  Tidal forces are important for understanding how close binary stars and
compact exoplanetary systems form and evolve. However, tides are difficult to
model and significant uncertainties exist about the strength of tides. Here, we
investigate tidal circularization in close binaries using a large sample of
well-characterised eclipsing systems. We searched TESS photometry from the
southern hemisphere for eclipsing binaries. We derive best-fit orbital and
stellar parameters by jointly modelling light curves and spectral energy
distributions. To determine the eccentricity distribution of eclipsing binaries
over a wide range of stellar temperatures ($3\,000-50\,000\,$K) and orbital
separations $a/R_1$ ($2-300$), we combine our newly obtained TESS sample with
eclipsing binaries observed from the ground and by the Kepler mission. We find
a clear dependency of stellar temperature and orbital separation in the
eccentricities of close binaries. We compare our observations with predictions
of the equilibrium and dynamical tides. We find that while cool binaries agree
with the predictions of the equilibrium tide, a large fraction of binaries with
temperatures between $6\,250\,$K and $10\,000\,$K and orbital separations
between $a/R_1 \sim 4$ and $10$ are found on circular orbits contrary to the
predictions of the dynamical tide. This suggests that some binaries with
radiative envelopes may be tidally circularised significantly more efficiently
than usually assumed. Our findings on orbital circularization have important
implications also in the context of hot Jupiters where tides have been invoked
to explain the observed difference in the spin-orbit alignment between hot and
cool host stars.
