Magnetic fields in axisymmetric neutron stars

We derive general equations for axisymmetric Newtonian magnetohydrodynamics and use these as the basis of a code for calculating equilibrium configurations of rotating magnetized neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism, the toroidal component appears to be bounded at less than 7 per cent. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work, we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10 per cent of the non-linear results if the ellipticity is less than 0.15 or the average field strength is less than 10¹⁷ G. We also consider how magnetized equilibrium structures vary for different polytropic indices.     

Torus formation in neutron star mergers and well-localized short gamma-ray bursts

Merging neutron stars (NSs) are hot candidates for the still enigmatic sources of short gamma-ray bursts (GRBs). If the central engines of the huge energy release are accreting relic black holes (BHs) of such mergers, it is important to understand how the properties of the BH–torus systems, in particular disc masses and mass and rotation rate of the compact remnant, are linked to the characterizing parameters of the NS binaries. For this purpose, we present relativistic smoothed particle hydrodynamic simulations with conformally flat approximation of the Einstein field equations and a physical, non-zero temperature equation of state. Thick disc formation is highlighted as a dynamical process caused by angular momentum transfer through tidal torques during the merging process of asymmetric systems or in the rapidly spinning triaxial post-merger object. Our simulations support the possibility that the first well-localized short and hard GRBs 050509b, 050709, 050724, 050813 have originated from NS merger events and are powered by neutrino-antineutrino annihilation around a relic BH–torus system. Using model parameters based on this assumption, we show that the measured GRB energies and durations lead to estimates for the accreted masses and BH mass accretion rates which are compatible with theoretical expectations. In particular, the low-energy output and short duration of GRB 050509b set a very strict upper limit of less than 100 ms for the time interval after the merging until the merger remnant has collapsed to a BH, leaving an accretion torus with a small mass of only  ∼0.01 M_⊙  . This favours a (nearly) symmetric NS+NS binary with a typical mass as progenitor system.     

Cosmological rates of coalescing neutron stars and GRB

Assuming that gamma-ray bursts (GRB) originate from binary neutron star (NS) or black holes (BH) merging in distant galaxies, theoretical logN-logS distributions for gamma-ray bursts (GRB) are calculated using the compact binaries coalescence rates computed for model galaxies with different star formation histories. A flat cosmological model ( = 1) with different values of the cosmological constant is used. The calculated source evolution predicts a 5–10 times increase of the source statistics at count rates 3–10 times lower than the existing BATSE sensitivity limit. The most important parameter in fitting the 2nd BATSE catalogue is the initial redshift of star formation, which is found to bez _* = 2 — 5 depending on a poorly determined average spectral index of GRB.     

The isotropic energy function and formation rate of short gamma-ray bursts

Gamma-ray bursts (GRBs) are brief,intense,gamma-ray flashes in the universe,lasting from a few milliseconds to a few thousand seconds.For short gamma-ray bursts (s GRBs) with duration less than 2 seconds,the isotropic energy (E_(iso)) function may be more scientifically meaningful and accurately measured than the luminosity (L_p) function.In this work we construct,for the first time,the isotropic energy function of s GRBs and estimate their formation rate.First,we derive the L_p-E_pcorrelation using22 s GRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi s GRBs.Then,we adopt the Lynden-Bell c~-method to study isotropic energy functions and formation rate of s GRBs without any assumption.A strong evolution of isotropic energy E_(iso)∝(1+z)~(5.79)is found,which is comparable to that between L_pand z.After removing effect of the cosmic evolution,the isotropic energy function can be reasonably fitted by a broken power law,which isφ(E_(iso,0))∝E~(-0)_(iso),._0~(45)for dim s GRBs andφ(E_(iso,0))∝E~(-1)_(iso),._0~(11)for bright s GRBs,with the break energy 4.92×10~(49)erg.We obtain the local formation rate of s GRBs is about 17.43 events Gpc~(-3)yr~(-1).If assuming a beaming angle is 6?to 26?,the local formation rate including off-axis s GRBs is estimated asρ_(0,all)=155.79-3202.35 events Gpc~(-3)yr~(-1).     

Improved correlation between the variability and peak luminosity of gamma-ray bursts

A new procedure for smoothing a gamma-ray burst (GRB) light curve and calculating its variability is presented. Applying the procedure to a sample of 25 long GRBs, we have obtained a very tight correlation between the variability and the peak luminosity. The only significant outlier in the sample is GRB 030329. With this outlier excluded, the data scatter is reduced by a factor of ∼3 compared to that of Guidorzi et al., measured by the deviation of fit. Possible causes for the outlier are discussed.     

