arXiv subjects

Paolo Padoan

Publications and source records attributed to Paolo Padoan.

At least 73 records · Page 4Linked to original sources

arXiv2007

The Statistics of Supersonic Isothermal Turbulence

We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We discuss numerical resolution issues and demonstrate convergence, in a statistical sense, of the inertial range dynamics in simulations on grids larger than 512^3 points. The simulations allowed us to measure the absolute velocity scaling exponents for the first time. The inertial range velocity scaling in this strongly compressible regime deviates substantially from the incompressible Kolmogorov laws. The slope of the velocity power spectrum, for instance, is -1.95 compared to -5/3 in the incompressible case. The exponent of the third-order velocity structure function is 1.28, while in incompressible turbulence it is known to be unity. We propose a natural extension of Kolmogorov's phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the Kolmogorov scaling of the power spectrum and structure functions of the density-weighted velocity v=ρ^{1/3}u. The low-order statistics of v appear to be invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of v is -1.69, and the exponent of the third-order structure function of v is unity. We also directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m = 2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.

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arXiv2007

Scaling Laws and Intermittency in Highly Compressible Turbulence

We use large-scale three-dimensional simulations of supersonic Euler turbulence to study the physics of a highly compressible cascade. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We find that the inertial range velocity scaling deviates strongly from the incompressible Kolmogorov laws. We propose an extension of Kolmogorov's K41 phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that low-order statistics of 'v' are invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69 and the third-order structure function of 'v' scales linearly with separation. We directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m=2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.

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arXiv2007

Two regimes of Turbulent Fragmentation and the stellar IMF from Primordial to Present Day Star Formation

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.

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arXiv2006

The Power Spectrum of Supersonic Turbulence in Perseus

We test a method of estimating the power spectrum of turbulence in molecular clouds based on the comparison of power spectra of integrated intensity maps and single-velocity-channel maps, suggested by Lazarian and Pogosyan. We use synthetic 13CO data from non-LTE radiative transfer calculations based on density and velocity fields of a simulation of supersonic hydrodynamic turbulence. We find that the method yields the correct power spectrum with good accuracy. We then apply the method to the Five College Radio Astronomy Observatory 13CO map of the Perseus region, from the COMPLETE website. We find a power law power spectrum with slope beta=1.81+-0.10. The values of beta as a function of velocity resolution are also confirmed using the lower resolution map of the same region obtained with the AT&T Bell Laboratories antenna. Because of its small uncertainty, this result provides a useful constraint for numerical codes used to simulate molecular cloud turbulence.

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arXiv2006

High Resolution Simulations of Supersonic Turbulence in Molecular Clouds

We present the results of three-dimensional simulations of supersonic Euler turbulence with grid resolutions up to 1024^3 points. Our numerical experiments describe nonmagnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We demonstrate that the inertial range scaling properties of turbulence in this strongly compressible regime deviate substantially from a Kolmogorov-like behavior previously recovered for mildly compressible transonic flows.

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arXiv2006

Can We Trust the Dust? Evidence of Dust Segregation in Molecular Clouds

Maps of estimated dust column density in molecular clouds are usually assumed to reliably trace the total gas column density structure. In this work we present results showing a clear discrepancy between the dust and the gas distribution in the Taurus molecular cloud complex. We compute the power spectrum of a 2MASS extinction map of the Taurus region and find it is much shallower than the power spectrum of a 13CO map of the same region previously analyzed. This discrepancy may be explained as the effect of grain growth on the grain extinction efficiency. However, this would require a wide range of maximum grain sizes, which is ruled out based on constraints from the extinction curve and the available grain models. We show that major effects due to CO formation and depletion are also ruled out. Our result may therefore suggest the existence of intrinsic spatial fluctuations of the dust to gas ratio, with amplitude increasing toward smaller scales. Preliminary results of numerical simulations of trajectories of inertial particles in turbulent flows illustrate how the process of clustering of dust grains by the cloud turbulence may lead to observable effects. However, these results cannot be directly applied to large scale supersonic and magnetized turbulence at present.

