Dark matter and galaxy formation

Transcription

1 Dark matter and galaxy formation Galaxy rotation The virial theorem Galaxy masses via K3 Mass-to-light ratios Rotation curves Milky Way Nearby galaxies Dark matter Baryonic or non-baryonic A problem with gravity? Galaxy formation Hierarchical merging Monolithic collapse Secular evolution

2 Galaxy Rotation Galaxies form via collapse due to gravity As they collapse the rotation increases (conservation of angular momentum) Eventually, equilibrium is reached: F = GMm 2 r GRAVITY = CENTRIFUGAL F = mv r 2

3 The Virial Theorem The Virial theorem applies when the galaxy is in equilibrium and we can equate these two Forces: mv 2 r v = = GMm r 2 GM r m r v v = the velocity of rotation at radius r which depends only on the mass interior to r

4 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? v = M = M = GM r 2 v r (2! 10 = G ! 10 kgs 5 2 )! 1.5! ! 10 4 " 11! 3! 10 16

5 The Mass-to-light Ratio For the same galaxy if its absolute magnitude is mags what is its mass- to- light raho? MGAL = X L X X X X GAL = GAL 2.7! 10 = 2! 10 = 1.2! 10 = M M # 5.47 M L # # L L # GAL 10! ( M GAL " M # 0.4( " 20.5" 5.48) ) So the mass- to- light raho (within the stellar disc) is: M 5.5 L!!

6 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: M $ M, so r # r " v! v A B A B A B We need to measure v as a function of r => Rotation curve

7 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 v( r) = "!! BULGE c

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

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10 MW rotation curve

11 A Universal Flat Rotation Curve

12 and a few more.

13 Implication At large radii: Hence: v A = v B GM A = r A GM r B B i.e., Mass is proportional to radius Or: r A!r B " M A!M B," M # R " = M V This is the equation for an isothermal sphere and implies a spherical halo of extra mass! R R 3! 1 R 2

14 Conclusions Almost all spiral galaxies have flat rotation curves Those that don t are usually interacting (not in equilibrium) 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 (isothermal sphere)

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

16 Dark Matter in Galaxy Clusters Original argument for Dark Matter originated in 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 Can measure mass of cluster from dynamics, lensing and SZ effect all imply a high mass-to-light ratio suggesting Dark Matter Further evidence comes from Cosmology Big Bang Nucleosynthesis predicts the baryon density Large scale structure predicts the mass density Above are off by a factor of 6 implying Dark Matter in non-baryonic

17 Mass via Grav. Lensing

18 To create realishc simulahons of Large Scale Structure a modest to high mass density is required (25% closure) To explain the element abundances in low metalicity stars a low baryonic mass density is required (4% closure) The baryonic maser we can idenhfy in galaxies adds up to and even smaller amount (2%) Results imply both a small missing baryonic component and a large non- baryonic mass component But what? Blue = data Red = simulahons

19 DARK MATTER candidates Normal (i.e., Baryonic) Ionised gas Cold dust Planets White dwarfs Black Holes MACHOS (Massive Compact Halo Objects) ExoHc (i.e., non- Baryonic) Cold - WIMPs (Weakly InteracHng Massive ParHcles) Warm Sterile Neutrinos, GravaHnos Hot - Neutrinos (A wee bit of nothing that spins) Many studies in progress Many DM experiments underway

20 Alternatively We do not have the correct theory of gravity Enhanced GR 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 the dark matter particle, or a more convincing theoretical model Both avenues being heavily pursued: MOND Modified Newtonian Gravity (non-relativistic) TeVeS Tensor Vector Scalar theory (relativistic version of MOND) Weyl Gravity Conformal Gravity (motivated by an attempt to unify gravity and EM) See recent paper on this topic:

21 How did Galaxies Form? Hierarchical merging For Mergers seen Ellipticals in high density environments Irrs isolated Against Ellipticals seen at early epochs Irregulars forming today Initial Collapse For Ellipticals are old Ellipticals seen at high z Spirals/Irrs rotating Irregulars forming today Against Mergers seen PROBABLY SOME OF EACH OCCURRING

22 How did Galaxies Form? TWO COMPETING SCENARIOES Hierarchical Merging Initial Collapse TIME

23 The Antennae Galaxy: mid-merger

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25 Formation of an Elliptical galaxy

26 Quiescent Period Era of SF, Mergers and HTF formation

27 Puang it together? ACCELERATING DECELERATING U Dark MaSer 0yrs 5Gyrs Rapid merging Baryonic MaSer SMBHs AGN COLLAPSE BULGES 13Gyrs?? Slow merging???? INFALL DISKS P- BULGES SECULAR?? 27

28 Model of energy output of Universe v data Orange = IniHal collapse & mergers Blue = Slow gas infall Black = Total energy Age of Universe OPTICAL UV NEAR- IR

29 Cluster Formation Simulation John Dubinski: