Testing the black hole no-hair theorem using LIGO extreme

mass ratio inspiral events

Jonathan Gair, IoA Cambridge

“Testing gravity in the next decade” workshop,

University of Birmingham, March 31st 2006

Talk Outline

• Description of extreme mass ratio inspirals (EMRIs) in context of LIGO and LISA

• Use of EMRIs to test general relativity and the no-hair theorem

• Spacetime mapping with EMRIs• Imprint of excess multipole moments on orbital dynamics• Detection of black hole ‘hair’ in GW observations• Outstanding issues

Acknowledgments

Work done in collaboration with:

Caltech:

Duncan Brown Geoffrey Lovelace

Steve Drasco Ilya Mandel

Hua Fang Yi Pan

Chao Li Kip Thorne

Others:

Stas Babak (AEI) Kostas Glampedakis (Southampton)

Yanbei Chen (AEI) Scott Hughes (MIT)

Curt Cutler (JPL)

• Inspiral of a compact object (CO), i.e., a white dwarf, neutron star or black hole, into a considerably more massive black hole.

• Mass ratio ranges from a few x 10-7 (LISA) to a few x 10-2 (LIGO). ‘Extreme’ mass ratio ensures CO acts like a test particle in the field of the central black hole.

• Gravitational waves (GWs) emitted during inspiral can be detected by our GW detectors. Characteristic frequency is determined by central black hole mass– LIGO is sensitive to M < ~100 M๏

– LISA is sensitive to M ~ few x 105 M๏ – 107 M๏

Extreme mass ratio inspirals

• Robust source for LISA – most galaxies harbour a supermassive black hole in their centre which is surrounded by a cluster of stars.

• Encounters between stars in the cluster can put COs onto orbits that pass close enough to the SMBH to be captured. Emission of GWs drives inspiral into the BH.

• Several alternative formation scenarios have been proposed recently which increase event rate

─ Tidal stripping of massive stars

─ Binary splitting

─ Triaxiality of galactic potentials

─ Resonant relaxation

LISA extreme mass ratio inspirals

• Astrophysical event rate not well constrained, but conservative estimates suggest that in a galaxy like the Milky Way there will be ~10-8 WD captures, ~10-8 NS captures and ~3 x 10-7 BH captures per year (standard scenario).

• LISA will observe inspirals for several years (~105 cycles) → the SNR for a source at 1 Gpc can be up to several hundred.

• Detection threshold using a ‘semi-coherent’ search is SNR ≈ 35 → LISA may see several hundred to several thousand events (JG et al. 2004).

• LISA EMRI events have the potential to be a very powerful probe of supermassive black holes in the Universe.

LISA extreme mass ratio inspirals

• Much more speculative source– There is some evidence that intermediate mass (~ 100 M๏) black holes

exist in the centres of globular clusters, e.g., X-ray emission from G1, M15.

– In the dense cluster centre environment, the IMBH may capture NSs or BHs, which inspiral and merge due to GW emission.

– Mass ratio (~0.01) is not as extreme as LISA events.

• Strict upper limit on rate is derived by assuming every globular cluster contains an IMBH that grows from 50 M๏to 100 M๏ by consumption of 1.4 M๏ NSs → 2.5 x 10-9 events Mpc-3 yr-1. Likely a significant overestimate!

• Mergers of BH + IMBH possibly more likely to be observed, due to effects of mass segregation (→ higher rate per cluster) and higher SNR.

• Advanced LIGO could detect events at up to 1 Gpc.

LIGO extreme mass ratio inspirals

Science with EMRIs

• EMRI orbits are typically inclined with respect to the spin axis of the central black hole and inspiral significantly over an observation – the inspiralling body extensively explores the black hole spacetime. Waveform traces the underlying orbit.

• LISA EMRI orbits are also eccentric and exhibit complicated zoom and whirl structure which maps out the underlying spacetime. This is reflected in the gravitational waveforms.

• Kerr inspirals reveal perihelion precession and spin induced precession of orbital plane.

• Waveforms have rich multipolar structure.