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arXiv2006

Current Advances in the Methodology and Computational Simulation of the Formation of Low-Mass Stars

Developing a theory of low-mass star formation ($\sim 0.1$ to 3~M$_{\odot}$) remains one of the most elusive and important goals of theoretical astrophysics. The star-formation process is the outcome of the complex dynamics of interstellar gas involving non-linear interactions of turbulence, gravity, magnetic field and radiation. The evolution of protostellar condensations, from the moment they are assembled by turbulent flows to the time they reach stellar densities, spans an enormous range of scales, resulting in a major computational challenge for simulations. Since the previous Protostars and Planets conference, dramatic advances in the development of new numerical algorithmic techniques have been successfully implemented on large scale parallel supercomputers. Among such techniques, Adaptive Mesh Refinement and Smooth Particle Hydrodynamics have provided frameworks to simulate the process of low-mass star formation with a very large dynamic range. It is now feasible to explore the turbulent fragmentation of molecular clouds and the gravitational collapse of cores into stars self-consistently within the same calculation. The increased sophistication of these powerful methods comes with substantial caveats associated with the use of the techniques and the interpretation of the numerical results. In this review, we examine what has been accomplished in the field and present a critique of both numerical methods and scientific results. We stress that computational simulations should obey the available observational constraints and demonstrate numerical convergence. Failing this, results of numerical simulations do not advance our understanding of low-mass star formation.

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arXiv2005

High Resolution Mapping of Interstellar Clouds by Near--IR Scattering

We discuss the possibility of mapping interstellar clouds at unprecedentedly high spatial resolution by means of near-IR imaging of their scattered light. We calculate the scattering of the interstellar radiation field by a cloud model obtained from the simulation of a supersonic turbulent flow. Synthetic maps of scattered light are computed in the J, H and K bands and are found to allow an accurate estimate of column density, in the range of visual extinction between 1 and 20 magnitudes. We provide a formalism to convert the intensity of scattered light at these near-IR bands into a total gas column density. We also show that this new method of mapping interstellar clouds is within the capability of existing near-IR facilities, which can achieve a spatial resolution of up to ~ 0.1 arcsec. This opens new perspectives in the study of interstellar dust and gas structure on very small scales. The validity of the method has been recently demonstrated by the extraordinary images of the Perseus region obtained by Foster & Goodman (2005), which motivated this investigation.

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arXiv2005

Adaptive Mesh Refinement for Supersonic Molecular Cloud Turbulence

We performed a series of three-dimensional numerical simulations of supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 1024^3 zones. Our experiments describe non-magnetized driven supersonic turbulent flows with an isothermal equation of state. Mesh refinement on shocks and shear is implemented to cover dynamically important structures with the highest resolution subgrids and calibrated to match the turbulence statistics obtained from the equivalent uniform grid simulations. We found that at a level of resolution slightly below 512^3, when a sufficient integral/dissipation scale separation is first achieved, the fraction of the box volume covered by the AMR subgrids first becomes smaller than unity. At the higher AMR levels subgrids start covering smaller and smaller fractions of the whole volume, which scale with the Reynolds number as Re^{-1/4}. We demonstrate the consistency of this scaling with a hypothesis that the most dynamically important structures in intermittent supersonic turbulence are strong shocks with a fractal dimension of two. We show that turbulence statistics derived from AMR simulations and simulations performed on uniform grids agree surprisingly well, even though only a fraction of the volume is covered by AMR subgrids. Based on these results, we discuss the signature of dissipative structures in the statistical properties of supersonic turbulence and their role in overall flow dynamics.

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arXiv2005

Confinement-Driven Spatial Variations in the Cosmic Ray Flux

Low-energy cosmic rays (CRs) are confined by self-generated MHD waves in the mostly neutral ISM. We show that the CR transport equation can be expressed as a continuity equation for the CR number density involving an effective convection velocity. Assuming balance between wave growth and ion-neutral damping, this equation gives a steady-state condition n_cr ~ n_i^1/2 up to a critical density for free streaming. This relation naturally accounts for the heretofore unexplained difference in CR ionization rates derived for dense diffuse clouds (McCall et al. 2003) and dark clouds, and predicts large spatial variations in the CR heating rate and pressure.

