Astrophysical jet

A collimated plasma outflow from an astrophysical engine, often associated with accretion. Magnetic stresses, rotation, pressure and interaction with an external medium shape its acceleration and confinement. Jets can carry particle kinetic energy, thermal energy and electromagnetic energy far beyond the compact launch region.

A jet with bulk velocity sufficiently close to the speed of light that relativistic aberration, frequency shifts and arrival-time effects strongly affect its appearance. The moving emitting pattern need not track the speed of every plasma component.

Rapidly varying high-energy sources can appear too dense in target photons to transmit their observed gamma rays. For an approximately isotropic stationary region with target-band luminosity $L_2$, radius $R$ and target photon energy ${ϵ}_2$, the target number density is $n\sim L_2/(4\pi R^{2}c{ϵ}_2)$. photon-photon pair production then gives optical depth $\tau \sim n\sigma R$. A luminosity variability size bound can make this very large. relativistic beaming both increases the inferred rest-frame size and reduces the inferred rest-frame radiation density, allowing escape. This radiation-opacity argument is distinct from gravitational stellar compactness and topological compactness.

For an internally illuminated isotropic rest-frame blob with an unbroken power-law spectrum, use $R^{\prime }\sim Dc\Delta t_{\mathrm{obs}}$, a corresponding-bin luminosity boost $D^4$, and the internal pair-production target energy in a relativistic blob. At fixed observed gamma-ray energy,Here $F_{\log }=\nu F_{\nu }$ and ${ϵ}_{20}$ is the target energy at $D=1$. The frequently used $D^{-6}$ is the $\alpha =1$ case, not a universal law for every spectral energy distribution. Geometry, spectral breaks and external illumination affect the result.

Let the relevant rest-frame photon-photon pair production energy product be $K={ϵ}_1^{\prime }{ϵ}_2^{\prime }$ for a specified collision-angle prescription. For fixed observed high-energy photon energy, ${ϵ}_1^{\prime }={ϵ}_{1,\mathrm{obs}}/D$, so the target has ${ϵ}_2^{\prime }=DK/{ϵ}_{1,\mathrm{obs}}$. Observing the same internally produced target population supplies a second Doppler factor, giving the displayed result. An external stationary radiation field requires its own angular transformation instead.

Coherent intrinsic luminosity variation on observed time $\Delta t_{\mathrm{obs}}$ bounds the characteristic emitting radius by a light-crossing argument. relativistic beaming shortens the observed interval by Doppler factor $D$, while cosmological redshift lengthens it by $1+z$. This bound assumes that the variation samples the emitting region causally; geometry, independent subregions and propagation-driven variation can change its interpretation.

A moving feature can have inferred transverse speed ${\beta }_{\mathrm{app}}c$ greater than $c$ because its second signal starts closer to the observer. The light-travel delay gives ${\beta }_{\mathrm{app}}=\beta \sin \theta /(1-\beta \cos \theta )$, whose maximum is $\Gamma \beta$ at $\cos \theta =\beta$. No local material or signal speed exceeds $c$.