeds for protostellar cores by Di Francesco et al.(2001) have been derived from the spectra obtained fromhigh spatial ( ∼ (cid:48)(cid:48) resolution) observations that may givehigher infall speeds compared to those from the spectra fromsingle-dish observations. However, the infall speeds derivedfrom Mottram et al. (2013) using radiative transfer modelsfor seven protostellar cores are found to be mostly between V infall ∼ . − . − when the infalling area is probedby the spatial scale equivalent to that of the KVN. Thus itseems evident that the infall speed of the envelope of theVeLLOs is smaller than that of the protostellar cores.It is worth noting that the infall speeds in the envelopesof the VeLLOs are mostly smaller than their sound speeds,which are primarily between ∼ . − .
24 km s − depend-ing on their temperatures, so called subsonic, while infall mo-tions in four sources are equivalent to their sound speeds,trans-sonic. This is in contrast with the starless cores forwhich their infall speeds are all subsonic and the protostel-2 M. K IM ET AL ..
24 km s − depend-ing on their temperatures, so called subsonic, while infall mo-tions in four sources are equivalent to their sound speeds,trans-sonic. This is in contrast with the starless cores forwhich their infall speeds are all subsonic and the protostel-2 M. K IM ET AL .. -2 -1 0 1 2 V HCN N u m b e r o f s o u r c e s -0.43±0.11N=52starless cores -2 -1 0 1 2 V HCN -0.36±0.10N=41cores with VeLLOs -2 -1 0 1 2 V HCN -0.09±0.09N=18protostellar cores
Figure 4.
Histograms of the normalized velocity difference for the starless cores (green), cores with VeLLOs (red), and protostellar cores(blue). The protostellar and starless cores data were given from Park et al. (1999) and Sohn et al. (2007), respectively. The values in theright-top corners in each panel indicate the mean and the SEM of each group and the number of sources considered. lar cores for which their infall speeds are mostly supersonic(the infall speeds for all protostellar cores are larger than thesound speeds ∼ .
24 km s − at a temperature of 20 K.)What would be the physical origin for the infall motionsderived from the line asymmetry observed toward the en-velopes where the VeLLOs are forming? These motionscould be gravitational or non-gravitational such as converg-ing flows, core accretion, or oscillatory motions. For thisdiscussion, we simply derive a mean gravitational free-fallspeed in a pressure-free dense core, which is given by V ff =(2 /π )(2 GM env /R ) / by dividing R with its free-fall timescale of the core τ ff = (3 π/ Gρ ) / where M env isthe mass of the core and ρ is its mean density. Here wederived M env by using 250 µ m continuum emission ob-tained from the Herschel
SPIRE for the area encompassedby a radius of 16 (cid:48)(cid:48) which corresponds to the radius of thebeam size of the KVN telescope. Considering an opticallythin approximation, the mass can be obtained by M env = d F ν / ( κ ν B ν ( T )) . Here, d is the distance to the source, F is the flux at 250 µ m from the Herschel
SPIRE, κ ν isthe opacity, and B ν ( T ) is the Planck function (Kim et al.2016) at the temperature T. The T here is the dust temper-ature adopted from the Herschel
Gould Belt survey archive(Andr´e et al. 2010) and found to be between 11.1–13.8 K forinfalling cores with the VeLLOs. For the opacity, the value of 0.19 cm / g was adopted from Ossenkopf & Henning (1994)at the wavelength of 250 µ m. At this opacity value, the op-tical depth at 250 µ m is found to be far less than 1, and thusour mass estimation using the optically thin approximation isthought to be reasonable.Figure 8 compares the infall speeds of our targets with themean free-fall speeds of the pressure-free theoretical coreswhose masses are the same as those of our observing targets,indicating that the motions derived from the line profiles formost of our targets seem to be well correlated with a simplemodel of gravitational contraction with the correlation coef-ficient of about 0.7. In fact, it is noted that the infall speedsdo not exactly correspond to the same values of the free-fallspeeds, but to about half of those values. Considering thelarge uncertainties in both the data and the applicability ofthe simple model we have used, however, V infall and V ff are thought to be well correlated.For example, for a line profile having a well-resolved dipor shoulder, a peak brightness temperature greater than 1 Kand a signal-to-noise ratio greater than 30, the infall speed es-timated using the HILL5 model is uncertain by 0.02 km s − (De Vries & Myers 2005). This becomes an additional sourceof uncertainty on top of the imprecision, or the variation( ∼ .
