Learning about Astrophysical Black Holes with Gravitational Waves

Transcription

1 Learning about Astrophysical Black Holes with Gravitational Waves Image: Steve Drasco, California Polytechnic State University and MIT How gravitational waves teach us about black holes and probe strong-field gravity

2 In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein s equations of general relativity provides the absolutely exact representation of untold numbers of black holes that populate the universe. Subramanyan Chandrasekhar The Nora and Edward Ryerson Lecture, University of Chicago, 22 April 1975.

3 It is well known that the Kerr solution provides the unique solution for stationary black holes in the universe. But a confirmation of the metric of the Kerr spacetime (or some aspect of it) cannot even be contemplated in the foreseeable future. Subramanyan Chandrasekhar The Karl Schwarzschild Lecture, Astronomischen Gesellschaft, Hamburg, 18 September 1986

4 Understanding BHs and GWs Both black holes and gravitational waves are solutions of the vacuum Einstein equations: G =0 To study black holes orbiting one another and the GWs they generate, just need to write down initial data, and solve this equation Essentially solved now after several decades of focused effort.

5 Understanding BHs and GWs Result: Gravitational waves carry imprint of orbit dynamics. Waves phase comes from kinematics of black holes as they orbit about one another. Simple limit for intuition: Treat binary s kinematics with Newtonian gravity, add lowest contribution to waves. E orb = GMµ 2r de dt = G d 3 I jk 5c 5 dt 3 d 3 I jk dt 3 = GM r 3 = 32G 5c 5 6 µ 2 r 4 Energy radiated away causes r to slowly decrease, so orbit frequency slowly increases.

6 Result: Gravitational waves carry imprint of orbit dynamics. Waves phase comes from kinematics of black holes as they orbit about one another. Result: Understanding BHs and GWs (t) = Frequency sweeps up at a rate controlled by the chirp mass measure the rate at which the frequency chirps, you measure this mass. c 3 GM 5/3 1 (t c t) Defined the chirp mass: M µ 3/5 M 2/5 3/8

7 Beyond the leading bit Preceding analysis uses only Newtonian gravity: Can regard this as the leading piece of full relativistic gravity Additional terms introduce dependence on other mass terms can measure more combinations than just chirp mass from inspiral.

8 Can keep going

9 and going. [Blanchet 2006, Liv Rev Rel 9, 4, Eq. (168)]

10 Gravitomagnetism Magnetic-like contribution to the spacetime drives magnetic-like precession of binary members spins. Orbital motion contribution. Contribution from other body s spin Leads to new forces, modifying the orbital acceleration felt by each body.

11 Gravitomagnetism Magnetic-like contribution to the spacetime drives magnetic-like precession of binary members spins. Angular momentum is globally conserved: J = L + S1 + S2 = constant Orbital plane precesses to compensate for precession of the individual spins.

12 Gravitomagnetism

13 GWs with spin vs GWs without Influence of spin strongly imprints the waveform. Simple chirp of two nonspinning black holes. Modulated chirp of two rapidly spinning black holes.

14 Ringdown Final waves: Last bit of radiation to leak out of the system as it settles down to the Kerr state. h ring = Ae t/ ring(m fin,a fin ) sin [2 f ring (M fin,a fin )+ ] Frequency and damping of these modes depend on and thus encode mass and spin of remnant BH. Example waveform: A few final cycles of inspiral followed by ringdown.

15 10s to 100s of Msun: 100s to 10s of Hz. Right in the sensitive band of LIGO and other ground-based GW detectors. Frequency bands Classical GR has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral ( ) c3 GM f ringdown ( ) c3 GM

16 GW Last ~8 cycles, corresponding to moments when binary s members merged into one: Observed signal (loud enough to stand above noise) consistent with template that assumes GR s black holes. m1 = (36 ± 4)M m2 = (29 ± 4)M mfin = (62 ± 4)M afin = 0.67 [+0.05/-0.07] Δm = (3 ± 0.5)M

17 GW About 55 cycles detected, corresponding to last several dozen orbits when the binary s members were still well separated: Signal needed correlation with a theoretical template in order to be detected in the noise. m1 = (14.2 [+8/-4])M m2 = (7.5 ± 2.3)M mfin = (20.8 [+6/-2])M afin = 0.74 ± 0.06 Δm = (1 [+0.1/-0.2])M

18 Signal versus noise Improved detectors will enhance our ability to learn about BH properties from the coalescence waves: Reduced low-f noise improves inspiral signal: More signal in band, enables better masses and spins; better knowledge of position on sky, distance to binary. Colpi & Sesana, arxiv:

19 Signal versus noise Improved detectors will enhance our ability to learn about BH properties from the coalescence waves: Reduced high-f noise improves ringdown signal: Better mass and spin of final remnant; measure mixture of modes present at end of coalescence. Colpi & Sesana, arxiv:

20 A few 10 4 to a few 10 7 Msun: Hz. Waves in the sensitive band of LISA can be heard to high redshift. Frequency bands Classical GR has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral ( ) c3 GM f ringdown ( ) c3 GM

21 ~10 8 through ~10 10 Msun: Nanohertz frequencies. Targets for pulsar timing arrays can probe massive black hole mergers to low redshift. Frequency bands Classical GR has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral ( ) c3 GM f ringdown ( ) c3 GM Movie courtesy Penn State Gravitational Wave Astronomy Group,

22 TeV Particle Astrophysics, 13 Sept 2016 LISA: tentative 2034 launch Go to space to escape low-frequency noise: sensitive in band ~ Hz < f < 1 Hz Several million km interferometer antenna in space. ESA mission details in flux. Working for NASA involvement. A target-rich frequency band.

23 LISA metrology Thanks to its much longer arms, effect of a GW is relatively large: h = Ground: h 10-21, L ~ kilometers: ΔL 10-3 fm Space: h 10-20, L ~ 10 6 kilometers: ΔL 10 pm L L About an order of magnitude from fringe shift of original Michelson interferometer. Measured at DC using his eyeball.

24 LISA noise Far more challenging: Ensuring the noise budget can be met for each element of a free-flying constellation of spacecraft. Launched: 3 Dec 2015 Arrived at L1: 22 Jan 2016 Began science operations: 8 Mar 2016 LISA Pathfinder: Testbed for technologies to demonstrate that free fall, control, and metrology can be done with the precision needed for LISA.

25 LISA noise Far more challenging: Ensuring the noise budget can be met for each element of a free-flying constellation of spacecraft. Significantly exceeded mission spec. LISA is within reach. Figure 1 of Armano et al, Phys. Rev. Lett. 116, (2016).

26 Science goals Science reach in this band known for some time. Antenna sensitivity to a variety of low-frequency sources. Taken from Gravitational Observatory Advisory Team (GOAT) report. Track growth and evolution of massive black holes from z ~ 15. Precisely measure black hole properties, test nature of gravity near them. Explore dynamical stellar populations around black holes in galaxy centers. Survey population of stellarmass compact remnants in Milky Way and into low-z universe. Constrain or probe exotic physics in the early universe.

27 Source goals Science goals met by measuring a range of sources that oscillate on periods of minutes to hours. Massive black hole binaries: Form as consequence of the hierarchical galaxy growth, in band for months to years. Extreme mass ratio binaries: Capture of stellar-mass compact body by massive black hole; also in band for months to years. Compact binaries: Stellar mass binaries in our galaxy (low masses) to z ~ 0.1 (high mass). Processes in the early universe

28 Massive black hole science Galaxies were built hierarchically: Big galaxies assembled through repeated mergers of subunits. Evidence from quasars tells us that black holes have existed since the earliest cosmic times. Combining these facts indicates that massive black hole mergers should be relatively common. As long as there are mergers with total masses (a few) 10 4 (1 + z) M/Msun (a few) 10 7 they will be in band of a spacebased low-f detector, and detectable out to z ~ 15.

