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 “mass-

to-light” ratio. M = 21030 kg.

L = 41026 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 mass-to-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…

Use same laws of motion as for planets going around a star…

Remember the case for planets…

Can rewrite this as

R

GMV

G

RVM star

star or 2

2

324

GP

DM star

Measuring mass from motion

(Newton’s Form of Kepler’s 3rd Law)

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

G

RVRM galaxy

2

)(

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.