Source Modeling, Numerical Simulations, and Data Analysis Joan Centrella Laboratory for High Energy Astrophysics NASA/Goddard Space Flight Center
Source Modeling • guide data analysis strategies • provide templates • identify sources Data Analysis • identify signals and sources • feedback to astrophysics • input to scenario building 1
Different scientific communities have different styles, approaches, and goals…. • Experimental Physics: traditional GW experimentalists + high energy physicists…. – build instruments, make measurements… – unambiguous detection of gravitational waves • Fundamental Physics: relativists…. – test GR and constrain theories of gravity – explore strong-field regime of gravity – unambiguous detection of black holes • Astrophysics: observers, theorists, modelers… – GW are a new window through which to observe the universe – build physical models of the sources – build scenarios for BH formation, stellar evolution, structure formation, cosmology…. 2
Data analysis: a simple view... • Analyze the data from the detectors • Identify the signals – separate out the instrumental noise…. – remove environmental, androgenic, etc. effects – obtain the physical signal coming from the astrophysical source: determine which quantities are measured, and their values… • Identify the sources: type, location.… 3
Astrophysical source modeling…. • Astrophysical scenarios – types of sources, rates, gross characteristics… – provides input to detailed modeling… • Models of specific sources – formation and evolution of sources – produce waveforms, spectra… • Two approaches to source modeling: – analytic : derive expressions for key features of model analytically or by the solution of ODEs – numerical simulations : large-scale computational models obtained by solving sets of coupled PDEs in 3-D • numerical relativity • GR hydrodynamics 4
Numerical simulations of astrophysical sources… • needed for many of the most interesting, energetic sources • pose challenges for data analysis • focus on 2 broad categories of sources: – Collapses • stellar collapse: Type II supernovae, AIC… • supermassive stars • Pop III stars – Mergers • NS/NS • NS/BH • BH/BH – stellar BHs – intermediate mass BHs – massive BHs (MBHs) 5
Collapses…. • Spherical: no GW • Axisymmetric: – Type II supernovae are the best-studied – many parameters: input physics, rotation laws…. – Zwerger-Mueller: most detailed study, catalog of 78 waveforms � short duration bursts: free-fall and bounce(s) with various waveform shapes 6
Rotational instabilities…. • Non-axisymmetric: rapidly rotating stars can undergo global rotational instability � bar formation • equilibrium cores: simulations show long-lived bar (New, Centrella, Tohline) • friction with envelope could disspiate bar • may be difficult to form bar during collapse (Brown) 7
Coalescing Binaries…. • Inspiral : widely separated, use PN approximation for point masses – early stages treated by analytic means � templates • Intermediate regime : PN approximation breaks down – “effective one body” techniques…. – quasi-equililbrium models…. • Plunge and merger : components depart from quasi- circular orbits and merge on dynamical timescales • Ringdown : merged object radiates GW and settles down into an equilibrium state – black hole : quasinormal ringing well-understood – neutron star : more work needed on modes… 8
Mergers…burst sources. • Need numerical simulations of Einstein eqns + GR hydro (for NS) • Plunge begins at or near the ISCO… • For NS/NS and NS/BH, signature of ISCO in data important to extract physical information (e.g. EOS…) • Sensitivity to system parameters: – SPH simulations of NS/NS merger by Faber and Rasio 9
Full GR codes currently not able to evolve > 1 orbit near ISCO due to instabilities � Efforts for using different techniques to evolve near ISCO, through merger, and in ringdown… • BH/BH mergers: Lazarus approach (Baker, Campanelli, Lousto and Takahashi) – Full GR Cactus code for merger – perturbation equations for ringdown • NS/NS mergers: QE models near ISCO (Duez, Baumgarte, Shapiro, Shibata, & Uryu) – quasi-equilib models – match to full 3-D numerical relativity simulation 10
Challenges for simulations… • Stability of numerical relativity codes… • Numerical dissipation:can cause spurious inspiral (New & Tohline) e.g. co-rotating equilibrium binary – stable when evolved in rotating frame – spirals in when evolved in inertial frame – lower order advection worsens the effect • How to handle the BHs: excision… • Push the limits of computer power • Multiple spatial and temporal scales � adaptive mesh refinement • Extraction of gravitational waves… • Novel approaches: Lazarus… • What quantities can be calculated that will help in confirming detection of various sources? 11
LIGO’s sensitivity to coalescing binaries and burst sources . . . 12
LISA will observe a rich variety of sources, from MBHs to Galactic binaries . . . 13
Challenges for data analysis.… • What strategies could be used to detect collapses and mergers? – matched filtering requires sufficient number of templates… – time-frequency, slope-detector, excess power statistic,…. • What strategies could be used to identify such sources? – specific type: merger versus collapse – specific case: • NS/NS merger vs. NS/BH merger…. • collapse of 10 M ∃ star vs. 20 M ∃ star …. • For LISA, will MBH/MBH coalescences obscure sources at smaller S/N? – remove bursts from data stream � “lose” this data – need to know rates… 14
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