We show that the ambipolar-diffusion--initiated fragmentation of molecular clouds leads simply and naturally to an initial core mass function (CMF) which is very similar to the initial stellar mass function (IMF) and in excellent agreement with existing observations. This agreement is robust provided that the three (input) free parameters remain within their range of values suggested by observations. Other, observationally testable, predictions are made.
We employ the three-dimensional magnetohydrodynamic simulation including ambipolar diffusion to study the gravitationally-driven fragmentation of subcritical molecular clouds, in which the gravitational fragmentation is stabilized as long as magnetic flux-freezing applies. The simulations show that the cores in an initially subcritical cloud generally develop gradually over an ambipolar diffusion time, which is about a few $\times 10^7$ years in a typical molecular cloud. On the other hand, the formation of collapsing cores in subcritical clouds is accelerated by supersonic nonlinear flows. Ou…
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 t…
Though flux freezing is a good approximation frequently assumed for molecular clouds, ambipolar diffusion (AD) is inevitable at certain scales. The scale at which AD sets in can be a crucial parameter for turbulence and the star formation process. However, both observation and simulation of AD are very challenging and our knowledge of it is very limited. We proposed earlier (Li and Houde 2008) that the difference between ion and neutral velocity spectra is a signature of turbulent AD and can be used to estimate the AD scales and magnetic field strength. Here we present observational evidence s…
Magnetic fields play a role in the dynamics of many astrophysical processes, but they are hard to detect. In a partially ionized plasma, a magnetic field works directly on the ionized medium but not on the neutral medium, which gives rise to a velocity drift between them: ambipolar diffusion. This process is suggested to be important in the process of star formation, but has never been directly observed. We introduce a method that could be used to detect ambipolar diffusion and the magnetic field that gives rise to it, where we exploit the velocity drift between the charged and neutral medium.…
Linear analysis of the formation of protostellar cores in planar magnetic interstellar clouds yields information about length scales involved in star formation. Combining these length scales with various distributions of other environmental variables, (i.e., column density and mass-to-flux ratio) and applying Monte Carlo methods allow us to produce synthetic core mass functions (CMFs) for different environmental conditions. Our analysis shows that the shape of the CMF is directly dependent on the physical conditions of the cloud. Specifically, magnetic fields act to broaden the mass function a…
Simulations generally show that non-self-gravitating clouds have a lognormal column density ($Σ$) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynam…
We analyze the properties of steady and time-dependent C shocks under conditions prevailing in giant molecular clouds. For steady C shocks, we show that ionization equilibrium holds and use numerical integrations to obtain the shock thickness mediated by ambipolar diffusion as a function of density, inflow velocity, magnetic field, and ionization fraction in the cloud. Our formula also agrees with an analytic estimate based on ion-neutral momentum exchange. Using time-dependent numerical simulations, we show that C shocks have a transient stage when the neutrals are compressed much more strong…
Ambipolar diffusion likely plays a pivotal role in the formation and evolution of dense cores in weakly-ionized molecular clouds. Linear analyses show that the evolutionary times and fragmentation scales are significantly greater than the hydrodynamic (Jeans) values even for clouds with mildly supercritical mass-to-flux ratio. We utilize values of fragmentation scales and growth times that correspond to typical ionization fractions within a molecular cloud, and apply to the context of the observed estimated lifetime of prestellar cores as well as the observed number of such embedded cores form…
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 ra…
In partially ionised plasmas, the magnetic field can become decoupled from the neutral gas and diffuse through it in a process known as ambipolar diffusion. Although ambipolar diffusion has been implemented in several grid codes, we here provide an implementation in smoothed particle magnetohydrodynamics (SPMHD). We use the strong coupling approximation in which the ion density is negligible, allowing a single fluid approach. The equations are derived to conserve energy, and to provide a positive definite contribution to the entropy. We test the implementation in both a simple 1D SPMHD code an…
We investigate the formation and evolution of giant molecular clouds (GMCs) by the collision of convergent warm neutral medium (WNM) streams in the interstellar medium, in the presence of magnetic fields and ambipolar diffusion (AD), focusing on the evolution of the star formation rate (SFR) and efficiency (SFE), as well as of the mass-to-magnetic-flux ratio (M2FR) in the forming clouds. We find that: 1) Clouds formed by supercritical inflow streams proceed directly to collapse, while clouds formed by subcritical streams first contract and then re-expand, oscillating on the scale of tens of My…
