= Doppler boosting of a moving blob
{c}
{title2=$F_\nu=D^{3+\alpha}F'_\nu$}
For an unresolved, isotropically emitting rest-frame blob with <power-law spectrum> $F'_\nu\propto\nu^{-\alpha}$, the observed <spectral flux density> at a fixed <frequency> is enhanced by $D^{3+\alpha}$. The factors follow from <Lorentz-invariant specific intensity> and the <frequency> shift. The bolometric or corresponding-logarithmic-bin <luminosity> transforms with $D^4$. A spatially steady continuous jet has a different equal-arrival-time sampling and can have exponent $2+\alpha$ instead.
Back to article page
