Inefficient star formation through turbulence, magnetic fields and feedback

Star formation is inefficient. Only a few percent of the available gas in molecular clouds forms stars, leading to the observed low star formation rate (SFR). The same holds when averaged over many molecular clouds, such that the SFR of whole galaxies is again surprisingly low. Indeed, considering the low temperatures, molecular clouds should be highly gravitationally unstable and collapse on their global mean freefall timescale. And yet, they are observed to live about 10-100 times longer, i.e., the SFR per freefall time (SFR_ff) is only a few percent. Thus, other physical mechanisms must counteract the quick global collapse. Turbulence, magnetic fields and stellar feedback have been proposed as regulating agents, but it is still unclear which of these processes is the most important and what their relative contributions are. Here we run high-resolution simulations including gravity, turbulence, magnetic fields, and jet/outflow feedback. We confirm that clouds collapse on a mean freefall time, if only gravity is considered, producing stars at an unrealistic rate. In contrast, if turbulence, magnetic fields, and feedback are included step-by-step, the SFR is reduced by a factor of 2-3 with each additional physical ingredient. When they all act in concert, we find a constant SFR_ff = 0.04, currently the closest match to observations, but still about a factor of 2-4 higher than the average. A detailed comparison with other simulations and with observations leads us to conclude that only models with turbulence producing large virial parameters, and including magnetic fields and feedback can produce realistic SFRs.Comment: 9 pages, 3 figures, MNRAS, in press, movies available: http://www.mso.anu.edu.au/~chfeder/pubs/ineff_sf/ineff_sf.html, see also astrobite article: http://astrobites.org/2015/04/28/why-is-star-formation-so-inefficient

The origin of physical variations in the star formation law

Observations of external galaxies and of local star-forming clouds in the Milky Way have suggested a variety of star formation laws, i.e., simple direct relations between the column density of star formation (Sigma_SFR: the amount of gas forming stars per unit area and time) and the column density of available gas (Sigma_gas). Extending previous studies, we show that these different, sometimes contradictory relations for Milky Way clouds, nearby galaxies, and high-redshift discs and starbursts can be combined in one universal star formation law in which Sigma_SFR is about 1% of the local gas collapse rate, Sigma_gas/t_ff, but a significant scatter remains in this relation. Using computer simulations and theoretical models, we find that the observed scatter may be primarily controlled by physical variations in the Mach number of the turbulence and by differences in the star formation efficiency. Secondary variations can be induced by changes in the virial parameter, turbulent driving and magnetic field. The predictions of our models are testable with observations that constrain both the Mach number and the star formation efficiency in Milky Way clouds, external disc and starburst galaxies at low and high redshift. We also find that reduced telescope resolution does not strongly affect such measurements when Sigma_SFR is plotted against Sigma_gas/t_ff.Comment: Published December 21, 2013 in MNRAS 436 (4): 3167-317

The density structure and star formation rate of non-isothermal polytropic turbulence

The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths, and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, P~rho^Gamma, T~rho^(Gamma-1). We use grid resolutions of 2048^3 cells and compare polytropic exponents Gamma=0.7 (soft EOS), Gamma=1 (isothermal EOS), and Gamma=5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for Gamma<1, while Gamma>1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for Gamma>1. In contrast, the PDF becomes closer to a lognormal distribution for Gamma<=1. We derive and test a new density variance - Mach number relation that takes Gamma into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of Gamma and find that it decreases by a factor of ~5 from Gamma=0.7 to Gamma=5/3.Comment: 18 pages, 10 figures, MNRAS accepted, simulation movies at http://www.mso.anu.edu.au/~chfeder/pubs/polytropic/polytropic.htm

The Star Formation Rate of Turbulent Magnetized Clouds: Comparing Theory, Simulations, and Observations

We derive and compare six theoretical models for the star formation rate (SFR) - the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle & Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC - all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields, and show that the SFR depends on four basic parameters: (1) virial parameter alpha_vir; (2) sonic Mach number M; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma beta=2(M_A/M)^2 with the Alfven Mach number M_A. We compare all six theories with MHD simulations, covering cloud masses of 300 to 4x10^6 solar masses and Mach numbers M = 3 to 50 and M_A = 1 to infinity, with solenoidal (b=1/3), mixed (b=0.4) and compressive turbulent (b=1) forcings. We find that the SFR increases by a factor of four between M=5 and 50 for compressive forcing and alpha_vir~1. Comparing forcing parameters, we see that the SFR is more than 10x higher with compressive than solenoidal forcing for Mach 10 simulations. The SFR and fragmentation are both reduced by a factor of two in strongly magnetized, trans-Alfvenic turbulence compared to hydrodynamic turbulence. All simulations are fit simultaneously by the multi-freefall KM and multi-freefall PN theories within a factor of two over two orders of magnitude in SFR. The simulated SFRs cover the range and correlation of SFR column density with gas column density observed in Galactic clouds, and agree well for star formation efficiencies SFE = 1% to 10% and local efficiencies epsilon = 0.3 to 0.7 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.Comment: 34 pages, 12 figures, ApJ in press, movies at http://www.ita.uni-heidelberg.de/~chfeder/pubs/sfr/sfr.shtm

