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We present new 3-mm continuum and molecular lines observations from the ATOMS survey towards the massive protostellar clump, MM1, located in the filamentary infrared dark cloud (IRDC), G034.43+00.24 (G34). The lines observed are the tracers of either dense gas (e.g. HCO+/H13CO+ J = 1-0) or outflows (e.g. CS J = 2-1). The most complete picture to date of seven cores in MM1 is revealed by dust continuum emission. These cores are found to be gravitationally bound, with virial parameter, $\alpha_{vir}, Comment: 14 pages with 6 figures, and in press

While magnetic fields are important in contemporary star formation, their role in primordial star formation is unknown. Magnetic fields of order 10^-16 G are produced by the Biermann battery due to the curved shocks and turbulence associated with the infall of gas into the dark matter minihalos that are the sites of formation of the first stars. These fields are rapidly amplified by a small-scale dynamo until they saturate at or near equipartition with the turbulence in the central region of the gas. Analytic results are given for the outcome of the dynamo, including the effect of compression in the collapsing gas. The mass-to-flux ratio in this gas is 2-3 times the critical value, comparable to that in contemporary star formation. Predictions of the outcomes of simulations using smooth particle hydrodynamics (SPH) and grid-based adaptive mesh refinement (AMR) are given. Because the numerical viscosity and resistivity for the standard resolution of 64 cells per Jeans length are several orders of magnitude greater than the physical values, dynamically significant magnetic fields affect a much smaller fraction of the mass in simulations than in reality. An appendix gives an analytic treatment of free-fall collapse, including that in a constant density background. Another appendix presents a new method of estimating the numerical viscosity; results are given for both SPH and grid-based codes., Comment: 28 pages, 4 figures, submitted to MNRAS

We perform ideal MHD high resolution AMR simulations with driven turbulence and self-gravity and find that long filamentary molecular clouds are formed at the converging locations of large-scale turbulence flows and the filaments are bounded by gravity. The magnetic field helps shape and reinforce the long filamentary structures. The main filamentary cloud has a length of ~4.4 pc. Instead of a monolithic cylindrical structure, the main cloud is shown to be a collection of fiber/web-like sub-structures similar to filamentary clouds such as L1495. Unless the line-of-sight is close to the mean field direction, the large-scale magnetic field and striations in the simulation are found roughly perpendicular to the long axis of the main cloud, similar to 1495. This provides strong support for a large-scale moderately strong magnetic field surrounding L1495. We find that the projection effect from observations can lead to incorrect interpretations of the true three-dimensional physical shape, size, and velocity structure of the clouds. Helical magnetic field structures found around filamentary clouds that are interpreted from Zeeman observations can be explained by a simple bending of the magnetic field that pierces through the cloud. We demonstrate that two dark clouds form a T-shape configuration which are strikingly similar to the Infrared dark cloud SDC13 leading to the interpretation that SDC13 results from a collision of two long filamentary clouds. We show that a moderately strong magnetic field (M_A ~ 1) is crucial for maintaining a long and slender filamentary cloud for a long period of time ~0.5 million years., 21 pages, 21 figure

