BM UMa: a middle shallow contact binary at pre-transition stage of evolution from W-type to A-type

In this study, all unpublished time series photometric data of BM UMa ($q \sim$ 2.0, P = 0.2712\,d) from available archives were re-investigated together with new data taken from the TNT-2.4m of the Thai National Observatory (TNO). Based on period analysis, there is a short-term variation superimposed on the long-term period decrease. The trend of period change can be fitted with a downward parabolic curve indicating a period decrease at a rate of $\mathrm{d}P/\mathrm{d}t = -3.36(\pm 0.02)\times10^{-8}$ d $\textrm{yr}^{-1}$. This long-term period decrease can be explained by mass transfer from the more massive component ($M_2 \sim 0.79 M_{\odot}$) to the less massive one ($M_1 \sim 0.39 M_{\odot}$), combination with AML. For photometric study, we found that the binary consists of K0\,V stars and at the middle shallow contact phase with evolution of fill-out factor from 8.8\,\% (in 2007) to 23.2\,\% (in 2020). Those results suggest that the binary is at pre-transition stage of evolution from W-type to A-type, agreeing to the results of statistical study of W-type contact binaries. The mass of $M_2$ will be decreased close to or below $M_1$ and the mass ratio will be decreased ($q < 1.0$). By this way, the binary will evolve into A-type as a deeper normal over-contact system with period increase. Finally the binary will end as a merger or a rapid-rotating single star when the mass ratio meet the critical value ($q < 0.094$), as well as produce a red nova.