A halo model approach for mock catalogs of time-variable strong gravitational lenses

TL;DR

This work develops a halo-model–based framework to generate mock catalogs of time-variable strong gravitational lenses that span galaxy-, group-, and cluster-scale deflectors. By combining dark matter halos, central and satellite galaxies, subhalos, and external shear, and computing lensing using glafic, the authors produce comprehensive mock catalogs of lensed QSOs and SNe for LSST, including time delays and highly magnified systems. A key result is that adopting a Salpeter IMF yields roughly double the lens counts compared with a Chabrier IMF, with the data-driven comparison to SQLS and Gaia favoring the Salpeter-like IMF for massive galaxies. The study also reveals substantial populations of cluster-scale lenses with image separations >10 arcsec and demonstrates the importance of environment in highly magnified systems. The SL-Hammocks code and the catalogs are publicly released to enable broader cosmological and lensing investigations.

Abstract

Time delays in both galaxy- and cluster-scale strong gravitational lenses have recently attracted a lot of attention in the context of the Hubble tension. Future wide-field cadenced surveys, such as the LSST, are anticipated to discover strong lenses across various scales. We generate mock catalogs of strongly lensed QSOs and SNe on galaxy-, group-, and cluster-scales based on a halo model that incorporates dark matter halos, galaxies, and subhalos. For the upcoming LSST survey, we predict that approximately 4000 lensed QSOs and 200 lensed SNe with resolved multiple images will be discovered. Among these, about 80 lensed QSOs and 10 lensed SNe will have maximum image separations larger than 10 arcsec, which roughly correspond to cluster-scale strong lensing. We find that adopting the Chabrier stellar IMF instead of the fiducial Salpeter IMF reduces the predicted number of strong lenses approximately by half, while the distributions of lens and source redshifts and image separations are not significantly changed. In addition to mock catalogs of multiple-image lens systems, we create mock catalogs of highly magnified systems, including both multiple-image and single-image systems. We find that such highly magnified systems are typically produced by massive galaxies, but non-negligible fraction of them are located in the outskirt of galaxy groups and clusters. Furthermore, we compare subsamples of our mock catalogs with lensed QSO samples constructed from the SDSS and Gaia to find that our mock catalogs with the fiducial Salpeter IMF reproduce the observation quite well. In contrast, our mock catalogs with the Chabrier IMF predict a significantly smaller number of lensed QSOs compared with observations, which adds evidence that the stellar IMF of massive galaxies is Salpeter-like. Our python code SL-Hammocks as well as the mock catalogs are made available online. (abridged)

Figures (20)

• Figure 1: Mean stellar mass fractions for central galaxies. The solid lines show the fractions in our fiducial Salpeter IMF case, while the dotted lines represent the ones in the Chabrier IMF case. We note that the star formation efficiency peaks at round masses slightly smaller than $10^{12}M_\odot$2013ApJ...762L..31B.
• Figure 2: Comparison between the velocity dispersion function derived with our model described in Sec. \ref{['sec: lensmodel']} (red) and that presented in 2018MNRAS.480.3842O (grey). The vertical axis shows the number of galaxies in each redshift bin with the width of $\Delta z=0.01$ for each velocity dispersion bin. Here, we set the area written on each panel to derive the number. Top left: $z=0.05$, Top center: $z=0.1$, Top right: $z=0.25$, Bottom left: $z=0.5$, Bottom center: $z=1.0$, Bottom right: $z=2.0$.
• Figure 3: Comparison between our model with observation data of SHELS F2 at intermediate redshifts, $z\lesssim 0.6$. Only the galaxy samples with stellar masses of $M_* \gtrsim 10^{10.7}~M_{\odot}$ are plotted. The four panels on the left side show effective radii as a function of stellar mass at $0.2<z<0.3$, $0.3<z<0.4$, $0.4<z<0.5$, and $0.5<z<0.6$, while the four panels on the right represent those of velocity dispersions. The thick solid lines show the center lines for the galaxy samples. The dark red and light red regions show the $68\%$ and $95\%$ areas for our galaxy samples, while the thin grey solid and dotted lines show the $68\%$ and $95\%$ areas for SHELS F2 galaxy samples. We set the area of $4.2~\mathrm{deg}^2$ to create a mock galaxy sample, matching the area covered by the SHELS F2 catalog. Note that we do not plot the error bars for the effective radii and velocity dispersions for the SHELS F2 data.
• Figure 4: The scatter of $_{e}$ for mock galaxies at given $z$ and $M_*$ calculated with our model. We compute the scatter only for mock galaxies with $10.5<\log_{10}(M_*/M_{\odot})<11.7$ at $z<2$. We set $2000~\mathrm{deg}^2$, $100~\mathrm{deg}^2$, and $20~\mathrm{deg}^2$ to create mock galaxy samples at $0.05<z<0.2$ (left), $0.2<z<0.6$ (middle), and $0.6<z<2.0$ (right), respectively. The calculation method of the scatter is as follows. We first divide our mock galaxies into ($z, M_*$)-bins. We then calculate the scatter of velocity dispersion for the sample of galaxies in each bin. We finally plot these histograms only using those bins that hold more than $\mathcal{O}(10^2)$ galaxy samples to ensure that the variance is properly computed. Here we set $(\Delta z,\Delta\log_{10}(M*/M_{\odot}))=(0.01,0.02)$ for the galaxy sample at $0.05<z<0.2$, $(0.02,0.02)$ at $0.2<z<0.6$, and $(0.1,0.02)$ at $0.6<z<2.0$ for a numerical reason. The grey dotted line appearing only in the left panel represents a best-fit value obtained for the SDSS galaxy sample at $0.05<z<0.2$ in 2020MNRAS.498.1101C, $_{\ln _e}= 0.075^{+ 0.003}_{- 0.003} ~\mathrm{dex}$. The orange-colored regions represent the $\pm 1$, $\pm 2$, and $\pm 3$ regions, in order from darkest to lightest.
• Figure 5: Our mock galaxy catalog is plotted on the MFP. The MFP is described by Eq. \ref{['eq: mfp_general']} with parameters of $(a,b,c,d) = (-0.84,1.63,-1.00,4.42)$, which is obtained for quiescent galaxies in 2009MNRAS.396.1171H. The blue dashed line displays the best-fit line for the SDSS sample of quiescent galaxies obtained in 2016ApJ...821..101Z.