Determination of the size, mass, and density of “exomoons” from photometric transit timing variations

Aims. Precise photometric measurements of the upcoming space missions allow the size, mass, and density of satellites of exoplanets to be determined. Here we present such an analysis using the photometric transit timing variation $({\rm TTV_p})$. Methods. We examined the light curve effects of both the transiting planet and its satellite. We define the photometric central time of the transit that is equivalent to the transit of a fixed photocenter. This point orbits the barycenter, and leads to the photometric transit timing variations. Results. The exact value of ${\rm TTV_p}$ depends on the ratio of the density, the mass, and the size of the satellite and the planet. Since two of those parameters are independent, a reliable estimation of the density ratio leads to an estimation of the size and the mass of the exomoon. Upper estimations of the parameters are possible in the case when an upper limit of ${\rm TTV_p}$ is known. In case the density ratio cannot be estimated reliably, we propose an approximation with assuming equal densities. The presented photocenter ${\rm TTV_p}$ analysis predicts the size of the satellite better than the mass. We simulated transits of the Earth-Moon system in front of the Sun. The estimated size and mass of the Moon are 0.020 Earth-mass and 0.274 Earth-size if equal densities are assumed. This result is comparable to the real values within a factor of 2. If we include the real density ratio (about 0.6), the results are 0.010 Earth-Mass and 0.253 Earth-size, which agree with the real values within 20%.