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I consider a scenario in which stellar winds within the dense
stellar nucleus are intercepted by the dormant massive black hole (BH)
sitting at the galaxian center, and quasi-sperical accretion of the wind onto
the BH occurs resulting in acceleration of relativistic electrons to produce
the spectrum $N(\gamma)\propto \gamma^{-p}$. Under assumption on equipartition
between the local energy density of the magnetic field and that of
relativistic electrons, the spectrum of synchrotron radio emission
is derived to be $\alpha=(13+2p)/(22+5p)$. It ranges between $\alpha =0.51$
to 0.56 for the range of $p$=3 to 1. The radius of the source is predicted
to vary with frequency as $r\propto \nu^{m}$, where $m=-4(4+p)/(22+5p)\approx
-0.7$; the higher the frequency, the more inner parts of the source are seen.
Since at radii $r
This model is applicable to nuclear radio sources in the nuclei of nearby
spiral galaxies such as M 81, M 104, etc., which have revealed the presence of
a central compact radio source whose prototype in the Milky Way galaxy is
Sgr A$^\star$. Similarly, in many early-type galaxies, parsec-scale radio
cores have been found. The most important common feature of these sources
is the inverted radio spectrum $S\propto \nu^\alpha$ with $\alpha =+0.3$ to
$+0.5$, which is consistent with the above model. The observed radio spectra
enable us to evaluate some important physical parameters of the accreting
sources.