We investigate the roles of magnetic fields and ambipolar diffusion during prestellar core formation in turbulent giant molecular clouds (GMCs), using three-dimensional numerical simulations. Our simulations focus on the shocked layer produced by a converging flow within a GMC, and survey varying ionization and angle between the upstream flow and magnetic field. We also include ideal magnetohydrodynamic (MHD) and hydrodynamic models. From our simulations, we identify hundreds of self-gravitating cores that form within 1 Myr, with masses M ~ 0.04 - 2.5 solar-mass and sizes L ~ 0.015 - 0.07 pc, …
We investigate differences in the molecular abundances between magnetically super- and sub-critical prestellar cores, performing three-dimensional non-ideal magnetohydrodynamical (MHD) simulations with varying densities and magnetic field strengths, and post-processing the results with a time-dependent gas-grain chemical code. Most molecular species show significantly more central depletion in subcritical models, due to the longer duration of collapse. However, the directly observable quantities - the molecule to hydrogen column density ratios - are generally too similar for observational data…
We study the effect of the non-linear process of ambipolar diffusion (joint transport of magnetic flux and charged particles relative to neutral particles) on the long-term behavior of a non-uniform magnetic field in a one-dimensional geometry. Our main focus is the dissipation of magnetic energy inside neutron stars(particularly magnetars), but our results have a wider application, particularly to the interstellar medium and the loss of magnetic flux from collapsing molecular cloud cores. Our system is a weakly ionized plasma in which neutral and charged particles can be converted into each o…
We clarify the mechanism of accelerated core formation by large-scale nonlinear flows in subcritical magnetic clouds by finding a semi-analytical formula for the core formation time and describing the physical processes that lead to them. Recent numerical simulations show that nonlinear flows induce rapid ambipolar diffusion that leads to localized supercritical regions that can collapse. Here, we employ non-ideal magnetohydrodynamic simulations including ambipolar diffusion for gravitationally stratified sheets threaded by vertical magnetic fields. One of the horizontal dimensions is eliminat…
We have coupled a chemical model with two dynamical models of collapsing low mass star-forming cores to predict abundances across the core of the commonly used infall tracers, CS and HCO$^+$, at various stages of the collapse. The models investigated are a new ambipolar diffusion model and the `inside-out' collapse model. We have then used these results as an input to a radiative transfer model to predict the line profiles of several transitions of these molecules. For the inside-out collapse model, we predict significant molecular depletion due to freeze-out in the core centre, which prevents…
We present a comprehensive study of MHD waves and instabilities in a weakly ionised system, e.g., an interstellar molecular cloud. We determine all the critical wavelengths of perturbations across which the sustainable wave modes can change radically (and so can their decay rates), and various instabilities are present or absent. These critical wavelengths are essential for understanding the effects of MHD waves (or turbulence) on the structure and evolution of molecular clouds. Depending on the angle of propagation relative to the magnetic field and the physical parameters of a cloud, there a…
Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β=0.1) and mildly supersonic turbulence (M=3, corresponding to an Alfven mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominate…
We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test and the Alfven wave test. For the latte…
In the present-day universe, magnetic fields play such essential roles in star formation as angular momentum transport and outflow driving, which control circumstellar disc formation/fragmentation and also the star formation efficiency. While only a much weaker field has been believed to exist in the early universe, recent theoretical studies find that strong fields can be generated by turbulent dynamo during the gravitational collapse. Here, we investigate the gravitational collapse of a cloud core ($\sim 10^{3}\ \rm cm^{-3}$) up to protostar formation ($\sim 10^{20}\ \rm cm^{-3}$) by non-ide…
We investigate whether or not the low ionisation fractions in molecular cloud cores can solve the `magnetic braking catastrophe', where magnetic fields prevent the formation of circumstellar discs around young stars. We perform three-dimensional smoothed particle non-ideal magnetohydrodynamics (MHD) simulations of the gravitational collapse of one solar mass molecular cloud cores, incorporating the effects of ambipolar diffusion, Ohmic resistivity and the Hall effect alongside a self-consistent calculation of the ionisation chemistry assuming 0.1 micron grains. When including only ambipolar di…