• Extreme mass ratio ensures waveform generation is a ‘clean’ problem and is relatively well understood.

• A typical observation includes ~104 (LIGO) →105 (LISA) waveform cycles →lots of information for spacetime mapping.

EMRI Science – probe of horizon

• The inspiralling object interacts with the horizon of the SMBH.

• Can be thought of as a tidal interaction or in terms of energy “falling into” the black hole.

• Objects without horizons (e.g., boson stars) will behave differently.

• The tidal coupling is encoded in the gravitational wave emission – provides a first opportunity to probe horizon dynamics.

• If the EMRI is generated by inspiral into a black hole, the waveforms provide measurements of the system parameters with unprecedented accuracy.

• If the GW is generated by inspiral into an object not described by the Kerr metric, the EMRI waveforms will tell us this, since they encode a map of the spacetime structure near the black hole.

• Analogy with geodesy led to the term ‘bothrodesy’ from the greek βοθρος meaning ‘sacrificial pit’ (ancient Greek).

• Or ‘cesspool’ (modern Greek)! We prefer ‘holiodesy’….• ‘No hair theorem’ tells us that all black holes are described by

the Kerr metric. If this is not true, the EMRI waveforms will be different in a quantifiable way.

Testing GR using EMRIs

• EMRI observations actually test whether an observed inspiral is described by an inspiral into a Kerr black hole. If it is not, there could be several reasons– Astrophysical “hair”. The presence of other material, e.g., an accretion

disc, could change the multipole structure of the system.

– The central object could be an exotic object consistent with GR, e.g., a supermassive boson star, rather than a black hole.

– The central object could have hair consistent with GR, e.g., due to the existence of extra dimensions.

– General Relativity could be the wrong theory of gravity.

• Must be careful to distinguish a test of GR from a test of the astrophysics of the system, if it is possible to distinguish the two.

• Need for waveform templates adds further complications.

“Testing General Relativity”

• Ryan (1995) demonstrated that, for nearly circular and equatorial orbits in an arbitrary axisymmetric spacetime, the multipole moments of the system are encoded in GW observables – can expand the energy spectrum, ΔE/μ, and precession rates, Ωp/Ω as functions of the orbital period, Ω.

• For the Kerr metric, all higher multipole moments are determined by the monopole and quadrupole moments

Spacetime mapping

• If measured multipole moments are inconsistent with the above, the system must deviate from the Kerr metric. Need 3 moments to rule out a Kerr BH, 4 to rule out a spinning boson star.

• Can easily generalize this result to eccentric, nearly equatorial orbits. More powerful as information is multiply encoded.

• Generalization to arbitrary orbits is difficult, as nature of third integral unknown. Third integral may not even exist.

• Ryan’s theorem tells us that the GWs encode the multipoles, but not how to extract that information.

• Multipole decomposition is an inconvenient way to characterize spacetimes, since need an infinite number to describe Kerr.

• Alternative approach is to consider spacetimes that are Kerr plus a small deviation. Formulate observation as a test of a null hypothesis that GWs are from a Kerr BH (Collins & Hughes 04).

• Presence of excess multipole moments alters orbital and precession frequencies, and their rate of change.

• Key observable is the number of cycles the fundamental frequency spends near frequency f

Spacetime mapping

• This also encodes the spacetime multipole moments, but how they are encoded is much more difficult to calculate.

• Fisher Matrix analysis using different types of waveforms (PN, perturbed Teukolsky, kludge) provides estimate of maximum deviation that could be mistaken for a Kerr inspiral.

• Using PN waveforms, Ryan (1997) found that a typical Adv LIGO event with a=0.8 would have δM2=0.56, compared to Kerr M2 of -0.64 → likely undetectable.

• New results suggest M2 may be determined more accurately from Adv LIGO observations.

• For a typical LISA event, δM2<0.01 → more promising. LISA should also measure higher multipoles.

• Quantify tidal coupling effect by modifying horizon flux

Spacetime mapping

• Estimate error Δε~1 for LIGO EMRIs → undetectable. LISA stands a better chance of detecting this effect.

• Dynamics of test-particles in perturbed spacetimes provide a diagnostic of such systems.

