  We investigate the evolution of star formation rates (SFRs), stellar masses,
and M/L$_{3.4 \mu m}$ ratios of brightest cluster galaxies (BCGs) in the COSMOS
survey since z ~ 1 to determine the contribution of star formation to the
growth-rate of BCG stellar mass over time. Through the spectral energy
distribution (SED) fitting of the GALEX, CFHT, Subaru, Vista, Spitzer, and
Herschel photometric data available in the COSMOS2015 catalog, we estimate the
stellar mass and SFR of each BCG. We use a modified version of the iSEDfit
package to fit the SEDs of our sample with both stellar and dust emission
models, as well as constrain the impact of star formation history assumptions
on our results. We find that in our sample of COSMOS BCGs, star formation
evolves similarly to that in BCGs in samples of more massive galaxy clusters.
However, compared to the latter, the magnitude of star formation in our sample
is lower by ~ 1 dex. Additionally, we find an evolution of BCG baryonic
mass-to-light ratio (M/L$_{3.4 \mu m}$) with redshift which is consistent with
a passively aging stellar population. We use this to build upon Wen et al.'s
(2013) low-redshift $\nu$L$_{3.4 \mu m}$-M$_{Stellar}$ relation, quantifying a
correlation between $\nu$L$_{3.4 \mu m}$ and M$_{Stellar}$ to z ~ 1. By
comparing our results to BCGs in Sunyaev-Zel'dovich and X-ray-selected samples
of galaxy clusters, we find evidence that the normalization of star formation
evolution in a cluster sample is driven by the mass range of the sample and may
be biased upwards by cool cores.
