Testing GR with LISA Leor Barack University of Southampton

Birmingham, March Why is LISA a good lab for fundamental physics?  Sources are of high SNR and/or long duration  Lots of info in waveform (note: “signal”=amplitude, not energy!)  Sources abundant  can repeat experiment with different sources  Automatic detection of wave polarization gives precise source orientation info (thus, e.g., no “ cos  ” problem)  Objects detectable to cosmological distances  can probe galactic history & evolution of fund parameters  Universe transparent to GWs since first sec  However: Bad sky resolution  Problem as sky location correlates with system parameters (and distance)  Here coordinated EM observations could help

Birmingham, March Fundamental physics with LISA  Strong-field gravity:  Mapping of BH spacetime and test of “No hair” theorem using EMRIs  Test of BH area theorem by measuring mass deficits in MBH-MBH merges.  Alternative theories of gravity:  Testing scalar-tensor theories using GWs from MBH binaries  Measuring speed of GWs and mass of graviton using MBH binaries  Bounding the mass of graviton using eccentric binaries  Bounding the mass of graviton via direct correlation of GW & EM observations of nearby WDs and NSs  Cosmology with LISA  Improving science return by coordinating observations in EM & GW bands

Birmingham, March Testing Strong-field gravity with LISA

Birmingham, March inspiralPeriastron precession Spin-Orbit coupling “Zoom-Whirl” effect Evolution of inclination angle Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes

Birmingham, March m= 1 M  M= 10 6 M  e fin = min 4 hours6 months Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes Sample waveform stretches

Birmingham, March “characteristic amplitude”, h c m = 10 M  M= 10 6 M  D= 1 Gpc e(plunge)=0.3 e(plunge-10yr)=0.77  Dots indicate (from left to right) state of system 5, 2, and 1 years before plunge.  Curves represent 10 yrs of source evolution (Barack & Cutler 2003) LISA’s noise curve Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes

Birmingham, March  “Geodesy” of black hole geometry: BHs have a unique multipolar structure, depending only on M and S : Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes  “No hair” theorem: All multipoles l >1 completely determined by M 00  M and S 10  S  By measuring 3 multipoles only, could potentially tell between a GR black hole, and something else, perhaps even more exotic

Birmingham, March  Could LISA tell a Kerr BH from something else? Ryan (1997): LISA could measure accurately 3-5 multipoles (if orbits are circular and equatorial, T obs = 2 yrs):  enough to “rule out” Kerr Black hole  enough to rule out a spinning Boson star (characterized by first 3 multipoles) Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes  How would this change with full parameter space of EMRI orbits?

Birmingham, March (For 10 M  onto 10 6 M  at 1Gpc, for various eccentricities and spins) How well could LISA tell the EMRI parameters? Barack and Cutler (2004) Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes

Birmingham, March  Is it really a Kerr BH? Does is have an event horizon?  Kedsen, Gair and Kaminkowski (2005): (nonrotating) supermassive Boson stars admit stable orbits within the star, below the Schwarzschild radius  Fang & Lovelace (2005): Back reaction from tidal rising on BH horizon  Glampedakis & Babak ( in progress): Kerr + generic quad. pert.  Gair et al (in progress): Do orbits in more generic spacetimes, close to Kerr, admit a 3 rd integral of motion? If not, waveform will provide a smoking gun for a non-Kerr object.  If non-Kerr: is it due to failure of GR or could be explained within GR (e.g., interaction with accretion disk)?  any info from EM observations could help! Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes

Birmingham, March Testing strong-field relativity by measuring mass deficits in MBH-MBH mergers Hughes & Menou (2005) Buonanno (2002)  From inspiral phase (using matched filters):  get m 1, m 2, s 1, s 2  From ringdown phase (from freq. and Q):  get M f, S f of merger product  Calculate Mass loss in GWs  Test Hawking’s “Area Theorem”: Although M f < m 1 + m 2, we must have A f > A 1 + A 2. (Area A obtained from mass and spin)

Birmingham, March Testing strong-field relativity by measuring mass deficits in MBH-MBH mergers Hughes & Menou (2005) “Golden binaries”: those with both inspiral and ringdown phases observable by LISA Total rate for Golden Binaries: ~1 for rare MBHs scenario ~5 for abundant MBHs scenario Total rate (rare MBHs) Golden only (abundant MBHs) Golden only (rare scenario)

Birmingham, March Testing Alternative theories with LISA

Birmingham, March Scalar-tensor theories of gravity  Variants and generalisations of Brans & Dicke (1960): Gravity described by a spacetime metric + scalar field , which may couple only to gravity (“metric” theories) or also to matter (“non-metric” theories).  Deviation from GR is parameterized by a “coupling parameter”  : General Relativity is retrieved at    Best experimental bound on  to date comes from solar-system gravitational time-delay measurements with Cassini spacecraft:  4  10 4

Birmingham, March  A finite value of  affects the GWs from binaries in two ways:  The radiation has a component with a monopolar polarization  Monopole and dipole backreaction alters the orbital evolution; phase evolution in long-lived binaries “amplifies” this effect over time.  Advantage of method:  may evolve over cosmological history. LISA could probe different cosmological epochs, which solar system measurements can’t.  Best sources: NS-MBH (have strongest dipole rad. reaction)  Given GW model and detector noise model, LISA bound on  can be estimated by working out the matched filtering variance- covariance matrix  and looking at the rms error     1/2 Testing scalar-tensor theories by measuring GWs from binaries

Birmingham, March Testing scalar-tensor theories by measuring GWs from binaries Will & Yunes (2004) NS-MBH binary Non-spinning objects, quasi-circular inspiral

Birmingham, March SNR=10 Int time= 1/2 year Testing scalar-tensor theories by measuring GWs from binaries Berti, Buonnanno & Will (2005) Including non-precessional spin effects (spin vectors aligned) Bound on  degrades significantly (Parameters are highly correlated  adding param’s “dilutes” available info) Inclusion of precession effects may decorrelate parameters and improve parameter estimation (Vecchio 2004) Independent knowledge of some source parameters (e.g. sky location) may improve bound significantly

Birmingham, March  In alternative theories the speed of GWs could differ from c because  Gravitation couples to “background” gravitational fields  GWs propagate into a higher-dim space while light is confined to 3d “brane”  Gravity is propagated by a massive field/particle (  dispersion) Speed of Gravitational Waves and the mass of graviton  Ways to measure the speed of GWs & the mass of graviton:  (“Static” Newtonian gravity) Check for violations of 1/r law:  (“Dynamic” GR) Take advantage of dispersion relation: Longer wavelengths propagate slower  (“Dynamic” GR) Compare arrival times of EM/Grav waves from same event: vast distance magnifies minute differences in speed

Birmingham, March  “Static” Newtonian gravity:  “Dynamic” relativity: Current (actual) bounds on g  From solar system planetary orbits (Talmagde et al 1988):  c > 2.8×10 12 km  From galaxy clusters (Goldhaber & Nieto 1974):  c  1×10 20 km ??  From rate of orbital decay in binary pulsar PSR B (Finn & Sutton 2002): c > 1.6×10 10 km

Birmingham, March Bounding g using LISA observations: A. Matched filtering of signals from MBH-MBH inspirals Waves from earlier stages of the inspiral (longer wavelength) propagate slightly slower than waves from later stages – an effect coded into the GW phase evolution Will (1998) Will & Yunes (2004) Non-spinning objects, quasi-circular inspiral

Birmingham, March Berti, Buonnanno & Will (2005) Including non-precessional spin effects (spin vectors aligned) Equal masses, D=3Gpc [Dashed line: ignoring data below Hz] Bounding g using LISA observations: A. Matched filtering of signals from MBH-MBH inspirals

Birmingham, March  Suppose that  EM is the orbital phase, measured optically, at t = t 0 (with error  EM )  Use LISA to measure  GW. If g = , then  GW  EM should be consistent with 0  Given  EM and  EM can give experimental bound on g  “Optimal” system for this experiment: f =2.06 mHz, M 1 =M 2 =1.4M  Bounding g using LISA observations: B. Direct correlation of GW/EM observations of nearby WD or NS binaries Larson & Hiscock (2000), Cutler, Hiscock & Larson (2003) Assuming |  EM |<<|  GW | gives  For “optimal” binary source: g  1×10 14 km   For “best” known binary: c  1×10 13 km (LMXB 4U : f =2.909 mHz, M 1 =0.07M , M 2 =1.4M  ): Constraints on orbital orientation from EM observations may improve limit significantly.

Birmingham, March If propagation is dispersive, higher harmonics of the GWs arrive slightly earlier than lower harmonics! Bound on c from eccentric EMRIs: D =1 Gpc, f =1 mHz, Based on 1 year of coherent data Bounding g using LISA observations: C. Measurements of GWs from eccentric binaries (Jones 2005) Distribution of GW power into harmonics e=0.7 e=0.5 e=0.2

Birmingham, March Cosmology with LISA

Birmingham, March  Chirping binaries as standard candles: Both GW amplitude and df/dt depend on the masses through same combination: the Chirp mass, So, from df/dt can infer GW absolute magnitude, and compare with “visual” GW magnitude to infer luminosity distance, d L.  If host galaxy identified in EM [morphological evidence, accretion disks, jets?] then given z and d L could measure the Hubble flow to high accuracy (~1%, Hughes and Holz 2005)  Conversely, if Hubble flow known to high accuracy by the time LISA flies, could use this info to help identify the host galaxy (Caveat: uncertainties from gravitational lensing reduce quality of standard candle) Cosmology with LISA

Birmingham, March Improving science return by coordinating observations in EM & GW bands Summary  Any additional info on source parameters from EM observations (most crucially, sky location) improves parameter extraction accuracy  Complementary info on source morphology from EM observations (disks, jets?) assists interpretation of GWs  GWs contain detailed info on source orientation (e.g., cos   Comparison of GW/EM arrival times provides info on speed of gravity  Combining luminosity distance (from GW) with red-shift info (from EM) provides valuable info on cosmological evolution  Direct imaging of BH horizon via radio interferometry ? For Sgr A* ( M =4  10 6, D =8 kpc):  ~ 0.02 mas  not beyond reach!

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Birmingham, March Testing strong-field relativity using Extreme-Mass-Ratio-Inspiral (EMRI) probes