Evolution of the galaxy stellar mass function: evidence for an increasing $M^*$ from $z=2$ to the present day

Utilising optical and near-infrared broadband photometry covering $> 5\,{\rm deg}^2$ in two of the most well-studied extragalactic legacy fields (COSMOS and XMM-LSS), we measure the galaxy stellar mass function (GSMF) between $0.1 < z < 2.0$. We explore in detail the effect of two source extraction methods (SExtractor and ProFound) in addition to the inclusion/exclusion of Spitzer IRAC 3.6 and 4.5$\mu$m photometry when measuring the GSMF. We find that including IRAC data reduces the number of massive ($\log_{10}(M/M_\odot) > 11.25$) galaxies found due to improved photometric redshift accuracy, but has little effect on the more numerous lower-mass galaxies. We fit the resultant GSMFs with double Schechter functions down to $\log_{10}(M/M_\odot)$ = 7.75 (9.75) at z = 0.1 (2.0) and find that the choice of source extraction software has no significant effect on the derived best-fit parameters. However, the choice of methodology used to correct for the Eddington bias has a larger impact on the high-mass end of the GSMF, which can partly explain the spread in derived $M^*$ values from previous studies. Using an empirical correction to model the intrinsic GSMF, we find evidence for an evolving characteristic stellar mass with $\delta \log_{10}(M^*/M_\odot)/\delta z$ = $-0.16\pm0.05 \, (-0.11\pm0.05)$, when using SExtractor (ProFound). We argue that with widely quenched star formation rates in massive galaxies at low redshift ($z<0.5$), additional growth via mergers is required in order to sustain such an evolution to a higher characteristic mass.