We investigate the effects of tidal interactions on the planetary orbits and stellar spin rates of the WASP-18 and WASP-19 planetary systems using a forward integration scheme .
By fitting the resulting evolutionary tracks to the observed eccentricity , semi-major axis and stellar rotation rate , and to the stellar age derived from isochronal fitting , we are able to place constraints on the stellar and planetary reduced tidal quality factors , Q ^ { \prime } _ { s } and Q ^ { \prime } _ { p } .
We find that for WASP-18 , \log ( Q ^ { \prime } _ { s } ) = 8.21 ^ { +0.90 } _ { -0.52 } and \log ( Q ^ { \prime } _ { p } ) = 7.77 ^ { +1.54 } _ { -1.25 } , implying a system age of 0.579 ^ { +0.305 } _ { -0.250 } Gyr .
For WASP-19 we obtain values of \log ( Q ^ { \prime } _ { s } ) = 6.47 ^ { +2.19 } _ { -0.95 } and \log ( Q ^ { \prime } _ { p } ) = 6.75 ^ { +1.86 } _ { -1.77 } , suggesting a system age of 1.60 ^ { +2.84 } _ { -0.79 } Gyr and a remaining lifetime of 0.0067 ^ { +1.1073 } _ { -0.0061 } Gyr .
We investigate a range of evolutionary histories consistent with these results and the observed parameters for both systems , and find that the majority imply that the stars have been spun up through tidal interactions as the planets spiral towards their Roche limits .
We examine a variety of evidence for WASP-19 A ’ s age , both for the value above and for a younger age consistent with gyrochronology , and conclude that the older estimate is more likely to be correct .
This suggests that WASP-19 b might be in the final stages of the spiral-in process , although we are unable to rule out the possibility that it has a substantial remaining lifetime .