Analysis of spin precession in binary black hole systems including quadrupole-monopole interaction

By É. Racine. 2008

160 citations recorded by the source corpus.

We analyze in detail the spin precession equations in binary black hole systems, when the tidal torque on a Kerr black hole due to quadrupole-monopole coupling is taken into account. We show that completing the precession equations with this term reveals the existence of a conserved quantity at 2PN order when averaging over orbital motion. This quantity allows one to solve the (orbit-averaged) precession equations exactly in the case of equal masses and arbitrary spins, neglecting radiation reaction. For unequal masses, an exact solution does not exist in closed form, but we are still able to derive accurate approximate analytic solutions. We also show how to incorporate radiation-reaction effects into our analytic solutions adiabatically, and compare the results to solutions obtained numerically. For various configurations of the binary, the relative difference in the accumulated orbital phase computed using our analytic solutions versus a full numerical solution varies from $\ensuremath{\sim}0.3%$ to $\ensuremath{\sim}1.8%$ over $\ensuremath{\sim}80\char21{}140$ orbital cycles accumulated while sweeping over the orbital frequency range $\ensuremath{\sim}20\char21{}300\text{ }\text{ }\mathrm{Hz}$. This typically corresponds to a discrepancy of order $\ensuremath{\sim}5\char21{}6$ radians. While this may not be accurate enough for implementation in LIGO template banks, we still believe that our new solutions are potentially quite useful for comparing numerical relativity simulations of spinning binary black hole systems with post-Newtonian theory. They can also be used to gain more understanding of precession effects, with potential application to the gravitational recoil problem, and to provide semianalytical templates for spinning, precessing binaries.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/97b8bd0b10436777ef8ca6ec2c4b63723b58d8e8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Michela Mapelli
2. D. Holz
3. Maya Fishbach
4. Mario Spera
5. N. Giacobbo
6. Ilya Mandel
7. E. Barausse
8. Luca Baiotti

In Nuclear and High Energy Physics

1. Michela Mapelli
2. D. Holz
3. Maya Fishbach
4. Mario Spera
5. T. Hinderer
6. B. Farr
7. E. A. Huerta
8. Daniel George

Citations in the corpus

• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs (2018, background): “Naturally, the priors for derived parameters, such as the effective aligned spin [22, 115] given in Eq.”
• Properties of the Binary Neutron Star Merger GW170817 (2018, background): “One benefit of considering the effective spin χeff is that it is approximately conserved throughout inspiral, even as the other components of spins undergo complicated precessional dynamics [130].”
• GWTC-2.1: Deep extended catalog of compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run (2021, background): “[188] Etienne Racine, “Analysis of spin precession in binary black hole systems including quadrupolemonopole interaction,” Phys.”
• Binary Black Hole Mergers in the First Advanced LIGO Observing Run (2016, unknown): “and the effective spin parameter [71–76]”
• 1-OGC: The First Open Gravitational-wave Catalog of Binary Mergers from Analysis of Public Advanced LIGO Data (2018, background): “Consequently, the total mass boundary of the search depends strongly on the “effective spin” (Racine 2008; Ajith et al. 2011), m m m m .”
• Binary Black Hole Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo (2018, background): “Additionally, ceff is conserved throughout 184 The data release for this work can be found athttps://dcc.ligo.org/LIGOP1800324/public. the binary evolution to high accuracy(Racine 2008; Gerosa et al. 2015).”
• THE FINAL SPIN FROM BINARY BLACK HOLES IN QUASI-CIRCULAR ORBITS (2016, background): “…is inspired by Damour (2001), who finds that the leading-order conservative spin-orbit dynamics depends on the spin only through Seff with ξ = 3/4, while the leadingorder conservative spin-spin dynamics depends on Seff with ξ = 1 (see also Racine 2008; Kesden et al. 2015; Gerosa et al. 2015).”