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A&A
Volume 689, September 2024
Article Number A267
Number of page(s) 11
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202348096
Published online 18 September 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Several high spatial resolution surveys of the dust continuum have characterized the statistics of multiple protostellar systems (Looney et al. 2000; Chen et al. 2013; Tobin et al. 2016b; Encalada et al. 2021; Tobin et al. 2022). These surveys provided information on the multiplicity fraction, the companion fraction, and the distribution of the components within systems, and they speculated about the formation scenarios based on the dust continuum alone. One missing piece of information is the physical conditions of the gas that surrounds the multiple systems. A large-scale mapping of molecular gas is necessary to understand the processes and physical conditions that occur within the protostellar cloud cores (Mairs et al. 2014, 2016).

A pilot sample of ten protostellar systems in Perseus was observed with the Atacama Pathfinder Experiment (APEX) to study the temperature-multiplicity relation at envelope scales (~7000 AU; Murillo et al. 2018). The results of the pilot study showed that temperature was not correlated with multiplicity, while cold-gas reservoirs might be more relevant to multiplicity. The small sample size did not provide a systematic view, however. It is necessary to trace the physical conditions of the gas from the molecular cloud down to the protostellar disk for a large sample of systems in order to determine whether the previously established correlations apply globally for the Perseus molecular cloud.

Molecular line observations allow us to probe the physical conditions. The kinetic gas temperature at molecular cloud scales can indirectly be derived from the I(HCN)/I(HNC) J=1–0 ratio (e.g., Graninger et al. 2014; Hacar et al. 2020; Pazukhin et al. 2022), which was found to be effective in the range of 15–40 K in observations (Hacar et al. 2020). Another often used tracer is ammonia NH3 (e.g., Friesen et al. 2017; Keown et al. 2019), which was previously used to calibrate the I(HCN)/I(HNC) ratio (Hacar et al. 2020; Pazukhin et al. 2022). Dust temperature maps have been derived through modified blackbody fitting of spectral energy distributions (SEDs; e.g., Lombardi et al. 2014; Zari et al. 2016). This enables a comparison between the gas and dust temperatures, which is important because neither is necessarily thermalized. The gas density and mass can be probed by N2H+, a cold and dense gas tracer, and HCO+, which typically traces warm dense gas (e.g., Hsieh et al. 2019; Murillo et al. 2022a). The dust envelope mass can be estimated from the 850 μm peak continuum emission (e.g., Jørgensen et al. 2004; Murillo et al. 2016). The effects on protostellar multiplicity at molecular cloud sclaes can be studied by combining these physical parameters with information on protostellar multiplicity from continuum surveys (e.g., Tobin et al. 2016b), source parameters derived from SEDs (e.g., Murillo et al. 2016), and outflow directions (e.g., Stephens et al. 2017).

A correlation between the N2H+ and NH3 column densities was found in starless and protostellar cores in Perseus, but not between N2H+ and the core density (Johnstone et al. 2010). A similar result was obtained for the entire NGC 1333 region (Hacar et al. 2017). An analysis of dust continuum masses versus the thermal and nonthermal Jeans mass at different scales that considers the multiplicity of protostars suggests that thermal support is significant at small scales (few 1000 AU), but not at molecular cloud scales (≥10 pc; Pokhrel et al. 2018). However, Pokhrel et al. (2018) assumed a single temperature for all cores. Massive cloud cores (≥40 M⊙) containing fragments with masses in the range of 2–4 M⊙ on average indicate the role of magnetic fields in controlling the mass and size of fragments within the cloud cores and the distribution of fragments (Palau et al. 2021). A comparison of protostellar multiplicity in Perseus with the dust core morphology and binary formation scenarios suggests that wide binaries either inspiral to become tight binaries or that one of the components is ejected (Sadavoy & Stahler 2017). Observations of dust polarization and molecular gas in Class 0 systems found magnetic fields that were aligned with the outflow axis and low angular momentum in the inner envelope for single sources (Galametz et al. 2020).

The multiplicity resulting from fragmentation is affected by mass, temperature, feedback, or turbulence, as discussed in recent reviews (Krumholz et al. 2014; Lee et al. 2020; Offner et al. 2023). Simple analytic models suggest that structure dictates fragmentation, and a cloud core with a few Jeans masses can already fragment (Kratter et al. 2008; Pon et al. 2011, 2012). Early models suggested that radiative feedback and gas heating could suppress core fragmentation by increasing the thermal Jeans mass (30 K at a few thousand AU; Krumholz 2006; extensive envelope heating out to a thousand AU scales; Bate 2012) even during the first collapse of the core (Boss et al. 2000; Whitehouse & Bate 2006). Other models suggested that radiative heating mainly affects disk scales (several 100 AU) rather than the cloud core (Offner et al. 2023 and references therein). Self-consistent hydrodynamical simulations that include mechanical feedback through outflows (e.g., Guszejnov et al. 2021; Mathew & Federrath 2021) seem to show that outflows affect the fragmentation process and the physical conditions of the cloud, which is consistent with observations (e.g., van Kempen et al. 2009; Yıldız et al. 2015). The combination of magnetic fields and radiation also affects the core fragmentation process to a certain degree (Commerçon et al. 2010; Hennebelle et al. 2011), while the ratio of the rotational to magnetic energy of the core is also found to control core fragmentation in the innermost regions (Machida et al. 2008 in the low-mass case; Mignon-Risse et al. 2023 in the high-mass case). Some models suggest that magnetic fields may enhance multiplicity (e.g., Offner et al. 2016; Lee et al. 2019; Mathew & Federrath 2021) but reduce higher-order multiple protostellar systems. On the other hand, nonideal magnetic processes were not found to inhibit protostellar multiplcity (e.g., Wurster et al. 2019). Another proposed mechanism for the formation of multiple protostellar systems is turbulent fragmentation (e.g., Offner et al. 2010; Padoan et al. 2014; Federrath 2015; Cunningham et al. 2018; Lee et al. 2019). Models of high-mass star formation find that turbulence that carries angular momentum promotes disk growth and subsequent fragmentation, whereas magnetic fields reduce initial fragmentation (Commerçon et al. 2011) and remove angular momentum on disk scales (via magnetic braking and outflows), and thereby, reduce disk fragmentation (Mignon-Risse et al. 2021).

