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Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

Galley, Chad R. and Rothstein, Ira Z. (2017) Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations. Physical Review D, 95 (10). Art. No. 10405. ISSN 2470-0010. https://resolver.caltech.edu/CaltechAUTHORS:20170531-132927692

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Abstract

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is v^5νΩ(t−t_0) where t_0 is the initial time, t is the time elapsed, and Ω and v are the angular orbital frequency and initial speed, respectively. ν is the binary’s symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second-order corrections of the leading radiation reaction force, which involves highly nontrivial checks of the formalism (i.e., its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging, we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevD.95.104054DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.104054PublisherArticle
https://arxiv.org/abs/1609.08268arXivDiscussion Paper
ORCID:
AuthorORCID
Rothstein, Ira Z.0000-0002-3374-4212
Additional Information:© 2017 American Physical Society. Received 28 October 2016; published 31 May 2017. We thank Luc Blanchet, Marc Favata, Bala Iyer, and Nico Yunes for useful discussions and comments on a previous draft. C. R. G. was supported by NSF Grants No. CAREER-0956189 and No. PHY-1404569 to the California Institute of Technology, by the Sherman Fairchild Foundation, and also thanks the Brinson Foundation for partial support. I. Z. R. was supported by Grant No. NSF-1407744.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFPHY-0956189
NSFPHY-1404569
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
NSFPHY-1407744
Issue or Number:10
Record Number:CaltechAUTHORS:20170531-132927692
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170531-132927692
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77862
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 May 2017 21:56
Last Modified:03 Oct 2019 18:02

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