The mean density of a star transited by a planet, brown dwarf or low mass star can be accurately measured from its light curve. This measurement can be combined with other observations to estimate its mass and age by comparison with stellar models. O
ur aim is to calculate the posterior probability distributions for the mass and age of a star given its density, effective temperature, metallicity and luminosity. We computed a large grid of stellar models that densely sample the appropriate mass and metallicity range. The posterior probability distributions are calculated using a Markov-chain Monte-Carlo method. The method has been validated by comparison to the results of other stellar models and by applying the method to stars in eclipsing binary systems with accurately measured masses and radii. We have explored the sensitivity of our results to the assumed values of the mixing-length parameter, $alpha_{rm MLT}$, and initial helium mass fraction, Y. For a star with a mass of 0.9 solar masses and an age of 4 Gyr our method recovers the mass of the star with a precision of 2% and the age to within 25% based on the density, effective temperature and metallicity predicted by a range of different stellar models. The masses of stars in eclipsing binaries are recovered to within the calculated uncertainties (typically 5%) in about 90% of cases. There is a tendency for the masses to be underestimated by about 0.1 solar masses for some stars with rotation periods P$_{rm rot}< 7$d. Our method makes it straightforward to determine accurately the joint posterior probability distribution for the mass and age of a star eclipsed by a planet or other dark body based on its observed properties and a state-of-the art set of stellar models.
The star 1SWASP J162842.31+101416.7 (WASP 1628+10) is one of several EL CVn-type stars recently identified using the WASP database, i.e., an eclipsing binary star in which an A-type dwarf star (WASP 1628+10A) eclipses the remnant of a disrupted red g
iant star (WASP1628+10B). We have measured the masses, radii and luminosities of the stars in WASP 1628+10 using photometry obtained in three bands (u, g, r) with the Ultracam instrument and medium-resolution spectroscopy. The properties of the remnant are well-matched by models for stars in a rarely-observed state evolving to higher effective temperatures at nearly constant luminosity prior to becoming a very low-mass white dwarf composed almost entirely of helium, i.e., we confirm that WASP 1628+10B is a pre-He-WD. WASP 1628+10A appears to be a normal A2V star with a mass of $1.36 pm 0.05 M_{odot}$. By fitting models to the spectrum of this star around the H$gamma$ line we find that it has an effective temperature T$_{rm eff,A} = 7500 pm 200$K and a metallicity [Fe/H]$ = -0.3 pm 0.3$. The mass of WASP 1628+10B is only $0.135 pm 0.02M_{odot}$. The effective temperature of this pre-He-WD is approximately 9200K. The Ultracam photometry of WASP 1628+10 shows variability at several frequencies around 40 cycles per day, which is typical for $delta$ Sct-type pulsations often observed in early A-type stars like WASP 1628+10A. We also observe frequencies near 114 cycles/day and 129 cycles/day, much higher than the frequencies normally seen in $delta$ Sct stars. Additional photometry through the primary eclipse will be required to confirm that these higher frequencies are due to pulsations in WASP 1628+10B. If confirmed, this would be only the second known example of a pre-He-WD showing high-frequency pulsations.
