Power-law asymptotic mass distributions for systems of accreting or fragmenting bodies

Details Power-law asymptotic mass distributions for systems of accreting or fragmenting bodies Power-law asymptotic mass distributions for systems of accreting or fragmenting bodies

Jun 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983mnras.203..987b&link_type=abstract

Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 203, June 1983, p. 987-1009.

Astronomy and Astrophysics

Astronomy

4

Deposition, Fragmentation, Interplanetary Medium, Mass Distribution, Asymptotic Methods, Collision Parameters, Rates (Per Time), Steady State, Time Dependence

Scientific paper

Power-law distributions for asymptotic solutions for rate equations governing accreting and fragmenting systems are investigated analytically as explanations for the majority of observed astronomical mass distributions. Account is taken of the effect of the mass dependence of the particle mean speed on the collision cross-section. Attention is constrained to mass distributions proportional to the reciprocal of the mass distribution index (s) root of the masses and the velocity distribution is proportional to the reciprocal of the velocity distribution index (h) root of the masses. It is shown that, for a geometric collision-cross section with velocity independent of mass, a value of 1.83 shows good agreement with data. Restriction of the values for h to zero or less permits s less than 2 to be used for accretion formation and s more than 2 to be related to fragmentation origins. It is noted that a continuous supply of small particles from an outside source is necessary for accretion to proceed. Time dependent solutions are demonstrated to be different for accretion and fragmentation when the s is held constant and h is no more than zero.

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