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

Jerry Gilfoyle Dark Matter 6 / 11

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