On the Scarcity of Dense Cores ($n>10^{5}$ cm^-3) in High-latitude Planck Galactic Cold Clumps

A thorough search of the SCUBA-2 850 $\mu$m data in the JCMT Science Archive¹¹1https://www.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/en/jcmt/, and crossmatching with 793 HLPCs that satisfy the latitude criterion of $|b|>30\arcdeg$, gave 138 observing fields in total. We dismiss six of the fields that have limited integration time or nonstandard scan modes. Different scan patterns include constant velocity daisy patterns (CV Daisy) and rotating curvy pong patterns (Curvy Pong), so the field offsets vary significantly between different patterns. We make sure that the observing fields cover the peak of PGCCs at 353 GHz. We also check superposition or repetition: if two fields cover the same PGCC, we choose the one with the higher sensitivity. After the work flow, a total of 70 SCUBA-2 fields are selected as the sample in this work.

Seventy HLPCs are shown with green crosses, overlaid on the background Planck 353 GHz (850 $\mu$m) continuum emission in Figure 1. White rectangles outline the CO emission regions defined by Dame et al. (1987). The clump-averaged $N_{\rm H_{2}}$ H₂ column density $N_{\rm H_{2}}$ was calculated assuming a dust-emissivity model at 857 GHz (Planck Collaboration et al., 2016). The $N_{\rm H_{2}}$ distributions of three samples–all the PGCCs, 793 high-latitude PGCCs, and 70 HLPCs–are plotted as gray, blue and orange histograms in Figure 2, respectively. 70 HLPCs has been evenly sampled in the $N_{\rm H_{2}}$ space, ensuring a similar distribution with its parent sample, 793 HL PGCCs. More importantly, the studied sample includes the densest clumps at the high-column-density end ($N_{\mathrm{H}_{2}}>2.0\times 10^{21}$ cm^-2). Considering that the denser clumps should be more likely to produce dense cores, we have covered the complete HLPCs where dense cores could form.

Three regions with relatively higher column density, namely the Orion Frontier, the MBM 12 Complex, and the L134 Complex, are further zoomed in with subpanels in Figure 1. The HLPCs therein correspond to those at the high-density end as mentioned above. The Orion Frontier contains the dark cloud L1642, which together with the MBM 12 Complex are two famous HL clouds that have confirmed star-forming activity (Malinen et al., 2014). The L134 Complex is another region containing several HLPCs, including the widely studied dark cloud L183 (Lee & Myers, 1999; Lee et al., 2001; Juvela et al., 2002; Pagani et al., 2003).

Distance is always a difficult quantity to estimate in astronomy. Previous studies have estimated the distances of HL molecular clouds to be 100 pc from the velocity dispersion and the scale height of an ensemble of clouds (Blitz et al., 1984; Magnani et al., 1985). The star counting confirms that the HL molecular clouds are indeed nearby objects with upper limit ranges from 125 to 275 pc (Magnani & de Vries, 1986). Using Strömgren photometry, Franco (1989) derive the distances of several HGaL clouds to be 100–230 pc. Both the small $V_{\mathrm{lsr}}$ and the lack of a double-sine wave signature in the distribution on the $l-V_{lsr}$ (Galactic longitude $l$) plane demonstrate that HL molecular gas belongs to the local interstellar medium (ISM) and is too close to the Sun for Galactic rotation to modulate the velocities (Magnani et al., 1996).

