# Non-uniform model for the synchrotron radiation of SgrA* and other low-luminosity galactic nuclei

## V. I. Slysh

Astro Space Center, Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

### Paper: Astronomy reports, May 2008, in press

**Abstract:**
The model of a non-uniform
source of synchrotron radiation with a power-law radial
distribution of the magnetic field and relativistic-electron
density along one- or two-sided jets is described.
Non-relativistic jets with both constant cross sections
(collimated jets) and the cross sections that are proportional to
distance (conical jets) are considered. Formulas that can be used
to determine source parameters from the spectral index, source
size, and index of the relativistic-electron energy spectrum based
on multi-frequency observations are obtained. In the case of a
conical jet, these formulas coincide with the analogous formulas
for a spherical source obtained by A.P.Marscher. Relations that
can be used to estimate the magnetic-field strength from the
brightness temperature in the self-absorbed region are also
obtained. As examples, the non-uniform source model is applied to
the compact radio sources at the centers of the Milky Way, SgrA*,
and the low-luminosity galactic nuclei M81* and M87*, which are
associated with supermassive black holes. The inner radius of the
radiation region is determined. For SgrA*, this distance turns out
to be comparable to the gravitational radius, smaller than the
radius of the last stable orbit for non-rotating black hole, and
consistent with the radius of the last stable orbit expected for a
rotating black hole. The inner radii in M81* and M87* are
15 R_{S}, an order of magnitude larger then for SgrA*. Estimates
of the magnetic field at the inner radius are 400 G for M81*,
0.65/5.3 kG for SgrA*, and 20/100 kG for M87*. These
magnetic fields and the Blandford-Znajek model for the radiation
of a rotating black hole are used to estimate the rotational speed
of the black holes, which is in agreement with the characteristic
variability time scales for these three objects. However, the
accuracy of these estimates is modest, and is limited primarily by
the accuracy of interferometric measurements at millimeter
wavelengths.

Preprints available from the authors at vslysh@asc.rssi.ru
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