ASTR 610 Theory of Galaxy Formation Lecture 16
ASTR 610 Theory of Galaxy Formation Lecture 16
ASTR 610 Theory of Galaxy Formation Lecture 16
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Disk <strong>Formation</strong>: The Standard Picture<br />
j d<br />
J d ≡ j d J vir<br />
If we define the parameter via , where is the angular<br />
momentum <strong>of</strong> the dark matter halo, then we can related J d to the spin parameter<br />
<strong>of</strong> the dark matter halo, according to<br />
J vir<br />
λ = J vir |E| 1/2<br />
GM 5/2<br />
vir<br />
= 1 j d<br />
J d |E| 1/2<br />
GM 5/2<br />
vir<br />
Using the virial theorem, according to which<br />
E = −K = − M vir V 2<br />
vir<br />
2<br />
, we have that<br />
J d = √ 2 j d λM vir R vir V vir<br />
J d =2M d R d V vir<br />
R d = √ 1 λ 2<br />
M d = m d M vir<br />
<br />
jd<br />
m d<br />
<br />
R vir<br />
Using the virial scaling relations for dark matter haloes this yields<br />
R d 10h −1 kpc<br />
<br />
jd λ<br />
m d 0.05<br />
Vvir<br />
200 km/s<br />
<br />
D −1 (z)<br />
<strong>ASTR</strong> <strong>610</strong>: <strong>Theory</strong> <strong>of</strong> <strong>Galaxy</strong> <strong>Formation</strong> © Frank van den Bosch: Yale 2012
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