1,256 research outputs found
More on super-replication formulae
We extend Norton-Borcherds-Koike's replication formulae to super-replicable
ones by working with the congruence groups and find the product
identities which characterize super-replicable functions. These will provide a
clue for constructing certain new infinite dimensional Lie superalgebras whose
denominator identities coincide with the above product identities. Therefore it
could be one way to find a connection between modular functions and infinite
dimensional Lie algebras.Comment: 28 page
Determination of Stellar Ellipticities in Future Microlensing Surveys
We propose a method that can determine the ellipticities of source stars of
microlensing events produced by binary lenses. The method is based on the fact
that the products of the caustic-crossing timescale, , and the cosine
of the caustic incidence angle of the source trajectory, , of the
individual caustic crossings are different for events involving an elliptical
source, while the products are the same for events associated with a circular
source. The product corresponds to the
caustic-crossing timescale when the incidence angle of the source trajectory is
. For the unique determination of the source ellipticity, resolutions
of at least three caustic crossings are required. Although this requirement is
difficult to achieve under the current observational setup based on
alert/follow-up mode, it will be possible with the advent of future lensing
experiments that will survey wide fields continuously at high cadence. For
typical Galactic bulge events, the difference in between
caustic crossings is of the order of minutes depending on the source
orientations and ellipticities. Considering the monitoring frequency of the
future lensing surveys of times/hr and the improved photometry
especially of the proposed space-based survey, we predict that ellipticity
determinations by the proposed method will be possible for a significant
fraction of multiple caustic-crossing binary lens events involving source stars
having non-negligible ellipticities.Comment: 6 pages, 4 figures, ApJ, submitte
Relativistic Conic Beams and Spatial Distribution of Gamma-Ray Bursts
We study the statistics of gamma-ray bursts, assuming that gamma-ray bursts
are cosmological and they are beamed in the form of a conical jet with a large
bulk Lorentz factor . In such a conic beam, the relativistic ejecta
may have a spatial variation in the bulk Lorentz factor and the density
distribution of gamma-ray emitting jet material. An apparent luminosity
function arises because the axis of the cone is randomly oriented with respect
to the observer's line of sight. The width and the shape of the luminosity
function are determined by the ratio of the beam opening angle of the conical
jet to the inverse of the bulk Lorentz factor, when the bulk Lorentz factor and
the jet material density is uniform on the photon emitting jet surface. We
calculate effects of spatial variation of the Lorentz factor and the spatial
density fluctuations within the cone on the luminosity function and the
statistics of gamma-ray bursts. In particular, we focus on the redshift
distribution of the observed gamma-ray bursts. The maximum distance to and the
average redshift of the gamma-ray bursts are strongly affected by the
beaming-induced luminosity function. The bursts with the angle-dependent
Lorentz factor which peaks at the center of the cone have substantially higher
average gamma-ray burst redshifts. When both the jet material density and the
Lorentz factor are inhomogeneous in the conical beam, the average redshift of
the bursts could be 5 times higher than that of the case in which relativistic
jet is completely homogeneous and structureless. Even the simplest models for
the gamma-ray burst jets and their apparent luminosity distributions have a
significant effect on the redshift distribution of the gamma-ray bursts.Comment: 15 pages, 4 figures, submitted to ApJ
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