Doctor of Philosophy

dissertationBeing the end-product of the hierarchical merging scenario, early-type (elliptical and lenticular) galaxies (ETGs) are the "live" fossil records that permit compelling tests of galaxy formation theories within a cosmological context. Also, ETGs can be extremely luminous and serve as the ideal cosmological tracers in the Universe. Additionally, the mysterious dark matter (DM), which is believed to constitute almost 85% of the observed mass portion, acts as the host of galaxies and hence plays a pivotal role in shaping the observed Universe. A thorough understanding of DM, including its nature, properties, and structures provides crucial insights into the fundamental laws of physics and cosmology. On the luminous side, a hierarchical Bayesian determination o f the velocity-dispersion function of approximately 430000 massive luminous red galaxies observed by the Baryon Oscillation Spectroscopic Survey (BOSS) is performed. We use the full velocity-dispersion likelihood function for each galaxy to make a self-consistent determination of the velocitydispersion distribution parameters as a function of absolute magnitude and redshift. Parameterizing the distribution at each point in the luminosity-redshift plane with a log-normal form, we detect significant evolution in the width of the distribution toward higher intrinsic scatter at higher redshifts, which indicates a more diverse heterogeneity in ETGs at earlier cosmic time. On the dark side, I report the discovery of 40 strong gravitational lenses in the SLACS for the Masses (S4TM) Survey and 33 additional systems with single-lensed images in S4TM and SLACS Surveys, for which upper limits of the Einstein radii are determined. A hierarchical Bayesian analysis reveals strong evidence (4a) of variations of the total mass-density structure toward shallower profiles at larger velocity dispersion when upper limits are incorporated. Estimating the stellar masses based on the HST I-band photometry, we find a significant trend of higher dark-matter fraction at higher velocity dispersion. A Salpeter initial mass function is substantially disfavored for all but the most massive lens galaxies by predicting stellar masses in excess of the total lensing-measured mass. An approach of constraining mass structure via a joint analysis of lensing and stellar kinematics is also outlined, the application of which on a sample of strong lenses shows a 4a evolution trend in the sense of steeper mass profiles at later cosmic times

Assessing the effect of lens mass model in cosmological application with updated galaxy-scale strong gravitational lensing sample

By comparing the dynamical and lensing masses of early-type lens galaxies, one can constrain both the cosmological parameters and the density profiles of galaxies. We explore the constraining power on cosmological parameters and the effect of the lens mass model in this method with 161 galaxy-scale strong lensing systems, which is currently the largest sample with both high resolution imaging and stellar dynamical data. We assume a power-law mass model for the lenses, and consider three different parameterizations for $\gamma$ (i.e., the slope of the total mass density profile) to include the effect of the dependence of $\gamma$ on redshift and surface mass density. When treating $\delta$ (i.e., the slope of the luminosity density profile) as a universal parameter for all lens galaxies, we find the limits on the cosmological parameter $\Omega_m$ are quite weak and biased, and also heavily dependent on the lens mass model in the scenarios of parameterizing $\gamma$ with three different forms. When treating $\delta$ as an observable for each lens, the unbiased estimate of $\Omega_m$ can be obtained only in the scenario of including the dependence of $\gamma$ on both the redshift and the surface mass density, that is $\Omega_m = 0.381^{+0.185}_{-0.154}$ at 68\% confidence level in the framework of a flat $\Lambda$CDM model. We conclude that the significant dependencies of $\gamma$ on both the redshift and the surface mass density, as well as the intrinsic scatter of $\delta$ among the lenses, need to be properly taken into account in this method.Comment: Accepted for publication in MNRAS; 17 pages, 5 figures, 2 table

The Magnification Invariant of Circularly-symmetric Lens Models

In the context of strong gravitational lensing, the magnification of image is of crucial importance to constrain various lens models. For several commonly used quadruple lens models, the magnification invariants, defined as the sum of the signed magnifications of images, have been analytically derived when the image multiplicity is a maximum. In this paper, we further study the magnification of several disk lens models, including (a) exponential disk lens, (b) Gaussian disk lens, (c) modified Hubble profile lens, and another two of the popular three-dimensional symmetrical lens model, (d) NFW lens and (e) Einasto lens. We find that magnification invariant does also exist for each lens model. Moreover, our results show that magnification invariants can be significantly changed by the characteristic surface mass density $\kappa_{\rm c}$.Comment: 14 pages, 6 figures. Accepted for publication in RA

Prediction of Supernova Rates in Known Galaxy-galaxy Strong-lens Systems

We propose a new strategy of finding strongly-lensed supernovae (SNe) by monitoring known galaxy-scale strong-lens systems. Strongly lensed SNe are potentially powerful tools for the study of cosmology, galaxy evolution, and stellar populations, but they are extremely rare. By targeting known strongly lensed starforming galaxies, our strategy significantly boosts the detection efficiency for lensed SNe compared to a blind search. As a reference sample, we compile the 128 galaxy-galaxy strong-lens systems from the Sloan Lens ACS Survey (SLACS), the SLACS for the Masses Survey, and the Baryon Oscillation Spectroscopic Survey Emission-Line Lens Survey. Within this sample, we estimate the rates of strongly-lensed Type Ia SN (SNIa) and core-collapse SN (CCSN) to be $1.23 \pm 0.12$ and $10.4 \pm 1.1$ events per year, respectively. The lensed SN images are expected to be widely separated with a median separation of 2 arcsec. Assuming a conservative fiducial lensing magnification factor of 5 for the most highly magnified SN image, we forecast that a monitoring program with a single-visit depth of 24.7 mag (5$\sigma$ point source, $r$ band) and a cadence of 5 days can detect 0.49 strongly-lensed SNIa event and 2.1 strongly-lensed CCSN events per year within this sample. Our proposed targeted-search strategy is particularly useful for prompt and efficient identifications and follow-up observations of strongly-lensed SN candidates. It also allows telescopes with small field of views and limited time to efficiently discover strongly-lensed SNe with a pencil-beam scanning strategy.Comment: 14 pages, 5 figures, ApJ in pres