Test-particle Case Research Articles

Gamma-ray properties of supernova remnants transporting into molecular clouds: the cases of IC 443 and W44

Motivated by the recent report of the detailed spectra of IC 443 and W44 based on four years of observations with the Fermi Large Area Telescope, gamma-rays produced via proton-proton interaction in the two supernova remnants (SNRs) have been investigated in the diffusive shock acceleration scenario. In the model, a part of the SNR shell transporting into ambient dense molecular clouds (MCs), and a shock with a relatively low Alfven Mach number can be produced. Relativistic protons are accelerated in the shock via the diffusive acceleration process; moreover, a break in the particle distribution is induced since the damping of Alfven waves when the shock transporting into partly ionized plasma. A spectrum of the accelerated protons in the shock can be obtained in the test-particle case, taking into account the effect of the ambient partly ionized plasma on the acceleration process. Furthermore, hadronic gamma-rays with a peak around several GeVs are reproduced as the protons inelastically colliding with the ambient matter of the crushed gas. The observed gamma-ray spectral distributions of the SNR IC 443 and W44 can be successfully reproduced using the static model in the test-particle scenario. It can be concluded that the observed gamma-rays can be explained in the diffusive shock case as the shock waves transporting into the dense MCs for the two remnants.

Acceleration of particles and shells by Reissner-Nordström naked singularities

We explore the Reissner-Nordstr\"om naked singularities with a charge $Q$ larger than its mass $M$ from the perspective of particle acceleration. We first consider a collision between two test particles following the radial geodesics in the Reissner-Nordstr\"om naked singular geometry. An initially radially ingoing particle turns back due to the repulsive effect of gravity in the vicinity of a naked singularity. Such a particle then collides with another radially ingoing particle. We show that the center of mass energy of collision taking place at $r\ensuremath{\approx}M$ is unbound, in the limit where the charge transcends the mass by an arbitrarily small amount $0<1\ensuremath{-}M/Q\ensuremath{\ll}1$. The acceleration process we describe avoids fine-tuning of the parameters of the particle geodesics for the unbound center of mass energy of collisions, and the proper time required for the process is also finite. We show that the coordinate time as observed by the distant observer required for the trans-Planckian collisions to occur around the naked singularity with one solar mass is merely of the order of million years, which is much smaller than the Hubble time. On the contrary, the time scale for collisions associated with an extremal black hole in an analogous situation is many orders of magnitude larger than the age of the Universe. We then study the collision of the neutral spherically symmetric shells made up of dust particles. In this case, it is possible to treat the situation by exactly taking into account the gravity due to the shells using Israel's thin shell formalism, and thus this treatment allows us to go beyond the test particle approximation. The center of mass energy of collision of the shells is then calculated in a situation analogous to the test particle case and is shown to be bounded above. However, we find that the energy of a collision between two constituent particles of the shells at the center of mass frame can exceed the Planck energy.

Hadronic gamma-ray emission from molecular clouds overtaken by supernova remnants

A model is proposed to describe the high-energy gamma-ray emission from a supernova remnant (SNR) interacting with a dense molecular cloud (MC). In this model, a shock with a low Alfvén Mach number can be produced when a part of a SNR shell drives into a dense MC, and then the proton spectrum in the test-particle case with the Alfvén drift is much softer than that for strong shocks; the γ-rays produced via inelastic proton–proton (pp) interaction from the SNR can be greatly enhanced. The model is applied to the five GeV-bright SNRs IC443, W51C, W44, W49B, and W28 which are known to be interacting with MCs. The γ-ray spectra of these SNRs can be reproduced as the pp interaction from the MCs overtaken by the SNR shocks within the test-particle diffusive shock acceleration regime. For the five SNRs, the spectral breaks around several GeV detected with the Fermi LAT are due to the softness of the energy distributions of the protons accelerated in the SNR shells with low Alfvén Mach numbers.

THE IMPACT OF EFFICIENT PARTICLE ACCELERATION ON THE EVOLUTION OF SUPERNOVA REMNANTS IN THE SEDOV-TAYLOR PHASE

We investigate the effects of the efficient production of cosmic rays on the evolution of supernova remnants (SNRs) in the adiabatic Sedov-Taylor phase. We model the SNR by coupling the hydrodynamic evolution with nonlinear diffusive shock acceleration (DSA), and track self-consistently the ionization state of the shock-heated plasma. Using a plasma emissivity code and the results of the model, we predict the thermal X-ray emission and combine it with the non-thermal component in order to obtain the complete spectrum in this energy range. Hence, we study how the interpretation of thermal X-ray observations is affected by the efficiency of the DSA process, and find that, compared to test particle cases, the efficient DSA example yields a smaller shock radius and speed, a larger compression ratio, and lower intensity X-ray thermal emission. We also find that a model where the shock is not assumed to produce CRs can fit the X-ray observational properties of an example with efficient particle acceleration, with a different set of input parameters, and in particular a much lower explosion energy. Additionally, we model the broadband non-thermal emission, and investigate what signatures result from the acceleration of particles.