Bimodal distribution of short gamma-ray bursts: Evidence for two distinct types of short gamma-ray bursts

GRB 170817A was confirmed to be associated with GW170817, which was produced by a neutron star - neutron star merger. It indicates that at least some short gamma-ray bursts come from binary neutron star mergers. Theoretically, it is widely accepted that short gamma-ray bursts can be produced by two distinctly different mechanisms, binary neutron star mergers and neutron star - black hole mergers. These two kinds of bursts should be different observationally due to their different trigger mechanisms. Motivated by this idea, we collect a universal data set constituted of 51 short gamma-ray bursts observed by Swift/BAT, among which 14 events have extended emission component. We study the observational features of these 51 events statistically. It is found that our samples consist of two distinct groups. They clearly show a bimodal distribution when their peak photon fluxes at 15–150 keV band are plotted against the corresponding fluences. Most interestingly, all the 14 short bursts with extended emission lie in a particular region of this plot. When the fluences are plotted against the burst durations, short bursts with extended emission again tend to concentrate in the long duration segment. These features strongly indicate that short gamma-ray bursts really may come from two distinct types of progenitors. We argue that those short gamma-ray bursts with extended emission come from the coalescence of neutron stars, while the short gamma-ray bursts without extended emission come from neutron star - black hole mergers.     

Supernovae-optical precursors of short gamma-ray bursts

The probability of observing “supernova-gamma-ray burst” (GRB) pair events and recurrent GRBs from one galaxy in a time interval of several years has been estimated. Supernova explosions in binary systems accompanied by the formation of a short-lived pair of compact objects can be the sources of such events. If a short GRB is generated during the collision of a pair, then approximately each of ∼300 short GRBs with redshift z must have an optical precursor—a supernova in the observer’s time interval <2(1 + z) yr. If the supernova explosion has the pattern of a hypernova, then a successive observation of long and short GRBs is possible. The scenario for the generation of multiple GRBs in collapsing galactic nuclei is also discussed.     

Early afterglows of short gamma-ray bursts

In the relativistic fireball model, the afterglow of a gamma-ray burst (GRB) is produced by synchrotron radiation of the electrons accelerated in the external shock that emerges as the relativistic flow moves. According to this model, the afterglow peaks on a time scale of ～10 s when observed in the soft gamma-ray band. The peak flux can be high enough to be detected by modern all-sky monitors. We investigate the emission from short (ΔT<1 s) GRBs on a time scale t≈10 s using BATSE/CGRO data. A significant flux is recorded for ～20% of the events. In most cases, the observed persistent emission can be explained in terms of the model as an early burst afterglow. No early afterglows of most short GRBs are observed. The model parameters for these bursts are constrained.     

Temporal properties of short gamma-ray bursts

We analyse a sample of bright short bursts from the BATSE 4B-catalog and find that many short bursts are highly variable  ( δt _min/ T ≪1  , where δt _min is the shortest pulse duration and T is the burst duration). This indicates that it is unlikely that short bursts are produced by external shocks. We also analyse the available (first  1–2 s)  high-resolution Time Tagged Events (TTE) data of some of the long bursts. We find that variability on a 10-ms time-scale is common in long bursts. This result shows that some long bursts are even more variable than it was thought before  ( δt _min/ T ≈10^-4–10^-3)  .     

Magnetic fields and rotation in white dwarfs and neutron stars

Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars  ( B_p ∼ 10¹¹–10¹⁵ G)  could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of   B_p ∼ 1100 G  for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators  ( P _rot∼ 50 –100 yr)  that have originated from single-star evolution, a group of strongly magnetized fast rotators  ( P _rot∼ 700 s)  , typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators ( P _rot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth , and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.     

Gamma-ray bursts from nearby neutron stars

We interpret the puzzling-ray bursts as emitted by cooling sparks from the surface of spasmodically accreting, old neutron stars. Their spiky, anisotropic radiation is oriented w.r.t. the galactic disk via interstellar accretion, whose orbital angular momentum tends to counteralign with the galactic spin; in this way, larger source numbers in directions of the galactic disk are compensated by smaller beaming probabilities, resulting in a near-isotropic arrival distribution, as observed by BATSE. The source distances range between 10 pc and 500 pc. Their radiated energies are of order 10³⁵ erg, corresponding to accreted clumps (blades) of typical mass 10¹⁵ g per burst. Magnetic surface field strengths range between 10¹⁰ and 10¹² G, somewhat weaker than those of newborn neutron stars.     