To give observational insight into the molecular gas environment around multiple protostellar systems, this work presents single-dish observations toward five subregions in the Perseus molecular cloud. The observations include on-the-fly (OTF) maps and single-pointing observations toward a sample of 37 protostellar systems. The spatial coverage of the OTF maps means that a few starless cores are also included in the sample. They serve to further reveal the physical conditions of the cores that form multiple protostellar systems. A brief overview of the Perseus molecular cloud and sample selection criteria is given in Sec. 2, and the source tables are given in Appendix A1. Observations are described in Sec. 3, along with details on frequency setup, data reduction, and imaging. Additional details are given in Appendices A and B. Section 4 briefly describes the resulting maps and spectra, and more detailed descriptions are provided in Appendix B. The derivation of the physical parameters, the statistics, and a discussion of the physical parameters versus multiplicity is described in Sects. 5 and 6. Our conclusions are given in Sec. 7.

2 Sample

The Perseus molecular cloud presents a wide range of star-forming environments; the distances vary between 279 and 302 pc (Zucker et al. 2018). The molecular cloud has been studied in molecular line emission (e.g., Arce et al. 2010; Curtis et al. 2010a,b; Curtis & Richer 2011; Walker-Smith et al. 2014; Hacar et al. 2017; Tafalla et al. 2021; Dame & Lada 2023), dust continuum (e.g. Hatchell et al. 2005; Enoch et al. 2006; Chen et al. 2016; Pokhrel et al. 2018), and dust polarization (e.g., NGC 1333; Doi et al. 2020, 2021; B1; Coudé et al. 2019). The gas kinematics at molecular cloud scales were reported for NGC 1333 (Hacar et al. 2017; Chen et al. 2020). The multiplicity of all Perseus protostars was characterized down to a projected separation of 15 AU (Tobin et al. 2016b). The parameters derived from SEDs, including Herschel Space Observatory PACS fluxes, are available for the Perseus protostellar sources (Murillo et al. 2016).

The maps presented in this work cover five subregions: NGC 1333, L1448, L1455, B1, and IC348 (Fig. 1). These maps cover clustered (NGC 1333), nonclustered (L1448, L1455, B1, IC348), externally irradiated (IC348, NGC 1333, L1448), and relatively isolated (B1, L1455) regions. The protostellar population we sampled includes objects from Class 0 to Class II that were obtained from the VLA Nascent Disk and Multiplicity Survey of Perseus Protostars (VANDAM) (Tobin et al. 2016b), as well as starless cores obtained from Hatchell et al. (2007). The multiplicity of these objects comprises bona fide single protostars and close (here defined as projected separations of <7″) and wide (defined in this work as projected separations of ≥ 7″) multiple protostellar systems. The projected separation classification is based on the systems that can be resolved with Herschel PACS observations (Murillo et al. 2016), and it is suitable for Nobeyama maps with a pixel size of 6″. The protostellar systems and starless cores are listed in Tables A.1 and A.2, respectively.

thumbnail Fig. 1

Kinetic gas temperature map derived from the I(HCN)/I(HNC) J=1–0 ratio (the color scale is the same as Fig. B.7) overlaid with the integrated intensity map of diazenylium N2H+ J=1–0 (gray contours in steps of 3, 5, 10, 15, 20, 25, and 30 K km s−1; see also Fig. B.4) for each observed region. All maps are shown with the same color-scale range for comparison. The σ value above each panel indicates the cutoff value for both maps. Stars mark the positions of protostellar sources, and squares mark the locations of starless cores. The filled circle marks the position of L1448 IRS2E, whose nature is debated. Straight lines indicate the outflow directions for the protostellar systems included in the MASSES survey (Stephens et al. 2017).

3 Observations

3.1 Nobeyama 45 m Radio Observatory

The observations of Perseus with the Nobeyama 45 m Radio Telescope (NRO) were made using the FOur-beam REceiver System on the 45 m Telescope (FOREST; Minamidani et al. 2016) frontend and with the Spectral Analysis Machine for the 45 m Telescope (SAM45; Kamazaki et al. 2012) backend in the project CG201020 (PI: N. M. Murillo). The observations were carried out between January and March 2021. The OTF mapping mode was used to make 162″ × 162″ maps with a 6″ grid to maximize the sample coverage (Table A.1) and time constraints. Smaller maps allowed an efficient use of the observing time (~45 minutes per map) and the streamlining of the data reduction. Because of time constraints, IRAS 03282+3035 is smaller (about 120″×130″), and B1-a was observed in only one frequency setup. the source can be detected in adjacent maps.

Two spectral setups were used to target eight molecular species: HCN J=1–0, HCO+ J=1–0, HNC J=1–0, HC3N J=10–9, c-C3H2 J=76,2−75,3, N2H+ J=1–0, 13CO J=1–0, and C18O J=1–0. We did not detect the targeted c-C3H2 transition (Eup = 87.45 K). Cyanoacetylene (HC3N J=10–9) will be discussed in a future work. The channel resolution of the spectral windows is 30.52 kHz (0.1 km s−1 per channel at 90.6 GHz) and the bandwidth is 125 MHz. The noise levels ranged between 0.3 and 3.3 K, with an angular resolution between 18.7″ (HCN) and 15.1″ (C18O). We adopted beam efficiencies ηmb of about 0.5 based on the measurements by NRO for the 2021–2022 observing season.

Standard data calibration and imaging for each datacube were done with the NOSTAR software package provided by NRO. Contiguous individual maps were combined into mosaics for NGC 1333, L1448, L1455, B1, and IC348 after determining the image center, bottom left corner, and top right corner coordinates. The maps for L1455 Per-emb 25 (hereafter Per25), IRAS 03292+3039 (hereafter IRAS 03292), and IRAS 03282+3035 (hereafter IRAS 03282) are shown individually given their locations in Perseus. All maps were clipped to only show values above 3σ or 5σ. Further analysis was carried out using CASA (CASA Team et al. 2022) and self-written Python scripts using the Astropy (Astropy Collaboration 2013, 2018) and PySpecKit (Ginsburg & Mirocha 2011) libraries. Intensity-integrated maps and respective uncertainties were obtained with the bettermoments Python library (Teague & Foreman-Mackey 2018; Teague 2019; see Appendix B for details).

