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Paolo Padoan

Publications and source records attributed to Paolo Padoan.

At least 55 records · Page 3Linked to original sources
arXiv2012

The Two States of Star Forming Clouds

We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512^3) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two super-Alfvénic and one trans-Alfvénic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties similar to non-self-gravitating in this regime, and we examine the effects of varied magnetic field strength on statistical properties: the density probability distribution function is approximately lognormal; velocity power spectral slopes decrease with field strength; alignment between velocity and magnetic field increases with field; the magnetic field probability distribution can be fit to a stretched exponential. The high density state is characterized by self-similar spheres; the density PDF is a power-law; collapse rate decreases with increasing mean field; density power spectra have positive slopes, P(ρ,k) \propto k; thermal-to-magnetic pressure ratios are unity for all simulations; dynamic-to-magnetic pressure ratios are larger than unity for all simulations; magnetic field distribution is a power-law. The high Alfvén Mach numbers in collapsing regions explain recent observations of magnetic influence decreasing with density. We also find that the high density state is found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored.

astro-ph.SR↗
arXiv2011

The observable prestellar phase of the IMF

The observed similarities between the mass function of prestellar cores (CMF) and the stellar initial mass function (IMF) have led to the suggestion that the IMF is already largely determined in the gas phase. However, theoretical arguments show that the CMF may differ significantly from the IMF. In this Letter, we study the relation between the CMF and the IMF, as predicted by the IMF model of Padoan and Nordlund. We show that 1) the observed mass of prestellar cores is on average a few times smaller than that of the stellar systems they generate; 2) the CMF rises monotonically with decreasing mass, with a noticeable change in slope at approximately 3-5 solar masses, depending on mean density; 3) the selection of cores with masses larger than half their Bonnor-Ebert mass yields a CMF approximately consistent with the system IMF, rescaled in mass by the same factor as our model IMF, and therefore suitable to estimate the local efficiency of star formation, and to study the dependence of the IMF peak on cloud properties; 4) only one in five pre-brown-dwarf core candidates is a true progenitor to a brown dwarf.

astro-ph.GA↗
arXiv2011

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

We study clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, $St$, defined as the ratio of the particle friction timescale, $τ_{\rm p} $, to the Kolmogorov timescale in the flow. In the dissipation range, the clustering intensity strongly peaks at $St \simeq 1$, and the RDF for $St \sim 1$ shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these scales, the strongest clustering is from particles with $τ_{\rm p}$ in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is $\simτ_{\rm p}$. Particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in recent models for planetesimal formation. We point out that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.

astro-ph.EP↗
arXiv2011

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

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.

astro-ph.SR↗
arXiv2011

Pop. III stars from turbulent fragmentation at redshift ~ 11

We report results from a cosmological simulation with non-equilibrium chemistry of 21 species, including H2, HD, and LiH molecular cooling. Starting from cosmological initial conditions, we focus on the evolution of the central 1.8 Kpc region of a 3 x 10^7 Msun halo. The crossing of a few 10^6 Msun halos and the gas accretion through larger scale filaments generate a turbulent environment within this region. Due to the short cooling time caused by the non-equilibrium formation of H2, the supersonic turbulence results in a very fragmented mass distribution, where dense, gravitationally unstable clumps emerge from a complex network of dense filaments. At z=10.87, we find approximately 25 well defined, gravitationally unstable clumps, with masses of 4 x 10^3-9 x 10^5 Msun, temperatures of approximately 300K, and cooling times much shorter than the free-fall time. Only the initial phase of the collapse of individual clumps is spatially resolved in the simulation. Depending on the density reached in the collapse, the estimated average Bonnor-Ebert masses are in the range 200-800 Msun. We speculate that each clump may further fragment into a cluster of stars with a characteristic mass in the neighborhood of 50 Msun. This process at z ~ 11 may represent the dominant mode of Pop. III star formation, causing a rapid chemical enrichment of the protogalactic environment.

