Relativistic Beaming Pattern

What you are seeing: a light source that emits equally in all directions in its own rest frame. When the source is moving toward you at high speed, special relativity concentrates the emission into a narrow cone pointing forward (along the direction of motion). This is "relativistic beaming". It is why blazar jets look much brighter when their axis points at us and dim when it does not. The scene shows the $D^{3+\alpha}$ emission pattern as a shaded 3D solid of revolution about the boost axis, plus a stream of photons sampled isotropically in the rest frame and aberrated into the lab frame, so sweeping $\gamma$ visibly collimates them from a broad teardrop into a $1/\gamma$ pencil beam.

The Doppler factor is $D(\theta) = 1 / [\gamma\,(1 - \beta \cos\theta)]$ where $\beta = v/c$, $\gamma = 1/\sqrt{1 - \beta^2}$, and $\theta$ is the angle to the line of sight in the lab frame. For an isotropic source the observed intensity scales as $D^{3 + \alpha}$ with $\alpha$ the spectral index. The half-angle of the forward beam shrinks like $1/\gamma$ at large $\gamma$.