Non-Extensive Thermostatistical Approach of the Peculiar Velocity Function of Galaxy Clusters

Details Non-Extensive Thermostatistical Approach of the Peculiar Velocity Function of Galaxy Clusters Non-Extensive Thermostatistical Approach of the Peculiar Velocity Function of Galaxy Clusters

1996-07-29

arxiv.org/abs/astro-ph/9607147v1

Astronomy and Astrophysics

Astrophysics

ReVTeX, 3 pages, 2 figures available on request

Scientific paper

We show that the observational data recently provided by Giovanelli et al. (1996 a, b) and discussed by Bahcall and Oh (1996) concerning the velocity distribution of clusters of galaxies can be naturally fitted by a statistical distribution which generalizes the Maxwell-Boltzmann one (herein recovered for the entropic index $q=1$). Indeed a recent generalization of the Boltzmann-Gibbs thermostatistics suggests for this problem that the probability function is given, within a simple phenomenological model, by \begin{eqnarray} P(>v) & = & \frac{ \int_{v}^{v_{max}} dv \left[ 1-(1-q)(v/v_0)^2 \right]^\frac{q}{1-q} } {\int_{0}^{v_{max}} dv \left[ 1-(1-q)(v/v_0)^2 \right]^\frac{q}{1-q}}, \nonumber \\ v_{max} & \equiv & \left\{ \begin{array}{ll} v_0 (1-q)^{-1/2} & \mbox{if $q<1$} \\ \infty & \mbox{if $q \geq 1$.} \end{array}\right. \nonumber \end{eqnarray} A remarkably good fitting with the data is obtained for $q=0.23^{+0.07}_{-0.05}$ and $v_0=490\pm 5$ km s$^{-1}$.

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