Pitch-angle diffusion and Bohm-type approximations in diffusive shock acceleration

The problem of accelerating cosmic rays is one of fundamental importance, particularly given the uncertainty in the conditions inside the acceleration sites. Here we examine diffusive shock acceleration in arbitrary turbulent magnetic fields, constructing a new model that is capable of bridging the gap between the very weak (δB/B 0 Lt 1) and the strong turbulence regimes. To describe the diffusion we provide a quantitative analytical description of the "Bohm exponent" in each regime. We show that our results converge to the well known quasi-linear theory in the weak turbulence regime. In the strong regime, we quantify the limitations of the Bohm-type models. Furthermore, our results account for the anomalous diffusive behavior which has been noted previously. Finally, we discuss the implications of our model in the study of possible acceleration sites in different astronomical objects

Synchrotron emission in small scale magnetic field as possible explanation for prompt emission spectra of gamma-ray bursts

Synchrotron emission is believed to be a major radiation mechanism during gamma-ray bursts' (GRBs) prompt emission phase. A significant drawback of this assumption is that the theoretical predicted spectrum, calculated within the framework of the ``internal shocks'' scenario using the standard assumption that the magnetic field maintains a steady value throughout the shocked region, leads to a slope F_\nu \propto \nu^{-1/2} below 100 keV, which is in contradiction to the much harder spectra observed. This is due to the electrons cooling time being much shorter than the dynamical time. In order to overcome this problem, we propose here that the magnetic field created by the internal shocks decays on a length scale much shorter than the comoving width of the plasma. We show that under this assumption synchrotron radiation can reproduce the observed prompt emission spectra of the majority of the bursts. We calculate the required decay length of the magnetic field, and find it to be \~10^4 - 10^5 cm (equivalent to 10^5 - 10^6 skin depths), much shorter than the characteristic comoving width of the plasma, ~3*10^{9} cm. We implement our model to the case of GRB050820A, where a break at <~ 4 keV was observed, and show that this break can be explained by synchrotron self absorption. We discuss the consequences of the small scale magnetic field scenario on current models of magnetic field generation in shock waves.Comment: Extended explanation on alternative emission models, the radiative efficiency and derivation of eq. 2. Minor typos and English corrections; Accepted for publication in Ap.

Peak energy clustering and efficiency in compact objects

We study the properties of plasmas containing a low energy thermal photon component at comoving temperature \theta \equiv kT'/m_e c^2 \sim 10^{-5} - 10^{-2} interacting with an energetic electron component, characteristic of, e.g., the dissipation phase of relativistic outflows in gamma-ray bursts (GRB's), X-ray flashes, and blazars. We show that, for scattering optical depths larger than a few, balance between Compton and inverse-Compton scattering leads to the accumulation of electrons at values of $\gamma\beta ~ 0.15 - 0.3$. For optical depths larger than ~ 100, this leads to a peak in the comoving photon spectrum at 1-10 keV, very weakly dependent on the values of the free parameters. In particular, these results are applicable to the internal shock model of GRB, as well as to slow dissipation models, e.g. as might be expected from reconnection, if the dissipation occurs at a sub-photospheric radii. For GRB bulk Lorentz factors ~ 100, this results in observed spectral peaks clustering in the 0.1-1 MeV range, with conversion efficiencies of electron into photon energy in the BATSE range of ~ 30%.Comment: Extended explanations about the electron energy balance; Refine figures; Accepted for publication in Ap.

The limited contribution of low- and high-luminosity gamma-ray bursts to ultra-high-energy cosmic rays

The acceleration site for ultra-high-energy cosmic rays (UHECRs) is still an open question despite extended research. In this paper, we reconsider the prompt phase of gamma-ray bursts (GRBs) as a possible candidate for this acceleration and constrain the maximum proton energy in optically thin synchrotron and photospheric models, using properties of the prompt photon spectra. We find that neither of the models favors acceleration of protons to 1020 eV in high-luminosity bursts. We repeat the calculations for low-luminosity GRBs (llGRBs) considering both protons and completely stripped iron and find that the highest obtainable energies are <1019 eV and <1020 eV for protons and iron respectively, regardless of the model. We conclude therefore that for our fiducial parameters, GRBs, including low-luminosity bursts, contribute little to nothing to the UHECRs observed. We further constrain the conditions necessary for an association between UHECRs and llGRBs and find that iron can be accelerated to 1020 eV in photospheric models, given very efficient acceleration and/or a small fractional energy given to a small fraction of accelerated electrons. This will necessarily result in high prompt optical fluxes, and the detection of such a signal could therefore be an indication of successful UHECR acceleration at the source

The observable effects of a photospheric component on GRB's and XRF's prompt emission spectrum

A thermal radiative component is likely to accompany the first stages of the prompt emission of Gamma-ray bursts (GRB's) and X-ray flashes (XRF's). We analyze the effect of such a component on the observable spectrum, assuming that the observable effects are due to a dissipation process occurring below or near the thermal photosphere. We consider both the internal shock model and a 'slow heating' model as possible dissipation mechanisms. For comparable energy densities in the thermal and the leptonic component, the dominant emission mechanism is Compton scattering. This leads to a nearly flat energy spectrum (\nu F_\nu \propto \nu^0) above the thermal peak at ~10-100 keV and below 10-100 MeV, for a wide range of optical depths 0.03 <~ \tau_{\gamma e} <~ 100, regardless of the details of the dissipation mechanism or the strength of the magnetic field. At lower energies steep slopes are expected, while above 100 MeV the spectrum depends on the details of the dissipation process. For higher values of the optical depth, a Wien peak is formed at 100 keV - 1 MeV, and no higher energy component exists. For any value of \tau_{\gamma e}, the number of pairs produced does not exceed the baryon related electrons by a factor larger than a few. We conclude that dissipation near the thermal photosphere can naturally explain both the steep slopes observed at low energies and a flat spectrum above 10 keV, thus providing an alternative scenario to the optically thin synchrotron - SSC model.Comment: Discussion added on the results of Baring & Braby (2004); Accepted for publication in Ap.

Time dependent numerical model for the emission of radiation from relativistic plasma

We describe a numerical model constructed for the study of the emission of radiation from relativistic plasma under conditions characteristic, e.g., to gamma-ray bursts (GRB's) and active galactic nuclei (AGN's). The model solves self consistently the kinetic equations for e^\pm and photons, describing cyclo-synchrotron emission, direct Compton and inverse Compton scattering, pair production and annihilation, including the evolution of high energy electromagnetic cascades. The code allows calculations over a wide range of particle energies, spanning more than 15 orders of magnitude in energy and time scales. Our unique algorithm, which enables to follow the particle distributions over a wide energy range, allows to accurately derive spectra at high energies, >100 \TeV. We present the kinetic equations that are being solved, detailed description of the equations describing the various physical processes, the solution method, and several examples of numerical results. Excellent agreement with analytical results of the synchrotron-SSC model is found for parameter space regions in which this approximation is valid, and several examples are presented of calculations for parameter space regions where analytic results are not available.Comment: Minor changes; References added, discussion on observational status added. Accepted for publication in Ap.

The Connection Between Thermal and Non-Thermal Emission in Gamma-ray Bursts: General Considerations and GRB090902B as a Case Study

Photospheric (thermal) emission is inherent to the gamma-ray burst (GRB) "fireball" model. We show here, that inclusion of this component in the analysis of the GRB prompt emission phase naturally explains some of the prompt GRB spectra seen by the Fermi satellite over its entire energy band. The sub-MeV peak is explained as multi-color black body emission, and the high energy tail, extending up to the GeV band, results from roughly similar contributions of synchrotron emission, synchrotron self Compton(SSC) and Comptonization of the thermal photons by energetic electrons originating after dissipation of the kinetic energy above the photosphere. We show how this analysis method results in a complete, self consistent picture of the physical conditions at both emission sites of the thermal and non-thermal radiation. We study the connection between the thermal and non-thermal parts of the spectrum, and show how the values of the free model parameters are deduced from the data. We demonstrate our analysis method on GRB090902B: We deduce a Lorentz factor in the range 920 <= \eta <= 1070, photospheric radius r_{ph} ~ 7.2 - 8.4 * 10^{11} cm and dissipation radius r_\gamma >= 3.5 - 4.1 * 10^{15} cm. By comparison to afterglow data, we deduce that a large fraction, epsilon_d ~85% - 95% of the kinetic energy is dissipated, and that large fraction, ~equipartition of this energy is carried by the electrons and the magnetic field. This high value of epsilon_d questions the "internal shock" scenario as the main energy dissipation mechanism for this GRB.Comment: 15 pages, 5 figures; minor revisions, typos corrected. Accepted for publication in MNRA