Prestellar cores are self-gravitating dense and cold structures within molecular clouds where future stars are born. They are expected, at the stage of transitioning to the protostellar phase, to harbor centrally concentrated dense (sub)structures that will seed the formation of a new star or the binary/multiple stellar systems. Characterizing this critical stage of evolution is key to our understanding of star formation. In this work, we report the detection of high-density (sub)structures on the thousand-astronomical-unit (au) scale in a sample of dense prestellar cores. Through our recent ALMA observations toward the Orion Planck Galactic Cold Clumps, we have found five extremely dense prestellar cores, which have centrally concentrated regions of ∼2000 au in size, and several 107 cm-3 in average density. Masses of these centrally dense regions are in the range of 0.30 to 6.89M⊙. For the first time, our higher resolution observations (0.8' ∼ 320 au) further reveal that one of the cores shows clear signatures of fragmentation; such individual substructures/fragments have sizes of 800-1700 au, masses of 0.08 to 0.84M⊙, densities of 2 - 8 × 107 cm-3, and separations of ∼1200 au. The substructures are massive enough (≳0.1M⊙) to form young stellar objects and are likely examples of the earliest stage of stellar embryos that can lead to widely (∼1200 au) separated multiple systems., L. acknowledges the support from the international partnership program of the Chinese Academy of Sciences through grant No.114231KYSB20200009, National Natural Science Foundation of China (NSFC) through grant NSFC No.12073061, and Shanghai Pujiang Program 20PJ1415500. N.H. acknowledges MoST 108-2112-M-001-017 and MoST 109-2112-M-001-023 grants. G.G. acknowledges support from ANID project AFB 170002. L.B. acknowledges support from ANID project AFB-170002. S.L.Q. is supported by the National Natural Science Foundation of China under grant No. U1631237. D.J. is supported by NRC Canada and by an NSERC Discovery Grant. V.M.P. acknowledges support by the Spanish MINECO under project AYA2017-88754-P, and financial support from the State Agency for Research of the Spanish Ministry of Science and Innovation through the “Unit of Excellence María de Maeztu 2020-2023” award to the Institute of Cosmos Sciences (CEX2019-000918-M). C.W.L. is supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2019R1A2C1010851). A.S. acknowledges financial support from the NSF through grant AST-1715876. The research was carried out in part at the Jet Propulsion Laboratory, which is operated for NASA by the California Institute of Technology. D. L. acknowledges support from NSFC No. 11911530226 and 11725313. K.T. was supported by JSPS KAKENHI grant No. 20H05645. J.H. thanks the NSFC grant No. 11873086 and Yunnan Province of China (No. 2017HC018).This work is sponsored (in part) by the Chinese Academy of Sciences (CAS), through a grant to the CAS South America Center for Astronomy (CASSACA) in Santiago, Chile.

We report studies of the relationships between the total bolometric luminosity ($L_{\rm bol}$ or $L_{\rm TIR}$) and the molecular line luminosities of $J=1-0$ transitions of H$^{13}$CN, H$^{13}$CO$^+$, HCN, and HCO$^+$ with data obtained from ACA observations in the "ATOMS" survey of 146 active Galactic star forming regions. The correlations between $L_{\rm bol}$ and molecular line luminosities $L'_{\rm mol}$ of the four transitions all appear to be approximately linear. Line emission of isotopologues shows as large scatters in $L_{\rm bol}$-$L'_{\rm mol}$ relations as their main line emission. The log($L_{\rm bol}$/$L'_{\rm mol}$) for different molecular line tracers have similar distributions. The $L_{\rm bol}$-to-$L'_{\rm mol}$ ratios do not change with galactocentric distances ($R_{\rm GC}$) and clump masses ($M_{\rm clump}$). The molecular line luminosity ratios (HCN-to-HCO$^+$, H$^{13}$CN-to-H$^{13}$CO$^+$, HCN-to-H$^{13}$CN and HCO$^+$-to-H$^{13}$CO$^+$) all appear constant against $L_{\rm bol}$, dust temperature ($T_{\rm d}$), $M_{\rm clump}$ and $R_{\rm GC}$. Our studies suggest that both the main lines and isotopologue lines are good tracers of the total masses of dense gas in Galactic molecular clumps. The large optical depths of main lines do not affect the interpretation of the slopes in star formation relations. We find that the mean star formation efficiency (SFE) of massive Galactic clumps in the "ATOMS" survey is reasonably consistent with other measures of the SFE for dense gas, even those using very different tracers or examining very different spatial scales., Comment: Published on MNRAS. The full tables are included in Tables.pdf or Tables.tex files, which can be downloaded from source files

