KMT-2016-BLG-2052L: Microlensing Binary Composed of M Dwarfs Revealed from a Very Long Time-scale Event

We present the analysis of a binary microlensing event KMT-2016-BLG-2052, for which the lensing-induced brightening of the source star lasted for 2 seasons. We determine the lens mass from the combined measurements of the microlens parallax $\text{pie}$ and angular Einstein radius $\text{thetae}$. The measured mass indicates that the lens is a binary composed of M dwarfs with masses of $M_1\sim 0.34M_{\odot }$ and $M_2\sim 0.17M_{\odot }$. The measured relative lens-source proper motion of $\mu \sim 3.9\mathrm{m}\mathrm{a}\mathrm{s}{\mathrm{y}\mathrm{r}}^{-1}$ is smaller than $\sim 5\mathrm{m}\mathrm{a}\mathrm{s}{\mathrm{y}\mathrm{r}}^{-1}$ of typical Galactic lensing events, while the estimated angular Einstein radius of $\text{thetae}\sim 1.2\mathrm{m}\mathrm{a}\mathrm{s}$ is substantially greater than the typical value of $\sim 0.5\mathrm{m}\mathrm{a}\mathrm{s}$. Therefore, it turns out that the long time scale of the event is caused by the combination of the slow $\mu$ and large $\text{thetae}$ rather than the heavy mass of the lens. From the simulation of Galactic lensing events with very long time scales ($t_{\mathrm{E}}\gtrsim 100$ days), we find that the probabilities that long time-scale events are produced by lenses with masses $\ge 1.0M_{\odot }$ and $\ge 3.0M_{\odot }$ are $\sim 19\mathrm{\%}$ and 2.6%, respectively, indicating that events produced by heavy lenses comprise a minor fraction of long time-scale events. The results indicate that it is essential to determine lens masses by measuring both $\text{pie}$ and $\text{thetae}$ in order to firmly identify heavy stellar remnants such as neutron stars and black holes.