## 3. Results of nucleosynthesis calculationsIn the first example, we start with a relativistic flow (polytropic
index ) with the accretion rate
, where,
is the Eddington accretion rate. We
use the mass of the central black hole to be
throughout. We choose a very high
viscosity and the corresponding
parameter (Shakura & Sunyaev 1973) is 0.2 in the sub-Keplerian
regime. The cooling is not as efficient as in a Keplerian disk:
, where,
and
are the heat generation and heat
loss rates respectively. The specific angular momentum at the inner
edge is (in units of
). The flow deviates from a Keplerian
disk at 4.15 Schwarzschild radii. It is to be noted that
includes The above depletion rates have been computed assuming Planckian
photon distribution corresponding to ion temperature
. The wavelength
at which the brightness is highest
at is shown in Fig. 1 in the dashed
curve (in units of cm). Also shown
is the where, and
are computed from 2 and 50 keV
respectively. The average becomes a function of the energy spectral
index
(), which in turn depends on the ion
and electron temperatures of the medium. We follow Chakrabarti &
Titarchuk (1995) to compute these relations. We note that
is
Fig. 2 shows the result of the numerical simulation for the disk model mentioned above. Logarithmic abundance of neutron is plotted against the logarithmic distance from the black hole. First simulation produced the dash-dotted curve for the neutron distribution, forming a miniature neutron torus. As fresh matter is added to the existing neutron disk, neutron abundance is increased as neutrons do not fall in rapidly. Thus the simulation is repeated several times in order to achieve a converging steady pattern of the neutron disk. Although fresh neutrons are deposited, the stability of the distribution is achieved through neutron decay and neutron capture reactions. Results after every ten iterations are plotted. The equilibrium neutron torus remains around the black hole indefinitely. The neutron abundance is clearly very significant (more than five per cent!).
We study yet another case where the accretion rate is smaller
() and the viscosity is so small
() and the disk so hot that the
sub-Keplerian flow deviates from a Keplerian disk farther away at
. The polytropic index is that of a
mono-atomic (ionized) hot gas . The
Compton cooling factor is as above since it is independent of the
accretion rates as long as the rate is low (Sunyaev & Titarchuk
1980; Chakrabarti & Titarchuk 1995). The cooling is assumed to be
very inefficient because of lower density:
. The specific angular momentum at
the inner edge of the disk is . In
Fig. 3, we show the logarithmic abundances of proton (p), helium
() and neutron (n) as functions of
the logarithmic distance from the black hole. Note that
dissociates completely at a distance
of around where the density and
temperatures are gm cm
© European Southern Observatory (ESO) 1999 Online publication: March 10, 1999 |