Comparison of Strong Gravitational Lens Model Software I. Time delay and mass calculations are sensitive to changes in redshift and are model dependent

Abstract

Analysis of strong gravitational lensing depends on software analysis of observational data. The purpose of this study was to evaluate the behavior of strong gravitational lens modeling software with changes in redshift. Four different strong gravitational lens software modeling codes were directly compared (Lenstool / glafic, two light traces mass codes, and GRALE / PixeLens, two non-light traces mass codes) in the analysis of model data as well as analysis of the giant gravitational quasar SDSSJ1004+4112. A generalized model for time delay calculation shows that calculated time delay is proportional to $D_{d}D_{s}/D_{ds}$.The percent change in time delays calculated for each system at each redshift tested were compared with percent change in the value of $D_{d}D_{s}/D_{ds}$. A simple point mass model was tested with each code. Five models were used with a constant $z_{lens}$ and a varying $z_{source}$, and five models with a constant $z_{source}$ and a varying $z_{lens}$. The effects of changing geometry were similarly investigated for SDSSJ1004+4112. In general, the changes in time delay were of a similar magnitude and direction although, some calculated time delays varied by as much as 30 percent from changes in $D_{d}D_{s}/D_{ds}$. Changes in calculated mass for the point mass model with a constant $z_{source}$ were almost identical to changes in $D_{d}D_{s}/D_{ds}$ for three of the four codes tested. These data demonstrate the effect of changes in redshift on parameters calculated by each of the codes as compared to changes in $D_{d}D_{s}/D_{ds}$. The paucity of existing direct comparison studies of strong gravitational lensing supports the need for more studies of this kind. These results show that even small changes in redshift affects the calculation of time delay and mass, and that the effect on the calculations is dependent on the particular software used.