Recently, the Gaia satellite has provided new photometric measurements toward galactic stars (Gaia Collaboration et al., 2016). Together with 2MASS and Pan-STARRS 1 optical and near-infrared photometry, Gaia DR2 parallaxes can help to infer distances and reddenings of $\sim$ 800 million stars. These stars trace the reddening on a small patch of the sky, along different lines of sight and different distance intervals, allowing us to build a 3D dust-reddening map (Green et al., 2014, 2019). In a given direction, a jump of dust reddening is expected at a distance where there is a dust clump. Distances are estimated by this method and are listed in column (9) of Table A1, with an average value of $200\pm 60$ pc, indicating that HLPCs are mostly local ISM. Adopting Eq. 1 in Xu et al. (2021) and considering that the Sun is 10 pc above the Galactic midplane (Griv et al., 2021), the altitude $z$ from the midplane (in units of parsecs) is calculated from $z=d\sin(b)+10$ where $d$ is the distance and $b$ is the latitude, and listed in column (10). We note that some fields may contain extragalactic objects, so the distance should be only for foreground Galactic dust.

We adopt the dendrogram algorithm (Rosolowsky et al., 2008) to extract dense structures and then measure their integrated flux, peak flux, size, and position by 2D Gaussian fitting. The details of the algorithm parameter settings and the source extraction procedure are introduced in Appendix B. Within the 70 input fields, we have initially detected a total of 20 sources that belong to 15 SCUBA-2 observing fields. The field names and extracted sources are listed in columns (1)–(2) of Table 1. Central coordinates, standard deviation of the deconvolved major and minor axes, integrated flux, and peak intensity are listed in columns (3)–(7).

The CV Daisy mode of observation can produce artifacts (Liu et al., 2018; Eden et al., 2019) that are extracted by the algorithm as false source detections. Therefore, we additionally require that both the peak intensity after being smoothed to the Planck beam and the total flux of the source at 353 GHz, are lower than those of the parent PGCC. This results in two sources, G50.41-35.40 SMM1 and G197.98+33.10 SMM1, being classified as artifacts and excluded from further analyses. We note that the flux given by the PGCC catalog should be from the cold residual map (Planck Collaboration et al., 2016), so the original Planck flux at 353 GHz could be even larger. However, considering the cold nature of dense cores, this should contribute little to the warm component.

We crossmatch the true detections within 1′ using SIMBAD²²2http://simbad.u-strasbg.fr/simbad/. We find that only one field, G6.04+36.77, pointing toward the molecular cloud L183, contains three resolved (or marginally resolved) sources, which were previously identified as low-mass prestellar cores (Dickens et al., 2000; Pagani et al., 2003). Our other detections are unresolved as point sources, classified as either young stellar object (YSO) or extragalactic object (point sources) – including gravitational lensed galaxy (LeG), BL Lacertae object (BLL), protocluster of galaxies (PClG), active nuclei candidate (AGN), and quasar (QSO). The determined identifiers and references are given in columns (8) and (9) of Table 1.

The physical parameters of the L183 dense cores are calculated in Appendix C. Throughout the paper, we adopt the empirical definition of dense core with typical size of $\lesssim 0.1$ pc and density of $10^{5}$–$10^{6}$ cm^-3 (Ward-Thompson et al., 1994, 1999; Kirk et al., 2005).

Having only one detection among the 70 HLPCs highlights the scarcity of dense cores at these latitudes. To further confirm this discrepancy compared to the low-latitude ($|b|<30\arcdeg$) counterpart, 1235 observing fields from the JCMT Large Project “SCUBA-2 Continuum Observations of Pre-protostellar Evolution” (SCOPE; Liu et al., 2018; Eden et al., 2019) are used as a comparison group because of the following two reasons: (1) twenty-one HLPC fields in this work come from the SCOPE project so that they have been observed with comparable sensitivities; (2) the SCOPE observations serve as a representative sample of PGCCs, with similar distributions in distance, size, and temperature, and with complete column density coverage over $10^{21}$ cm^-2 (Liu et al., 2018).

