3,667 research outputs found
1+1+2 Electromagnetic perturbations on general LRS space-times: Regge-Wheeler and Bardeen-Press equations
We use the, covariant and gauge-invariant, 1+1+2 formalism developed by
Clarkson and Barrett, and develop new techniques, to decouple electromagnetic
(EM) perturbations on arbitrary locally rotationally symmetric (LRS)
space-times. Ultimately, we derive 3 decoupled complex equations governing 3
complex scalars. One of these is a new Regge-Wheeler (RW) equation generalized
for LRS space-times, whereas the remaining two are new generalizations of the
Bardeen-Press (BP) equations. This is achieved by first using linear algebra
techniques to rewrite the first-order Maxwell equations in a new complex 1+1+2
form which is conducive to decoupling. This new complex system immediately
yields the generalized RW equation, and furthermore, we also derive a decoupled
equation governing a newly defined complex EM 2-vector. Subsequently, a further
decomposition of the 1+1+2 formalism into a 1+1+1+1 formalism is developed,
allowing us to decompose the complex EM 2-vector, and its governing equations,
into spin-weighted scalars, giving rise to the generalized BP equations
The Arches Cluster: Extended Structure and Tidal Radius
At a projected distance of ~26 pc from Sgr A*, the Arches cluster provides
insight to star formation in the extreme Galactic Center (GC) environment.
Despite its importance, many key properties such as the cluster's internal
structure and orbital history are not well known. We present an astrometric and
photometric study of the outer region of the Arches cluster (R > 6.25") using
HST WFC3IR. Using proper motions we calculate membership probabilities for
stars down to F153M = 20 mag (~2.5 M_sun) over a 120" x 120" field of view, an
area 144 times larger than previous astrometric studies of the cluster. We
construct the radial profile of the Arches to a radius of 75" (~3 pc at 8 kpc),
which can be well described by a single power law. From this profile we place a
3-sigma lower limit of 2.8 pc on the observed tidal radius, which is larger
than the predicted tidal radius (1 - 2.5 pc). Evidence of mass segregation is
observed throughout the cluster and no tidal tail structures are apparent along
the orbital path. The absence of breaks in the profile suggests that the Arches
has not likely experienced its closest approach to the GC between ~0.2 - 1 Myr
ago. If accurate, this constraint indicates that the cluster is on a prograde
orbit and is located front of the sky plane that intersects Sgr A*. However,
further simulations of clusters in the GC potential are required to interpret
the observed profile with more confidence.Comment: 24 pages (17-page main text, 7-page appendix), 24 figures, accepted
to Ap
1+1+2 Electromagnetic perturbations on non-vacuum LRS class II space-times: Decoupling scalar and 2-vector harmonic amplitudes
We use the covariant and gauge-invariant 1+1+2 formalism of Clarkson and
Barrett \cite{Clarkson2003} to analyze electromagnetic (EM) perturbations on
non-vacuum {\it locally rotationally symmetric} (LRS) class II space-times.
Ultimately, we show how to derive six real decoupled equations governing the
total of six EM scalar and 2-vector harmonic amplitudes. Four of these are new,
and result from expanding the complex EM 2-vector which we defined in
\cite{Burston2007} in terms of EM 2-vector harmonic amplitudes. We are then
able to show that there are four precise combinations of the amplitudes that
decouple, two of these are polar perturbations whereas the remaining two are
axial. The remaining two decoupled equations are the generalized Regge-Wheeler
equations which were developed previously in \cite{Betschart2004}, and these
govern the two EM scalar harmonic amplitudes. However, our analysis generalizes
this by including a full description and classification of energy-momentum
sources, such as charges and currents.Comment: 9 page
The Quintuplet Cluster: Extended Structure and Tidal Radius
The Quintuplet star cluster is one of only three known young ( Myr)
massive (M M) clusters within pc of the Galactic
Center. In order to explore star cluster formation and evolution in this
extreme environment, we analyze the Quintuplet's dynamical structure. Using the
HST WFC3-IR instrument, we take astrometric and photometric observations of the
Quintuplet covering a field-of-view, which is times
larger than those of previous proper motion studies of the Quintuplet. We
generate a catalog of the Quintuplet region with multi-band, near-infrared
photometry, proper motions, and cluster membership probabilities for
stars. We present the radial density profile of candidate Quintuplet
cluster members with M out to pc from the cluster
center. A lower limit of pc is placed on the tidal radius,
indicating the lack of a tidal truncation within this radius range. Only weak
evidence for mass segregation is found, in contrast to the strong mass
segregation found in the Arches cluster, a second and slightly younger massive
cluster near the Galactic Center. It is possible that tidal stripping hampers a
mass segregation signature, though we find no evidence of spatial asymmetry.
Assuming that the Arches and Quintuplet formed with comparable extent, our
measurement of the Quintuplet's comparatively large core radius of
pc provides strong empirical evidence that young massive
clusters in the Galactic Center dissolve on a several Myr timescale.Comment: 25 pages (21-page main text, 4-page appendix), 18 figures, submitted
to Ap
On detecting terrestrial planets with timing of giant planet transits
The transits of a planet on a Keplerian orbit occur at time intervals exactly
equal to the period of the orbit. If a second planet is introduced the orbit is
not Keplerian and the transits are no longer exactly periodic. We compute the
magnitude of these variations in the timing of the transits, dt. We investigate
analytically several limiting cases: (i) interior perturbing planets with much
smaller periods; (ii) exterior perturbing planets on eccentric orbits with much
larger periods; (iii) both planets on circular orbits with arbitrary period
ratio but not in resonance; and (iv) planets on initially circular orbits
locked in resonance. Case (iv) is perhaps the most interesting case since some
systems are known to be in resonances and the perturbations are the largest. As
long as the perturber is more massive than the transiting planet, the timing
variations would be of order of the period regardless of the perturber mass!
For lighter perturbers, we show that the timing variations are smaller than the
period by the perturber to transiting planet mass ratio. An earth mass planet
in 2:1 resonance with a 3-day period transiting planet (e.g. HD 209458b) would
cause timing variations of order 3 minutes, which would be accumulated over a
year. These are easily detectable with current ground-based measurements. For
the case of both planets on eccentric orbits, we compute numerically the
transit timing variations for several cases of known multiplanet systems
assuming they were edge-on. Transit timing measurements may be used to
constrain the masses and radii of the planetary system and, when combined with
radial velocity measurements, to break the degeneracy between mass and radius
of the host star. (abstract truncated)Comment: 21 pages, 9 figures, submitted to MNRA
A generalized linear Hubble law for an inhomogeneous barotropic Universe
In this work, I present a generalized linear Hubble law for a barotropic
spherically symmetric inhomogeneous spacetime, which is in principle compatible
with the acceleration of the cosmic expansion obtained as a result of high
redshift Supernovae data. The new Hubble function, defined by this law, has two
additional terms besides an expansion one, similar to the usual volume
expansion one of the FLRW models, but now due to an angular expansion. The
first additional term is dipolar and is a consequence of the existence of a
kinematic acceleration of the observer, generated by a negative gradient of
pressure or of mass-energy density. The second one is quadrupolar and due to
the shear. Both additional terms are anisotropic for off-centre observers,
because of to their dependence on a telescopic angle of observation. This
generalized linear Hubble law could explain, in a cosmological setting, the
observed large scale flow of matter, without to have recourse to peculiar
velocity-type newtonian models. It is pointed out also, that the matter dipole
direction should coincide with the CBR dipole one.Comment: 9 pages, LaTeX, to be published in Class. Quantum Gra
Existence and Uniqueness of Tri-tronqu\'ee Solutions of the second Painlev\'e hierarchy
The first five classical Painlev\'e equations are known to have solutions
described by divergent asymptotic power series near infinity. Here we prove
that such solutions also exist for the infinite hierarchy of equations
associated with the second Painlev\'e equation. Moreover we prove that these
are unique in certain sectors near infinity.Comment: 13 pages, Late
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