Black Hole Physics via Gravitational Waves Image: Steve Drasco, California Polytechnic State University and MIT How to use gravitational wave observations to probe astrophysical black holes
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.
Scott A. Hughes, MIT BHI Conference, 8 May 2017 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
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.
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. Scott A. Hughes, MIT BHI Conference, 8 May 2017
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) = 5 256 Frequency sweep controlled by the chirp mass: Measure the rate at which the frequency c 3 GM 5/3 changes, you measure this mass. 1 (t c t) Defined the chirp mass: M µ 3/5 M 2/5 3/8
Need to go beyond leading bit Preceding analysis uses only Newtonian gravity: This emerges as the leading term in relativistic gravity. Higher-order terms have new mass dependences: Make it possible to measure combinations other than chirp mass from inspiral.
Can keep going! Scott A. Hughes, MIT BHI Conference, 8 May 2017
and going. [Blanchet 2006, Liv Rev Rel 9, 4, Eq. (168)]
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.
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.
Gravitomagnetism Scott A. Hughes, MIT BHI Conference, 8 May 2017
Scott A. Hughes, MIT BHI Conference, 8 May 2017 GWs with spin vs GWs without Influence of spin strongly imprints waveform: Both amplitude and phase modulated as binary s members spins precess about one another.
Ringdown Black holes have light rings as the system settles down, the final waves we hear are those which are trapped on that light ring and then leak out. 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.
Frequency bands General relativity has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral (0.02 0.05) c3 GM f ringdown (0.06 0.15) c3 GM
10s to 100s of Msun: f ~ 100s to 10s of Hz. Right in the sensitive band of LIGO and other ground-based GW detectors. Frequency bands General relativity has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral (0.02 0.05) c3 GM f ringdown (0.06 0.15) c3 GM
Frequency bands General relativity has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral (0.02 0.05) c3 GM f ringdown (0.06 0.15) c3 GM ~10 4 to ~10 7 Msun: f ~ 0.1 10-5 Hz. Waves in the sensitive band of LISA can be heard to high redshift.
Frequency bands General relativity has no intrinsic scale: Frequencies which characterize GWs from black hole systems are determined by the mass scale. f inspiral (0.02 0.05) c3 GM f ringdown (0.06 0.15) c3 GM ~10 8 through ~10 10 Msun: f ~ Nanohertz. Targets for pulsar timing arrays can probe massive black hole mergers to low redshift. Movie courtesy Penn State Gravitational Wave Astronomy Group, http://gwastro.org
Astronomy of merging BHs Assume general relativity: Measuring GWs from BHs enables a census of black holes and their properties. We already have been surprised: First empirical evidence for BHs in this mass range, and that they can form binaries which merge quickly. Image: LIGO
Scott A. Hughes, MIT BHI Conference, 8 May 2017 Astronomy of merging BHs Assume general relativity: Measuring GWs from BHs enables a census of black holes and their properties. Improved detectors will enhance our ability to learn about BH properties from the coalescence waves: Reduced low-f noise improves inspiral signal: Better masses and spins (crucial for learning about formation mechanism); better knowledge of position on sky, distance to the binary. Colpi & Sesana, arxiv:1610.05309
Scott A. Hughes, MIT BHI Conference, 8 May 2017 Astronomy of merging BHs Assume general relativity: Measuring GWs from BHs enables a census of black holes and their properties. 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:1610.05309
Astronomy of merging BHs Assume general relativity: Measuring GWs from BHs enables a census of black holes and their properties. LISA: Will track how massive black holes build by mergers out to z ~ 15 20 Figure: The Gravitational Universe, arxiv:1305.5720
Astronomy of merging BHs Assume general relativity: Measuring GWs from BHs enables a census of black holes and their properties. And will measure extreme mass ratio captures to z ~ 1: Sources that spend 10 4 10 5 orbits in strong field, measure BH properties with very high precision. Galaxy Stellar cluster Galactic nucleus Figure courtesy Marc Freitag Massive Black Hole
Physics of black hole spacetime Orbits highly sensitive to detailed properties of black hole spacetime hence GWs generated by these orbits are sensitive to spacetime properties. GW measurements offer a tool for formulating precision tests of BH spacetime properties. Example: Ringdown spectroscopy. h ring = Ae t/ ring sin(2 f ring t + ) GR s black holes make very specific predictions for how fring and τring depend on only mass and spin measure multiple modes, can test this prediction.
Physics of black hole spacetime Orbits highly sensitive to detailed properties of black hole spacetime hence GWs generated by these orbits are sensitive to spacetime properties. GW measurements offer a tool for formulating precision tests of BH spacetime properties. Example: Spacetime multipoles. M l + is l = M(ia) l Spacetimes of compact bodies can be characterized by multipole moments for black holes, no-hair means that these moments depend on only two numbers, the black hole s mass and spin.
Physics of black hole spacetime Orbits highly sensitive to detailed properties of black hole spacetime hence GWs generated by these orbits are sensitive to spacetime properties. GW measurements offer a tool for formulating precision tests of BH spacetime properties. Example: Spacetime multipoles. M l + is l = M(ia) l Measure three or more of these multipoles: You have a consistency test for the nature of black hole spacetimes.
Scott A. Hughes, MIT GW probes of black holes: Amazing, and getting better GWs probe spacetime dynamics carry a clean encoding of strong-field spacetimes. Provides precision measurements of black hole properties: Good for astronomy, good for gravity physics.