Time-dependent Particle Acceleration Research Articles

A time-dependent particle acceleration and emission model: understanding particle spectral evolution and blazar flares

ABSTRACT The jets of blazars are renowned for their multiwavelength flares and rapid extreme variability; however, there are still some important unanswered questions about the physical processes responsible for these spectral and temporal changes in emission properties. In this article, we develop a time-dependent particle evolution model for the time-varying emission spectrum of blazars. In the model, we introduce time-dependent electric and magnetic fields, which consistently include the variability of relevant physical quantities in the transport equation. The evolution of the electron distribution is solved numerically from a generalized transport equation that contains terms describing the electrostatic, first- and second-order Fermi acceleration, escape of particles due to both advection and spatial diffusion, and also energy losses due to synchrotron emission and inverse-Compton scattering of both synchrotron and external ambient photon fields. We find that the light-curve profiles of blazars are consistent with the particle spectral evolution resulting from time-dependent electric and magnetic fields, rather than the effects of acceleration or cooling processes. The proposed model is able to account simultaneously for the variability of both the energy spectrum and the light-curve profile of the BL Lac object Mrk 421, with reasonable assumptions about the physical parameters. The results indicate strongly that the magnetic field evolution in the dissipated region of a blazar jet can account for the variabilities.

Gamma-ray emission from internal shocks in novae

Context. Gamma-ray emission at energies ≥100 MeV has been detected from nine novae using the Fermi Large Area Telescope (LAT), and can be explained by particle acceleration at shocks in these systems. Eight out of these nine objects are classical novae in which interaction of the ejecta with a tenuous circumbinary material is not expected to generate detectable gamma-ray emission. Aim. We examine whether particle acceleration at internal shocks can account for the gamma-ray emission from these novae. The shocks result from the interaction of a fast wind radiatively-driven by nuclear burning on the white dwarf with material ejected in the initial runaway stage of the nova outburst. Methods. We present a one-dimensional model for the dynamics of a forward and reverse shock system in a nova ejecta, and for the associated time-dependent particle acceleration and high-energy gamma-ray emission. Non-thermal proton and electron spectra are calculated by solving a time-dependent transport equation for particle injection, acceleration, losses, and escape from the shock region. The predicted emission is compared to LAT observations of V407 Cyg, V1324 Sco, V959 Mon, V339 Del, V1369 Cen, and V5668 Sgr. Results. The ≥100 MeV gamma-ray emission arises predominantly from particles accelerated up to ~100 GeV at the reverse shock and undergoing hadronic interactions in the dense cooling layer downstream of the shock. The emission rises within days after the onset of the wind, quickly reaches a maximum, and its subsequent decrease reflects mostly the time evolution of the wind properties. Comparison to gamma-ray data points to a typical scenario where an ejecta of mass 10−5–10−4 M⊙ expands in a homologous way with a maximum velocity of 1000–2000 km s−1, followed within a day by a wind with a velocity <2000 km s−1 and a mass-loss rate of 10−4–10−3 M⊙ yr−1 declining over a time scale of a few days. Because of the large uncertainties in the measurements, many parameters of the problem are degenerate and/or poorly constrained except for the wind velocity, the relatively low values of which result in the majority of best-fit models having gamma-ray spectra with a high-energy turnover below ~10 GeV. Our typical model is able to account for the main features in the observations of the recent gamma-ray nova ASASSN-16ma. Conclusions. The internal shock model can account for the gamma-ray emission of the novae detected by Fermi LAT. Gamma-ray observations hold potential for probing the mechanism of mass ejection in novae, but should be combined to diagnostics of the thermal emission at lower energies to be more constraining.

Anomalous Distributions of Primary Cosmic Rays as Evidence for Time-dependent Particle Acceleration in Supernova Remnants

Abstract Recent precise measurements of cosmic-ray (CR) spectra show that the energy distribution of protons is softer than those of heavier nuclei, and there are spectral hardenings for all nuclear compositions above ∼200 GV. Models proposed for these anomalies generally assume steady-state solutions of the particle acceleration process. We show that if the diffusion coefficient has a weak dependence on the particle rigidity near shock fronts of supernova remnants (SNRs), time-dependent solutions of the linear diffusive shock acceleration at two stages of SNR evolution can naturally account for these anomalies. The high-energy component of CRs is dominated by acceleration in the free expansion and adiabatic phases with enriched heavy elements and a high shock speed. The low-energy component may be attributed to acceleration by slow shocks propagating in dense molecular clouds with low metallicity in the radiative phase. Instead of a single power-law distribution, the spectra of time-dependent solutions soften gradually with the increase of energy, which may be responsible for the “knee” of CRs.

Time-dependent particle acceleration in a Fermi reservoir

Context. A steady model was presented by Burn, in which energy conservation is used to constrain the parameters of stochastic Fermi acceleration. A steady model, however, is unlikely to be adequate for particle acceleration in impulsive solar flares. Aims. This paper describes a time-dependent model for particle acceleration in a Fermi reservoir Methods. The calculation is based on the original formulation of stochastic acceleration by Fermi, with additional physically motivated assumptions about the turbulent and particle energy densities within the reservoir, that are similar to those of the steady analysis. The problem is reduced to an integro-differential equation that possesses an analytical solution. Results. The model predicts the formation of a power-law differential energy spectrum N(E) ∼ E−2, that is observable outside the reservoir. The predicted spectral index is independent of the parameters of the model. The results may help in understanding particle acceleration in solar flares and other astrophysical applications.

Time-dependent particle acceleration in supernova remnants in different environments

We simulate time-dependent particle acceleration in the blast wave of a young supernova remnant (SNR), using a Monte Carlo approach for the diffusion and acceleration of the particles, coupled to an MHD code. We calculate the distribution function of the cosmic rays concurrently with the hydrodynamic evolution of the SNR, and compare the results with those obtained using simple steady-state models. The surrounding medium into which the supernova remnant evolves turns out to be of great influence on the maximum energy to which particles are accelerated. In particular, a shock going through a $\rho \propto r^{-2}$ density profile causes acceleration to typically much higher energies than a shock going through a medium with a homogeneous density profile. We find systematic differences between steady-state analytical models and our time-dependent calculation in terms of spectral slope, maximum energy, and the shape of the cut-off of the particle spectrum at the highest energies. We also find that, provided that the magnetic field at the reverse shock is sufficiently strong to confine particles, cosmic rays can be easily re-accelerated at the reverse shock.

A Stochastic Simulation Method for Particle Acceleration and Non-Thermal Photon Emission in Astrophysical Processes

A versatile numerical method is developed to simulate the time dependent particle acceleration in shocks and the non-thermal photon emission thereof. Our method is based on Itô's stochastic differential equations coupled with a particle splitting. This method is applied to photon emission from young supernova remnants.

Time-dependent shock acceleration of energetic electrons including synchrotron losses

The present investigation of the time-dependent particle acceleration problem in strong shocks, including synchrotron radiation losses, solves the transport equation analytically by means of Laplace transforms. The particle distribution thus obtained is then transformed numerically into real space for the cases of continuous and impulsive injections of particles at the shock. While in the continuous case the steady-state spectrum undergoes evolution, impulsive injection is noted to yield such unpredicted features as a pile-up of high-energy particles or a steep power-law with time-dependent spectral index. The time-dependent calculations reveal varying spectral shapes and more complex features for the higher energies which may be useful in the interpretation of outburst spectra.