3.2 Atacama Pathfinder Experiment

Single-pointing observations of HNC J=4–3 toward 37 protostellar systems were performed with the Atacama Pathfinder Experiment (APEX; Güsten et al. 2006) using the APEX-2 and First Light APEX Submillimeter Heterodyne (FLASH+) receivers. Some of the protostellar systems covered by the NRO maps were not observed with APEX (e.g., NGC 1333 IRAS 4). Ten protostellar systems were observed with APEX-2 (Murillo et al. 2018). The HNC J=4–3 spectra have native channel widths of 0.1 km s−1, and they were binned to 0.4 km s−1 to increase the signal-to-noise ratio (S/N). Typical noise levels range between 20 and 100 mK for HNC J=4–3 with APEX-2 for a channel width of 0.4 km s−1 and a half-power beam width (HPBW) of 18″. FLASH+ observations (Project ID: O-0104.F-9307B) of 27 protostellar systems were made on six dates: 11, 15–18, and 20 October 2019. The central frequency of the spectral setup was 361.16978 GHz and the bandwidth was 4 GHz. Typical noise levels ranged between 25 and 145 mK for a channel width of 0.4 km s−1 and a HPBW of 18″. A beam efficiency of ηmb = 0.73 was adopted for both instruments.

3.3 Data from the literature

Observations of HNC J=4–3 with the James Clerk Maxwell Telescope (JCMT) toward NGC 1333 IRAS 4 were obtained from the tabulated values in Koumpia et al. (2016). The angular resolution of the JCMT observations is 15″, and thus, we applied a beam dilution correction of 0.69 to the values from Koumpia et al. (2016) in order to compare them with our APEX data. The Perseus dust temperature map and its corresponding uncertainty map (Zari et al. 2016) were downloaded from the CDS archive2. The dust temperature was derived from the combined Herschel and Planck maps of Perseus using an SED fitting with a modified blackbody assumption. The Green Bank Ammonia Survey (GAS) map of NGC 1333 (Friesen et al. 2017) was obtained from the Dataverse archive and was derived from fitting the NH3 line emission. Information on molecular outflows driven by the protostars included in the NRO maps was obtained from the MASSES survey (Stephens et al. 2017).

4 Results

4.1 Nobeyama maps

In this paper, we focus on emission from HCN, HCO+, HNC, N2H+, 13CO, and C18O, which all lie in the J=1–0 transition. A detailed description and the integrated intensity maps of each molecular species are given in Appendix B. The source positions (Hatchell et al. 2007; Tobin et al. 2016b) and known outflow directions (Stephens et al. 2017) are plotted in all maps. The spatial gas distributions of HCN, HCO+, HNC, and N2H+ show bright and extended emission around higher-order multiple pro-tostellar systems (>2 components) and weaker more compact emission around isolated systems or close binaries and single protostars (Figs. B.1–B.4). The strongest emission of these four species is mainly located in NGC 1333 and L1448. The spatial distribution of the two CO isotopologs 13CO and C18O does not match any of the other molecular lines. The main core of the B1 region presents the brightest C18O emission, but HCO+ and 13CO are weaker.

4.2 Single-pointing observations of HNC

Single-pointing observations with APEX detected HNC J=4–3 toward all sources in the sample with an S/N of 4 or higher. The APEX observations did not include the NGC 1333 IRAS 4 mini-cluster HH211, L1455 IRS2 (Table A.1) or the starless cores (Table A.2). The peak values range from 0.17 to 3.3 K, with an average noise level of 50 mK. The strongest HNC J=4–3 emission (S/N > 48) is present toward L1448 C, NGC 1333 IRAS 6, NGC 1333 SVS13, and B1–C. The weakest emission (4 < S/N < 6) is present toward NGC 1333 EDJ2009156, IC348 EDJ2009366, and NGC 1333 IRAS 5 Per63. 1The average line width for the HNC J=4–3 transition is 1 km s−1, with a range of 0.5–1.9 km s−1.

The spectrum from the HNC J=1–0 NRO maps was extracted from 18″ circular regions centered on the positions listed in Table A.1 to match the beam size of the APEX observations. The peak brightness varied from 1.4 to 7.2 K, with an average noise level of 144 mK. The weakest emission was found toward two sources, L1455 Per25 (S/N = 8) and NGC 1333 IRAS 4C (S/N = 9). All other source positions have emission with an S/N > 11. The J=1–0 transition presents an average line width of 1.5 km s−1 with a range of 0.9 to 2.3 km s−1. This is slightly wider than the 4–3 transition.

5 Analysis

The physical parameters analyzed in this section are mean values obtained from within a circular region of 18″ in diameter, centered on the sources listed in Tables A.1 and A.2, and they are referred to as the physical parameters of the source for simplicity. The reported values therefore consider envelope scales (~5000 AU) and not the entire molecular cloud.

5.1 Envelope dust mass

We calculated the envelope dust mass based on the relation from Jørgensen et al. (2009), Menv=0.44M⊙(Lbol1 L⊙)−0.36(S 850μm1 Jy beam−1)1.2(d125 pc)1.2,$\[M_{\mathrm{env}}=0.44 M_{\odot}\left(\frac{L_{\mathrm{bol}}}{1 ~L_{\odot}}\right)^{-0.36}\left(\frac{S_{~850 \mu \mathrm{m}}}{1 ~\mathrm{Jy} ~\mathrm{beam}^{-1}}\right)^{1.2}\left(\frac{d}{125 ~\mathrm{pc}}\right)^{1.2},\]$(1)

where the envelope dust mass, Menv, was calculated from the 850 μm dust continuum peak intensity S850μm within the 18″ beam (~5000 AU), the bolometric luminosity Lbol, and the distance d. The dust continuum map at 850 μm was obtained from the COMPLETE survey map of Perseus (Kirk et al. 2006), and the peaks were obtained from within circular regions of 18″, centered on the sources in our sample (Tables A.1 or A.2). The distance d for each subregion was taken from Zucker et al. (2018), and we adopted 288 pc for L1448, 299 pc for NGC 1333 and L1455, 301 pc for B1, and 295 pc for IC348.

5.2 Kinetic gas temperature from I(HCN)/I(HNC)

The clipped (3 or 5σ) integrated-intensity HCN and HNC maps were used to make the I(HCN)/I(HNC) J=1–0 ratio map, which was then converted into kinetic temperature using the equations from Hacar et al. (2020), TK[K]=10×[I(HCN)I(HNC)]if[I(HCN)I(HNC)]≤4. $\[T_K[K]=10 \times\left[\frac{I(\mathrm{HCN})}{I(\mathrm{HNC})}\right] { if }\left[\frac{I(\mathrm{HCN})}{I(\mathrm{HNC})}\right] \leq 4 \text {. }\]$(2)

We note that the I(HCN)/I(HNC) J=1–0 maps are insensitive to temperatures <15 K and >40 K. The values beyond these limits were therefore abitrarily set to the 15 and 40 K for the subsequent calculations of physical parameters. The I(HCN)/I(HNC) J=1–0 ratio uncertainty map was generated, assuming zero covariance, with the relation σTK2=TK2[(σI(HCN)I(HCN))2+(σI(HNC)I(HNC))2].$\[\sigma_{T_K}^2=T_K^2\left[\left(\frac{\sigma_{I(\mathrm{HCN})}}{I(\mathrm{HCN})}\right)^2+\left(\frac{\sigma_{I(\mathrm{HNC})}}{I(\mathrm{HNC})}\right)^2\right].\]$(3)

Errors were extracted from the uncertainty map using circular regions of 18″.