The "ATOMS," standing for {\it ALMA Three-millimeter Observations of Massive Star-forming regions}, survey has observed 146 active star forming regions with ALMA Band 3, aiming to systematically investigate the spatial distribution of various dense gas tracers in a large sample of Galactic massive clumps, to study the roles of stellar feedback in star formation, and to characterize filamentary structures inside massive clumps. In this work, the observations, data analysis, and example science of the "ATOMS" survey are presented, using a case study for the G9.62+0.19 complex. Toward this source, some transitions, commonly assumed to trace dense gas, including CS $J = 2-1$, HCO$^+$ $J = 1-0$ and HCN $J = 1-0$, are found to show extended gas emission in low density regions within the clump; less than 25\% of their emission is from dense cores. SO, CH$_3$OH, H$^{13}$CN and HC$_3$N show similar morphologies in their spatial distributions and reveal well the dense cores. Widespread narrow SiO emission is present (over $\sim$1 pc), which may be caused by slow shocks from large--scale colliding flows or H{\sc ii} regions. Stellar feedback from an expanding H{\sc ii} region has greatly reshaped the natal clump, significantly changed the spatial distribution of gas, and may also account for the sequential high-mass star formation in the G9.62+0.19 complex. The ATOMS survey data can be jointly analyzed with other survey data, e.g., "MALT90", "Orion B", "EMPIRE", "ALMA\_IMF", and "ALMAGAL", to deepen our understandings of "dense gas" star formation scaling relations and massive proto-cluster formation., Comment: published on MNRAS

Star formation in a filamentary infrared dark cloud (IRDC) is simulated over a dynamic range of 4.2 pc to 28 au for a period of $3.5\times 10^5$ yr, including magnetic fields and both radiative and outflow feedback from the protostars. At the end of the simulation, the star formation efficiency is 4.3 per cent and the star formation rate per free fall time is $\epsilon_{\rm ff}\simeq 0.04$, within the range of observed values (Krumholz et al. 2012a). The total stellar mass increases as $\sim\,t^2$, whereas the number of protostars increases as $\sim\,t^{1.5}$. We find that the density profile around most of the simulated protostars is $\sim\,\rho\propto r^{-1.5}$, as predicted by Murray & Chang (2015). At the end of the simulation, the protostellar mass function approaches the Chabrier (2005) stellar initial mass function. We infer that the time to form a star of median mass $0.2\,M_\odot$ is about $1.4\times 10^5$~yr from the median mass accretion rate. We find good agreement among the protostellar luminosities observed in the large sample of Dunham et al. (2013), our simulation, and a theoretical estimate, and conclude that the classical protostellar luminosity problem Kenyon et al. (1990) is resolved. The multiplicity of the stellar systems in the simulation agrees to within a factor 2 of observations of Class I young stellar objects; most of the simulated multiple systems are unbound. Bipolar protostellar outflows are launched using a sub-grid model, and extend up to 1 pc from their host star. The mass-velocity relation of the simulated outflows is consistent with both observation and theory., Comment: 24 pages, 18 figures

We present the first release of the data and compact-source catalogue for the JCMT Large Program SCUBA-2 Continuum Observations of Pre-protostellar Evolution (SCOPE). SCOPE consists of 850-um continuum observations of 1235 Planck Galactic Cold Clumps (PGCCs) made with the Submillimetre Common-User Bolometer Array 2 on the James Clerk Maxwell Telescope. These data are at an angular resolution of 14.4 arcsec, significantly improving upon the 353-GHz resolution of Planck at 5 arcmin, and allowing for a catalogue of 3528 compact sources in 558 PGCCs. We find that the detected PGCCs have significant sub-structure, with 61 per cent of detected PGCCs having 3 or more compact sources, with filamentary structure also prevalent within the sample. A detection rate of 45 per cent is found across the survey, which is 95 per cent complete to Planck column densities of $N_{H_{2}}$ $>$ 5 $\times$ 10$^{21}$ cm$^{-2}$. By positionally associating the SCOPE compact sources with YSOs, the star formation efficiency, as measured by the ratio of luminosity to mass, in nearby clouds is found to be similar to that in the more distant Galactic Plane, with the column density distributions also indistinguishable from each other., 16 pages, 13 figures, 1 table. Accepted for publication in MNRAS