29 Extreme mass ratio inspirals Capture of stellar mass compact objects onto relativistic orbits of black holes in galaxy cores. Stellar cluster Galactic nucleus Galaxy Massive Black Hole EMRI setting, courtesy Marc D. Freitag

30 Similar to galactic center S-stars Analogous to orbits we see in center of our galaxy, but much closer to large black hole also smaller body must be compact (NS star or small BH) else it will tidally disrupt. Animation courtesy Genzel group, Max-Planck-Institut für Extraterrestrische Physik

31 Relativity view Special limit of two-body problem: One body far more massive than other. Binary dominated by large black hole GWs encode its properties. Large mass ratio consequences: 1. Model perturbatively: Can understand system using simpler equations than full Einstein. 2. Evolve slowly: Duration scales as (Mbig/Msmall), small body slowly spirals through strong-field of big BH. Expect ~10 5 cycles in band need very precise models to accurately match phase.

32 Need precise wave models Instantaneous EMRI amplitude will typically be factor ~ smaller than noise! Data analysis rule of thumb: Coherently matching wave for N cycles boosts SNR by N 1/2. Need to develop models capable of tracking system for ~10 5 orbits deep in Kerr strong field.

33 Need precise wave models Instantaneous EMRI amplitude will typically be factor ~ smaller than noise! Data analysis rule of thumb: Coherently matching wave for N cycles boosts SNR by N 1/2. Need to develop models capable of tracking system for ~10 5 orbits deep in Kerr strong field.

34 Need precise wave models Instantaneous EMRI amplitude will typically be factor ~ smaller than noise! Data analysis rule of thumb: Coherently matching wave for N cycles boosts SNR by N 1/2. Need to develop models capable of tracking system for ~10 5 orbits deep in Kerr strong field.

35 Need precise wave models Instantaneous EMRI amplitude will typically be factor ~ smaller than noise! Measure mass, spin, mass ratio: δm/m, δa, δη ~ Measure orbit s geometry: δe0 ~ δ(spin direction) ~ a few deg 2 δ(orbit plane) ~ 10 deg 2 Measure distance to binary: δd/d ~ Barack & Cutler PRD 69, (2004)

36 Measure shape of Kerr Kerr metric only depends on two parameters but has a shape that can be characterized by an infinite number of multipole moments. Analogy: Newtonian potential of a gravitating body. Blm coefficients determine potential s shape, can be mapped by orbits. Connect to an interior description they tell us how mass is distributed.

37 Measure shape of Kerr Kerr metric only depends on two parameters but has a shape that can be characterized by an infinite number of multipole moments. Analogy: Newtonian potential of a gravitating body. Blm coefficients determine potential s shape, can be mapped by orbits. Connect to an interior description they tell us how mass is distributed. GRACE gravity model

38 Measure shape of Kerr In GR, two families of multipole moments are needed to describe spacetimes: Ml: Mass multipole. For a fluid body, describes angular distribution of mass. Sl: Current multipole. For a fluid body, describes angular distribution of mass flow. For black hole spacetimes, there is a very simple relation between these moments: M l + is l = M(ia) l

39 Orbit spectroscopy Kerr black hole orbits are characterized by 3 frequencies, determined by hole s mass and spin, and by the orbit geometry: Ωr: freq. of radial motion Ωθ: freq. of polar motion Ωφ: freq. of axial motion f Asymptotes to Kepler s law at large r Orbits of bodies in strong-field of Kerr spacetime periodic at these frequencies, and generate gravitational waves with these frequencies. rmin

40 Orbit spectroscopy If multipole moments differ from those of Kerr, then the orbital frequencies will differ. One example of how orbit frequencies are shifted from the Kerr values, if the black hole has the wrong l = 2 moment. From Vigeland & Hughes, PRD 81, (2010)

41 Orbit spectroscopy If multipole moments differ from those of Kerr, then the orbital frequencies will differ. Precision measurement of an inspiral will track phase through a sequence of orbital frequencies null hypothesis is that these frequencies will only depend on the black hole s mass and spin.

