Internal shocks in relativistic outflows: collisions of magnetized shells

(Abridged): We study the collision of magnetized irregularities (shells) in relativistic outflows in order to explain the origin of the generic phenomenology observed in the non-thermal emission of both blazars and gamma-ray bursts. We focus on the influence of the magnetic field on the collision dynamics, and we further investigate how the properties of the observed radiation depend on the strength of the initial magnetic field and on the initial internal energy density of the flow. The collisions of magnetized shells and the radiation resulting from these collisions are calculated using the 1D relativistic magnetohydrodynamics code MRGENESIS. The interaction of the shells with the external medium prior to their collision is also determined using an exact solver for the corresponding 1D relativistic magnetohydrodynamic Riemann problem. Our simulations show that two magnetization parameters - the ratio of magnetic energy density and thermal energy density, \alpha_B, and the ratio of magnetic energy density and mass-energy density, \sigma - play an important role in the pre-collision phase, while the dynamics of the collision and the properties of the light curves depend mostly on the magnetization parameter \sigma. The interaction of the shells with the external medium changes the flow properties at their edges prior to the collision. For sufficiently dense shells moving at large Lorentz factors (\simgt 25) these properties depend only on the magnetization parameter \sigma. Internal shocks in GRBs may reach maximum efficiencies of conversion of kinetic into thermal energy between 6% and 10%, while in case of blazars, the maximum efficiencies are \sim 2%.Comment: 17 pages, 18 figures. 2 new references have been added. Accepted for publication in Astronomy and Astrophysic

Relativistic MHD Simulations of Jets with Toroidal Magnetic Fields

This paper presents an application of the recent relativistic HLLC approximate Riemann solver by Mignone & Bodo to magnetized flows with vanishing normal component of the magnetic field. The numerical scheme is validated in two dimensions by investigating the propagation of axisymmetric jets with toroidal magnetic fields. The selected jet models show that the HLLC solver yields sharper resolution of contact and shear waves and better convergence properties over the traditional HLL approach.Comment: 12 pages, 5 figure

The magnetohydrodynamic instability of current-carrying jets

Magnetohydrodynamic instabilities can be responsible for the formation of structures with various scales in astrophysical jets. We consider the stability properties of jets containing both the azimuthal and axial field of subthermal strength. A magnetic field with complex topology in jets is suggested by theoretical models and is consistent with recent observations. Stability is discussed by means of a linear analysis of the ideal magnetohydrodynamic equations. We argue that in azimuthal and axial magnetic fields the jet is always unstable to non-axisymmetric perturbations. Stabilization does not occur even if the strengths of these field components are comparable. If the axial field is weaker than the azimuthal one, instability occurs for perturbations with any azimuthal wave number $m$, and the growth rate reaches a saturation value for low values of $m$. If the axial field is stronger than the toroidal one, the instability shows for perturbations with relatively high $m$.Comment: 9 pages, 9 figures, to appear on A&

Equation of State in Relativistic Magnetohydrodynamics: variable versus constant adiabatic index

The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications, is compared with a more realistic equation of state that better approximates the single-specie relativistic gas. The paper focus on three different topics. First, the influence of a more realistic equation of state on the propagation of fast magneto-sonic shocks is investigated. This calls into question the validity of the constant $\Gamma$-law equation of state in problems where the temperature of the gas substantially changes across hydromagnetic waves. Second, we present a new inversion scheme to recover primitive variables (such as rest-mass density and pressure) from conservative ones that allows for a general equation of state and avoids catastrophic numerical cancellations in the non-relativistic and ultrarelativistic limits. Finally, selected numerical tests of astrophysical relevance (including magnetized accretion flows around Kerr black holes) are compared using different equations of state. Our main conclusion is that the choice of a realistic equation of state can considerably bear upon the solution when transitions from cold to hot gas (or viceversa) are present. Under these circumstances, a polytropic equation of state can significantly endanger the solution.Comment: 14 pages, 14 figure

On the dynamic efficiency of internal shocks in magnetized relativistic outflows

We study the dynamic efficiency of conversion of kinetic-to-thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We model internal shocks as being caused by collisions of shells of plasma with the same energy flux and a non-zero relative velocity. The contact surface, where the interaction between the shells takes place, can break up either into two oppositely moving shocks (in the frame where the contact surface is at rest), or into a reverse shock and a forward rarefaction. We find that for moderately magnetized shocks (magnetization $\sigma\simeq 0.1$), the dynamic efficiency in a single two-shell interaction can be as large as 40%. Thus, the dynamic efficiency of moderately magnetized shocks is larger than in the corresponding unmagnetized two-shell interaction. If the slower shell propagates with a sufficiently large velocity, the efficiency is only weakly dependent on its Lorentz factor. Consequently, the dynamic efficiency of shell interactions in the magnetized flow of blazars and gamma-ray bursts is effectively the same. These results are quantitatively rather independent on the equation of state of the plasma. The radiative efficiency of the process is expected to be a fraction $f_r<1$ of the estimated dynamic one, the exact value of $f_r$ depending on the particularities of the emission processes which radiate away the thermal or magnetic energy of the shocked states.Comment: Accepted for publication in MNRAS. 8 pages, 6 figures. The definitive version is available at http://www.blackwell-synergy.co

An HLLC Solver for Relativistic Flows -- II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The HLLC solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper (Mignone & Bodo 2004) to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave. Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the contrained tranport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one and two dimensional numerical test problems.Comment: 17 pages, 12 figure

Risco a partir do coeficiente beta do Modelo CAPM e sua relação com o Dividend Yield das empresas do ISE-Índice de Sustentabilidade Empresarial- da BMFBovespa do período 2004/2015.

