h5 - distance from the Galactic center varied with height...

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Homework # 5, due 10 Mar 1. In example given in the notes describing the observations of col- lapsing clouds, it is indicated in some cases that there is a locus of points for which v r is constant. v r is the radial velocity seen by an observer in the ± z direction (see the relevant figure). For the case that v ( r ) = v 0 r - 1 , find equations for ( r, θ ), or ( x, y ) where r = p x 2 + y 2 and θ = tan - 1 ( x/y ), of the locus of points for which v r = 2 v 0 /R i = constant. Here, R i is the outer radius of the collapsing region. Show that in the case v ( r ) = v 0 r there is no locus of points for which v r is constant. 2. In a Stromgren sphere containing H and He in solar proportions, why can’t the ionization front for He + ever be larger than that for H + ? 3. Suppose the number density of bright F dwarfs, at the Sun’s radial
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Unformatted text preview: distance from the Galactic center, varied with height above the Galactic plane as n ( z ) = n e-z/z h where z h = 285 pc. Also suppose that the velocity dispersion of these dwarfs varies with z as σ 2 z = σ 2 z (1 + z/z h ) , σ z = 14 km s-1 . Show that the surface mass density within 1 kpc of the plane is Σ( < 1 kpc) ’ 90 M ² pc-2 . What factor is this larger than the surface mass density in the Galactic disc at the Sun’s position? If, instead, one assumed that the velocity dispersion was inde-pendent of height above the Galactic plane, what would you find for Σ( < 1 kpc)?...
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