TESS asteroseismology of the Kepler red giants

The recently launched TESS mission is for the first time giving us the potential to perform inference asteroseismology across the whole sky. TESS observed the Kepler field entirely in its Sector 14 and partly in Sector 15. Here, we seek to detect oscillations in the red giants observed by TESS in the Kepler field of view. Using the full 4-yr Kepler results as the ground truth, we aim to characterise how well the seismic signal can be detected using TESS data. Because our data are based on one and two sectors of observation, our results will be representative of what one can expect for the vast majority of the TESS data. We detect clear oscillations in $\sim$3000 stars with another $\sim$1000 borderline (low S/N) cases, all of which yield a measurement of the frequency of maximum acoustic power, numax. In comparison, a simple calculation predicts $\sim$4500 stars would show detectable oscillations. Of the clear detections we reliably measure the frequency separation between overtone radial modes, dnu, in 570 stars, meaning an overall dnu yield of 20%, which splits into a one-sector yield of 14% and a two-sector yield of 26%. These yields imply that typical (1-2 sector) TESS data will result in significant detection biases. Hence, to boost the number of stars, one might need to use only numax as the seismic input for stellar property estimation. On the up side, we find little or no bias in the seismic measurements and typical scatter relative to the Kepler `truth' is about 5-6% in numax and 2-3% in dnu. These values, coupled with typical uncertainties in parallax, Teff, and Fe/H in a grid-based approach, would provide internal uncertainties of 3% in inferred stellar radius, 6% in mass and 20% in age. Finally, despite relatively large pixels of TESS, we find red giant seismology is not expected to be significantly affected by blending for stars with Tmag < 12.5.