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Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods

Favata, Marc (2011) Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods. Physical Review D, 83 (2). Art. No. 024027. ISSN 2470-0010.

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Barack and Sago [Phys. Rev. Lett. 102, 191101 (2009)] have recently computed the shift of the innermost stable circular orbit (ISCO) of the Schwarzschild spacetime due to the conservative self-force that arises from the finite-mass of an orbiting test-particle. This calculation of the ISCO shift is one of the first concrete results of the self-force program, and provides an exact (fully relativistic) point of comparison with approximate post-Newtonian (PN) computations of the ISCO. Here this exact ISCO shift is compared with nearly all known PN-based methods. These include both "nonresummed" and "resummed" approaches (the latter reproduce the test-particle limit by construction). The best agreement with the exact (Barack-Sago) result is found when the pseudo-4PN coefficient of the effective-one-body (EOB) metric is fit to numerical relativity simulations. However, if one considers uncalibrated methods based only on the currently known 3PN-order conservative dynamics, the best agreement is found from the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)], which relies only on the (nonresummed) 3PN equations of motion. This method reproduces the exact testparticle limit without any resummation. A comparison of PN methods with the ISCO in the equal-mass case (computed via sequences of numerical relativity initial-data sets) is also performed. Here a (different) nonresummed method also performs very well (as was previously shown). These results suggest that the EOB approach—while exactly incorporating the conservative test-particle dynamics and having several other important advantages—does not (in the absence of calibration) incorporate conservative self-force effects more accurately than standard PN methods. I also consider how the conservative self-force ISCO shift, combined in some cases with numerical relativity computations of the ISCO, can be used to constrain our knowledge of (1) the EOB effective metric, (2) phenomenological inspiral-merger-ringdown templates, and (3) 4PN- and 5PN-order terms in the PN orbital energy. These constraints could help in constructing better gravitational-wave templates. Lastly, I suggest a new method to calibrate unknown PN terms in inspiral templates using numerical-relativity calculations.

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Additional Information:© 2011 American Physical Society. Received 26 August 2010; published 21 January 2011. This research was supported through an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory, administered by Oak Ridge Associated Universities through a contract with NASA. I gratefully acknowledge Emanuele Berti, Luc Blanchet, Alessandra Buonanno, and Alexandre Le Tiec for detailed comments on this manuscript. For helpful discussions I thank Parameswaran Ajith, Curt Cutler, Harald Pfeiffer, Mark Scheel, Michele Vallisneri, Bernard Whiting, and participants at a Perimeter Institute conference in June 2010. I also thank the anonymous referee for helpful comments that improved this manuscript.
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Issue or Number:2
Classification Code:PACS: 04.25.Nx, 04.25.-g, 04.25.D-, 04.30.-w
Record Number:CaltechAUTHORS:20110301-113227754
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Official Citation:Conservative self-force correction to the innermost stable circular orbit: Comparison with multiple post-Newtonian-based methods Marc Favata Published 21 January 2011 (26 pages) 024027
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22578
Deposited By: Ruth Sustaita
Deposited On:03 Mar 2011 04:39
Last Modified:03 Oct 2019 02:38

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