AS1001:Extra-Galactic Astronomy

Lecture 5: Dark Matter

Simon Driver Theatre Bspd3@st-andrews.ac.uk

http://www-star.st-and.ac.uk/~spd3

Stars and Gas in Galaxies• Stars form from gas in galaxy• In the high-density regions the gas is

converted into Stars

– Elliptical: very little gas content– ~ all gas converted into stars =>

– Spiral: some gas content• most gas converted =>

– Irregular: lots of gas• little gas converted =>

Distribution of Gas and Stars

STARLIGHT GAS (HI)

M82

NGC 3077

M81

Dark Matter• However, we believe that GAS+STARS

only make up 10% of a galaxies total mass• The rest is in the form of DARK MATTER• We believe this because of the rotation

curves which imply more mass than we candetect in STARS+GAS

• Lets see why…

Galaxy Rotation

• Galaxies form via collapse due to gravity• As they collapse the rotation increases

(conservation of angular momentum)

• Eventually, equilibrium is reached:

GRAVITATIONALFORCE = ROTATIONAL

FORCE

Equilibrium• INWARD FORCE = GRAVITY

– M=Mass interior to radius r– m=Mass of a typical star

• OUTWARD FORCE = CENTRIPETAL

The Virial Theorem• The Virial theorem applies when the galaxy is

in equilibrium and we can equate these twoForces:

• v = the velocity of rotation at radius r whichdepends only on the mass interior to r

mv

r

The Mass of a Galaxy A star at the edge of a distant galaxy has a

velocity about the galaxy’s centre of 200km/s. Its distance from the centre of thegalaxy is 15 kpc. What is the mass of thegalaxy ?

The Mass-to-light Ratio For the same galaxy if its absolute magnitude

is -20.5 mags what is its mass-to-light ratio ?

So the mass-to-light ratio (within the stellar disc) is:

The Mass Distribution• Stars and gas are centrally concentrated• Hence if stars trace the mass then the mass

must also be centrally concentrated• Stars at large radii should see almost all the

mass, i.e.,

• If stars trace mass:A B

We need to measure v as a function of r => Rotation curve

Measuring Rotation CurvesTake spectra at different locations in the galaxy

The two spectra are slightlyoffset and this differencegives a velocity difference between the centre and theedge of the galaxy

I

I

λΔλ

Rotation Curves• As the stars and gas

are centrallyconcentrated weexpect: v ∼ r -0.5

• But by measuringrotation curves weobserve:

• A flat rotation curvebeyond the stellarpopulation

RADIUSV

ELOC

ITY

RADIUS

VELO

CITY B A

B A

=> Additional Mass Component

A Universal Flat Rotation Curve

Implication• At large radii:

• Hence:

• i.e., Mass is proportional to radius• Or:

• This is the equation for an isothermal sphereand implies a spherical halo of extra mass

Our Working Galaxy Model

BULGEDARK MATTER HALO

STELLAR DISK

HI GAS DISK GLOBULAR CLUSTER

COMPANION

Dark Matter in Galaxy Clusters• Pre-dates rotation curve observations and

analysis• Discovered by Fritz Zwicky (1930s)• Motions of galaxies within clusters suggests

clusters should not be bound: very largevelocities observed

• The fact that clusters are bound indicatesmore mass than present in luminous matter

• Dark matter required to keep cluster bound

Conclusions• All spiral galaxies have flat rotation curves• Stars do not trace the mass• Stars are a minor mass component, about 10%• Some kind of DARK MATTER must exist• It must be distributed in a large outer halo

DARK MATTER candidates• Normal (i.e., Baryonic)

– Ionised gas– Cold dust– Planets– White dwarfs– Black Holes– MACHOS (Massive Compact Halo Objects)

• Exotic (i.e., non-Baryonic)– WIMPS (Weakly Interacting Massive Particles)– Neutrinos (A wee bit of nothing that spins)

Alternatively…• We do not have the correct theory of gravity• In the same way that Newtonian gravity

could not explain all observations (e.g.,Mercury’s orbit), General Relativity maynot be the whole story…

• We either need an observationalbreakthrough to “discover” dark matter, or aconvincing theoretical model

Class Test Next Tuesday• 8 questions, each worth 5 marks, try all 8• 4 questions on The Galaxy• 4 questions on Galaxies & Cosmology

• G&C: first six lectures (I.e., inc this week)

Lecture 1: Distances• Standard Candles:

• Period-Luminosity relation / Cepheidvariables•DON’T: remember formula•DO: understand calibration; importance of Cepheids•Calculate d given P, m•Calculate m given d, P

Lecture 2: Galaxy Morphology• Hubble tuning fork; why not evolutionary

sequence• Galaxy types: Ellipticals, Spirals, Irregulars• Main features of each type. Components• Why are ellipticals red?• Understand: young & hot = blue

old & cool = redi.e., Bν(T*) ; L ~ T 4 (Keith’s course)

Lecture 3: Galaxy Fundamentals

• How many stars? Assume FG = n*F*

F* = “Average star”Use:

• Formation scenarios. Observations for & against• Space density of galaxies: what d and V can we

see if we observe m = 14 and we know M = -20• How far apart are galaxies?• How are galaxies clustered? Soap suds, galaxies

found on the bubble surfaces: filaments & voids

• Mass to Light ratios:

X = 1 for Sun; X ~10 for a galaxyGalaxy M/L ratios indicate dark matter

• Average density of Universe

Lecture 4: Galaxy Spectra• Continuum; Absorption lines; Emission lines• 4000A break: blanket effect of absorption in

stellar atmospheres. Strong in ellipticals, weakerin spirals, absent in irregulars.

• Absorption lines: metals in stellar atmospheres => old stars => ellipticals, spiral bulges

• Emission lines: hot gas ionized by hot stars => young stars => spiral disks, irregulars

• Radial velocities:

Lecture 5: Dark Matter• Virial Equilibrium: Rotation = Gravity

=> circular orbits:• Calculate galactic masses given v and r• Rotation curves: stars trace mass => v ~ 1/r0.5

Observe: v = constant => additional mass• v = const => ρ ~ 1/r2 => spherical isothermal halo• Dark matter in galaxy clusters: galaxies moving

too fast to stay bound• Conclusion: 90% of the Universe is made up of

dark matter… OR we have wrong theory of gravity