Statistical analysis of asteroseismic indices and stellar parameters of TESS-observed δ Scuti stars

Context. Over the last few years, delta Scuti stars have been at the center of the attention of the asteroseismology community thanks to the derivation of seismic indices connected to stellar parameters. The statistical analysis of the wealth of data offered by a large space survey such as the Transiting Exoplanet Survey Satellite (TESS), the identification of new delta Scuti stars, and the correlation between asteroseismic indices and stellar parameters in the resulting sample are therefore of utmost interest. Aims. The goal of our study is to analyze the statistical properties of stellar parameters and characterize the asteroseismic indices of delta Scuti stars observed in TESS cycle 4. Methods. We used TESS 2 min cadence photometric data and the corresponding Fourier transform to identify delta Scuti stars. The asteroseismic indices for these stars were determined using an empirical relation and a 2D autocorrelation method. Results. We discovered 765 delta Scuti stars from the data obtained by the TESS mission, from Sectors 40-55, corresponding to cycle 4 and observed with a 2 min cadence. Of these stars, 179 delta Scuti stars have low-resolution spectral parameters from LAMOST. We first analyzed the relation between pulsation and stellar parameters from TESS observations and the distribution of delta Scuti stars with two different stellar parameters, TESS Input Catalog (TIC) and Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), within the classical instability strip. Most of the stars lie within the instability strip and follow the period-luminosity relation of delta Scuti stars. Additionally, the majority of the stars exhibit pulsation properties consistent with those expected for delta Scuti stars, including periods falling within the typical range, amplitudes at the millimagnitude level, and fundamental parameters such as spectral type, effective temperature, log g, and luminosity that match the characteristics of delta Scuti stars. This confirms the reliability of the delta Scuti stars we have identified. We subsequently obtained the large frequency separation (triangle nu), v(max), and nu(Amax) for 179 delta Scuti stars with LAMOST parameters by using an empirical relation and a 2D autocorrelation method, and obtained the relations between these asteroseismic indices. These stars will provide significant support for a deeper study of the internal structure and evolution of stars.