The Correlation of Spectral Lag Evolution with Prompt Optical Emission in GRB 080319B

We report on observations of correlated behavior between the prompt gamma-ray and optical emission from GRB 080319B, which confirm that (i) they occurred within the same astrophysical source region and (ii) their respective radiation mechanisms were dynamically coupled. Our results, based upon a new CCF methodology for determining the time-resolved spectral lag, are summarized as follows. First, the evolution in the arrival offset of prompt gamma-ray photon counts between Swift-BAT 15-25 keV and 50-100 keV energy bands (intrinsic gamma-ray spectral lag) appears to be anti-correlated with the arrival offset between prompt 15-350 keV gamma-rays and the optical emission observed by TORTORA (extrinsic optical/gamma-ray spectral lag), thus effectively partitioning the burst into two main episodes at ~T+28+/-2 sec. Second, the rise and decline of prompt optical emission at ~T+10+/-1 sec and ~T+50+/-1 sec, respectively, both coincide with discontinuities in the hard to soft evolution of the photon index for a power law fit to 15-150 keV Swift-BAT data at ~T+8+/-2 sec and ~T+48+/-1 sec. These spectral energy changes also coincide with intervals whose time-resolved spectral lag values are consistent with zero, at ~T+12+/-2 sec and ~T+50+/-2 sec. These results, which are robust across heuristic permutations of Swift-BAT energy channels and varying temporal bin resolution, have also been corroborated via independent analysis of Konus-Wind data. This potential discovery may provide the first observational evidence for an implicit connection between spectral lags and GRB emission mechanisms in the context of canonical fireball phenomenology. Future work includes exploring a subset of bursts with prompt optical emission to probe the unique or ubiquitous nature of this result.Comment: 6 pages, 3 figures. Contributed to the Proceedings of the Sixth Huntsville GRB Symposium. Edited by C.A. Meegan, N. Gehrels, and C. Kouvelioto

Microscopic processes in global relativistic jets containing helical magnetic fields

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton (e−–p+) and electron–positron (e±) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of “global” jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e−–p+ jet simulation a recollimation-like instability occurs and jet electrons are strongly perturbed. In the e± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields

Microscopic Processes in Global Relativistic Jets Containing Helical Magnetic Fields

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton ( e − – p + ) and electron–positron ( e ± ) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of “global” jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e − – p + jet simulation a recollimation-like instability occurs and jet electrons are strongly perturbed. In the e ± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.This work is supported by NSF AST-0908010, AST-0908040, NASA-NNX09AD16G, NNX12AH06G, NNX13AP-21G, and NNX13AP14G grants. The work of J.N. and O.K. has been supported by Narodowe Centrum Nauki through research project DEC-2013/10/E/ST9/00662. Y.M. is supported by the ERC Synergy Grant “BlackHoleCam—Imaging the Event Horizon of Black Holes” (Grant No. 610058). M.P. acknowledges support through grant PO 1508/1-2 of the Deutsche Forschungsgemeinschaft. Simulations were performed using Pleiades and Endeavor facilities at NASA Advanced Supercomputing (NAS), and using Gordon and Comet at The San Diego Supercomputer Center (SDSC), and Stampede at The Texas Advanced Computing Center, which are supported by the NSF. This research was started during the program “Chirps, Mergers and Explosions: The Final Moments of Coalescing Compact Binaries” at the Kavli Institute for Theoretical Physics, which is supported by the National Science Foundation under grant No. PHY05-51164. The first velocity shear results using an electron positron plasma were obtained during the Summer Aspen workshop “Astrophysical Mechanisms of Particle Acceleration and Escape from the Accelerators” held at the Aspen Center for Physics (1–15 September 2013). We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI