730 research outputs found

### Discovery of a 3.6-hr Eclipsing Luminous X-Ray Binary in the Galaxy NGC 4214

We report the discovery of an eclipsing X-ray binary with a 3.62-hr period
within 24" of the center of the dwarf starburst galaxy NGC 4214. The orbital
period places interesting constraints on the nature of the binary, and allows
for a few very different interpretations. The most likely possibility is that
the source lies within NGC 4214 and has an X-ray luminosity of up to 7 e38
ergs/s. In this case the binary may well be comprised of a naked He-burning
donor star with a neutron-star accretor, though a stellar-mass black-hole
accretor cannot be completely excluded. There is no obvious evidence for a
strong stellar wind in the X-ray orbital light curve that would be expected
from a massive He star; thus, the mass of the He star should be <3-4 solar
masses. If correct, this would represent a new class of very luminous X-ray
binary -- perhaps related to Cyg X-3. Other less likely possibilities include a
conventional low-mass X-ray binary that somehow manages to produce such a high
X-ray luminosity and is apparently persistent over an interval of years; or a
foreground AM Her binary of much lower luminosity that fortuitously lies in the
direction of NGC 4214. Any model for this system must accommodate the lack of
an optical counterpart down to a limiting magnitude of 22.6 in the visible.Comment: 7 pages, ApJ accepted versio

### The Distance Geometry of Music

We demonstrate relationships between the classic Euclidean algorithm and many
other fields of study, particularly in the context of music and distance
geometry. Specifically, we show how the structure of the Euclidean algorithm
defines a family of rhythms which encompass over forty timelines
(\emph{ostinatos}) from traditional world music. We prove that these
\emph{Euclidean rhythms} have the mathematical property that their onset
patterns are distributed as evenly as possible: they maximize the sum of the
Euclidean distances between all pairs of onsets, viewing onsets as points on a
circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this
notion of \emph{evenness}. We also show that essentially all Euclidean rhythms
are \emph{deep}: each distinct distance between onsets occurs with a unique
multiplicity, and these multiplicies form an interval $1,2,...,k-1$. Finally,
we characterize all deep rhythms, showing that they form a subclass of
generated rhythms, which in turn proves a useful property called shelling. All
of our results for musical rhythms apply equally well to musical scales. In
addition, many of the problems we explore are interesting in their own right as
distance geometry problems on the circle; some of the same problems were
explored by Erd\H{o}s in the plane.Comment: This is the full version of the paper: "The distance geometry of deep
rhythms and scales." 17th Canadian Conference on Computational Geometry (CCCG
'05), University of Windsor, Canada, 200

### New Constraints on Quantum Gravity from X-ray and Gamma-Ray Observations

One aspect of the quantum nature of spacetime is its "foaminess" at very
small scales. Many models for spacetime foam are defined by the accumulation
power $\alpha$, which parameterizes the rate at which Planck-scale spatial
uncertainties (and thephase shifts they produce) may accumulate over large
path-lengths. Here $\alpha$ is defined by theexpression for the path-length
fluctuations, $\delta \ell$, of a source at distance $\ell$, wherein $\delta
\ell \simeq \ell^{1 - \alpha} \ell_P^{\alpha}$, with $\ell_P$ being the Planck
length. We reassess previous proposals to use astronomical observations
ofdistant quasars and AGN to test models of spacetime foam. We show explicitly
how wavefront distortions on small scales cause the image intensity to decay to
the point where distant objects become undetectable when the path-length
fluctuations become comparable to the wavelength of the radiation. We use X-ray
observations from {\em Chandra} to set the constraint $\alpha \gtrsim 0.58$,
which rules out the random walk model (with $\alpha = 1/2$). Much firmer
constraints canbe set utilizing detections of quasars at GeV energies with {\em
Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $\alpha
\gtrsim 0.67$ and $\alpha \gtrsim 0.72$, respectively. These limits on $\alpha$
seem to rule out $\alpha = 2/3$, the model of some physical interest.Comment: 11 pages, 9 figures, ApJ, in pres

### An Optimal Algorithm to Compute the Inverse Beacon Attraction Region

The beacon model is a recent paradigm for guiding the trajectory of messages or small robotic agents in complex environments. A beacon is a fixed point with an attraction pull that can move points within a given polygon. Points move greedily towards a beacon: if unobstructed, they move along a straight line to the beacon, and otherwise they slide on the edges of the polygon. The Euclidean distance from a moving point to a beacon is monotonically decreasing. A given beacon attracts a point if the point eventually reaches the beacon.
The problem of attracting all points within a polygon with a set of beacons can be viewed as a variation of the art gallery problem. Unlike most variations, the beacon attraction has the intriguing property of being asymmetric, leading to separate definitions of attraction region and inverse attraction region. The attraction region of a beacon is the set of points that it attracts. It is connected and can be computed in linear time for simple polygons. By contrast, it is known that the inverse attraction region of a point - the set of beacon positions that attract it - could have Omega(n) disjoint connected components.
In this paper, we prove that, in spite of this, the total complexity of the inverse attraction region of a point in a simple polygon is linear, and present a O(n log n) time algorithm to construct it. This improves upon the best previous algorithm which required O(n^3) time and O(n^2) space. Furthermore we prove a matching Omega(n log n) lower bound for this task in the algebraic computation tree model of computation, even if the polygon is monotone

### Transits and Occultations of an Earth-Sized Planet in an 8.5-Hour Orbit

We report the discovery of an Earth-sized planet ($1.16\pm 0.19 R_\oplus$) in
an 8.5-hour orbit around a late G-type star (KIC 8435766, Kepler-78). The
object was identified in a search for short-period planets in the {\it Kepler}
database and confirmed to be a transiting planet (as opposed to an eclipsing
stellar system) through the absence of ellipsoidal light variations or
substantial radial-velocity variations. The unusually short orbital period and
the relative brightness of the host star ($m_{\rm Kep}$ = 11.5) enable robust
detections of the changing illumination of the visible hemisphere of the
planet, as well as the occultations of the planet by the star. We interpret
these signals as representing a combination of reflected and reprocessed light,
with the highest planet dayside temperature in the range of 2300 K to 3100 K.
Follow-up spectroscopy combined with finer sampling photometric observations
will further pin down the system parameters and may even yield the mass of the
planet.Comment: Accepted for publication, ApJ, 10 pages and 6 figure

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