Considering the beam dilution effects for marginally resolved sources, the column densities are corrected by a beam filling factor $B_{\rm ff}=(\theta_{i}^{2})/\theta_{\rm PSF}^{2}$ where $\theta_{\rm PSF}=4\mbox{$.\!\!\arcmin$}3$ is the Planck beam size at 857 GHz (Planck Collaboration et al., 2016) and $\theta_{i}$ is the intrinsic size deconvolved from the beam. For extended sources of which intrinsic size exceeds the beam size, $B_{\rm ff}$ is set to 1, and no correction is performed. As a result, the corrected column density $N^{\prime}_{\rm H_{2}}$ increases by a factor of 1.1 on average and 9 at maximum.

In Figure 3, we present the number distributions of different samples across a set of $N^{\prime}_{\rm H_{2}}$ bins, denoted as ${S_{{\rm samp},i}}$ where $i$ indicates bin index. Specifically, the distributions for the low-latitude SCOPE fields and the HLPC fields are depicted using the gray and blue histograms, respectively. We also collect the number distribution of those fields with dense cores detected $\{S_{{\rm det},i}\}$. The dense core detection rate (DCDR), defined as $\{S_{{\rm det},i}/S_{{\rm samp},i}\}$, is shown with connected data points. For the low-latitude SCOPE, the DCDR experiences a pronounced increase at a threshold of column density around $N_{\rm H_{2}}\simeq 1.0\times 10^{21}$ cm^-2, reaching 90% at the $N_{\rm H_{2}}\simeq 5.0\times 10^{21}$ cm^-2 regime. The column density threshold for forming dense cores is consistent with what has been found in Gould Belt clouds (e.g., Johnstone et al., 2004). The sudden peak at $3\times 10^{20}$ cm^-2 likely results from the limited sample size. In contrast to the DCDR of the low-latitude SCOPE clumps, the DCDR for the HLPCs remains zero for $N_{\rm H_{2}}<1.0\times 10^{22}$ cm^-2, until dense cores in the HLPC G6.04+36.77 are detected.

The SCOPE serve as a gauge to tell whether the HLPCs have significantly scarce dense cores. Given the null hypothesis that the HLPCs share a DCDR greater or equal to that of the SCOPE, the number of the HLPC fields containing dense cores in each bin of $N_{\rm H_{2}}\geq 10^{21}$ cm^-2 can be predicted, as $\{S_{{\rm pred},i}\}_{\rm HLPC}$. The one-sided Mann–Whitney U test (Mann & Whitney, 1947) is performed between the $\{S_{{\rm pred},i}\}_{\rm HLPC}$ and $\{S_{{\rm det},i}\}_{\rm HLPC}$, giving a p-value of $4.8\times 10^{-3}$. This is $\ll 0.05$, thus robustly excluding the null hypothesis. In other words, dense cores are scarce in HLPCs compared to the low latitude.

The scarcity of detection does not necessarily indicate the scarcity of dense cores, primarily due to two factors: (1) the limited sensitivity of identifying sources and (2) the absence of large-scale flux in the SCUBA-2 data processing. Therefore, to understand what the scarcity of dense cores means, it is essential to clarify what “dense” means.

Prestellar cores are observed to have flat inner-density gradients that approach $\rho\sim r^{-2}$ beyond a few thousand astronomical units (Ward-Thompson et al., 1994, 1999; Kirk et al., 2005), which can be reproduced by a nonmagnetic and Plummer-like model (Whitworth & Ward-Thompson, 2001) as

where $n_{c}$ is the central H₂ number density and $R_{\rm flat}$ is the flat inner radius. The column density profile of such a model core has the analytical form of

where $p$ is the distance from core center in the plane of the sky (Dapp & Basu, 2009) and $R_{\rm out}=0.2$ pc $\simeq 40000$ au defines the boundary of core.

Using the combined ammonia data from the Green Bank Telescope and Karl G. Jansky Very Large Array, the temperatures of the three prestellar cores are observed to have a minor decrease toward the center of the core $\lesssim 2000$ au (Lin et al., 2023). Therefore, we consider a constant temperature profile as $T(r)=T_{0}=10$ K in the following discussion.

