arXiv subjects

Paolo Padoan

Publications and source records attributed to Paolo Padoan.

At least 37 records · Page 2Linked to original sources

arXiv2018

Dust polarisation studies on MHD simulations of molecular clouds: methods comparison for the relative orientations analysis

Context. Polarized dust emission can be used as a probe for magnetic fields at different scales. In particular, the analysis of the relative orientation between the density structures and the magnetic field projected on the plane of the sky can provide information on the role of magnetic fields in shaping the structure of molecular clouds. Aims. The relative orientation has been investigated using different methods. Our goal is to explicitly compare two of them: the Rolling Hough Transform (RHT) and the gradient technique. Methods. We have applied the RHT method and the gradient technique to two regions, identified in surface brightness maps at 353 GHz generated via MHD simulations post-processed using radiative transfer modelling. For both methods we have derived the relative orientation between the magnetic field and the density structures, to which we have applied two different statistics, the histogram of relative orientation (HRO) statistic and the projected Rayleigh statistic (PRS). Results. The samples of pixels selected by each method are substantially different. When the methods are applied to the same pixel selection, the results in terms of relative orientation as a function of column density are consistent between each other. When each method is applied to its own pixel selection, the differences are apparent. In Region 1, the RHT method roughly reproduces the observed trend of the relative orientation becoming more perpendicular for increasing column density, while the gradient method, applied at the same resolution as RHT, gives the opposite trend, with the relative orientation moving towards a more parallel alignment. In Region 2, the situation is reversed. The inconsistent results, which are due to the different pixel selections operated by the methods and to the intrinsic differences between them, provide complementary valuable information. Abridged.

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arXiv2018

Detailed Balance and Exact Results for Density Fluctuations in Supersonic Turbulence

The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in compressible turbulence in two forms: a first-order partial differential equation involving the average divergence conditioned on the flow density, $\langle \nabla \cdot {\bs u} | s\rangle$, and a Fokker-Planck equation with the drift and diffusion coefficients equal to $-\langle {\bs u} \cdot \nabla s | s\rangle$ and $\langle {\bs u} \cdot \nabla s | s\rangle$, respectively. Assuming statistical homogeneity only, the detailed balance at steady state leads to two exact results, $\langle \nabla \cdot {\bs u} | s \rangle =0$, and $\langle {\bs u} \cdot \nabla s | s\rangle=0$. The former indicates a balance of the flow divergence over all expanding and contracting regions at each given density. The exact results provide an objective criterion to judge the accuracy of numerical codes with respect to the density statistics in supersonic turbulence. We also present a method to estimate the effective numerical diffusion as a function of the flow density and discuss its effects on the shape of the density PDF.

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arXiv2018

The CARMA-NRO Orion Survey

We present the first results from a new, high resolution, $^{12}$CO(1-0), $^{13}$CO(1-0), and C$^{18}$O(1-0) molecular line survey of the Orion A cloud, hereafter referred to as the CARMA-NRO Orion Survey. CARMA observations have been combined with single-dish data from the Nobeyama 45m telescope to provide extended images at about 0.01 pc resolution, with a dynamic range of approximately 1200 in spatial scale. Here we describe the practical details of the data combination in uv space, including flux scale matching, the conversion of single dish data to visibilities, and joint deconvolution of single dish and interferometric data. A $Δ$-variance analysis indicates that no artifacts are caused by combining data from the two instruments. Initial analysis of the data cubes, including moment maps, average spectra, channel maps, position-velocity diagrams, excitation temperature, column density, and line ratio maps provides evidence of complex and interesting structures such as filaments, bipolar outflows, shells, bubbles, and photo-eroded pillars. The implications for star formation processes are profound and follow-up scientific studies by the CARMA-NRO Orion team are now underway. We plan to make all the data products described here generally accessible; some are already available at https://dataverse.harvard.edu/dataverse/CARMA-NRO-Orion

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arXiv2018

The stellar IMF from Isothermal MHD Turbulence

We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwarfs to massive stars. Our simulations represent a generic 4 pc region within a typical Galactic molecular cloud, with a mass of 3000 Msun and an rms velocity 10 times the isothermal sound speed and 5 times the average Alfven velocity, in agreement with observations. We achieve a maximum resolution of 50 au and a maximum duration of star formation of 4.0 Myr, forming up to a thousand sink particles whose mass distribution closely matches the observed stellar IMF. A large set of medium-size simulations is used to test the sink particle algorithm, while larger simulations are used to test the numerical convergence of the IMF and the dependence of the IMF turnover on physical parameters predicted by the turbulent fragmentation model. We find a clear trend toward numerical convergence and strong support for the model predictions, including the initial time evolution of the IMF. We conclude that the physics of isothermal MHD turbulence is sufficient to explain the origin of the IMF.