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arXiv2005

A Solution to the Protostellar Accretion Problem

Accretion rates of order 10^-8 M_\odot/yr are observed in young protostars of approximately a solar mass with evidence of circumstellar disks. The accretion rate is significantly lower for protostars of smaller mass, approximately proportional to the second power of the stellar mass, \dot{M}_accr\propto M^2. The traditional view is that the observed accretion is the consequence of the angular momentum transport in isolated protostellar disks, controlled by disk turbulence or self--gravity. However, these processes are not well understood and the observed protostellar accretion, a fundamental aspect of star formation, remains an unsolved problem. In this letter we propose the protostellar accretion rate is controlled by accretion from the large scale gas distribution in the parent cloud, not by the isolated disk evolution. Describing this process as Bondi--Hoyle accretion, we obtain accretion rates comparable to the observed ones. We also reproduce the observed dependence of the accretion rate on the protostellar mass. These results are based on realistic values of the ambient gas density and velocity, as inferred from numerical simulations of star formation in self--gravitating turbulent clouds.

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arXiv2004

Brown Dwarfs from Turbulent Fragmentation

The origin of brown dwarfs (BDs) is an important component of the theory of star formation, because BDs are approximately as numerous as solar mass stars. It has been suggested that BDs originate from the gravitational fragmentation of protostellar disks, a very different mechanism from the formation of hydrogen burning stars. We propose that BDs are instead formed by the process of turbulent fragmentation, like more massive stars. In numerical simulations of turbulence and star formation we find that gravitationally unstable density peaks of BD mass are commonly formed by the turbulent flow. These density peaks collapse into BD mass objects with circumstellar disks, like more massive protostars. We rely on numerical experiments with very large resolution, achieved with adaptive mesh refinement (AMR). The turbulence simulation presented here is the first AMR turbulence experiment ever attempted and achieves an effective resolution of 1024^3 computational zones. The star formation simulation achieves an effective resolution of (10^6)^3 computational zones, from a cloud size of 5pc to protostellar disks resolved down to 1AU.

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arXiv2004

The Stellar IMF as a Property of Turbulence

We propose to interpret the stellar IMF as a property of the turbulence in the star--forming gas. Gravitationally unstable density enhancements in the turbulent flow collapse and form stars. Their mass distribution can be derived analytically from the power spectrum of the turbulent flow and the isothermal shock jump conditions in the magnetized gas. For a power spectrum index β=1.74, consistent with Larson's velocity dispersion--size relation as well as with new numerical and analytic results on supersonic turbulence, we obtain a power law mass distribution of dense cores with a slope equal to 3/(4-β)=1.33, consistent with the slope of Salpeter's stellar IMF. Below one solar mass, the mass distribution flattens and turns around at a fraction of a solar mass, as observed for the stellar IMF in a number of stellar clusters, because only the densest cores are gravitationally unstable. The mass distribution at low masses is determined by the Log--Normal distribution of the gas density. The intermittent nature of this distribution is responsible for the generation of a significant number of collapsing cores of brown dwarf mass.

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arXiv2004

The "Mysterious" Origin of Brown Dwarfs

Hundreds of brown dwarfs (BDs) have been discovered in the last few years in stellar clusters and among field stars. BDs are almost as numerous as hydrogen burning stars and so a theory of star formation should also explain their origin. The ``mystery'' of the origin of BDs is that their mass is two orders of magnitude smaller than the average Jeans' mass in star--forming clouds, and yet they are so common. In this work we investigate the possibility that gravitationally unstable protostellar cores of BD mass are formed directly by the process of turbulent fragmentation. Supersonic turbulence in molecular clouds generates a complex density field with a very large density contrast. As a result, a fraction of BD mass cores formed by the turbulent flow are dense enough to be gravitationally unstable. We find that with density, temperature and rms Mach number typical of cluster--forming regions, turbulent fragmentation can account for the observed BD abundance.

