how much does a galaxy weigh? - university of richmondggilfoyl/cm/... · tom panel) for the spiral...
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How Much Does a Galaxy Weigh?
NGC3198Jerry Gilfoyle Dark Matter 1 / 11
Galactic Structure
Jerry Gilfoyle Dark Matter 2 / 11
How Much Does a Galaxy Weigh?
Consider the light profile (toppanel) and rotation curve (bot-tom panel) for the spiral galaxyNGC3198. The bottom panelshows the observed rotationcurve (dots) and the rotationcurve (solid line) expected forthe light distribution of the toppanel. (1) What is the rota-tion curve implied by the mea-sured light curve? (2) What isthe density curve implied by themeasured rotation curve? (3)What is the ratio of the massescalculated in Parts 1 and 2.
Jerry Gilfoyle Dark Matter 3 / 11
Weighing a Galaxy
Luminosity
Num
ber
Measured Luminosity ofa Galaxy
Nu
mb
er
a GalaxyExtracted Mass Distribution of
Mass
Jerry Gilfoyle Dark Matter 4 / 11
Potential From a Uniform Spherical Mass
Spherical shell of
mass M R>a
a
dM
r
a sin θ
a R
Spherical shell of
mass M
a
dM
a R
a sin θ
R<a
r
Jerry Gilfoyle Dark Matter 5 / 11
Potential and Force From a Uniform Spherical Mass
r
r’
a
y
x
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Rotation Curve Based on Observed Luminosity Distributionfor NGC3198
0 5 10 15 20 25 300
0.00001
0.00002
0.00003
0.00004
0.00005
Radius in kpc
Vel
ocity
(a.u
.)
Jerry Gilfoyle Dark Matter 7 / 11
Galactic Density Profiles
Density from rotation curve
Density fromluminosity curve
0 5 10 15 20 25 3010-6
10-5
10-4
0.001
0.010
0.100
1
Radius in kpc
ρ(a
.u.)
Jerry Gilfoyle Dark Matter 8 / 11
Galactic Density Profiles
Density from rotation curve
Density fromluminosity curve Missing mass
0 5 10 15 20 25 3010-6
10-5
10-4
0.001
0.010
0.100
1
Radius in kpc
ρ(a
.u.)
Jerry Gilfoyle Dark Matter 9 / 11
What Do Galaxies Really Look Like?
Jerry Gilfoyle Dark Matter 10 / 11
How big is NGC3198?
Radio image of NGC3198 atop a negative of an optical picture.Jerry Gilfoyle Dark Matter 11 / 11