Massive Black Hole Mergers: As Sources and Simulations

1. Massive Black Hole Mergers: As Sources and Simulations John Baker Gravitational Astrophysics Laboratory NASA/GSFC CGWP Sources & Simulations February 03, 2005

2. Massive Black Hole Mergers • MBHs are believed to lurk at centers of all galaxies with bulges • Most galaxies are believed to have at least one merger  massive black hole binary mergers • Merger rates: • depend on size of “seed” black holes, accretion rates, merger efficiency... • expect ~ 10s (more or less) per year • Gravitational waves from final merger are detectable by LISA to high z (eg ~20) • Observations of such events by LISA… • may be used to map merger history of MBHs (and their host structures) to high z • May provide tests of strong GR dynamics

3. Some relevant astrophysics… • Theory (Look out to z~20, prefer small MBH) • ΛCDM models … are they correct? • Small primordial density fluctuations in dark matter grow over time • Matter collects in gravitational potential wells and small galaxies with small MBH form • As the potential wells deepen the galaxies merge progressively • Predicts many smaller (104-105 MSun) binaries • Do the MBH usually merge? • Dynamical friction turns off as the binary hardens • Three-body interactions can take over but there must be a processwhich continues to bring objects near the binary • Observation (Look to z>2, prefer large MBH) • Is there a shortage of smaller (<106 MSun) black holes (eg in SDSS)? • Dearth of merger candidates at z<1-2 • Do larger MBH form earlier? (possible interpretation of recent X-ray observations)

4. Detecting MBH binary mergers with LISA • LISA measures strain due to incoming GW signals • Instrumental strain noise spectrum • Characteristic strain of GW signal • LISA measures redshifted frequency • Expected signal-to-noise ratio (SNR) for obs of a chirping source using matched filtering • For a detection, source must be within LISA’s band of sensitivity at good SNR

5. MBH binary inspirals and LISA • symbols at 10 yrs, 1 yr, 1 mo, & 1 d before the onset of merger, and at the onset of merger (the merger & subsequent ringdown occurs at higher frequencies)

6. LISA…observation is in the motion… • Joint NASA/ESA mission • all-sky monitor, measures both GW polarizations  2 time series • 3 spacecraft • equilateral triangle • arm length L = 5 x 106 km • orbits Sun at 1 AU • 20o behind Earth in its orbit • Detector motions • orbital motion around the Sun • yearly rotation of the triangular spacecraft constellation around the normal to the detector plane tilted at 60oto ecliptic • These motions induce modulations of incident GW signal that encode sky position and orientation of source

7. Observing MBH binary mergers with LISA • For a good observation, want masses, spins, sky position, z… • This information must be extracted from LISA’s data stream • Source parameters are entangled: • Track phase of inspiral waveform measure (1+z)m1 and (1+z)m2 • Overall amplitudes of waveforms depend on • Luminosity distance D(z) (Knowing cosmology, invert D(z) to get redshift) • chirp mass M = M2/5m3/5 (M = total mass, m = reduced mass) • orientation and sky position • Info on orientation and sky position (and thus z) is encoded in modulations of LISA’s signal due to its yearly motion  need source to be within band of sensitivity for significant fraction of LISA’s yearly orbit

8. Information extraction vs observation time m1 = 106 Msun m2 = 105 Msun z = 1 The signal needs to be visible for 6 months before coalescence in order to preserve information extraction Courtesy A Vecchio

9. Observing – MBH inspirals 1 • An MBH binary can be observed by LISA for 6 months in band if it’s ‘x’ is above a given sensitivity curve. X’s label systems. Space of X’s looks like… x x x x x x x

10. Science Reach – MBH inspirals • An MBH binary with chirp mass M at redshift z can be observed by LISA for 6 months in band if it is above a given sensitivity curve

11. Observing MBH binary mergers with LISA • Detection: LISA data stream contains source signal at good SNR • Observation: source parameters can be extracted accurately • How to extract source parameters? • Use motion-induced modulations  Source must be w/in LISA’s band for ~ 6 months • Can we relax the 6-month rule….and demands on low frequency sensitivity? • Other options… • Tolerate incomplete information…e.g. just get (1+z)M….many more systems accessible…. • Include multipole components higher than quadrupole • May get useful source info from merger/ringdown phase (But we have to understand mergers first)

