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Estimating spinning binary parameters and testing alternative theories of gravity with LISA

Estimating spinning binary parameters and testing alternative theories of gravity with LISA. Emanuele Berti EB, A. Buonanno, C. M. Will, gr-qc/0411129+gr-qc/0504017 EB, A. Buonanno, Y. Chen, in preparation EB, V. Cardoso, C. M. Will, in preparation LISA images and animations from:

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Estimating spinning binary parameters and testing alternative theories of gravity with LISA

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  1. Estimating spinning binary parameters and testing alternative theories of gravity with LISA Emanuele Berti EB, A. Buonanno, C. M. Will, gr-qc/0411129+gr-qc/0504017 EB, A. Buonanno, Y. Chen, in preparation EB, V. Cardoso, C. M. Will, in preparation LISA images and animations from: http://lisa.jpl.nasa.gov

  2. Outline 1) Brief overview of the LISA mission and noise 2) Typical target binaries for LISA * High mass-ratio inspirals * Supermassive black hole (SMBH) binaries (observational evidence and event rates) 3) Gravitational-wave templates for nonprecessing binaries * Monte Carlo simulations for parameter estimation * Bounds on alternative theories of gravity (Brans-Dicke, massive-graviton theories) 4) LISA and the formation history of SMBH binaries (effect of LISA low-frequency noise) 5) Work In Progress Effect of systematic errors on parameter estimation Inspiral vs. ringdown for SMBHs

  3. LISA orbit Joint ESA-NASA spaceborne GW observatory sensitive to 10-5 Hz<f<1 Hz 3 spacecraft in heliocentric trajectory trailing 20° behind the Earth Equilateral triangle, armlength=5x106 km 60° inclination with respect to the ecliptic

  4. A simple model of LISA response

  5. LISA orbit - continued Unbarred coords: LISA frame Barred coords: Solar System frame Taking into account LISA’s orbital motion we can estimate * distance to the binary * angular resolution Cutler 97

  6. LISA noise and sources * SMBH binaries:M~105-107 Msun IMBH binaries: M~102-104 Msun * Neutron star-IMBH binaries:MIMBH~102-104 Msun

  7. LISA reachfor NS-BH and SMBH binaries Luminosity distance DL for NS-BH binaries detected with SNR=10 Event rate is uncertain !! Gair et al. 04, Will 04 SNR for equal mass BH-BH binaries as a function of total mass at DL=3 Gpc (z~0.5)

  8. SMBH binaries Relativity: * Inspiral PN waveforms -> High-precision tests of GR * Merger waveforms -> Tests of nonlinear gravity * Ringdown waveforms -> Tests of the no-hair theorem Astrophysics: * Cosmic history of SMBHs and IMBH/SMBH formation from high z to the present; indirectly, hints on structure formation * “Final parsec problem”: how does a SMBH binary become “hard” enough for GWs to drive merger? LISA measures M=(1+z)Msource High SNR,good sensitivity only in a certain SMBH mass/redshift range Orbital dynamics following galaxy merger and event rates are uncertain

  9. SMBH binaries and galaxy mergers * SMBHs are present in bulges of nearly all local galaxies * Galaxy mergers produce SMBH binaries Some circumstantialobservational evidence for “hard” SMBH binaries: Blazar OJ 287 (optical variability with P=11.86yrs) Radio galaxy 3C 66B (elliptical motion of radio core with P=1 yr) SMBH binary formation(Merritt & Milosavljevic 04) 1) Galaxies merge, BHs sink to center by dynamical friction 2) Gravitational slingshot interactions with stars inside the “loss cone” (or gas accretion onto the binary) increase the binary’s binding energy 3) Gravitational radiation dominates (“final parsec problem”: need mechanism to refill the loss cone) Some observational evidence that coalescence is the norm(Haenhelt 03)