42 Horizon coupling When we calculate waves from a binary, we have two pieces: Flux that goes to infinity, and flux that goes down the black hole s event horizon. Flux to infinity has simple behavior: de dt > 0 Always takes energy away from the binary.

43 Horizon coupling When we calculate waves from a binary, we have two pieces: Flux that goes to infinity, and flux that goes down the black hole s event horizon. Horizon flux is a bit weird: Its sign depends on relative frequency of orbit and BH spin. de dt H > 0 If Ωorb > ΩH Horizon takes energy away if orbit is faster than hole s spin

44 Horizon coupling When we calculate waves from a binary, we have two pieces: Flux that goes to infinity, and flux that goes down the black hole s event horizon. Horizon flux is a bit weird: Its sign depends on relative frequency of orbit and BH spin. de dt H < 0 If Ωorb < ΩH but adds energy to orbit if hole spins faster than orbit.

45 Horizon coupling Example: 1 Msun body spiraling into 10 6 Msun black hole; spin 5% max. Turn off horizon flux, inspiral slightly slowed: Takes about an extra day over 18 month inspiral. From Hughes, PRD 64, (2001) In accord with intuition: Flux from horizon takes energy from orbit faster.

46 Horizon coupling Same system, but with spin 99.8% maximum: With horizon flux Without Horizon flux slows inspiral by up to 4 weeks

47 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : Gravity of moon raises tide on planet planet bulges in response.

48 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : Planet s fluid is viscous. The bulging response will lag applied tide in time.

49 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : If planet spins slower than orbit s frequency, the bulge lags orbit s position.

50 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : Bulge exerts a torque that takes angular momentum from orbit slowing it down (and speeding up planet s spin).

51 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : If planet spins faster than orbit s frequency, bulge leads orbit s position.

52 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : Bulge exerts a torque that adds angular momentum to orbit speeding it up (and slowing down planet s spin).

53 Why doesn t horizon always absorb energy from the energy? Consider an apparently totally different effect in Newtonian gravity: Tidal orbit coupling. Consider a moon orbiting a fluid planet : Net effect: Orbit loses energy if Ωorb > ΩP Orbit gains energy if Ωorb < ΩP Exactly like the horizon absorption effect.

54 Tidal distortion of horizons Flux language misleads but can be recast in a dual description as tidal deformation of BH. Foundations developed by Hawking and Hartle: Key point is similarity between entropy generation in fluids and entropy generation in event horizon. Fluids: Flow lines sheared by tide. Sheared fluid generates heat, which generates entropy. Rate set by viscosity. T fluid ds dt =2 η = shear viscosity ij ij σij = shear of fluid (trace-free part of gradient of fluid velocity) Tfluid = fluid temperature S = entropy generated in fluid Image credit: Wikipedia article Streamlines, streaklines, and pathlines"

55 Tidal distortion of horizons Flux language misleads but can be recast in a dual description as tidal deformation of BH. Foundations developed by Hawking and Hartle: Key point is similarity between entropy generation in fluids and entropy generation in event horizon. Black hole: Horizon generators sheared by tide. Black hole mechanics: This generates area which (via Bekenstein and Hawking) is entropy. Constant of proportionality is viscosity. T H ds dt =2 H µ µ σµν = shear of horizon generators (trace-free part of gradient of generators 4-momentum) ηh = Horizon shear viscosity = (1/16π)(c 3 /G) TH = Bekenstein-Hawking temperature

56 Horizon coupling Using this language, recast the down-horizon GW flux describes tidal bulge on horizon. O Sullivan & Hughes, PRD 90, (2014); PRD 94, (2016). Another null test: Does the horizon coupling agree with the Kerr horizon viscosity?

57 The end of the beginning LIGO s observations have validated the promise of GW astronomy, unveiling new BH populations and probing gravity as never before. Strong-field gravity is now becoming a data-driven subject.