Nonlinear Particle Acceleration in Relativistic Shocks

Monte Carlo techniques are used to model nonlinear particle acceleration in parallel collisionless shocks of various speeds, including mildly relativistic ones. When the acceleration is efficient, the backreaction of accelerated particles modifies the shock structure and causes the compression ratio, r, to increase above test-particle values. Modified shocks with Lorentz factors less than about 3 can have compression ratios considerably greater than 3 and the momentum distribution of energetic particles no longer follows a power law relation. These results may be important for the interpretation of gamma-ray bursts if mildly relativistic internal and/or afterglow shocks play an important role accelerating particles that produce the observed radiation. For shock Lorentz factors greater than about 10, r approaches 3 and the so-called `universal' test-particle result of N(E) proportional to E^{-2.3} is obtained for sufficiently energetic particles. In all cases, the absolute normalization of the particle distribution follows directly from our model assumptions and is explicitly determined.Comment: Updated version, Astroparticle Physics, in press, 29 pages, 13 figure

Risks Posed to Drinking Water Aquifers Due to Leakage of Dissolved CO2 in Improperly Abandoned Wellbores

In order to ensure safe long-term storage of carbon dioxide in geologic formations, the risks posed by improperly abandoned wells must be understood and minimalized. In addition to supercritical and gaseous CO2, brine containing dissolved CO2 poses a leakage risk. CO2 dissolution in brine leads to denser brine and better long-term storage security, but its leakage risk is not zero. Under specific circumstances with formation overpressure or overlying aquifer drawdown, dissolved brine can flow up improperly abandoned wells where it can potentially enter and contaminate drinking water aquifers. The possibility that depressurization in the wellbore may cause CO2 exsolution from brine to form a separate buoyant gas phase is of primary concern. Analytical as well as numerical models are used to evaluate these effects in wellbores as well as to examine the effects of system parameters on brine leakage rates through wellbores. A simple analytical model for uniform density flow is used to evaluate the effects of physical parameters on fluid leakage. It is a useful screening tool for estimating leading order effects of system parameters on leakage of CO2 laden brine. The TOUGH2-ECO2N simulator is also used to evaluate wellbore leakage of dissolved CO2 considering gas exsolution due to pressure, temperature, phase, and salinity changes. Simulations identify the conditions under which a separate gas phase exsolves in a wellbore during CO2 laden brine leakage. Up to 20% of the dissolved brine is found to exsolve in the numerical simulations. This gas accumulates along the top of a drinking water aquifer as a buoyant phase. Simulations also show that the degree of leakage is constrained by the properties of the well, with the permeability of the well being of chief importance. However, at high well permeabilities, simulations show that the geologic formations provide more resistance to flow than the well and constrain leakage rates. Additional analyses are performed in order to see how dissolved CO2 may leak from a wellbore in a geologic system of stratified permeable layers. It is found that the presence of stratigraphy limits the possibility of upward migration of dissolved CO2, whether through overpressure of drawdown

Diffusive Shock Acceleration of High Energy Cosmic Rays

The process of diffusive acceleration of charged particles in shocked plasmas is widely invoked in astrophysics to account for the ubiquitous presence of signatures of non-thermal relativistic electrons and ions in the universe. A key characteristic of this statistical energization mechanism is the absence of a momentum scale; astrophysical systems generally only impose scales at the injection (low energy) and loss (high energy) ends of the particle spectrum. The existence of structure in the cosmic ray spectrum (the "knee") at around 3000 TeV has promoted contentions that there are at least two origins for cosmic rays, a galactic one supplying those up to the knee, and even beyond, and perhaps an extragalactic one that can explain even the ultra-high energy cosmic rays (UHECRs) seen at 1-300 EeV. Accounting for the UHECRs with familiar astrophysical sites of acceleration has historically proven difficult due to the need to assume high magnetic fields in order to reduce the shortest diffusive acceleration timescale, the ion gyroperiod, to meaningful values. Yet active galaxies and gamma-ray bursts remain strong and interesting candidate sources for UHECRs, turning the theoretical focus to relativistic shocks. This review summarizes properties of diffusive shock acceleration that are salient to the issue of UHECR generation. These include spectral indices, acceleration efficencies and timescales, as functions of the shock speed and mean field orientation, and also the nature of the field turbulence. The interpretation of these characteristics in the context of gamma-ray burst models for the production of UHECRs is also examined.Comment: 10 pages, 2 embedded figures, To appear in Nuclear Physics B, Proceedings Supplements, as part of the volume for the CRIS 2004, Cosmic Ray International Seminar: "GZK and Surroundings.

