Simulations of single- and two-component galaxy decompositions for spectroscopically selected galaxies from the Sloan Digital Sky Survey

We present the results of fitting simulations of an unbiased sample of SDSS galaxies utilizing the fitting routine GALFIT and analysis pipeline PyMorph. These simulations are used to test the two-dimensional decompositions of SDSS galaxies. The simulations show that single S{\'e}rsic models of SDSS data are recovered with $\sigma_{\mathrm{mag}} \approx 0.025$ mag and $\sigma_{\mathrm{radius}} \approx 5\%$. The global values (half-light radius and magnitude) are equally well constrained when a two-component model is used. Sub-components of two-component models present more scatter. SDSS resolution is the primary source of error in the recovery of models. We use a simple statistical correction of the biases in fitted parameters, providing an example using the S{\'e}rsic index. Fitting a two-component S{\'e}rsic + Exponential model to a single S{\'e}rsic galaxy results in a noisier, but unbiased, recovery of the input parameters ($\sigma_{\mathrm{total mag}} \approx 0.075$ mag and $\sigma_{\mathrm{radius}} \approx 10\%$); fitting a single S{\'e}rsic profile to a two-component system results in biases of total magnitude and halflight radius of $\approx 0.05-0.10$ mag and 5\%-10\% in radius. Using an F-test to select the best fit model from among the single- and two-component models is sufficient to remove this bias. We recommend fitting a two-component model to all galaxies when attempting to measure global parameters such as total magnitude and halflight radius.