We present photometry of four transits of the planetary system HAT-P-13 , obtained using defocussed telescopes .
We analyse these , plus nine datasets from the literature , in order to determine the physical properties of the system .
The mass and radius of the star are M _ { A } = 1.320 \pm 0.048 \pm 0.039 { M } _ { \odot } and R _ { A } = 1.756 \pm 0.043 \pm 0.017 { R } _ { \odot } ( statistical and systematic errorbars ) .
We find the equivalent quantities for the transiting planet to be M _ { b } = 0.906 \pm 0.024 \pm 0.018 { M } _ { Jup } and R _ { b } = 1.487 \pm 0.038 \pm 0.015 { R } _ { Jup } , with an equilibrium temperature of T _ { eq } ^ { \prime } = 1725 \pm 31 K. Compared to previous results , which were based on much sparser photometric data , we find the star to be more massive and evolved , and the planet to be larger , hotter and more rarefied .
The properties of the planet are not matched by standard models of irradiated gas giants .
Its large radius anomaly is in line with the observation that the hottest planets are the most inflated , but at odds with the suggestion of inverse proportionality to the \left [ \frac { Fe } { H } \right ] of the parent star .
We assemble all available times of transit midpoint and determine a new linear ephemeris .
Previous findings of transit timing variations in the HAT-P-13 system are shown to disagree with these measurements , and can be attributed to small-number statistics .