Transit timing analysis of the exoplanets TrES-1 and TrES-2

The aim of this work is a detailed analysis of transit light curves from TrES-1 and TrES-2, obtained over a period of three to four years, in order to search for variabilities in observed mid-transit times and to set limits for the presence of additional third bodies. Using the IAC 80cm telescope, we observed transits of TrES-1 and TrES-2 over several years. Based on these new data and previously published work, we studied the observed light curves and searched for variations in the difference between observed and calculated (based on a fixed ephemeris) transit times. To model possible transit timing variations, we used polynomials of different orders, simulated O-C diagrams corresponding to a perturbing third mass and sinusoidal fits. For each model we calculated the $\chi^2$ residuals and the False Alarm Probability (FAP). For TrES-1 we can exclude planetary companions ($>$ 1 M$_{\oplus}$) in the 3:2 and 2:1 MMRs with high FAPs based on our transit observations from ground. Additionally, the presence of a light time effect caused by e. g. a 0.09 M_Sun mass star at a distance of 7.8 AU is possible. As for TrES-2, we found a better ephemeris of T$_c = 2 453 957.63512(28) + 2.4706101(18) \times$Epoch and a good fit for a sine function with a period of 0.2 days, compatible with a moon around TrES-2 and an amplitude of 57 s, but it was not a uniquely low $\chi^2$ value that would indicate a clear signal. In both cases, TrES-1 and TrES-2, we were able to put upper limits on the presence of additional perturbers masses. We also conclude that any sinusoidal variations that might be indicative of exomoons need to be confirmed with higher statistical significance by further observations, noting that TrES-2 is in the field-of-view of the Kepler Space Telescope.

This upper mass limit is clearly way below our detection limit for masses causing transit timing variations in the system TrES-1 and TrES-2. The closest moon at this upper mass limit would cause a timing amplitude of the order of 10^-6 s, which is not detectable even from space by several orders of magnitude.

Remember that both TrES planets transit across their host star. If it were a binary planet or 52-Earth-mass trojan exoplanet, it would have been detected.

Sedna wrote:Plus, if it's confirmed, it shows that we are able to find moons with that size and, more generally, we are able to detect Earth-like moons.

This upper mass limit is clearly way below our detection limit for masses causing transit timing variations in the system TrES-1 and TrES-2. The closest moon at this upper mass limit would cause a timing amplitude of the order of 10^-6 s, which is not detectable even from space by several orders of magnitude.

Stalker wrote:I do not succeed in understanding. Were these moons discovered or are them only hypothetical? And how one they discovered? Can you give me a paper concerning the moon of HD 209458 b?

Sedna wrote:About the burning question of the tidal lock, some of you says that the moons of planets very close to their stars would be tidally locked to the host stars. But in the Hill Sphere of the planet, the gravity of the planet is higher than the gravity of the star, so the moons would tend to be tidally locked to the planet instead of the star.

Sedna wrote:PS: Does somebody know how to put the HTML code option ON ?

The wording of the abstract is kind of confusing, especially their use of the word "possible", which could be interpreted as "slightly suggested by the data", or "not ruled out."

Can you give me a paper concerning the moon of HD 209458 b?

which is not detectable even from space by several orders of magnitude.

Sedna wrote:Yes, but why people said that Kepler will or would be able to detect exomoons ?

Abstract wrote:We find that habitable-zone exomoons down to 0.2 Earth masses may be detected and ~25,000 stars could be surveyed for habitable-zone exomoons within Kepler's field-of-view. A Galactic Plane survey with Kepler-class photometry could potentially survey over one million stars for habitable-zone exomoons. In conclusion, we propose that habitable exomoons will be detectable should they exist in the local part of the galaxy.

Lazarus wrote:Well going to the formula in the paper referenced for tidal limits, for TrES-2 I get a moon mass limit of 10^-6 Earth masses for Q_p=10⁵. On the other hand the paper I referred to above suggests that for hot Jupiter satellites, Q_p values of ~10¹² might be more appropriate, which boosts the limit to about 10 Earth masses for this planet.

Sedna wrote:A super-Earth moon around such planets, isn't that too big ?

Sirius_Alpha wrote:It's too big under the assumption that Q_p = 10⁵.
It's okay under the assumption that Q_p = 10¹².
(where Q_p is the tidal dissipation parameter, and is a quantization of how efficient the planet is at dissipating tidal energy).

Ultimately, it comes down to what value of Q_p better fits these planets, and this isn't a value that is easy to measure. It's commonly assumed that Q_p = 10⁵, but if it isn't, then that changes the limit as to what the maximum moon mass can be.

Lazarus wrote:Of course there's also the issue of whether such a moon could form in the first place... theoretical predictions suggest that the maximum moon mass is a few ×10^-4 of the mass of the gas giant, but then again there is no observational evidence for scaling ratios of exomoons around exoplanets. There's also the possibility of capturing a terrestrial planet.