Figure 1 shows the derived kinetic gas temperature TK map. The integrated-intensity map of N2H+ J=1–0, tracing cold dense gas, is overlaid on the TK map. The subregion mean I(HCN)/I(HNC) ratio was calculated considering all the pixels above 5σ, resulting in mean ratios of 1.5±0.6 for NGC 1333, 1.5±0.8 for L1448, 2.0±0.9 for IC348, 1.7±1.1 for B1, 1.1±0.4 for L1455, 2.5±1.1 for IRAS 03292, 1.2±0.4 for IRAS 03282, and 1.4±0.4 for L1455 Per25. The TK map without overlay is shown in Fig. B.7, and Figs. B.1–B.6 show the TK map contours overlaid on the integrated-intensity maps of the other molecules for comparison. Table A.4 lists the mean I(HCN)/I(HNC) J=1–0 ratios, the uncertainty, and the adopted TK within 18″ circular regions centered on the sources in the sample.

The mean TK versus Lbol (Table A.1) and Menv (Table A.5) for each source are plotted in Fig. 2 along with the dust temperature Tdust from combined Herschel and Planck maps (36″ within the Herschel map area; Zari et al. 2016). For sources in NGC 1333, the NH3 kinetic gas temperature TK,NH3$\[T_{K, \mathrm{NH}_3}\]$, from the Green Bank Ammonia Survey was included (GAS; 32″ beam; Friesen et al. 2017) for comparison. The values were all obtained from within a circular region with a diameter of 18″, and they are listed in Table A.4.

5.3 H2 density from HNC J = 4–3/J= 1–0

Considering the kinetic temperature constraints derived from I(HCN)/I(HNC) and the availability of HNC J=1–0 and 4–3 data with the same angular resolution, we derived the H2 volumetric density n(H2) based on observational data and radiative transfer models. Non-local thermal equilibrium (non-LTE) excitation and radiative transfer calculations using the code RADEX (van der Tak et al. 2007) were performed to model the HNC J=4–3 / J=1–0 ratio with respect to the H2 volumetric density n(H2) and kinetic gas temperature. Using these models, the observed HNC J=4–3 / J=1–0 ratio (assuming both transitions arise from the same gas) together with TK enabled us to obtain mean n(H2) within 5000 AU regions. The APEX and NRO observations have the same angular resolution (~18″), and thus, no beam dilution correction was needed. A beam dilution correction (0.69) was applied to the JCMT data (15″ beam).

The calculations adopted an N(HNC) = 1013 cm−2 and a line width of 1 km s−1 (see Sec. 4.2) because these parameters reproduce the observed HNC peak emission best. The modeled n(H2) values were selected using the TK and HNC J=4–3 / J=1–0 ratio constraints with the corresponding uncertainties for each source. The obtained n(H2) values for each source were then averaged and the standard derivation calculated to obtain the adopted value and corresponding uncertainty per source. The adopted n(H2) with derived TK and corresponding uncertainties are listed in Table A.5. When N(HNC) is an order of magnitude higher, this results in n(H2) near or below the critical density of the HNC 1–0 transition (~2×105 cm−3 between 5 and 40 K). When N(HNC) is an order of magnitude lower than adopted, n(H2) varies between 7×106 and 2×109 cm−3, which are typical densities of low-mass protostellar envelope models at R < 1000 AU (e.g., Jørgensen et al. 2005; van ’t Hoff et al. 2018). Broader line widths of 1.5 and 2.0 km s−1 (see Sec. 4.2) vary the calculated mean n(H2) by less than 10%, except for L1448 C, which varies by as much as 60%. The n(H2) derived from the HNC J=4–3 / J=1–0 ratio versus Lbol and Menv are shown in Fig. 2.

thumbnail Fig. 2

Gas and dust temperature (first row), derived H2 volumetric density from the HNC J=4–3/J=1–0 ratio (second row), and derived N2H+ J=1–0 and HCO+ J=1–0 column density (third row) vs. source bolometric luminosity Lbol (left column) and envelope mass Menv (right column). In the bottom row, the error bars are about the size of the plotted points. The starless cores (squares) HH211, and L1445 IRS2 adopt the average H2 volume density for their respective region (see Table A.5).

5.4 Column density and gas mass from N2/H+ J = 1–0 and HCO+ J = 1–0

The n(H2) (Sect. 5.3), TK (Sect. 5.2), peak brightness temperature and line width were used to derive the column density of N2H+ (N(N2H+)) and HCO+ (N(HCO+)) using RADEX. An average of each subregion was calculated and adopted as the n(H2) for sources without HNC J=43 data. The uncertainties for the column densities were calculated by using the lower and upper limits of n(H2) and TK in the RADEX calculations and then taking the average and standard deviation of all three values. Changes of an order of magnitude in n(H2) do not significantly affect the derived N(N2H+) and N(HCO+). To test whether using TK,TK,NH3$\[T_K, T_{K, \mathrm{NH}_3}\]$ or Tdust affected the calculations, N(N2H+) and N(HCO+) toward NGC 1333 were derived using the available temperatures. The results show that N(N2H+) and N(HCO+) are the same regardless of the temperature, which indicates that the calculations are sensitive to the line peak brightness temperature and line width of the corresponding emission.

The weaker and optically thin component of N2H+ at 93.1739 GHz was used to derive N(N2H+) because it is optically thin and less prone to blending. The bettermoments Python library (Teague & Foreman-Mackey 2018; Teague 2019) was used to perform a Gaussian fit in order to obtain peak brightness temperature and line width N2H+ and HCO+ maps. The mean peak brightness temperatures and line widths were then extracted for the source positions within regions of 18″.

