19,143 research outputs found
A formalism for the construction of binary neutron stars with arbitrary circulation
Most numerical models of binary stars - in particular neutron stars in
compact binaries - assume the companions to be either corotational or
irrotational. Either one of these assumptions leads to a significant
simplification in the hydrodynamic equations of stationary equilibrium. In this
paper we develop a new formalism for the construction of binary stars with
circulation intermediate between corotational and irrotational. Generalizing
the equations for irrotational flow we cast the Euler equation, which is an
algebraic equation in the case of corotational or irrotational fluid flow, as
an elliptic equation for a new auxiliary quantity. We also suggest a
parameterized decomposition of the fluid flow that allows for a variation of
the stellar circulation.Comment: 8 pages, no figures; published version with erratu
Luminosity versus Rotation in a Supermassive Star
We determine the effect of rotation on the luminosity of supermassive stars.
We apply the Roche model to calculate analytically the emitted radiation from a
uniformly rotating, radiation-dominated supermassive configuration. We find
that the luminosity at maximum rotation, when mass at the equator orbits at the
Kepler period, is reduced by ~36% below the usual Eddington luminosity from the
corresponding nonrotating star. A supermassive star is believed to evolve in a
quasistationary manner along such a maximally rotating ``mass-shedding''
sequence before reaching the point of dynamical instability; hence this reduced
luminosity determines the evolutionary timescale. Our result therefore implies
that the lifetime of a supermassive star prior to dynamical collapse is ~56%
longer than the value typically estimated by employing the usual Eddington
luminosity.Comment: 5 pages, 2 figures, uses emulateapj.sty; to appear in Ap
Photoassociation adiabatic passage of ultracold Rb atoms to form ultracold Rb_2 molecules
We theoretically explore photoassociation by Adiabatic Passage of two
colliding cold ^{85}Rb atoms in an atomic trap to form an ultracold Rb_2
molecule. We consider the incoherent thermal nature of the scattering process
in a trap and show that coherent manipulations of the atomic ensemble, such as
adiabatic passage, are feasible if performed within the coherence time window
dictated by the temperature, which is relatively long for cold atoms. We show
that a sequence of ~2*10^7 pulses of moderate intensities, each lasting ~750
ns, can photoassociate a large fraction of the atomic ensemble at temperature
of 100 microkelvin and density of 10^{11} atoms/cm^3. Use of multiple pulse
sequences makes it possible to populate the ground vibrational state. Employing
spontaneous decay from a selected excited state, one can accumulate the
molecules in a narrow distribution of vibrational states in the ground
electronic potential. Alternatively, by removing the created molecules from the
beam path between pulse sets, one can create a low-density ensemble of
molecules in their ground ro-vibrational state.Comment: RevTex, 23 pages, 9 figure
Gravity darkening and brightening in binaries
We apply a von Zeipel gravity darkening model to corotating binaries to
obtain a simple, analytical expression for the emergent radiative flux from a
tidally distorted primary orbiting a point-mass secondary. We adopt a simple
Roche model to determine the envelope structure of the primary, assumed massive
and centrally condensed, and use the results to calculate the flux. As for
single rotating stars, gravity darkening reduces the flux along the stellar
equator of the primary, but, unlike for rotating stars, we find that gravity
brightening enhances the flux in a region around the stellar poles. We identify
a critical limiting separation beyond which hydrostatic equilibrium no longer
is possible, whereby the flux vanishes at the point on the stellar equator of
the primary facing the companion. For equal-mass binaries, the total luminosity
is reduced by about 13 % when this limiting separation is reached.Comment: 7 pages, 5 figures, matches version published in Astrophysical
Journa
Merger of white dwarf-neutron star binaries: Prelude to hydrodynamic simulations in general relativity
White dwarf-neutron star binaries generate detectable gravitational
radiation. We construct Newtonian equilibrium models of corotational white
dwarf-neutron star (WDNS) binaries in circular orbit and find that these models
terminate at the Roche limit. At this point the binary will undergo either
stable mass transfer (SMT) and evolve on a secular time scale, or unstable mass
transfer (UMT), which results in the tidal disruption of the WD. The path a
given binary will follow depends primarily on its mass ratio. We analyze the
fate of known WDNS binaries and use population synthesis results to estimate
the number of LISA-resolved galactic binaries that will undergo either SMT or
UMT. We model the quasistationary SMT epoch by solving a set of simple ordinary
differential equations and compute the corresponding gravitational waveforms.
Finally, we discuss in general terms the possible fate of binaries that undergo
UMT and construct approximate Newtonian equilibrium configurations of merged
WDNS remnants. We use these configurations to assess plausible outcomes of our
future, fully relativistic simulations of these systems. If sufficient WD
debris lands on the NS, the remnant may collapse, whereby the gravitational
waves from the inspiral, merger, and collapse phases will sweep from LISA
through LIGO frequency bands. If the debris forms a disk about the NS, it may
fragment and form planets.Comment: 28 pages, 25 figures, 6 table
Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths
The problem of counting plane trees with edges and an even or an odd
number of leaves was studied by Eu, Liu and Yeh, in connection with an identity
on coloring nets due to Stanley. This identity was also obtained by Bonin,
Shapiro and Simion in their study of Schr\"oder paths, and it was recently
derived by Coker using the Lagrange inversion formula. An equivalent problem
for partitions was independently studied by Klazar. We present three parity
reversing involutions, one for unlabelled plane trees, the other for labelled
plane trees and one for 2-Motzkin paths which are in one-to-one correspondence
with Dyck paths.Comment: 8 pages, 4 figure
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