The near-core rotation of HD 112429 A Doradus star with TESS photometry and legacy spectroscopy

Context. The Transiting Exoplanet Survey Satellite (TESS) provides us with high-precision photometric observations of large numbers of bright stars over more than 70% of the entire sky, allowing us to revisit and characterise well-known stars. Aims. We aim to conduct an asteroseismic analysis of the gamma Doradus (gamma Dor) star HD 112429 using both the available ground-based spectroscopy and TESS photometry, and assess the conditions required to measure the near-core rotation rate and buoyancy travel time. Methods. We collected and reduced the available five sectors of short-cadence TESS photometry of this star, as well as 672 legacy observations from six medium- to high-resolution ground-based spectrographs. We determined the stellar pulsation frequencies from both data sets using iterative prewhitening, did asymptotic g mode modelling of the star, and investigated the corresponding spectral line profile variations using the pixel-by-pixel method. Results. We validate the pulsation frequencies from the TESS data down to S/N >= 5.6, confirming recent reports in the literature that the classical criterion S/N >= 4 does not suffice for space-based observations. We identify the pulsations as prograde dipole g modes and r-mode pulsations, and measure a near-core rotation rate of 1.536 (3) d(-1) and a buoyancy travel time Pi(0) of 4190 (50) s. These results are in agreement with the observed spectral line profile variations, which were qualitatively evaluated using a newly developed toy model. We establish a set of conditions that have to be fulfilled for an asymptotic asteroseismic analysis of g-mode pulsators. In the case of HD 112429, two TESS sectors of space photometry suffice. Conclusions. Although a detailed asteroseismic modelling analysis is not viable for g-mode pulsators with only short or sparse light curves of space photometry, it is possible to determine global asteroseismic quantities for a subset of these stars. Thanks to the ongoing TESS mission, this will allow us to characterise many more stars than only those with years of data.