Evidence for luminosity evolution of long gamma-ray bursts in Swift data

We compute the luminosity function (LF) and the formation rate of long gamma-ray bursts (GRBs) by fitting the observed differential peak flux distribution obtained by the Burst and Transient Source Experiment (BATSE) in two different scenarios: (i) the GRB luminosity evolves with redshift and (ii) GRBs form preferentially in low-metallicity environments. In both cases, model predictions are consistent with the Swift number counts and with the number of detections at   z > 2.5  and >3.5. To discriminate between the two evolutionary scenarios, we compare the model results with the number of luminous bursts (i.e. with isotropic peak luminosity in excess of 10⁵³ erg s⁻¹) detected by Swift in its first 3 yr of mission. Our sample conservatively contains only bursts with good redshift determination and measured peak energy. We find that pure luminosity evolution models can account for the number of sure identifications. In the case of a pure density evolution scenario, models with   Z _th > 0.3 Z_⊙  are ruled out with high confidence. For lower metallicity thresholds, the model results are still statistically consistent with available lower limits. However, many factors can increase the discrepancy between model results and data, indicating that some luminosity evolution in the GRB LF may be needed also for such low values of Z _th. Finally, using these new constraints, we derive robust upper limits on the bright end of the GRB LF, showing that this cannot be steeper than ∼2.6.     

Gamma-ray bursts from high velocity neutron stars

We investigate the viability of the Galactic corona model of -ray bursts by calculating the spatial distribution of neutron stars born with high velocities in the Galactic disk, and comparing the resulting brightness and angular distribution with the BATSE data. We find that the Galactic corona model can reproduce the BATSE peak flux and angular distribution data for neutron star kick velocities 800 km s^–1, source turn-on ages 10 Myrs, and sampling depths 100 kpc d _max 400 kpc.     

Gamma-ray luminosity function of gamma-ray bright AGNs

Detection of γ-ray emissions from a class of active galactic nuclei (viz blazars),has been one of the important findings from the Compton Gamma-Ray Observatory (CGRO). However, their-γ-ray luminosity function has not been well determined. Few at-tempts have been made in earlier works, where BL Lacs and Flat Spectrum Radio Quasars (FSRQs) have been considered as a single source class. In this paper, we investigated the evolution and γ-ray luminosity function of FSRQs and BL Lacs separately. Our investi-gation indicates no evolution for BL Lacs, however FSRQs show significant evolution. Pure luminosity evolution is assumed for FSRQs and exponential and power law evolu-tion models are examined. Due to the small number of sources, the low luminosity end index of the luminosity function for FSRQs is constrained with an upper limit. BL Lac lu-minosity function shows no signature of break. As a consistency check, the model source distributions derived from these luminosity functions show no significant departure from the observed source distributions.     

Anisotropy in the sky distribution of short gamma-ray bursts

We analyze the sky distribution of various types of cosmic gamma-ray bursts (GRBs): short, long, and intermediate; they are determined by burst duration T ₉₀ (T ₉₀ is the time during which 90% of the burst energy is accumulated). We have found an anisotropy in the distribution of intermediate (2 s < T ₉₀ < 8 s) and short (T ₉₀ < 8 s) GRBs in the form of spots with an enhanced GRB concentration near the Galactic coordinates l=115° and b=30°. Given the BATSE nonuniform exposure function, the statistical significance of the anisotropy is 99.89% for intermediate GRBs and 99.99% for short GRBs. Thus, we suggest that this anisotropy has a natural origin and is not caused by BATSE instrumental effects.     

Distribution of gamma-ray bursts in halo neutron star-comet models

The motions of comets and neutron stars have been integrated over five billion years in the Galactic potential to determine a gamma-ray burst distribution, presuming that bursts are the result of interactions between these two families of objects. The comets originate in two distinct populations - one from ejection by stars in the Galactic disk, and the other from ejection by stars in globular clusters. No choice of the free parameters resulted in agreement with both the isotropy data and the log(N >F)-log(F) data.