The near-core rotation of HD 112429. A γ 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 γ Doradus (γ 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 Π₀ 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.

TESS light curve and spectra are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/662/A58