Gravitational radiation reaction in compact binary systems: Contribution of the magnetic dipole–magnetic dipole interaction

Abstract

We study the gravitational radiation reaction in compact binary systems composed of neutron stars with spin and huge magnetic dipole moments (magnetars). The magnetic dipole moments undergo a precessional motion about the respective spins. At sufficiently high values of the magnetic dipole moments, their interaction generates second post-Newtonian order contributions both to the equations of motion and to the gravitational radiation escaping the system. We parametrize the radial motion and average over a radial period in order to find the secular contributions to the energy and magnitude of the orbital angular momentum losses, in the generic case of eccentric orbits. Similarly as for the spin-orbit, spin-spin, quadrupole-monopole interactions, here too we deduce the secular evolution of the relative orientations of the orbital angular momentum and spins. These equations, supplemented by the evolution equations for the angles characterizing the orientation of the dipole moments form a first order differential system, which is closed. The circular orbit limit of the energy loss agrees with Ioka and Taniguchi's earlier result.

Kepler equation for inspiralling compact binaries

“…In a coordinate systems K with the axes ĉ;L ĉ;L, whereĉ is the unit vector in the J L direction, the polar angles i and i of the spins are defined asŜ i sin i cos i ; sin i sin i ; cos i (see [19]). In the coordinate system K i with the axes b i ;Ŝ i b i ;Ŝ i , whereb i are the unit vectors in the S i L directions, respectively, the polar angles i and i of the the magnetic dipole moments d i ared i sin i cos i ; sin i sin i ; cos i (see [27]). The quadrupolar parameters (see [26] From (3) a radial equation can be derived…”

“…The explicit values of L in the case of spin-spin, quadrupole-monopole, and magnetic dipole-dipole interactions were computed in [25][26][27]. A is the magnitude of the Laplace-Runge-Lenz vector characterizing a Keplerian motion with E and L. The coefficients A i in Eq.…”

“…The advantage of the generalized eccentric anomaly parametrization and generalized true anomaly parametrization is that a simple technique based on the residue theorem can be applied for computing secular effects [36]. The scheme was applied individually for each of the SO, SS, QM, DD perturbations in [19,[25][26][27], respectively. It is straightforward to derive the PN contribution to these parametrizations.…”

Kompakt kettős rendszerek poszt-newtoni fejlődése

“…Ez abból adódik, hogy SS, QḾ es DD esetekben a pálya-impulzusmomentum nagysága nem mozgásállandó, hanem a valódi anomália harmonikus függvénye [38], [83]és [93] (a δLés δE mennyiségek a 2. 3.…”

“…jelennek meg, a DD veszteségeiben, viszont a dipólmomentumok leírásához szükséges α ié s β i szögek is szükségesek (8.ábra), melyek miatt az előző differenciálegyenlet megoldhatóságához hozzá kell venni ezen szögek sugárzásból adódó fejlődési egyenleteit is [93].…”