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The thermomagnetic evolution of the young neutron star in Cassiopea A is studied by considering fast neutrino emission processes. In particular, we consider neutron star models obtained from the equation of state computed in the framework of the Brueckner-Bethe-Goldstone many-body theory and variational methods, and models obtained with the Akmal-Pandharipande-Ravenhall equation of state. It is shown that it is possible to explain a fast cooling regime as the one observed in the neutron star in Cassiopea A if the Joule heating produced by dissipation of the small-scale magnetic field in the crust is taken into account. We thus argue that it is difficult to put severe constraints on the superfluid gap if the Joule heating is considered., Comment: 4 pages, 2 figures, to appear on A&A Letters

Magnetohydrodynamic (MHD) instabilities can play an important role in the structure and dynamics of the pulsar magnetosphere. We consider the instabilitycaused by differential rotation that is suggested by many theoretical models. Stability is considered by means of a linear analysis within the frane of the force-free MHD. We argue that differentially rotating magnetospheres are unstable for any particular geometry of the magnetic field and rotation law. The characteristic growth time of instability is of the order of the rotation period. The instability can lead to fluctuations of the emission and enhancement of diffusion in the magnetosphere., Comment: 5 pages; to appear in Astronomy and Astrophysics

MHD waves can be responsible for plasma fluctuations and short-term variations of the pulsar emission. We consider the properties of plane and cylindrical waves that can exist in the force-free magnetosphere. Waves are considered by means of a linear analysis of the force-free MHD equations. We argue that these particular types of waves can exist in the magnetosphere of pulsars. These waves are closely related to the Alfven waves of the standard magnetohydrodynamics but are modified by the force-free condition and non-zero charge density. We derive the dispersion relation for magnetospheric waves and show that the wave periods are likely within the range $\sim 10^{-2}-10^(-4}$ s depending on the magnetospheric parameters., Comment: 4 pages; to appear in Astronomy and Astrophysics

Magnetorotational instability (MRI) has been suggested to lead a rapid growth of the magnetic field in core collapse supernovae and produce departures from spherical syymmetry that can be important in determining the explosion mechanism. We address the problem of stability in differentially rotating magnetized proto-neutron stars at the beginning of their evolution. Criteria for MRI in proto-neutron stars are derived without simplying assumptions about a weak magnetic field and are substantially different from the standard condition. If the magnetic field is strong, MRI can occur only in the neighbourhood of the region where the spherical radial component of the magnetic field vanishes. The growth rate of MRI is relatively low except for perturbations with very small scales which usually are not detected in numerical simulations. We find that MRI in proto-neutron stars grows more slowly than than the double diffusive instability analogous the Goldreich-Schubert-Fricke instability in ordinary stars., Comment: 6 pages, 2 figures, accepted for publication in Astronomy and Astrophysics

We study the efficiency of Joule heating in the crustal layers of young neutron stars. It is shown that dissipation of the magnetic field is highly inhomogeneous in the crust with much faster dissipation in relatively low density layers. In young neutron stars, the rate of Joule heating in the crust can exceed the standard luminosity of non-magnetic star and can even be comparable to the luminosity of magnetars. The results of calculations are compared with the available observational data. We argue that the crustal field model can well account for the data on the surface temperature and magnetic field of young neutron stars., Comment: 8 pages, 5 figures; accepted by Astronomy and Astrophysics

We consider stability of differentially rotating non-magnetic proto-neutron stars. When neutrino transport is efficient, the star can be subject to a diffusive instability that can occur even in the convectively stable region. The instability arises on the time-scale comparable to the time-scale of thermal diffusion. Hydrodynamic motions driven by the instability can lead to anisotropy in the neutrino flux since the instability is suppressed near the equator and rotation axis., Comment: 6 pages. Accepted for publication in A&A

We study the stability of a compressible differentially rotating flows in the presence of the magnetic field, and we show that the compressibility profoundly alters the previous results for a magnetized incompressible flow. The necessary condition of newly found instability can be easily satisfied in various flows in laboratory and astrophysical conditions and reads $B_{s} B_{\phi} \Omega' \neq 0$ where $B_{s}$ and $B_{\phi}$ are the radial and azimuthal components of the magnetic field, $\Omega' = d \Omega/ds$ with $s$ being the cylindrical radius. Contrary to the well-known magnetorotational instability that occurs only if $\Omega$ decreases with $s$, the instability considered in this paper may occur at any sign of $\Omega'$. The instability can operate even in a very strong magnetic field which entirely suppresses the standard magnetorotational instability. The growth time of instability can be as short as few rotation periods., Comment: 5 pages, 3 figures