The role of turbulence during the formation of circumbinary discs

Most stars form in binaries and the evolution of their discs remains poorly understood. To shed light on this subject, we carry out 3D ideal MHD simulations with the AMR code FLASH of binary star formation for separations of $10-20\,\mathrm{AU}$. We run a simulation with no initial turbulence (NT), and two with turbulent Mach numbers of $\mathcal{M} = \sigma_v/c_s = 0.1$ and $0.2$ (T1 and T2) for $5000\,\mathrm{yr}$ after protostar formation. By the end of the simulations the circumbinary discs in NT and T1, if any, have radii of $\lesssim20\,\mathrm{AU}$ with masses $\lesssim0.02\,\mathrm{M}_\odot$, while T2 hosts a circumbinary disc with radius $\sim70-80\,\mathrm{AU}$ and mass $\sim0.12\,\mathrm{M}_\odot$. These circumbinary discs formed from the disruption of circumstellar discs and harden the binary orbit. Our simulated binaries launch large single outflows. We find that NT drives the most massive outflows, and also removes large quantities of linear and angular momentum. T2 produces the least efficient outflows concerning mass, momentum and angular momentum ($\sim$61 per cent, $\sim$71 per cent, $\sim$68 per cent of the respective quantities in NT). We conclude that while turbulence helps to build circumbinary discs which organise magnetic fields for efficient outflow launching, too much turbulence may also disrupt the ordered magnetic field structure required for magneto-centrifugal launching of jets and outflows. We also see evidence for episodic accretion during the binary star evolution. We conclude that the role of turbulence in building large circumbinary discs may explain some observed very old ($>10\,\mathrm{Myr}$) circumbinary discs. The longer lifetime of circumbinary discs may increase the likelihood of planet formation.Comment: Accepted to MNRAS. 17 pages, 11 figures. arXiv admin note: text overlap with arXiv:1705.0815

On the Star Formation Efficiency of Turbulent Magnetized Clouds

We study the star formation efficiency (SFE) in simulations and observations of turbulent, magnetized, molecular clouds. We find that the probability density functions (PDFs) of the density and the column density in our simulations with solenoidal, mixed, and compressive forcing of the turbulence, sonic Mach numbers of 3-50, and magnetic fields in the super- to the trans-Alfvenic regime, all develop power-law tails of flattening slope with increasing SFE. The high-density tails of the PDFs are consistent with equivalent radial density profiles, rho ~ r^(-kappa) with kappa ~ 1.5-2.5, in agreement with observations. Studying velocity-size scalings, we find that all the simulations are consistent with the observed v ~ l^(1/2) scaling of supersonic turbulence, and seem to approach Kolmogorov turbulence with v ~ l^(1/3) below the sonic scale. The velocity-size scaling is, however, largely independent of the SFE. In contrast, the density-size and column density-size scalings are highly sensitive to star formation. We find that the power-law slope alpha of the density power spectrum, P(rho,k) ~ k^alpha, or equivalently the Delta-variance spectrum of column density, DV(Sigma,l) ~ l^(-alpha), switches sign from alpha 0 when star formation proceeds (SFE > 0). We provide a relation to compute the SFE from a measurement of alpha. Studying the literature, we find values ranging from alpha = -1.6 to +1.6 in observations covering scales from the large-scale atomic medium, over cold molecular clouds, down to dense star-forming cores. From those alpha values, we infer SFEs and find good agreement with independent measurements based on young stellar object (YSO) counts, where available. Our SFE-alpha relation provides an independent estimate of the SFE based on the column density map of a cloud alone, without requiring a priori knowledge of star-formation activity or YSO counts.Comment: 23 pages, 14 figures, ApJ in press, more info at http://www.ita.uni-heidelberg.de/~chfeder/pubs/sfe/sfe.shtml?lang=e

A Fluid-Dynamical Subgrid Scale Model for Highly Compressible Astrophysical Turbulence

We formulate and implement the Euler equations with SGS dynamics and provide numerical tests of an SGS turbulence energy model that predicts the turbulent pressure of unresolved velocity fluctuations and the rate of dissipation for highly compressible turbulence. We test closures for the turbulence energy cascade by filtering data from high-resolution simulations of forced isothermal and adiabatic turbulence. Optimal properties and an excellent correlation are found for a linear combination of the eddy-viscosity closure that is employed in LES of weakly compressible turbulence and a term that is non-linear in the Jacobian matrix of the velocity. Using this mixed closure, the SGS turbulence energy model is validated in LES of turbulence with stochastic forcing. It is found that the SGS model satisfies several important requirements: 1. The mean SGS turbulence energy follows a power law for varying grid scale. 2. The root mean square (RMS) Mach number of the unresolved velocity fluctuations is proportional to the RMS Mach number of the resolved turbulence, independent of the forcing. 3. The rate of dissipation and the turbulence energy flux are constant. Moreover, we discuss difficulties with direct estimates of the turbulent pressure and the dissipation rate on the basis of resolved flow quantities that have recently been proposed. In combination with the energy injection by stellar feedback and other unresolved processes, the proposed SGS model is applicable to a variety of problems in computational astrophysics. Computing the SGS turbulence energy, the treatment of star formation and stellar feedback in galaxy simulations can be improved. Further, we expect that the turbulent pressure on the grid scale affects the stability of gas against gravitational collapse.Comment: 19 pages, 16 figures, submitted to A&

An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds

We introduce a new method for observationally estimating the fraction of momentum density (${\rho}{\mathbf{v}}$) power contained in solenoidal modes (for which $\nabla \cdot {\rho}{\mathbf{v}} = 0$) in molecular clouds. The method is successfully tested with numerical simulations of supersonic turbulence that produce the full range of possible solenoidal/compressible fractions. At present the method assumes statistical isotropy, and does not account for anisotropies caused by (e.g.) magnetic fields. We also introduce a framework for statistically describing density--velocity correlations in turbulent clouds.Comment: 20 pages, 13 figures, accepted for publication in MNRA