Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999pasj...51..211a&link_type=abstract
Publications of the Astronomical Society of Japan, v.51, p.211-219.
Astronomy and Astrophysics
Astronomy
Cosmology, Galaxies: Interacting, Methods: Analytical, Numerical, Time
Scientific paper
The two-body relaxation time of gravitationally interacting galaxies in the Einstein--de Sitter universe is studied. First, we reformulate the scattering problem so that the time change of the cross section due to cosmic expansion can be taken into account. Next we calculate numerically the orbits of encounters to various sets of orbital parameters while specifying the initial states of the encounters: initial separation, impact parameter, and initial relative velocity between two galaxies. By combining the results of these studies, we obtain the two-body relaxation time as a function of the relative velocity v_0 at the initial epoch and the number density n of galaxies within proto-clusters of galaxies. The relaxation time is roughly the free-fall time for a small relative velocity, v_0 <= 300 km s^{{-1}} {(m / 10^{{11} MO )}^{1/3}} {[11/(1+z)]}^{{1/2}} , while it is proportional to {v_0}3 for a high relative velocity. The effects of the cosmic expansion make the relaxation time longer than that in non-expanding systems, especially for proto-clusters of galaxies with the number density n < 3 x 103 Mpc^{{-3} (10^{{11}} MO /m){[(1+z)/11]}} 3 , where m is the mass of a galaxy and z is its redshift.
Ardi Eliani
Inagaki Shogo
Tsuchiya Toshio
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