Distribution of stars perpendicular to the plane of the galaxy |
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| Authors: | S Chatterjee |
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| Institution: | (1) Indian Institute of Astrophysics, 560 034 Bangalore |
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| Abstract: | We present here rigorous analytical solutions for the Boltzmann-Poisson equation concerning the distribution of stars above
the galactic plane. The number density of stars is considered to follow a behaviour n(m,0) ∼H(m - m0)m−x, wherem is the mass of a star andx an arbitrary exponent greater than 2 and also the velocity dispersion of the stars is assumed to behave as < v2(m)> ∼ m−θ the exponent θ being arbitrary and positive. It is shown that an analytic expression can be found for the gravitational field
Kz, in terms of confluent hypergeometric functions, the limiting trends being Kz∼z for z →0, while Kz
→ constant for z → infinity. We also study the behaviour of < |z(m)|2>,i.e. the dispersion of the distance from the galactic disc for the stars of massm. It is seen that the quantity < |z(m)|2>∼ mt-θ, for m→ t, while it departs significantly from this harmonic oscillator behaviour for stars of lighter masses. It is suggested
that observation of < |z(m)|2> can be used as a probe to findx and hence obtain information about the mass spectrum. |
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| Keywords: | mass spectrum self consistent field velocity dispersion |
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