J. A. Miralles

Magneto-thermal evolution of neutron stars

Context. The presence of magnetic fields in the crust of neutron stars c auses a non-spherically symmetric temperature distribution. The strong temperature dependence of the magnetic diffusivity and thermal conductivity, together with the heat generated by magnetic dissipation, couple the magnetic and thermal evolution of NSs, that cannot be formulated as separated one‐dimensional problems. Aims. We study the mutual influence of thermal and magnetic evoluti on in a neutron star’s crust in axial symmetry. Taking into account realistic microphysical inputs, we find the heat rel eased by Joule effect consistent with the circulation of currents in the crust , and we incorporate its effects in 2‐dimensional cooling calculations. Methods. We solve the induction equation numerically using a hybrid method (spectral in angles, but a finite‐di fferences scheme in the radial direction), coupled to the thermal diffusion equation. To improve the boundary conditions, we also revisit the envelope stationary solutions updating the well known Tb− Ts‐relations to include the effect of 2‐D heat transfer calculations and new microphysical inputs. Results. We present the first long term 2‐dimensional simulations of t he coupled magneto-thermal evolution of neutron stars. This substantially improves previous works in which a very crude approximation in at least one of the parts (thermal or magnetic diffusion) has been adopted. Our results show that the feedback between Joule heating and magnetic diffusion is strong, resulting in a faster dissipation of the stronger fields during the first 10 5 − 10 6 years of a NS’s life. As a consequence, all neutron stars born with fields larger than a critical value (> 5×10 13 G) reach similar field strengths (≈ 2−3×10 13 G) at late times. Irrespectively of the initial magnetic field strength, after 10 6 years the temperature becomes so low that the magnetic diffusion timescale becomes longer than the typical ages of radio‐pulsars, thus resulting in apparently no diss ipation of the field in old NS. We also confirm the strong correl ation between the magnetic field and the surface temperature of relatively young NSs discussed in preliminary works. The effective temperature of models with strong internal toroidal components are systematically higher than those of models with purely poloidal fie lds, due to the additional energy reservoir stored in the toroidal field tha t is gradually released as the field dissipates.

SPECTRAL EVOLUTION OF SUPERLUMINAL COMPONENTS IN PARSEC-SCALE JETS

We present numerical simulations of the spectral evolution and emission of radio components in relativistic jets. We compute jet models by means of a relativistic hydrodynamics code. We have developed an algorithm (SPEV) for the transport of a population of nonthermal electrons including radiative losses. For large values of the ratio of gas pressure to magnetic field energy density, αB ~ 6 × 104, quiescent jet models show substantial spectral evolution, with observational consequences only above radio frequencies. Larger values of the magnetic field (αB ~ 6 × 102), such that synchrotron losses are moderately important at radio frequencies, present a larger ratio of shocked-to-unshocked regions brightness than the models without radiative losses, despite the fact that they correspond to the same underlying hydrodynamic structure. We also show that jets with a positive photon spectral index result if the lower limit γmin of the nonthermal particle energy distribution is large enough. A temporary increase of the Lorentz factor at the jet inlet produces a traveling perturbation that appears in the synthetic maps as a superluminal component. We show that trailing components can be originated not only in pressure matched jets, but also in overpressured ones, where the existence of recollimation shocks does not allow for a direct identification of such features as Kelvin-Helmholtz modes, and its observational imprint depends on the observing frequency. If the magnetic field is large (αB ~ 6 × 102), the spectral index in the rarefaction trailing the traveling perturbation does not change much with respect to the same model without any hydrodynamic perturbation. If the synchrotron losses are considered the spectral index displays a smaller value than in the corresponding region of the quiescent jet model.

Population synthesis studies of isolated neutron stars with magnetic field decay

We perform population synthesis studies of different types of neutron stars (NSs) (thermally emitting isolated NSs, normal radio pulsars, magnetars) taking into account the magnetic field decay and using results from the most recent advances in NS cooling theory. For the first time, we confront our results with observations using simultaneously the log N-log S distribution for nearby isolated NSs, the log N-log L distribution for magnetars, and the distribution of radio pulsars in the P-P diagram. For this purpose, we fix a baseline NS model (all microphysics input), and other relevant parameters to standard values (velocity distribution, mass spectrum, birth rates, etc.), allowing us to vary the initial magnetic field strength. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a lognormal law with (log (B 0 /G)〉 ∼ 13.25 and σ log B 0 ∼ 0.6. The typical scenario includes about 10 per cent of NSs born as magnetars, significant magnetic field decay during the first million years of a NS life (only about a factor of 2 for low-field NSs but more than an order of magnitude for magnetars), and a mass distribution function dominated by low-mass objects. This model explains satisfactorily all known populations. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible.

Anisotropic thermal emission from magnetized neutron stars

Context. The thermal emission from isolated neutron stars is not well understood. The X-ray spectrum is very close to a blackbody but there is a systematic optical excess flux with respect to the extrapolation to low energy of the best blackbody fit. This fact, in combination with the observed pulsations in the X-ray flux, can be explained by anisotropies in the surface temperature distribution. Aims. We study the thermal emission from neutron stars with strong magnetic fields B > 10 13 G in order to explain the origin of the anisotropy. Methods. We find (numerically) stationary solutions in axial symmetry of the heat transport equations in the neutron star crust and the condensed envelope. The anisotropy in the conductivity tensor is included consistently. Results. The presence of magnetic fields of the expected strength leads to anisotropy in the surface temperature. Models with toroidal components similar to or larger than the poloidal field reproduce qualitatively the observed spectral properties and variability of isolated neutron stars. Our models also predict spectral features at energies between 0.2 and 0.6 keV for B = 10 13 -10 14 .

