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Register a new userDynamics of the TrES-2 system
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Added by
Florian Freistetter
Publication date
2009
fields
Physics
and research's language is
English
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The TrES-2 system harbors one planet which was discovered with the transit technique. In this work we investigate the dynamical behavior of possible additional, lower-mass planets. We identify the regions where such planets can move on stable orbits and show how they depend on the initial eccentricity and inclination. We find, that there are stable regions inside and outside the orbit of TrES-2b where additional, smaller planets can move. We also show that those planets can have a large orbital inclination which makes a detection with the transit technique very difficult.
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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-squared residuals and the False Alarm Probability (FAP). For TrES-1 we can exclude planetary companions (>1 M_earth) in the 3:2 and 2:1 MMRs having 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 Tc = 2,453,957.63512(28) + 2.4706101(18) x 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-squared 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.
We report on observations of several transit events of the transiting planet TrES-2 obtained with the Cassegrain-Teleskop-Kamera at the University Observatory Jena. Between March 2007 and November 2008 ten different transits and almost a complete orbital period were observed. Overall, in 40 nights of observation 4291 exposures (in total 71.52 h of observation) of the TrES-2 parent star were taken. With the transit timings for TrES-2 from the 34 events published by the TrES-network, the Transit Light Curve project and the Exoplanet Transit Database plus our own ten transits, we find that the orbital period is P=(2.470614 +/- 0.000001) d, a slight change by ~0.6 s compared to the previously published period. We present new ephemeris for this transiting planet. Furthermore, we found a second dip after the transit which could either be due to a blended variable star or occultation of a second star or even an additional object in the system. Our observations will be useful for future investigations of timing variations caused by additional perturbing planets and/or stellar spots and/or moons.
We present nine newly observed transits of TrES-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. A Markov-Chain Monte-Carlo analysis was used to determine the planet-star radius ratio and inclination of the system, which were found to be Rp/Rstar=0.1664^{+0.0011}_{-0.0018} and i = 81.73^{+0.13}_{-0.04} respectively, consistent with previous results. The central transit times and uncertainties were also calculated, using a residual-permutation algorithm as an independent check on the errors. A re-analysis of eight previously published TrES-3 light curves was conducted to determine the transit times and uncertainties using consistent techniques. Whilst the transit times were not found to be in agreement with a linear ephemeris, giving chi^2 = 35.07 for 15 degrees of freedom, we interpret this to be the result of systematics in the light curves rather than a real transit timing variation. This is because the light curves that show the largest deviation from a constant period either have relatively little out-of-transit coverage, or have clear systematics. A new ephemeris was calculated using the transit times, and was found to be T_c(0) = 2454632.62610 +- 0.00006 HJD and P = 1.3061864 +- 0.0000005 days. The transit times were then used to place upper mass limits as a function of the period ratio of a potential perturbing planet, showing that our data are sufficiently sensitive to have probed for sub-Earth mass planets in both interior and exterior 2:1 resonances, assuming the additional planet is in an initially circular orbit.
Pulsar timing arrays (PTAs) can be used to study the Solar-system ephemeris (SSE), the errors of which can lead to correlated timing residuals and significantly contribute to the PTA noise budget. Most Solar-system studies with PTAs assume the dominance of the term from the shift of the Solar-system barycentre (SSB). However, it is unclear to which extent this approximation can be valid, since the perturbations on the planetary orbits may become important as data precision keeps increasing. To better understand the effects of SSE uncertainties on pulsar timing, we develop the LINIMOSS dynamical model of the Solar system, based on the SSE of Guangyu Li. Using the same input parameters as DE435, the calculated planetary positions by LINIMOSS are compatible with DE435 at centimetre level over a 20-year timespan, which is sufficiently precise for pulsar-timing applications. We utilize LINIMOSS to investigate the effects of SSE errors on pulsar timing in a fully dynamical way, by perturbing one SSE parameter per trial and examining the induced timing residuals. For the outer planets, the timing residuals are dominated by the SSB shift, as assumed in previous work. For the inner planets, the variations in the orbit of the Earth are more prominent, making previously adopted assumptions insufficient. The power spectra of the timing residuals have complex structures, which may introduce false signals in the search of gravitational waves. We also study how to infer the SSE parameters using PTAs, and calculate the accuracy of parameter estimation.
We develop atmosphere models of two of the three Kepler-field planets that were known prior to the start of the Kepler mission (HAT-P-7b and TrES-2). We find that published Kepler and Spitzer data for HAT-P-7b appear to require an extremely hot upper atmosphere on the dayside, with a strong thermal inversion and little day-night redistribution. The Spitzer data for TrES-2 suggest a mild thermal inversion with moderate day-night redistribution. We examine the effect of nonequilibrium chemistry on TrES-2 model atmospheres and find that methane levels must be adjusted by extreme amounts in order to cause even mild changes in atmospheric structure and emergent spectra. Our best-fit models to the Spitzer data for TrES-2 lead us to predict a low secondary eclipse planet-star flux ratio (~2 x 10^-5) in the Kepler bandpass, which is consistent with what very recent observations have found. Finally, we consider how the Kepler-band optical flux from a hot exoplanet depends on the strength of a possible extra optical absorber in the upper atmosphere. We find that the optical flux is not monotonic in optical opacity, and the non-monotonicity is greater for brighter, hotter stars.
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