Transcript Testing the black hole no-hair theorem using LIGO extreme mass

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)
Extreme mass ratio inspirals
• 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๏
LISA 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.
LIGO 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.
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.
Testing GR using EMRIs
• 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 General Relativity”
• 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.
Spacetime mapping
• 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
• 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.
Spacetime mapping
• 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
• This also encodes the spacetime multipole moments, but how
they are encoded is much more difficult to calculate.
Spacetime mapping
• 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
• Estimate error Δε~1 for LIGO EMRIs → undetectable. LISA
stands a better chance of detecting this effect.
Orbital dynamics in perturbed spacetimes
• 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.
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.
+
Detection of “quasi-Kerr” EMRIs
• 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 timefrequency 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.
A few outstanding issues
• 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.
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.