AlphaTg: GUI application for flux and limb derivatives of UBVRI, Kepler and TESS pass-bands for asteroseismology applications

The flux derivatives, limb darkening integrals and limb darkening derivatives have been used in many astronomical applications. Among these applications, the flux and limb darkening derivatives are mandatory parameters in asteroseismology whenever determining the theoretical amplitudes of stellar pulsations. The amplitude ratio method, which compares the observed amplitudes of UBVRI color bands with the theoretical amplitudes is widely used in asteroseismology. The computation of theoretical amplitudes is very complex and time-consuming due to the dependency on several parameters, including flux and limb darkening derivatives. Besides, more theoretical amplitude models are needed to compare with the observations for an ideal conclusion. In addition, the computation of synthetic line profiles in spectroscopy is also used the flux and limb darkening derivatives; therefore, we introduce the AlphaTg code to determine flux and limb darkening derivatives in a single application to minimize the complexity of computation. The facility enables to compute flux derivatives for any effective temperature (Teff) within the range of 3500 K ≤ Teff ≤ 50000 K and any gravity value within the range of 0.0 ≤ log (g) ≤ 5.0 for UBVRI, Kepler and TESS photometric systems. The limb darkening derivatives can be determined for a spherical degree, l = 0, 1, and 2 for linear, quadratic and non-linear limb darkening laws for the effective temperature range of 3500 K ≤ Teff ≤ 50000 K and gravity range of 1.0 ≤ log (g) ≤ 5.0. A case study is also discussed to explain the usage and limitations of the application.