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Pulsating hydrogen-deficient white dwarfs and pre-white dwarfs observed with TESS -- IV. Discovery of two new GW Vir stars: TIC0403800675 and TIC1989122424

We present two new GW Vir-type pulsating white dwarf stars, TIC\,0403800675 (WD\,J115727.68-280349.64) and TIC\,1989122424 (WD J211738.38-552801.18) discovered in the Transiting Exoplanet Survey Satellite (TESS) photometric data. For both stars, the TESS light curves reveal the presence of oscillations with periods in a narrow range between 400 and 410\,s, which are associated with typical gravity ($g$)-modes. Follow-up ground-based spectroscopy shows that both stars have similar effective temperature ($T_\mathrm{eff} = 110,000 \pm 10,000$\,K) and surface gravity ($\log g = 7.5 \pm 0.5$), but different He/C composition (mass fractions): He\,=\,0.75 and C\,=\,0.25 for TIC\,0403800675, and He\,=\,0.50 and C\,=\,0.50 for TIC\,1989122424. By performing a fit to their spectral energy distributions, we found for both stars radii and luminosities of $R=0.019\pm0.002\,R_\odot$ and $\log(L/L_\odot)=1.68^{+0.15}_{-0.24}$, respectively. By employing evolutionary tracks of PG~1159 stars, we find the masses of both stars to be $0.56\pm0.18 M_{\odot}$ from the $\log g$-$T_\mathrm{eff}$ diagram and $0.60^{+0.11}_{-0.09} M_{\odot}$ from the Hertzsprung Russell diagram.