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arXiv2004

Electron Abundance in Protostellar Cores

The determination of the fractional electron abundance, Xe, in protostellar cores relies on observations of molecules, such as DCO+, H13CO+ and CO, and on chemical models to interpret their abundance. Studies of protostellar cores have revealed significant variations of Xe from core to core within a range 10^-8<Xe<10^-6. The physical origin of these large variations in Xe is not well understood, unless unlikely variations in the cosmic ray ionization rate or ad hoc values of metal depletion are assumed. In this work we explore other potential causes of these variations in Xe, including core age, extinction and density. We compute numerically the intensity of the radiation field within a density distribution generated by supersonic turbulence. Taking into account the lines of sight in all directions, the effective visual extinction in dense regions is found to be always much lower than the extinction derived from the column density along a fixed line of sight. Dense cores with volume and column densities comparable to observed protostellar cores have relatively low mass-averaged visual extinction, 2mag <= A_V <= 5mag, such that photo-ionization can sometimes be as important as cosmic ray ionization. Chemical models, including gas-grain chemistry and time dependent gas depletion and desorption, are computed for values of visual extinction in the range 2mag <= A_V <= 6mag, and for a hydrogen gas density of 10^4cm^-3$, typical of protostellar cores. The models presented here can reproduce some of the observed variations of ion abundance from core to core as the combined effect of visual extinction and age variations. The range of electron abundances predicted by the models is relatively insenstive to density over 10^4 to 10^6 cm^{-3}.

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arXiv2004

Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence

Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this letter we propose a unified approach for obtaining the velocity scaling in compressible and super--Alfvénic turbulence, valid for arbitrary sonic Mach number, \ms. We demonstrate with numerical simulations that the scaling can be described with the She--Lévêque formalism, where only one parameter, interpreted as the Hausdorff dimension of the most intense dissipative structures, needs to be varied as a function of \ms. Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations.

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arXiv2004

Synthetic stellar populations: single stellar populations, stellar interior models and primordial proto-galaxies

We present a new set of stellar interior and synthesis models for predicting the integrated emission from stellar populations in star clusters and galaxies of arbitrary age and metallicity. This work differs from existing spectral synthesis codes in a number of important ways, namely (1) the incorporation of new stellar evolutionary tracks, with sufficient resolution in mass to sample rapid stages of stellar evolution; (2) a physically consistent treatment of evolution in the HR diagram, including the approach to the main sequence and the effects of mass loss on the giant and horizontal-branch phases. Unlike several existing models, ours yield consistent ages when used to date a coeval stellar population from a wide range of spectral features and colour indexes. We rigorously discuss degeneracies in the age-metallicity plane and show that inclusion of spectral features blueward of 4500 AA, suffices to break any remaining degeneracy and that with moderate S/N spectra (10 per 20AA, resolution element) age and metallicity are not degenerate. We also study sources of systematic errors in deriving the age of a single stellar population and conclude that they are not larger than 10-15%. We illustrate the use of single stellar populations by predicting the colors of primordial proto-galaxies and show that one can first find them and then deduce the form of the IMF for the early generation of stars in the universe. Finally, we provide accurate analytic fitting formulas for ultra fast computation of colors of single stellar populations. The models can be found at http://www.physics.upenn.edu/~raulj

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arXiv2004

The Average Magnetic Field Strength in Molecular Clouds: New Evidence of Super-Alfvenic Turbulence

The magnetic field strength in molecular clouds is a fundamental quantity for theories of star formation. It is estimated by Zeeman splitting measurements in a few dense molecular cores, but its volume--averaged value within large molecular clouds (over several parsecs) is still uncertain. In this work we provide a new method to constrain the average magnetic field strength in molecular clouds. We compare the power spectrum of gas density of molecular clouds with that of two $350^3$ numerical simulations of supersonic MHD turbulence. The numerical simulation with approximate equipartition of kinetic and magnetic energies (model A) yields the column density power spectrum $P(k)\propto k^{-2.25\pm 0.01}$, the super--Alfvénic simulation (model B) $P(k)\propto k^{-2.71\pm 0.01}$. The column density power spectrum of the Perseus, Taurus and Rosetta molecular cloud complexes is found to be well approximated by a power law, $P_{\rm o}(k)\propto k^{-a}$, with $a=2.74\pm 0.07$, $2.74\pm 0.08$ and $2.76\pm 0.08$ respectively. We conclude that the observations are consistent with the presence of super--Alfvénic turbulence in molecular clouds (model B) while model A is inconsistent (more than 99% confidence) with the observations.

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