What we know about the coevolution of mass and spin in black holes: Accretion vs mergers Large spin vs small

Transcription

1 What we know about the coevolution of mass and spin in black holes: Accretion vs mergers Large spin vs small

2 Conclusions Accretion tends to make black holes spin faster Mergers tend to make black holes spin slower

3 Conclusions Accretion tends to make black holes spin faster Mergers tend to make black holes spin slower Even when the members of a premerger binary are of comparable mass!

4 Basic physics: Strong field orbits of black holes Very non-newtonian potential sets the radial motion: Have possibility for orbits that are unstable - plunging into the black hole.

5 Basic physics: Strong field orbits of black holes Very non-newtonian potential sets the radial motion: Have possibility for orbits that are unstable - plunging into the black hole.

6 Basic physics: Strong field orbits of black holes Very non-newtonian potential sets the radial motion: Have possibility for orbits that are unstable - plunging into the black hole.

7 Basic physics: Strong field orbits of black holes When material on such an orbit plunges, mass and spin evolves by Mass and spin coevolution thus boils down to mapping the energy and angular momentum of the last stable orbit (LSO).

8 Last stable orbit for Kerr holes When black hole spin is included, not quite so simple! Radius of the LSO depends upon orbit s orientation relative to the hole s spin.

9 Last stable orbit for Kerr holes When black hole spin is included, not quite so simple! Radius of the LSO depends upon orbit s orientation relative to the hole s spin. Notice: Higher inclination orbits have much larger radius!

10 Angular momentum at LSO Since the orbital radius varies so much, the magnitude of the orbital angular momentum likewise varies. Retrograde orbits have a much larger lever arm than prograde ones!

11 Punchline: The capture cross section for retrograde orbits is larger than for prograde orbits; Retrograde orbits have a larger lever arm at plunge. Per unit plunging mass, retrograde captures slow the spin more than prograde captures speed spin up.

12 Example: Thin disk accretion (Thorne 1974) Bardeen (1970) had shown that matter accreting in a thin disk evolved a hole s mass and spin according to Result: A non-spinning hole is driven to the maximal Kerr value after (roughly) doubling its mass

13 Thorne s correction: Photons from disk Hot disk radiates! Radiation is (more or less) isotropic in rest frame of disk - photons either escape to infinity or are captured by the hole. For rapid rotation, capture cross section for counter-orbiting photons is much larger than that for co-orbiting photons! Spin evolution is buffered:

14 Neglected physics: Magnetic fields Thorne noted that including magnetic fields would change the mass/spin coevolution. Basic idea: Imagine that field lines thread the inner edge of the disk and the event horizon. Disk is a good conductor: lines anchored there. Horizon is an OK conductor; lines aren t perfectly anchored but do grab on. Magnetic fields exert torque on the hole!

15 Intuition about this torque Imagine that the field lines want to rigidly anchor to both the inner edge of the disk and to the hole s event horizon: Disk and horizon will tend to be driven into corotation with each other! Can analytically solve for the black hole spin to which the system would be driven in this case:

16 Intuition about this torque Imagine that the field lines want to rigidly anchor to both the inner edge of the disk and to the hole s event horizon: Disk and horizon will tend to be driven into corotation with each other! Can analytically solve for the black hole spin to which the system would be driven in this case:

17 Gammie, Shapiro, & McKinney Self-consistently solve MHD equations on a Kerr background, allowing both the field and the hole to evolve to equilibrium. Find a ~ 0.9 for range of models considered! Similar results obtained by Hawley & Krolik From Gammie, Shapiro, & McKinney, ApJ 2004, 602, 312

18 Punchline for accretion If we start with a black hole that is slowly rotating and allow matter to accrete onto it, it will be driven to rather rapid rotation. Key reason for this: Each mass element that one accretes has the same angular momentum. However, it will not be driven to the maximal Kerr value a = 1! Deviation from 1 may tell us a lot about accretion mechanism.

19 Mergers Key difference with mergers: Have no reason to expect aligned angular momentum! Intuition: Consider limit of small mass ratio. If population of small masses is isotropic, expect equal numbers of prograde and retrograde captures.

20 Mergers Key difference with mergers: Have no reason to expect aligned angular momentum! Intuition: Consider limit of small mass ratio. If population of small masses is isotropic, expect equal numbers of prograde and retrograde captures. Doctrine of Original Spin: Vector S remains constant while mass grows. a = S /M 2 rapidly shrinks!

21 Mergers Doctrine underestimates rate at which spin bleeds away by neglecting lever arm effect. Hughes & Blandford (2003): Gives a Fokker-Planck description of mass-spin coevolution for capture of small bodies. Result: a(t) = a(0)[m(0)/m(t)] 2.4 Spin rapidly dies. Eventually random walks with <a> ~ 2q 1/2 [~ 0.6 for mergers as seen by Volonteri et al.]

22 Major mergers Final result suggests that large spin is possible if mass ratio q ~ 1! Such a binary cannot be treated with perturbative techniques of Hughes & Blandford: Must directly integrate Einstein field equations.

23 Major mergers Final result suggests that large spin is possible if mass ratio q ~ 1! Such a binary cannot be treated with perturbative techniques of Hughes & Blandford: Must directly integrate Einstein field equations. Several groups can now successfully evolve binary black holes from wide separations through plunge and merger!

24 Merger of spinning black holes Group at U. Texas (Brownsville) has examined merger of black holes with large parallel spins. Result: A period of centrifugal hangup in which the system strongly radiates gravitational waves, shedding angular momentum! Can end up with spin comparable to that found in accretion models (a ~ 0.9); still much smaller than Kerr maximum. Requires some fine tuning: Spins must be initially large and parallel.

25 Merger of spinning black holes Result is very young: see gr-qc/ (Capanelli, Lousto, & Zlochower) and grqc/ (Baker et al [Goddard group]). Cannot yet do very asymmetric systems - e.g., spinning binaries with q 1, or misaligned spins. Will be some time before codes can handle these relevant cases.

26 Merger of spinning black holes Result is very young: see gr-qc/ (Capanelli, Lousto, & Zlochower) and grqc/ (Baker et al [Goddard group]). Cannot yet do very asymmetric systems - e.g., spinning binaries with q 1, or misaligned spins. Will be some time before codes can handle these relevant cases. Conjecture: Asymmetric binaries will be stronger radiators and thus will have even smaller final spin.

27 Merger of spinning black holes Result is very young: see gr-qc/ (Capanelli, Lousto, & Zlochower) and grqc/ (Baker et al [Goddard group]). Cannot yet do very asymmetric systems - e.g., spinning binaries with q 1, or misaligned spins. Will be some time before codes can handle these relevant cases. Recent progress has been amazing: Numerical relativity is now providing astrophysically interesting results!

28 Summary Nature s black holes are entirely described by two quantities: Their mass M and their spin S. Joint evolution surely contains important clues to their growth history! Great motivator to accurately measure black hole spin. Accretion spins up but not all the way. Magnetic coupling will limit max spin. Mergers spin down. Unequivocal in the limit of many small mass captures. Numerical relativity now approaching the general case!