astro-ph.CO↗
arXiv2010

The Star Formation Rate of Supersonic MHD Turbulence

This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, alpha_vir, the rms sonic Mach number, M_S,0, and the ratio of mean gas pressure to mean magnetic pressure, beta_0. The SFR is predicted to decrease with increasing alpha_vir (stronger turbulence relative to gravity), to increase with increasing M_S,0 (for constant values of alpha_vir), and to depend weakly on beta_0 for values typical of star forming regions (M_S,0 ~ 4-20 and beta_0 ~ 1-20). In the unrealistic limit of beta_0 -> infinity, that is in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvenic turbulence). In this non-magnetized limit, our definition of the critical density for star formation has the same dependence on alpha_vir, and almost the same dependence on M_S,0, as in the model of Krumholz and McKee, although our physical derivation does not rely on the concepts of local turbulent pressure and sonic scale. However, our model predicts a different dependence of the SFR on alpha_vir and M_S,0 than the model of Krumholz and McKee. The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations are shown to agree very well with the theoretical predictions.

astro-ph.GA↗
arXiv2010

Mass and Magnetic distributions in Self Gravitating Super Alfvenic Turbulence with AMR

In this work, we present the mass and magnetic distributions found in a recent Adaptive Mesh Refinement (AMR) MHD simulation of supersonic, \sa, self gravitating turbulence. Powerlaw tails are found in both volume density and magnetic field probability density functions, with $P(ρ) \propto ρ^{-1.67}$ and $P(B)\propto B^{-2.74}$. A power law is also found between magnetic field strength and density, with $B\propto ρ^{0.48}$, throughout the collapsing gas. The mass distribution of gravitationally bound cores is shown to be in excellent agreement with recent observation of prestellar cores. The mass to flux distribution of cores is also found to be in excellent agreement with recent Zeeman splitting measurements.

astro-ph.GA↗
arXiv2010

Relative Velocity of Inertial Particles in Turbulent Flows

We present a model for the relative velocity of inertial particles in turbulent flows. Our general formulation shows that the relative velocity has contributions from two terms, referred to as the generalized acceleration and generalized shear terms, because they reduce to the well known acceleration and shear terms in the Saffman-Turner limit. The generalized shear term represents particles' memory of the flow velocity difference along their trajectories and depends on the inertial particle pair dispersion backward in time. The importance of this backward dispersion in determining the particle relative velocity is emphasized. We find that our model with a two-phase separation behavior, an early ballistic phase and a later tracer-like phase, as found by recent simulations for the forward (in time) dispersion of inertial particle pairs, gives good fits to the measured relative speeds from simulations at low Reynolds numbers. In the monodisperse case with identical particles, the generalized acceleration term vanishes and the relative velocity is determined by the generalized shear term. At large Reynolds numbers, our model gives a $St^{1/2}$ dependence of the relative velocity on the Stokes number $St$ in the inertial range for both the ballistic behavior and the Richardson separation law. This leads to the same inertial-range scaling for the two-phase separation that well fits the simulation results. Our calculations for the bidisperse case show that, with the friction timescale of one particle fixed, the relative speed as a function of the other particle's friction time has a dip when the two timescales are similar. We find that the primary contribution at the dip is from the generalized shear term, while the generalized acceleration term is dominant for particles of very different sizes.

physics.flu-dyn↗
arXiv2010

The IMF of stellar clusters: effects of accretion and feedback

(abridged) We develop a model which describes the coevolution of the mass function of dense cores and of the IMF in a protocluster clump. In the model, cores injected in the clump evolve under the effect of gas accretion. Accretion onto the cores follows a time-dependent accretion rate that describes accretion in a turbulent medium. Once the accretion timescales of cores exceed their contraction timescales, they are turned into stars. We include the effect of feedback by the newly formed massive stars through their stellar winds. A fraction of the wind's energy is assumed to counter gravity and disperse the gas from the protocluster and as a consequence, quench further star formation. The latter effect sets the final IMF of the cluster. We apply our model to a clump that is expected to resemble the progenitor clump of the Orion Nebula Cluster (ONC). Our model is able to reproduce both the shape and normalization of the ONC's IMF and the mass function of dense cores in Orion. The complex features of the ONC's IMF,i.e., a shallow slope in the mass range ~0.3-2.5 Msol,a steeper slope in the mass range ~2.5-12 Msol, and a nearly flat tail at the high mass end are reproduced. The model predicts a 'rapid' star formation process with an age spread for the stars of 2.3 10^5 yr which is consistent with the fact that 80% of the ONC's stars have ages of <=0.3 Myr. The model predicts a primordial mass segregation with the most massive stars being born in the region between 2-4 times the core radius of the cluster. In parallel, the model also reproduces, simultaneously, the mass function of dense cores in Orion. We study the effects of varying the model parameters on the resulting IMF and show that the IMF of stellar clusters is expected to show significant variations, provided variations in the clumps and cores properties exist.

astro-ph.GA↗
arXiv2009

Self-organization in Turbulent Molecular Clouds: Compressional versus Solenoidal Modes

We use three-dimensional numerical simulations to study self-organization in supersonic turbulence in molecular clouds. Our numerical experiments describe decaying and driven turbulent flows with an isothermal equation of state, sonic Mach numbers from 2 to 10, and various degrees of magnetization. We focus on properties of the velocity field and, specifically, on the level of its potential (dilatational) component as a function of turbulent Mach number, magnetic field strength, and scale. We show how extreme choices of either purely solenoidal or purely potential forcing can reduce the extent of the inertial range in the context of periodic box models for molecular cloud turbulence. We suggest an optimized forcing to maximize the effective Reynolds number in numerical models.

astro-ph.GA↗
arXiv2009

The Power Spectrum of Turbulence in NGC 1333: Outflows or Large-Scale Driving?

Is the turbulence in cluster-forming regions internally driven by stellar outflows or the consequence of a large-scale turbulent cascade? We address this question by studying the turbulent energy spectrum in NGC 1333. Using synthetic 13CO maps computed with a snapshot of a supersonic turbulence simulation, we show that the VCS method of Lazarian and Pogosyan provides an accurate estimate of the turbulent energy spectrum. We then apply this method to the 13CO map of NGC 1333 from the COMPLETE database. We find the turbulent energy spectrum is a power law, E(k) k^-beta, in the range of scales 0.06 pc < ell < 1.5 pc, with slope beta=1.85\pm 0.04. The estimated energy injection scale of stellar outflows in NGC 1333 is ell_inj 0.3 pc, well resolved by the observations. There is no evidence of the flattening of the energy spectrum above the scale ell_inj predicted by outflow-driven simulations and analytical models. The power spectrum of integrated intensity is also a nearly perfect power law in the range of scales 0.16 pc < ell < 7.9 pc, with no feature above ell_inj. We conclude that the observed turbulence in NGC 1333 does not appear to be driven primarily by stellar outflows.

astro-ph.GA↗
arXiv2009

Simulating Supersonic Turbulence in Magnetized Molecular Clouds

We present results of large-scale three-dimensional simulations of weakly magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our numerical experiments are carried out with the Piecewise Parabolic Method on a Local Stencil and assume an isothermal equation of state. The turbulence is driven by a large-scale isotropic solenoidal force in a periodic computational domain and fully develops in a few flow crossing times. We then evolve the flow for a number of flow crossing times and analyze various statistical properties of the saturated turbulent state. We show that the energy transfer rate in the inertial range of scales is surprisingly close to a constant, indicating that Kolmogorov's phenomenology for incompressible turbulence can be extended to magnetized supersonic flows. We also discuss numerical dissipation effects and convergence of different turbulence diagnostics as grid resolution refines from 256^3 to 1024^3 cells.

astro-ph.GA↗
arXiv2009

The Super-Alfvénic Model of Molecular Clouds: Predictions for Mass-to-Flux and Turbulent-to-Magnetic Energy Ratios

Recent measurements of the Zeeman effect in dark-cloud cores provide important tests for theories of cloud dynamics and prestellar core formation. In this Letter we report results of simulated Zeeman measurements, based on radiative transfer calculations through a snapshot of a simulation of supersonic and super-Alfvénic turbulence. We have previously shown that the same simulation yields a relative mass-to-flux ratio (core versus envelope) in agreement with the observations (and in contradiction with the ambipolar-drift model of core formation). Here we show that the mass-to-flux and turbulent-to-magnetic-energy ratios in the simulated cores agree with observed values as well. The mean magnetic field strength in the simulation is very low, \bar{B}=0.34 \muG, presumably lower than the mean field in molecular clouds. Nonetheless, high magnetic field values are found in dense cores, in agreement with the observations (the rms field, amplified by the turbulence, is B_{rms}=3.05 \muG). We conclude that a strong large-scale mean magnetic field is not required by Zeeman effect measurements to date, although it is not ruled out by this work.

