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Register a new userThe Role of Gravity in Producing Power-Law Mass Functions
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Aleksandra Kuznetsova
Publication date
2018
fields
Physics
and research's language is
English
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Numerical simulations of star formation have found that a power-law mass function can develop at high masses. In a previous paper, we employed isothermal simulations which created large numbers of sinks over a large range in masses to show that the power law exponent of the mass function, $dN/dlog M propto M^{Gamma}$, asymptotically and accurately approaches $Gamma = -1.$ Simple analytic models show that such a power law can develop if the mass accretion rate $dot{M} propto M^2$, as in Bondi-Hoyle accretion; however, the sink mass accretion rates in the simulations show significant departures from this relation. In this paper we show that the expected accretion rate dependence is more closely realized provided the gravitating mass is taken to be the sum of the sink mass and the mass in the near environment. This reconciles the observed mass functions with the accretion rate dependencies, and demonstrates that power-law upper mass functions are essentially the result of gravitational focusing, a mechanism present in, for example, the competitive accretion model.
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We introduce a new multi-power-law distribution for the Initial Mass Function (IMF) to explore its potential properties. It follows on prior work that introduced mechanisms accounting for mass accretion in star formation, developed within the framework of general evolution equations for the mass distribution of accreting and non-accreting (proto)stars. This paper uses the same fundamental framework to demonstrate that the interplay between a mass-dependent and a time-dependent step-like dropout rate from accretion leads to IMFs that exhibit multiple power laws for an exponential mass growth. While the mass-dependent accretion and its dropout is intrinsic to each star, the time-dependent dropout might be tied to a specific history such as the rapid consumption of nebular material by nearby stars or the sweeping away of some material by shock waves. The time-dependent dropout folded into the mass-dependent process of star formation is shown to have a significant influence on the IMFs.
We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a combination of the Navier-Stokes continuity equations for the fluid motions and the Poisson equation for the gravity. It extends upon previous approaches first by including gravity, second by considering the PDF as a dynamical system, not a stationary one. We derive the transport equations of the density PDF, characterize its evolution and determine the density threshold above which gravity strongly affects and eventually dominates the dynamics of turbulence. We demonstrate the occurence of {it two} power law tails in the PDF, with two characteristic exponents, corresponding to two different stages in the balance between turbulence and gravity. Another important result of this study is to provide a procedure to relate the observed {it column density} PDFs to the corresponding {it volume density} PDFs. This allows to infer, from the observation of column-densities, various physical parameters characterizing molecular clouds, notably the virial parameter. Furthermore, the theory offers the possibility to date the clouds in units of ${t}_{rm coll}$, the time since a statistically significant fraction of the cloud started to collapse. The theoretical results and diagnostics reproduce very well numerical simulations and observations of star-forming clouds. The theory provides a sound theoretical foundation and quantitative diagnostics to analyze observations or numerical simulations of star-forming regions and to characterize the evolution of the density PDF in various regions of molecular clouds.
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We study the star formation (SF) law in 12 Galactic molecular clouds with ongoing high-mass star formation (HMSF) activity, as traced by the presence of a bright IRAS source and other HMSF tracers. We define the molecular cloud (MC) associated to each IRAS source using 13CO line emission, and count the young stellar objects (YSOs) within these clouds using GLIMPSE and MIPSGAL 24 micron Spitzer databases.The masses for high luminosity YSOs (Lbol>10~Lsun) are determined individually using Pre Main Sequence evolutionary tracks and the evolutionary stages of the sources, whereas a mean mass of 0.5 Msun was adopted to determine the masses in the low luminosity YSO population. The star formation rate surface density (sigsfr) corresponding to a gas surface density (siggas) in each MC is obtained by counting the number of the YSOs within successive contours of 13CO line emission. We find a break in the relation between sigsfr and siggas, with the relation being power-law (sigsfr ~ siggas^N) with the index N varying between 1.4 and 3.6 above the break. The siggas at the break is between 150-360 Msun/pc^2 for the sample clouds, which compares well with the threshold gas density found in recent studies of Galactic star-forming regions. Our clouds treated as a whole lie between the Kennicutt (1998) relation and the linear relation for Galactic and extra-galactic dense star-forming regions. We find a tendency for the high-mass YSOs to be found preferentially in dense regions at densities higher than 1200 Msun/pc^2 (~0.25 g/cm^2).
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