Inverse of the quality function of the period fit in the case when we allow the periods to be associated to ℓ = 1 and ℓ = 2 modes in terms of the effective temperature for the ultra-massive DA WD model sequences with different stellar masses (M_⋆) and H envelope thicknesses [log(M_H/M_⋆)], as indicated. Vertical dashed line and gray strip correspond to the spectroscopic effective temperature of BPM 37093 and its uncertainties (T_eff = 11 370 ± 500 K). We note the strong maximum in (χ²)⁻¹ for M_⋆ = 1.16 M_⊙ and log(M_H/M_⋆) =  − 6 at T_eff ∼ 11 650 K. This corresponds to our “best-fit” model (see text for details).