18 research outputs found
Fragmentation of a dynamically condensing radiative layer
In this paper, the stability of a dynamically condensing radiative gas layer
is investigated by linear analysis. Our own time-dependent, self-similar
solutions describing a dynamical condensing radiative gas layer are used as an
unperturbed state. We consider perturbations that are both perpendicular and
parallel to the direction of condensation. The transverse wave number of the
perturbation is defined by . For , it is found that the condensing gas
layer is unstable. However, the growth rate is too low to become nonlinear
during dynamical condensation. For , in general, perturbation equations
for constant wave number cannot be reduced to an eigenvalue problem due to the
unsteady unperturbed state. Therefore, direct numerical integration of the
perturbation equations is performed. For comparison, an eigenvalue problem
neglecting the time evolution of the unperturbed state is also solved and both
results agree well. The gas layer is unstable for all wave numbers, and the
growth rate depends a little on wave number. The behaviour of the perturbation
is specified by at the centre, where the cooling length,
, represents the length that a sound wave can travel during
the cooling time. For , the perturbation grows
isobarically.
For , the perturbation grows because each part has a
different collapse time without interaction. Since the growth rate is
sufficiently high, it is not long before the perturbations become nonlinear
during the dynamical condensation. Therefore, according to the linear analysis,
the cooling layer is expected to split into fragments with various scales.Comment: 12 pages, 10 figures, accepted for publication in Astronomy &
Astrophysic
Conditions for Gravitational Instability in Protoplanetary Disks
Gravitational instability is one of considerable mechanisms to explain the
formation of giant planets. We study the gravitational stability for the
protoplanetary disks around a protostar. The temperature and Toomre's Q-value
are calculated by assuming local equilibrium between viscous heating and
radiative cooling (local thermal equilibrium). We assume constant
viscosity and use a cooling function with realistic opacity. Then, we derive
the critical surface density that is necessary for a disk to
become gravitationally unstable as a function of . This critical surface
density is strongly affected by the temperature dependence of
the opacity. At the radius AU, where ices form, the value of
changes discontinuously by one order of magnitude. This
is determined only by local thermal process and criterion of
gravitational instability. By comparing a given surface density profile to
, one can discuss the gravitational instability of
protoplanetary disks. As an example, we discuss the gravitational instability
of two semi-analytic models for protoplanetary disks. One is the steady state
accretion disk, which is realized after the viscous evolution. The other is the
disk that has the same angular momentum distribution with its parent cloud
core, which corresponds to the disk that has just formed. As a result, it is
found that the disks tend to become gravitationally unstable for because ices enable the disks to become low temperature. In the region
closer to the protostar than , it is difficult for a typical
protoplanetary disk to fragment because of the high temperature and the large
Coriolis force. From this result, we conclude that the fragmentation near the
central star is possible but difficult.Comment: accepted for publication in PASJ. Draft version with 26 pages, 8
figures, 1 tabl
Gravitational Instability of Shocked Interstellar Gas Layers
In this paper we investigate gravitational instability of shocked gas layers
using linear analysis. An unperturbed state is a self-gravitating isothermal
layer which grows with time by the accretion of gas through shock fronts due to
a cloud-cloud collision. Since the unperturbed state is not static, and cannot
be described by a self-similar solution, we numerically solved the perturbation
equations and directly integrated them over time. We took account of the
distribution of physical quantities across the thickness. Linearized
Rankine-Hugoniot relations were imposed at shock fronts as boundary conditions.
The following results are found from our unsteady linear analysis: the
perturbation initially evolves in oscillatory mode, and begins to grow at a
certain epoch. The wavenumber of the fastest growing mode is given by
k=2\sqrt{2\pi G\rho_\mathrm{E} {\cal M\mit}}/c_\mathrm{s}, where
and \cal M\mit are the density of parent
clouds, the sound velocity and the Mach number of the collision velocity,
respectively. For this mode, the transition epoch from oscillatory to growing
mode is given by t_g = 1.2/\sqrt{2\pi G\rho_\mathrm{E} {\cal M\mit}}. The
epoch at which the fastest growing mode becomes non-linear is given by
2.4\delta_0^{-0.1}/\sqrt{2\pi G \rho_\mathrm{E}{\cal M\mit}}, where
is the initial amplitude of the perturbation of the column density.
As an application of our linear analysis, we investigate criteria for
collision-induced fragmentation. Collision-induced fragmentation will occur
only when parent clouds are cold, or ,
where and are the radius and the mass of parent clouds, respectively.Comment: 12 pages, 21 figures, accepted for publication in PAS
Gravitational Fragmentation of Expanding Shells. I. Linear Analysis
We perform a linear perturbation analysis of expanding shells driven by
expansions of HII regions. The ambient gas is assumed to be uniform. As an
unperturbed state, we develop a semi-analytic method for deriving the time
evolution of the density profile across the thickness. It is found that the
time evolution of the density profile can be divided into three evolutionary
phases, deceleration-dominated, intermediate, and self-gravity-dominated
phases. The density peak moves relatively from the shock front to the contact
discontinuity as the shell expands. We perform a linear analysis taking into
account the asymmetric density profile obtained by the semi-analytic method,
and imposing the boundary conditions for the shock front and the contact
discontinuity while the evolutionary effect of the shell is neglected. It is
found that the growth rate is enhanced compared with the previous studies based
on the thin-shell approximation. This is due to the boundary effect of the
contact discontinuity and asymmetric density profile that were not taken into
account in previous works.Comment: 13 pages, 13 figures, to be published in the Astrophysical Journa
Dust-cooling--induced Fragmentation of Low-metallicity Clouds
Dynamical collapse and fragmentation of low-metallicity cloud cores is
studied using three-dimensional hydrodynamical calculations, with particular
attention devoted whether the cores fragment in the dust-cooling phase or not.
The cores become elongated in this phase, being unstable to non-spherical
perturbation due to the sudden temperature decrease. In the metallicity range
of 10^{-6}-10^{-5}Z_sun, cores with an initial axis ratio >2 reach a critical
value of the axis ratio (>30) and fragment into multiple small clumps. This
provides a possible mechanism to produce low-mass stars in ultra-metal-poor
environments.Comment: 4 pages, 3 figures, ApJ Letters in pres
Gravitational Fragmentation of Expanding Shells. I. Linear Analysis
We perform a linear perturbation analysis of expanding shells driven by
expansions of HII regions. The ambient gas is assumed to be uniform. As an
unperturbed state, we develop a semi-analytic method for deriving the time
evolution of the density profile across the thickness. It is found that the
time evolution of the density profile can be divided into three evolutionary
phases, deceleration-dominated, intermediate, and self-gravity-dominated
phases. The density peak moves relatively from the shock front to the contact
discontinuity as the shell expands. We perform a linear analysis taking into
account the asymmetric density profile obtained by the semi-analytic method,
and imposing the boundary conditions for the shock front and the contact
discontinuity while the evolutionary effect of the shell is neglected. It is
found that the growth rate is enhanced compared with the previous studies based
on the thin-shell approximation. This is due to the boundary effect of the
contact discontinuity and asymmetric density profile that were not taken into
account in previous works.Comment: 13 pages, 13 figures, to be published in the Astrophysical Journa
TeV Gamma-Rays from Old Supernova Remnants
We study the emission from an old supernova remnant (SNR) with an age of
around 10^5 yrs and that from a giant molecular cloud (GMC) encountered by the
SNR. When the SNR age is around 10^5 yrs, proton acceleration is efficient
enough to emit TeV gamma-rays both at the shock of the SNR and that in the GMC.
The maximum energy of primarily accelerated electrons is so small that TeV
gamma-rays and X-rays are dominated by hadronic processes, pi^0-decay and
synchrotron radiation from secondary electrons, respectively. However, if the
SNR is older than several 10^5 yrs, there are few high-energy particles
emitting TeV gamma-rays because of the energy loss effect and/or the wave
damping effect occurring at low-velocity isothermal shocks. For old SNRs or
SNR-GMC interacting systems capable of generating TeV gamma-ray emitting
particles, we calculated the ratio of TeV gamma-ray (1-10 TeV) to X-ray (2-10
keV) energy flux and found that it can be more than ~10^2. Such a source
showing large flux ratio may be a possible origin of recently discovered
unidentified TeV sources.Comment: 10 pages, 6 figures, 2 tables, MNRAS in pres