Renormalized second post-Newtonian spin contributions to the accumulated orbital phase for LISA sources

László Árpád Gergely, Balázs Mikóczi

Research output: Article

4 Citations (Scopus)


We give here a new third post-Newtonian (3PN) spin-spin contribution (in the PN parameter ε) to the accumulated orbital phase of a compact binary, arising from the spin-orbit precessional motion of the spins. In the equal mass case, this contribution vanishes, but Laser Interferometer Space Antenna (LISA) sources of merging supermassive binary black holes have typically a mass ratio of 1:10. For such nonequal masses, this 3PN correction is periodic in time, with a period approximately ε-1 times larger than the period of gravitational waves. We derive a renormalized and simpler expression of the spin-spin coefficient at 2PN, as an average over the time scale of this period of the combined 2PN and 3PN contribution. We also find that for LISA sources the quadrupole-monopole contribution to the phase dominates over the spin-spin contribution, while the self-spin contribution is negligible even for the dominant spin. Finally, we define a renormalized total spin coefficient σ̄ to be employed in the search for gravitational waves emitted by LISA sources.

Original languageEnglish
Article number064023
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number6
Publication statusPublished - márc. 2 2009

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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