The gas mass in M⊙ for N2H+ (Mgas(N2H+)) and HCO+ (Mgas(HCO+)) within region diameters of 18″ was derived with Mgas=Mr( g mol−1)N( cm−2)A( cm2)NA( mol−1)Msun,g (g)M⊙,$\[M_{{gas }}=\frac{M_r\left(\mathrm{~g} \mathrm{~mol}^{-1}\right) N\left(\mathrm{~cm}^{-2}\right) A\left(\mathrm{~cm}^2\right)}{N_A\left(\mathrm{~mol}^{-1}\right) M_{{sun,g }}~(\mathrm{g})} M_{\odot},\]$(4)

where Mr is the mean molecular weight (29.022 and 29.018 g mol−1 for N2H+ and HCO+, respectively), NA is Avogadro’s constant, N is the derived gas column density, A is the area, and Msun,g is the solar mass in gram. The uncertainty was obtained with the same equation, but with N being the uncertainty of the derived column density. The distances we used are the same as noted in Sect. 5.1.

The derived N(N2H+) and N(HCO+) are plotted in Fig. 2 versus Lbol and Menv. The HHCO+ column density is lower by a factor of ~16 than the N2H+ column density, and both follow the same trend (Fig. 2, Table A.5). Hence, Mgas(N2H+) is shown in the subsequent plots to illustrate the relation of the gas mass, dust mass, and multiplicity in Fig. 3, with Mgas(HCO+) following the same trend.

Within the regions probed (18″, 5000 AU), N2H+ traces cold (≤20–30 K) dense (typically ≥ 105 cm−3) gas, and HCO+ traces warmer gas (>20–30 K). This arises because the chemical formation and destruction pathways of both molecules are related to the presence of CO (e.g., Murillo et al. 2022a). N2H+ is present in the gas phase when CO is frozen out onto the dust grains (temperatures below 20–30 K). The HCO+ formation requires CO to be in the gas phase and is destroyed by molecules such as water, and thus, HCO+ is present in the gas at temperatures above 20–30 K and up to 100 K.

thumbnail Fig. 3

Relations of the N2H+ gas mass, Mgas(N2H+), and envelope dust mass, Mmenv, for the sample. The orange stars show multiple systems, the cyan diamonds show binary systems, and the gray circles show single protostellar systems. Each panel represents one of four ways of grouping the sample and their corresponding correlations. The lines and shaded areas show the linear regression for the data with the corresponding color. The solid lines indicate statistically significant correlations (Pearson r and Spearman ρ p-values <0.05), and the dashed lines show subsamples with p-values >0.05; see Sect. 5.5 for a discussion of the figure).

5.5 Statistics

Three statistical tests were performed to examine the relations between the physical parameters and multiplicity. The number of protostellar components was taken from Tobin et al. (2016b) and was updated based on Reynolds et al. (2024). A two-sample Anderson-Darling (AD)3 test assuming normal distribution was used to determine whether the parameters shared the same parent distribution. An AD statistic < 1.961 and p-value > 0.05 indicates that both samples arise from the same parent distribution. The Pearson linear correlation coefficient (r) and Spearman’s rank correlation coefficient (ρ) were used to find correlated parameters. The values of r and ρ range from −1 to 1, for negative slope to positive slope correlations, respectively, with values closer to 1 (absolute value) indicating stronger correlations. Statistically significant correlations are identified by p-values < 0.05. Linear regression was used to visualize the correlations between physical parameters. All tests were made using the statistical functions in the Python library Scipy. Five classification schemes, excluding starless cores, were used for the statistical tests:

  1. Full sample, parameters within a region diameter of 18″. The sample size was 46 sources.

  2. Multiplicity within a region diameter of 18″: Each continuum peak is a separate system (e.g., SVS13A, B, and C are three individual systems). This scheme considers that sources with separations larger than 5000 AU are not gravitationally bound. The bin sizes were for multiples 2 systems, for binaries 12 systems, and for singles 32 systems.

  3. System multiplicity with binaries having separations <7″. This scheme considers core versus disk fragmentation scenarios. The bin sizes for multiples were 11 systems, for binaries 7 systems, and for singles 11 systems.

  4. System multiplicity following the classification of singles (one component), binaries (two components), and higherorder multiples (more than two components). The bin sizes were for multiples 6 systems, for binaries 12 systems, and for singles 11 systems.

  5. System multiplicity where multiples are systems with two or more components, examining the scenario in which all multiple systems share the formation mechanisms. The bin sizes were for multiples 18 systems and for singles 11 systems.

As a system, we considered all the protostars within a common core, and thus, Mgas(N2H+), Mgas(HCO+), and Menv of a system is the sum of the masses of each of its components. Parameters such as TK,NH3$\[T_{K, \mathrm{NH}_3}\]$, Tdust, Tk, n(H2), N(N2H+), and N(HCO+) were averaged from all the components.

5.5.1 Temperature

For the full sample, the AD test indicates that TK,NH3$\[T_{K, \mathrm{NH}_3}\]$ (Friesen et al. 2017), Tdust (Zari et al. 2016), and TK (this work) do not share a common parent distribution. When the lower limit of 15 K was not applied to the I(HCN)/I(HNC) J=1–0 ratio (see Sec. 5.2), then TK,NH3$\[T_{K, \mathrm{NH}_3}\]$ and TK shared the same parent distribution (p-value = 0.71). However, we adopted TK with the 15 K lower limit. For the full sample, Tdust shows a correlation with Lbol (r ~ 0.7, ρ ~ 0.7, p-value ≪0.05), but not with mass. Given the method used to obtain Tdust (see Sec. 3.3, Zari et al. 2016) and Lbol (Murillo et al. 2016), the correlation is expected as the quantities are not independent. We found a weak correlation between the number of protostellar components and Tdust, but this may be skewed because the source with the highest luminosity also has the highest number of components (SVS13A, 117 L⊙, four protostars), while single sources have Lbol ≤ 12 L⊙. On the other hand, TK shows no correlation with Lbol, mass, or the number of protostellar components for any of the five classification schemes we used.

For NGC 1333, TK,NH3$\[T_{K, \mathrm{NH}_3}\]$ shows a correlation with the bolometric luminosity (r ~ 0.6, ρ ~ 0.6, p-value < 0.006), N(N2H+), N(HCO+) and the corresponding gas masses (r ~ 0.6, ρ ~ 0.6, p-value < 0.006). In the method used to derive TK,NH3$\[T_{K, \mathrm{NH}_3}\]$, N(NH3) is implicitly dependent on the kinetic gas temperature (Friesen et al. 2017). This result suggests that N(N2H+) and N(NH3) are correlated, which confirms previous work (Johnstone et al. 2010).

