The X-ray rim of the SN 1006 remnant is a thin shell of synchrotron emission from…

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Radiation, radiative transfer and stellar atmospheres · Astrophysical fluid dynamics and plasmas

Stars from the Inside, Ch Stellar explosions: core collapse, the neutrino-driven shock, radioactive light and remnants

Problem

The X-ray rim of the SN 1006 remnant is a thin shell of synchrotron emission from electrons accelerated at its shock front. At distance

D = 2.2\,\mathrm{kpc}

the rim's angular width is

5.0\,\mathrm{arcsec}

(

1\,\mathrm{arcsec} = 4.848\times10^{-6}\,\mathrm{rad}

), the shock speed is

v_s = 5000\,\mathrm{km\,s^{-1}}

, and the rim is observed at a characteristic X-ray photon energy

\varepsilon = 1.0\,\mathrm{keV}

. Use these standard results for an electron of Lorentz factor

\gamma

in a magnetic field

B

: it radiates synchrotron photons near a frequency

\nu \approx \gamma^2\nu_g

, where

\nu_g = eB/(2\pi m_e)

is the non-relativistic gyrofrequency, and it loses most of its energy on a synchrotron cooling timescale

t_{\rm syn} = \frac{3m_ec\mu_0}{2\sigma_T\gamma B^2}.

For a strong shock the gas immediately behind it flows at one quarter of the shock speed relative to the shock,

v_d = v_s/4

; take the observed rim width to be the distance

w = v_d t_{\rm syn}

that the radiating electrons advect downstream before they cool. ((a)) Combine these relations to estimate the magnetic field

B

in the emitting region. ((b)) Find the Lorentz factor and energy (in TeV) of the electrons responsible, and check this is consistent with the claim that such rims come from electrons of tens of TeV.

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