A Mechanical Model for Magnetized Relativistic Blastwaves

Abstract

The evolution of a relativistic blastwave is usually delineated under the assumption of pressure balance between forward- and reverse-shocked regions. However, such a treatment usually violates the energy conservation law, and is inconsistent with existing MHD numerical simulation results. A mechanical model of non-magnetized blastwaves was proposed in previous work to solve the problem. In this paper, we generalize the mechanical model to the case of a blastwave driven by an ejecta with an arbitrary magnetization parameter ${\sigma }_{\mathrm{ej}}$. We test our modified mechanical model by considering a long-lasting magnetized ejecta and found that it is much better than the pressure-balance treatment in terms of energy conservation. For a constant central engine wind luminosity $L_{\mathrm{ej}}=10^{47}\mathrm{erg}{\mathrm{s}}^{-1}$ and ${\sigma }_{\mathrm{ej}}<10$, the deviation from energy conservation is negligibly small at small radii, but only reaches less than $25\%$ even at $10^{19}\mathrm{cm}$ from the central engine. For a finite life time of the central engine, the reverse shock crosses the magnetized ejecta earlier for the ejecta with a higher ${\sigma }_{\mathrm{ej}}$, which is consistent with previous analytical and numerical results. In general, the mechanical model is more precise than the traditional analytical models with results closer to those of numerical simulations.

arXiv commentAccepted for publication in MNRAS; 8 pages, 2 figures

References in corpus (31)

• The Physics of Gamma-Ray Bursts and Relativistic Jets
• The X-ray counterpart to the gravitational wave event GW 170817
• The Internal-Collision-Induced Magnetic Reconnection and Turbulence (ICMART) Model of Gamma-Ray Bursts
• Gamma-ray Burst Afterglow with Continuous Energy Injection: Signature of a Highly-Magnetized Millisecond Pulsar
• Predictions for The Very Early Afterglow and The Optical Flash
• Hydrodynamic Time Scales and Temporal Structure of GRBs
• Gamma-ray burst early optical afterglows: implications for the initial Lorentz factor and the central engine
• Optical and X-ray emission from stable millisecond magnetars formed from the merger of binary neutron stars
• GRB 990123: Reverse and Internal Shock Flashes and Late Afterglow
• A Complete Reference of the Analytical Synchrotron External Shock Models of Gamma-Ray Bursts
• Gamma-ray burst early afterglows: reverse shock emission from an arbitrarily magnetized ejecta
• Bright "merger-nova" from the remnant of a neutron star binary merger: A signature of a newly born, massive, millisecond magnetar
• The Evolution of a Structured Relativistic Jet and GRB Afterglow Light-Curves
• Fast cooling synchrotron radiation in a decaying magnetic field and $\gamma$-ray burst emission mechanism
• Detection of Gamma-Ray Polarization in Prompt Emission of GRB 100826A
• Optical Flashes and Radio Flares in GRBs afterglow: Numerical Study
• Constraints on binary neutron star merger product from short GRB observations
• Early Optical Afterglows from Wind-Type Gamma-Ray Bursts
• Deceleration of arbitrarily magnetized GRB ejecta: the complete evolution
• Optical Flashes and Very Early Afterglows in Wind Environments
• Signature of gravitational radiation in afterglow of short Gamma-Ray Bursts?
• The allowed parameter space of a long-lived neutron star as the merger remnant of GW170817
• The very early afterglow powered by the ultra-relativistic mildly magnetized outflows
• Magnetorotational core collapse of possible GRB progenitors. II. Formation of protomagnetars and collapsars
• On the existence of a reverse shock in magnetized GRB ejecta
• Dynamics and Afterglow Light Curves of GRB Blast Waves with a Long-lived Reverse Shock
• Magnetohydrodynamic Effects in Propagating Relativistic Jets: Reverse Shock and Magnetic Acceleration
• Multiwavelength afterglow light curves from magnetized GRB flows
• Mechanical Model for Relativistic Blast Waves
• A Semi-analytic Formulation for Relativistic Blast Waves with a Long-lived Reverse Shock
• An energy-conserving dynamical model of GRB afterglows from magnetized forward and reverse shocks

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