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 Galaxies: Observational Facts<br />
Exponential Surface Brightness Pr<strong>of</strong>iles<br />
Because <strong>of</strong> their close-to-exponential appearance, disk galaxies are <strong>of</strong>ten modelled<br />
as infinitesimally thin, exponential disks:<br />
surface brightness<br />
surface mass density<br />
I(R) =I 0 e −R/R d<br />
Σ(R) =Σ 0 e −R/R d<br />
L d =2π<br />
M d =2π<br />
∞<br />
0<br />
∞<br />
0<br />
I(R) R dR =2π I 0 R 2 d<br />
Σ(R) R dR =2π Σ 0 R 2 d<br />
circular velocity<br />
V 2<br />
c,d(R) =−4πGΣ 0 R 2 d y [I 0 (y) K 0 (y) − I 1 (y) K 1 (y)]<br />
disk scale length<br />
R d stellar mass-to-light ratio M d /L d =Σ 0 /I 0<br />
y ≡ R/(2 R d )<br />
modified Bessel functions<br />
I n (x) K n (x)<br />
The circular velocity curve reaches a maximum at R 2.<strong>16</strong> R d<br />
For more realistic models, with non-zero thickness, see MBW §11.1.1...<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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