Assuming optically thin dust emission, the column density can be used to synthesize model intensity as,

where $\Omega=\pi\theta_{\rm beam}^{2}/4\ln 2$ measures the solid angle (in unit of radian) per JCMT beam (with FWHM of $\theta_{\rm beam}$), $\mu_{\rm H_{2}}=2.81$ is the molecular weight per hydrogen molecule (Evans et al., 2022), $m_{\rm H}$ is the mass of a hydrogen atom, $\kappa_{\nu}=1.22$ cm² g^-1 (Beckwith et al., 1990) is the dust opacity at frequency of $\nu=350$ GHz ($\sim 850$ $\mu$m), $B_{\nu}(T_{\rm dust})$ is the Planck function at a given dust temperature $T_{\rm dust}$, and $\mathcal{R}=100$ is the gas-to-dust mass ratio.

Now we synthesize the SCUBA-2 image $\widetilde{I}_{\nu}(x,y)$ by adding a high-frequency filter $\sqrt{u^{2}+v^{2}}>\xi$, where $\xi$ corresponds to $200\arcsec$ in the frequency space (Mairs et al., 2015),

where $J_{\nu}(u,v)=\iint I_{\nu}(x,y)e^{-i2\pi(ux+vy)}\mathrm{d}x\mathrm{d}y$ is the synthetic model in the Fourier frequency space. As a result, the synthetic observed intensity $\widetilde{I}_{\nu}(x,y)$ can simulate the observed large-scale missing flux at the SCUBA-2 data processing.

In Figure 4, the background color map shows observed peak intensities $\widetilde{I}^{\rm peak}_{\nu}=\widetilde{I}_{\nu}(0,0)$ across the 2D parameter space of flat radius $R_{\rm flat}\in[10^{3},10^{4.5}]$ au and central density $n_{c}\in[10^{3.5},10^{6}]$ cm^-3. The prestellar cores have been reported to have $R_{\rm flat}>2500$ au (Ward-Thompson et al., 1999; Kirk et al., 2005), which are delineated by the left green dashed line in Figure 4. The right green dashed line marks 20,000 au, which corresponds to 0.1 pc.

Consistent with the criteria in the source extraction algorithm (see Appendix B), a threshold of $3\sigma$ is adopted to constrain the upper limit of $\widetilde{I}^{\rm peak}_{\nu}$. As a result, the gray shaded region traces the permissible parameter interval for an undetected core in our observations. In other words, if such cores exist, they should have $n_{c}<10^{5}$ cm^-3, which is considerably less dense than those that have been identified in nearby low-mass cloud cores (Ward-Thompson et al., 1999; Kirk et al., 2005).

To further demonstrate this upper limit of density, we smooth the images to a resolution of 20″. With better sensitivity, two new cores (on in HLPC G159.41-34.37 and one in G161.87-35.76) are identified by the same algorithm and parameter input, which are called weakly detected cores. They have radii of about 6700 and 7500 au and averaged density of $2.8\times 10^{4}$ cm^-3 and $3.1\times 10^{4}$ cm^-3, respectively. The two cores are labeled as orange rectangles in Figure 4. We also retrieve Herschel cold cores in L134 (HLPCs G4.13+35.75 and G4.17+36.67 in our survey), MBM12 (G159.21-34.28, G158.51-33.99, G159.14-33.79, G159.23-34.51, G159.41-34.37, G159.66-34.31), L1642 (G210.90-36.55), and LDN1780 (G358.96+36.81, G359.21+36.89) from Montillaud et al. (2015) which are labeled as green triangles. As they all lie in the gray region which is below the sensitivity limit, these cold cores are not dense enough for detection and are consistently below the density limit of $10^{5}$ cm^-3. As noted by Ward-Thompson et al. (2016), SCUBA-2 selects the densest cores from a population at a given temperature, which makes SCUBA-2 ideal for identifying those cores in Herschel catalogs that are closest to forming stars. So it is of great interest to study how these low-density cores form and whether they can still form stars or are transient objects.

