A Balescu-Lenard type kinetic equation fot the collisional evolution of stable self-gravitating systems

A kinetic equation for the collisional evolution of stable, bound, self gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self consistent dressing by collective gravitational interaction of the colliding particles, for the system's inhomogeneity and for different constituent's masses. The evolution of the one-body distribution function is described in action angle space. The collision operators are expressed in terms of the collective response function allowed by the existing distribution functions at any given time and involve particles in resonant motions. The set of equations which describe the coupled evolution of the distribution functions and of the potential is derived for spherical systems. In the homogeneous limit, which sacrifices the description of the evolution of the spatial structure of the system, but retains the effects of collective gravitational dressing, the kinetic equation reduces to a form similar to the Balescu-Lenard equation of plasma physics.Comment: 20 pages 1 figur

The magnetic coupling of planets and small bodies with a pulsar's wind

We investigate the electromagnetic interaction of a relativistic stellar wind with a planet or a smaller body in orbit around a pulsar. This may be relevant to objects such as PSR B1257+12 and PSR B1620-26 that are expected to hold a planetary system, or to pulsars with suspected asteroids or comets. Most models of pulsar winds predict that, albeit highly relativistic, they are slower than Alfv\'en waves. In that case, a pair of stationary Alfv\'en waves, called Alfv\'en wings (AW), is expected to form on the sides of the planet. The wings expand far into the pulsar's wind and they could be strong sources of radio emissions. The Alfv\'en wings would cause a significant drift over small bodies such as asteroids and comets.Comment: proceeding of the SF2A conference in Nice, 201

Towards a theory of extremely intermittent pulsars II: Asteroids at a close distance

We investigate whether there may be one or many companions orbiting at close distance to the light cylinder around the extremely intermittent pulsars PSR B1931+24 and PSR J1841-0500. These pulsars, behaving in a standard way when they are active, also "switch off" for durations of several days, during which their magnetospheric activity is interrupted or reduced. We constrained our analysis on eight fundamental properties of PSR B1931+24 that summarise the observations. We considered that the disruption/activation of the magnetospheric activity would be caused by the direct interaction of the star with the Alfv\'en wings emanating from the companions. We also considered the recurrence period of 70 days to be the period of precession of the periastron of the companions orbit. We analysed in which way the time scale of the "on/off" pseudo-cycle would be conditioned by the precession of the periastron and not by the orbital time scale, and we derived a set of orbital constraints that we solved. We then compared the model, based on PSR 1931+24, with the known properties of PSR 1841+0500. We conclude that PSR B1931+24 may be surrounded at a close distance to the star by a stream of small bodies of kilometric or sub-kilometric sizes that could originate from the tidal disruption of a body of moderate size that fell at a close distance to the neutron star on an initially very eccentric orbit. This scenario is also compatible with the properties of PSR J1841-0500, although the properties of PSR J1841-0500 are, by now, less constrained. These results raise new questions. Why are the asteroids not yet evaporated ? What kind of interaction can explain the disruption of the magnetospheric activity ? These questions are the object of two papers in preparation that will complete the present analysis.Comment: Accepted for publication in Astronomy and Astrophysic

Towards a theory of extremely intermittent pulsars I: Does something orbits PSR B1931 + 24 ?

We investigate whether one or many companions are orbiting the extremely intermittent pulsar PSR B1931+24. We constrained our analysis on previous observations of eight fundamental properties of PSR B1931+24. The most puzzling properties are the intermittent nature of the pulsar's activity, with active and quiet phases that alternate quasi-periodically; the variation of the slowing-down rate of its period between active and quiet phases; and because there are no timing residuals, it is highly unlikely that the pulsar has a massive companion. Here, we examine the effects that one putative companion immersed in the magnetospheric plasma or the wind of the pulsar might have, as well as the associated electric current distribution. We analysed several possibilities for the distance and orbit of this hypothetical companion and the nature of its interaction with the neutron star. We show that if the quasi-periodic behaviour of PSR B1931+24 was caused by a companion orbiting the star with a period of 35 or 70 days, the radio emissions, usually considered to be those of the pulsar would in that specific case be emitted in the companion's environment. We analysed four possible configurations and conclude that none of them would explain the whole set of peculiar properties of PSR 1931+24. We furthermore considered a period 70 days for the precession of the periastron associated to an orbit very close to the neutron star. This hypothesis is analysed in a companion paper.Comment: Accepted for publication in Astrnomy and Astrophysic

Particle acceleration by circularly and elliptically polarised dispersive Alfven waves in a transversely inhomogeneous plasma in the inertial and kinetic regimes

