14,408 research outputs found
Self-Similar Graphs
For any graph on vertices and for any {\em symmetric} subgraph of
, we construct an infinite sequence of graphs based on the pair
. The First graph in the sequence is , then at each stage replacing
every vertex of the previous graph by a copy of and every edge of the
previous graph by a copy of the new graph is constructed. We call these
graphs {\em self-similar} graphs. We are interested in delineating those pairs
for which the chromatic numbers of the graphs in the sequence are
bounded. Here we have some partial results. When is a complete graph and
is a special matching we show that every graph in the resulting sequence is
an {\em expander} graph.Comment: 13 pages, 1 tabl
Curvature and Acoustic Instabilities in Rotating Fluid Disks
The stability of a rotating fluid disk to the formation of spiral arms is
studied in the tightwinding approximation in the linear regime. The dispersion
relation for spirals that was derived by Bertin et al. is shown to contain a
new, acoustic instability beyond the Lindblad resonances that depends only on
pressure and rotation. In this regime, pressure and gravity exchange roles as
drivers and inhibitors of spiral wave structures. Other instabilities that are
enhanced by pressure are also found in the general dispersion relation by
including higher order terms in the small parameter 1/kr for wavenumber k and
radius r. These instabilities are present even for large values of Toomre's
parameter Q. Unstable growth rates are determined in four cases: a
self-gravitating disk with a flat rotation curve, a self-gravitating disk with
solid body rotation, a non-self-gravitating disk with solid body rotation, and
a non-self-gravitating disk with Keplerian rotation. The most important
application appears to be as a source of spiral structure, possibly leading to
accretion in non-self-gravitating disks, such as some galactic nuclear disks,
disks around black holes, and proto-planetary disks. All of these examples have
short orbital times so the unstable growth time can be small.Comment: 30 pages, 5 figures, scheduled for ApJ 520, August 1, 199
The Formation of the First Stars II. Radiative Feedback Processes and Implications for the Initial Mass Function
We consider the radiative feedback processes that operate during the
formation of the first stars, including the photodissociation of H_2, Ly-alpha
radiation pressure, formation and expansion of an HII region, and disk
photoevaporation. These processes may inhibit continued accretion once the
stellar mass has reached a critical value, and we evaluate this mass separately
for each process. Photodissociation of H_2 in the local dark matter minihalo
occurs relatively early in the growth of the protostar, but we argue this does
not affect subsequent accretion since by this time the depth of the potential
is large enough for accretion to be mediated by atomic cooling. However,
neighboring starless minihalos can be affected. Ionization creates an HII
region in the infalling envelope above and below the accretion disk. Ly-alpha
radiation pressure acting at the boundary of the HII region is effective at
reversing infall from narrow polar directions when the star reaches ~20-30Msun,
but cannot prevent infall from other directions. Expansion of the HII region
beyond the gravitational escape radius for ionized gas occurs at masses
~50-100Msun, depending on the accretion rate and angular momentum of the
inflow. However, again, accretion from the equatorial regions can continue
since the neutral accretion disk has a finite thickness and shields a
substantial fraction of the accretion envelope from direct ionizing flux. At
higher stellar masses, ~140Msun in the fiducial case, the combination of
declining accretion rates and increasing photoevaporation-driven mass loss from
the disk act to effectively halt the increase in the protostellar mass. We
identify this process as the mechanism that terminates the growth of Population
III stars... (abridged)Comment: 31 pages, including 10 figures, accepted to Ap
Flows, Fragmentation, and Star Formation. I. Low-mass Stars in Taurus
The remarkably filamentary spatial distribution of young stars in the Taurus
molecular cloud has significant implications for understanding low-mass star
formation in relatively quiescent conditions. The large scale and regular
spacing of the filaments suggests that small-scale turbulence is of limited
importance, which could be consistent with driving on large scales by flows
which produced the cloud. The small spatial dispersion of stars from gaseous
filaments indicates that the low-mass stars are generally born with small
velocity dispersions relative to their natal gas, of order the sound speed or
less. The spatial distribution of the stars exhibits a mean separation of about
0.25 pc, comparable to the estimated Jeans length in the densest gaseous
filaments, and is consistent with roughly uniform density along the filaments.
The efficiency of star formation in filaments is much higher than elsewhere,
with an associated higher frequency of protostars and accreting T Tauri stars.
The protostellar cores generally are aligned with the filaments, suggesting
that they are produced by gravitational fragmentation, resulting in initially
quasi-prolate cores. Given the absence of massive stars which could strongly
dominate cloud dynamics, Taurus provides important tests of theories of
dispersed low-mass star formation and numerical simulations of molecular cloud
structure and evolution.Comment: 32 pages, 9 figures: to appear in Ap
Statistics of Core Lifetimes in Numerical Simulations of Turbulent, Magnetically Supercritical Molecular Clouds
We present measurements of the mean dense core lifetimes in numerical
simulations of magnetically supercritical, turbulent, isothermal molecular
clouds, in order to compare with observational determinations. "Prestellar"
lifetimes (given as a function of the mean density within the cores, which in
turn is determined by the density threshold n_thr used to define them) are
consistent with observationally reported values, ranging from a few to several
free-fall times. We also present estimates of the fraction of cores in the
"prestellar", "stellar'', and "failed" (those cores that redisperse back into
the environment) stages as a function of n_thr. The number ratios are measured
indirectly in the simulations due to their resolution limitations. Our approach
contains one free parameter, the lifetime of a protostellar object t_yso (Class
0 + Class I stages), which is outside the realm of the simulations. Assuming a
value t_yso = 0.46 Myr, we obtain number ratios of starless to stellar cores
ranging from 4-5 at n_thr = 1.5 x 10^4 cm^-3 to 1 at n_thr = 1.2 x 10^5 cm^-3,
again in good agreement with observational determinations. We also find that
the mass in the failed cores is comparable to that in stellar cores at n_thr =
1.5 x 10^4 cm^-3, but becomes negligible at n_thr = 1.2 x 10^5 cm^-3, in
agreement with recent observational suggestions that at the latter densities
the cores are in general gravitationally dominated. We conclude by noting that
the timescale for core contraction and collapse is virtually the same in the
subcritical, ambipolar diffusion-mediated model of star formation, in the model
of star formation in turbulent supercritical clouds, and in a model
intermediate between the previous two, for currently accepted values of the
clouds' magnetic criticality.Comment: 25 pages, 8 figures, ApJ accepted. Fig.1 animation is at
http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies/Galvan_etal07/Galvan_etal07.htm
Dilute gas of ultracold two-level atoms inside a cavity; generalized Dicke model
We consider a gas of ultracold two-level atoms confined in a cavity, taking
into account for atomic center-of-mass motion and cavity mode variations. We
use the generalized Dicke model, and analyze separately the cases of a
Gaussian, and a standing wave mode shape. Owing to the interplay between
external motional energies of the atoms and internal atomic and field energies,
the phase-diagrams exhibit novel features not encountered in the standard Dicke
model, such as the existence of first and second order phase transitions
between normal and superradiant phases. Due to the quantum description of
atomic motion, internal and external atomic degrees of freedom are highly
correlated leading to modified normal and superradiant phases.Comment: 10 pages, 7 figure
Turbulent Cooling Flows in Molecular Clouds
We propose that inward, subsonic flows arise from the local dissipation of
turbulent motions in molecular clouds. Such "turbulent cooling flows" may
account for recent observations of spatially extended inward motions towards
dense cores. These pressure-driven flows may arise from various types of
turbulence and dissipation mechanisms. For the example of MHD waves and
turbulence damped by ion-neutral friction, sustained cooling flow requires that
the outer gas be sufficiently turbulent, that the inner gas have marginal
field-neutral coupling, and that this coupling decrease sufficiently rapidly
with increasing density. These conditions are most likely met at the transition
between outer regions ionized primarily by UV photons and inner regions ionized
primarily by cosmic rays. If so, turbulent cooling flows can help form dense
cores, with speeds faster than expected for ambipolar diffusion. Such motions
could reduce the time needed for dense core formation and could precede and
enhance the motions of star-forming gravitational infall.Comment: To appear ApJL, Nov.10, 4 ApJ style pages, Postscrip
A Prediction of Brown Dwarfs in Ultracold Molecular Gas
A recent model for the stellar initial mass function (IMF), in which the
stellar masses are randomly sampled down to the thermal Jeans mass from
hierarchically structured pre-stellar clouds, predicts that regions of
ultra-cold CO gas, such as those recently found in nearby galaxies by Allen and
collaborators, should make an abundance of Brown Dwarfs with relatively few
normal stars. This result comes from the low value of the thermal Jeans mass,
considering that the hierarchical cloud model always gives the Salpeter IMF
slope above this lower mass limit. The ultracold CO clouds in the inner disk of
M31 have T~3K and pressures that are probably 10 times higher than in the solar
neighborhood. This gives a mass at the peak of the IMF equal to 0.01 Msun, well
below the Brown Dwarf limit of 0.08 Msun. Using a functional approximation to
the IMF, the ultracold clouds would have 50% of the star-like mass and 90% of
the objects below the Brown Dwarf limit. The brightest of the Brown Dwarfs in
M31 should have an apparent, extinction-corrected K-band magnitude of ~21 mag
in their pre-main sequence phase.Comment: 13 pages, 2 figures, to be published in Astrophysical Journal, Vol
522, September 10, 199
On the rotating wave approximation in the adiabatic limit
I revisit a longstanding question in quantum optics; When is the rotating
wave approximation justified? In terms of the Jaynes-Cummings and Rabi models I
demonstrate that the approximation in general breaks down in the adiabatic
limit regardless of system parameters. This is explicitly shown by comparing
Berry phases of the two models, where it is found that this geometrical phase
is strictly zero in the Rabi model contrary to the non-trivial Berry phase of
the Jaynes-Cummings model. The source of this surprising result is traced back
to different topologies in the two models.Comment: 8 pages, 3 figure
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