On the accuracy of the Perturbative Approach for Strong Lensing: Local Distortion for Pseudo-Elliptical Models

The Perturbative Approach (PA) introduced by \citet{alard07} provides analytic solutions for gravitational arcs by solving the lens equation linearized around the Einstein ring solution. This is a powerful method for lens inversion and simulations in that it can be used, in principle, for generic lens models. In this paper we aim to quantify the domain of validity of this method for three quantities derived from the linearized mapping: caustics, critical curves, and the deformation cross section (i.e. the arc cross section in the infinitesimal circular source approximation). We consider lens models with elliptical potentials, in particular the Singular Isothermal Elliptic Potential and Pseudo-Elliptical Navarro--Frenk--White models. We show that the PA is exact for this first model. For the second, we obtain constraints on the model parameter space (given by the potential ellipticity parameter $\varepsilon$ and characteristic convergence $\kappa_s$) such that the PA is accurate for the aforementioned quantities. In this process we obtain analytic expressions for several lensing functions, which are valid for the PA in general. The determination of this domain of validity could have significant implications for the use of the PA, but it still needs to be probed with extended sources.Comment: Accepted for publication in MNRA

First Galaxy-Galaxy Lensing Measurement of Satellite Halo Mass in the CFHT Stripe-82 Survey

We select satellite galaxies from the galaxy group catalog constructed with the SDSS spectroscopic galaxies and measure the tangential shear around these galaxies with source catalog extracted from CFHT/MegaCam Stripe-82 Survey to constrain the mass of subhalos associated with them. The lensing signal is measured around satellites in groups with masses in the range [10^{13}, 5x10^{14}]h^{-1}M_{sun}, and is found to agree well with theoretical expectation. Fitting the data with a truncated NFW profile, we obtain an average subhalo mass of log M_{sub}= 11.68 \pm 0.67 for satellites whose projected distances to central galaxies are in the range [0.1, 0.3] h^{-1}Mpc, and log M_{sub}= 11.68 \pm 0.76 for satellites with projected halo-centric distance in [0.3, 0.5] h^{-1}Mpc. The best-fit subhalo masses are comparable to the truncated subhalo masses assigned to satellite galaxies using abundance matching and about 5 to 10 times higher than the average stellar mass of the lensing satellite galaxies.Comment: 7 pages, 4 figures, accepted by MNRA

The Mass-Concentration Relation and the Stellar-to-Halo Mass Ratio in the CFHT Stripe 82 Survey

We present a new measurement of the mass-concentration relation and the stellar-to-halo mass ratio over the halo mass range $5\times 10^{12}$ to $2\times 10^{14}M_{\odot}$. To achieve this, we use weak lensing measurements from the CFHT Stripe 82 Survey (CS82), combined with the central galaxies from the redMaPPer cluster catalogue and the LOWZ/CMASS galaxy sample of the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Tenth Data Release. The stacked lensing signals around these samples are modelled as a sum of contributions from the central galaxy, its dark matter halo, and the neighboring halos, as well as a term for possible centering errors. We measure the mass-concentration relation: $c_{200c}(M)=A(\frac{M_{200c}}{M_0})^{B}$ with $A=5.24\pm1.24, B=-0.13\pm0.10$ for $0.2<z<0.4$ and $A=6.61\pm0.75, B=-0.15\pm0.05$ for $0.4<z<0.6$. These amplitudes and slopes are completely consistent with predictions from recent simulations. We also measure the stellar-to-halo mass ratio for our samples, and find results consistent with previous measurements from lensing and other techniques.Comment: 10 pages, 3 figures, 3 table

Measuring subhalo mass in redMaPPer clusters with CFHT Stripe 82 Survey

We use the shear catalog from the CFHT Stripe-82 Survey to measure the subhalo masses of satellite galaxies in redMaPPer clusters. Assuming a Chabrier Initial Mass Function (IMF) and a truncated NFW model for the subhalo mass distribution, we find that the sub-halo mass to galaxy stellar mass ratio increases as a function of projected halo-centric radius $r_p$, from $M_{\rm sub}/M_{\rm star}=4.43^{+ 6.63}_{- 2.23}$ at $r_p \in [0.1,0.3]$ $h^{-1}Mpc$ to $M_{\rm sub}/M_{\rm star}=75.40^{+ 19.73}_{- 19.09}$ at $r_p \in [0.6,0.9]$ $h^{-1}Mpc$. We also investigate the dependence of subhalo masses on stellar mass by splitting satellite galaxies into two stellar mass bins: $10<\log(M_{\rm star}/M_{\rm sun})<10.5$ and $11<\log(M_{\rm star}/M_{\rm sun})<12$. The best-fit subhalo mass of the more massive satellite galaxy bin is larger than that of the less massive satellites: $\log(M_{\rm sub}/M_{\rm sun})=11.14 ^{+ 0.66 }_{- 0.73}$ ($M_{\rm sub}/M_{\rm star}=19.5^{+19.8}_{-17.9}$) versus $\log(M_{\rm sub}/M_{\rm sun})=12.38 ^{+ 0.16 }_{- 0.16}$ ($M_{\rm sub}/M_{\rm star}=21.1^{+7.4}_{-7.7}$).Comment: 10 pages, 8 figures, accepted by MNRA

Weak-lensing calibration of a stellar mass-based mass proxy for redMaPPer and Voronoi Tessellation clusters in SDSS Stripe 82

We present the first weak lensing calibration of $\mu_{\star}$, a new galaxy cluster mass proxy corresponding to the total stellar mass of red and blue members, in two cluster samples selected from the SDSS Stripe 82 data: 230 redMaPPer clusters at redshift $0.1\leq z<0.33$ and 136 Voronoi Tessellation (VT) clusters at $0.1 \leq z < 0.6$. We use the CS82 shear catalog and stack the clusters in $\mu_{\star}$ bins to measure a mass-observable power law relation. For redMaPPer clusters we obtain $M_0 = (1.77 \pm 0.36) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 1.74 \pm 0.62$. For VT clusters, we find $M_0 = (4.31 \pm 0.89) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 0.59 \pm 0.54$ and $M_0 = (3.67 \pm 0.56) \times 10^{14}h^{-1} M_{\odot}$, $\alpha = 0.68 \pm 0.49$ for a low and a high redshift bin, respectively. Our results are consistent, internally and with the literature, indicating that our method can be applied to any cluster finding algorithm. In particular, we recommend that $\mu_{\star}$ be used as the mass proxy for VT clusters. Catalogs including $\mu_{\star}$ measurements will enable its use in studies of galaxy evolution in clusters and cluster cosmology.Comment: Updated to be consistent with the published versio