5.5.2 Density

For the full sample, the AD test indicates that N(N2H+) and N(HCO+) are not drawn from the same parent distribution. The n(H2) shows a weak correlation with the dust temperature (r ~ 0.4, ρ ~ 0.3, p-value < 0.04) and an even weaker linear but not ranked correlation with Lbol (r ~ 0.3, p-value ~0.03). No correlation is found between TK and the derived n(H2) from this work, or between the number of protostellar components and n(H2). A visual representation of n(H2) versus TK and dense cold-gas (N2H+) maps is shown in Fig. B.8.

In contrast, N(N2H+) and N(HCO+) show no correlation with Tdust, Lbol, TK, Menv, or the number of protostellar components. As expected from the method used in this work, N(N2H+) and N(HCO+) show a perfect correlation with Mtot(N2H+) and Mtot(HCO+) (r ~ 1.0, ρ ~ 1.0, with very low p-values). Hence, the correlation tests were not run on the subsamples from classification schemes 2–5 for N(N2H+) and N(HCO+) because the column densities would follow the same trends as the gas mass.

5.5.3 Mass

For all five classification schemes, Mgas(N2H+), Mgas(HCO+), and Menv are not consistent with being drawn from the same parent distribution. The AD test shows that the same mass parameters between the binary and single protostellar subsamples in classification schemes 2–4 are drawn from the same parent distribution, with p-values > 0.4 for gas masses and p-values > 0.3 for dust masses. This shared distribution is visible in the Menv versus Mgas(N2H+) plots (Figs. 3 and C.1). The multiples subsample in classification schemes 3 and 4 does not share a parent distribution with the binary and single subsamples for any of the tested parameters. For classification scheme 5, Mgas(N2H+) and Mgas(HCO+) for the multiple and single populations are found to be drawn from the same parent distribution (AD test p-value ~ 0.1), but the Menv does not show the same result (AD test p-value ~0.03).

For the full sample, Menv shows a positive correlation with Mgas(N2H+) and Mgas(HCO+), both cases having r ~ 0.7, ρ ~ 0.7, with p-value ≪0.05. For classification scheme 2, Menv shows a positive correlation with Mgas(N2H+) and Mgas(HCO+) for the binary (r ~ 0.7, ρ ~ 0.7, p-value <0.02) and single (r ~ 0.6, ρ ~ 0.6, p-value ≪0.01) subsamples (Fig. 3, first panel). The multiples subsample only contained two sources, and we were therefore unable to perform a significant statistical analysis.

For classification scheme 3 (binaries with separations of <7″; Fig. 3, second panel), strong positive correlations are found between dust and gas masses for singles (r ~ 0.6, ρ ~ 0.6, p-value ≪0.05) and multiples (r ~ 0.7, ρ ~ 0.8, p-value ≪0.05). The binary subsample is not correlated according to the Pearson r and Spearman ρ tests. This may be due to the small sample size of the binaries (seven sources).

In classification scheme 4 (binaries with two components; Fig. 3, third panel), Menv shows a positive correlation to the gas masses for binaries (r ~ 0.7, ρ ~ 0.8, p-value <0.01) and singles (r ~ 0.8, ρ ~ 0.7, p-value <0.03). The multiples subsample has a small sample size (six sources), and thus, it does not show a statistically significant correlation. Classification scheme 5 (multiples have >two components; Fig. 3, fourth panel) shows a correlation between Menv and gas mass for multiples (r ~ 0.8, ρ ~ 0.9, p-value ≪0.001) and singles (r ~ 0.8, ρ ~ 0.7, p-value <0.03).

5.5.4 Number of components

For the full sample and classification scheme 5, the number of protostellar components shows a positive correlation with dust and gas masses (r ~ 0.6, ρ ~ 0.6, with a p-value ≪0.05). For classification scheme 3, a correlation is found for the multiples subsample between the gas masses and number of protostellar components (r ~ 0.8, ρ ~ 0.8, with a p-value <0.004), but not with Menv. Based on the Pearson r and Spearman ρ coefficients, there is no correlation between the number of protostellar components and mass for the multiples subsample in classification scheme 4. However, this might again be due to the small sample size. Figure C.1 plots the masses versus the number of components.

6 Discussion

6.1 Physical parameters that affect multiplicity

We used single-dish observations of molecular line emission toward five subregions in the Perseus molecular cloud to derive the kinetic gas temperature, the volumetric and column densities, and the gas masses at protostellar envelope scales. These physical parameters have been proposed, through theory, models, or previous observations, as key to determining the multiplicity of low-mass protostellar systems. Based on the derived physical parameters and the statistical tests applied to the resulting sample, we found that the kinetic gas temperature, TK, is not related to multiplicity or to the number of protostellar sources in a system in the Perseus molecular cloud. The kinetic gas temperature from ammonia, TK,NH3$\[T_{K, \mathrm{NH}_3}\]$, is related to the gas mass, as well as Lbol, in NGC 1333. This is more likely due to the method used to estimate the kinetic gas temperature (Friesen et al. 2017), however, than to an additional correlation. The dust temperature, Tdust, shows correlations to Lbol and a weak correlation to n(H2). Our results are consistent with the temperature-multiplicity relation found in APEX observations of H2CO and DCO+ at 217 and 360 GHz (Murillo et al. 2018). We note that any of the three temperatures we used leads to practically the same derived H2 volume density, gas column density, and gas mass. We caution that implicit dependences may lead to apparent correlations, however.

It is interesting to note that no variation along the outflow direction (green straight lines in Fig. 1) is seen, especially within the dense regions. Outflows have been shown to output sufficient energy and luminosity into the molecular cloud (Plunkett et al. 2013; Dionatos & Güdel 2017). UV-heated gas has been found within outflow cavities (Yıldız et al. 2015), and the gas temperatures within outflows obtained from 13CO J=10–9/J=3–2 J=10–9/J=6–5 suggest temperatures of ≥50 K, assuming an n(H2) of 105−106 cm−3 (Murillo et al. 2018). Even with the ~ 5 K uncertainty of the I(HCN)/I(HNC) method, significant temperature variation along the outflow directions should therefore be detected. Warm regions (>20 K) are seen mainly outside of the dense areas traced by N2H+ and tend to align with outflow directions (e.g., NGC 1333: IRAS 2, IRAS 4, and IRAS 7; L448 C), or regions that most likely are externally irradiated (e.g., L1448 N, IC348).

