victoria13
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The equation for the isotropic velocity dispersion of the stars, sigma(r), is
the Jeans equation,
GM(< r)/r^2 = −(1/p*)d/dr(p*sigma^2)
Assume that the stellar density p*(r) = 0.8ptot(r), where ptot(r)~1/r^2,
as derived earlier. Show that a constant velocity dispersion, sigma(r) = sigma0,
is a solution to this equation, and evaluate sigma0 for this galaxy. Express
your answer in km s−1.
From the previous part of the question we have ptot(r)=(kT/2piG(mu)mp)(1/r^2).
basically i don't understand what it means by "show that sigma0 is a solution... i stick it into the equation and come out with sigma0 squared=GM(<r)/2r... but that isn't showing its a solution as such... any help??
the Jeans equation,
GM(< r)/r^2 = −(1/p*)d/dr(p*sigma^2)
Assume that the stellar density p*(r) = 0.8ptot(r), where ptot(r)~1/r^2,
as derived earlier. Show that a constant velocity dispersion, sigma(r) = sigma0,
is a solution to this equation, and evaluate sigma0 for this galaxy. Express
your answer in km s−1.
From the previous part of the question we have ptot(r)=(kT/2piG(mu)mp)(1/r^2).
basically i don't understand what it means by "show that sigma0 is a solution... i stick it into the equation and come out with sigma0 squared=GM(<r)/2r... but that isn't showing its a solution as such... any help??