Particle acceleration at travelling shocks in the heliosphere
Abstract
The acceleration of energetic protons from the solar wind (SW) distribution by traveling interplanetary
shocks is investigated. The SW velocity distribution is represented using kappa functions, which are transformed in response to simulated shock transitions in the plasma flow speed, number density, and temperature. These heated SW distributions are specified as a particle source at shocks from which particles with sufficient energy can be injected into the diffusive shock acceleration (DSA) process. DSA is modeled within the context of the Parker transport equation, which is solved using time-backward integrated stochastic differential equations. Two broad applications are considered: firstly, the acceleration of particles at fast-moving interplanetary shocks driven by coronal mass ejections (CMEs), and secondly,
the acceleration of particles at the compression waves bounding corotating interaction regions (CIRs). For CME-driven shocks, it is shown that the maximum attainable energies of shock accelerated spectra are limited by the shocks’ transit times, while spectra may be accelerated to higher energies in the presence of enhanced magnetic turbulence or at faster-moving shocks. Indeed, simulations suggest fast-moving shocks are more likely to produce very high-energy particles, while strong shocks, associated with harder shock-accelerated spectra, are associated with higher intensities of energetic particles. The prior heating of the solar wind distribution is found to complement shock acceleration in reproducing the intensities of typical energetic storm particle (ESP) events, especially where injection energies are high. Moreover, simulations
of 0.2 to 1 MeV proton intensities are presented that reproduce the observed flat energy spectra prior to shock passages, owing to the modulation of low-energy particles. Whereas spectra adhering to the predictions of DSA are usually indicative of local acceleration, the modulation of spectra at low energies emerges as a recurring signature of particles transported to the observer from remote acceleration sites. In these cases, magnetic connections are important for particle transport between the shock and the observer, especially where the observer is not in the direct path of the shock, whereas perpendicular diffusion becomes more important when magnetic connections are absent. At CIRs, accelerated particle intensities consistently peak near the trailing edge. These peak intensities scale proportional to local compression ratios, but only if energy distributions display the features of DSA, which ostensibly occurs when particles are accelerated locally. By contrast, when accelerated spectra are appreciably modulated, which is likely indicative of an increased proportion of remotely accelerated particles, no correlation is found between peak intensities and local compression ratios. DSA is demonstrated to reproduce many of the salient features of ESPs and CIR particles, highlighting its prevalence as an acceleration mechanism at interplanetary shocks. As a source population, the heated SW distribution makes an important contribution in this regard, providing large numbers of adequately energized seed particles for DSA to reproduce typical energetic particle intensities.