Résumé
We present an analysis of the first 20-second cadence light curves obtained
by the TESS space telescope during its extended mission. We find a precision
improvement of 20-second data compared to 2-minute data for bright stars when
binned to the same cadence (~10-25% better for T<~8 mag, reaching equal
precision at T~13 mag), consistent with pre-flight expectations based on
differences in cosmic ray mitigation algorithms. We present two results enabled
by this improvement. First, we use 20-second data to detect oscillations in
three solar analogs (gamma Pav, zeta Tuc and pi Men) and use asteroseismology
to measure their radii, masses, densities and ages to ~1%, ~3%, ~1% and ~20%
respectively, including systematic errors. Combining our asteroseismic ages
with chromospheric activity measurements we find evidence that the spread in
the activity-age relation is linked to stellar mass and thus convection-zone
depth. Second, we combine 20-second data and published radial velocities to
re-characterize pi Men c, which is now the closest transiting exoplanet for
which detailed asteroseismology of the host star is possible. We show that pi
Men c is located at the upper edge of the planet radius valley for its orbital
period, confirming that it has likely retained a volatile atmosphere and that
the "asteroseismic radius valley" remains devoid of planets. Our analysis
favors a low eccentricity for pi Men c (<0.1 at 68% confidence), suggesting
efficient tidal dissipation (Q/k <~ 2400) if it formed via high-eccentricity
migration. Combined, these early results demonstrate the strong potential of
TESS 20-second cadence data for stellar astrophysics and exoplanet science.