THE ROLE OF DIFFUSIVE SHOCK ACCELERATION ON NONEQUILIBRIUM IONIZATION IN SUPERNOVA REMNANTS

We present results of semi-analytic calculations which show clear evidence for changes in the non-equilibrium ionization behind a supernova remnant forward shock undergoing efficient diffusive shock acceleration (DSA). The efficient acceleration of particles (i.e., cosmic rays) lowers the shock temperature and raises the density of the shocked gas, thus altering the ionization state of the plasma in comparison to the test particle approximation where cosmic rays gain an insignificant fraction of the shock energy. The differences between the test particle and efficient acceleration cases are substantial and occur for both slow and fast temperature equilibration rates: in cases of higher acceleration efficiency, particular ion states are more populated at lower electron temperatures. We also present results which show that, in the efficient shock acceleration case, higher ionization fractions are reached noticeably closer to the shock front than in the test-particle case, clearly indicating that DSA may enhance thermal X-ray production. We attribute this to the higher postshock densities which lead to faster electron temperature equilibration and higher ionization rates. These spatial differences should be resolvable with current and future X-ray missions, and can be used as diagnostics in estimating the acceleration efficiency in cosmic-ray modified shocks.

The New Transiting Planet OGLE‐TR‐56b: Orbit and Atmosphere

Motivated by the identification of the very close-in extrasolar giant planet OGLE-TR-56b (P = 1.2 days, a = 0.023 AU, Mp = 0.9MJ), we explore implications of its existence for problems of tidal dissipation, planet migration, and atmospheric stability. The small orbit of OGLE-TR-56b makes the planet an interesting test particle case for tidal dissipation in stellar convection zones. We show that it favors prescriptions of suppressed convective eddy viscosity. Precise timing of the transits of OGLE-TR-56b might place interesting constraints on stellar convection theory if orbital period change is detected in the near future. Another interesting issue related to the new planet is the origin of its close orbit; OGLE-TR-56b may be a survivor of Roche lobe overflow mass loss. Living in such close proximity to its parent star, OGLE-TR-56b should have temperatures in the dayside hemisphere reaching 1900 K, and we find that only few condensates could form clouds, if at all, under those conditions—mostly Al2O3 and Fe(s). We explore the issue of atmosphere evaporation and find that the planet's atmosphere is stable over its lifetime. The large size of the planet (Rp = 1.3 ± 0.15 RJ) might also require additional energy, similar to HD 209458b.

Nonlinear Particle Acceleration in Oblique Shocks

We have developed a Monte Carlo technique for self-consistently calculating the hydrodynamic structure of oblique, steady-state shocks, together with the first-order Fermi acceleration process and associated non-thermal particle distributions. This is the first internally consistent treatment of modified shocks that includes cross-field diffusion of particles. Our method overcomes the injection problem faced by analytic descriptions of shock acceleration, and the lack of adequate dynamic range and artificial suppression of cross-field diffusion faced by plasma simulations; it currently provides the most broad and versatile description of collisionless shocks undergoing efficient particle acceleration. We present solutions for plasma quantities and particle distributions upstream and downstream of shocks, illustrating the strong differences observed between non-linear and test-particle cases. It is found that there are only marginal differences in the injection efficiency and resultant spectra for two extreme scattering modes, namely large-angle scattering and pitch-angle diffusion, for a wide range of shock parameters, i.e., for subluminal shocks with field obliquities less than or equal to 75 degrees and de Hoffmann-Teller frame speeds much less than the speed of light.

Diffuse minor ions upstream of simulated quasi‐parallel shocks

We have performed a number of one‐dimensional hybrid (particle ions, massless fluid electrons) simulations of quasi‐parallel collisionless shocks in order to elucidate the origin of diffuse upstream minor ions. Minor ions are treated self‐consistently by the hybrid code; however, a number of runs have also been performed wherein the minor ions are treated as test particles. We have investigated the dependence of the density ratio bias factor fnof; (the alpha to proton ratio of the diffuse ions normalized to the solar wind ratio) on shock Mach number, solar wind beta (thermal to magnetic pressure) and on angle ΘBno between shock normal and magnetic field and found strong dependencies on all parameters. An addition of 5% alpha particles changes the shock structure, resulting in a significant modification of the density ratio bias factor as compared to the test particle cases. In the case of a low beta solar wind (β ≃ 0.1) the solar wind alpha particles penetrate the shock ramp rather unaffected and gyrate in the downstream magnetic field as a whole. The alpha particle beam returns occasionally to the shock ramp and spatially localized clouds of alpha particles can be found in the upstream region. With increasing Mach number the gyroradius of the alpha particles increases and it becomes easier for the alpha particle beam to return from downstream to the shock; a high density of clouds is found upstream. In the case of a higher beta solar wind (β≳0.5) and moderate Mach numbers, no localized alpha particle clouds leave from downstream into the upstream region. This can be attributed to the smoother shock transition in the case of higher beta shocks. The effect of beta and Mach number is counteracting: high Mach number shocks can lead even at higher beta to minor ion clouds in the upstream region. Higher beta shock simulations result in an increase of fnof; with beta and ΘBno. The increase with beta is due to the fact that diffuse ions originate mainly from the high‐energy tail of the distribution in the upstream rest frame. It is suggested that large ΘBno implies a more tangential downstream field and the alpha particles reach the shock during their downstream gyration easier.