AS1001:Extra-Galactic Astronomy

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1 AS1001:Extra-Galactic Astronomy Lecture 5: Dark Matter Simon Driver Theatre B spd3@st-andrews.ac.uk

2 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 =>

3 Distribution of Gas and Stars M82 M81 NGC 3077 STARLIGHT GAS (HI)

4 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 can detect in STARS+GAS Lets see why

5 Galaxy Rotation Galaxies form via collapse due to gravity As they collapse the rotation increases (conservation of angular momentum) Eventually, equilibrium is reached: GRAVITATIONAL FORCE = ROTATIONAL FORCE

6 Equilibrium INWARD FORCE = GRAVITY M=Mass interior to radius r m=mass of a typical star OUTWARD FORCE = CENTRIPETAL

7 The Virial Theorem The Virial theorem applies when the galaxy is in equilibrium and we can equate these two Forces: m v r v = the velocity of rotation at radius r which depends only on the mass interior to r

8 The Mass of a Galaxy A star at the edge of a distant galaxy has a velocity about the galaxy s centre of 200 km/s. Its distance from the centre of the galaxy is 15 kpc. What is the mass of the galaxy?

9 The Mass-to-light Ratio For the same galaxy if its absolute magnitude is mags what is its mass-to-light ratio? So the mass-to-light ratio (within the stellar disc) is:

10 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., A B If stars trace mass: We need to measure v as a function of r => Rotation curve

11 Measuring Rotation Curves Take spectra at different locations in the galaxy I I Δλ λ The two spectra are slightly offset and this difference gives a velocity difference between the centre and the edge of the galaxy

12 Rotation Curves As the stars and gas are centrally concentrated we expect: v r -0.5 VELOCITY B A RADIUS But by measuring rotation curves we observe: A flat rotation curve beyond the stellar population VELOCITY B A RADIUS => Additional Mass Component

13 A Universal Flat Rotation Curve

14 At large radii: Implication Hence: i.e., Mass is proportional to radius Or: This is the equation for an isothermal sphere and implies a spherical halo of extra mass

15 Our Working Galaxy Model HI GAS DISK GLOBULAR CLUSTER COMPANION DARK MATTER HALO STELLAR DISK BULGE

16 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 large velocities observed The fact that clusters are bound indicates more mass than present in luminous matter Dark matter required to keep cluster bound

17 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

18 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)

19 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 may not be the whole story We either need an observational breakthrough to discover dark matter, or a convincing theoretical model

20 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)

21 Lecture 1: Distances Standard Candles: Period-Luminosity relation / Cepheid variables DON T: remember formula DO: understand calibration; importance of Cepheids Calculate d given P, m Calculate m given d, P

22 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 = red i.e., B ν (T * ) ; L ~ T 4 (Keith s course)

23 Lecture 3: Galaxy Fundamentals How many stars? Assume F G = 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

24 Mass to Light ratios: X = 1 for Sun; X ~10 for a galaxy Galaxy M/L ratios indicate dark matter Average density of Universe

25 Lecture 4: Galaxy Spectra Continuum; Absorption lines; Emission lines 4000A break: blanket effect of absorption in stellar atmospheres. Strong in ellipticals, weaker in 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:

26 Lecture 5: Dark Matter Virial Equilibrium: Rotation = Gravity => circular orbits: Calculate galactic masses given v and r Rotation curves: stars trace mass => v ~ 1/r 0.5 Observe: v = constant => additional mass v = const => ρ ~ 1/r 2 => 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

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