Magnetic diffusion plays a vital role in star formation. We trace its influence from interstellar cloud scales down to star-disk scales. On both scales, we find that magnetic diffusion can be significantly enhanced by the buildup of strong gradients in magnetic field structure. Large scale nonlinear flows can create compressed cloud layers within which ambipolar diffusion occurs rapidly. However, in the flux-freezing limit that may be applicable to photoionized molecular cloud envelopes, supersonic motions can persist for long times if driven by an externally generated magnetic field that corr…
Disks are essential to the formation of both stars and planets, but how they form in magnetized molecular cloud cores remains debated. This work focuses on how the disk formation is affected by turbulence and ambipolar diffusion (AD), both separately and in combination, with an emphasis on the protostellar mass accretion phase of star formation. We find that a relatively strong, sonic turbulence on the core scale strongly warps but does not completely disrupt the well-known magnetically-induced flattened pseudodisk that dominates the inner protostellar accretion flow in the laminar case, in ag…
We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux is largely removed by magnetic diffusion in the first core phase and that the plasma $β$ of the centre of the first core becomes large, $β>10^4$. Thus, proper treatment of first core phase is crucial in investigating the formation of protostar and disc. On the other hand, in an ideal simulation, $β\sim 10$ at the centre of the first core. The simu…
In a previous paper we formulated the problem of the formation and evolution of fragments (or cores) in magnetically-supported, self-gravitating molecular clouds in axisymmetric geometry, accounting for the effects of ambipolar diffusion and Ohmic dissipation, grain chemistry and dynamics, and radiative transfer. Here we present results of star formation simulations that accurately track the evolution of a protostellar fragment over eleven orders of magnitude in density (from 300 cm^-3 to \approx 10^14 cm^-3), i.e., from the early ambipolar-diffusion--initiated fragmentation phase, through the…
We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (Ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheet-like cloud or disk. Our results show that there is a…
The turbulent motion within molecular clouds is a key factor controlling star formation. Turbulence supports molecular cloud cores from evolving to gravitational collapse and hence sets a lower bound on the size of molecular cloud cores in which star formation can occur. On the other hand, without a continuous external energy source maintaining the turbulence, such as in molecular clouds, the turbulence decays with an energy dissipation time comparable to the dynamic timescale of clouds, which could change the size limits obtained from Jean's criterion by assuming constant turbulence intensiti…
Magnetic fields play an important role in star formation by regulating the removal of angular momentum from collapsing molecular cloud cores. Hall diffusion is known to be important to the magnetic field behaviour at many of the intermediate densities and field strengths encountered during the gravitational collapse of molecular cloud cores into protostars, and yet its role in the star formation process is not well-studied. We present a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, and similarity solutions t…
We conducted an infrared search for faint companions around 351 young stellar objects in the rho Ophiucus molecular cloud and the Serpens molecular cloud. Nine objects in the Spitzer/IRAC archival images were identified as young stellar companion candidates. They showed an intrinsic infrared excess; one object was extremely red both in the [3.6] - [4.5] color and in the [4.5] - [5.8] color, and two objects were red in the [4.5] - [5.8] color. They were as faint as 15 mag in the [3.6] band. Follow-up K-band spectroscopy revealed that three objects had deep water absorption bands, indicative of …
Recent observational results for magnetic fields in molecular clouds reviewed by Crutcher (2012) seem to be inconsistent with the predictions of the ambipolar diffusion theory of star formation. These include the measured decrease in mass to flux ratio between envelopes and cores, the failure to detect any self-gravitating magnetically subcritical clouds, the determination of the flat PDF of the total magnetic field strengths implying that there are many clouds with very weak magnetic fields, and the observed scaling $B \propto ρ^{2/3}$ that implies gravitational contraction with weak magnetic…
The dense molecular cloud cores that form stars, like other self-gravitating objects, undergo bulk oscillations. Just at the point of gravitational instability, their fundamental oscillation mode has zero frequency. We study, using perturbation theory, the evolution of a spherical cloud that possesses such a frozen mode. We find that the cloud undergoes a prolonged epoch of subsonic, accelerating contraction. This slow contraction occurs whether the cloud is initially inflated or compressed by the oscillation. The subsonic motion described here could underlie the spectral infall signature obse…
The transport of angular momentum is capital during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. We investigate the impact of including resistive MHD in simulations of the gravitational collapse of a 1 solar mass gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. We used the AMR code RAMSES to perform two 3D simulati…
We develop analytic approximations to the density evolution of prestellar cores, based on the results of hydrodynamical simulations. We use these approximations as input for a time-dependent gas-grain chemical code to investigate the effects of differing modes of collapse on the molecular abundances in the core. We confirm that our method can provide reasonable agreement with an exact numerical solution of both the hydrodynamics and chemistry while being significantly less computationally expensive, allowing a large grid of models varying multiple input parameters to be run. We present results…
We report Submillimeter Array molecular line observations in the 345 GHz band of five massive dense cores, Cyg-N38, Cyg-N43, Cyg-N48, Cyg-N51, and Cyg-N53 in the DR21 filament. The molecular line data reveal several dynamical features of the cores: (1) prominent outflows in all cores seen in the CO and SiO lines, (2) significant velocity gradients in Cyg-N43 and Cyg-N48 seen in the H13CN and H13CO+ lines suggesting 0.1-pc-scale rotational motions, and (3) possible infalls in Cyg-N48 found in the SiO and SO lines. Comparing the molecular line data and our dust polarization data in Ching et al. …
In this paper, we introduce Nicil: Non-Ideal magnetohydrodynamics Coefficients and Ionisation Library. Nicil is a stand-alone Fortran90 module that calculates the ionisation values and the coefficients of the non-ideal magnetohydrodynamics terms of Ohmic resistivity, the Hall effect, and ambipolar diffusion. The module is fully parameterised such that the user can decide which processes to include and decide upon the values of the free parameters, making this a versatile and customisable code. The module includes both cosmic ray and thermal ionisation; the former includes two ion species and t…
The principle of the background-eliminated extinction-parallax (BEEP) method is examining the extinction difference between on- and off-cloud regions to reveal the extinction jump caused by molecular clouds, thereby revealing the distance in complex dust environments. The BEEP method requires high-quality images of molecular clouds and high-precision stellar parallaxes and extinction data, which can be provided by the Milky Way Imaging Scroll Painting (MWISP) CO survey and the Gaia DR2 catalog, as well as supplementary AV extinction data. In this work, the BEEP method is further improved (BEEP…
We present a new method of calculating distances of molecular clouds in the Galactic plane, using CO observations and the Gaia DR2 parallax and G-band extinction ($A_G$) measurements. Due to the complexity of dust environments in the Galactic plane, $A_G$ contains irregular variations, which is difficult to model. To overcome this difficulty, we propose that the $A_G$ of off-cloud stars (Gaia stars around molecular clouds) can be used as a baseline to calibrate the $A_G$ of on-cloud stars (Gaia stars toward molecular clouds), which removes the $A_G$ components that are unrelated to molecular c…
We report the distances of molecular clouds at high Galactic latitudes (|b|>10$^\circ$) derived from parallax and G band extinction (A$_{\rm G}$) measurements in the second Gaia data release, Gaia DR2. Aided by Bayesian analyses, we determined distances by identifying the breakpoint in the extinction A$_{\rm G}$ towards molecular clouds and using the extinction A$_{\rm G}$ of Gaia stars around molecular clouds to confirm the breakpoint. We use nearby star-forming regions, such as Orion, Taurus, Cepheus, and Perseus, whose distances are well-known to examine the reliability of our method. By co…
We describe an overall picture of galactic-scale star formation. Recent high-resolution magneto-hydrodynamical simulations of two-fluid dynamics with cooling/heating and thermal conduction have shown that the formation of molecular clouds requires multiple episodes of supersonic compression. This finding enables us to create a scenario in which molecular clouds form in interacting shells or bubbles on a galactic scale. First we estimate the ensemble-averaged growth rate of molecular clouds over a timescale larger than a million years. Next we perform radiation hydrodynamics simulations to eval…
While the importance of supernova feedback in galaxies is well established, its role on the scale of molecular clouds is still debated. In this work, we focus on the impact of supernovae on individual clouds, using a high-resolution magneto-hydrodynamic simulation of a region of 250 pc where we resolve the formation of individual massive stars. The supernova feedback is implemented with real supernovae that are the natural evolution of the resolved massive stars, so their position and timing are self-consistent. We select a large sample of molecular clouds from the simulation to investigate th…
Distance measurements to molecular clouds are essential and important. We present directly measured distances to 169 molecular clouds in the fourth quadrant of the Milky Way. Based on the near-infrared photometry from the Two Micron All Sky Survey and the Vista Variables in the Via Lactea Survey, we select red clump stars in the overlapping directions of the individual molecular clouds and infer the bin averaged extinction values and distances to these stars. We track the extinction versus distance profiles of the sightlines toward the clouds and fit them with Gaussian dust distribution models…
