Constraining white dwarf viscosity through tidal heating in detached binary systems

Although the internal structure of white dwarfs is considered to be generally well understood, the source and entity of viscosity is still very uncertain. We propose here to study white dwarf viscous properties using short period (< 1 hr), detached white dwarf binaries, such as the newly discovered ~12.8 min system. These binaries are wide enough that mass transfer has not yet started but close enough that the least massive component is subject to a measurable tidal deformation. The associated tidal torque transfers orbital energy, which is partially converted into heat by the action of viscosity within the deformed star. As a consequence, its outer non-degenerate layers expand, and the star puffs up. We self-consistently calculate the fractional change in radius, and the degree of asynchronism (ratio of stellar to orbital spin) as a function of the viscous time. Specializing our calculations to J0651, we find that the discrepancy between the measured radius of the secondary star and He white dwarf model predictions can be interpreted as tidal inflation if the viscous timescale is either ~2 10^5 yr or ~10^4 yr. Such values point to a non-microscopic viscosity, possibly given by tidally induced turbulence, or by magnetic field stresses with a magnetic field strength of 10-100 Gauss. Fortunately, these two timescales produce very different degree of asynchronism, with the shortest one, bringing the system much closer to synchronisation. A measurement of the stellar spin can thus univocally determined the mean viscosity. Extrapolating the secondary's radial expansion, we predict that the star will fill is Roche lobe at a separation which is 1.2-1.3 smaller than the current one. Applying this method to a future sample of systems can allow us to learn whether viscosity changes with mass and/or nuclear composition.Comment: 7 pages, 6 figures, MNRAS submitte

Gravitational Radiation from Newborn Magnetars

There is growing evidence that two classes of high-energy sources, the Soft Gamma Repeaters and the Anomalous X-ray Pulsars contain slowly spinning ``magnetars'', i.e. neutron stars whose emission is powered by the release of energy from their extremely strong magnetic fields (>10^15 G. We show here that the enormous energy liberated in the 2004 December 27 giant flare from SGR1806-20 (~5 10^46 erg), together with the likely recurrence time of such events, requires an internal field strength of > 10^16 G. Toroidal magnetic fields of this strength are within an order of magnitude of the maximum fields that can be generated in the core of differentially-rotating neutron stars immediately after their formation, if their initial spin period is of a few milliseconds. A substantial deformation of the neutron star is induced by these magnetic fields and, provided the deformation axis is offset from the spin axis, a newborn fast-spinning magnetar would radiate for a few weeks a strong gravitational wave signal the frequency of which (0.5-2 kHz range) decreases in time. The signal from a newborn magnetar with internal field > 10^16.5 G could be detected with Advanced LIGO-class detectors up to the distance of the Virgo cluster (characteristic amplitude h_c about 10^-21). Magnetars are expected to form in Virgo at a rate approx. 1/yr. If a fraction of these have sufficiently high internal magnetic field, then newborn magnetars constitute a promising new class of gravitational wave emitters.Comment: Accepted for publication on ApJ Letter

Neutron star bulk viscosity, "spin-flip" and GW emission of newly born magnetars

The viscosity-driven "spin-flip" instability in newborn magnetars with interior toroidal magnetic fields is re-examined. We calculate the bulk viscosity coefficient ($\zeta$) of cold, $npe \mu$ matter in neutron stars (NS), for selected values of the nuclear symmetry energy and in the regime where $\beta$-equilibration is slower than characteristic oscillation periods. We show that: i) $\zeta$ is larger than previously assumed and the instability timescale correspondingly shorter; ii) for a magnetically-induced ellipticity $\epsilon_B \lesssim 4 \times 10^{-3}$, typically expected in newborn magnetars, spin-flip occurs for initial spin periods $\lesssim 2-3$ ms, with some dependence on the NS equation of state (EoS). We then calculate the detectability of GW signals emitted by newborn magnetars subject to "spin-flip", by accounting also for the reduction in range resulting from realistic signal searches. For an optimal range of $\epsilon_B \sim (1-5) \times 10^{-3}$, and birth spin period $\lesssim 2$ ms, we estimate an horizon of $\gtrsim 4$ Mpc, and $\gtrsim 30$ Mpc, for Advanced and third generation interferometers at design sensitivity, respectively. A supernova (or a kilonova) is expected as the electromagnetic counterpart of such GW events. Outside of the optimal range for GW emission, EM torques are more efficient in extracting the NS spin energy, which may power even brighter EM transients.Comment: 10 pages, 4 figures, accepted for publication in MNRA

