30 research outputs found
On the magnetic field evolution timescale in superconducting neutron star cores
We revisit the various approximations employed to study the long-term
evolution of the magnetic field in neutron star cores and discuss their
limitations and possible improvements. A recent controversy on the correct form
of the induction equation and the relevant evolution timescale in
superconducting neutron star cores is addressed and clarified. We show that
this ambiguity in the estimation of timescales arises as a consequence of
nominally large terms that appear in the induction equation, but which are, in
fact, mostly irrotational. This subtlety leads to a discrepancy by many orders
of magnitude when velocity fields are absent or ignored. Even when internal
velocity fields are accounted for, only the solenoidal part of the electric
field contributes to the induction equation, which can be substantially smaller
than the irrotational part. We also argue that stationary velocity fields must
be incorporated in the slow evolution of the magnetic field as the next level
of approximation.Comment: 6 pages, version accepted by MNRA
The relevance of ambipolar diffusion for neutron star evolution
We study ambipolar diffusion in strongly magnetised neutron stars, with
special focus on the effects of neutrino reaction rates and the impact of a
superfluid/superconducting transition in the neutron star core. For
axisymmetric magnetic field configurations, we determine the deviation from
equilibrium induced by the magnetic force and calculate the velocity of
the slow, quasi-stationary, ambipolar drift. We study the temperature
dependence of the velocity pattern and clearly identify the transition to a
predominantly solenoidal flow. For stars without superconducting/superfluid
constituents and with a mixed poloidal-toroidal magnetic field of typical
magnetar strength, we find that ambipolar diffusion proceeds fast enough to
have a significant impact on the magnetic field evolution only at low core
temperatures, K. The ambipolar diffusion timescale
becomes appreciably shorter when fast neutrino reactions are present, because
the possibility to balance part of the magnetic force with pressure gradients
is reduced. We also find short ambipolar diffusion timescales in the case of
superconducting cores for K, due to the reduced interaction
between protons and neutrons. In the most favourable scenario, with fast
neutrino reactions and superconducting cores, ambipolar diffusion results in
advection velocities of several km/kyr. This velocity can substantially
reorganize magnetic fields in magnetar cores, in a way that can only be
confirmed by dynamical simulations.Comment: 14 pages, 11 figures, version accepted for publication in MNRA
The force-free twisted magnetosphere of a neutron star
We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to 40 per cent with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large-scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to 25 per cent, which would be the available energy budget in the event of a fast, global magnetospheric reorganization commonly associated with magnetar flares. We have also found the interesting result of the existence of a critical twist (φmax ≲ 1.5 rad), beyond which we cannot find any more numerical solutions. Combining the models considered in this paper with the evolution of the interior of neutron stars will allow us to study the influence of the magnetosphere on the long-term magnetic, thermal, and rotational evolution.This work is supported in part by the Spanish MINECO grants AYA2013-40979-P, AYA2013-42184-P, and AYA2015-66899-C2-2-P, the grant of Generalitat Valenciana PROMETEOII-2014-069, the European Union ERC Starting Grant 259276-CAMAP, and by the New Compstar COST action MP1304
Long-term evolution of the force-free twisted magnetosphere of a magnetar
We study the long-term quasi-steady evolution of the force-free magnetosphere of a magnetar coupled to its internal magnetic field. We find that magnetospheric currents can be maintained on long time-scales of the order of thousands of years. Meanwhile, the energy, helicity and twist stored in the magnetosphere all gradually increase over the course of this evolution, until a critical point is reached, beyond which a force-free magnetosphere cannot be constructed. At this point, some large-scale magnetospheric rearrangement, possibly resulting in an outburst or a flare, must occur, releasing a large fraction of the stored energy, helicity and twist. After that, the quasi-steady evolution should continue in a similar manner from the new initial conditions. The time-scale for reaching this critical point depends on the overall magnetic field strength and on the relative fraction of the toroidal field. The energy stored in the force-free magnetosphere is found to be up to ∼30 per cent larger than the corresponding vacuum energy. This implies that for a 1014 G field at the pole, the energy budget available for fast magnetospheric events is of the order of a few 1044 erg. The spin-down rate is estimated to increase by up to ∼60 per cent, since the dipole content in the magnetosphere is enhanced by the currents present there. A rough estimate of the braking index n reveals that it is systematically n < 3 for the most part of the evolution, consistent with actual measurements for pulsars and early estimates for several magnetars.This work is supported in part by the Spanish MINECO grants AYA2015-66899-C2-1-P, AYA2015-66899-C2-2-P, the grant of Generalitat Valenciana PROMETEOII-2014-069 and by the New Compstar COST action MP1304
Crust-magnetosphere coupling during magnetar evolution and implications for the surface temperature
We study the coupling of the force-free magnetosphere to the long-term
internal evolution of a magnetar. We allow the relation between the poloidal
and toroidal stream functions - that characterizes the magnetosphere - to
evolve freely without constraining its particular form. We find that, on
time-scales of the order of kyr, the energy stored in the magnetosphere
gradually increases, as the toroidal region grows and the field lines expand
outwards. This continues until a critical point is reached beyond which
force-free solutions for the magnetosphere can no longer be constructed, likely
leading to some large-scale magnetospheric reorganization. The energy budget
available for such events can be as high as several erg for fields
of G. Subsequently, starting from the new initial conditions, the
evolution proceeds in a similar manner. The time-scale to reach the critical
point scales inversely with the magnetic field amplitude. Allowing currents to
pass through the last few meters below the surface, where the magnetic
diffusivity is orders of magnitude larger than in the crust, should give rise
to a considerable amount of energy deposition through Joule heating. We
estimate that the effective surface temperature could increase locally from
keV to keV, in good agreement with observations.
