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تسجيل مستخدم جديدRefining the transit timing and photometric analysis of TRAPPIST-1: Masses, radii, densities, dynamics, and ephemerides
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We have collected transit times for the TRAPPIST-1 system with the Spitzer Space Telescope over four years. We add to these ground-based, HST and K2 transit time measurements, and revisit an N-body dynamical analysis of the seven-planet system using our complete set of times from which we refine the mass ratios of the planets to the star. We next carry out a photodynamical analysis of the Spitzer light curves to derive the density of the host star and the planet densities. We find that all seven planets densities may be described with a single rocky mass-radius relation which is depleted in iron relative to Earth, with Fe 21 wt% versus 32 wt% for Earth, and otherwise Earth-like in composition. Alternatively, the planets may have an Earth-like composition, but enhanced in light elements, such as a surface water layer or a core-free structure with oxidized iron in the mantle. We measure planet masses to a precision of 3-5%, equivalent to a radial-velocity (RV) precision of 2.5 cm/sec, or two orders of magnitude more precise than current RV capabilities. We find the eccentricities of the planets are very small; the orbits are extremely coplanar; and the system is stable on 10 Myr timescales. We find evidence of infrequent timing outliers which we cannot explain with an eighth planet; we instead account for the outliers using a robust likelihood function. We forecast JWST timing observations, and speculate on possible implications of the planet densities for the formation, migration and evolution of the planet system.
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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 additi
onal 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.
Transit Timing Variations, or TTVs, can be a very efficient way of constraining masses and eccentricities of multi-planet systems. Recent measurements of the TTVs of TRAPPIST-1 led to an estimate of the masses of the planets, enabling an estimate of
their densities. A recent TTV analysis using data obtained in the past two years yields a 34% and 13% increase in mass for TRAPPIST-1b and c, respectively. In most studies to date, a Newtonian N-body model is used to fit the masses of the planets, while sometimes general relativity is accounted for. Using the Posidonius N-body code, we show that in the case of the TRAPPIST-1 system, non-Newtonian effects might be also relevant to correctly model the dynamics of the system and the resulting TTVs. In particular, using standard values of the tidal Love number $k_2$ (accounting for the tidal deformation) and the fluid Love number $k_{2f}$ (accounting for the rotational flattening) leads to differences in the TTVs of TRAPPIST-1b and c similar to the differences caused by general relativity. We also show that relaxing the values of tidal Love number $k_2$ and the fluid Love number $k_{2f}$ can lead to TTVs which differ by as much as a few 10~s on a $3-4$-year timescale, which is a potentially observable level. The high values of the Love numbers needed to reach observable levels for the TTVs could be achieved for planets with a liquid ocean, which, if detected, might then be interpreted as a sign that TRAPPIST-1b and TRAPPIST-1c could have a liquid magma ocean. For TRAPPIST-1 and similar systems, the models to fit the TTVs should potentially account for general relativity, for the tidal deformation of the planets, for the rotational deformation of the planets and, to a lesser extent, for the rotational deformation of the star, which would add up to 7x2+1 = 15 additional free parameters in the case of TRAPPIST-1.
The newly detected TRAPPIST-1 system, with seven low-mass, roughly Earth-sized planets transiting a nearby ultra-cool dwarf, is one of the most important exoplanet discoveries to date. The short baseline of the available discovery observations, howev
er, means that the planetary masses (obtained through measurement of transit timing variations of the planets of the system) are not yet well constrained. The masses reported in the discovery paper were derived using a combination of photometric timing measurements obtained from the ground and from the Spitzer spacecraft, and have uncertainties ranging from 30% to nearly 100%, with the mass of the outermost, $P=18.8,{rm d}$, planet h remaining unmeasured. Here, we present an analysis that supplements the timing measurements of the discovery paper with 73.6 days of photometry obtained by the K2 Mission. Our analysis refines the orbital parameters for all of the planets in the system. We substantially improve the upper bounds on eccentricity for inner six planets (finding $e<0.02$ for inner six known members of the system), and we derive masses of $0.79pm 0.27 ,M_{oplus}$, $1.63pm 0.63,M_{oplus}$, $0.33pm 0.15,M_{oplus}$, $0.24^{+0.56}_{-0.24},M_{oplus}$, $0.36pm 0.12,M_{oplus}$, $0.566pm 0.038,M_{oplus}$, and $0.086pm 0.084,M_{oplus}$ for planets b, c, d, e, f, g, and h, respectively.
We conducted a global analysis of the TRAPPIST Ultra-Cool Dwarf Transit Survey - a prototype of the SPECULOOS transit search conducted with the TRAPPIST-South robotic telescope in Chile from 2011 to 2017 - to estimate the occurrence rate of close-in
planets such as TRAPPIST-1b orbiting ultra-cool dwarfs. For this purpose, the photometric data of 40 nearby ultra-cool dwarfs were reanalysed in a self-consistent and fully automated manner starting from the raw images. The pipeline developed specifically for this task generates differential light curves, removes non-planetary photometric features and stellar variability, and searches for transits. It identifies the transits of TRAPPIST-1b and TRAPPIST-1c without any human intervention. To test the pipeline and the potential output of similar surveys, we injected planetary transits into the light curves on a star-by-star basis and tested whether the pipeline is able to detect them. The achieved photometric precision enables us to identify Earth-sized planets orbiting ultra-cool dwarfs as validated by the injection tests. Our planet-injection simulation further suggests a lower limit of 10 per cent on the occurrence rate of planets similar to TRAPPIST-1b with a radius between 1 and 1.3 $R_oplus$ and the orbital period between 1.4 and 1.8 days.
CoRoT, the pioneer space-based transit search, steadily provides thousands of high-precision light curves with continuous time sampling over periods of up to 5 months. The transits of a planet perturbed by an additional object are not strictly period
ic. By studying the transit timing variations (TTVs), additional objects can be detected in the system. A transit timing analysis of CoRoT-1b is carried out to constrain the existence of additional planets in the system. We used data obtained by an improved version of the CoRoT data pipeline (version 2.0). Individual transits were fitted to determine the mid-transit times, and we analyzed the derived $O-C$ diagram. N-body integrations were used to place limits on secondary planets. No periodic timing variations with a period shorter than the observational window (55 days) are found. The presence of an Earth-mass Trojan is not likely. A planet of mass greater than $sim 1$ Earth mass can be ruled out by the present data if the object is in a 2:1 (exterior) mean motion resonance with CoRoT-1b. Considering initially circular orbits: (i) super-Earths (less than 10 Earth-masses) are excluded for periods less than about 3.5 days, (ii) Saturn-like planets can be ruled out for periods less than about 5 days, (iii) Jupiter-like planets should have a minimum orbital period of about 6.5 days.
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