• It is remarkable that the equations of motion separate for geodesic motion in the Kerr spacetime, giving a third integral, the Carter constant. Very surprising if this generalised.

• Most orbits in most ‘quasi-Kerr’ spacetimes possess a third integral. Deviations only show up in precession and inspiral rates – in principle, allows generalization of Ryan’s theorem.

• In certain cases, the third integral is lost. In general, this occurs in astrophysically uninteresting regions of parameter space, but if observed it is a ‘smoking gun’– See loss of third integral in Poincaré map of orbits

– Difference in Fourier transform of regular versus ergodic orbit is very striking.

– If timescale over which orbit wanders due to absence of a third integral is shorter than radiation reaction timescale, the effect will be observable in the GW emission.

Orbital dynamics in perturbed spacetimes

EMRI detection

+

• EMRI events observed by LIGO or LISA are typically very faint.

• Basic technique for detection is matched filtering using a bank of templates.

• Overlap of template with data pulls signal out of the noise.

• Difficult to detect GWs that differ from templates in our bank.

• Further complications in LISA from confusion with other EMRIs and other LISA sources. LIGO sources more isolated.

• Need huge number of templates.

• To “test GR” must be able to detect GWs from non-standard systems– Use “kludge” or phenomenological templates. Increases computational

cost and makes interpretation complicated.

– Use only Kerr templates and regard observations as hypothesis tests.

– Hope to detect inspiral during a stage when it is close to a Kerr inspiral. If inspiral subsequently vanishes or persists after it should have plunged, identify the system as non-Kerr.

– Use non-template based methods, e.g., time-frequency analysis. Under ideal assumptions, could detect an EMRI out to 2Gpc in a time-frequency analysis.

• For example, an inspiral into a boson star would initially look like a Kerr inspiral, but would persist after “plunge”.

• A time-frequency analysis of a system that evolved from a regular orbital phase to an ergodic orbital phase would reveal loss of the third integral.

Detection of “quasi-Kerr” EMRIs

• Need to be able to distinguish whether deviations arise from violations of GR or presence of an exotic object– Imprint of horizon versus matter surface on waveform.

– Consider evolutions in PPN formalism or other theories of gravity.

– How accurate are our waveform models?

• Extend results to inspirals of generic orbits. Difficult due to complicated dynamics and issue of evolving the orbit.

• Extend analysis to include both tidal coupling and excess multipoles. How can we disentangle the two effects?

• Are there robust observables that provide a “smoking gun” for a non-Kerr system?

• Can we distinguish excess multipoles arising from astrophysical sources from those arising from exotica? Can coincident EM observations help distinguish GR violations from other effects?

• Must develop detection algorithms to use in data analysis. For LISA, must understand effects of source confusion.

A few outstanding issues

Commonality with SKA

• In principle, EMRIs detected with LIGO and LISA could be detected by SKA, if the compact object was a pulsar.

• Such a system would have to be in our own galaxy. The event rate is far too low to make such a combined detection likely.

• Precursor system, i.e., a pulsar in a wide orbit about a companion BH, is more likely, but the lifetime is probably still too short. If SKA finds a pulsar near Sgr A*, this will evolve into a LISA EMRI or burst source.

• BH-pulsar systems with comparable mass constituents may be detected by SKA. If the black hole deviates from Kerr, the effects on the orbital dynamics discussed here might be evident. However, these effects are much weaker in a wide binary.

• SKA/LIGO/LISA probe different mass ranges – 1 M๏ to 107 M๏ – complementary observations

Summary

• The detection of GWs from EMRIs will present a new and exciting way to probe the physics of black holes.

• LIGO EMRI events are very speculative, but Advanced LIGO may detect a few events. LISA should see EMRI events and could detect as many as several thousand during the mission lifetime.

• EMRI detections will test GR theory in the strong field region near the horizon of SMBHs.

• Identification of deviations from Kerr inspirals is a difficult problem, but it should be possible at some level.

• Observation of an event during a “Kerr-like” phase of its evolution or the use of non-template-based methods offer the best hope for detection.