Geodesic motions versus hydrodynamic flows in a gravitating perfect fluid: Dynamical equivalence and consequences

Stimulated by the methods applied for the observational determination of masses in the central regions of the AGNs, we examine the conditions under which, in the interior of a gravitating perfect fluid source, the geodesic motions and the general relativistic hydrodynamic flows are dynamically equivalent to each other. Dynamical equivalence rests on the functional similarity between the corresponding (covariantly expressed) differential equations of motion and is obtained by conformal transformations. In this case, the spaces of the solutions of these two kinds of motion are isomorphic. In other words, given a solution to the problem "hydrodynamic flow in a perfect fluid", one can always construct a solution formally equivalent to the problem "geodesic motion of a fluid element" and vice versa. Accordingly, we show that, the observationally determined nuclear mass of the AGNs is being overestimated with respect to the real, physical one. We evaluate the corresponding mass-excess and show that it is not always negligible with respect to the mass ofthe central dark object, while, under circumstances, can be even larger than the rest-mass of the circumnuclear gas involved.Comment: LaTeX file, 22 page

The Crab Nebula: interpretation of CHANDRA observations

We interpret the observed X-ray morphology of the central part of the Crab Nebula (torus + jets) in terms of the standard theory by Kennel and Coroniti (1984). The only new element is the inclusion of anisotropy in the energy flux from the pulsar in the theory. In the standard theory of relativistic winds, the Lorentz factor of the particles in front of the shock that terminates the pulsar relativistic wind depends on the polar angle as $\gamma=\gamma_0+\gamma_m\sin^2\theta$, where $\gamma_0 \sim 200$ and $\gamma_m \sim 4.5\times 10^6$. The plasma flow in the wind is isotropic. After the passage of the pulsar wind through the shock, the flow becomes subsonic with a roughly constant (over the plerion volume) pressure $P={1\over 3}n\epsilon$, where $n$ is the plasma particle density and $\epsilon$ is the mean particle energy. Since $\epsilon \sim \gamma mc^2$, a low-density region filled with the most energetic electrons is formed near the equator. A bright torus of synchrotron radiation develops here. Jet-like regions are formed along the pulsar rotation axis, where the particle density is almost four orders of magnitude higher than that in the equatorial plane, because the particle energy there is four orders of magnitude lower. The energy of these particles is too low to produce detectable synchrotron radiation. However, these quasi-jets become comparable in brightness to the torus if additional particle acceleration takes place in the plerion. We also present the results of our study of the hydrodynamic interaction between an anisotropic wind and the interstellar medium. We compare the calculated and observed distributions of the volume intensity of X-ray radiation.Comment: 38 pages, 5 figures. To be published in Astronomy Letters, 2002, N 6, p.