05 km s − ) due to the noise quoted for the lower SNRsources in this paper. We also note that the free-fall time is a NFALL -1 0 1 V HCN V N T / V T -1 0 1 V HCN -1 0 1 V HCN
Figure 5.
The distribution of the ratios of thermal and non-thermal motion components as a function of the normalized velocity differencesfor the starless cores (green), cores with VeLLOs (red), and protostellar cores (blue). The numeric values in the right-top corners in each panelindicate the mean and the SEM for the ratios between two motion components of each group and the number of sources considered. T M B ( K ) = 4.4 ± 0.2V sys = 6.004 ± 0.003 km/sV infall = 0.061 ± 0.005 km/s v = 0.178 ± 0.003 km/sT peak = 7.22 ± 0.09 K Figure 6.
Best-fit results of the HILL5 model in HCN (J=1-0 F=2-1) spectrum of J0330326. The overlaid red profile shows a best-fitone of the HILL5 model. The errors for the fit parameters given inthe legend are 1 σ uncertainties of the parameters obtained from theHILL5 model fits for 1000 artificial spectra produced by the best fitparameters and observational rms. V infall (km/s)0123456 N u m b e r o f s o u r c e s Figure 7.
Histogram of the infall speeds for 15 cores with VeLLOs.The vertical line indicates the median value of 0.16 km s − . time scale which is only useful as a guide and hence cannotbe used for an exact prediction, since the initial conditionssuch as a uniform density, pressure-free sphere collapsing4 M. K IM ET AL ..
Histogram of the infall speeds for 15 cores with VeLLOs.The vertical line indicates the median value of 0.16 km s − . time scale which is only useful as a guide and hence cannotbe used for an exact prediction, since the initial conditionssuch as a uniform density, pressure-free sphere collapsing4 M. K IM ET AL .. Table 3.
VeLLO-related physical properties
Name V infall V ff M env M (cid:48)(cid:48) env ˙ M infall ˙ M COacc T d collapsing age M staracc M starfinal (km s − ) (km s − ) ( M (cid:12) ) ( M (cid:12) ) ( M (cid:12) yr − ) ( M (cid:12) yr − ) (K) (Myr) ( M (cid:12) ) ( M (cid:12) ) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)J032832 0.17 ± ± ± ± ± × − ± × − ∗ ± ± ± . J033032 0.06 ± ± ± ± ± × − ± × − ± ± ± . J0418402 0.03 ± ± ± ± ± × − ± × − ∗ ± ± ± . L1521F-IRS 0.03 ± ± ± ± ± × − ± × − ± ± ± . J0430149 0.12 ± ± ± ± ± × − ± × − ∗ ± ± ± . L328-IRS 0.04 ± ± ± ± ± × − ± × − ± ± ± . J1830144 0.17 ± ± ± ± ± × − ± × − ∗ ± ± ± . J1830156 0.27 ± ± ± ± ± × − ± × − ∗ ± ± ± . ∗∗ J1830162 0.22 ± ± ± ± ± × − ± × − ∗ ± ± ± . ∗∗ J1832424 0.10 ± ± ± ± ± × − ± × − ∗ ± ± ± . L1148-IRS 0.11 ± ± ± ± ± × − ± × − ± ± ± . J2102212 0.22 ± ± ± ± ± × − ± × − ± ± ± . ∗∗ J2102273 0.16 ± ± ± ± ± × − · · · ± · · · · · · J2144570 0.16 ± ± ± ± ± × − · · · ± · · · · · · J2229594 0.24 ± ± ± ± ± × − ± × − ∗ ± ± ± . ∗∗ N OTE —Col.(1) lists the source name. Col.(2) gives the infall speed derived from HILL5 model fit for HCN (1-0) line. Its error is given by 1 σ uncertainty of the speed obtained fromthe HILL5 model fits for 1000 artificial spectra produced by the best fit parameters and observational rms. Col.(3) indicates free-fall speeds for the envelope by the area encompassedby the radius ( ∼ (cid:48)(cid:48) ) of the KVN telescope. Col.(4) gives the envelope mass which is based on the photometry with CSAR (Kim et al. 2016). Col.(5) lists the envelope mass basedon the aperture photometry of 250 µ m Herschel flux for the area encompassed by the radius ( ∼ (cid:48)(cid:48) ) of the KVN telescope. The uncertainty was calculated based on the photometryerror. Col.(6) and Col.