Inverse-Compton drag on a Highly Magnetized GRB jet in Stellar Envelope

The collimation and evolution of relativistic outflows in $\gamma$-ray bursts (GRBs) are determined by their interaction with the stellar envelope through which they travel before reaching the much larger distance where the energy is dissipated and $\gamma$-rays are produced. We consider the case of a Poynting flux dominated relativistic outflow and show that it suffers strong inverse-Compton (IC) scattering drag near the stellar surface and the jet is slowed down to sub-relativistic speed if its initial magnetization parameter ($\sigma_0$) is larger than about 10$^5$. If the temperature of the cocoon surrounding the jet were to be larger than about 10 keV, then an optically thick layer of electrons and positrons forms at the interface of the cocoon and the jet, and one might expect this pair screen to protect the interior of the jet from IC drag. However, the pair screen turns out to be ephemeral, and instead of shielding the jet it speeds up the IC drag on it. Although a high $\sigma_0$ jet might not survive its passage through the star, a fraction of its energy is converted to 1-100 MeV radiation that escapes the star and appears as a bright flash lasting for about 10 s

Radiative Transfer Problem in the Presence of Strong Magnetic Fields. Analytical and Numerical Treatment.

In this thesis we investigate analytical and numerical methods to find a solution of the radiative transfer equation in the presence of strong magnetic fields. My Ph.D research theme is focused on those astrophysical objects which presumably show an evidence of a strong magnetic field (B & 1012 G), with a particular emphasis on the physics of X-ray spectral formation in these objects. The radiative transfer equation which describes spectral formation is, in general, rather complicated because of its integro-differential nature. If we are interested in finding a solution, even numerically, we need to simplify the problem. For instance, we assume that stellar atmospheres can be represented, in first approximation, by a plane-parallel slab of fully ionized plasma of non-relativistic thermal electrons with an external uniform magnetic field. Since we are interested in modelling the high energy photon emission coming from the interaction with such medium, we assume also that the dominant radiative process which modifies the X-ray photon spectrum is multiple inverse Compton scattering. We propose two approaches to the study of this problem and we discuss the related solutions. In the first part of this thesis, we present an analytical and numerical study of the radiative transfer problem in the presence of a strong uniform magnetic field (B & 4:4 � 1013G) taking place in a medium filled by non-relativistic thermal electrons in plane-parallel geometry. Even after making some initial assumptions, the equation governing such system is still an integro-differential equation. Additional conditions are required to handle the radiative transfer equation the with separation of variable method. Then the radiative transfer problem can be reduced to the solution of the equation which has a diffusion operator for the energy variable and an integral operator for the space variable. Such an integro-differential equation was firstly derived and its solution was estimated in 1988 by Lyubarskii in [1],[2]. We have solved numerically the equation proposed by Lyubarskii and we have confirmed this solution using the analytical methods. The second part of the thesis is devoted to the description of a numerical algorithm that we implemented for the resolution of radiative transfer equation, when it reduces to a pure differential form. This is usually the case when the Fokker-Planck (diffusion) approximation is applicable. The algorithm is essentially based on relaxation methods and, generally, it solves all inhomogeneous second order elliptic partial differential equations with vanishing mixed derivatives. The numerical code gives a stable solution of the equation when the system has reached its steady-state equilibrium. We test the code solving the radiative transfer problem in the case of cylindrical accretion onto a magnetised neutron star, when a combined effect of bulk and thermal Comptonization takes place. Finally, we implemented the algorithm in the X-ray spectral fitting package XSPEC and we successfully fitted the X-ray spectra of the two Supergiant Fast X-ray Transients (SFXTs) XTE J1739-302 and IGR J17544-2619, observed with the Swift Gamma-ray Burst Telescope. Our model is then compared with other XSPEC models we used during the X-ray spectral fitting procedure and we briefly discuss possible implications on the geometry of these systems. I critically discuss and compare the results presented in the thesis in the conclusion section