We consider dynamo action under the combined influence of turbulence and large-scale shear in sheared jets. Shear can stretch turbulent magnetic field lines in such a way that even turbulent motions showing mirror symmetry become suitable for generation of a large-scale magnetic field. We derive the integral induction equation governing the behaviour of the mean field in jets. The main result is that sheared jets may generate a large-scale magnetic field if shear is sufficiently strong. The generated mean field is mainly concentrated in a magnetic sheath surrounding the central region of a jet, and it exhibits sign reversals in the direction of the jet axis. Typically, the magnetic field in a sheath is dominated by the component along the jet that can reach equipartition with the kinetic energy of particles, The field in the central region of jets has a more disordered structure., Comment: 7 pages, accepted for publication in A&A

We discuss the mean-field dynamo action in protoneutron stars that are subject to instabilities during the early evolutionary phase. The mean field is generated in the neutron-finger unstable region where the Rossby number is $\sim 1$ and mean-field dynamo is efficient. Depending on the rotation rate, the mean-field dynamo can lead to the formation of three different types of pulsars. If the initial period of the protoneutron star is short, then the generated large-scale field is very strong ($> 3 \times 10^{13}$G) and exceeds the small-scale field at the neutron star surface. If rotation is moderate, then the pulsars are formed with more or less standard dipole fields ($< 3 \times 10^{13}$G) but with surface small-scale magnetic fields stronger than the dipole field. If rotation is very slow, then the mean-field dynamo does not operate, and the neutron star has no global field. Nevertheless, strong small-scale fields are generated in such pulsars, and they can manifest themselves as objects with very low spin-down rate but with a strong magnetic field inferred from the spectral features., Comment: 4 pages, 2 figures, to appear on A&A

We study the secular instability of magnetized differentially rotating radiative zones taking account of viscosity and magnetic and thermal diffusivities. The considered instability generalizes the well-known Goldreich-Schubert-Fricke instability for the case of a sufficiently strong magnetic field. In magnetized stars, instability can lead to a formation of non-spherical unstable zones where weak turbulence mixes the material between the surface and interiors. Such unstable zones can manifest themselves by a non-spherical distribution of abundance anormalies on the stellar surface., Comment: 8 pages, accepted by Astronomy and Astrophysics

We study the relation between the mean effective surface temperature T_s and the internal temperature T_b for magnetic neutron stars, assuming that the magnetic field near the surface has a presumably small-scale structure. The heavy-element (iron) and light-element (accreted) heat-blanketing envelopes are considered, and the results are compared with the case of a dipole magnetic field. We argue that the difference in the T_b(T_s)-relation for different magnetic configurations is always much smaller than a possible difference caused by variations of the chemical composition in the envelope., Comment: 5 pages, 2 figures. V2: a typo corrected. Accepted by A&A

We consider the stability properties of the ocean of accreting magnetic neutron stars. It turns out that the ocean is always unstable due to the combined influence of the temperature and chemical composition gradients along the surface and of the Hall effect. Both the oscillatory and non-oscillatory modes can be unstable in accreting stars. The oscillatory instability grows on a short timescale of the order os 0.1-10 s depending on the lengthscale of a surface inhomogeneity and the wavelength of perturbations. The instability of non-oscillatory modes is typically much slower and can develop on a timescale of hours or days. Instability generates a weak turbulence that can be responsible for mixing between the surface and deep ocean layers and for spreading the accreted material over the stellar surface. Spectral features of heavy elements can be detected in the atmospheres of accreting stars due to mixing, and these features should be different in neutron stars with stable and unstable burning. Motions caused by instability can also be the reason for slow variations in the luminosity., Comment: 10 pages, accepted by Astronomy and Astrophysics

