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 alfv\'{e}nic 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, $\epsilon_{\rm ff}$, on the above parameters. Our main results are: i) $\epsilon_{\rm ff}$ 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 $\epsilon_{\rm ff}$, but only to a point, beyond which $\epsilon_{\rm ff}$ increases with a further decrease of ${\cal M}_{\rm a}$. iii) For values of ${\cal M}_{\rm a}$ characteristic of star-forming regions, $\epsilon_{\rm ff}$ 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 $\epsilon_{\rm ff}$, and depending only on $t_{\rm ff}/t_{\rm dyn}$: $\epsilon_{\rm ff} \approx \epsilon_{\rm wind} \exp(-1.6 \,t_{\rm ff}/t_{\rm dyn})$. 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.Comment: ApJ Letters - in pres

The density variance -- Mach number relation in supersonic, isothermal turbulence

We examine the relation between the density variance and the mean-square Mach number in supersonic, isothermal turbulence, assumed in several recent analytic models of the star formation process. From a series of calculations of supersonic, hydrodynamic turbulence driven using purely solenoidal Fourier modes, we find that the `standard' relationship between the variance in the log of density and the Mach number squared, i.e., sigma^2_(ln rho/rhobar)=ln (1+b^2 M^2), with b = 1/3 is a good fit to the numerical results in the supersonic regime up to at least Mach 20, similar to previous determinations at lower Mach numbers. While direct measurements of the variance in linear density are found to be severely underestimated by finite resolution effects, it is possible to infer the linear density variance via the assumption of log-normality in the Probability Distribution Function. The inferred relationship with Mach number, consistent with sigma_(rho/rhobar) ~ b M with b=1/3, is, however, significantly shallower than observational determinations of the relationship in the Taurus Molecular Cloud and IC5146 (both consistent with b~ 0.5), implying that additional physics such as gravity is important in these clouds and/or that turbulent driving in the ISM contains a significant compressive component. Magnetic fields are not found to change this picture significantly, in general reducing the measured variances and thus worsening the discrepancy with observations.Comment: 5 pages, 4 figures, emulateapj. v2: accepted to ApJL, minor changes onl

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.Comment: Submitted to APJ Letters on September 22, 2009 - Accepted on November 18, 200

Towards deterministic subspace identification for autonomous nonlinear systems

The problem of identifying deterministic autonomous linear and nonlinear systems is studied. A specific version of the theory of deterministic subspace identification for discrete-time autonomous linear systems is developed in continuous time. By combining the subspace approach to linear identification and the differential-geometric approach to nonlinear control systems, a novel identification framework for continuous-time autonomous nonlinear systems is developed

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 $P(\rho) \propto \rho^{-1.67}$ and $P(B)\propto B^{-2.74}$. A power law is also found between magnetic field strength and density, with $B\propto \rho^{0.48}$, 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.Comment: 9 pages, 10 figures (3 color). Submitted to the Astrophysical Journa

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

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.Comment: ApJ Letters, accepte