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Register a new userA modified Kwee - van Woerden method for eclipse minimum timing with reliable error estimates
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The Kwee - van Woerden (KvW) method used for the determination of eclipse minimum times has been a staple in eclipsing binary research for decades, due its simplicity and the independence of external input parameters, which also makes it well-suited to obtaining timings of exoplanet transits. However, its estimates of the timing error have been known to have a low reliability. During the analysis of very precise photometry of CM Draconis eclipses from TESS space mission data, KvWs original equation for the timing error estimate produced numerical errors, which evidenced a fundamental problem in this equation. This contribution introduces an improved approach for calculating the timing error with the KvW method. A code that implements this improved method, together with several further updates of the original method, are presented. An example of the application to CM Draconis light curves from TESS is given. The eclipse minimum times are derived with the KvW methods three original light curve folds, but also with five and seven folds. The use of five or more folds produces minimum timings with a substantially better precision. The improved method of error calculation delivers consistent timing errors which are in excellent agreement with error estimates obtained by other means. In the case of TESS data from CM Draconis, minimum times with an average precision of 1.1 seconds are obtained. Reliable timing errors are also a valuable indicator for evaluating if a given scatter in an O-C diagram is caused by measurement errors or by a physical period variation.
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We report eclipse timing variation analyses of 26 compact hierarchical triple stars comprised of an eccentric eclipsing (inner) binary and a relatively close tertiary component found in the {em Kepler} field. We simultaneously fit the primary and secondary $O-C$ curves of each system for the light-travel time effect (LTTE), as well as dynamical perturbations caused by the tertiary on different timescales. For the first time, we include those contributions of three-body interactions which originate from the eccentric nature of the inner binary. These effects manifest themselves both on the period of the triple system, $P_2$, and on the longer apse-node timescale. We demonstrate that consideration of the dynamically forced rapid apsidal motion yields an efficient and independent tool for the determination of the binary orbits eccentricity and orientation, as well as the 3D configuration of the triple. Modeling the forced apsidal motion also helps to resolve the degeneracy between the shapes of the LTTE and the dynamical delay terms on the $P_2$ timescale, due to the strong dependence of the apsidal motion period on the triples mass ratio. This can lead to the independent determination of the binary and tertiary masses without the need for independent radial velocity measurements. Through the use of our analytic method for fitting $O-C$ curves we have obtained robust solutions for system parameters for the ten most ideal triples of our sample, and only somewhat less robust, but yet acceptable, fits for the remaining systems. Finally we study the results of our 26 system parameter fits via a set of distributions of various physically important parameters, including mutual inclination angle, and mass and period ratios.
The light curve of 1SWASP J140747.93-394542.6, a $sim$16 Myr old star in the Sco-Cen OB association, underwent a complex series of deep eclipses that lasted 56 days, centered on April 2007. This light curve is interpreted as the transit of a giant ring system that is filling up a fraction of the Hill sphere of an unseen secondary companion, J1407b. We fit the light curve with a model of an azimuthally symmetric ring system, including spatial scales down to the temporal limit set by the stars diameter and relative velocity. The best ring model has 37 rings and extends out to a radius of 0.6 AU (90 million km), and the rings have an estimated total mass on the order of $100 M_{Moon}$. The ring system has one clearly defined gap at 0.4 AU (61 million km), which we hypothesize is being cleared out by a $< 0.8 M_{oplus}$ exosatellite orbiting around J1407b. This eclipse and model implies that we are seeing a circumplanetary disk undergoing a dynamic transition to an exosatellite-sculpted ring structure and is one of the first seen outside our Solar system.
The analysis of the CoRoT space mission data was performed aiming to test a method that selects, among the several light curves observed, the transiting systems that likely host a low-mass star orbiting the main target. The method identifies stellar companions by fitting a model to the observed transits. Applying this model, that uses equations like Keplers third law and an empirical mass-radius relation, it is possible to estimate the mass and radius of the primary and secondary objects as well as the semimajor axis and inclination angle of the orbit. We focus on how the method can be used in the characterisation of transiting systems having a low-mass stellar companion with no need to be monitored with radial-velocity measurements or ground-based photometric observations. The model, which provides a good estimate of the system parameters, is also useful as a complementary approach to select possible planetary candidates. A list of confirmed binaries together with our estimate of their parameters are presented. The characterisation of the first twelve detected CoRoT exoplanetary systems was also performed and agrees very well with the results of their respective announcement papers. The comparison with confirmed systems validates our method, specially when the radius of the secondary companion is smaller than 1.5 Rjup, in the case of planets, or larger than 2 Rjup, in the case of low-mass stars. Intermediate situations are not conclusive.
We present the first results of a Kepler survey of 41 eclipsing binaries that we undertook to search for third star companions. Such tertiaries will periodically alter the eclipse timings through light travel time and dynamical effects. We discuss the prevalence of starspots and pulsation among these binaries and how these phenomena influence the eclipse times. There is no evidence of short period companions (P < 700 d) among this sample, but we do find evidence for long term timing variations in 14 targets (34%). We argue that this finding is consistent with the presence of tertiary companions among a significant fraction of the targets, especially if many have orbits measured in decades. This result supports the idea that the formation of close binaries involves the deposition of angular momentum into the orbital motion of a third star.
Context: Transit or eclipse timing variations have proven to be a valuable tool in exoplanet research. However, no simple way to estimate the potential precision of such timing measures has been presented yet, nor are guidelines available regarding the relation between timing errors and sampling rate. Aims: A `timing error estimator (TEE) equation is presented that requires only basic transit parameters as input. With the TEE, it is straightforward to estimate timing precisions both for actual data as well as for future instruments, such as the TESS and PLATO space missions. Methods: A derivation of the timing error based on a trapezoidal transit shape is given. We also verify the TEE on realistically modeled transits using Monte Carlo simulations and determine its validity range, exploring in particular the interplay between ingress/egress times and sampling rates. Results: The simulations show that the TEE gives timing errors very close to the correct value, as long as the temporal sampling is faster than transit ingress/egress durations and transits with very low S/N are avoided. Conclusions: The TEE is a useful tool to estimate eclipse or transit timing errors in actual and future data-sets. In combination with an equation to estimate period errors (Deeg 2015), predictions for the ephemeris precision of long-coverage observations are possible as well. The tests for the TEEs validity-range led also to implications for instrumental design: Temporal sampling has to be faster than transit in- or egress durations, or a loss in timing-precision will occur. An application to the TESS mission shows that transits close to its detection limit will have timing uncertainties that exceed 1 hour within a few months after their acquisition. Prompt follow-up observations will be needed to avoid a `loosing of their ephemeris.
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