Theoretical Distribution of Substance Density in Protoplanetary Disk at the Pre-Solar Stage of it's Evolution

Details Theoretical Distribution of Substance Density in Protoplanetary Disk at the Pre-Solar Stage of it's Evolution Theoretical Distribution of Substance Density in Protoplanetary Disk at the Pre-Solar Stage of it's Evolution

Aug 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006iaujd..11e..17b&link_type=abstract

Pre-Solar Grains as Astrophysical Tools, 26th meeting of the IAU, Joint Discussion 11, 21 August 2006, Prague, Czech Republic, J

Astronomy and Astrophysics

Astrophysics

Scientific paper

Now some different models of density distribution in a protoplanetary disk (at the next stage after accretion of protostellar cloud) are reviewing. However, proper theoretical description of distribution law is not still exist. A derivation of formula for stationary density distribution under the assumption of Bolzman statistical approach correctness is presented. It is well known, that stationary distribution is not possible for gas in gravitational potential "1/R" type. However, we consider, that protoplanetary disk has clearly defined external boundary. So, Bolzman distribution does not produce divergence of density in that case, because area of distribution is finite. Hydrodynamical processes, that led to this state, were not taken in account, because they did not change turning moment of the disk. A theoretical consideration of gravitational self-interaction of the gas with central protostar gravity's effect on the disk is presented. As the primary spherically symmetric protostellar cloud had uniform rotation, the contribution of centrifugal potential to total potential energy of particles has been considered. After the formation of the protoplanetary disk, turbulence inside it was deeply dumped by energy dissipation. So, we may consider the disk being without turbulence. Derived distribution of density is described by Volterra's non-linear integral equation. General form of this equation is invariable against to considering of dissipation processes in the cloud at the stage of its accretion. So we can investigate its solution for broad class of initial conditions. Analysis of the equation's solution, that was found in quadrature form, allows to get a good agreement of theoretically calculated distribution of the protoplanetary disk matter with really observable masses of the inner Solar system planets, if they had totally utilized dust component of the disk inside their feeding area.

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