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

The TESS space mission provides us with high-precision photometric observations of bright stars over more than 70% of the entire sky, allowing us to revisit and characterise well-known stars. We aim to conduct an asteroseismic analysis of the gamma Doradus star HD112429 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. We collect and reduce 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 determine the stellar pulsation frequencies from both data sets using iterative prewhitening, do asymptotic g mode modelling of the star and investigate the corresponding spectral line profile variations using the pixel-by-pixel method. We validate the pulsation frequencies from the TESS data up to $S/N \geq 5.6$, confirming recent reports in the literature that the classical criterion $S/N \geq 4$ 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 $Π_0$ 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 HD112429, two TESS sectors of space photometry suffice. Although a detailed asteroseismic modelling analysis is not viable for g-mode pulsators with only short or sparse light curves of space photometry, we find that it is possible to determine global asteroseismic quantities for a subset of these stars. (abbreviated.)