1. Extragalactic Astronomy & Cosmology Second-Half Review [4246] Physics 316

2. Jane Turner [4246] PHY 316 (2003 Spring) What have we covered…. Black Holes: Formation/ Observational Evidence AGN Dark matter: Evidence for/candidates for Jeans Mass: Gravitational collapse of clouds Scale factor/Geometries for Universe/ Robertson- Walker metric -Friedmann equation (evolution of R)

3. Jane Turner [4246] PHY 316 (2003 Spring) What have we covered…. Fates of the Universe Big Bang/Cosmic Microwave Background Big Bang Nucleosynthesis and the Early Universe Inflation

4. Jane Turner [4246] PHY 316 (2003 Spring) Black Holes - formation Reminder: When stellar fuel is used up - core collapses What happens next depends on the stars mass Stellar cores white dwarf More massive stars explode as supernovae, if the remaining core mass is > 1.4 M  a neutron star is formed If remaining core mass is > 2-3 M  then even neutron degeneracy cannot support the star against gravity -black hole forms

5. Jane Turner [4246] PHY 316 (2003 Spring) GR - Black Holes -Schwarzschild Schwarzschild found a solution to Einsteins metric, which describes the gravitational field around a point mass which is not rotating  s 2 =(1-2GM/c 2 R)c 2  t 2 - (  R 2 /(1-2GM/c 2 R) -R 2 (  2 +sin 2  2 )) The Schwarzschild metric An equation for the geometry of space around the exterior of a mass -coordinates for an observer at great distance Assumed a vacuum (set stress-energy tensor to zero) Spherical source, distance from center is R Altitude is  and azimuth is  and gravity does not change with time The ‘radius’ of such an object is R s =2GM/c 2 Schwarzschild Radius

6. Jane Turner [4246] PHY 316 (2003 Spring) GR - Black Holes -Schwarzschild  s 2 =(1-2GM/c 2 R)c 2  t 2 - (1/(1-2GM/c 2 R)  R 2 -R 2 (  2 +sin 2  2 )) consider , , ie a simple radial line (1- R s /R)c 2  t 2 represents the effect on time as a function of R  s 2 =(1- R s /R)c 2  t 2 -  R 2 /(1- R s /R) Now product of (1- R s /R)c 2  t 2 must always equal the invariant proper time interval Coeff of  t ~zero at R= R s, so  t must become large (gravitational time dilation) time appears to stop to outside observer

7. Jane Turner [4246] PHY 316 (2003 Spring) Gravitational Redshift The gravitational redshift is defined to be z =( obs - em )/ em = obs / em - 1 light frequency suffers time dilation such that z= [  (1-R s /R) ] -1 -1

8. Jane Turner [4246] PHY 316 (2003 Spring) Schwarzschild:Singularities & Event Horizons R s is the radius defining the event horizon Other important radii are: 1.5 R s the last orbit for photons- light bent so strongly it circles the hole, within this radius light cannot orbit, must travel radially in/out 3R s - the last stable orbit for particles

9. Jane Turner [4246] PHY 316 (2003 Spring) Observed Characteristics of AGN  Broad Optical Line Emission from highly ionized gas  Large luminosity over broad waveband - from very small nuclear region  Strong flux of hard X-rays - vary on timescales down to minutes

10. Jane Turner [4246] PHY 316 (2003 Spring) Schematic for inner regions Power law has N(E)  E - 

11. Jane Turner [4246] PHY 316 (2003 Spring) Signatures of material spiraling onto a black hole

12. Jane Turner [4246] PHY 316 (2003 Spring) 3 ways to look for evidence of DM 1)Look at motion of luminous bodies affected by DM 2)Measure temperature of hot gas held in galaxy/cluster by gravity 3)Look at how clusters of galaxies bend light - gravitational lenses

13. Jane Turner [4246] PHY 316 (2003 Spring) What started the search for DM ? The first evidence that we were not seeing all the mass which exists came from the rotation curves of spiral galaxies Rotation curves tell you about the mass as a function of radius from M = r x v 2 G Measuring spiral galaxies we expected the mass distribution to follow that of the light

