16,396 research outputs found
Microlensing of Sub-parsec Massive Binary Black Holes in Lensed QSOs: Light Curves and Size-Wavelength Relation
Sub-parsec binary massive black holes (BBHs) are long anticipated to exist in
many QSOs but remain observationally elusive. In this paper, we propose a novel
method to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSO
hosts a sub-parsec BBH in its center, it is expected that the BBH is surrounded
by a circum-binary disk, each component of the BBH is surrounded by a small
accretion disk, and a gap is opened by the secondary component in between the
circum-binary disk and the two small disks. Assuming such a BBH structure, we
generate mock microlensing light curves for some QSO systems that host BBHs
with typical physical parameters. We show that microlensing light curves of a
BBH QSO system at the infrared-optical-UV bands can be significantly different
from those of corresponding QSO system with a single massive black hole (MBH),
mainly because of the existence of the gap and the rotation of the BBH (and its
associated small disks) around the center of mass. We estimate the half-light
radii of the emission region at different wavelengths from mock light curves
and find that the obtained half-light radius vs. wavelength relations of BBH
QSO systems can be much flatter than those of single MBH QSO systems at a
wavelength range determined by the BBH parameters, such as the total mass, mass
ratio, separation, accretion rates, etc. The difference is primarily due to the
existence of the gap. Such unique features on the light curves and half-light
radius-wavelength relations of BBH QSO systems can be used to select and probe
sub-parsec BBHs in a large number of lensed QSOs to be discovered by current
and future surveys, including the Panoramic Survey Telescope and Rapid Response
System (Pan-STARRS), the Large Synoptic Survey telescope (LSST) and Euclid.Comment: 18 pages, 17 figures, accepted for publication in the Astrophysical
Journa
Ergodicity for the -type Markov Chain
Ergodicity is a fundamental issue for a stochastic process. In this paper, we
refine results on ergodicity for a general type of Markov chain to a specific
type or the -type Markov chain, which has many interesting and
important applications in various areas. It is of interest to obtain conditions
in terms of system parameters or the given information about the process, under
which the chain has various ergodic properties. Specifically, we provide
necessary and sufficient conditions for geometric, strong and polynomial
ergodicity, respectively.Comment: 16 page
Photometric properties and luminosity function of nearby massive early-type galaxies
We perform photometric analyses for a bright early-type galaxy (ETG) sample
with 2949 galaxies ( mag) in the redshift range of 0.05 to
0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo
1. We measure the Petrosian and isophotal magnitudes, as well as the
corresponding half-light radius for each galaxy. We find that for brightest
galaxies ( mag), our Petrosian magnitudes, and isophotal
magnitudes to 25 and 1\% of the sky brightness are on
average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian
values, respectively. In the first case the underestimations are caused by
overestimations in the sky background by the SDSS PHOTO algorithm, while the
latter two are also due to deeper photometry. Similarly, the typical half-light
radii () measured by the SDSS algorithm are smaller than our
measurements. As a result, the bright-end of the -band luminosity function
is found to decline more slowly than previous works. Our measured luminosity
densities at the bright end are more than one order of magnitude higher than
those of Blanton et al. (2003), and the stellar mass densities at and are a few tenths
and a factor of few higher than those of Bernardi et al. (2010). These results
may significantly alleviate the tension in the assembly of massive galaxies
between observations and predictions of the hierarchical structure formation
model.Comment: 43 pages, 14 figures, version accepted for publication in the
Astrophysical Journa
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