Forward Modeling of the $\delta$ Sct Star V1790 Ori: $\Delta \nu$, $\Omega$, Resolution and Non-adiabatic Effects
We investigate the role of large separation, rotational correction order, structural resolution, and non-adiabatic effects in modelling the rotating $\delta$ Scuti star V1790 Ori. From TESS data, we extract 69 frequencies and determine $\Delta\nu \simeq 82$ $\mu$Hz. Rotating MESA models are computed at low and high resolution; their pulsation frequencies are calculated with GYRE (adiabatic/non-adiabatic, first-order rotation) and FILOU (adiabatic, second-order rotation). Using $\Delta\nu$ as a structural constraint is necessary to reduce model degeneracy. For the selected minimum-misfit reference model, considering only the 40 modes with consistent $(n,\ell,m)$ labels, the RMS$_{40}$ theoretical frequency differences are 0.442 $\mu$Hz (resolution), 0.062 $\mu$Hz (non-adiabatic), and 2.962 $\mu$Hz (GYRE vs FILOU); including all 48 frequencies gives RMS$_{48}$ values of 1.033, 2.326, and 3.931 $\mu$Hz. Relative to observations, higher resolution reduces residuals from 4.457 to 4.387 $\mu$Hz (RMS$_{40}$) and from 4.715 to 4.682 $\mu$Hz (RMS$_{48}$); non-adiabatic effects change them marginally to 4.381 and 4.673 $\mu$Hz. FILOU gives the largest residuals: 5.331 $\mu$Hz (RMS$_{40}$) and 5.270 $\mu$Hz (RMS$_{48}$). Second-order rotation produces the largest frequency shifts, but improving agreement with observations requires denser grids and self-consistent FILOU optimisation. The 260.672 $\mu$Hz peak -- previously identified as the fundamental radial mode -- shows uncertain identification. The results should be interpreted as diagnostics of modelling systematics and mode-identification robustness.