Sensitivity analysis of a galaxy formation model

Abstract

We present the first application of a variance-based sensitivity analysis (SA) to a model that aims to predict the evolution and properties of the whole galaxy population. SA is a well-established technique in other quantitative sciences, but is a relatively novel tool for the evaluation of astrophysical models. We perform a multi-parameter exploration of the GALFORM semi-analytic galaxy formation model, to compute how sensitive the present-day K-band luminosity function is to varying different model parameters. The parameter space is scanned using a low-discrepancy sampling technique proposed by Saltelli. We first demonstrate the usefulness of the SA approach by varying just two model parameters, one which controls supernova feedback and the other the heating of gas by AGN. The SA analysis matches our physical intuition regarding how these parameters affect the predictions for different parts of the galaxy luminosity function. We then use SA to compute Sobol’ sensitivity indices varying seven model parameters, connecting the variance in the model output to the variance in the input parameters. The sensitivity is computed in luminosity bins, allowing us to probe the origin of the model predictions in detail. We discover that the SA correctly identifies the least- and most important parameters. Moreover, the SA also captures the combined responses of varying multiple parameters at the same time. Our study marks a much needed step away from the traditional “one-at-a-time” parameter variation often used in this area and improves the transparency of multi-parameter models of galaxy formation.