Similar to their low-mass counterparts, massive stars likely form via the collapse of pre-stellar molecular cores. Recent observations suggest that most massive cores are subvirial (i.e., not supported by turbulence) and therefore are likely unstable to gravitational collapse. Here we perform radiation hydrodynamic simulations to follow the collapse of turbulent massive pre-stellar cores with subvirial and virialized initial conditions to explore how their dynamic state affects the formation of massive stars and core fragmentation into companion stars. We find that subvirial cores undergo rapid monolithic collapse resulting in higher accretion rates at early times as compared to the collapse of virialized cores that have the same physical properties. In contrast, we find that virialized cores undergo a slower, gradual collapse and significant turbulent fragmentation at early times resulting in numerous companion stars. In the absence of strong magnetic fields and protostellar outflows we find that the faster growth rate of massive stars that are born out of subvirial cores leads to an increase in the radiative heating of the core thereby further suppressing fragmentation at early times when turbulent fragmentation occurs for virialized cores. Regardless of initial condition, we find that the massive accretion disks that form around massive stars dominant the accretion flow onto the star at late times and eventually become gravitationally unstable and fragment to form companion stars at late times., Accepted to ApJ, 22 pages, 12 figures

We present the B-fields mapped in IRDC G34.43+0.24 using 850\,$\mu$m polarized dust emission observed with the POL-2 instrument at JCMT. We examine the magnetic field geometries and strengths in the northern, central, and southern regions of the filament. The overall field geometry is ordered and aligned closely perpendicular to the filament's main axis, particularly in regions containing the central clumps MM1 and MM2, whereas MM3 in the north has field orientations aligned with its major axis. The overall field orientations are uniform at large (POL-2 at 14$\arcsec$ and SHARP at 10$\arcsec$) to small scales (TADPOL at 2.5$\arcsec$ and SMA at 1.5$\arcsec$) in the MM1 and MM2 regions. SHARP/CSO observations in MM3 at 350\,$\mu$m from Tang et al. show a similar trend as seen in our POL-2 observations. TADPOL observations demonstrate a well-defined field geometry in MM1/MM2 consistent with MHD simulations of accreting filaments. We obtained a plane-of-sky magnetic field strength of 470$\pm$190\,$\mu$G, 100$\pm$40\,$\mu$G, and 60$\pm$34\,$\mu$G in the central, northern and southern regions of G34, respectively, using the updated Davis-Chandrasekhar-Fermi relation. The estimated value of field strength, combined with column density and velocity dispersion values available in the literature, suggests G34 to be marginally critical with criticality parameter $\rm \lambda$ values 0.8$\pm$0.4, 1.1$\pm$0.8, and 0.9$\pm$0.5 in the central, northern, and southern regions, respectively. The turbulent motions in G34 are sub-Alfv\'{e}nic with Alfv\'{e}nic Mach numbers of 0.34$\pm$0.13, 0.53$\pm$0.30, and 0.49$\pm$0.26 in the three regions. The observed aligned B-fields in G34.43+0.24 are consistent with theoretical models suggesting that B-fields play an important role in guiding the contraction of the cloud driven by gravity., Comment: 16 pages, 10 figures, Accepted for publication in ApJ

