AM CVn binaries consist of a WD accreting from a hydrogen-deficient star (or WD) companion (Warner, 1995;Solheim, 2010). In their formation history (Fig. 1.6 and Section 1.3.1.1), AM CVns form after at least one CE phase of their progenitor system. The current RLO is initiated, due to orbital damping caused by GW radiation, at orbital periods of typically 5−20 min (depending on the nature and the temperature of the companion star), and the mass-transfer rate is determined

A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic-field-aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalises previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g., spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin downs, and are not purely dipolar.

We construct multipole moments for stationary, asymptotically flat, spacetime solutions to higherorder curvature theories of gravity. The moments are defined using 3+1 techniques involving timelike Killing vector constructions as in the classic papers by Geroch and Hansen. Using the fact that the Kerr-Newman metric is a vacuum solution to a particular class of f (R) theories of gravity, we compute all its moments, and find that they admit recurrence relations similar to those for the Kerr solution in general relativity. It has been proposed previously that modelling the measured frequencies of quasi-periodic oscillations from galactic microquasars enables experimental tests of the no-hair theorem. We explore the possibility that, even if the no-hair relation is found to break down in the context of general relativity, there may be an f (R) counterpart that is preserved. We apply the results to the microquasars GRS 1915+105 and GRO J1655-40 using the diskoseismology and kinematic resonance models, and constrain the spins and 'charges' [which are not really electric charges in the f (R) context] of their black holes.

Fast radio bursts are millisecond-duration radio pulses of extragalactic origin. A recent statistical analysis has found that the burst energetics of the repeating source FRB 121102 follow a power-law, with an exponent that is curiously consistent with the Gutenberg-Richter law for earthquakes. This hints that repeat-bursters may be compact objects undergoing violent tectonic activity. For young magnetars, possessing crustal magnetic fields which are both strong (B 10 15 G) and highly multipolar, Hall drift can instigate significant field rearrangements even on century long timescales. This reconfiguration generates zones of magnetic stress throughout the outer layers of the star, potentially strong enough to facilitate frequent crustal failures. In this paper, assuming a quake scenario, we show how the crustal field evolution, which determines the resulting fracture geometries, can be tied to burst properties. Highly anisotropic stresses are generated by the rapid evolution of multipolar fields, implying that small, localised cracks can occur sporadically throughout the crust during the Hall evolution. Each of these shallow fractures may release bursts of energy, consistent in magnitude with those seen in the repeating sources FRB 121102 and FRB 180814.J0422+73.

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