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arXiv2017

The magnetic field of molecular clouds

The magnetic field of molecular clouds (MCs) plays an important role in the process of star formation: it determins the statistical properties of supersonic turbulence that controls the fragmentation of MCs, controls the angular momentum transport during the protostellar collapse, and affects the stability of circumstellar disks. In this work, we focus on the problem of the determination of the magnetic field strength. We review the idea that the MC turbulence is super-Alfvénic, and we argue that MCs are bound to be born super-Alfvénic. We show that this scenario is supported by results from a recent simulation of supernova-driven turbulence on a scale of 250 pc, where the turbulent cascade is resolved on a wide range of scales, including the interior of MCs.

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arXiv2017

Supernova Driving. IV. The Star Formation Rate of Molecular Clouds

We compute the star formation rate (SFR) in molecular clouds (MCs) that originate {\it ab initio} in a new, higher-resolution simulation of supernova-driven turbulence. Because of the large number of well-resolved clouds with self-consistent boundary and initial conditions, we obtain a large range of cloud physical parameters with realistic statistical distributions, an unprecedented sample of star-forming regions to test SFR models and to interpret observational surveys. We confirm the dependence of the SFR per free-fall time, $SFR_{\rm ff}$, on the virial parameter, $α_{\rm vir}$, found in previous simulations, and compare a revised version of our turbulent fragmentation model with the numerical results. The dependences on Mach number, ${\cal M}$, gas to magnetic pressure ratio, $β$, and compressive to solenoidal power ratio, $χ$ at fixed $α_{\rm vir}$ are not well constrained, because of random scatter due to time and cloud-to-cloud variations in $SFR_{\rm ff}$. We find that $SFR_{\rm ff}$ in MCs can take any value in the range $0 \le SFR_{\rm ff} \lesssim 0.2$, and its probability distribution peaks at a value $SFR_{\rm ff}\approx 0.025$, consistent with observations. The values of $SFR_{\rm ff}$ and the scatter in the $SFR_{\rm ff}$--$α_{\rm vir}$ relation are consistent with recent measurements in nearby MCs and in clouds near the Galactic center. Although not explicitly modeled by the theory, the scatter is consistent with the physical assumptions of our revised model and may also result in part from a lack of statistical equilibrium of the turbulence, due to the transient nature of MCs.

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arXiv2016

Supernova Driving. II. Compressive Ratio in Molecular-Cloud Turbulence

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value $\approx 0.3$, lower than the equilibrium value of $\approx 0.5$ found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density PDF is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included.

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arXiv2016

Supernova Driving. III. Synthetic Molecular Cloud Observations

We present a comparison of molecular clouds (MCs) from a simulation of supernova-driven interstellar medium (ISM) turbulence with real MCs from the Outer Galaxy Survey. The radiative transfer calculations to compute synthetic CO spectra are carried out assuming the CO relative abundance depends only on gas density, according to four different models. Synthetic MCs are selected above a threshold brightness temperature value, $T_{\rm B,min}=1.4$ K, of the $J=1-0$ $^{12}$CO line, generating 16 synthetic catalogs (four different spatial resolutions and four CO abundance models), each containing up to several thousands MCs. The comparison with the observations focuses on the mass and size distributions and on the velocity-size and mass-size Larson relations. The mass and size distributions are found to be consistent with the observations, with no significant variations with spatial resolution or chemical model, except in the case of the unrealistic model with constant CO abundance. The velocity-size relation is slightly too steep for some of the models, while the mass-size relation is a bit too shallow for all models only at a spatial resolution $dx\approx 1$ pc. The normalizations of the Larson relations show a clear dependence on spatial resolution, for both the synthetic and the real MCs. The comparison of the velocity-size normalization suggests that the SN rate in the Perseus arm is approximately 70\% or less of the rate adopted in the simulation. Overall, the realistic properties of the synthetic clouds confirm that supernova-driven turbulence can explain the origin and dynamics of MCs.

