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Testing GR with LISA

Testing GR with LISA. Leor Barack University of Southampton. 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

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Testing GR with LISA

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  1. Testing GR with LISA Leor Barack University of Southampton

  2. 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 “cosi” problem) • Objects detectable to cosmological distances can probe galactic history & evolution of fund parameters • Universe transparent to GWs since first 10-43 sec • However: Bad sky resolution  Problem as sky location correlates with system parameters (and distance)  Here coordinated EM observations could help Birmingham, March 2006

  3. 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 2006

  4. Testing Strong-field gravity with LISA Birmingham, March 2006

  5. Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes inspiral Periastron precession “Zoom-Whirl” effect Spin-Orbit coupling Evolution of inclination angle Birmingham, March 2006

  6. 30 min 6 months 4 hours Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes Sample waveform stretches m= 1 M M= 106 M efin=0.3 Birmingham, March 2006

  7. “characteristic amplitude”, hc Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes (Barack & Cutler 2003) m = 10 M M= 106 M D= 1 Gpc e(plunge)=0.3 e(plunge-10yr)=0.77 LISA’s noise curve • Curves represent 10 yrs of source evolution • Dots indicate (from left to right) state of system 5, 2, and 1 years before plunge. Birmingham, March 2006

  8. Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes • “Geodesy” of black hole geometry: BHs have a unique multipolar structure, depending only on M and S: “No hair” theorem: All multipoles l >1 completely determined by M00M and S10 S  By measuring 3 multipoles only, could potentially tell between a GR black hole, and something else, perhaps even more exotic Birmingham, March 2006

  9. Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes • Could LISA tell a Kerr BH from something else? Ryan (1997): LISA could measure accurately 3-5 multipoles (if orbits are circular and equatorial, Tobs = 2 yrs): • enough to “rule out” Kerr Black hole • enough to rule out a spinning Boson star (characterized by first 3 multipoles) • How would this change with full parameter space of EMRI orbits? Birmingham, March 2006

  10. Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes How well could LISA tell the EMRI parameters? (For 10 M onto 106 M at 1Gpc, for various eccentricities and spins) Barack and Cutler (2004) Birmingham, March 2006

  11. Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes • 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 (2005 + in progress): Kerr + generic quad. pert. • Gair et al (in progress): Do orbits in more generic spacetimes, close to Kerr, admit a 3rd 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! Birmingham, March 2006

  12. Buonanno (2002) • Calculate Mass loss in GWs • Test Hawking’s “Area Theorem”: Although Mf < m1+ m2, we must have Af > A1 + A2 . (Area A obtained from mass and spin) Testing strong-field relativityby measuring mass deficits in MBH-MBH mergersHughes & Menou (2005) • From inspiral phase (using matched filters): •  get m1, m2, s1, s2 • From ringdown phase (from freq. and Q): •  get Mf, Sf of merger product Birmingham, March 2006

  13. Testing strong-field relativityby measuring mass deficits in MBH-MBH mergersHughes & Menou (2005) “Golden binaries”: those with both inspiral and ringdown phases observable by LISA Total rate (rare MBHs) Golden only (abundant MBHs) Total rate for Golden Binaries: ~1 for rare MBHs scenario ~5 for abundant MBHs scenario Golden only (rare scenario) Birmingham, March 2006

  14. Testing Alternative theories with LISA Birmingham, March 2006

  15. Best experimental bound on w to date comes from solar-system gravitational time-delay measurements with Cassini spacecraft: w > 4104 Scalar-tensor theories of gravity • Variants and generalisations of Brans & Dicke (1960): Gravity described by a spacetime metric + scalar field f, which may couple only to gravity (“metric” theories) or also to matter (“non-metric” theories). • Deviation from GR is parameterized by a “coupling parameter” w: General Relativity is retrieved at w Birmingham, March 2006

  16. Testing scalar-tensor theoriesby measuring GWs from binaries • A finite value of w 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: w 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 w can be estimated by working out the matched filtering variance-covariance matrix L and looking at the rms error Dw ~ (Lww)-1/2 Birmingham, March 2006

  17. Testing scalar-tensor theoriesby measuring GWs from binaries Will & Yunes (2004) NS-MBH binary Non-spinning objects, quasi-circular inspiral Birmingham, March 2006

  18. SNR=10 Int time= 1/2 year Testing scalar-tensor theoriesby measuring GWs from binaries Berti, Buonnanno & Will (2005) Including non-precessional spin effects (spin vectors aligned) Bound on w 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 2006

  19. (“Static” Newtonian gravity) Check for violations of 1/r law: • (“Dynamic” GR) Take advantage of dispersion relation: Longer wavelengths propagate slower Speed of Gravitational Waves and the mass of graviton • 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) • Ways to measure the speed of GWs & the mass of graviton: • (“Dynamic” GR) Compare arrival times of EM/Grav waves from same event: vast distance magnifies minute differences in speed Birmingham, March 2006

  20. From solar system planetary orbits (Talmagde et al 1988): lc > 2.8×1012 km • From galaxy clusters (Goldhaber & Nieto 1974): lc 1×1020 km ?? • From rate of orbital decay in binary pulsar PSR B1534+12 (Finn & Sutton 2002): lc > 1.6×1010 km Current (actual) bounds on lg • “Static” Newtonian gravity: • “Dynamic” relativity: Birmingham, March 2006

  21. Will (1998) Will & Yunes (2004) Non-spinning objects, quasi-circular inspiral Bounding lg 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 Birmingham, March 2006

  22. Bounding lg using LISA observations:A. Matched filtering of signals from MBH-MBH inspirals Berti, Buonnanno & Will (2005) Including non-precessional spin effects (spin vectors aligned) Equal masses, D=3Gpc [Dashed line: ignoring data below 10-4 Hz] Birmingham, March 2006

  23. Bounding lg using LISA observations:B. Direct correlation of GW/EM observations of nearby WD or NS binaries Larson & Hiscock (2000), Cutler, Hiscock & Larson (2003) • Suppose that fEM is the orbital phase, measured optically, at t = t0 (with error dfEM) • Use LISA to measure fGW. If lg= , then fGW-fEM should be consistent with 0 • Given dfEM and dfEM can give experimental bound on lg • “Optimal” system for this experiment: f=2.06 mHz, M1=M2=1.4M • Assuming |dfEM|<<| dfGW| gives • For “optimal” binary source: lg1×1014 km • For “best” known binary: lc 1×1013 km (LMXB 4U1820-30: f=2.909 mHz, M1=0.07M , M2=1.4M): Constraints on orbital orientation from EM observations may improve limit significantly. Birmingham, March 2006

  24. e=0.7 e=0.2 e=0.5 1017 Distribution of GW power into harmonics Bound on lc from eccentric EMRIs: D=1 Gpc, f=1 mHz, Based on 1 year of coherent data 1016 Bounding lg using LISA observations:C. Measurements of GWs from eccentric binaries (Jones 2005) If propagation is dispersive, higher harmonics of the GWs arrive slightly earlier than lower harmonics! Birmingham, March 2006

  25. Cosmology with LISA Birmingham, March 2006

  26. Cosmology with LISA • 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, dL. • If host galaxy identified in EM [morphological evidence, accretion disks, jets?] then given z and dL 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) Birmingham, March 2006

  27. Direct imaging of BH horizon via radio interferometry ? For Sgr A* (M=4106, D=8 kpc): q~ 0.02 mas not beyond reach! 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 i) • 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 Birmingham, March 2006

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  29. Testing strong-field relativityusing Extreme-Mass-Ratio-Inspiral (EMRI) probes Birmingham, March 2006

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