Thermal radiation from magnetic neutron star surfaces

We investigate the thermal emission from magnetic neutron star surfaces in which the cohesive effects of the magnetic field have produced the condensation of the atmosphere and the external layers. This may happen for sufficiently cool (T ≤ 10 6 ) atmospheres with moderately intense magnetic fields (about 10 13 G for Fe atmospheres). The thermal emission from an isothermal bare surface of a neutron star shows no remarkable spectral features, but it is significantly depressed at energies below some threshold energy. However, since the thermal conductivity is very different in the normal and parallel directions to the magnetic field lines, the presence of the magnetic field is expected to produce a highly anisotropic temperature distribution, depending on the magnetic field geometry. In this case the observed flux of such an object looks very similar to a BB spectrum, but depressed by a nearly constant factor at all energies. This results in a systematic underestimation of the area of the emitter (and therefore its size) by a factor 5-10 (2-3).

Stability analysis of relativistic jets from collapsars and its implications on the short-term variability of gamma-ray bursts

We consider the transverse structure and stability properties of relativistic jets formed in the course of the collapse of a massive progenitor. Our numerical simulations show the presence of a strong shear in the bulk velocity of such jets. This shear can be responsible for a very rapid shear-driven instability that arises for any velocity profile. This conclusion has been confirmed both by numerical simulations and theoretical analysis. The instability leads to rapid fluctuations of the main hydrodynamical parameters (density, pressure, Lorentz factor, etc.). However, the perturbations of the density are eectively decoupled from those of the pressure because the beam of the jet is radiation-dominated. The characteristic growth time of instability is much shorter than the life time of the jet and, therefore, may lead to a complete turbulent beam. In the course of the non-linear evolution, these fluctuations may yield to internal shocks which can be randomly distributed in the jet. In the case that internal shocks in a ultrarelativistic outflow are responsible for the observed phenomenology of gamma-ray bursts, the proposed instability can well account for the short-term variability of gamma-ray light curves down to milliseconds.We consider the transverse structure and stability properties of relativistic jets formed in the course of the collapse of a massive progenitor. Our numerical simulations show the presence of a strong shear in the bulk velocity of such jets. This shear can be responsible for a very rapid shear--driven instability that arises for any velocity profile. This conclusion has been confirmed both by numerical simulations and theoretical analysis. The instability leads to rapid fluctuations of the main hydrodynamical parameters (density, pressure, Lorentz factor, etc.). However, the perturbations of the density are effectively decoupled from those of the pressure because the beam of the jet is radiation--dominated. The characteristic growth time of instability is much shorter than the life time of the jet and, therefore, may lead to a complete turbulent beam. In the course of the non-linear evolution, these fluctuations may yield to internal shocks which can be randomly distributed in the jet. In the case that internal shocks in a ultrarelativistic outflow are responsible for the observed phenomenology of gamma-ray bursts, the proposed instability can well account for the short-term variability of gamma-ray light curves down to milliseconds.

Resonant Kelvin-Helmholtz modes in sheared relativistic flows

Certain aspects of the (linear and nonlinear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz factors up to 20, specific internal energies approximately 60c2). As a distinct feature of our work, we have combined the analytical linear approach with high-resolution relativistic hydrodynamical simulations, which has allowed us (i) to identify, in the linear regime, resonant modes specific to the relativistic shear layer, (ii) to confirm the result of the linear analysis with numerical simulations, and (iii) more interestingly, to follow the instability development through the nonlinear regime. We find that very-high-order reflection modes with dominant growth rates can modify the global, long-term stability of the relativistic flow. We discuss the dependence of these resonant modes on the jet flow Lorentz factor and specific internal energy and on the shear-layer thickness. The results could have potential applications in the field of extragalactic relativistic jets.

Anisotropic convection in rotating proto-neutron stars

We study the conditions for convective instability in rotating, non-magnetic proto-neutron stars. The criteria that determine stability of nascent neutron stars are analogous to the Solberg-Hoiland conditions but including the presence of lepton gradients. Our results show that, for standard angular velocity profiles, convectively unstable modes with wave-vectors parallel to the rotation axis are suppressed by a stable angular momentum profile, while unstable modes with wave-vectors perpendicular to the axis remain unaltered. Since the wave-vector is perpendicular to the velocity perturbation, the directional selection of the unstable modes may result in fluid motions along the direction of the rotation axis. This occurs in rigidly rotating stars as well as in the inner core of differentially rotating stars. Our results provide a natural source of asymmetry for proto-neutron stars with the only requirement that angular velocities be of the order of the convective characteristic frequency.

Riemann Solvers in General Relativistic Hydrodynamics

Our contribution concerns with the numerical solution of the 3D general relativistic hydrodynamical system of equations within the framework of the{3+1} formalism. We summarize the theoretical ingredients which are necessary in order to build up a numerical scheme based on the solution of local Riemann problems. Hence, the full spectral decomposition of the Jacobian matrices of the system, i.e., the eigenvalues and the right and left eigenvectors, is explicitly shown. An alternative approach consists in using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows. Our proposal relies on a local change of coordinates in terms of which the spacetime metric is locally Minkowskian and permits an accurate description of numerical general relativistic hydrodynamics.

Population synthesis of isolated neutron stars with magneto-rotational evolution – II. From radio-pulsars to magnetars

This work was supported in part by the grants AYA2013-42184-P and Prometeu/2014/69, and by the New Comp-star COST action MP1304. MG is supported by the fellowship BES-2011-049123. DV and NR acknowledges support from grants AYA2012-39303 and SGR2014-1073. NR is additionally supported by an NWO Vidi award.