  10. SMBH binary event rates • * Haenhelt 94: rate can be high if BHs reside in DM halos • * Menou et al. 01: ubiquity of BHs in galaxies today • consistent with small occupation number at high z • Total of about 10 events/yrout to z=5 • * Rhook & Wyithe 05: revise Wyithe & Loeb 03 (optimistic) • and find consistent rates of about 15 events/yr; • most events originate at z=3-4 • * Sesana et al. 04: binaries can be ejected from core, • a 3 year LISA mission could resolve 35 mergers at 2<z<6 • 9 events/yr with one binary more massive than 105 Msun • * Enoki et al. 04: events visible • out to z=1 (M=108 Msun) or out to z=3 (M=106 Msun) • * Islam et al., Koushiappas: more optimistic rates, • different mechanism to “seed” galaxies with BHs at large z • “Average” prediction: expect ~10 events/year at 2<z<6

  11. GW templates for circular orbits Spin-orbit, 1.5PN Spin-spin, 2PN Brans-Dicke: dipole radiation; best bounds from NS-IMBH Massive graviton: D-dependent delay in wave propagation Best bounds from SMBH binaries at large distance

  12. Parameter estimation

  13. Monte Carlo distributions for a SMBH binary – 1

  14. Monte Carlo distributions for a SMBH binary - 2

  15. Bound on the graviton Compton wavelength We only include spin-orbit (spin-spin: Fisher matrix becomes non-invertible)

  16. Monte Carlo distributions for a NS-IMBH binary - 1

  17. Monte Carlo distributions for a NS-IMBH binary - 2

  18. Correlations and angular resolution Insensitive to inclusion of spin-orbit Maximum increases when we include spin-orbit

  19. Bound on Brans-Dicke parameter We only include spin-orbit (spin-spin: Fisher matrix becomes non-invertible)

  20. Average errors for a SMBH binary as a function of M

  21. Graviton Compton wavelength Will 98 (LIGO and LISA), Will & Yunes 04 (LISA SCG, angle-average, no spins) Binary at DL=3 Gpc (z~0.5) Solar system bound (Yukawa-term deviations from Kepler’s third law): bound lg~3x1012 km Alternatives: Sutton & Finn 02 (binary pulsars); Cutler, Hiscock & Larson 03 (GW phase vs. orbital phase); Jones 04 (eccentricity)

  22. Brans-Dicke parameter (SNR=10) Will 94, Damour & Esposito-Farése 98 (LIGO) Scharre & Will 02, Will & Yunes 04 (LISA, angle-average, no spins)

  23. Average errors as functionsof cosmological redshift Hughes 02: LISA only measures redshifted combinations of the intrinsic binary parameters (masses, spin) of the form M=(1+z)Msource, J=(1+z)2Jsource Measuring (luminosity) distance DL(z,cosmology)and assuming cosmology is known, find z(DL) and remove degeneracy (106+106) (107+107)

  24. Percentage of “useful” SMBH binaries How many (nonspinning) binaries can we observe with: * Error on the chirp mass <0.1%? * Error on the reduced mass <1%? (“Golden” binaries) *Error on distance <10%? (~uncertainty on cosmology) (106+106) (107+107)

  25. Parameter estimationand the LISA low-frequency noise Degradation in parameter estimation for SMBH binaries if we can only trust the noise curve down to f=10-4 Hz (“Standard” value in BBW: f=10-5 Hz) Results for nonspinning binaries at DL=3 Gpc

  26. Systematic errors in parameter estimation Spin effects known only up to 2PN: we work at 2PN Omitting spin effects, the waveform is now known to 3.5PN Blanchet, Damour, Esposito-Farése & Iyer 04 Effect on parameter estimation for LIGO-Virgo: EB & Buonanno (unpublished) Arun, Iyer, Sathyaprakash & Sundararajan 05 Estimates of chirp mass (reduced mass) improve by 19% (52%) respectively from 2PN to 3.5PN, but improvement is non-monotonic ------------------------------------------------------------------------------------ LISA: the effect of high-PN orders can be dramatic! Number of cycles contributed by high PN orders is usually large EB, Buonanno & Chen, work in progress: * Study convergence of the PN series for LISA * Truncate signal 1 day/week/month before merger? (idea: get rid of region where PN convergence is poor)

