warfreak131
Mar8-11, 09:35 PM
1. The problem statement, all variables and given/known data
Suppose the number density of bright F dwarf stars at the Sun's radial distance from the Galactic center, varied with height above the galactic plane as:
n(z)=n0 exp(-z/h)
where h = 250 pc. Also suppose that the velocity dispersion of these dwarfs varies with z as \sigma_{z}^{2}=\sigma_{z_{0}}^{2}(1+\frac{z}{h}) where \sigma_{z_{0}}=14 km/s.
Show that the surface mass density within 1 kilo parsec of the plane is
\Sigma=90 M_{sun} / pc^{2}
2. Relevant equations
3. The attempt at a solution
I literally have no idea where to start, I've been working on this question for hours and have not gotten any progress. I've searched google top and bottom looking for an explanation. All I can find is research papers that give no derivation, or the websites use quantites and methods other than what is given to me in the question.
Suppose the number density of bright F dwarf stars at the Sun's radial distance from the Galactic center, varied with height above the galactic plane as:
n(z)=n0 exp(-z/h)
where h = 250 pc. Also suppose that the velocity dispersion of these dwarfs varies with z as \sigma_{z}^{2}=\sigma_{z_{0}}^{2}(1+\frac{z}{h}) where \sigma_{z_{0}}=14 km/s.
Show that the surface mass density within 1 kilo parsec of the plane is
\Sigma=90 M_{sun} / pc^{2}
2. Relevant equations
3. The attempt at a solution
I literally have no idea where to start, I've been working on this question for hours and have not gotten any progress. I've searched google top and bottom looking for an explanation. All I can find is research papers that give no derivation, or the websites use quantites and methods other than what is given to me in the question.