There is a lack of relation between the volumetric H2 gas density, n(H2), and the number of protostellar components. This is consistent with studies that failed to find a correlation between N(N2H+) and the cloud core density (Johnstone et al. 2010). The N(N2H+) derived in our work matches that of Johnstone et al. (2010). The same work found a correlation between N(NH3) and N(N2H+), which was interpreted to show that both molecules arise from the same gas, which is also supported by the results of the current work.

The gas column densities, and consequently, the gas masses, show strong positive correlations with multiplicity and with the number of protostellar components. The correlations are consistent, regardless of whether the multiplicity is within regions of ~5000 AU (18″) or much larger cloud cores. In general, cold Mgas(N2H+) is a factor of ~16 higher than warm Mgas(HCO+). An explanation for the difference in the warm- and cold-gas masses is that protostars do not heat their envelopes to a large extent, and the envelopes therefore mainly contain cold gas. Additionally, the angular resolution of the observations is bound to pick up more of the cold-gas emission, which would bias the cold- to warm-gas ratio. The former has been shown by models (e.g., Murillo et al. 2022b) and suggested by observations of episodic accretion (e.g., Hsieh et al. 2018, 2019) and variability (e.g., Johnstone et al. 2022), with most of the protostellar heating escaping through the outflow cavities. Another possibility is that the gas masses we derived are biased due to the constant abundances of N2H+ and HCO+ that we adopted for simplicity in the calculations.

Binaries and singles are found to be drawn from the same parent distribution for Mgas(N2H+), Mgas(HCO+), and Menv. This is true, regardless of whether the binary subsample consists of only close systems (separations ≤7″) or of all systems with two protostellar components. The gas and dust mass trends found for single and binary protostellar systems would support the results from analytic models that suggest that structures with a few Jeans masses can readily collapse and fragment to form protostars (Pon et al. 2011), and earlier studies that reported lower dust masses for close binary systems in comparison to single systems (which would affect disk formation and evolution; Harris et al. 2012). If the dust and gas masses are similar for singles and binaries, another factor must determine whether a single or binary system is formed.

Our statistical tests indicate that higher-order multiple systems (three or more components) are not drawn from the same parent distributions as binaries and singles. Higher-order multiples have consistently higher gas and dust masses than binaries and singles. It is unclear whether the high gas masses are initially available or accumulated dynamically, and which process stops a cloud core from fragmenting when a few Jeans masses are accumulated. Mairs et al. (2014) showed based on observations and simulations that protostars start to form when the cores cross the Jeans-unstable threshold and often continue to gain mass from the cloud. However, Mairs et al. (2014) did not consider multiplicity because they were inable to follow both mechanical and radiative feedback. Some studies suggested that velocity-coherent gas structures in the molecular clouds move material toward protostars (Hacar et al. 2017; Chen et al. 2020), and magnetic fields and turbulence may help in the process of fragmentation (e.g., Offner et al. 2016; Lee et al. 2019; Mathew & Federrath 2021). As mentioned in Lee et al. (2019), these studies did not resolve disks and only accounted for turbulent fragmentation. Disk fragmentation (e.g., Wurster et al. 2019), and in particular, hierarchical fragmentation, might contribute as well. However, this is highly dependent on the adopted cooling function and thermodynamic properties of the gas.

While studying these processes is beyond the scope of the current work, the higher-order multiple systems may provide some insight into this point. Within L1448 N, the triple system in component B presents the highest cold-gas and dust masses within L1448 N (Fig. 3) and shows evidence of recent fragmentation (Tobin et al. 2016a). In contrast, NGC 1333 SVS13A has the lowest gas and dust mass in the SVS13 system, but recent studies have reported a small-scale accretion flow in NGC 1333 SVS13A (Diaz-Rodriguez et al. 2022; Hsieh et al. 2023). Toward IRAS 03292, Reynolds et al. (2024) identified several condensations in dust continuum observations, while Taniguchi et al. (2024) recently reported infall from 25 000 AU scales onto the cloud core. Whether a physical connection exists between envelope-scale and molecular-cloud-scale accretion is still unclear.

6.2 Models versus observations

The presence of protostars in cloud cores down to the low end of the sampled range show that there was at least one Jeans mass of material during collapse. Analytic studies (e.g., Pon et al. 2011) reached a similar conclusion and stated that cores with a few Jeans masses can readily fragment if turbulence and magnetic fields are present. Prestellar core substructure has been proposed as a mechanism to determine whether a core forms a single or multiple protostellar system. Earlier observations did not find substructure like this (e.g., Dunham et al. 2016; Kirk et al. 2017), but more recent observations reported substructure in a starless core (e.g., Sahu et al. 2021). Simulations of turbulent fragmentation models based on observational data (e.g., Offner et al. 2012; Dunham et al. 2016) indeed suggested that substructures would not be detectable based on the typical gas densities of the prestellar cores. Our results suggest that the amount of mass, rather than density substructures, may be key in fragmentation and formation of multiple protostellar systems. While gas mass may not be linked to hierarchy based on models (Lee et al. 2019), observations point to a relation between number of protostars and the mass. If protostellar cloud cores have a mechanism to replenish the gas mass (e.g., via molecular cloud velocity coherent gas flows; Hacar et al. 2017; Chen et al. 2020 or mediated along the magnetic field lines, Coudé et al. 2019; Doi et al. 2020, 2021), this replenishment of material could affect the hierarchy of the system through uneven mass distribution. Observational evidence shows an uneven distribution of the dust mass (Tobin et al. 2010) and gas mass (e.g., at envelope to disk scales in IRAS 16293, Murillo et al. 2022b). Speculating even further, cloud cores that receive more gas replenishment would lead to the formation of higher-order multiple protostellar systems, and have larger (cold-) gas mass reservoirs.

The TK maps of Perseus show that low-mass protostars doe not heat their immediate environment efficiently. Hence, heating cannot readily suppress fragmentation at scales beyond a few 100 AU (disk scales), as pointed out in previous work (e.g., Harsono et al. 2011; Krumholz et al. 2014; Murillo et al. 2016; Offner et al. 2023; Mignon-Risse et al. 2021). Observational evidence of disk fragmentation does exist (e.g., Tobin et al. 2016a). Simulations of low-mass star formation that included outflows (e.g., Guszejnov et al. 2021; Mathew & Federrath 2021) produced lower molecular cloud temperatures since most of the heating from protostars will escape through the outflow cavity (as shown from observations; e.g., Yıldız et al. 2015). These simulations are consistent with the derived kinetic gas temperature maps presented in this work, as well as with previous observational work (e.g., Friesen et al. 2017). However, our study does not support the scenario in which outflows play a role in defining stellar masses in protostellar systems (Guszejnov et al. 2021; Mathew & Federrath 2021).