How stellar feedback from high-mass stars (e.g., H{\sc ii} regions) influences the surrounding interstellar medium and regulates new star formation is still unclear. To address this question, we observed the G9.62+0.19 complex in 850 $\mu$m continuum with the JCMT/POL-2 polarimeter. An ordered magnetic field has been discovered in its youngest clump, the G9.62 clump. The magnetic field strength is determined to be $\sim$1 mG. Magnetic field plays a larger role than turbulence in supporting the clump. However, the G9.62 clump is still unstable against gravitational collapse even if thermal, turbulent, and magnetic field support are taken into account all together. The magnetic field segments in the outskirts of the G9.62 clump seem to point toward the clump center, resembling a dragged-in morphology, indicating that the clump is likely undergoing magnetically-regulated global collapse. However, The magnetic field in its central region is aligned with the shells of the photodissociation regions (PDRs) and is approximately parallel to the ionization (or shock) front, indicating that the magnetic field therein is likely compressed by the expanding H{\sc ii} regions that formed in the same complex., Comment: 8 pages, 3 figures, accepted to be published on ApJ letter

Stars rarely form in isolation. Nearly half of the stars in the Milky Way have a companion, and this fraction increases in star-forming regions. However, why some dense cores and filaments form bound pairs while others form single stars remains unclear. We present a set of three-dimensional, gravo-magnetohydrodynamic simulations of turbulent star-forming clouds, aimed at understanding the formation and evolution of multiple-star systems formed through large scale (>~$10^3$ AU) turbulent fragmentation. We investigate three global magnetic field strengths, with global mass-to-flux ratios of $\mu_\phi$=2, 8, and 32. The initial separations of protostars in multiples depends on the global magnetic field strength, with stronger magnetic fields (e.g., $\mu_\phi$=2) suppressing fragmentation on smaller scales. The overall multiplicity fraction (MF) is between 0.4-0.6 for our strong and intermediate magnetic field strengths, which is in agreement with observations. The weak field case has a lower fraction. The MF is relatively constant throughout the simulations, even though stellar densities increase as collapse continues. While the MF rarely exceeds 60% in all three simulations, over 80% of all protostars are part of a binary system at some point. We additionally find that the distribution of binary spin mis-alignment angles is consistent with a randomized distribution. In all three simulations, several binaries originate with wide separations and dynamically evolve to, Comment: Accepted to ApJ. 28 pages, 23 figures, comments from the community welcomed

Magnetic field is one of the key agents that play a crucial role in shaping molecular clouds and regulating star formation, yet the complete information on the magnetic field is not well constrained due to the limitations in observations. We study the magnetic field in the massive infrared dark cloud G035.39-00.33 from dust continuum polarization observations at 850 $\micron$ with SCUBA-2/POL-2 at JCMT. The magnetic field tends to be perpendicular to the densest part of the main filament (F$_{M}$), whereas it has a less defined relative orientation in the rest of the structure, where it tends to be parallel to some diffuse regions. A mean plane-of-the-sky magnetic field strength of $\sim$50 $\mu$G for F$_{M}$ is obtained using Davis-Chandrasekhar-Fermi method. Based on $^{13}$CO (1-0) line observations, we suggest a formation scenario of F$_{M}$ due to large-scale ($\sim$10 pc) cloud-cloud collision. Using additional NH$_3$ line data, we estimate that F$_{M}$ will be gravitationally unstable if it is only supported by thermal pressure and turbulence. The northern part of F$_{M}$, however, can be stabilized by a modest additional support from the local magnetic field. The middle and southern parts of F$_{M}$ are likely unstable even if the magnetic field support is taken into account. We claim that the clumps in F$_{M}$ may be supported by turbulence and magnetic fields against gravitational collapse. Finally, we identified for the first time a massive ($\sim$200 M$_{\sun}$), collapsing starless clump candidate, "c8", in G035.39-00.33. The magnetic field surrounding "c8" is likely pinched, hinting at an accretion flow along the filament., Comment: Published on ApJ, 27 pages

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256^3 and 512^3 simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li, McKee, & Klein (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence., 37 pages, 11 figures, 4 tables

