Home
Our goal is to infer Mstar and redshift jointly for all galaxies in our strong lens fields, our calibration (CFHTLenS) fields, and the corresponding analog fields in the Millennium Simulation. We can then use these to infer, approximately, the external convergence in our lens fields - but we need to estimate the systematic errors that we have likely incurred by doing this.
WEIGHT RATIOS USING PHOTOZ AND DERIVED STELLAR MASSES
Here are the results of the complete analysis using the Millennium Simulation to infer realistic error bars on weighted count ratios.
We used two of the semi-analytical galaxy models included in the simulation, which paint galaxies with realistic colors onto the simulated halos: Guo and SA. We attached realistic magnitude-dependent error bars to the galaxy fluxes, and computed photo-z with BPZ from either ugriz or ugriJHK fluxes (to match our lens field data and CFHTLENS, respectively).
The catalogue z vs. photo-z plots for Guo and SA, respectively, are shown below. The SA galaxies show less scatter and bias than Guo.
Below are the catalogue vs. derived stellar masses for Guo and SA, respectively. The stellar masses were derived with Lephare, where the redshift was fixed at the BPZ-derived value. Again, the SA results are better overall.
When computing weighted ratios we take ratios of weighted sums of galaxies, where in the nominator of the ratios we use ugriJHK data, and in the denominator we use ugriz data. Also, for the nominator we used a similar fraction of "specz" data to the one we have in the real lens field. We computed not only weighted sums, but also weighted medians * galaxy counts, which should be less affected by outliers. We explored limiting magnitudes of i=23,23.5 and 24, and galaxies over radii of 45, 60, 90 and 120 arcsec.
The two plots below show true vs. derived weighted ratios for Guo and SA, respectively, for both weighted sums and weighted medians * galaxy counts.
Ratios incorporating Mstar^2 and Mstar^3 show large scatter and are systematically underestimated. This systematic offset is a result of using a different set of filters in the nominator and denominator, and would disappear if near-IR filters were used throughout. As seen, the offset is fixed for SA by the use of weighted medians * galaxy counts, while for Guo it becomes a constant offset in the opposite direction. However, if we decide to use only Mstar to first power, weighted medians * galaxy counts has a larger scatter, and it is better to use weighted sums, since the offset is small enough to be neglected.
As shown in the plot below, the offset is larger for a deeper magnitude limit.
)
Also, as shown below, the scatter is larger for smaller aperture radii.
In the ratio plots above we have sampled from the P(z) and P(M|z) of each galaxy 20 times, but it appears that if we only take the best-fit redshift and its associated median Mstar, the scatter is slightly smaller. For this latter case, the rms on the Mstar-weighted count ratio is below:
maglim/radius
23 23.5 24
45 0.13 0.12 0.11
60 0.11 0.10 0.09
90 0.09 0.08 0.08
120 0.08 0.07 0.06