Dynamical System of Scalar Field from 2-Dimension to 3-D and its Cosmological Implication

We give the three-dimensional dynamical autonomous systems for most of the popular scalar field dark energy models including (phantom) quintessence, (phantom) tachyon, k-essence and general non-canonical scalar field models, change the dynamical variables from variables $(x, y, \lambda)$ to observable related variables $(w_{\phi}, \Omega_{\phi}, \lambda)$, and show the intimate relationships between those scalar fields that the three-dimensional system of k-essence can reduce to (phantom) tachyon, general non-canonical scalar field can reduce to (phantom) quintessence and k-essence can also reduce to (phantom) quintessence for some special cases. For the applications of the three-dimensional dynamical systems, we investigate several special cases and give the exactly dynamical solutions in detail. In the end of this paper, we argue that, it is more convenient and also has more physical meaning to express the differential equations of dynamical systems in $(w_{\phi}, \Omega_{\phi}, \lambda)$ instead of variables $(x, y, \lambda)$ and to investigate the dynamical system in 3-Dimension instead of 2-Dimension. We also raise a question about the possibility of the chaotic behavior in the spatially flat single scalar field FRW cosmological models in the presence of ordinary matter.Comment: 20 pages, 8 figures,some references added. Minor changes according to the suggestions from referee

The Host Haloes of Lyman Break Galaxies and Sub-millimeter Sources

We use the observed sizes and star formation rates of Lyman-break galaxies (LBGs) to understand their properties expected in the hierarchical scenario of galaxy formation. The observed size distribution constrains the masses of the host haloes of LBGs from below, while the observed star-formation distribution constrains the masses from above. Assuming a flat CDM model with a cosmological constant ($\Omega_\Lambda=0.7$), we find that consistency with observations requires the circular velocities of LBG host haloes to be in the range 100--$300 {\rm km s^{-1}}$. The predicted comoving correlation length of these objects is $\sim 3 h^{-1}{\rm Mpc}$, and the predicted velocity dispersion of their stellar contents is typically $70 {\rm km s^{-1}}$. The same prescription applied to larger haloes in the CDM cosmogony predicts the existence of galaxies with star formation rates $\sim 1000 {\rm M_\odot yr^{-1}}$ at redshift $z\sim 3$. We explore the possibility of identifying these galaxies to be the bright sub-millimeter (sub-mm) sources detected by SCUBA. The model predicts that the host haloes of these sub-mm sources are massive. These galaxies are predicted to be strongly correlated, with a comoving correlation length of $\sim 7 h^{-1}{\rm Mpc}$. The descendants of the bright sub-mm sources should reside in clusters of galaxies at the present time, and it is likely that these objects are the progenitors of giant ellipticals. The model predicts the existence of a relatively bright and red population of galaxies at $z\sim 3$, which may be observed in the K-band.Comment: 27 pages, 14 figures, submitted to MNRA

The Fundamental Plane of Spiral Galaxies: Theoretical Expectations

Current theory of disk galaxy formation is used to study fundamental-plane (FP) type of relations for disk galaxies. We examine how the changes in model parameters affect these relations and explore the possibility of using such relations to constrain theoretical models. The distribution of galaxy disks in the space of their fundamental properties are predicted to be concentrated in a plane, with the Tully-Fisher (TF) relation (a relation between luminosity $L$ and maximum rotation velocity $V_m$) being an almost edge-on view. Using rotation velocities at larger radii generally leads to larger TF scatter. In searching for a third parameter, we find that both the disk scale-length $R_d$ (or surface brightness) and the rotation-curve shape are correlated with the TF scatter. The FP relation in the (\Log L, \Log V_m, \Log R_d)-space obtained from the theory is $L\propto R_d^{\alpha'} V_m^{\beta'}$, with ${\alpha'}\sim 0.50$ and ${\beta'}\sim 2.60$, consistent with the preliminary result we obtain from observational data. Among the model parameters we probe, variation in any of them can generate significant scatter in the TF relation, but the effects of the spin parameter and halo concentration can be reduced significantly by introducing $R_d$ while the scatter caused by varying $m_d$ (the ratio between disk mass and halo mass) is most effectively reduced by introducing the parameters which describes the rotation-curve shape. The TF and FP relations combined should therefore provide useful constraints on models of galaxy formation.Comment: 25 pages, 11 figures, 4 tables; submitted to MNRA

Mass Reconstruction of Galaxy-scale Strong Gravitational Lenses Using a Broken Power-law Model

With mock strong gravitational lensing images, we investigate the performance of the broken power-law (BPL) model proposed by \citet{2020ApJ...892...62D} on the mass reconstruction of galaxy-scale lenses. An end-to-end test is carried out, including the creation of mock strong lensing images, the subtraction of lens light, and the reconstruction of lensed images, where the lenses are selected from the galaxies in the Illustris-1 simulation. We notice that, regardless of the adopted mass models (the BPL model or its special cases), the Einstein radius can be robustly determined from imaging data alone, and the median bias is typically less than $1\%$. Away from the Einstein radius, the lens mass distribution tends to be harder to measure, especially at radii where there are no lensed images detected. We find that, with rigid priors, the BPL model can clearly outperform the single power-law models by achieving $<5\%$ median bias on the radial convergence profile within the Einstein radius. As for the source light reconstructions, they are found to be sensitive to both lens light contamination and lens mass models, where the BPL model with rigid priors still performs best when there is no lens light contamination. We show that, by correcting for the projection effect, the BPL model can estimate the aperture and luminosity weighted line-of-sight velocity dispersions to an accuracy of $\sim6\%$ scatter. These results highlight the great potential of the BPL model in strong lensing related studies.Comment: Accepted for publication in ApJ, 24 pages, 13 figures, 2 table

Galaxy-galaxy weak-lensing measurement from SDSS: II. host halo properties of galaxy groups

As the second paper of a series on studying galaxy-galaxy lensing signals using the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our measurement and modelling of the lensing signals around groups of galaxies. We divide the groups into four halo mass bins, and measure the signals around four different halo-center tracers: brightest central galaxy (BCG), luminosity-weighted center, number-weighted center and X-ray peak position. For X-ray and SDSS DR7 cross identified groups, we further split the groups into low and high X-ray emission subsamples, both of which are assigned with two halo-center tracers, BCGs and X-ray peak positions. The galaxy-galaxy lensing signals show that BCGs, among the four candidates, are the best halo-center tracers. We model the lensing signals using a combination of four contributions: off-centered NFW host halo profile, sub-halo contribution, stellar contribution, and projected 2-halo term. We sample the posterior of 5 parameters i.e., halo mass, concentration, off-centering distance, sub halo mass, and fraction of subhalos via a MCMC package using the galaxy-galaxy lensing signals. After taking into account the sampling effects (e.g. Eddington bias), we found the best fit halo masses obtained from lensing signals are quite consistent with those obtained in the group catalog based on an abundance matching method, except in the lowest mass bin. Subject headings: (cosmology:) gravitational lensing, galaxies: clusters: generalComment: 12 pages, 7 figures, submitted to Ap