EPIC 228782059: Asteroseismology of What Could Be the Coolest Pulsating Helium-atmosphere White Dwarf (DBV) Known

We present analysis of a new pulsating helium-atmosphere (DB) white dwarf, EPIC~228782059, discovered from 55.1~days of {\em K2} photometry. The long duration, high quality light curves reveal 11 independent dipole and quadruple modes, from which we derive a rotational period of $34.1 \pm 0.4$~hr for the star. An optimal model is obtained from a series of grids constructed using the White Dwarf Evolution Code, which returns $M_{*} = 0.685 \pm 0.003 M_{\odot}$, $T_{\rm{eff}}= 21{,}910 \pm 23$\,K and $\log g = 8.14 \pm0.01$\,dex. These values are comparable to those derived from spectroscopy by Koester \& Kepler ($20{,}860 \pm 160$\,K and $7.94 \pm0.03$\,dex). If these values are confirmed or better constrained by other independent works, it would make EPIC~228782059 one of the coolest pulsating DB white dwarf star known, and would be helpful to test different physical treatments of convection, and to further investigate the theoretical instability strip of DB white dwarf stars.