Stability Analysis Of The Spin Evolution Fixed Points In Inspiraling Compact Binaries With Black Hole, Neutron Star, Gravastar, Or Boson Star Components

Based on a recently derived secular spin evolution of black holes, neutron stars, gravastars, or boson stars in precessing compact binaries on eccentric orbit, we carry out a linear stability analysis of fixed point configurations. We identify the aligned and more generic coplanar configurations of the spins and orbital angular momentum as fixed points. Through a dynamical system analysis, we investigate their linear stability as function of the mass quadrupole parameter. Our most important results are as follows. Marginal stability holds for the binary configurations with both spins antialigned to the orbital angular momentum, for both spins aligned to the orbital angular momentum (with the exception of certain quadrupolar parameter ranges of neutron stars and boson stars), and for the extremal mass ratio. For equal masses, the configurations of one of the spins aligned and the other antialigned is stable for gravastar binaries, for neutron star binaries in the high quadrupolar parameter range, and for boson star binaries. For some unequal mass gravastar binaries, black hole binaries or neutron star binaries, a transition from stability to instability can occur during the inspiral, when one of the spins is aligned, while the other is antialigned to the orbital angular momentum. We also discover a transitional instability regime during the inspiral of certain gravastar, neutron star, or boson star binaries with opposing spins. For coplanar configurations we recover the marginally stable configurations leading to the libration phenomenon identified in previous numerical investigations lacking mass quadrupole contributions, and we analyze how it is affected by the quadrupolar structure of the sources. We also investigate the linear stability of black hole, neutron star, and boson star binaries, also of mixed black hole - gravastar, black hole - neutron star and black hole - boson star binaries. We fmd instabilities only for the gravastar - gravastar, boson star - boson star and black hole - boson star binaries. For a given spin configuration, marginal stability strongly depends on the value of the quadrupolar parameters. The stability region is larger for neutron star binaries than for black hole binaries, while the mixed systems have a restricted stability parameter region.