Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach

We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known ord...

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Main Authors: Diego Montalvo, Adam Smith-Orlik, Saeed Rastgoo, Laura Sagunski, Niklas Becker, Hazkeel Khan
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Universe
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Online Access:https://www.mdpi.com/2218-1997/10/11/427
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author Diego Montalvo
Adam Smith-Orlik
Saeed Rastgoo
Laura Sagunski
Niklas Becker
Hazkeel Khan
author_facet Diego Montalvo
Adam Smith-Orlik
Saeed Rastgoo
Laura Sagunski
Niklas Becker
Hazkeel Khan
author_sort Diego Montalvo
collection DOAJ
description We apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known order, as well as any other environmental effect around the binary, as long as their dissipation power or force formulae are known. In particular, in this work, we employ this method to study a black hole–black hole binary system of mass ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>5</mn></msup></semantics></math></inline-formula> by including post-Newtonian effects of order 1PN and 2.5PN, as well as the effect of relativistic dynamical friction. We obtain the modified orbits and the corresponding modified gravitational waveform. Finally, we contrast these modifications against the LISA sensitivity curve in frequency space and show that this observatory can detect the associated signals.
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spelling doaj-art-db54ef3de87544fd87bc88d7ad30fa172025-08-20T01:54:04ZengMDPI AGUniverse2218-19972024-11-01101142710.3390/universe10110427Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian ApproachDiego Montalvo0Adam Smith-Orlik1Saeed Rastgoo2Laura Sagunski3Niklas Becker4Hazkeel Khan5Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, CanadaDepartment of Physics and Astronomy, York University, 4700 Keele Street, Toronto, ON M3J 1P3, CanadaDepartment of Physics, University of Alberta, Edmonton, AB T6G 2G1, CanadaInstitute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main, GermanyInstitute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main, GermanyDepartment of Physics and Astronomy, York University, 4700 Keele Street, Toronto, ON M3J 1P3, CanadaWe apply the Lagrangian method to study the post-Newtonian evolution of a compact binary system with environmental effects, including a dark matter spike, and obtain the resulting gravitational wave emission. This formalism allows one to incorporate post-Newtonian effects up to any desired known order, as well as any other environmental effect around the binary, as long as their dissipation power or force formulae are known. In particular, in this work, we employ this method to study a black hole–black hole binary system of mass ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mn>5</mn></msup></semantics></math></inline-formula> by including post-Newtonian effects of order 1PN and 2.5PN, as well as the effect of relativistic dynamical friction. We obtain the modified orbits and the corresponding modified gravitational waveform. Finally, we contrast these modifications against the LISA sensitivity curve in frequency space and show that this observatory can detect the associated signals.https://www.mdpi.com/2218-1997/10/11/427dark matterspikegravitational wavescompact binariespost-Newtonian approximation
spellingShingle Diego Montalvo
Adam Smith-Orlik
Saeed Rastgoo
Laura Sagunski
Niklas Becker
Hazkeel Khan
Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach
Universe
dark matter
spike
gravitational waves
compact binaries
post-Newtonian approximation
title Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach
title_full Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach
title_fullStr Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach
title_full_unstemmed Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach
title_short Post-Newtonian Effects in Compact Binaries with a Dark Matter Spike: A Lagrangian Approach
title_sort post newtonian effects in compact binaries with a dark matter spike a lagrangian approach
topic dark matter
spike
gravitational waves
compact binaries
post-Newtonian approximation
url https://www.mdpi.com/2218-1997/10/11/427
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AT laurasagunski postnewtonianeffectsincompactbinarieswithadarkmatterspikealagrangianapproach
AT niklasbecker postnewtonianeffectsincompactbinarieswithadarkmatterspikealagrangianapproach
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