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Massive Black Hole Mergers: As Sources and Simulations. John Baker Gravitational Astrophysics Laboratory NASA/GSFC. CGWP Sources & Simulations February 03, 2005. Massive Black Hole Mergers. MBHs are believed to lurk at centers of all galaxies with bulges

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Massive black hole mergers as sources and simulations

Massive Black Hole Mergers: As Sources and Simulations

John Baker

Gravitational Astrophysics Laboratory

NASA/GSFC

CGWP Sources & Simulations February 03, 2005


Massive black hole mergers
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


Some relevant astrophysics
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)


Detecting mbh binary mergers with lisa
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


Mbh binary inspirals and lisa
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)


Lisa observation is in the motion
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


Observing mbh binary mergers with lisa
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


Information extraction vs observation time
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


Observing mbh inspirals 1
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


Science reach mbh inspirals
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


Observing mbh binary mergers with lisa1
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)


Numerical simulations for lisa science
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


Higher order finite differencing with lazev
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


Higher order finite differencing with lazev1
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)


Higher order finite differencing with lazev2

|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)


Higher order finite differencing with lazev3
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


    Mesh refinement with hahndol
    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


    Mesh refinement testing with hahndol
    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)


    Binary bh mesh refinement testing with hahndol
    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


    Binary bh mesh refinement testing with hahndol the movie
    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


    Summary
    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)


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