The Padoan and Nordlund model of the stellar initial mass function (IMF) is derived from low order statistics of supersonic turbulence, neglecting gravity (e.g. gravitational fragmentation, accretion and merging). In this work the predictions of that model are tested using the largest numerical experiments of supersonic hydrodynamic (HD) and magneto-hydrodynamic (MHD) turbulence to date (~1000^3 computational zones) and three different codes (Enzo, Zeus and the Stagger Code). The model predicts a power law distribution for large masses, related to the turbulence energy power spectrum slope, and the shock jump conditions. This power law mass distribution is confirmed by the numerical experiments. The model also predicts a sharp difference between the HD and MHD regimes, which is recovered in the experiments as well, implying that the magnetic field, even below energy equipartition on the large scale, is a crucial component of the process of turbulent fragmentation. These results suggest that the stellar IMF of primordial stars may differ from that in later epochs of star formation, due to differences in both gas temperature and magnetic field strength. In particular, we find that the IMF of primordial stars born in turbulent clouds may be narrowly peaked around a mass of order 10 solar masses, as long as the column density of such clouds is not much in excess of 10^22 cm^-2.

The most accurate measurements of magnetic fields in star-forming gas are based on the Zeeman observations analyzed by Crutcher et al. (2010). We show that their finding that the 3D magnetic field scales approximately as density$^{0.65}$ can also be obtained from analysis of the observed line-of-sight fields. We present two large-scale AMR MHD simulations of several thousand $M_\odot$ of turbulent, isothermal, self-gravitating gas, one with a strong initial magnetic field (Alfven Mach number $M_{A,0}= 1$) and one with a weak initial field ($M_{A,0}=10$). We construct samples of the 100 most massive clumps in each simulation and show that they exhibit a power-law relation between field strength and density in excellent agreement with the observed one. Our results imply that the average field in molecular clumps in the interstellar medium is $ \sim 42 n_{H,4}^{0.65} \mu$G. Furthermore, the median value of the ratio of the line-of-sight field to density$^{0.65}$ in the simulations is within a factor of about (1.3, 1.7) of the observed value for the strong and weak field cases, respectively. The median value of the mass-to-flux ratio, normalized to the critical value, is 70% of the line-of-sight value. This is larger than the 50% usually cited for spherical clouds because the actual mass-to-flux ratio depends on the volume-weighted field, whereas the observed one depends on the mass-weighted field. Our results indicate that the typical molecular clump in the ISM is significantly supercritical (~ factor of 3). The results of our strong-field model are in very good quantitative agreement with the observations of Li et al. (2009), which show a strong correlation in field orientation between small and large scales. Because there is a negligible correlation in the weak-field model, we conclude that molecular clouds form from strongly magnetized (although magnetically supercritical) gas., Comment: 31 pages, 14 figures, MNRAS accepted

The intermittent dissipation of interstellar turbulence is an important energy source in the diffuse ISM. Though on average smaller than the heating rates due to cosmic rays and the photoelectric effect on dust grains, the turbulent cascade can channel large amounts of energy into a relatively small fraction of the gas that consequently undergoes significant heating and chemical enrichment. In particular, this mechanism has been proposed as a solution to the long-standing problem of the high abundance of CH+ along diffuse molecular sight lines, which steady-state, low temperature models under-produce by over an order of magnitude. While much work has been done on the structure and chemistry of these small-scale dissipation zones, comparatively little attention has been paid to relating these zones to the properties of the large-scale turbulence. In this paper, we attempt to bridge this gap by estimating the temperature and CH+ column density along diffuse molecular sight-lines by post-processing 3-dimensional MHD turbulence simulations. Assuming reasonable values for the cloud density (30 / cm^3), size (20 pc), and velocity dispersion (2.3 km / s), we find that our computed abundances compare well with CH+ column density observations, as well as with observations of emission lines from rotationally excited H2 molecules., Comment: 13 pages, 10 figures, accepted by MNRAS

Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma $\beta_0$ of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers ($M_rms = 17.3$) and smaller plasma beta ($\beta_0 = 0.0067$) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations., Comment: 22 pages, 13 figures, accepted by ApJ

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems., Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 2011

