Search

We obtain two equations (following from two different approaches) for the density profile in a self-gravitating polytropic cylindrically symmetric and rotating turbulent gas disk. The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state of the gas changes from isothermal (in the outer cloud layers) to one of "hard polytrope", and the symmetry changes from spherical to cylindrical. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation describes the balance of the kinetic, thermal and gravitational energy of a fluid element. We also introduce a method for approximating density profile solutions (in a power-law form), leading to the emergence of three different regimes. We apply, as well, dynamical analysis of the motion of a fluid element. Only one of the regimes is in accordance with the two approaches (energy and force balance). It corresponds to a density profile of a slope -2, polytropic exponent 3/2, and sub-Keplerian rotation of the disk, when the gravity is balanced by the thermal pressure. It also matches with some observations and numerical works and, in particular, leads to a second power-law tail (of a slope approx. -1) of the density distribution function in dense, self-gravitating cloud regions., Comment: 11 pages, 1 figure

In the present work we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov \& Stefanov in two previous papers, clarifying some aspects of turbulence and extending the model to account not only for supersonic flows but for trans- and subsonic ones as well. Make use of the Eulerian virial theorem at an arbitrary scale, far from the cloud core, we derive an equation for the density profile and solve it in approximate way. The result confirms the solution $\varrho(\ell)=\ell^{-2}$ found in the previous papers. This solution corresponds to three possible configurations for the energy balance. For trans- or subsonic flows, we obtain a balance between the gravitational and thermal energy (Case 1) or between the gravitational, turbulent and thermal energies (Case 2) while for supersonic flows, the possible balance is between the gravitational and turbulent energy (Case 3). In Cases 1 and 2 the energy of the fluid element can be negative or zero end thus the solution is dynamically stable and shall be long lived. In Case 3 the energy of the fluid element is positive or zero, i.e., the solution is unstable or at best marginally bound. At scales near the core, one cannot neglect the second derivative of the moment of inertia of the gas, which prevents derivation of an analytic equation for the density profile. However, we obtain that gas near the core is not virialized and its state is marginally bound since the energy of the fluid element vanishes., Comment: 12 pages, no figures; accepted for publication in MNRAS

We obtain an equation for the density profile in a self-gravitating polytropic spherically symmetric turbulent fluid with an equation of state $p_{\rm gas}\propto \rho^\Gamma$. This is done in the framework of ensembles of molecular clouds represented by single abstract objects as introduced by Donkov et al. (2017). The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state changes from isothermal (in the outer cloud layers) with $\Gamma=1$ to one of `hard polytrope' with exponent $\Gamma>1$. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation reproduces the Bernoulli equation for the proposed model and describes the balance of the kinetic, thermal and gravitational energy of a fluid element. We propose as well a method to obtain approximate solutions in a power-law form which results in four solutions corresponding to different density profiles, polytropic exponents and energy balance equations for a fluid element. One of them, a density profile with slope $-3$ and polytropic exponent $\Gamma=4/3$, matches with observations and numerical works and, in particular, leads to a second power-law tail of the density distribution function in dense, self-gravitating cloud regions., Comment: 10 pages, 1 figure; accepted for publication in MNRAS

The mass function of clumps observed in molecular clouds raises interesting theoretical issues, especially in its relation to the stellar initial mass function. We propose a statistical model of the mass function of prestellar cores (CMF), formed in self-gravitating isothermal clouds at a given stage of their evolution. The latter is characterized by the mass-density probability distribution function ($\rho$-PDF), which is a power-law with slope $q$. The variety of MCs is divided in ensembles according to the PDF slope and each ensemble is represented by a single spherical cloud. The cores are considered as elements of self-similar structure typical for fractal clouds and are modeled by spherical objects populating each cloud shell. Our model assumes relations between size, mass and density of the statistical cores. Out of them a core mass-density relationship $\rho\propto m^x$ is derived where $x=1/(1+q)$. We found that $q$ determines the existence or non-existence of a threshold density for core collapse. The derived general CMF is a power law of slope $-1$ while the CMF of gravitationally unstable cores has a slope $(-1 + x/2)$, comparable with the slopes of the high-mass part of the stellar initial mass function and of observational CMFs., Comment: 12 pages, 5 figures; to appear in A&A

Recently Stanchev et al. (2015) proposed a technique to derive density scaling relations in a star-forming region from analysis of the probability distribution function of column density. We address the possible dependence of the outcome on the selection of probe zones, applying the method to Planck dust-opacity data on Orion A. The derived steep scaling relation of mean density with index -1.6 in the molecular cloud (so called `Central filament') points to its self-gravitating nature. The result is reproduced also for large parts of the clouds' vicinity which indicates major role of gravity in the energy balance of the entire star-forming region., Comment: 9 pages, 5 figures, A talk, presented at the 10th Serbian-Bulgarian Astronomical Conference, Belgrade, Serbia, May 30 - June 3, 2016