A new model for QPOs in accreting black holes: application to the microquasar GRS 1915+105

(abridged) In this paper we extend the idea suggested previously by Petri (2005a,b) that the high frequency quasi-periodic oscillations observed in low-mass X-ray binaries may be explained as a resonant oscillation of the accretion disk with a rotating asymmetric background (gravitational or magnetic) field imposed by the compact object. Here, we apply this general idea to black hole binaries. It is assumed that a test particle experiences a similar parametric resonance mechanism such as the one described in paper I and II but now the resonance is induced by the interaction between a spiral density wave in the accretion disk, excited close to the innermost stable circular orbit, and vertical epicyclic oscillations. We use the Kerr spacetime geometry to deduce the characteristic frequencies of this test particle. The response of the test particle is maximal when the frequency ratio of the two strongest resonances is equal to 3:2 as observed in black hole candidates. Finally, applying our model to the microquasar GRS 1915+105, we reproduce the correct value of several HF-QPOs. Indeed the presence of the 168/113/56/42/28 Hz features in the power spectrum time analysis is predicted. Moreover, based only on the two HF-QPO frequencies, our model is able to constrain the mass $M_{\rm BH}$ and angular momentum $a_{\rm BH}$ of the accreting black hole.Comment: Accepted for publication in Astrophysics & Space Scienc

Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma

We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.Comment: Accepted by PPC

PIC Simulations of the Temperature Anisotropy-Driven Weibel Instability: Analyzing the perpendicular mode

An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this nonlinear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this 2-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation.Comment: accepted by Plasma Physics and Controlled Fusio

Particle-in-cell simulations of shock-driven reconnection in relativistic striped winds

By means of two- and three-dimensional particle-in-cell simulations, we investigate the process of driven magnetic reconnection at the termination shock of relativistic striped flows. In pulsar winds and in magnetar-powered relativistic jets, the flow consists of stripes of alternating magnetic field polarity, separated by current sheets of hot plasma. At the wind termination shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Irrespective of the stripe wavelength "lambda" or the wind magnetization "sigma" (in the regime sigma>>1 of magnetically-dominated flows), shock-driven reconnection transfers all the magnetic energy of alternating fields to the particles, whose average Lorentz factor increases by a factor of sigma with respect to the pre-shock value. In the limit lambda/(r_L*sigma)>>1, where r_L is the relativistic Larmor radius in the wind, the post-shock particle spectrum approaches a flat power-law tail with slope around -1.5, populated by particles accelerated by the reconnection electric field. The presence of a current-aligned "guide" magnetic field suppresses the acceleration of particles only when the guide field is stronger than the alternating component. Our findings place important constraints on the models of non-thermal radiation from Pulsar Wind Nebulae and relativistic jets.Comment: 25 pages, 14 figures, movies available at https://www.cfa.harvard.edu/~lsironi/sironi_movies.tar ; in press, special issue of Computational Science and Discovery on selected research from the 22nd International Conference on Numerical Simulation of Plasma

Numerical solution of the linear dispersion relation in a relativistic pair plasma

We describe an algorithm that computes the linear dispersion relation of waves and instabilities in relativistic plasmas within a Vlasov-Maxwell description. The method used is fully relativistic and involves explicit integration of particle orbits along the unperturbed equilibrium trajectories. We check the algorithm against the dispersion curves for a single component magnetised plasma and for an unmagnetised plasma with counter-streaming components in the non-relativistic case. New results on the growth rate of the Weibel or two-stream instability in a hot unmagnetised pair plasma consisting of two counter-streaming relativistic Maxwellians are presented. These are relevant to the physics of the relativistic plasmas found in gamma-ray bursts, relativistic jets and pulsar winds.Comment: Accepted by Plasma Physics and Controlled Fusio

Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz & Klu{\'z}niak (\cite{Abramowicz2001}). In a first paper (P\'etri \cite{Petri2005a}, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. We show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric sonance. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.Comment: Accepte

The theory of pulsar winds and nebulae

We review current theoretical ideas on pulsar winds and their surrounding nebulae. Relativistic MHD models of the wind of the aligned rotator, and of the striped wind, together with models of magnetic dissipation are discussed. It is shown that the observational signature of this dissipation is likely to be point-like, rather than extended, and that pulsed emission may be produced. The possible pulse shapes and polarisation properties are described. Particle acceleration at the termination shock of the wind is discussed, and it is argued that two distinct mechanisms must be operating, with the first-order Fermi mechanism producing the high-energy electrons (above 1 TeV) and either magnetic annihilation or resonant absorption of ion cyclotron waves responsible for the 100 MeV to 1 TeV electrons. Finally, MHD models of the morphology of the nebula are discussed and compared with observation.Comment: 33 pages, to appear in Springer Lecture Notes on "Neutron stars and pulsars, 40 years after the discovery", ed W.Becke

Constraining the magnetic field geometry of the millisecond pulsar PSRJ0030+0451 from joint radio, thermal X-ray, and γ-ray emission

Context. With the advent of multi-wavelength electromagnetic observations of neutron stars - spanning many decades in photon energies - from radio wavelengths up to X-rays and γ-rays, it has become possible to significantly constrain the geometry and the location of the associated emission regions. Aims. In this work, we use results from the modelling of thermal X-ray observations of PSR J0030+0451 from the Neutron Star Interior Composition Explorer (NICER) mission and phase-aligned radio and γ-ray pulse profiles to constrain the geometry of an off-centred dipole that is able to reproduce the light curves in these respective bands simultaneously. Methods. To this aim, we deduced a configuration with a simple dipole off-centred from the location of the centre of the thermal X-ray hot spots. We show that the geometry is compatible with independent constraints from radio and -ray pulsations only, leading to a fixed magnetic obliquity of α ≈ 75° and a line-of-sight inclination angle of ζ ≈ 54°. Results. We demonstrate that an off-centred dipole cannot be rejected by accounting for the thermal X-ray pulse profiles. Moreover, the crescent shape of one spot is interpreted as the consequence of a small-scale surface dipole on top of the large-scale off-centred dipole

New constraints on Planck-scale Lorentz Violation in QED from the Crab Nebula

We set constraints on O(E/M) Lorentz Violation in QED in an effective field theory framework. A major consequence of such assumptions is the modification of the dispersion relations for electrons/positrons and photons, which in turn can affect the electromagnetic output of astrophysical objects. We compare the information provided by multiwavelength observations with a full and self-consistent computation of the broad-band spectrum of the Crab Nebula. We cast constraints of order 10^{-5} at 95% confidence level on the lepton Lorentz Violation parameters.Comment: 23 pages, 9 figures. v2: added comments and references, matches version accepted by JCA

PIC simulations of the Thermal Anisotropy-Driven Weibel Instability: Field growth and phase space evolution upon saturation

The Weibel instability is investigated with PIC simulations of an initially unmagnetized and spatially uniform electron plasma. This instability, which is driven by the thermally anisotropic electron distribution, generates electromagnetic waves with wave vectors perpendicular to the direction of the higher temperature. Two simulations are performed: A 2D simulation, with a simulation plane that includes the direction of higher temperature, demonstrates that the wave spectrum is initially confined to one dimension. The electric field components in the simulation plane generated by the instability equalize at the end of the simulation through a secondary instability. A 1D PIC simulation with a high resolution, where the simulation box is aligned with the wave vectors of the growing waves, reveals details of the electron phase space distribution and permits a comparison of the magnetic and electric fields when the instability saturates. It is shown that the electrostatic field is driven by the magnetic pressure gradient and that it and the magnetic field redistribute the electrons in space.Comment: Plasma Phys Controll Fusion, in press (to appear in june 2009