TESS first look at evolved compact pulsators: asteroseismology of the pulsating helium-atmosphere white dwarf TIC 257459955

Pulsation frequencies reveal the interior structures of white dwarfstars, shedding light on the properties of these compact objects that represent the final evolutionary stage of most stars. Two-minute cadencephotometry from TESS will record pulsation signatures from bright white dwarfsover the entire sky. We aim to demonstrate the sensitivity of TESS data to measuring pulsations of helium-atmosphere white dwarfsin the DBV instability strip, and what asteroseismic analysis of these measurements can constrain about their stellar structures. We present a case study of the pulsating DBV WD 0158$-$160 that was observed as TIC 257459955 with the 2-minute cadencefor 20.3 days in TESS Sector 3. We measure the frequencies of variability of TIC 257459955 with an iterative periodogramand prewhitening procedure. The measured frequencies are compared to calculations from two sets of white dwarfmodels to constrain the stellar parameters: the fully evolutionary models from LPCODE, and the structural models from WDEC. We detect and measure the frequencies of nine pulsation modes and eleven combination frequencies of WD 0158$-$160 to $\sim0.01 \mu$Hz precision. Most, if not all, of the observed pulsations belong to an incomplete sequence of dipole ($\ell=1$) modes with a mean period spacing of $38.1\pm1.0$ s. The global best-fit seismic models from both codes have effective temperaturesthat are $\gtrsim3000$ K hotter than archival spectroscopic values of $24{,}100-25{,}500$ K; however, cooler secondary solutions are found that are consistent with both the spectroscopic effective temperatureand distance constraints from Gaia astrometry.