  27. From inspiral to ringdown Ringdown: damped exponential oscillations with complex (QNM) frequencies wlm,n=wR+iwI The SNR for detection of each QNM depends on: * The black hole’s angular momentum,a=J/M * The energy radiated in the mode,Erad=erdM Standard lore: l=m=2 (“bar” mode) should dominate

  28. Inspiral vs. ringdown Angular momentum: small effect a=0.98 a=0.80 a=0 erd is crucial: need numerical relativity How is energy distributed with (l,m,n)?? Brandt & Seidel 96: distorted BHs Sperhake et al. 05: head-on

  29. Conclusions Binary parameters in the gravitational-wave phase are highly correlated: adding parameters dilutes available information Errors on parameters increase when we include spins aligned/antialigned with orbital angular momentum For SMBH binary mass measurements are degraded by factors: ~10 (chirp mass), ~20-100 (reduced mass) including the SO term; additional factor ~3-5 including also the SS term Brans-Dicke bound reduced by ~30-80 by SO Massive graviton bound reduced by ~4-5 by SO ------------------------------------------------------------------------------------ Future work * Spin precession could help decorrelate parameters(Vecchio) * Eccentricity could remove degeneracies(Hellings & Moore) * Systematics might be comparable to statistical errors for large SNR * Inspiral vs. ringdown: multi-mode formalism for parameter estimation

  30. (Very partial) reference list * Flanagan & Hughes, PRD 57, 4535 (1998): inspiral, merger, ringdown * Cutler, PRD 57, 7089 (1997): parameter estimation formalism * Schutz, Nature 323, 310 (1986): binaries as standard candles * Markovic, PRD 48, 4738 (1993): cosmology with binaries * Hughes, MNRAS 331, 805 (2002): cosmology, inspiral & ringdown * Holz & Hughes, astro-ph/0212218+CQG 20, S65 (2003): Cosmology with SMBHs; EM counterparts, lensing * Hughes & Menou, astro-ph/0410148: “golden binaries” * Vecchio, PRD 70, 042001 (2004): precessing binaries * EB, Buonanno & Will, gr-qc/0411129+0504017: parameter estimation * Seto, PRD 66, 122001 (2002): finite armlength * Damour, Iyer & Gopakumar, PRD 70, 064028 (2004): PN with eccentricity * Hellings & Moore, CQG 20, S181 (2003): higher harmonics * Rogan & Bose, CQG 21, S1607 (2004): dependence on sky position * Miller & Colbert, IJMPD 13, 1 (2004): IMBHs * Merritt & Milosavljevic, astro-ph/0410364: SMBH binary formation

  31. Tidal deformations in the pre-merger phase for binary neutron stars • In Newtonian theory (see eg. Kopal) rotational deformations and tidally-induced deformations in a binary (equilibrium tides) are described by the so-called apsidal constants kl. For homogeneous stars, kl=3/[4(l-1)] • The l-th apsidal constant is related to the l-th multipole moment • (eg., for a Kerr black hole k2 is the same • as for a homogeneous Newtonian star) • In Newtonian theory, to linear order, • k2 for tidal and rotational deformations is the same • ------------------------------------------------------------------------------------ • State of the art simulations of the pre-merger phase • (eg. the LORENE code) assume • Quasiequilibrium • Synchronized (corotating) or better, irrotational flow • Conformal flatness • Barotropic EOS (usually a polytropicwith G=2)

  32. Post-Newtonian diagnostic for binary neutron stars Mora & Will 03; EB, Iyer & Will, work in progress Point masses k2=k3=0 Uniform density k2=3/4,k3=3/8 “Half uniform density” k2=3/4,k3=3/8 G=2 polytrope k2=0.260,k3=0.106 G=2 polytrope+ eccentricity

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