Spinning compact binary inspiral. II. Conservative angular dynamics

Abstract

We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole -mass monopole effects, for generic (noncircular, nonspherical) orbits. More specifically, we give a closed system of first order ordinary differential equations for the orbital elements of the osculating ellipse and for the angles characterizing the spin orientations with respect to the osculating orbit.We also prove that (i) the relative angle of the spins stays constant for equal mass black holes, irrespective of their orientation, and (ii) the special configuration of equal mass black holes with equal, but antialigned spins, both laying in the plane of motion (leading to the largest recoil found in numerical simulations) is preserved at 2PN level of accuracy, with leading order spin-orbit, spin-spin and mass quadrupolar contributions included.

Spinning compact binary dynamics and chameleon orbits

“…[23]; however for the contribution L SO we adopt the expression given in Ref. [26], which holds true in the Newton-Wigner-Price [38] spin supplementary condition (SSC), employed in this paper.…”

“…These corrections to the dynamics have been discussed extensively in Refs. [20][21][22][23][24][25][26], while the backreaction of gravitational radiation in Refs. [23,[27][28][29][30][31][32][33], and implications on galactic jets in Refs.…”

“…We rewrite the full set of conservative evolution equations, first derived in Refs. [25]- [26], in terms of a set of dimensionless variables evolving in a dimensionless time, in a form suitable to monitor both bounded and unbounded orbits (as defined by their osculating orbital elements in a local, Newtonian sense).…”

Szupernagy tömegű fekete lyuk kettősökre utaló jelek rádió-hangos aktív galaxismagok jeteiben

“…Gergely és munkatársai részletesen tárgyalják a spinek jelenlétében megvalósuló bonyolult dinamikát a [68] és [67] munkákban. Az említett spin-pálya, spin-spin, és kvadrupól-monopól tagokon túl mágneses dipólus, ön-spin és sugárzási visszahatási tagok is megjelennek a magasabb rendű dinamikában.…”

“…A keleti irány az x-, míg az északi irány az y-tengelyt definiálja. Ez a komponens 5 epocha kivételével (1994,67,1996,05,1996,57,1996,74,1996,93) hibahatáron belül stacionárius helyzetű. Jobb oldalon ugyanezen komponens relatív magszeparációi az idő függvényében.…”