32,210 research outputs found
Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity
We study the oscillations of relativistic stars, incorporating key physics
associated with internal composition, thermal gradients and crust elasticity.
Our aim is to develop a formalism which is able to account for the
state-of-the-art understanding of the complex physics associated with these
systems. As a first step, we build models using a modern equation of state
including composition gradients and density discontinuities associated with
internal phase-transitions (like the crust-core transition and the point where
muons first appear in the core). In order to understand the nature of the
oscillation spectrum, we carry out cooling simulations to provide realistic
snapshots of the temperature distribution in the interior as the star evolves
through adolescence. The associated thermal pressure is incorporated in the
perturbation analysis, and we discuss the presence of -modes arising as a
result of thermal effects. We also consider interface modes due to
phase-transitions and the gradual formation of the star's crust and the
emergence of a set of shear modes.Comment: 27 pages, 14 figure
Stellar Velocity Dispersion and Black Hole Mass in the Blazar Markarian 501
The recently discovered correlation between black hole mass and stellar
velocity dispersion provides a new method to determine the masses of black
holes in active galaxies. We have obtained optical spectra of Markarian 501, a
nearby gamma-ray blazar with emission extending to TeV energies. The stellar
velocity dispersion of the host galaxy, measured from the calcium triplet lines
in a 2"x3.7" aperture, is 372 +/- 18 km/s. If Mrk 501 follows the M-sigma
correlation defined for local galaxies, then its central black hole has a mass
of (0.9-3.4)x10^9 solar masses. This is significantly larger than some previous
estimates for the central mass in Mrk 501 that have been based on models for
its nonthermal emission. The host galaxy luminosity implies a black hole of
6x10^8 solar masses, but this is not in severe conflict with the mass derived
from the M-sigma relation because the M_BH-L_bulge correlation has a large
intrinsic scatter. Using the emission-line luminosity to estimate the
bolometric luminosity of the central engine, we find that Mrk 501 radiates at
an extremely sub-Eddington level of L/L_Edd ~ 10^-4. Further applications of
the M-sigma relation to radio-loud active galactic nuclei may be useful for
interpreting unified models and understanding the relationship between radio
galaxies and BL Lac objects.Comment: To appear in ApJ Letters. 5 pages, 2 figure
On some further properties of nonzero-sum diffential games
Optimality principle and open loop-closed loop control relations in nonzero-sum differential game
Buoyancy and g-modes in young superfluid neutron stars
We consider the local dynamics of a realistic neutron star core, including
composition gradients, superfluidity and thermal effects. The main focus is on
the gravity g-modes, which are supported by composition stratification and
thermal gradients. We derive the equations that govern this problem in full
detail, paying particular attention to the input that needs to be provided
through the equation of state and distinguishing between normal and superfluid
regions. The analysis highlights a number of key issues that should be kept in
mind whenever equation of state data is compiled from nuclear physics for use
in neutron star calculations. We provide explicit results for a particular
stellar model and a specific nucleonic equation of state, making use of cooling
simulations to show how the local wave spectrum evolves as the star ages. Our
results show that the composition gradient is effectively dominated by the
muons whenever they are present. When the star cools below the superfluid
transition, the support for g-modes at lower densities (where there are no
muons) is entirely thermal. We confirm the recent suggestion that the g-modes
in this region may be unstable, but our results indicate that this instability
will be weak and would only be present for a brief period of the star's life.
Our analysis accounts for the presence of thermal excitations encoded in
entrainment between the entropy and the superfluid component. Finally, we
discuss the complete spectrum, including the normal sound waves and, in
superfluid regions, the second sound.Comment: 29 pages, 9 figures, submitted to MNRA
Distributed Stochastic Optimization over Time-Varying Noisy Network
This paper is concerned with distributed stochastic multi-agent optimization
problem over a class of time-varying network with slowly decreasing
communication noise effects. This paper considers the problem in composite
optimization setting which is more general in noisy network optimization. It is
noteworthy that existing methods for noisy network optimization are Euclidean
projection based. We present two related different classes of non-Euclidean
methods and investigate their convergence behavior. One is distributed
stochastic composite mirror descent type method (DSCMD-N) which provides a more
general algorithm framework than former works in this literature. As a
counterpart, we also consider a composite dual averaging type method (DSCDA-N)
for noisy network optimization. Some main error bounds for DSCMD-N and DSCDA-N
are obtained. The trade-off among stepsizes, noise decreasing rates,
convergence rates of algorithm is analyzed in detail. To the best of our
knowledge, this is the first work to analyze and derive convergence rates of
optimization algorithm in noisy network optimization. We show that an optimal
rate of in nonsmooth convex optimization can be obtained for
proposed methods under appropriate communication noise condition. Moveover,
convergence rates in different orders are comprehensively derived in both
expectation convergence and high probability convergence sense.Comment: 27 page
Implications of an r-mode in XTE J1751-305: Mass, radius and spin evolution
Recently Strohmayer and Mahmoodifar presented evidence for a coherent
oscillation in the X-ray light curve of the accreting millisecond pulsar XTE
J1751-305, using data taken by RXTE during the 2002 outburst of this source.
They noted that a possible explanation includes the excitation of a non-radial
oscillation mode of the neutron star, either in the form of a g-mode or an
r-mode. The r-mode interpretation has connections with proposed spin-evolution
scenarios for systems such as XTE J1751-305. Here we examine in detail this
interesting possible interpretation. Using the ratio of the observed
oscillation frequency to the star's spin frequency, we derive an approximate
neutron star mass-radius relation which yields reasonable values for the mass
over the range of expected stellar radius (as constrained by observations of
radius-expansion burst sources). However, we argue that the large mode
amplitude suggested by the Strohmayer and Mahmoodifar analysis would inevitably
lead to a large spin-down of the star, inconsistent with its observed spin
evolution, regardless of whether the r-mode itself is in a stable or unstable
regime. We therefore conclude that the r-mode interpretation of the observed
oscillation is not consistent with our current understanding of neutron star
dynamics and must be considered unlikely. Finally we note that, subject to the
availability of a sufficiently accurate timing model, a direct
gravitational-wave search may be able to confirm or reject an r-mode
interpretation unambiguously, should such an event, with a similar inferred
mode amplitude, recur during the Advanced detector era.Comment: 8 pages, 3 figures; submitted to MNRA
- …