A Structured Leptonic Jet Model of the "Orphan" TeV Gamma-Ray Flares in TeV Blazars

The emission spectra of TeV blazars extend up to tens of TeV and the emission mechanism of the TeV $\gamma$-rays is explained by synchrotron self-Compton scattering in leptonic models. In these models the time variabilities of X-rays and TeV $\gamma$-rays are correlated. However, recent observations of 1ES 1959+650 and Mrk 421 have found the ``orphan'' TeV $\gamma$-ray flares, i.e., TeV $\gamma$-ray flares without simultaneous X-ray flares. In this paper we propose a model for the ``orphan'' TeV $\gamma$-ray flares, employing an inhomogeneous leptonic jet model. After a primary flare that accompanies flare-up both in X-rays and TeV $\gamma$-rays, radiation propagates in various directions in the comoving frame of the jet. When a dense region in the jet receives the radiation, X-rays are scattered by relativistic electrons/positrons to become TeV $\gamma$-rays. These $\gamma$-ray photons are observed as an ``orphan'' TeV $\gamma$-ray flare. The observed delay time between the primary and ``orphan'' flares is about two weeks and this is accounted for in our model for parameters such as $\Gamma = 20$, $d = 4 \times 10^{17}$cm, $\alpha = 3$, and $\eta = 1$, where $\Gamma$ is the bulk Lorentz factor of the jet, $d$ is the distance between the central black hole and the primary flare site, $\alpha/\Gamma$ is the angle between the jet axis and the direction of the motion of the dense region that scatters incoming X-rays produced by the primary flare, and $\eta/\Gamma$ is the angle between the jet axis and the line of sight.