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

Object DUO 2: A New Binary Lens Candidate

We present the light curve of an unusual variable object, DUO 2, detected during the search for microlensing events by the DUO project. The star remained stable for more than 150 days before it brightened by more than two magnitudes in 6 days in the B and R bands. The light curves are achromatic during the variability. We consider possible explanations of the photometric behavior, with particular emphasis on the binary lens interpretation of the event. The masses of the lenses are quite small, with the companion possibly in the range of a brown dwarf or even a few times of Jupiter. We report evidence of blending of the source by a companion through the first detection of shift in the light centroid among all the microlensing experiments. This shift sets a lower limit of $0.3^{\prime\prime}$ on the separation between the stars. The best lens model obtained requires moderate blending, which was what motivated us to check the centroid shift that was subsequently found. The best lens model predicts a separation of $1^{\prime\prime}$ between the two blended stars. This prediction was recently tested using two CCD images taken under good seeing conditions. Both images show two components. Their separation and position angle are in good agreement with our model.Comment: uuencoded, compressed PostScript, 4 pages, 4 figures (in text). Accepted for publication in Astronomy and Astrophysics Letter

Sketch-based virtual human modelling and animation

Animated virtual humans created by skilled artists play a remarkable role in today’s public entertainment. However, ordinary users are still treated as audiences due to the lack of appropriate expertise, equipment, and computer skills. We developed a new method and a novel sketching interface, which enable anyone who can draw to “sketch-out” 3D virtual humans and animation. We devised a “Stick FigureFleshing-outSkin Mapping” graphical pipeline, which decomposes the complexity of figure drawing and considerably boosts the modelling and animation efficiency. We developed a gesture-based method for 3D pose reconstruction from 2D stick figure drawings. We investigated a “Creative Model-based Method”, which performs a human perception process to transfer users’ 2D freehand sketches into 3D human bodies of various body sizes, shapes and fat distributions. Our current system supports character animation in various forms including articulated figure animation, 3D mesh model animation, and 2D contour/NPR animation with personalised drawing styles. Moreover, this interface also supports sketch-based crowd animation and 2D storyboarding of 3D multiple character interactions. A preliminary user study was conducted to support the overall system design. Our system has been formally tested by various users on Tablet PC. After minimal training, even a beginner can create vivid virtual humans and animate them within minutes

Sketching-out virtual humans: From 2d storyboarding to immediate 3d character animation

Virtual beings are playing a remarkable role in today’s public entertainment, while ordinary users are still treated as audiences due to the lack of appropriate expertise, equipment, and computer skills. In this paper, we present a fast and intuitive storyboarding interface, which enables users to sketch-out 3D virtual humans, 2D/3D animations, and character intercommunication. We devised an intuitive “stick figurefleshing-outskin mapping” graphical animation pipeline, which realises the whole process of key framing, 3D pose reconstruction, virtual human modelling, motion path/timing control, and the final animation synthesis by almost pure 2D sketching. A “creative model-based method” is developed, which emulates a human perception process, to generate the 3D human bodies of variational sizes, shapes, and fat distributions. Meanwhile, our current system also supports the sketch-based crowd animation and the storyboarding of the 3D multiple character intercommunication. This system has been formally tested by various users on Tablet PC. After minimal training, even a beginner can create vivid virtual humans and animate them within minutes

Sketching-out virtual humans: A smart interface for human modelling and animation

In this paper, we present a fast and intuitive interface for sketching out 3D virtual humans and animation. The user draws stick figure key frames first and chooses one for “fleshing-out” with freehand body contours. The system automatically constructs a plausible 3D skin surface from the rendered figure, and maps it onto the posed stick figures to produce the 3D character animation. A “creative model-based method” is developed, which performs a human perception process to generate 3D human bodies of various body sizes, shapes and fat distributions. In this approach, an anatomical 3D generic model has been created with three distinct layers: skeleton, fat tissue, and skin. It can be transformed sequentially through rigid morphing, fatness morphing, and surface fitting to match the original 2D sketch. An auto-beautification function is also offered to regularise the 3D asymmetrical bodies from users’ imperfect figure sketches. Our current system delivers character animation in various forms, including articulated figure animation, 3D mesh model animation, 2D contour figure animation, and even 2D NPR animation with personalised drawing styles. The system has been formally tested by various users on Tablet PC. After minimal training, even a beginner can create vivid virtual humans and animate them within minutes

Delay-dependent robust stability of stochastic delay systems with Markovian switching

In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method

Limits on the evolution of galaxies from the statistics of gravitational lenses

We use gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS) to constrain the evolution of galaxies since redshift $z \sim 1$ in the current \LCDM cosmology. This constraint is unique as it is based on a mass-selected lens sample of galaxies. Our method of statistical analysis is the same as in Chae (2003). We parametrise the early-type number density evolution in the form of $(1+z)^{\nu_n}$ and the velocity dispersion as $(1+z)^{\nu_v}$. We find that $\nu_n=-0.11^{+0.82}_{-0.89}$ ($1\sigma$) if we assume $\nu_v =0$, implying that the number density of early-type galaxies is within 50% to 164% of the present-day value at redshift $z=1$. Allowing the velocity dispersion to evolve, we find that $\nu_v=-0.4^{+0.5}_{-0.4}$ ($1\sigma$), indicating that the velocity dispersion must be within 57% and 107% of the present-day value at $z=1$. These results are consistent with the early formation and passive evolution of early-type galaxies. More stringent limits from lensing can be obtained from future large lens surveys and by using very high-redshift quasars (z \ga 5) such as those found from the Sloan Digital Sky Survey.Comment: 10 pages (preprint format), 2 figures, ApJL in press (December 20th issue

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