As indicated by the black curves, peak intensity of a synthetic model $I^{\rm peak}_{\nu}$ is always below the corresponding $\widetilde{I}^{\rm peak}_{\nu}$ outlined by white curves. The difference reflects the missing large-scale flux, which increases in importance from 0.06 to 0.31 dex with $R_{\rm flat}$ from 2500 to 20,000 au. Therefore, if we do not consider missing flux, the density limit can be even lower, especially for those cores with larger flat radius.

Low density and high virial parameter lead to a challenge for direct gravitational collapse and then star formation of HL clouds. Observationally, it is consistent with infrared cirrus which is thought to be hostile to star formation (Low et al., 1984) and the dispersed populations of pre-main-sequence stars (see review by McGehee, 2008). Recently, a clear decreasing trend of N₂H⁺ (1–0) and C₂H (1–0) detection rates with latitude is found by Xu et al. (2021). Besides, HCN (1–0) and HCO⁺ (1–0) line survey by Braine et al. (2023) reveals that HL molecular clouds have lower dense gas fractions compared to those in the Galactic plane. Theoretically, based on Jeans mass arguments, these low-density turbulent clouds have molecular gas mass lower than the turbulent Jeans mass (see Table 5 in Xu et al., 2021), therefore unable to fragment into dense dust cores, or protostellar embryos, which agrees with the scarcity of dense cores observed by SCUBA-2.

Previous studies have reported that the virial parameters of the PGCCs in the Taurus region (Taurus clumps hereafter) are predominantly greater than 1, with a median value of approximately 9 (Meng et al., 2013). This value is considerably lower than the median virial parameter of HLPCs, which stands at about 35. The Taurus clumps covered by the SCOPE project are designated as the Taurus SCOPE subsample. Figure 3 displays the number distribution and the DCDR for the Taurus SCOPE in orange. In the same way as above, the Mann-Whitney U test gives a $p$-value of $0.042<0.05$, thus favoring that the DCDR of the Taurus clumps is statistically larger than that of HLPCs. Interestingly, the Taurus clumps also exhibit a significantly smaller DCDR compared to the low-latitude SCOPE clumps, as evidenced by a Mann-Whitney U test p-value of $5.4\times 10^{-3}$. This indicates that dense cores within the Taurus clumps are relatively rarer compared to other SCOPE clumps. Consequently, the Taurus clumps occupy an intermediate position between the HLPCs and low-latitude SCOPE clumps in terms of DCDR and virial parameter. The observed trend of decreasing DCDR with increasing virial parameter further substantiates the link between core formation efficiency and the dynamic state of the gas, as previously suggested (Eden et al., 2019).

HLPCs have a distance of 200 pc which is highly consistent with the radius of the Local Bubble (LB) created by supernovae (Zucker et al., 2022). The LB is reported to expand and sweep up the ambient interstellar medium into a shell that has now fragmented and collapsed into the most prominent nearby molecular clouds. Interestingly, Zucker et al. (2022) also found that the Taurus star formation region is very likely being compressed by two super bubbles: the local super bubble and the smaller Per-Tau super bubble. If so, it is probable that the formation of dense cores can be hindered by supernova shocks in the solar neighborhood. If the HLPCs and the Taurus clumps were on the shell of LB, the scarcity of dense cores should favor turbulence-inhibited rather than supernova-driven star formation.

On the other hand, the scarcity itself is what gives the only detection (L183) in our survey, as well as a few other clouds (such as MBM 12 and 20), unique status. The capacity of these high-latitude clouds to form cold molecular cores and young stars could arise from a confluence of conditions including variations in the interstellar radiation field, changes in dust grain size and chemistry, the occurrence of shocks, and transient events in the ISM (McGehee, 2008). Consequently, in-depth explorations of the physical and chemical processes within these high-latitude dense cores, for example the L183 dense cores, are merited.