Introduction to Cosmology Ryden · Problem 11.4

Structure Formation: Gravitational Instability

Physics — Astrophysics · galaxy-formation-dynamical-time-redshift

Problem

Suppose that the stars in a disk galaxy have a constant orbital speed

v

out to the edge of its spherical dark halo, at a distance

R_{\rm halo}

from the galaxy's center. If a bound structure, such as a galaxy, forms by gravitational collapse of an initially small density perturbation, the minimum time for collapse is

t_{\rm min} \approx t_{\rm dyn} \approx 1/\sqrt{G\bar{\rho}}

. Show that

t_{\rm min} \approx R_{\rm halo}/v

for a disk galaxy. What is

t_{\rm min}

for our own galaxy? What is the maximum possible redshift at which you would expect to see galaxies comparable in

v

and

R_{\rm halo}

to our own galaxy? (Assume the Benchmark Model is correct.)

Related theory

Galaxy Formation

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