Using Gamma-Ray Burst Prompt Emission to Probe Relativistic Shock Acceleration

It is widely accepted that the prompt transient signal in the 10 keV - 10 GeV band from gamma-ray bursts (GRBs) arises from multiple shocks internal to the ultra-relativistic expansion. The detailed understanding of the dissipation and accompanying acceleration at these shocks is a currently topical subject. This paper explores the relationship between GRB prompt emission spectra and the electron (or ion) acceleration properties at the relativistic shocks that pertain to GRB models. The focus is on the array of possible high-energy power-law indices in accelerated populations, highlighting how spectra above 1 MeV can probe the field obliquity in GRB internal shocks, and the character of hydromagnetic turbulence in their environs. It is emphasized that diffusive shock acceleration theory generates no canonical spectrum at relativistic MHD discontinuities. This diversity is commensurate with the significant range of spectral indices discerned in prompt burst emission. Such system diagnostics are now being enhanced by the broadband spectral coverage of bursts by the Fermi Gamma-Ray Space Telescope; while the Gamma-Ray Burst Monitor (GBM) provides key diagnostics on the lower energy portions of the particle population, the focus here is on constraints in the non-thermal, power-law regime of the particle distribution that are provided by the Large Area Telescope (LAT).Comment: 15 pages, 2 figures. Accepted for publication in Advances of Space Researc

Diffusive Shock Acceleration in Unmodified Relativistic, Oblique Shocks

We present results from a fully relativistic Monte Carlo simulation of diffusive shock acceleration (DSA) in unmodified shocks. The computer code uses a single algorithmic sequence to smoothly span the range from nonrelativistic speeds to fully relativistic shocks of arbitrary obliquity, providing a powerful consistency check. While known results are obtained for nonrelativistic and ultra-relativistic parallel shocks, new results are presented for the less explored trans- relativistic regime and for oblique, fully relativistic shocks. We find, for a wide trans-relativistic range extending to shock Lorentz factors >30, that the particle spectrum produced by DSA varies strongly from the canonical f(p) proportional to p^{-4.23} spectrum known to result in ultra-relativistic shocks. Trans- relativistic shocks may play an important role in gamma-ray bursts and other sources and most relativistic shocks will be highly oblique.Comment: Accepted for publication in Astroparticle Physics, August 2004, 22 pages, 14 figure

Measuring Column Densities in Quasar Outflows: VLT Observations of QSO 2359-1241

We present high resolution spectroscopic VLT observations of the outflow seen in QSO 2359-1241. These data contain absorption troughs from five resonance Fe II lines with a resolution of ~7 km/s and signal-to-noise ratio per resolution element of order 100. We use this unprecedented high quality data set to investigate the physical distribution of the material in front of the source, and by that determine the column densities of the absorbed troughs. We find that the apparent optical depth model gives a very poor fit to the data and greatly underestimates the column density measurements. Power-law distributions and partial covering models give much better fits with some advantage to power-law models, while both models yield similar column density estimates. The better fit of the power-law model solves a long standing problem plaguing the partial covering model when applied to large distance scale outflow: How to obtain a velocity dependent covering factor for an outflow situated at distances thousands of time greater than the size of the AGN emission source. This problem does not affect power-law models. Therefore, based on the better fit and plausibility of the physical model, we conclude that in QSO 2359-1241, the outflow covers the full extent of the emission source but in a non-homogeneous way.Comment: 27 pages, 6 figures, to appear on ApJ Jul 10. The full (online) version of figure 2 can be obtained here: http://www.phys.vt.edu/~arav/f2_online_version.p

Particle acceleration in ultra-relativistic oblique shock waves

We perform Monte Carlo simulations of diffusive shock acceleration at highly relativistic oblique shock waves. High upstream flow Lorentz gamma factors are used, which are relevant to models of ultra relativistic particle shock acceleration in Active Galactic Nuclei (AGN) central engines and relativistic jets and Gamma Ray Burst (GRB) fireballs. We investigate numerically the acceleration properties -in the ultra relativistic flow regime of $\Gamma \sim 10-10^{3}$- such as angular distribution, acceleration time constant, particle energy gain versus number of crossings and spectral shapes. We perform calculations for sub-luminal and super-luminal shocks, using two different approaches respectively. The $\Gamma^{2}$ energization for the first crossing cycle and the significantly large energy gain for subsequent crossings as well as the high 'speed up' factors found, are important in supporting the Vietri and Waxman models on GRB ultra-high energy cosmic ray, neutrino, and gamma-ray output.Comment: 24 pages, 35 figures, accepted for publication in Astroparticle Physic

Magnetic fields and cosmic rays in GRBs. A self-similar collisionless foreshock

Cosmic rays accelerated by a shock form a streaming distribution of outgoing particles in the foreshock region. If the ambient fields are negligible compared to the shock and cosmic ray energetics, a stronger magnetic field can be generated in the shock upstream via the streaming (Weibel-type) instability. Here we develop a self-similar model of the foreshock region and calculate its structure, e.g., the magnetic field strength, its coherence scale, etc., as a function of the distance from the shock. Our model indicates that the entire foreshock region of thickness $\sim R/(2\Gamma_{\rm sh}^2)$, being comparable to the shock radius in the late afterglow phase when $\Gamma_{\rm sh}\sim1$, can be populated with large-scale and rather strong magnetic fields (of sub-gauss strengths with the coherence length of order $10^{17} {\rm cm}$) compared to the typical interstellar medium magnetic fields. The presence of such fields in the foreshock region is important for high efficiency of Fermi acceleration at the shock. Radiation from accelerated electrons in the foreshock fields can constitute a separate emission region radiating in the UV/optical through radio band, depending on time and shock parameters. We also speculate that these fields being eventually transported into the shock downstream can greatly increase radiative efficiency of a gamma-ray burst afterglow shock.Comment: 10 pages, 1 figure. Submitted to Ap

The effect of energy amplification variance on the shock-acceleration

The shock-acceleration theory predicts a power-law energy spectrum in the test particle approximation, and there are two ways to calculate a power-law index, Peacock's approximation and Vietri's formulation. In Peacock's approximation, it is assumed that particles cross a shock front many times and energy-gains for each step are fully uncorrelated. On the other hand, correlation of the distribution of an energy-gain factor for a particle is considered in Vietri's formulation. We examine how Peacock's approximation differs from Vietri's formulation. It is useful to know when we can use Peacock's approximation because Peacock's approximation is simple to derive the power-law index. In addition, we focus on how the variance of the energy-gain factor has an influence on the difference between Vietri's formulation and Peacock's approximation. The effect of the variance has not been examined well until now. For demonstration, we consider two cases for the scattering in the upstream: the large-angle scattering (model A) and the regular deflection by large-scale magnetic fields (model B). Especially there is no correlation among the distribution of an energy-gain factor for every step in model A. In this model, we see the power-law index derived from Peacock's approximation differs from the one derived from Vietri's formulation when we consider the mildly-relativistic shock, and the variance of the energy-gain factor affects this difference. We can use Peacock's approximation for a non-relativistic shock and a highly-relativistic shock because the effect of the variance is hidden. In model B, we see the difference of the power-law converging along the shock velocity.Comment: 8 pages, 7 figures, accepted for publication in MNRA

Lepton Acceleration in Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) act as calorimeters for the relativistic pair winds emanating from within the pulsar light cylinder. Their radiative dissipation in various wavebands is significantly different from that of their pulsar central engines: the broadband spectra of PWNe possess characteristics distinct from those of pulsars, thereby demanding a site of lepton acceleration remote from the pulsar magnetosphere. A principal candidate for this locale is the pulsar wind termination shock, a putatively highly-oblique, ultra-relativistic MHD discontinuity. This paper summarizes key characteristics of relativistic shock acceleration germane to PWNe, using predominantly Monte Carlo simulation techniques that compare well with semi-analytic solutions of the diffusion-convection equation. The array of potential spectral indices for the pair distribution function is explored, defining how these depend critically on the parameters of the turbulent plasma in the shock environs. Injection efficiencies into the acceleration process are also addressed. Informative constraints on the frequency of particle scattering and the level of field turbulence are identified using the multiwavelength observations of selected PWNe. These suggest that the termination shock can be comfortably invoked as a principal injector of energetic leptons into PWNe without resorting to unrealistic properties for the shock layer turbulence or MHD structure.Comment: 19 pages, 5 figures, invited review to appear in Proc. of the inaugural ICREA Workshop on "The High-Energy Emission from Pulsars and their Systems" (2010), eds. N. Rea and D. Torres, (Springer Astrophysics and Space Science series