We have investigated the turbulent mean-field dynamo action in protoneutron stars that are subject to convective and neutron finger instabilities during the early evolutionary phase. While the first one develops mostly in the inner regions of the star, the second one is favored in the outer regions, where the Rossby number is much smaller and a mean-field dynamo action is more efficient. By solving the mean-field induction equation we have computed the critical spin period below which no dynamo action is possible and found it to be $\sim 1$ s for a wide range of stellar models and for both axisymmetric and non-axisymmetric magnetic fields. Because this critical period is substantially longer than the characteristic spin period of very young pulsars, we expect that a mean-field dynamo will be effective for most protoneutron stars. The saturation dipole field estimated by making use of the model of ``global'' quenching fits well the pulsar magnetic fields inferred from the spin-down data. Apart from the large scale magnetic field, our model predicts also a generation of small scale fields which are typically stronger than the poloidal field and can survive during the lifetime of pulsars. Extremely rapidly rotating protoneutron stars ($P \sim 1$ ms) may have the dipole field $\sim (3-6) \times 10^{14}$ G., Comment: 7 pages, 6 figures, to appear on A&A

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., Comment: 5 pages, 4 figures, final version to appear in A&A

We consider generation and evolution of small-scale magnetic fields in neutron stars. These fields can be generated by small-scale turbulent dynamo action soon after the collapse when the proto-neutron star is subject to convective and neutron finger instabilities. After instabilities stop, small-scale fields should be frozen into the crust that forms initially at high density about 10^{14} g/cm^{3} and then spreads to the surface. Because of high crustal conductivity, magnetic fields with the lengthscale about 1-3 km can survive in the crust as long as 10-100 Myr and form a sunspot-like structure at the surface of radiopulsars.

The stability properties of inviscid protostellar disks are examined taking into account the Hall effect and buoyancy. Depending on the parameters, different types of instabilities can exist in different regions of disks. In a very low ionized region, the instability associated with baroclinic effects of buoyancy is likely most efficient. The Hall-driven shear instability can lead to destabilization of regions with a higher ionization. The magnetorotational instability modified by buoyancy can only be a destabilizing factor in regions with strong magnetic field or a relatively high conductivity ($\sigma B^2 / \rho > a_e \Omega$, with $a_e$ the magnetization parameter of electrons)., Comment: 8 pages, 2 figures, submitted to Astron. Astrophys

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., Comment: 8 pages, 5 figures. Received 2 July 2002 / Accepted 30 August 2002 in A&A

The stability properties of newly born neutron stars, or proto--neutron stars, are considered. We take into account dissipative processes, such as neutrino transport and viscosity, in the presence of a magnetic field. In order to find the regions of the star subject to different sorts of instability, we derive the general instability criteria and apply it to evolutionary models of PNSs. The influence of the magnetic field on instabilities is analyzed and the critical magnetic field stabilizing the star is obtained. In the light of our results, we estimate of the maximum poloidal magnetic field that might be present in young pulsars or magnetars., Comment: 18 pages, 4 figures, to appear in Astrophysical Journal

The linear hydrodynamic stability of proto-neutron stars (PNSs) is considered taking into account dissipative processes such as neutrino transport and viscosity. We obtain the general instability criteria which differ essentially from the well-known Ledoux criterion used in previous studies. We apply the criteria to evolutive models of PNSs that, in general, can be subject to the various known regimes such as neutron fingers and convective instabilities. Our results indicate that the fingers instability arises in a more extended region of the stellar volume and lasts a longer time than expected., Comment: 17 pages, 3 figures. Accepted for publication in Astrophysical Journal

The evolution of neutron stars in close binary systems with a low-mass companion is considered assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario of the evolution in a close binary system in accordance with which the neutron star passes throughout four evolutionary phases ("isolated pulsar" -- "propeller" -- accretion from the wind of a companion -- accretion due to Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties both of the neutron star and low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period being processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as $10^{10}$ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The considered model can well account for the origin of millisecond pulsars., Comment: 18 pages + 10 figures, uses epsf.sty. Accepted by MNRAS

We have derived an analytic solution to the asymptotic behavior of dipolar magnetic fields that are generated in the crusts of neutron stars. We show that if the conductivity is due to impurity scattering, as expected for late stages of evolution, the surface field strength at the magnetic pole declines with the power law B(sub p) approximately = (t/t(sub 0))(exp -2/3). The results are shown to be qualitatively consistent with detailed numerical calculations. These latter results are consistent with some recent analyses of pulsar statistics and the magnetic fields of several binary pulsars with white dwarf companions whose ages have been determined. The dependence of the surface magnetic field on spin period of the pulsar is derived.