Complete gravitational waveforms from black-hole binaries with non-precessing spins

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1 Complete gravitational waveforms from black-hole binaries with non-precessing spins P. Ajith LIGO Lab & Theoretical Astrophysics - Caltech / AEI Hannover In collaboration with M. Hannam, S. Husa, B. Bruegmann, Y. Chen, N. Dorband, D. Mueller, F. Ohme, D. Pollney, C. Reisswig, L. Santamaria and J. Seiler MG12 Paris16 July 2009

2 Motivation Recent progress in Analytical & Numerical Relativity waveform templates modelling inspiral, merger and ring down (IMR) stages of the BBH coalescence can be constructed. [Ajith et al (2008), Buonanno et al (2007), Damour & Nagar (2008)] Dramatic improvement in the sensitivity, distance reach and parameter estimation in the searches for high-mass BBHs. IMR waveforms are also employed in the exploration of various questions related to GW astronomy. [Ajith & Bose (2009), Sesana et al (2009] Limitations These templates model non-spinning BH binaries, while most of the BHs in nature may be highly spinning [Volonteri et al (2005), Shapiro (2005)]. Potential loss of events due to signal-template mismatch. 2

3 Non-precessing spins: why bother? Issues with spinning IMR waveforms: Spin adds 6 additional parameters in the template bank more false alarms. [e.g., Van Den Broeck et al (2009)] Requires systematic and accurate exploration of the large parameter space using NR simulations might not be possible in the near future. Non-precessing spins: Population synthesis studies indicate that small angles between spin and orbital angular momentum is astrophysically preferred high expectation for such a population to exist [Grandclement et al (2004), Kalogera (2004)] Interesting physics, such as orbital hang-up effect. Such signals are loud better chances of detection! Degeneracy in the parameter space this class of binaries can be modelled by adding just one extra parameter in the waveforms. 3

4 IMR waveforms for binaries with non-precessing spins Strategy: Construct hybrid PN-NR waveforms at different points in the parameter space by combining PN and NR waveforms. Parametrize the hybrid waveforms in the frequency domain in terms of 12 phenomenological parameters: Reparametrize the phenomenological parameters in terms of the physical parameters and match them to the analytical waveforms from BH perturbation theory in the extreme-mass-ratio limit. Include spin effects in terms of a single parameter 4

5 NR simulations Performed with the BAM (Jena) and CCATIE (AEI) codes, covering a good fraction of the parameter space. Equal-spin simulations (BAM) Used to construct the analytical template family Unequal-spin simulations (CCATIE/BAM) Used to test the new templates 5

6 NR simulations Performed with the BAM (Jena) and CCATIE (AEI) codes, covering a good fraction of the parameter space. Equal-spin simulations (BAM) Unequal-spin simulations (CCATIE/BAM) Inputs from BH perturbation Used to construct the analytical template family Used to test the new templates 6

7 Constructing hybrid waveforms Hybrid waveforms are constructed by matching PN and NR waveforms in an overlapping time interval. PN TaylorT1 waveforms with 3.5PN phase and 3PN amplitude (spin dependent corrections up to 2.5PN). [Arun et al (2009), Blanchet et al (2004, 2008)] 7

8 Parametrizing the hybrid waveforms Fit the hybrid waveforms in frequency domain in terms of 12 phenom parameters: A(Mf) merger fits PN Lorentzian fits 8

9 Parametrizing the hybrid waveforms Fit the hybrid waveforms in frequency domain in terms of 12 phenom parameters: PN corrections to inspiral amplitude Spin-dependent parameters describing the merger amplitude Log terms in the test-mass v (πmf)1/3 limit (from BH perturbation) 9

10 From phenomenological to physical parameters Reparametrize the phenom parameters in terms of physical parameters 10

11 From phenomenological to physical parameters Reparametrize the phenom parameters in terms of physical parameters... and match them to the BH perturbation waveforms in the test-mass limit. SPA phasing (inspiral) coefficients in the test-mass limit 11

12 EMR limit : Caveats Assumes that phase of the merger and ring-down is a continuation of the adiabatic inspiral. [Bardeen et al (1972), Tagoshi et al (1996)] Assumes that the functional form of the plunge in the EMR limit is the same as that of the merger in the comparable-mass regime. 12

13 EMR limit : Caveats Assumes that phase of the merger and ring-down is a continuation of the adiabatic inspiral. [Bardeen et al (1972), Tagoshi et al (1996)] Assumes that the functional form of the plunge in the EMR limit is the same as that of the merger in the comparable-mass regime. In the EMR limit, it is expected that the the waveform will be dominated by the long inspiral, followed by a short plunge and ring down. Inspiral is guaranteed to be well modeled. Imposition of the EMR limit ensures that the waveform family is well behaved outside the parameter range where the NR data is available. 13

14 Effectualness and faithfulness of the new templates Fitting factor and faithfulness of the new templates with equal-spin hybrid waveforms. FF and faithfulness > Highly effectual and faithful. 14

15 Effectualness and faithfulness of the new templates Unequal-spins effectual and faithful (>0.98) for equal-mass binaries. Effectual (>0.98) for unequal-mass binaries with unequal spins. 15

16 Distance reach of BBH searches Effective distance to optimallyoriented (equal-mass) binaries producing SNR 8 at Initial LIGO. Horizon distances up to ~1Gpc for LIGO / ~2Gpc for eligo / ~20 Gpc for AdvLIGO for highly spinning binaries (χ ~ 0.85). ~70% improvement in the distance reach compared to non-spinning binaries potential 5 improvement in the event rates! 16

17 Summary and outlook First ready-to-use analytical IMR waveforms for BH binaries with non-precessing spins combining state-of-the-art results from PN/NR/BH perturbation. Significant fraction of signals can be missed if searched using non-spinning IMR templates. Dramatic improvement in the distance reach for high-mass binary BHs. Can be used in LIGO's searches template-based and burst searches. More accurate PN/NR calculations can be incorporated when available in future. Ongoing work Improved ways of constructing hybrid, modelling ring down. Higher harmonics. Better treatment of the plunge in the EMR limit. 17

18 Non-precessing spins: why bother? Searching for non-precessing binaries using non-spinning templates [Ajith et al (2008)]: 18

19 Non-precessing spins: why bother? Searching for non-precessing binaries using non-spinning templates [Ajith et al (2008)]: Potential loss of up to 50% of signals (FF ~ 0.75) Estimated parameters will be significantly biased (faith. ~ 0.3) Fitting factor (match maximized over all templates in a template bank). Faithfulness (match using the same parameters). 19