14. Jane Turner [4246] PHY 316 (2003 Spring) 2) DM Evidence from Hot Halos While the most visible part of a galaxy is the globular clusters in the halo, they only make up a small part of the halo mass Hot gas shines in X-rays - need a lot of unseen mass to gravitationally bind this to the halo

15. Jane Turner [4246] PHY 316 (2003 Spring) DM Evidence from Cluster Gas X-ray emitting gas - can measure temperature of the gas -know how much matter needed to gravitationally bind this gas to the cluster How about on larger scales?? There is evidence for more material than we can see between the galaxies in clusters Also, measure vel. dispersion again, but using the galaxies

16. Jane Turner [4246] PHY 316 (2003 Spring) Masses of Clusters of galaxies 1) Can find mass within a distance r of the galactic center: v is the velocity of objects moving under gravity. Can be applied to clusters of galaxies -use average speed of galaxies & the cluster radius in the orbital velocity law. 2) When we measure the temperature of hot, intracluster gas from its X- ray emission, we must first convert the gas temperature into an average speed for the gas particles. Can use which gives the approx average speeds of hydrogen nuclei in a gas of temperature T- once we find this speed, use it in the orbital velocity law.

17. Jane Turner [4246] PHY 316 (2003 Spring) 3) Gravitational lensing Use gravitational lensing to map distribution of dark matter Angle of deflection  mass

18. Jane Turner [4246] PHY 316 (2003 Spring) Overdense regions - Jeans Mass u Imagine a smooth distribution of matter containing a slightly denser-than-average region u WHAT HAPPENS? u Answer depends on relative strength of two forces u gravity u fluid pressure

19. Jane Turner [4246] PHY 316 (2003 Spring) JEANS MASS M J obtained by equating gravitational energy of the perturbation (which controls its collapse) with the thermal energy (generates pressure to oppose collapse)  is the density of the clump

20. Jane Turner [4246] PHY 316 (2003 Spring) JEANS MASS - more detail In early Universe (at a time called the decoupling time) when T~ 3000 K, n ~ 6 x 10 3 -> M J ~ 10 5 M  In the interstellar medium T~1000, n~ 10 3 -> M J ~ 500 M  So in the early universe the smallest thing which could collapse was massive ! 10 5 M  Today, smallish molecular clouds can collapse - form individual stars. Jeans mass versus time/conditions for the early universe is an important constraint on how galaxies formed!

21. Jane Turner [4246] PHY 316 (2003 Spring) The Cosmic Microwave Background (CMB) u There is more radiation filling the universe than that from stars u Something called the Cosmic Background Radiation (CBR) fills the sky in all directions at wavelengths too long for our eyes to see

22. Jane Turner [4246] PHY 316 (2003 Spring) The Cosmic Microwave Background (CMB) u The expanding universe has caused CBR to redshift to longer wavelengths from its original energy! u The cosmos must have once been ablaze with this radiation-this is the radiation predicted to have been produced in the Big Bang!

23. Jane Turner [4246] PHY 316 (2003 Spring) The CMB: DMR map of the microwave sky… u CMB is extremely isotropic -if we measure the universe to be isotropic, and we’re not located at a special place in the Universe, we can also deduce that the Universe is homogeneous! Spectrum has precisely the shape predicted by theory… “Blackbody” spectrum, Characteristic temperature 2.728K

24. Jane Turner [4246] PHY 316 (2003 Spring) CBR Fluctuations u Why are the fluctuations important? u Before recombination, fluctuations in the radiation field meant fluctuations in mass density u After recombination, these small fluctuations in density can get amplified (slightly dense regions get denser & denser due to gravity) u Growing fluctuations eventually collapse to give galaxies & clusters u By studying these fluctuations, we are looking at the “seeds” that grow to become galaxies, stars, planets… u  T ~ 30 millionths of a Kelvin

25. Jane Turner [4246] PHY 316 (2003 Spring) Overview -The Big Bang + inflation is the current paradigm - this seems to be OK w.r.t. nucleosynthesis, and solves some philosophical questions like horizon, structure, relic problems -a 'flat' universe seems consistent with all observables -don’t know what 'dark matter' is although 'certainly' there - not sure what it is composed of although some contributors known - have not a clue what 'dark energy' is ~ 70% of the mass-energy dominating the behaviour of the universe today