Este estudo teve como objetivo identificar se ativos com maior risco mensurável pelo coeficiente beta possuem dividend yield diferente das com menor risco. A amostra deste estudo é representada pelos ativos de empresas de capital aberto com listagem no índice de sustentabilidade empresarial (ISE), considerados os 23 ativos que possuem dados quanto ao retorno diário em pelo menos 90% de cada um dos trimestres analisados no período que corresponde a 01/01/2004 até 01/01/2015. A pesquisa se caracteriza como descritiva, documental e de caráter quantitativo. Após a separação dos ativos em três grupos distintos, considerando a média dos 44 trimestres estudados, os resultados indicam que o grupo 1, composto pelos ativos com menor coeficiente Beta, possuem em média um dividend yield maior em 30,44% se comparado ao grupo 2, e 126% maior do que a média do grupo 3, que é composto pelos ativos com maior coeficiente Beta.

Multiwavelength afterglow light curves from magnetized GRB flows

We use high-resolution relativistic MHD simulations coupled with a radiative transfer code to compute multiwavelength afterglow light curves of magnetized ejecta of gamma-ray bursts interacting with a uniform circumburst medium. The aim of our study is to determine how the magnetization of the ejecta at large distance from the central engine influences the afterglow emission, and to assess whether observations can be reliably used to infer the strength of the magnetic field. We find that, for typical parameters of the ejecta, the emission from the reverse shock peaks for magnetization $\sigma_0 \sim 0.01 - 0.1$ of the flow, and that it is greatly suppressed for higher $\sigma_0$. The emission from the forward shock shows an achromatic break shortly after the end of the burst marking the onset of the self-similar evolution of the blast wave. Fitting the early afterglow of GRB 990123 and 090102 with our numerical models we infer respective magnetizations of $\sigma_0 \sim 0.01$ and $\sigma_0 \sim 0.1$ for these bursts. We argue that the lack of observed reverse shock emission from the majority of the bursts can be understood if \sigma_0 \simmore 0.1, since we obtain that the luminosity of the reverse shock decreases significantly for $\sigma_0 \sim 1$. For ejecta with \sigma_0 \simmore 0.1 our models predict that there is sufficient energy left in the magnetic field, at least during an interval of ~10 times the burst duration, to produce a substantial emission if the magnetic energy can be dissipated (for instance, due to resistive effects) and radiated away.Comment: 9 pages, 9 figures. Submitted to MNRAS

General relativistic simulations of pasive-magneto-rotational core collapse with microphysics

This paper presents results from axisymmetric simulations of magneto-rotational stellar core collapse to neutron stars in general relativity using the passive field approximation for the magnetic field. These simulations are performed using a new general relativistic numerical code specifically designed to study this astrophysical scenario. The code is based on the conformally-flat approximation of Einstein's field equations and conservative formulations of the magneto-hydrodynamics equations. The code has been recently upgraded to incorporate a tabulated, microphysical equation of state and an approximate deleptonization scheme. This allows us to perform the most realistic simulations of magneto-rotational core collapse to date, which are compared with simulations employing a simplified (hybrid) equation of state, widely used in the relativistic core collapse community. Furthermore, state-of-the-art (unmagnetized) initial models from stellar evolution are used. In general, stellar evolution models predict weak magnetic fields in the progenitors, which justifies our simplification of performing the computations under the approach that we call the passive field approximation for the magnetic field. Our results show that for the core collapse models with microphysics the saturation of the magnetic field cannot be reached within dynamical time scales by winding up the poloidal magnetic field into a toroidal one. We estimate the effect of other amplification mechanisms including the magneto-rotational instability (MRI) and several types of dynamos.Comment: 25 pages, 15 figures, accepted for publication in Astronomy & Astrophysics July 31, 2007. Added 1 figure and a new subsectio

Deceleration of arbitrarily magnetized GRB ejecta: the complete evolution

(Abridged) We aim to quantitatively understand the dynamical effect and observational signatures of magnetization of the GRB ejecta on the onset of the afterglow. We perform ultrahigh-resolution one-dimensional relativistic MHD simulations of the interaction of a radially expanding, magnetized ejecta with the interstellar medium. The need of ultrahigh numerical resolution derives from the extreme jump conditions in the region of interaction between the ejecta and the circumburst medium. We study the evolution of an ultrarelativistic shell all the way to a the self-similar asymptotic phase. Our simulations show that the complete evolution can be characterized in terms of two parameters, namely, the \xi parameter introduced by Sari & Piran (1995) and the magnetization \sigma_0. We exploit this property by producing numerical models where the shell Lorentz factor is \gamma_0 ~ tens and rescaling the results to arbitrarily large \gamma_0. We find that the reverse shock is typically very weak or absent for ejecta characterized by \sigma_0 >~ 1. The onset of the forward shock emission is strongly affected by the magnetization. On the other hand, the magnetic energy of the shell is transfered to the external medium on a short timescale (~several times the duration of the burst). The later forward shock emission does not contain information for the initial magnetization of the flow. The asymptotic evolution of strongly magnetized shells, after they have suffred a substantial deceleration, resembles that of hydrodynamic shells, i.e., they fully enter in the Blandford-McKee self-similar regime.Comment: 14 pages, 10 figures, accepted for publication in Astronomy and Astrophysic