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arXiv2016

Supernova Driving. I. The Origin of Molecular Cloud Turbulence

Turbulence is ubiquitous in molecular clouds (MCs), but its origin is still unclear because MCs are usually assumed to live longer than the turbulence dissipation time. Interstellar medium (ISM) turbulence is likely driven by SN explosions, but it has never been demonstrated that SN explosions can establish and maintain a turbulent cascade inside MCs consistent with the observations. In this work, we carry out a simulation of SN-driven turbulence in a volume of (250 pc)$^3$, specifically designed to test if SN driving alone can be responsible for the observed turbulence inside MCs. We find that SN driving establishes a velocity scaling consistent with the usual scaling laws of supersonic turbulence, suggesting that previous idealized simulations of MC turbulence, driven with a random, large-scale volume force, were correctly adopted as appropriate models for MC turbulence, despite the artificial driving. We also find that the same scaling laws extend to the interior of MCs, and that the velocity-size relation of the MCs selected from our simulation is consistent with that of MCs from the Outer-Galaxy Survey, the largest MC sample available. The mass-size relation and the mass and size probability distributions also compare successfully with those of the Outer Galaxy Survey. Finally, we show that MC turbulence is super-Alfvénic with respect to both the mean and rms magnetic-field strength. We conclude that MC structure and dynamics are the natural result of SN-driven turbulence.

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arXiv2015

Protostellar accretion traced with chemistry: Comparing synthetic C18O maps of embedded protostars to real observations

Context: Understanding how protostars accrete their mass is a central question of star formation. One aspect of this is trying to understand whether the time evolution of accretion rates in deeply embedded objects is best characterised by a smooth decline from early to late stages or by intermittent bursts of high accretion. Aims: We create synthetic observations of deeply embedded protostars in a large numerical simulation of a molecular cloud, which are compared directly to real observations. The goal is to compare episodic accretion events in the simulation to observations and to test the methodology used for analysing the observations. Methods: Simple freeze-out and sublimation chemistry is added to the simulation, and synthetic C$^{18}$O line cubes are created for a large number of simulated protostars. The spatial extent of C$^{18}$O is measured for the simulated protostars and compared directly to a sample of 16 deeply embedded protostars observed with the Submillimeter Array. If CO is distributed over a larger area than predicted based on the protostellar luminosity, it may indicate that the luminosity has been higher in the past and that CO is still in the process of refreezing. Results: Approximately 1% of the protostars in the simulation show extended C$^{18}$O emission, as opposed to approximately 50% in the observations, indicating that the magnitude and frequency of episodic accretion events in the simulation is too low relative to observations. The protostellar accretion rates in the simulation are primarily modulated by infall from the larger scales of the molecular cloud, and do not include any disk physics. The discrepancy between simulation and observations is taken as support for the necessity of disks, even in deeply embedded objects, to produce episodic accretion events of sufficient frequency and amplitude.

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arXiv2015

The relative and absolute ages of old globular clusters in the LCDM framework

Old Globular Clusters (GCs) in the Milky Way have ages of about 13 Gyr, placing their formation time in the reionization epoch. We propose a novel scenario for the formation of these systems based on the merger of two or more atomic cooling halos at high-redshift (z>6). First generation stars are formed as an intense burst in the center of a minihalo that grows above the threshold for hydrogen cooling (halo mass M_h~10^8 Msun) by undergoing a major merger within its cooling timescale (~150 Myr). Subsequent minor mergers and sustained gas infall bring new supply of pristine gas at the halo center, creating conditions that can trigger new episodes of star formation. The dark-matter halo around the GC is then stripped during assembly of the host galaxy halo. Minihalo merging is efficient only in a short redshift window, set by the LCDM parameters, allowing us to make a strong prediction on the age distribution for old GCs. From cosmological simulations we derive an average merging redshift =9 and narrow distribution Dz=2, implying average GC age =13.0+/-0.2 Gyr including ~0.2 Gyr of star formation delay. Qualitatively, our scenario reproduces other general old GC properties (characteristic masses and number of objects, metallicity versus galactocentric radius anticorrelation, radial distribution), but unlike age, these generally depend on details of baryonic physics. In addition to improved age measurements, direct validation of the model at z~10 may be within reach of ultradeep gravitationally lensed observations with the James Webb Space Telescope.

