1. Supermassive black holes in galaxy centres Andrew King Theoretical Astrophysics Group, University of Leicester, UK

2. black holes escape velocity from a gravitating mass M and radius R is hence for an object so condensed that (`Schwarzschild radius’) we have black! (full description requires general relativity)

3. importance of black holes, or what’s all the fuss? a mass m in a circular orbit of radius r has total energy (wrt infinity) hence if, we have, so letting matter fall close to a black hole releases binding energy comparable to rest-mass energy this infall process is called ` accretion ’

4. accretion = release of gravitational energy from infalling matter matter falls in from distance energy released as electromagnetic (or other) radiation accreting object

5. GR: typical BH accretion energy yield is ~10% of rest-mass energy ( erg/g) cf nuclear fusion (e.g. stars, supernovae): yield is only ~0.7% of rest—mass energy accretion on to a black hole must power the most luminous phenomena in the universe BH accretion is the most efficient way of using normal matter to get energy

6. quasars: erg/s requires accretion luminosity

7. why black holes in galaxy centres? 1. centre of our own galaxy has a black hole

8. why black holes in galaxy centres? 1. centre of our own galaxy has a black hole

9. stars near Galactic Centre seen to move (infrared images) orbits tracked for 16 years: one star (S2) has closed its orbit (Kepler)  point mass S2 has period 15.6 years, eccentricity 0.87 pericentre distance = 17 light—hours (< 100 x Earth—Sun distance) velocity 5000 km/s at pericentre  enclosed point mass orbits of all other stars agree a massive black hole is only reasonable explanation

10. why black holes in galaxy centres? 2. radiation background of the Universe as black holes grow, they radiate this light is still travelling through the Universe X—ray background  quasar light  mass in quasar nuclei density of quasar nuclei mass (= black holes!) is about per medium—sized galaxy all such galaxies have supermassive black holes in their centres!

11. why black holes in galaxy centres? 3. central point mass in galaxies correlates with gross properties

12. galaxies bulge disc BH

13. why black holes in galaxy centres? 3. central point mass in galaxies correlates with gross properties measure point mass using central gas velocities etc measure velocity dispersion and total stellar mass in galaxy bulge these correlate!

14. black hole mass knows about galaxy velocity dispersion!

15. black hole mass knows about bulge mass:

16. galaxies bulge disc BH stars move too fast compared with enclosed visible matter: galaxy mass dominated by `dark matter’, mass = 6 times visible mass dark matter interacts ONLY via gravity

17. dark matter halo dominates large-scale gravity

18. cosmological picture of growth : big galaxy swallows small merger

19. merger destabilizes gas near black hole  accretion central black holes coalesce galaxy nucleus become active (quasar) black hole grows, galaxy bulge grows major mergers make galaxies elliptical (all bulge) questions: 1. does this account for huge BH masses? (does anything limit accretion rate?) 2. correlation of BH mass with galaxy properties? cosmological picture of growth

20. limits on accretion accretion produces radiation: radiation makes pressure – can this inhibit further accretion? radiation pressure acts on electrons; but electrons and ions (protons) cannot separate because of Coulomb force. radiation pressure force on an electron is (in spherical symmetry). gravitational force on electron—proton pair is

21. thus accretion is inhibited once, i.e. once Eddington limit: similar if no spherical symmetry: luminosity requires minimum mass bright quasars must have in practice Eddington limit can be broken by factors ~ few, at most. accretion rate is also limited

22. black hole growth can we grow masses at redshifts z = 6 (Barth et al., 2003; Willott et al., 2003), only years after the Big Bang?

23. is limited by Eddington, i.e. ( `opacity’) and some of rest—mass energy turned into radiation, i.e.

24. these combine to give with yr thus final mass exponentially sensitive to 1/efficiency

25. BH spin parameter determines efficiency BH spin a.m. is with

26. thus = 0.43 (maximal a = 1) restricts growth to only : growing from to by z = 6 requires i.e. a < 0.5 — even lower a is needed if BH does not accrete continuously at Eddington rate rapid black—hole growth requires low spin is this possible?

27. accretion disc formation infalling mass does not hit accretor in general, but must orbit it — initial orbit is a rosette, but self—intersections  dissipation  energy loss, but no angular momentum loss Kepler orbit with lowest energy for fixed a.m. is circle. thus orbit circularizes with radius fixed by original specific a.m.