12. Numerical Simulations for LISA science • Astrophysics: • Merger kicks ejection rates • Remnant spins  population stats. • Parameter Estimation: • Better estimates  more systems accessible (larger z, larger masses) and less reliance on low-frequency band • High SNR implies small details in waveforms may be useful • Improved sensitivity to other sources: • “cocktail party problem” • LISA analysis requires fitting ALL sources simultaneously • How good do simulations have to be? • Any understanding may be useful • Ultimately want high-precision waveforms: eg. Run for 10000 M, with 0.1% accuracy. • Moving toward more accurate waveforms: • Higher order finite differencing • Adaptive mesh refinement

13. Higher order finite differencing with LazEv • Why not second order differencing? • For 3+1D simulations: work ~ h-4; • error ~ hn  error ~ work-n/2 • To reduce error from O(1) to O(0.01) you need to work 10000 times as hard if n=2. • LazEv: • A general Cactus-based evolution tool • Developed by Yosef Zlochower, J.B., and Lazarus-UTB team • Includes 4th order BSSN formulation of Einstein’s equations. • Designed for generalization to higher-order and other formulations. • 4th-order runs here use (Kreiss-Oliger) dissipation

14. Higher order finite differencing with LazEv • LazEv with 1D Gowdy wave “Mexico test” (Y. Zlochower, et al) • h=0.2/ρ, ρ=2,4,8 • Evolves backward in time • Excellent convergence for 1000 crossing times • Error reduced byfactor of 256 |ρ4 CHam|L2 t (crossing)

15. |ρ4 CHam|L2 Higher order finite differencing with LazEv • LazEv with 2D gauge wave “Mexico test”: (Y. Zlochower, et al) • h=0.2/ρ, ρ=2,4,8 • Strong wave (A=0.1) • “X”=crossing times • Excellent convergence for 60 crossing times • Error reduced byfactor of 256 t (crossing)

16. Higher order finite differencing with LazEv • LazEv with BBH example: (Y. Zlochower, et al ) • Black holes released from rest at ISCO separation • Punctures crash with 4th order shift-advection • Mixed w/ 2nd order shift-advection • Full 4th order with excision • Both approaches at two resolutions compared • Preliminary result! • Re[ψ4]l=m=2 t/M

17. Mesh Refinement with Hahndol • Why use AMR? • Multiple scales O(M) at black hole O(100M) for orbit wave • Can achieve higher resolution in critical regions • Can push outer boundary far away. • Hahndol code for AMR: (GSFC NumRel team ) • Block-based mesh refinement using PARAMESH • BSSN formalism w/ 2nd order finite differencing (for now) • Guard cells (ghostzones) at refinement boundaries filled by quadratic or cubic interpolation • Thoroughly investigating interface performance

18. Mesh Refinement testing with Hahndol • Wave propagation • Teukolsky wave tests • 1BH strong field convergence studies • Geodesic slicing • 1+log slicing • Quadratic or cubic guard cell filling • Gamma-driver gauge (in progress) • 2BH test • Head-on collision waves (in progress) • AMR studies • Brill wave collapse (in progress)

19. Binary BH Mesh Refinement testing with Hahndol • Brill-Lindquist data at ISCO separation • 1+log slicing • cubic guard cell filling • Γ-driver shift • Eight-level FMR • h=M/32 and M/16 out to x=2M • Outer boundary at 256M • Preliminary result

20. Binary BH Mesh Refinement testing with Hahndol: The movie • Same run fromlast slide • Computationaldomain • To 256M • Domain shown x,y,z ≤ 64M • Quantity shown • ||ψ4|| • Interfaces shown • At 2, 4, 8, 16 and 32M • Resolution in visible regions • M/32 to M

21. Summary • MBH-MBH systems are an exciting source for LISA observations • Understanding of these systems based on numerical simulations will be of great valuefor LISA science • Development toward higher-fidelity simulations is progressing on two technologies • Higher-order differencing (Lazarus-UTB) • Mesh refinement (GSFC)