Class 23: The mass of galaxies
and the need for dark matter


How do you measure the mass of a
galaxy?
What is “dark matter” and why do we
need it?
Measuring mass from light

First think about
stars…






We want mass, but
see light.
Construct the “massto-light” ratio.
M = 21030 kg.
L = 41026 W.
M /L = 5000 kg/W.
From now on, we will
use M /L as a
standard reference.
Other stars

Let’s use starlight to “weigh” a whole galaxy…
have to average M/L over all stars.

Different types of stars have different massto-light ratios (recall L  M4).




Massive stars have small M/L.
Low-mass stars have large M/L.
Neutron stars and black holes hardly shine at all
(they have very high M/L).
Averaging stars near the Sun, get
M/L  10 M /L.



For typical spiral, measure L ~ 1010 L.
So, mass of stars is M ~ 10L ~ 1011 M.
But, there’s another way to measure mass…
Measuring mass from motion


Use same laws of motion as for planets
going around a star…
Remember the case for planets…
4 2 D 3
M star 
GP2

(Newton’s Form of
Kepler’s 3rd Law)
Can rewrite this as
V 2R
M star 
G
or
GM star
V
R
Velocity dependence on radius for
a planet orbiting a star…
V  R-½

Apply same arguments to a galaxy…

Consider a star in the
galaxy at distance R
from center orbiting at
speed V.

Then, mass of the
galaxy within radius R,
M(<R) is given by
2
V R
M galaxy ( R ) 
G
What do we see?
Real measurements

Orbital speed of stars/gas stays flat as
far out as we can track it.




Means that enclosed mass increases linearly
with distance… even beyond point where
starlight stops.
So, in these outer regions of galaxies, the
mass isn’t luminous…
This is DARK MATTER.
All galaxies seem to be embedded in
giant dark matter balls (called halos).
Called a dark matter “halo”
What is dark matter?

Is dark matter normal dust/gas?






No!! Solid arguments from cosmology limit the
amount of “normal” matter to less than that needed
for dark matter halos.
So, this is something new… non-baryonic matter.
I.e., matter not based on protons and neutrons.
80-90% of matter in universe is non-baryonic dark
matter!!
What is this stuff?
Neutrinos (a mundane possibility)?



They are part of the “standard model” of particle
physics… they have been detected and studied.
Maybe the dark matter is in the form of neutrinos?
No… each neutrino has very small mass, and there
are not enough of them to make the dark mass.

WIMPs


Weakly Interacting Massive Particles.
Generic name for any particle that has a lot of mass,
but interacts weakly with normal matter.
 Must be massive, to give required mass.
 Must be weakly interacting, in order to have avoided
detection (i.e. cannot absorb or emit E/M radiation).

Various possibilities suggested by Particle Physics
Theory…
 Super-symmetric particles.
 Gauge bosons.

Many experiments currently on-going…
ASIDE: Dark Energy

New probes (e.g. MAP) show that
Universe is only 4% normal matter!



22% dark matter.
73% “dark energy”!
MAP and other evidence shows that
there is something “resisting” gravity in
the Universe, increasing expansion rate.

A new “dark energy” – some new force of
nature that acts only on very large scales.
 Cosmic strings?
Microwave Anisotropy Probe (MAP) results
Shows subtle variations in
temperature across sky.