159 research outputs found

### On the thermal stability of transonic accretion discs

Nonlinear time-dependent calculations have been carried out in order to study
the evolution of the thermal instability for optically thick, transonic, slim
accretion discs around black holes. In the present calculations we have
investigated only the original version of the slim disc model with low
viscosity. This version does not yet contain several important non-local
effects but our aim is to use it as a standard reference against which to
compare the results from forthcoming studies in which additional effects will
be added one by one thus giving a systematic way of understanding the
contribution from each of them. A range of results for different cases is
presented showing a number of interesting features. One preliminary conclusion
is that the stabilizing effect of advection seems not to be strong enough in
these low viscosity models to allow for limit cycle behaviour to occur.Comment: 23 pages, Latex, 11 Postscript figures, accepted by MNRA

### Spectral variability in transonic discs around black holes

Transonic discs with accretion rates relevant to intrinsically bright
Galactic X-ray sources ($L\approx 10^{38}$-$10^{39} {\rm erg s}^{-1}$) exhibit
a time dependent cyclic behaviour due to the onset of a thermal instability
driven by radiation pressure. In this paper we calculate radiation spectra
emitted from thermally-unstable discs to provide detailed theoretical
predictions for observationally relevant quantities. The emergent spectrum has
been obtained by solving self-consistently the vertical structure and radiative
transfer in the disc atmosphere. We focus on four particular stages of the disc
evolution, the maximal evacuation stage and three intermediate stages during
the replenishment phase. The disc is found to undergo rather dramatic spectral
changes during the evolution, emitting mainly in the 1-10 keV band during
outburst and in the 0.1-1 keV band off-outburst. Local spectra, although
different in shape from a blackbody at the disc effective temperature, may be
characterized in terms of a hardening factor $f$. We have found that $f$ is
rather constant both in radius and in time, with a typical value $\sim 1.65$.Comment: 10 pages Latex with 11 ps figures. Accepted for publication in MNRA

### On the migration-induced resonances in a system of two planets with masses in the Earth mass range

We investigate orbital resonances expected to arise when a system of two
planets, with masses in the range 1-4 Earth masses, undergoes convergent
migration while embedded in a section of gaseous disc where the flow is
laminar. We consider surface densities corresponding to 0.5-4 times that
expected for a minimum mass solar nebula at 5.2 AU. Using hydrodynamic
simulations we find that when the configuration is such that convergent
migration occurs the planets can become locked in a first order
commensurability for which the period ratio is (p+1)/p with p being an integer
and migrate together maintaining it for many orbits. Relatively rapid
convergent migration as tends to occur for disparate masses, results in
commensurabilities with p larger than 2. However, in these cases the dynamics
is found to have a stochastic character. When the convergent migration is
slower, such as occurs in the equal mass case, lower p commensurabilities such
as 3:2 are attained which show much greater stability. In one already known
example of a system with nearly equal masses in the several Earth mass range
(planets around pulsar PSR B1257+12) the two largest planets are intriguingly
close to a 3:2 commensurability. A very similar behaviour is obtained when the
systems are modeled using an N body code with simple prescriptions for the disc
planet interaction. Using that, we found that an 8:7 resonance established in a
hydrodynamic simulation run for 10-100 thousand orbits could be maintained for
more than million orbits. Resonant capture leads to a rise in eccentricities
that can be predicted using a simple analytic model constructed in this paper.
We find that the system with the 8:7 commensurability is fully consistent with
this prediction.Comment: 26 pages with 19 low resolution Postscript figures, abstract
abridged, accepted for publication in MNRA

### Two-dimensional radiation-hydrodynamic model for limit-cycle oscillations of luminous accretion disks

We investigate the time evolution of luminous accretion disks around black
holes, conducting the two-dimensional radiation-hydrodynamic simulations. We
adopt the alpha prescription for the viscosity. The radial-azimuthal component
of viscous stress tensor is assumed to be proportional to the total pressure in
the optically thick region, while the gas pressure in the optically thin
regime. The viscosity parameter, alpha, is taken to be 0.1. We find the
limit-cycle variation in luminosity between high and low states. When we set
the mass input rate from the outer disk boundary to be 100 L_E/c^2, the
luminosity suddenly rises from 0.3L_E to 2L_E, where L_E is the Eddington
luminosity. It decays after retaining high value for about 40 s. Our numerical
results can explain the variation amplitude and duration of the recurrent
outbursts observed in microquasar, GRS 1915+105. We show that the
multi-dimensional effects play an important role in the high-luminosity state.
In this state, the outflow is driven by the strong radiation force, and some
part of radiation energy dissipated inside the disk is swallowed by the black
hole due to the photon-trapping effects. This trapped luminosity is comparable
to the disk luminosity. We also calculate two more cases: one with a much
larger accretion rate than the critical value for the instability and the other
with the viscous stress tensor being proportional to the gas pressure only even
when the radiation pressure is dominant. We find no quasi-periodic light
variations in these cases. This confirms that the limit-cycle behavior found in
the simulations is caused by the disk instability.Comment: 6 pages, 4 figures, accepted for publication in ApJ (ApJ 01 April
2006, v640, 2 issue

### Conditions for the occurrence of mean-motion resonances in a low mass planetary system

The dynamical interactions that occur in newly formed planetary systems may
reflect the conditions occurring in the protoplanetary disk out of which they
formed. With this in mind, we explore the attainment and maintenance of orbital
resonances by migrating planets in the terrestrial mass range. Migration time
scales varying between millions of years and thousands of years are considered.
In the former case, for which the migration time is comparable to the lifetime
of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter,
relatively rapid migration regime commensurabilities of high degree such as 8:7
or 11:10 may be formed. However, in any one large-scale migration several
different commensurabilities may be formed sequentially, each being associated
with significant orbital evolution. We also use a simple analytic theory to
develop conditions for first order commensurabilities to be formed. These
depend on the degree of the commensurability, the imposed migration and
circularization rates, and the planet mass ratios. These conditions are found
to be consistent with the results of our simulations.Comment: 11 pages with 4 figures, pdflatex, to appear in the proceedings of
the conference "Extra-solar Planets in Multi-body Systems: Theory and
Observations"; eds. K. Gozdziewski, A. Niedzielski and J. Schneider, EAS
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