TY - JOUR

T1 - Accuracy of the post-Newtonian approximation. II. Optimal asymptotic expansion of the energy flux for quasicircular, extreme mass-ratio inspirals into a Kerr black hole

AU - Zhang, Zhongyang

AU - Yunes, Nicolás

AU - Berti, Emanuele

PY - 2011/7/15

Y1 - 2011/7/15

N2 - We study the effect of black hole spin on the accuracy of the post-Newtonian approximation. We focus on the gravitational energy flux for the quasicircular, equatorial, extreme mass-ratio inspiral of a compact object into a Kerr black hole of mass M and spin J. For a given dimensionless spin a≡J/M2 (in geometrical units G=c=1), the energy flux depends only on the orbital velocity v or (equivalently) on the Boyer-Lindquist orbital radius r. We investigate the formal region of validity of the Taylor post-Newtonian expansion of the energy flux (which is known up to order v8 beyond the quadrupole formula), generalizing previous work by two of us. The error function used to determine the region of validity of the post-Newtonian expansion can have two qualitatively different kinds of behavior, and we deal with these two cases separately. We find that, at any fixed post-Newtonian order, the edge of the region of validity (as measured by v/vISCO, where v ISCO is the orbital velocity at the innermost stable circular orbit) is only weakly dependent on a. Unlike in the nonspinning case, the lack of sufficiently high-order terms does not allow us to determine if there is a convergent to divergent transition at order v6. Independent of a, the inclusion of angular multipoles up to and including ℓ=5 in the numerical flux is necessary to achieve the level of accuracy of the best-known (N=8) post-Newtonian expansion of the energy flux.

AB - We study the effect of black hole spin on the accuracy of the post-Newtonian approximation. We focus on the gravitational energy flux for the quasicircular, equatorial, extreme mass-ratio inspiral of a compact object into a Kerr black hole of mass M and spin J. For a given dimensionless spin a≡J/M2 (in geometrical units G=c=1), the energy flux depends only on the orbital velocity v or (equivalently) on the Boyer-Lindquist orbital radius r. We investigate the formal region of validity of the Taylor post-Newtonian expansion of the energy flux (which is known up to order v8 beyond the quadrupole formula), generalizing previous work by two of us. The error function used to determine the region of validity of the post-Newtonian expansion can have two qualitatively different kinds of behavior, and we deal with these two cases separately. We find that, at any fixed post-Newtonian order, the edge of the region of validity (as measured by v/vISCO, where v ISCO is the orbital velocity at the innermost stable circular orbit) is only weakly dependent on a. Unlike in the nonspinning case, the lack of sufficiently high-order terms does not allow us to determine if there is a convergent to divergent transition at order v6. Independent of a, the inclusion of angular multipoles up to and including ℓ=5 in the numerical flux is necessary to achieve the level of accuracy of the best-known (N=8) post-Newtonian expansion of the energy flux.

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U2 - 10.1103/PhysRevD.84.024029

DO - 10.1103/PhysRevD.84.024029

M3 - Article

AN - SCOPUS:80051684678

SN - 1550-7998

VL - 84

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

IS - 2

M1 - 024029

ER -