Abstract
We consider steady-state mass distributions (mass functions) attained at the nonlinear stage of fragmentation as a result of fragment coalescence. The influence of the fragment velocity distribution on the mass function is discussed. The kinetic equations governing the fragments “quasiparticles” are solved using the group symmetry properties of the collision integral. We have calculated power indices and locations of the breaking points for the mss spectrum (luminosity function) associated with the transition from the collisionless Lynden-Bell type to the Maxwellian distribution, as well as with the predominance of either purely geometric or Newtonian collision cross sections. The power indices found are in a reasonable agreement with the values observed for star or galaxy clusters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Silk, Fragmentation of Molecular Clouds, inProtostars and Planets, T. Gehrels, ed. (Univ. of Arizona Press, Tucson, Arizona, 1978).
J. M. Scalo, Stellar Mass Spectrum, inProtostars and Planets, T. Gehrels, ed. (Univ. of Arizona Press, Tucson, Arizona, 1978).
G. B. Field and W. C. Saslaw,Astrophys. J. 142:568 (1965).
M. V. Penston, V. A. Munday, D. I. Stickland, and M. J. Penston,Mon. Not. R. Astron. Soc. 142:355 (1969).
B. A. Trubnikov,Sov. Phys.-Dokl. 196:1316 (1971);197:59 (1971), original pagination.
J. Silk and T. Takahashi,Astrophys. J. 229:242 (1979).
V. S. Safronov and A. V. Vityazev, Genesis of the Solar System, inAdvances in Science and Technology, Series “Astronomy” (VINITI, Moscow, 1983).
D. Lynden-Bell,Mon. Not. R. Astron. Soc. 136:101 (1967).
L. I. Vinokurov and A. V. Kars,Proc. Izv. Ukr. Acad. Sci. A4:56 (1983), in Russian.
V. E. Zakharov,PMTF (J. Appl. Math. Theor. Phys.) 4:35 (1965), original pagination.
A. V. Kats and V. M. Kontorovich,Sov. Phys.-JETP 64:153 (1973), original pagination.
B. B. Kadomtsev and V. M. Kontorovich,Izv. VUZ Radioflz. 17:511 (1974), in Russian.
A. V. Kats and V. M. Kontorovich,Physica 86A:471 (1977).
L. D. Landau and E. M. Lifshitz,Mechanics (Nauka, Moscow, 1973), in Russian.
L. I. Vinokurov and A. V. Kats,Proc. (Izv.) Acad. Sci. USSR, Ser. “Phys. Atmosph. Ocean”16:601 (1980).
A. A. Lushnikov and V. N. Piskunov,Kolloid. Zh. 39:1076 (1977), in Russian.
B. N. Sergeev,Sov. Phys.-Dokl. 237:1322 (1975), original pagination.
V. I. Smirnov,Proc. Izv. Acad. Sci. USSR, Ser. “Phys. Atm. Ocean” 13:274 (1977).
B. B. Kadomtsev,Collective Phenomena in Plasmas (Nauka, Moscow, 1976), in Russian.
I. Tarrab,Astron. Astrophys. 109:285 (1982).
N. Bahcall,Ann. Rev. Astron. Astrophys. 15:505 (1977).
E. O. Abell,Astrophys. J. 213:327 (1977).
J. Silk and C. Norman,Astrophys. J. 247:59 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vinokurov, L.I., Kats, A.V. & Kontorovich, V.M. The relation between the velocity and mass distributions. The role of collisionless relaxation processes. J Stat Phys 38, 217–229 (1985). https://doi.org/10.1007/BF01017859
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01017859