The Flux Ratio of a Jet to Its Counterjet Revisited

A general relativistic formula for the flux density ratio of a nuclear jet to its counterjet is obtained. The key general relativistic effect, i.e., light bending by the black hole, favors the visibility of the counterjet. The formula is significantly different from the one that considers only Doppler effects when the angle between a line of sight and the jet, i, is small, say, i < 10°. It is found that gravitational lensing plays a vital role if i ~ 1°, although the probability of this effect dominating is small. It is possible for a counterjet to be visible even if the jet has a high value of Lorentz factor, γ. Lensed counterjets will only be visible for subluminal sources.

We apply the more general formula to the recently observed counterjet in NGC 1275 and show that the value of i is slightly smaller than when derived by the traditional formula. For reasonable assumptions about other parameters, we set limits on the viewing angle of i > 16° and on the spectral index of α < 1.6.