Modelling of the surface emission of the low magnetic field magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6×1012G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. None the less, the modelling allows us to place constraints on the system geometry (i.e. the angles ψ and ξ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to 65° ≲ ψ + ξ ≲ 125° or 235° ≲ ψ + ξ ≲ 295°; (b) the temperature contrast between the poles and the equator must be at least a factor of ∼6, and (c) the size of the hottest region ranges between 0.2 and 0.7 km (including uncertainties on the source distance). Lastly, we interpret our findings within the context of internal and external heating models.

On the steric and mass-induced contributions to the annual sea level variations in the Mediterranean Sea

The sea level variation (SLVtotal) is the sum of two major contributions: steric and mass-induced. The steric SLVsteric is that resulting from the thermal and salinity changes in a given water column. It only involves volume change, hence has no gravitational effect. The mass-induced SLVmass, on the other hand, arises from adding or subtracting water mass to or from the water column and has direct gravitational signature. We examine the closure of the seasonal SLV budget and estimate the relative importance of the two contributions in the Mediterranean Sea as a function of time. We use ocean altimetry data (from TOPEX/Poseidon, Jason 1, ERS, and ENVISAT missions) to estimate SLVtotal, temperature, and salinity data (from the Estimating the Circulation and Climate of the Ocean ocean model) to estimate SLVsteric, and time variable gravity data (from Gravity Recovery and Climate Experiment (GRACE) Project, April 2002 to July 2004) to estimate SLVmass. We find that the annual cycle of SLVtotal in the Mediterranean is mainly driven by SLVsteric but moderately offset by SLVmass. The agreement between the seasonal SLVmass estimations from SLVtotal – SLVsteric and from GRACE is quite remarkable; the annual cycle reaches the maximum value in mid-February, almost half a cycle later than SLVtotal or SLVsteric, which peak by mid-October and mid-September, respectively. Thus, when sea level is rising (falling), the Mediterranean Sea is actually losing (gaining) mass. Furthermore, as SLVmass is balanced by vertical (precipitation minus evaporation, P–E) and horizontal (exchange of water with the Atlantic, Black Sea, and river runoff) mass fluxes, we compared it with the P–E determined from meteorological data to estimate the annual cycle of the horizontal flux.

A strongly magnetized pulsar within the grasp of the milky way’s supermassive black hole

The center of our Galaxy hosts a supermassive black hole, Sagittarius (Sgr) A∗. Young, massive stars within 0.5 pc of Sgr A∗ are evidence of an episode of intense star formation near the black hole a few million years ago, which might have left behind a young neutron star traveling deep into Sgr A∗’s gravitational potential. On 2013 April 25, a short X-ray burst was observed from the direction of the Galactic center. With a series of observations with the Chandra and the Swift satellites, we pinpoint the associated magnetar at an angular distance of 2.4±0.3 arcsec from Sgr A∗, and refine the source spin period and its derivative (P = 3.7635537(2) s and ˙ P = 6.61(4) × 10−12 s s−1), confirmed by quasi simultaneous radio observations performed with the Green Bank Telescope and Parkes Radio Telescope, which also constrain a dispersion measure of DM = 1750 ± 50 pc cm−3, the highest ever observed for a radio pulsar. We have found that this X-ray source is a young magnetar at ≈0.07–2 pc from Sgr A∗. Simulations of its possible motion around Sgr A∗ show that it is likely (∼90% probability) in a bound orbit around the black hole. The radiation front produced by the past activity from the magnetar passing through the molecular clouds surrounding the Galactic center region might be responsible for a large fraction of the light echoes observed in the Fe fluorescence features.

Numerical resolution of Emden's equation using Adomian polynomials

Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

Pulsar science with the SKA

The unprecedented sensitivity and large field of view of SKA will be of paramount importance for pulsar science, and for many related research fields. In particular, beside the obvious discovery of many more pulsars (even those with very low luminosity), and the extremely accurate timing analysis of the current pulsar population, SKA will allow to use pulsars to measure or put strong constraints on gravitational waves, Galactic magnetism, planet masses, general relativity and nuclear physics.

Constraining the GRB-Magnetar Model by Means of the Galactic Pulsar Population

A large fraction of Gamma-ray bursts (GRBs) displays an X-ray plateau phase within <105 s from the prompt emission, proposed to be powered by the spin-down energy of a rapidly spinning newly born magnetar. In this work we use the properties of the Galactic neutron star population to constrain the GRB-magnetar scenario. We re-analyze the X-ray plateaus of all Swift GRBs with known redshift, between 2005 January and 2014 August. From the derived initial magnetic field distribution for the possible magnetars left behind by the GRBs, we study the evolution and properties of a simulated GRB-magnetar population using numerical simulations of magnetic field evolution, coupled with Monte Carlo simulations of Pulsar Population Synthesis in our Galaxy. We find that if the GRB X-ray plateaus are powered by the rotational energy of a newly formed magnetar, the current observational properties of the Galactic magnetar population are not compatible with being formed within the GRB scenario (regardless of the GRB type or rate at z = 0). Direct consequences would be that we should allow the existence of magnetars and "super-magnetars" having different progenitors, and that Type Ib/c SNe related to Long GRBs form systematically neutron stars with higher initial magnetic fields. We put an upper limit of ≤16 "super-magnetars" formed by a GRB in our Galaxy in the past Myr (at 99% c.l.). This limit is somewhat smaller than what is roughly expected from Long GRB rates, although the very large uncertainties do not allow us to draw strong conclusion in this respect.