Ambipolar diffusion is important in redistributing magnetic flux and in damping Alfven waves in molecular clouds. The importance of ambipolar diffusion on a length scale $\ell$ is governed by the ambipolar diffusion Reynolds number, $\rad=\ell/\lad$, where $\lad$ is the characteristic length scale for ambipolar diffusion. The logarithmic mean of the AD Reynolds number in a sample of 15 molecular clumps with measured magnetic fields (Crutcher 1999) is 17, comparable to the theoretically expected value. We identify several regimes of ambipolar diffusion in a turbulent medium, depending on the ratio of the flow time to collision times between ions and neutrals; the clumps observed by Crutcher (1999) are all in the standard regime of ambipolar diffusion, in which the neutrals and ions are coupled over a flow time. We have carried out two-fluid simulations of ambipolar diffusion in isothermal, turbulent boxes for a range of values of $\rad$. The mean Mach numbers were fixed at $\calm=3$ and $\ma=0.67$; self-gravity was not included. We study the properties of overdensities--i.e., clumps--in the simulation and show that the slope of the higher-mass portion of the clump mass spectrum increases as $\rad$ decreases, which is qualitatively consistent with Padoan et al. (2007)'s finding that the mass spectrum in hydrodynamic turbulence is significantly steeper than in ideal MHD turbulence. For a value of $\rad$ similar to the observed value, we find a slope that is consistent with that of the high-mass end of the Initial Mass Function for stars. However, the value we find for the spectral index in our ideal MHD simulation differs from theirs, presumably because our simulations have different initial conditions. This suggests that the mass spectrum of the clumps in the Padoan et al. (2007) turbulent fragmentation model for the IMF depends on the environment, which would conflict with evidence ..., 33 pages, 7 figures

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256{sup 3} and 512{sup 3} simulations on supersonic but sub-Alfvenic turbulent systems with AD using the Heavy-Ion Approximation developed in Li et al. (2006). Our calculations are based on the assumption that the number of ions is conserved, but we show that these results approximately apply to the case of time-dependent ionization in molecular clouds as well. Convergence studies allow us to determine the optimal value of the ionization mass fraction when using the heavy-ion approximation for low Mach number, sub-Alfvenic turbulent systems. We find that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. Changes in the density PDF, total magnetic energy, and ionization fraction are determined as a function of the AD Reynolds number. The power spectra for the neutral gas properties of a strongly magnetized medium with a low AD Reynolds number are similar to those for a weakly magnetized medium; in particular, the power spectrum of the neutral velocity is close to that for Burgers turbulence.

The dynamical state of star-forming molecular clouds cannot be understood without determining the structure and strength of their magnetic fields. Measurements of polarized far-infrared radiation from thermally aligned dust grains are used to map the orientation of the field and estimate its strength, but the accuracy of the results has remained in doubt. In order to assess the reliability of this method, we apply it to simulated far-infrared polarization maps derived from three-dimensional simulations of supersonic magnetohydrodynamical turbulence, and compare the estimated values to the known magnetic field strengths in the simulations. We investigate the effects of limited telescope resolution and self-gravity on the structure of the maps. Limited observational resolution affects the field structure such that small scale variations can be completely suppressed, thus giving the impression of a very homogeneous field. The Chandrasekhar-Fermi method of estimating the mean magnetic field in a turbulent medium is tested, and we suggest an extension to measure the rms field. Both methods yield results within a factor of 2 for field strengths typical of molecular clouds, with the modified version returning more reliable estimates for slightly weaker fields. However, neither method alone works well for very weak fields, missing them by a factor of up to 150. Taking the geometric mean of both methods estimates even the weakest fields accurately within a factor of 2.5. Limited telescope resolution leads to a systematic overestimation of the field strengths for all methods. We discuss the effects responsible for this overestimation and show how to extract information on the underlying (turbulent) power spectrum., 30 pages, 15 figures (figs 1, 4, 5 reduced quality), submitted to ApJ Hires version of figs 1, 4, 5 see ftp://ftp.mpia-hd.mpg.de/pub/heitsch/HZM00/hiresfigs.tar.gz

