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.