The jet-disk symbiosis without maximal jets: 1-D hydrodynamical jets revisited

In this work we discuss the recent criticism by Zdziarski of the maximal jet model derived in Falcke & Biermann (1995). We agree with Zdziarski that in general a jet's internal energy is not bounded by its rest-mass energy density. We describe the effects of the mistake on conclusions that have been made using the maximal jet model and show when a maximal jet is an appropriate assumption. The maximal jet model was used to derive a 1-D hydrodynamical model of jets in agnjet, a model that does multiwavelength fitting of quiescent/hard state X-ray binaries and low-luminosity active galactic nuclei. We correct algebraic mistakes made in the derivation of the 1-D Euler equation and relax the maximal jet assumption. We show that the corrections cause minor differences as long as the jet has a small opening angle and a small terminal Lorentz factor. We find that the major conclusion from the maximal jet model, the jet-disk symbiosis, can be generally applied to astrophysical jets. We also show that isothermal jets are required to match the flat radio spectra seen in low-luminosity X-ray binaries and active galactic nuclei, in agreement with other works.Comment: 7 pages, accepted by A&

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation

Numerical solution of the radiative transfer equation: X-ray spectral formation from cylindrical accretion onto a magnetized neutron star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.Comment: 13 pages, 20 figures, accepted for publication in A&

Exploring the role of composition and mass loading on the properties of hadronic jets

Astrophysical jets are relativistic outflows that remain collimated for remarkably many orders of magnitude. Despite decades of research, the origin of cosmic rays (CRs) remains unclear, but jets launched by both supermassive black holes in the centre of galaxies and stellar-mass black holes harboured in X-ray binaries (BHXBs) are among the candidate sources for CR acceleration. When CRs accelerate in astrophysical jets, they initiate particle cascades that form gamma-rays and neutrinos. In the so-called hadronic scenario, the population of accelerated CRs requires a significant amount of energy to properly explain the spectral constraints, similarly to a purely leptonic scenario. The amount of energy required often exceeds the Eddington limit or even the total energy available within the jets. The exact energy source for the accelerated protons is unclear, but due to energy conservation along the jets, it is believed to come from the jet itself via transfer of energy from the magnetic fields or kinetic energy from the outflow. To address this hadronic energy issue and to self-consistently evolve the energy flux along the flows, we explore a novel treatment for including hadronic content, in which instabilities along the jet/wind border play a critical role. We discuss the impact of the different jet compositions on the jet dynamics for a pair dominated and an electron-proton jet and, consequently, the emitted spectrum, accounting for both leptonic and hadronic processes. Finally, we discuss the implications of this mass-loading scenario to address the proton energy issue

The Evolution of Gamma-ray Burst Jet Opening Angle through Cosmic Time

Jet opening angles of long gamma-ray bursts (lGRBs) appear to evolve in cosmic time, with lGRBs at higher redshifts being on average more narrowly beamed than those at lower redshifts. We examine the nature of this anti-correlation in the context of collimation by the progenitor stellar envelope. First, we show that the data indicate a strong correlation between gamma-ray luminosity and jet opening angle, and suggest this is a natural selection effect - only the most luminous GRBs are able to successfully launch jets with large opening angles. Then, by considering progenitor properties expected to evolve through cosmic time, we show that denser stars lead to more collimated jets; we argue that the apparent anti-correlation between opening angle and redshift can be accounted for if lGRB massive star progenitors at high redshifts have higher average density compared to those at lower redshifts. This may be viable for an evolving IMF - under the assumption that average density scales directly with mass, this relationship is consistent with the form of the IMF mass evolution suggested in the literature. The jet angle-redshift anti-correlation may also be explained if the lGRB progenitor population is dominated by massive stars at high redshift, while lower redshift lGRBs allow for a greater diversity of progenitor systems (that may fail to collimate the jet as acutely). Overall, however, we find both the jet angle-redshift anti-correlation and jet angle-luminosity correlation are consistent with the conditions of jet launch through, and collimation by, the envelope of a massive star progenitor