(7) provide the mass infall rate derived from the infall speed and the mass accretion rate inferred from CO outflow (Kim et al. 2019), respectively. The massaccretion rates marked with ∗ were derived from this study. Col.(8) lists the dust temperature and its ∼ uncertainty (Roy et al. 2014). Col.(9) indicates the period for the expansionsound wave in an isothermal sphere to travel to its radius which is half of our observing beam size in here(Shu 1977). Col.(10) lists the possible central mass of the VeLLOs toacquire with the mass accretion rates during the collapsing age given in Col.(9). Col.(11) indicates a possible final mass of the VeLLO to achieve, a sum of the possible central mass(in Col.(9)) plus the portion ( ∼ . ) of the envelope mass (in Col.(4)). The stellar masses ( M star ) with ∗∗ were calculated using the envelope mass given in Col.(5). The ellipsissymbols ( · · · ) are to indicate “No outflow observation” and thus no further estimation of its corresponding physical quantities. V ff (km/s) V i n f a ll ( k m / s ) Figure 8.
Comparison of the infall velocities for 15 cores with VeL-LOs with their free-fall velocities. The black dotted line indicatesthe positions where V infall is equal to V ff . The grey dashed line isa line for the linear least-squares fit to the data. Its slope and Pearsoncorrelation coefficient are 0.60 ± from a rest condition with no rotation and no magnetic field are not realistic. Given the large uncertainties in the measure-ments of the infall speeds and and the unrealistic simplicityof the collapse model in calculating the free-fall speeds, itseems reasonable to say that as a group they show signifi-cant consistency between the infall speeds and about half thefree-fall speeds.Therefore, our results indicate that the infall motions in-ferred by the spectral infall asymmetry in the envelopes withVeLLOs are more likely gravitational, favoring models ofgravitational infall motion over models of non-gravitationalmotion such as converging flows (e.g., Gong & Ostriker2009), or oscillation motions without infall (e.g., Broderick& Keto 2010) as it is unlikely that the models other thangravitational infall models can produce this relation (e.g., Seoet al. 2019).Alternatively, it may be possible that the collapsing radiusis far smaller than the telescope beam size for our observa-tions ( ∼ , au for the most distant target), making theinfall speed to be lower than the speed estimated by the grav-itational collapse of the beam area. It is noted that there aretwo sources (J0430149 and J2229594) for which V ff s are NFALL V infall s. For those two sources, the infallmotions inferred by the spectral infall asymmetry in the en-velopes may be more likely fully gravitational. If then, it maybe possible that their collapsing radius may be close to 2300au or 5600 au, which is the linear radius of the HPBW ofthe KVN telescope at the distances of two VeLLOs. On theother hand, there are other targets whose infall velocities aresmaller than the free fall velocity at the distances comparableto those of these two sources. This indicates that the collaps-ing radius of the core may not be uniquely determined butvariable depending on the physical status of the core. Anyfurther quantitative discussion in comparison of our obser-vations with results predicted by the various models dealingwith gas infall motions is beyond the scope of this paper andwe leave this issue for future study.4.4. Mass infall rates and mass accretion rates toward theVeLLOs, and their implication
In this section, we consider the mass infall rates from theenvelopes of the VeLLOs and the mass accretion rates to-ward the VeLLOs as useful physical quantities to help tounderstand the physical processes involved in the forma-tion of the VeLLOs from their parent envelopes. The massinfall rates were derived using the infall speeds obtainedfrom our model fitting, with ˙ M infall = 4 πR in ρ V infall ,where ρ is the mean density of the envelope given by M env / (4 / πR in ) and R in is the half of FWHM (16 (cid:48)(cid:48) ) ofour observing KVN telescope. It is assumed that the en-velope has a uniform density ρ and the infall is sphericallysymmetric with a speed of V infall . Estimated mass infallrates range from − to − M (cid:12) yr − , with the medianvalue of . ± . × − M (cid:12) yr − (Table 3). The values of κ can be a significant contributor to the uncertainties in themass and then the mass infall rate, which may vary within afactor of 2 due to the uncertainty in the value of κ (Ossenkopf& Henning 1994). We note that line profiles showing an in-fall asymmetry can be affected by an outflow activity in theirshapes if it is strong enough, and thus the infall speed and themass infall rate that we derived can be affected. We foundthat 13 out of 15 sources for which infall speeds are derivedfrom their infall asymmetric profiles have possible outflowwings from the CO observations by Kim et al. (2019), butthey are found to be all weak enough not to significantly af-fect the derived values of infall speed and the mass infall rate.The mass accretion rate can be obtained by using CO ob-servations around the outflow regions. Kim et al. (2019)made a single pointing and/or a mapping survey of 68 VeL-LOs in CO lines, finding the evidence for outflows over 16dense cores having the VeLLOs.We found that there are 5 outflow sources identified fromthe CO mapping survey for which the mass infall rates wereestimated in this study. For these sources, we used the mass accretion rates given by Kim et al. (2019). We also foundthat there are 8 more outflow sources identified from the sin-gle pointing CO observations for which the mass infall rateswere estimated in this study. for these sources we calculatedthe mass accretion rates using the equation given by Kimet al. (2019) with the same parameters assumed in their study; ˙ M acc = f ent ˙ M acc ˙ M w v w F sin i cos i , where f ent is the entrainmentefficiency (0.25), ˙ M acc ˙ M w the ratio of the mass accretion rate tothe mass loss rate in the jet/wind (10), v w is the velocity ofthe jet/wind (150 km s − ), F is the outflow force, and i is theinclination angle of the outflow (57. ◦ L int ( L )10 M i n f a ll ( M / y r ) Figure 9.
Mass infall rates toward the VeLLOs versus their internalluminosities. The Pearson correlation coefficient of the linear least-squares fit to the data is 0.70.
The mass infall rates toward the VeLLOs that we derivedcan be compared with what the collapse models predict. Themass infall rate based on the inside-out collapse model (Shu1977), ˙ M = 0 . a /G , where a is the sound speed, is esti-6 M. K IM ET AL .mated to be . − . × − M (cid:12) yr − for isothermal coreswhose temperatures are given as dust temperatures listed inTable 3, being consistent with the mass infall rates that weobtained for our targets within an order of magnitude range.The good correlation found between the mass infall ratesand the internal luminosities, and the consistency of the massinfall rates with the values predicted with the inside-out col-lapse model again indicate that the infall asymmetry ob-served in the envelope of 0.04 pc (32 (cid:48)(cid:48) ) extent may have re-sulted in due to the gravitational infall motion. M infall ( M / yr )109876543 l o g M C O a cc ( M / y r ) Figure 10.
Mass infall rates versus the mass accretion rates towardthe VeLLOs. The filled and open circles indicate the mass accretionrates obtained from CO observations in a mapping mode and a sin-gle pointing mode in CO line (Kim et al. 2019), respectively. Thedashed and dotted lines are the positions where the ratios of ˙ M COacc / ˙ M infall are 1.0, 0.1 and 0.01, respectively. Next we compare the mass infall rates with the mass ac-cretion rates for our samples in Figure 10 to see how theyare related. In this figure, the mass infall rates of almost halfsamples are similar the values of the mass accretion rates,while the mass infall rates for the rest of samples are largerthan the mass accretion rates. We speculate that for the caseof the sources for which the mass accretion rates are com-parable with the mass infall rates, the infalling material isexpected to reach the central source through the normal ac-cretion processes. However, for most sources for which themass accretion rates are one order of magnitude lower thanthe mass infall rates, it may be possible that they are currentlyaccreting only a small portion of the infalling material in aquiescent manner while most of the material is getting accu-mulated for future episodic accretion events. It may also bepossible that the latter group’s sources may be accreting only a fraction of the infalling material from the envelopes asso-ciated with them, while most of the infalling material mayget ejected in the form of outflow winds before it reaches theVeLLOs.4.5.
Implication on the identity of the VeLLOs
Study of the VeLLOs are important to understand how faintprotostars collect material from their envelopes and yet re-main faint. The study is also useful to identify the precur-sors of brown dwarfs which in turn would help us to under-stand the processes involved in their formation and evolution.In fact, by inferring the final masses that our target sourcescan possibly achieve, we can identify some of the potentialprecursors of brown dwarfs among the sources studied here.For that, first, we calculated the possible central mass of theVeLLOs by assuming that their central sources are acquir-ing the mass with the mass accretion rates during the dura-tion of isothermal inside-out collapse by Shu (1977), whichcan be derived as the period for the expansion sound wave totravel to the radius of our observing beam size. Then assum-ing that the central source will collect the additional massfrom its envelope with a core-to-star formation efficiency of ∼ . (e.g., Evans et al. 2009), the final masses of the VeL-LOs that could be collected during the whole duration of thestar/brown dwarf formation can be inferred as a sum of thepossible central mass plus the portion ( ∼ . ) of the enve-lope mass. Those inferred values are listed in the last columnof Table 3. We find that most of our targets would have astellar mass while at least two (J0418402 and J0430149) ofour targets would have a brown dwarf mass within the uncer-tainty. It is interesting to note that the final masses of thesetwo sources will be in the brown-dwarf mass regime, eventhough we assume that the entire infalling material finallyarrive at the central sources. Further studies of these twosources in future may help us to better test the proto-browndwarf nature of these sources. In conclusion, it is inferredthat the VeLLOs studied here are mostly faint protostars andproto-brown dwarfs (at least in two cases) and thus may beextremely important objects to study the early formation pro-cesses of low-mass protostars or proto-brown dwarfs. SUMMARYWe conducted single pointing observations toward thedense cores harboring VeLLOs in optically thick (HCN 1-0)and thin ( N H + δV )between two tracers, finding that the majority (21) of our NFALL δV distribution of the dense cores with theVeLLOs is highly skewed to the blue, indicating the infallingmotions in their envelopes are dominant. This is found tobe more similar to that of the starless cores than that of thenormal protostars, implying that the influence of the VeLLOformation activity on its envelope is minimal on a scale tracedby the single dish telescopes.(2) The distribution of line widths in the dense cores withthe VeLLOs indicates that they are mostly in the regimewhere thermal motions are dominant, while a significantnumber (about 20 %) of the sources are located in a domi-nant turbulence regime. This is in good agreement with thekinematic environment of the starless cores that are in a stateof thermal infall unlike the protostellar cores dominated bythe turbulent motion.(3) We derived the infall speeds of the infall motions foundin the envelopes of the VeLLOs and the related physicalquantities by applying the HILL5 radiative transfer modelto the HCN spectra of the sources showing infall signature.The resulting infall speeds for the sources are in the range . < V infall < . − with the median value of .
