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 ($M_{\rm r}<-22.5$ 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 ($M_{\rm r}<-23$ mag), our Petrosian magnitudes, and isophotal magnitudes to 25 ${\rm mag/arcsec^2}$ 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 ($r_{50}$) measured by the SDSS algorithm are smaller than our measurements. As a result, the bright-end of the $r$-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 $M_{\ast}\sim 5\times10^{11} M_{\odot}$ and $M_{\ast}\sim 10^{12} M_{\odot}$ 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

Analysis of Temporal Features of Gamma Ray Bursts in the Internal Shock Model

In a recent paper we have calculated the power density spectrum of Gamma-Ray Bursts arising from multiple shocks in a relativistic wind. The wind optical thickness is one of the factors to which the power spectrum is most sensitive, therefore we have further developed our model by taking into account the photon down-scattering on the cold electrons in the wind. For an almost optically thick wind we identify a combination of ejection features and wind parameters that yield bursts with an average power spectrum in agreement with the observations, and with an efficiency of converting the wind kinetic energy in 50-300 keV emission of order 1%. For the same set of model features the interval time between peaks and pulse fluences have distributions consistent with the log-normal distribution observed in real bursts.Comment: ApJ in press, 2000; with slight revisions; 12 pag, 6 fi

Quantum Algorithm to Solve Satisfiability Problems

A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit Exact Cover problems. The time cost of this algorithm on general SAT problems is discussed.Comment: 5 pages, 3 figure

Is the Number of Giant Arcs in LCDM Consistent With Observations?

We use high-resolution N-body simulations to study the galaxy-cluster cross-sections and the abundance of giant arcs in the $\Lambda$CDM model. Clusters are selected from the simulations using the friends-of-friends method, and their cross-sections for forming giant arcs are analyzed. The background sources are assumed to follow a uniform ellipticity distribution from 0 to 0.5 and to have an area identical to a circular source with diameter 1\arcsec. We find that the optical depth scales as the source redshift approximately as \tau_{1''} = 2.25 \times 10^{-6}/[1+(\zs/3.14)^{-3.42}] (0.6<\zs<7). The amplitude is about 50% higher for an effective source diameter of 0.5\arcsec. The optimal lens redshift for giant arcs with the length-to-width ratio ($L/W$) larger than 10 increases from 0.3 for \zs=1, to 0.5 for \zs=2, and to 0.7-0.8 for \zs>3. The optical depth is sensitive to the source redshift, in qualitative agreement with Wambsganss et al. (2004). However, our overall optical depth appears to be only $\sim$ 10% to 70% of those from previous studies. The differences can be mostly explained by different power spectrum normalizations ($\sigma_8$) used and different ways of determining the $L/W$ ratio. Finite source size and ellipticity have modest effects on the optical depth. We also found that the number of highly magnified (with magnification $|\mu|>10$) and ``undistorted'' images (with $L/W<3$) is comparable to the number of giant arcs with $|\mu|>10$ and $L/W>10$. We conclude that our predicted rate of giant arcs may be lower than the observed rate, although the precise `discrepancy' is still unclear due to uncertainties both in theory and observations.Comment: Revised version after the referee's reports (32 pages,13figures). The paper has been significantly revised with many additions. The new version includes more detailed comparisons with previous studies, including the effects of source size and ellipticity. New discussions about the redshift distribution of lensing clusters and the width of giant arcs have been adde

The first direct detection of a gravitational micro-lens toward the Galactic bulge

We present a direct detection of the gravitational lens that caused the microlensing event MACHO-95-BLG-37. This is the first fully resolved microlensing system involving a source in the Galactic bulge, and the second such system in general. The lens and source are clearly resolved in images taken with the High Resolution Channel of the Advanced Camera for Surveys on board the Hubble Space Telescope (HST) ~9 years after the microlensing event. The presently available data are not sufficient for the final, unambiguous identification of the gravitational lens and the microlensed source. While the light curve models combined with the high resolution photometry for individual objects indicate that the source is red and the lens is blue, the color-magnitude diagram for the line of sight and the observed proper motions strongly support the opposite case. The first scenario points to a metal-poor lens with mass M = ~0.6 M_Sun at the distance D_l = ~4 kpc. In the second scenario the lens could be a main-sequence star with M = 0.8 - 0.9 M_Sun about half-way to the Galactic bulge or in the foreground disk, depending on the extinction.Comment: Accepted for publication in Ap

Semileptonic Decay of BB and D→K0∗(1430)ℓˉνD\to K^*_0(1430) \bar{\ell}\nu From QCD Sum Rule

We calculate $B_{(s)}$, and $D_{(s)}$ to $K^*_0(1430)$ transition form factors, and study semileptonic decays of $B_{(s)}$ and $D_{(s)}\to K_0^*(1430) \bar{\ell}\nu$ based on QCD sum rule. Measuring these semileptonic decays with high statistics will give valuable information on the nature of light scalar mesons.Comment: 13 pages, 5 figures,latex,typos and errors correcte

Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany