Asteroseismology of the pulsating extremely low-mass white dwarf SDSS J111215.82+111745.0: a model with $p$-mode pulsations consistent with the observations

SDSS J111215.82+111745.0 is the second pulsating extremely low-mass white dwarf discovered. Two short-period pulsations, 107.56 and 134.275 s, were detected on this star, which would be the first observed pressure mode ($p$-mode) pulsations observed on a white dwarf. While the two potential $p$-modes have yet to be confirmed, they make SDSS J111215.82+111745.0 an interesting object. In this work, we analyzed the whole set of seven periods observed on SDSS J111215.82+111745.0. We adopt three independent period-spacing tests to reveal a roughly 93.4 s mean period spacing of $\mathrm{\ell }=1$ $g$-modes, which gives added credence to the $\mathrm{\ell }=1$ identifications. Then we perform asteroseismic modeling for this star, in which the H chemical profile is taken as a variable. The stellar parameters $M=0.1650\pm 0.0137$ $M_{\odot }$ and $T_{\mathrm{e}\mathrm{f}\mathrm{f}}=9750\pm 560$ K are determined from the best-fit model and the H/He chemical profiles are also defined. The two suspected $p$-modes are also well represented in the best-fit model, and both the stellar parameters and the pulsation frequencies are in good agreement with the values derived from spectroscopy.