Asteroseismology of 687 TESS Red Giants: Individual Frequencies and Asymptotic Parameters

The individual modes and asymptotic parameters are important characteristics of stellar oscillation. Using TESS 2 minute cadence data from Sectors 1 to 75, we perform asteroseismic analysis of 687 red giants, and provide their oscillation mode parameters. The mode parameters, including frequencies ν _n _, _l , amplitudes A _n _, _l , and line widths Γ _n _, _l , are obtained through Markov Chain Monte Carlo fitting. The median uncertainty for frequency is 0.047 μ Hz. Using the radial mode frequencies, we calculate the values of Δ ν , and derive asymptotic parameters ( ϵ _p , ϵ _c , δν _0 _l , q , and ΔΠ _1 ) based on l = 0, 1, 2 modes. For red giants with Δ ν > 15.6 μ Hz, there is a weaker correlation between δν _02 and Δ ν , and a stronger mass dependence, compared to stars with lower Δ ν . Additionally, the ratio δν _02 /Δ ν presents a pronounced increase with Δ ν decrease, as these stars undergo rapid core contraction and their convective envelopes extend deep into the interior. At this stage, the ratio δν _02 /Δ ν may serve as a robust indicator for diagnosing the location of the convective boundary. Furthermore, the ϵ _c values can be a potential index to distinguish red clump (RC) and secondary RC stars from red giant branch stars in the TESS field.