28. thus in general matter orbits accretor accretion requires angular momentum loss – specific a.m. at accretor (last orbit) is smaller than initial by factor energy loss through dissipation is quicker than angular momentum loss; matter spirals in through a sequence of circular Kepler orbits, angular momentum carried out by disc spreading to larger radii this is an accretion disc

29. accretion discs are universal : matter usually has far too much a.m. to accrete directly – matter velocity not `aimed’ precisely at the accretor! in a galaxy, interstellar gas at radius R from central black hole has specific a.m., where M is enclosed galaxy mass; far higher than can accrete to the hole, which is angular momentum increases in dynamical importance as matter gets close to accretor: matter may be captured gravitationally at large radius with `low’ a.m. (e.g. from interstellar medium) but still has far too much a.m. to accrete

30. accretion to central object central object gains a.m. and spins up at rate reaches maximum spin rate (a ~1 for black hole) after accreting ~ M if starts from low spin ‘centrifugal’ processes prevent further spinup BH gains mass significantly – does it spin up?

31. mergers can be both prograde and retrograde with equal probability!

32. accreting (or coalescing) from a retrograde orbit has a bigger effect since last stable orbit has larger lever arm than prograde one

33. BH coalescences cause net spindown because of this is this true of accretion? actually yes, but Lense—Thirring effect complicates things — to the point where people had the answer wrong for several years

34. Lense—Thirring: plane of circular geodesic precesses about black hole spin axis: precession rate changes with radius, so dissipation between adjacent disc rings causes spin-disc co— or counteralignment – occurs on dissipation timescale — fast compared with time to change BH mass and a.m.

35. older treatment of this effect predicted co—alignment as only stable endpoint so every retrograde accretion event would become prograde on short timescale  almost all mass accreted from prograde orbits  BH spinup on mass—doubling timescale since spin and efficiency high, mass grows only by a factor ~ 20  massive ‘seed’ black holes required in early universe?

36. BUT — this older result was WRONG! it implicitly assumed a.m. of disc >> spin a.m. of BH however, large disc a.m.  large disc  self-gravitating at edge limited disc a.m. means stable counteralignment occurs spin now slowly decreasing (but non—zero)

37. evolution of BH mass and spin

38. growth from even stellar—mass values to several possible within years, as required lower radiation efficiency ~ 5% agrees better with radiation background several other observational advantages (jet directions, GR recoil)

39. super—Eddington accretion: must have been common as most SMBH grew (z ~2), so outflows what do we know about accretion at super (hyper)—Eddington rates? BH—galaxy correlations

40. outflow is optically thick to scattering: radiation field L » L Edd transfers » all its momentum to it

41. response to super—Eddington accretion: expel excess accretion as an outflow with thrust given purely by L Edd, i.e. outflows with Eddington thrust must have been common as SMBH grew possible connection to large—scale galaxy properties: outflow sweeps up all the gas inside the galaxy bulge but dark matter remains

42. galaxy bulge matter originally distributed so that with outflow sweeps gas into a shell (`snowplough’)

43. swept-up gas ambient gas outflow

44. speed depends on whether gas cools or not if not, gas pressure adds to driving by ram pressure of outflow cooling is by `inverse Compton effect’, i.e. hot electrons bathed in cooler radiation from quasar close to quasar this mechanism is effective at large distance from the quasar the radiation field is too dilute to cool effectively — shell speeds up at such radii

45. at radius R total weight of shell is if cooling is effective, Eddington thrust must be large enough to support this weight, i.e. or (full derivation gives this value)

46. has no free parameter predicted relation

47. very close to observed relation (Ferrarese & Merritt, 2000; Gebhardt et al., 2000; Tremaine et al, 2002)

48. ultimately shell too large to cool (quasar radiation too dilute) now gas pressure adds to thrust driving gas out, shell accelerates gas outside cooling radius driven off completely remaining gas makes bulge stars — black—hole bulge mass relation

49. only mass inside cooling radius ends as bulge stars, giving or

50. good agreement with observation:

51. this picture predicts that the black holes in merging galaxies should (usually!) coalesce is this observable?

52. Gravitational waves from BH coalescence? would constrain recoil, BH spins, etc

53. summary black hole accretion powers the brightest objects in the Universe supermassive black hole in centre of every large galaxy BH mass correlates with galaxy properties galaxies and BHs grow by galaxy mergers random nature of mergers keeps BH spin low, allowing rapid growth high accretion rates drive outflows  BH—galaxy correlations