vc   = 220.*km
r    = 8.5*kpc
rho  = vc^2/(4.d0*!dpi*g*r^2)
print,' dm density = ',rho/(msun/pc^3),' solar masses per pc^3'


;
n = 1 ; density in particles per cm^-3
alpha = 3.1d-13
dotN = 1.d48 ; rate of ionizing photons
;
rs = (3.d0*dotn/(4.d0*!dpi*alpha*n^2))^(1.d0/3.d0)
print,' rs = ',rs/pc,' pc '