691 research outputs found
Exploring the long-term variability and evolutionary stage of the interacting binary DQ Velorum
To progress in the comprehension of the double periodic variable (DPV)
phenomenon, we analyse a series of optical spectra of the DPV system DQ Velorum
during much of its long-term cycle. In addition, we investigate the
evolutionary history of DQ Vel using theoretical evolutionary models to obtain
the best representation for the current observed stellar and orbital parameters
of the binary. We investigate the evolution of DQ Vel through theoretical
evolutionary models to estimate the age and the mass transfer rate which are
compared with those of its twin V393 Scorpii. Donor subtracted spectra covering
around 60% of the long-term cycle, allow us to investigate time-modulated
spectral variations of the gainer star plus the disc. We compare the observed
stellar parameters of the system with a grid of theoretical evolutionary tracks
computed under a conservative and a non-conservative evolution regime. We have
found that the EW of Balmer and helium lines in the donor subtracted spectra
are modulated with the long-term cycle. We observe a strenghtening in the EWs
in all analysed spectral features at the minimum of the long-term cycle which
might be related to an extra line emission during the maximum of the long-term
variability. Difference spectra obtained at the secondary eclipse support this
scenario. We have found that a non-conservative evolutionary model is a better
representation for the current observed properties of the system. The best
evolutionary model suggests that DQ Vel has an age of 7.40 x 10^{7} yr and is
currently in a low mass transfer rate (-9.8x10^{-9} Msun/yr) stage, after a
mass transfer burst episode. Comparing the evolutionary stages of DQ Vel and
V393 Sco we observed that the former is an older system with a lower mass
transfer rate. This might explain the differences observed in the physical
parameters of their accretion discs.Comment: 10 pages, 13 figure
Moments of a single entry of circular orthogonal ensembles and Weingarten calculus
Consider a symmetric unitary random matrix
from a circular orthogonal ensemble. In this paper, we study moments of a
single entry . For a diagonal entry we give the explicit
values of the moments, and for an off-diagonal entry we give leading
and subleading terms in the asymptotic expansion with respect to a large matrix
size . Our technique is to apply the Weingarten calculus for a
Haar-distributed unitary matrix.Comment: 17 page
General moments of the inverse real Wishart distribution and orthogonal Weingarten functions
Let be a random positive definite symmetric matrix distributed according
to a real Wishart distribution and let be its inverse
matrix. We compute general moments explicitly. To do so, we employ the orthogonal Weingarten
function, which was recently introduced in the study for Haar-distributed
orthogonal matrices. As applications, we give formulas for moments of traces of
a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it
includes Appendi
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