Synchrotron radiation from electrons with a pitch-angle distribution

Abstract

In most astrophysical processes involving synchrotron radiation, the pitch-angle distribution of the electrons is assumed to be isotropic. However, if electrons are accelerated anisotropically, e.g, in a relativistic shock wave with an ordered magnetic field or in magnetic reconnection regions, the electron pitch angles might be anisotropic. In this work, we study synchrotron radiation from electrons with a pitch-angle distribution with respect to a large-scale uniform magnetic field. Assuming that the pitch-angle distribution is normal with a scatter of ${\sigma }_p$ and that the viewing direction is where the pitch-angle direction peaks, we find that for electrons with a Lorentz factor $\gamma$, the observed flux satisfies $F_{\nu }\propto {\nu }^{2/3}$ for $\nu \ll {\nu }_{\mathrm{cr}}$ (${\nu }_{\mathrm{cr}}$ is the critical frequency of synchrotron), if ${\sigma }_p\lesssim 1/\gamma$ is satisfied. On the other hand, if ${\sigma }_p\gg 1/\gamma$, the spectrum below ${\nu }_{\mathrm{cr}}$ is a broken power law with a break frequency ${\nu }_{\mathrm{br}}\sim 2{\nu }_{\mathrm{cr}}/{\sigma }_p^3{\gamma }^3$, e.g., $F_{\nu }\propto {\nu }^{2/3}$ for $\nu \ll {\nu }_{\mathrm{br}}$ and $F_{\nu }\propto {\nu }^{1/3}$ for ${\nu }_{\mathrm{br}}\ll \nu \ll {\nu }_{\mathrm{cr}}$. Thus the ultimate synchrotron line of death is $F_{\nu }\propto {\nu }^{2/3}$. We discuss the application of this theory to blazars and gamma-ray bursts (GRBs).

6 pages, 5 figures, accepted for publication in ApJL

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• Hard Synchrotron Spectra from Magnetically Dominated Plasma Turbulence
• Synchrotron radiation in $\gamma$-ray burst prompt emission
• Pitch-Angle Anisotropy Imprinted by Relativistic Magnetic Reconnection
• Radio Analysis of SN 2004C Reveals an Unusual CSM Density Profile as a Harbinger of Core Collapse
• The Photosphere Emission Spectrum of Hybrid Relativistic Outflow for Gamma-ray Bursts
• Concurrent Particle Acceleration and Pitch-Angle Anisotropy Driven by Magnetic Reconnection: Ion-Electron Plasmas
• Coherent Curvature Radiation Spectrum by Dynamically Fluctuating Bunches in Magnetospheres
• Non-thermal Synchrotron Emission and Polarization Signatures during Black Hole Flux Eruptions
• Spectropolarimetry of synchrotron radiation from relativistic electrons with anisotropic pitch-angle and various energy distributions
• Electron Spectrum for the Prompt Emission of Gamma-ray Bursts in the Synchrotron Radiation Scenario
• Spectral Diversities of Gamma-ray Bursts in High Energy Bands: Hints from Turbulent Cascade