Abstract:
We present here rigourous analytical solutions of the Boltzmann-Poisson equations concerning the distribution of stars perpendicular to the galactic plane. The number density of stars at the galactic disk is assumed to follow n(m,0)~H(m-m_0_)m^-x^, where m is the mass of the star and x is an arbitrary exponent greater than 2, while H(m-m_0_) is the unit Heaviside step function. The velocity dispersion of the stars is assumed to arise from the stellar motion in a random force field - leading to <v^2^(m)>~constant for m<=m_*_, <v^2^(m)>~m^-θ^, for m>m_*_, where m_*_ is the stellar mass for which the stellar life-time equals the galactic age. It is seen that the height distribution of stars is very sensitive to the values of x and θ. Finally we have derived an expression connecting the surface density volume density and velocity dispersion of stars, and show that this relation is a sensitive function of θ and x and use them to obtain certain plausible numbers for our Galaxy in the limits of the present day data.
