Numerical Methods for the Inverse Nonlinear Fourier Transform

We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the proposed method requires the lowest number of operationsComment: To be presented at the Tyrrhenian International Workshop on Digital Communications (TIWDC) 201

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

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

Approximate analytical calculations of photon geodesics in the Schwarzschild metric

We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been introduced empirically. We then derive for the first time an approximate analytical equation for the solid angle. We discuss the accuracy and range of applicability of the new equations and present a few simple applications of them to known astrophysical problems.Comment: 8 pages, 10 Figures; Received: 08 June 2016 / Accepted: 04 August 2016and accepted from A&

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

A universal relation for the propeller mechanisms in magnetic rotating stars at different scales

Accretion of matter onto a magnetic, rotating object can be strongly affected by the interaction with its magnetic field. This occurs in a variety of astrophysical settings involving young stellar objects, white dwarfs, and neutron stars. As matter is endowed with angular momentum, its inflow toward the star is often mediated by an accretion disc. The pressure of matter and that originating from the stellar magnetic field balance at the magnetospheric radius: at smaller distances the motion of matter is dominated by the magnetic field, and funnelling towards the magnetic poles ensues. However, if the star, and thus its magnetosphere, is fast spinning, most of the inflowing matter will be halted at the magnetospheric radius by centrifugal forces, resulting in a characteristic reduction of the accretion luminosity. The onset of this mechanism, called the propeller, has been widely adopted to interpret a distinctive knee in the decaying phase of the light curve of several transiently accreting X-ray pulsar systems. By comparing the observed luminosity at the knee for different classes of objects with the value predicted by accretion theory on the basis of the independently measured magnetic field, spin-period, mass, and radius of the star, we disclose here a general relation for the onset of the propeller which spans about eight orders of magnitude in spin period and ten in magnetic moment. The parameter-dependence and normalisation constant that we determine are in agreement with basic accretion theory.Comment: 11 pages, 3 figures. Accepted for publication in A&

Testing Gravity with Quasi Periodic Oscillations from accreting Black Holes: the Case of Einstein-Dilaton-Gauss-Bonnet Theory

Quasi-Periodic Oscillations (QPOs) observed in the X-ray flux emitted by accreting black holes, are associated to phenomena occurring near the horizon. Future very large area X-ray instruments will be able to measure QPO frequencies with very high precision, thus probing this strong-field region. By using the relativistic precession model, we show the way in which QPO frequencies could be used to test general relativity against those alternative theories of gravity which predict deviations from the classical theory in the strong-field regime. We consider one of the best motivated strong-curvature corrections to general relativity, namely the Einstein-Dilaton-Gauss-Bonnet theory, and show that a detection of QPOs with the expected sensitivity of the proposed ESA M-class mission LOFT would set the most stringent constraints on the parameter space of this theory.Comment: 10 pages, 5 figures, 1 table; minor changes to match the version appearing on Ap