16 km s − .These values are found to be well correlated to about halfof the gravitational free-fall speeds from pressure-free en-velopes, indicating that the infall motions inferred from thespectral infall asymmetry in the envelopes with the VeLLOsare more likely gravitational considering the large uncertain-ties in both the data and the applicability of the simple col-lapse model.Alternatively, these smaller values of the infall speeds maybe due to the collapsing radii of the envelopes being smallerthan our telescope beam size. Nonetheless, we found twosources (J0430149 and J2229594) for which V ff s are aboutthe same as V infall s. If this indicates that the infall motionsin these sources are from a fully gravitational origin, theircollapsing radii are expected to be 2300 au or 5600 au.(4) The mass infall rates ˙M infall for our targets were esti-mated to be mostly of the order of ∼ − M (cid:12) yr − with themedian value of . × − M (cid:12) yr − and compared amongother physical properties such as their internal luminosities,and the mass infall rates ( . − . × − M (cid:12) yr − ) bythe inside-out collapse model. We found that there is a fairlygood relation between the mass infall rates and the internal luminosities, and also the mass infall rates are consistent withthe values predicted with the inside-out collapse model. Thisagain indicates that the infall asymmetry observed toward theVeLLOs may have resulted in due to the gravitational infallmotions in their envelopes.(5) From the comparison of the mass infall rates for asub-sample of targets with the corresponding mass accretionrates, it was found that in almost half of the sources the massinfall and mass accretion rates are comparable while in therest the mass infall rates are an order of magnitude largerthan their mass accretion rates. The sources in the formergroup are expected to accrete material continuously. On theother hand, those in the latter group are probably the sourceswhere the envelope material is either at present quiescentlyaccreting at a low rate expecting for their future episodic highaccretion events or the sources where the envelope materialmay get ejected out in outflow activities and never reach theVeLLOs.(6) Considering the mass infall rates and the mass accre-tion rates of our sources, the duration of isothermal inside-out collapse in the envelope of the telescope beam size, andthe envelope masses, we estimated the final expected massesof the VeLLOs, finding that most of our targets would have astellar mass while at least two (J0418402 and J0430149) ofour targets would have a brown dwarf mass. This concludesthat the VeLLOs can be either faint protostars or proto-browndwarfs, confirming them to be extremely important objects tostudy the early formation processes of low-mass protostars orproto-brown dwarfs.Future spectroscopic observations with facilities of highangular resolution and high sensitivity such as ALMA willbe highly helpful to better test their true nature.We thank an anonymous referee for valuable comments,which greatly helped to improve the paper. This work wassupported by Basic Science Research Program though theNational Research Foundation of Korea (NRF) funded bythe Ministry of Education, Science, and Technology (NRF-2017R1A6A3A01075724 and NRF-2019R1A2C1010851).This research has made use of data from the Her-schel Gould Belt survey (HGBS) project (http://gouldbelt-herschel.cea.fr). The HGBS is a Herschel Key Programmejointly carried out by SPIRE Specialist Astronomy Group 3(SAG 3), scientists of several institutes in the PACS Consor-tium (CEA Saclay, INAF-IFSI Rome and INAF-Arcetri, KULeuven, MPIA Heidelberg), and scientists of the HerschelScience Center (HSC).REFERENCES Afonso, J. M., Yun, J. L., & Clemens, D. P. 1998, AJ, 115, 1111Andr´e, P., Men’ ’shchikov, A. ., Bontemps, S., et al. 2010, A&A,518, L102 Barsony, M., Barsony, M., Ressler, M. E. ., et al. 2005, ApJ, 630,381
IM ET AL ..