Similarly, the power input from the interior into the magnetosphere could be as
high as erg/s, which is consistent with peak luminosities
observed during magnetar outbursts. Therefore, a detailed treatment of currents
flowing through the envelope may be needed to explain the thermal properties of
magnetars.Comment: 9 pages, 9 figures; updated version accepted for publication by MNRA
Magnetic winding and turbulence in ultra-hot Jupiters
While magnetism in exoplanets remains largely unknown, Hot Jupiters have been
considered as natural candidates to harbour intense magnetic fields, both due
to their large masses and their high energy budgets coming from irradiation as
a consequence of their vicinity to their host stars. In this work we perform
MHD simulations of a narrow day-side atmospheric column of ultra-hot Jupiters,
suitable for very high local temperatures (T > 3000 K). Since the conductivity
in this regime is very high, the dominant effect is winding due to the intense
zonal winds. By including a forcing that mimics the wind profiles obtained in
global circulation models, the shear layer induces a strong toroidal magnetic
field (locally reaching hundreds of gauss), supported by meridional currents.
Such fields and the sustaining currents dont depend on the internally
generated field, but are all confined in the thin (less than a scale-height)
shear layer around 1 bar. Additionally, we add random perturbations that induce
turbulent motions, which lead to further (but much smaller) magnetic field
generation to a broader range of depths. These results allow an evaluation of
the currents induced by the atmospheric dynamo. Although here we use ideal MHD
and the only resistivity comes from the numerical scheme, we estimate
a-posteriori the amount of Ohmic heat deposited in the outer layers, which
could be employed in evolutionary models for Hot Jupiters' inflated radii.Comment: submitted for publication in MNRA
Revisiting the Flowers-Ruderman instability of magnetic stars
In 1977, Flowers and Ruderman described a perturbation that destabilises a
purely dipolar magnetic field in a fluid star. They considered the effect of
cutting the star in half along a plane containing the symmetry axis and
rotating each half by 90\degr in opposite directions, which would cause the
energy of the magnetic field in the exterior of the star to be greatly reduced,
just as it happens with a pair of aligned magnets. We formally solve for the
energy of the external magnetic field and check that it decreases monotonously
along the entire rotation. We also describe the instability using perturbation
theory, and see that it happens due to the work done by the interaction of the
magnetic field with surface currents. Finally, we consider the stabilising
effect of adding a toroidal field by studying the potential energy perturbation
when the rotation is not done along a sharp cut, but with a continuous
displacement field that switches the direction of rotation across a region of
small but finite width. Using these results, we estimate the relative strengths
of the toroidal and poloidal field needed to make the star stable to this
displacement and see that the energy of the toroidal field required for
stabilisation is much smaller than the energy of the poloidal field. We also
show that, contrary to a common argument, the Flowers-Ruderman instability
cannot be applied many times in a row to reduce the external magnetic energy
indefinitely.Comment: Uploaded complete version with corrections from the MNRAS refere
The force-free twisted magnetosphere of a neutron star – II. Degeneracies of the Grad–Shafranov equation
We extend our previous study of equilibrium solutions of non-rotating force-free magnetospheres of neutron stars. We show that multiple solutions exist for the same sets of parameters, implying that the solutions are degenerate. We are able to obtain configurations with disconnected field lines, however, in nearly all cases these correspond to degenerate higher energy solutions. We carry out a wide parametric search in order to understand the properties of the solutions. We confirm our previous results that the lower energy solutions have up to ∼ 25 per cent more energy than the vacuum case, helicity of the order of ∼5 (in some defined units), maximum twist of ∼1.5 rad and a dipole strength that is up to ∼ 40 per cent larger than the vacuum dipole. Including the degenerate higher energy solutions allows for larger theoretical limits of up to ∼ 80 per cent more energy with respect to the vacuum case, helicity of the order of ∼8 and a dipole strength that can now be up to four times that of the vacuum dipole, while the twist can be significantly larger and even diverge for configurations with disconnected domains. The higher energy solutions are probably unstable, therefore, it is unlikely that such magnetospheres exist under normal conditions in magnetars and high magnetic field pulsars.This work is supported in part by the Spanish MINECO/FEDER grants AYA2015-66899-C2-1-P, AYA2015-66899-C2-2-P, the grant of Generalitat Valenciana PROMETEOII-2014-069, and by the New Compstar COST action MP1304