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arXiv2014

Turbulence-Induced Relative Velocity of Dust particles IV: the Collision Kernel

Motivated by its importance for modeling dust particle growth in protoplanetary disks, we study turbulence-induced collision statistics of inertial particles as a function of the particle friction time, tau_p. We show that turbulent clustering significantly enhances the collision rate for particles of similar sizes with tau_p corresponding to the inertial range of the flow. If the friction time, tau_p,h, of the larger particle is in the inertial range, the collision kernel per unit cross section increases with increasing friction time, tau_p,l, of the smaller particle, and reaches the maximum at tau_p,l = tau_p,h, where the clustering effect peaks. This feature is not captured by the commonly-used kernel formula, which neglects the effect of clustering. We argue that turbulent clustering helps alleviate the bouncing barrier problem for planetesimal formation. We also investigate the collision velocity statistics using a collision-rate weighting factor to account for higher collision frequency for particle pairs with larger relative velocity. For tau_p,h in the inertial range, the rms relative velocity with collision-rate weighting is found to be invariant with tau_p,l and scales with tau_p,h roughly as ~ tau_p,h^(1/2). The weighting factor favors collisions with larger relative velocity, and including it leads to more destructive and less sticking collisions. We compare two collision kernel formulations based on spherical and cylindrical geometries. The two formulations give consistent results for the collision rate and the collision-rate weighted statistics, except that the spherical formulation predicts more head-on collisions than the cylindrical formulation.

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arXiv2014

Infall-Driven Protostellar Accretion and the Solution to the Luminosity Problem

We investigate the role of mass infall in the formation and evolution of protostars. To avoid ad hoc initial and boundary conditions, we consider the infall resulting self-consistently from modeling the formation of stellar clusters in turbulent molecular clouds. We show that infall rates in turbulent clouds are comparable to accretion rates inferred from protostellar luminosities or measured in pre-main-sequence stars. They should not be neglected in modeling the luminosity of protostars and the evolution of disks, even after the embedded protostellar phase. We find large variations of infall rates from protostar to protostar, and large fluctuations during the evolution of individuals protostars. In most cases, the infall rate is initially of order 10$^{-5}$\msun\ yr$^{-1}$, and may either decay rapidly in the formation of low-mass stars, or remain relatively large when more massive stars are formed. The simulation reproduces well the observed characteristic values and scatter of protostellar luminosities and matches the observed protostellar luminosity function. The luminosity problem is therefore solved once realistic protostellar infall histories are accounted for, with no need for extreme accretion episodes. These results are based on a simulation of randomly-driven magneto-hydrodynamic turbulence on a scale of 4pc, including self-gravity, adaptive-mesh refinement to a resolution of 50AU, and accreting sink particles. The simulation yields a low star formation rate, consistent with the observations, and a mass distribution of sink particles consistent with the observed stellar initial mass function during the whole duration of the simulation, forming nearly 1,300 sink particles over 3.2 Myr.

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arXiv2014

Turbulence-Induced Relative Velocity of Dust Particles III: The Probability Distribution

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau_p1 and tau_p2, of two particles of arbitrary sizes. The friction time of particles included in the simulation ranges from 0.1 tau_eta to 54T_L, with tau_eta and T_L the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau_p1, the PDF is the fattest for equal-size particles (tau_p2~tau_p1), and becomes thinner at both tau_p2 tau_p1. Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in 1/2 >T_L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanerary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.

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arXiv2014

Turbulence-Induced Relative Velocity of Dust Particles II: The Bidisperse Case

We extend our earlier work on turbulence-induced relative velocity between equal-size particles (Pan and Padoan, Paper I) to particles of arbitrarily different sizes. The Pan and Padoan (PP10) model shows that the relative velocity between different particles has two contributions, named the generalized shear and acceleration terms, respectively. The generalized shear term represents the particles' memory of the spatial flow velocity difference across the particle distance in the past, while the acceleration term is associated with the temporal flow velocity difference on individual particle trajectories. Using the simulation of Paper I, we compute the root-mean-square relative velocity, ^1/2, as a function of the friction times, tau_p1 and tau_p2, of the two particles, and show that the PP10 prediction is in satisfactory agreement with the data, confirming its physical picture. For a given tau_p1 below the Lagrangian correlation time of the flow, T_L, ^1/2 as a function of tau_p2 shows a dip at tau_p2~tau_p1, indicating tighter velocity correlation between similar particles. Defining a ratio f=tau_pl/tau_ph, with tau_pl and tau_ph the friction times of the smaller and larger particles, we find that ^1/2 increases with decreasing f due to the generalized acceleration contribution, which dominates at f<1/4. At a fixed f, our model predicts that ^1/2 scales as tau_ph^1/2 for tau_p,h in the inertial range of the flow, stays roughly constant for T_L >T_L/f. The acceleration term is independent of the particle distance, r, and thus reduces the r-dependence of ^1/2 in the bidisperse case.