NuSTAR J095551+6940.8: a highly magnetised neutron star with super-Eddington mass accretion

The identification of the Ultraluminous X-ray source (ULX) X-2 in M82 as an accreting pulsar has shed new light on the nature of a subset of ULXs, while rising new questions on the nature of the super-Eddington accretion. Here, by numerically solving the torque equation of the accreting pulsar within the framework of the magnetically threaded-disk scenario, we show that three classes of solutions, corresponding to different values of the magnetic field, are mathematically allowed. We argue that the highest magnetic field one, corresponding to B $\sim 10^{13}$ G, is favoured based on physical considerations and the observed properties of the source. In particular, that is the only solution which can account for the observed variations in $\dot{P}$ (over four time intervals) without requiring major changes in $\dot{M}$, which would be at odds with the approximately constant X-ray emission of the source during the same time. For this solution, we find that the source can only accomodate a moderate amount of beaming, 0.5 $\lesssim b < 1$. Last, we show that the upper limit on the luminosity, L$_X < 2.5 \times 10^{38}$ erg s$^{-1}$ from archival observations, is consistent with a highly-magnetized neutron star being in the propeller phase at that time.Comment: 8 pages, 3 figures, accepted for publication on MNRA

Tidal torque induced by orbital decay in compact object binaries

As we observe in the moon-earth system, tidal interactions in binary systems can lead to angular momentum exchange. The presence of viscosity is generally regarded as the condition for such transfer to happen. In this paper, we show how the orbital evolution can cause a persistent torque between the binary components, even for inviscid bodies. This preferentially occurs at the final stage of coalescence of compact binaries, when the orbit shrinks successively by gravitational waves and plunging on a timescale shorter than the viscous timescale. The total orbital energy transferred to the secondary by this torque is ~0.01 of its binding energy. We further show that this persistent torque induces a differentially rotating quadrupole perturbation. Specializing to the case of a secondary neutron star, we find that this non equilibrium state has an associated free energy of 10^47-10^48 erg, just prior to coalescence. This energy is likely stored in internal fluid motions, with a sizable amount of differential rotation. By tapping this free energy reservoir, a preexisting weak magnetic field could be amplified up to a strength of ~10^15 Gauss. Such a dynamically driven tidal torque can thus recycle an old neutron star into a highly magnetized neutron star, with possible observational consequences at merger.Comment: 14 pages, 8 figures, new sections added, accepted on Sept.19, published on MNRA

Magnetar central engines in gamma-ray busts follow the universal relation of accreting magnetic stars

Gamma-ray bursts (GRBs), both long and short, are explosive events whose inner engine is generally expected to be a black hole or a highly magnetic neutron star (magnetar) accreting high density matter. Recognizing the nature of GRB central engines, and in particular the formation of neutron stars (NSs), is of high astrophysical significance. A possible signature of NSs in GRBs is the presence of a plateau in the early X-ray afterglow. Here we carefully select a subset of long and short GRBs with a clear plateau, and look for an additional NS signature in their prompt emission, namely a transition between accretion and propeller in analogy with accreting, magnetic compact objects in other astrophysical sources. We estimate from the prompt emission the minimum accretion luminosity below which the propeller mechanism sets in, and the NS magnetic field and spin period from the plateau. We demonstrate that these three quantities obey the same universal relation in GRBs as in other accreting compact objects switching from accretion to propeller. This relation provides also an estimate of the radiative efficiency of GRBs, which we find to be several times lower than radiatively efficient accretion in X-ray binaries and in agreement with theoretical expectations. These results provide additional support to the idea that at least some GRBs are powered by magnetars surrounded by an accretion disc.Comment: 15 pages, 5 figures, accepted for publication in The Astrophysical Journal Letter