AST-12

Synchrotron critical frequency

ν_c = (3/2) γ² ν_L, ν_L = e B / (2π m). Peak of the synchrotron spectrum.

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RadiationSynchrotron

Governing equation

\nu_c=\tfrac32\gamma^2 eB/(2\pi m)

where

\gamma: Lorentz factor (—)
B: Field (µT)
\nu_c: Critical frequency (MHz)

Lecture brief

Historical brief

Hubble expansion, Jeans collapse, Eddington luminosity, Bondi accretion and Stefan–Boltzmann stars are the first astrophysical budgets. The sheets scale a star, a cloud and a horizon. This sheet (AST-12 — Synchrotron critical frequency) is the form associated with Synchrotron. Working symbols: $\gamma$ , $B$ $\rightarrow$ $\nu_c$ . Power ∝ γ² B². Radio galaxies and supernova remnants shine this way.

Purpose

Purpose: compute

\nu_c

from

\gamma

B

in Astrophysics via

\nu_c=\tfrac32\gamma^2 eB/(2\pi m)

ν_c = (3/2) γ² ν_L, ν_L = e B / (2π m). Peak of the synchrotron spectrum. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\gamma = 10000.000\,\mathrm{—}

B = 1.000\,\mathrm{\mu T}

, the governing relation

\nu_c=\tfrac32\gamma^2 eB/(2\pi m)

yields

\nu_c = 4.20e+6\,\mathrm{MHz}

. A relativistic electron, a B field, a beamed glow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Lorentz factor \gamma10000 —Field B1 µT

Outputs

Critical frequency \nu_c4198873.48 MHz

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Narration of this film

A relativistic electron, a B field, a beamed glow.

Power ∝ γ² B². Radio galaxies and supernova remnants shine this way.

Reading speed

Watch on YouTube