astro-ph.GA↗
arXiv2009

Simulations of Supersonic Turbulence in Molecular Clouds: Evidence for a New Universality

We use three-dimensional simulations to study the statistics of supersonic turbulence in molecular clouds. Our numerical experiments describe driven turbulent flows with an isothermal equation of state, Mach numbers around 10, and various degrees of magnetization. We first support the so-called 1/3-rule of Kritsuk et al. 2007 with our new data from a larger 2048^3 simulation. We then attempt to extend the 1/3-rule to supersonic MHD turbulence and get encouraging preliminary results based on a set of 512^3 simulations. Our results suggest an interesting new approach to tackle universal scaling relations and intermittency in supersonic MHD turbulence.

astro-ph.GA↗
arXiv2009

Dissipative Structures in Supersonic Turbulence

We show that density-weighted moments of the dissipation rate, $ε_l$, averaged over a scale $l$, in supersonic turbulence can be successfully explained by the She and Lévêque model [Phys. Rev. Lett. {\bf 72}, 336 (1994)]. A general method is developed to measure the two parameters of the model, $γ$ and $d$, based directly on their physical interpretations as the scaling exponent of the dissipation rate in the most intermittent structures ($γ$) and the dimension of the structures ($d$). We find that the best-fit parameters ($γ=0.71$ and $d=1.90$) derived from the $ε_l$ scalings in a simulation of supersonic turbulence at Mach 6 agree with their direct measurements, confirming the validity of the model in supersonic turbulence.

astro-ph↗
arXiv2008

The Temperature of Interstellar Clouds from Turbulent Heating

To evaluate the effect of turbulent heating in the thermal balance of interstellar clouds, we develop an extension of the log-Poisson intermittency model to supersonic turbulence. The model depends on a parameter, d, interpreted as the dimension of the most dissipative structures. By comparing the model with the probability distribution of the turbulent dissipation rate in a simulation of supersonic and super-Alfvenic turbulence, we find a best-fit value of d=1.64. We apply this intermittency model to the computation of the mass-weighted probability distribution of the gas temperature of molecular clouds, high-mass star-forming cores, and cold diffuse HI clouds. Our main results are: i) The mean gas temperature in molecular clouds can be explained as the effect of turbulent heating alone, while cosmic ray heating may dominate only in regions where the turbulent heating is low; ii) The mean gas temperature in high-mass star-forming cores with typical FWHM of ~6 km/s (corresponding to a 1D rms velocity of 2.5 km/s) may be completely controlled by turbulent heating, which predicts a mean value of approximately 36 K, two to three times larger than the mean gas temperature in the absence of turbulent heating; iii) The intermittency of the turbulent heating can generate enough hot regions in cold diffuse HI clouds to explain the observed CH+ abundance, if the rms velocity on a scale of 1 pc is at least 3 km/s, in agreement with previous results based on incompressible turbulence. Because of its importance in the thermal balance of molecular clouds and high-mass star-forming cores, the process of turbulent heating may be central in setting the characteristic stellar mass and in regulating molecular chemical reactions.

astro-ph↗
arXiv2008

The Super-Alfvénic Model of Molecular Clouds: Predictions for Zeeman Splitting Measurements

We present synthetic OH Zeeman splitting measurements of a super-Alfvenic model of molecular clouds. We select dense cores from synthetic 13CO maps computed from the largest simulation to date of supersonic and super-Alfvenic turbulence. The synthetic Zeeman splitting measurements in the cores yield a relation between the magnetic field strength, B, and the column density, N, in good agreement with the observations. The large scatter in B at a fixed value of N is partly due to intrinsic variations in the magnetic field strength from core to core. We also compute the relative mass-to-flux ratio between the center of the cores and their envelopes, ${\cal R}_μ$, and show that super-Alfvenic turbulence produces a significant scatter also in ${\cal R}_μ$, including negative values (field reversal between core center and envelope). We find ${\cal R}_μ<1$ for 70% of the cores, and ${\cal R}_μ<0$ for 12%. Of the cores with $|B_{\rm LOS}|>10$ \muG, 81% have ${\cal R}_μ<1$. These predictions of the super-Alfvenic model are in stark contrast to the ambipolar drift model of core formation, where only ${\cal R}_μ>1$ is allowed.

astro-ph↗