The temperature of the gas in molecular clouds is a key determinant of the characteristic mass of star formation. Ambipolar diffusion (AD) is considered one of the most important heating mechanisms in weakly ionized molecular clouds. In this work, we study the AD heating rate using 2-fluid turbulence simulations and compare it with the overall heating rate due to turbulent dissipation. We find that for observed molecular clouds, which typically have Alfven Mach numbers of ~1 (Crutcher 1999) and AD Reynolds numbers of ~20 (McKee et al. 2010), about 70% of the total turbulent dissipation is in the form of AD heating. AD has an important effect on the length scale where energy is dissipated: when AD heating is strong, most of the energy in the cascade is removed by ion-neutral drift, with a comparatively small amount of energy making it down to small scales. We derive a relation for the AD heating rate that describes the results of our simulations to within a factor of two. Turbulent dissipation, including AD heating, is generally less important that cosmic-ray heating in molecular clouds, although there is substantial scatter in both., Comment: 11 pages, 4 figures, accepted by ApJ

In order to understand the initial conditions and early evolution of star formation in a wide range of Galactic environments, we carried out an investigation of 64 Planck Galactic cold clumps (PGCCs) in the second quadrant of the Milky Way. Using the 13CO and C18O J = 1-0 lines and 850 μm continuum observations, we investigated cloud fragmentation and evolution associated with star formation. We extracted 468 clumps and 117 cores from the 13CO line and 850 μm continuum maps, respectively. We made use of the Bayesian distance calculator and derived the distances of all 64 PGCCs. We found that in general, the mass-size plane follows a relation of m ̃ r 1.67. At a given scale, the masses of our objects are around 1/10 of that of typical Galactic massive star-forming regions. Analysis of the clump and core masses, virial parameters, densities, and mass- size relation suggests that the PGCCs in our sample have a low core formation efficiency (̃3.0%), and most PGCCs are likely low-mass star- forming candidates. Statistical study indicates that the 850 μm cores are more turbulent, more optically thick, and denser than the 13CO clumps for star formation candidates, suggesting that the 850 μm cores are likely more appropriate future star formation candidates than the 13CO clumps.

Stellar feedback from high-mass stars (e.g., H{\sc ii} regions) can strongly influence the surrounding interstellar medium and regulate star formation. Our new ALMA observations reveal sequential high-mass star formation taking place within one sub-virial filamentary clump (the G9.62 clump) in the G9.62+0.19 complex. The 12 dense cores (MM 1-12) detected by ALMA are at very different evolutionary stages, from starless core phase to UC H{\sc ii} region phase. Three dense cores (MM6, MM7/G, MM8/F) are associated with outflows. The mass-velocity diagrams of outflows associated with MM7/G and MM8/F can be well fitted with broken power laws. The mass-velocity diagram of SiO outflow associated with MM8/F breaks much earlier than other outflow tracers (e.g., CO, SO, CS, HCN), suggesting that SiO traces newly shocked gas, while the other molecular lines (e.g., CO, SO, CS, HCN) mainly trace the ambient gas continuously entrained by outflow jets. Five cores (MM1, MM3, MM5, MM9, MM10) are massive starless core candidates whose masses are estimated to be larger than 25 M$_{\sun}$, assuming a dust temperature of $\leq$ 20 K. The shocks from the expanding H{\sc ii} regions ("B" \& "C") to the west may have great impact on the G9.62 clump through compressing it into a filament and inducing core collapse successively, leading to sequential star formation. Our findings suggest that stellar feedback from H{\sc ii} regions may enhance the star formation efficiency and suppress the low-mass star formation in adjacent pre-existing massive clumps., Accepted to ApJ

The low dust temperatures (, Comment: Accepted for publication in the ApJS