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arXiv2013

The Star Formation Rate of Molecular Clouds

We review recent advances in the analytical and numerical modeling of the star formation rate in molecular clouds and discuss the available observational constraints. We focus on molecular clouds as the fundamental star formation sites, rather than on the larger-scale processes that form the clouds and set their properties. Molecular clouds are shaped into a complex filamentary structure by supersonic turbulence, with only a small fraction of the cloud mass channeled into collapsing protostars over a free-fall time of the system. In recent years, the physics of supersonic turbulence has been widely explored with computer simulations, leading to statistical models of this fragmentation process, and to the prediction of the star formation rate as a function of fundamental physical parameters of molecular clouds, such as the virial parameter, the rms Mach number, the compressive fraction of the turbulence driver, and the ratio of gas to magnetic pressure. Infrared space telescopes, as well as ground-based observatories have provided unprecedented probes of the filamentary structure of molecular clouds and the location of forming stars within them.

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arXiv2013

Turbulence-Induced Relative Velocity of Dust Particles I: Identical Particles

We study the relative velocity of inertial particles suspended in turbulent flows and discuss implications for dust particle collisions in protoplanetary disks. We simulate a weakly compressible turbulent flow, evolving 14 particle species with friction timescale, tau_p, covering the entire range of scales in the flow. The particle Stokes numbers, St, measuring the ratio of tau_p to the Kolmogorov timescale, are in the range from ~0.1 to ~800. Using simulation results, we show that the model by Pan & Padoan (PP10) gives satisfactory predictions for the rms relative velocity between identical particles. The probability distribution function (PDF) of the relative velocity is found to be highly non-Gaussian. The PDF tails are well described by a 4/3 stretched exponential function for particles with tau_p ~ 1-2 T_L, where T_L is the Lagrangian correlation timescale, consistent with a prediction based on PP10. The PDF approaches Gaussian only for very large particles with tau_p >~ 54 T_L. We split particle pairs at given distances into two types with low and high relative speeds, referred to as continuous and caustic types, respectively, and compute their contributions to the collision kernel. Although amplified by the effect of clustering, the continuous contribution vanishes in the limit of infinitesimal particle distance, where the caustic contribution dominates. The caustic kernel per unit cross section rises rapidly as St increases toward ~1, reaches a maximum at tau_p ~ 2 T_L, and decreases as tau_p^{-1/2} for tau_p >> T_L.

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arXiv2012

A Simple Law of Star Formation

We show that supersonic MHD turbulence yields a star formation rate (SFR) as low as observed in molecular clouds (MCs), for characteristic values of the free-fall time divided by the dynamical time, $t_{\rm ff}/t_{\rm dyn}$, the alfvénic Mach number, ${\cal M}_{\rm a}$, and the sonic Mach number, ${\cal M}_{\rm s}$. Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, $ε_{\rm ff}$, on the above parameters. Our main results are: i) $ε_{\rm ff}$ decreases exponentially with increasing $t_{\rm ff}/t_{\rm dyn}$, but is insensitive to changes in ${\cal M}_{\rm s}$, for constant values of $t_{\rm ff}/t_{\rm dyn}$ and ${\cal M}_{\rm a}$. ii) Decreasing values of ${\cal M}_{\rm a}$ (stronger magnetic fields) reduce $ε_{\rm ff}$, but only to a point, beyond which $ε_{\rm ff}$ increases with a further decrease of ${\cal M}_{\rm a}$. iii) For values of ${\cal M}_{\rm a}$ characteristic of star-forming regions, $ε_{\rm ff}$ varies with ${\cal M}_{\rm a}$ by less than a factor of two. We propose a simple star-formation law, based on the empirical fit to the minimum $ε_{\rm ff}$, and depending only on $t_{\rm ff}/t_{\rm dyn}$: $ε_{\rm ff} \approx ε_{\rm wind} \exp(-1.6 \,t_{\rm ff}/t_{\rm dyn})$. Because it only depends on the mean gas density and rms velocity, this law is straightforward to implement in simulations and analytical models of galaxy formation and evolution.

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