Dispersive Alfven waves (DAWs) offer, an alternative to magnetic reconnection, opportunity to accelerate solar flare particles. We study the effect of DAW polarisation, L-, R-, circular and elliptical, in different regimes inertial and kinetic on the efficiency of particle acceleration. We use 2.5D PIC simulations to study how particles are accelerated when DAW, triggered by a solar flare, propagates in transversely inhomogeneous plasma that mimics solar coronal loop. (i) In inertial regime, fraction of accelerated electrons (along the magnetic field), in density gradient regions is ~20% by the time when DAW develops 3 wavelengths and is increasing to ~30% by the time DAW develops 13 wavelengths. In all considered cases ions are heated in transverse to the magnetic field direction and fraction of the heated particles is ~35%. (ii) The case of R-circular, L- and R- elliptical polarisation DAWs, with the electric field in the non-ignorable transverse direction exceeding several times that of in the ignorable direction, produce more pronounced parallel electron beams and transverse ion beams in the ignorable direction. In the inertial regime such polarisations yield the fraction of accelerated electrons ~20%. In the kinetic regime this increases to ~35%. (iii) The parallel electric field that is generated in the density inhomogeneity regions is independent of m_i/m_e and exceeds the Dreicer value by 8 orders of magnitude. (iv) Electron beam velocity has the phase velocity of the DAW. Thus electron acceleration is via Landau damping of DAWs. For the Alfven speeds of 0.3c the considered mechanism can accelerate electrons to energies circa 20 keV. (v) The increase of mass ratio from m_i/m_e=16 to 73.44 increases the fraction of accelerated electrons from 20% to 30-35% (depending on DAW polarisation). For the mass ratio m_i/m_e=1836 the fraction of accelerated electrons would be >35%.Comment: Final accepted version. To appear in Physics of Plasmas, volume 18, issue 9 (September 2011

Do asteroids evaporate near pulsars? Induction heating by pulsar waves revisited

We investigate the evaporation of close-by pulsar companions, such as planets, asteroids, and white dwarfs, by induction heating. Assuming that the outflow energy is dominated by a Poynting flux (or pulsar wave) at the location of the companions, we calculate their evaporation timescales, by applying the Mie theory. Depending on the size of the companion compared to the incident electromagnetic wavelength, the heating regime varies and can lead to a total evaporation of the companion. In particular, we find that inductive heating is mostly inefficient for small pulsar companions, although it is generally considered the dominant process. Small objects like asteroids can survive induction heating for $10^4\,$years at distances as small as $1\,R_\odot$ from the neutron star. For degenerate companions, induction heating cannot lead to evaporation and another source of heating (likely by kinetic energy of the pulsar wind) has to be considered. It was recently proposed that bodies orbiting pulsars are the cause of fast radio bursts; the present results explain how those bodies can survive in the pulsar's highly energetic environment.Comment: 10 pages, 4 figures, 1 table, accepted by A&

Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems

General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding particles and their self-consistent dressing by collective gravitational interactions. The associated Fokker-Planck equation is shown to be fully consistent with the corresponding inhomogeneous Balescu-Lenard equation and, in the weak self-gravitating limit, to the inhomogeneous Landau equation. Hence it provides an alternative derivation to both and demonstrates their equivalence. The corresponding stochastic Langevin equations are presented: they can be a practical alternative to numerically solving the inhomogeneous Fokker-Planck and Balescu-Lenard equations. The present formalism allows for a self-consistent description of the secular evolution of different populations covering a spectrum of masses, with a proper accounting of the induced secular mass segregation, which should be of interest to various astrophysical contexts, from galactic centers to protostellar discs.Comment: 27 pages, 1 figur

On the Mechanical Energy Available to Drive Solar Flares

Where does solar flare energy come from? More specifically, assuming that the ultimate source of flare energy is mechanical energy in the convection zone, how is this translated into energy dissipated or stored in the corona? This question appears to have been given relatively little thought, as attention has been focussed predominantly on mechanisms for the rapid dissipation of coronal magnetic energy by way of MHD instabilities and plasma micro instabilities. We consider three types of flare theory: the steady state "photospheric dynamo" model in which flare power represents coronal dissipation of currents generated simultaneously by sub-photospheric flows; the "magnetic energy storage" model where sub-photospheric flows again induce coronal currents but which in this case are built up over a longer period before being released suddenly; and "emerging flux" models, in which new magnetic flux rising to the photosphere already contains free energy, and does not require subsequent stressing by photospheric motions. We conclude that photospheric dynamos can power only very minor flares; that coronal energy storage can in principle meet the requirements of a major flare, although perhaps not the very largest flares, but that difficulties in coupling efficiently to the energy source may limit this mechanism to moderate sized flares; and that emerging magnetic flux tubes, generated in the solar interior, can carry sufficient free energy to power even the largest flares ever observed.Comment: 14 pages, 1 figur