Next-to-leading order spin-orbit effects in the equations of motion, energy loss and phase evolution of binaries of compact bodies in the effective field theory approach

Abstract

We compute spin-orbit effects in the equations of motion, binding energy and energy loss of binary systems of compact objects at the next-to-leading order in the post-Newtonian (PN) approximation in the effective field theory (EFT) framework. We then use these quantities to compute the evolution of the orbital frequency and accumulated orbital phase including spin-orbit effects beyond the dominant order. To obtain the results presented in this paper, we make use of known ingredients in the EFT literature, such as the potential and the multipole moments with spin effects at next-to-leading order, and which are given in the linearized harmonic gauge and with the spins in the locally flat frame. We also obtain the correction to the center-of-mass frame caused by spin-orbit effects at next-to-leading order. We demonstrate the equivalence between our EFT results and those which were obtained elsewhere using different formalisms. The results presented in this paper provide us with the final ingredients for the construction of theoretical templates for gravitational waves including next-to-leading order spin-orbit effects, which will be presented in a future publication.

arXiv comment19 pages, 1 figure

References in corpus (54)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• GW190814: Gravitational Waves from the Coalescence of a 23 M${}_{\odot }$ Black Hole with a 2.6 M${}_{\odot }$ Compact Object
• GW190425: Observation of a Compact Binary Coalescence with Total Mass $\sim 3.4M_{\odot }$
• GW190521: A Binary Black Hole Merger with a Total Mass of $150M_{\odot }$
• GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• An Effective Field Theory of Gravity for Extended Objects
• GW190412: Observation of a Binary-Black-Hole Coalescence with Asymmetric Masses
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Post-Newtonian corrections to the motion of spinning bodies in NRGR
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Higher-order spin effects in the dynamics of compact binaries II. Radiation field
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries
• Gravitational radiative corrections from effective field theory
• Spin(1)Spin(2) Effects in the Motion of Inspiralling Compact Binaries at Third Order in the Post-Newtonian Expansion
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries
• Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
• Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Effective field theory methods to model compact binaries
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. III. Radiation reaction for binary systems with spinning bodies
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction
• Radiation reaction and gravitational waves in the effective field theory approach
• Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order
• The Turbulent Origin of Outflow and Spin Misalignment in Multiple Star Systems
• Leading order finite size effects with spins for inspiralling compact binaries
• Next-to-next-to-leading order spin-orbit effects in the equations of motion of compact binary systems
• Spin induced multipole moments for the gravitational wave flux from binary inspirals to third Post-Newtonian order
• Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme
• Fingerprints of binary black hole formation channels encoded in the mass and spin of merger remnants
• Multipole expansion at the level of the action
• On the Apparent Ambiguities in the Post-Newtonian Expansion for Binary Systems
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme
• Canonical Formulation of Spin in General Relativity
• Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects
• Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects
• NNNLO gravitational quadratic-in-spin interactions at the quartic order in G
• Using final black hole spins and masses to infer the formation history of the observed population of gravitational wave sources
• Radiation reaction at 3.5 post-Newtonian order in effective field theory
• Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach
• Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations
• Analytic Solutions to Compact Binary Inspirals With Leading Order Spin-Orbit Contribution Using The Dynamical Renormalization Group

Cited by in corpus (7)

• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Radiation Reaction for Non-Spinning Bodies at 4.5PN in the Effective Field Theory Approach