Given the inefficiency of heating in suppressing fragmentation together with similar cloud core masses for single and binary systems, another physical process must be preventing fragmentation. Various models including magnetic fields on 103 AU scales suggest that the magnetic pressure helps to stabilize prestellar cores against fragmentation (e.g., the review by Padoan et al. 2014). Additionally, models of massive star formation considering fragmentation and magnetic fields (e.g., Mignon-Risse et al. 2021) indicate that magnetic pressure dominates thermal pressure overall. The same was suggested for low-mass star formation if the gas temperature maps we presented here along with the magnetic field maps of B1 and NGC 1333 (Coudé et al. 2019; Doi et al. 2020) and the inferred magnetic field pressure are considered. However, the gas temperature and magnetic field maps for NGC 1333 and B1 need to be directly compared to determine whether magnetic pressure dominates thermal pressure.

7 Conclusions

We presented Nobeyama 45m Radio Observatory OTF maps and APEX single-pointing observations of HNC J=4–3 toward five subregions in the Perseus molecular cloud with an angular resolution of ~18″. Emission from HCN J=1–0, HCO+ J=1–0, HNC J=1–0, N2H+ J=1–0, 13CO J=1–0, and C18O J=1–0 is detected toward all mapped regions. The spatial distribution of each molecular species was compared to the protostellar and starless core population along with the outflow directions. The kinetic gas temperature maps were derived from the I(HCN)/I(HNC) J=1–0 ratio maps and were quantitatively compared to gas and dust temperature maps from the literature. The molecular hydrogen density was derived from the HNC J=4–3/J=1–0 ratio. Using the derived kinetic gas temperature and n(H2), we derived the column densities and total gas masses from N2H+ and HCO+. These quantities provide a physical characterization of protostellar cloud cores at ~5000 AU scales. The derived parameters, along with source bolometric luminosity, dust envelope mass, and clustering, were compared with the multiplicity of the protostellar sources in order to determine the factors that affect multiple star formation at molecular cloud scales. The following conclusions were drawn from the data.

  1. Gas and dust masses are the main factors that define the multiplicity in protostellar systems for the Perseus star-forming region at 5000 AU scales. Higher gas and dust masses are needed to produce higher-order multiples.

  2. The kinetic gas temperature TK and n(H2) are not related to multiplicity, dust, or gas mass within the Perseus molecular cloud. A weak correlation is found between n(H2) and Lbol, but not between TK and Lbol.

  3. The continuous relation in gas and dust masses, regardless of the sample grouping, suggests a continuum in the formation mechanisms rather than distinct formation mechanisms for close and wide multiple protostellar systems.

  4. The results presented here do not support the scenario that outflows set the stellar masses in low-mass star formation.

We demonstrated that it is relevant to consider the gas masses for the formation of multiple protostellar systems. The physical characterization of cloud cores carried out in this work needs to be repeated at different scales in order to study whether the relation between mass and multiplicity is scale dependent. This would be of particular interest for an exploration of why the masses of single protostellar systems and close binaries are similar.

Acknowledgements

This paper made use of Nobeyama data, and APEX data. The Nobeyama 45-m radio telescope is operated by Nobeyama Radio Observatory, a branch of National Astronomical Observatory of Japan. We are grateful to the APEX staff for support with these observations. Observing time for the APEX data was obtained via Max Planck Institute for Radio Astronomy, Onsala Space Observatory and European Southern Observatory. This study is supported by a grant-in-aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (20H05645, 20H05845 and 20H05844) and by a pioneering project in RIKEN Evolution of Matter in the Universe (r-EMU). The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. N.M.M. acknowledges support from the RIKEN Special Postdoctoral Researcher Program (Fellowships). D.H. is supported by Center for Informatics and Computation in Astronomy (CICA) grant and grant number 110J0353I9 from the Ministry of Education of Taiwan. D.H. acknowledges support from the National Technology and Science Council of Taiwan through grant number 111B3005191. A.H. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No.851435) D.J. is supported by NRC Canada and by an NSERC Discovery Grant. R.M.R. acknowledges funding from CNES through a postdoctoral fellowship. Y.-L.Y. acknowledges support from Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (20H05845, 20H05844, 22K20389), and a pioneering project in RIKEN (Evolution of Matter in the Universe).

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1

Appendices are only available in electronic form at Zenedo.org, https://zenodo.org/records/12797204

3

The Scipy function used, anderson_ksamp, requires a sample size of 2 or more, as noted in the Scipy API https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.anderson_ksamp.html. The calculated statistic of the test increases with decreasing sample size.

All Figures

thumbnail Fig. 1

Kinetic gas temperature map derived from the I(HCN)/I(HNC) J=1–0 ratio (the color scale is the same as Fig. B.7) overlaid with the integrated intensity map of diazenylium N2H+ J=1–0 (gray contours in steps of 3, 5, 10, 15, 20, 25, and 30 K km s−1; see also Fig. B.4) for each observed region. All maps are shown with the same color-scale range for comparison. The σ value above each panel indicates the cutoff value for both maps. Stars mark the positions of protostellar sources, and squares mark the locations of starless cores. The filled circle marks the position of L1448 IRS2E, whose nature is debated. Straight lines indicate the outflow directions for the protostellar systems included in the MASSES survey (Stephens et al. 2017).
In the text
thumbnail Fig. 2

Gas and dust temperature (first row), derived H2 volumetric density from the HNC J=4–3/J=1–0 ratio (second row), and derived N2H+ J=1–0 and HCO+ J=1–0 column density (third row) vs. source bolometric luminosity Lbol (left column) and envelope mass Menv (right column). In the bottom row, the error bars are about the size of the plotted points. The starless cores (squares) HH211, and L1445 IRS2 adopt the average H2 volume density for their respective region (see Table A.5).
In the text
thumbnail Fig. 3

Relations of the N2H+ gas mass, Mgas(N2H+), and envelope dust mass, Mmenv, for the sample. The orange stars show multiple systems, the cyan diamonds show binary systems, and the gray circles show single protostellar systems. Each panel represents one of four ways of grouping the sample and their corresponding correlations. The lines and shaded areas show the linear regression for the data with the corresponding color. The solid lines indicate statistically significant correlations (Pearson r and Spearman ρ p-values <0.05), and the dashed lines show subsamples with p-values >0.05; see Sect. 5.5 for a discussion of the figure).
In the text

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