Period, epoch and prediction errors of ephemeris from continuous sets of timing measurements

Space missions such as Kepler and CoRoT have led to large numbers of eclipse or transit measurements in nearly continuous time series. This paper shows how to obtain the period error in such measurements from a basic linear least-squares fit, and how to correctly derive the timing error in the prediction of future transit or eclipse events. Assuming strict periodicity, a formula for the period error of such time series is derived: sigma_P = sigma_T (12/( N^3-N))^0.5, where sigma_P is the period error; sigma_T the timing error of a single measurement and N the number of measurements. Relative to the iterative method for period error estimation by Mighell & Plavchan (2013), this much simpler formula leads to smaller period errors, whose correctness has been verified through simulations. For the prediction of times of future periodic events, the usual linear ephemeris where epoch errors are quoted for the first time measurement, are prone to overestimation of the error of that prediction. This may be avoided by a correction for the duration of the time series. An alternative is the derivation of ephemerides whose reference epoch and epoch error are given for the centre of the time series. For long continuous or near-continuous time series whose acquisition is completed, such central epochs should be the preferred way for the quotation of linear ephemerides. While this work was motivated from the analysis of eclipse timing measures in space-based light curves, it should be applicable to any other problem with an uninterrupted sequence of discrete timings for which the determination of a zero point, of a constant period and of the associated errors is needed.Comment: Astronomy and Astrophysics, accepte

TEE, a simple estimator for the precision of eclipse and transit minimum times

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 TEE's 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.Comment: Accepted by A&A. Version 2 with updated timing uncertainties of TESS mission due to correction of a figure in Sullivan et al. 201

Deep CCD Photometry and the Initial Mass Function of the Core of the OB Cluster Berkeley 86

Based on photometry of deep CCD frames of the central region of the OB cluster Berkeley 86, we derive the cluster mass function. The absence of current star formation, and the cluster\u27s young age of about 6Myrs, leads to the conclusion that the initial mass function (IMF) and the current mass function are identical for stars with m\u3c 10msun_. In the range of 1.2-20msun_, an IMF with a slope of {GAMMA}=-1.3+/-0.3 is found. This value agrees well with other recent determinations of young clusters IMFs which are close to the classical Salpeter IMF with {GAMMA}=-1.35. Sections of the IMF of Berkeley 86 that are significantly steeper, or flatter, are most likely the result of a dip in the star\u27s mass distribution in the range of 3.5-10msun_. Similar dips may have led to steep IMFs over narrow mass ranges, as reported in the literature for some other clusters. No sign for a low mass turn-over in the IMF of Berkeley 86 is found for masses extending down to 0.85 msun _ (Refer to PDF file for exact formulas)

The orbital phases and secondary transit of Kepler-10b - A physical interpretation based on the Lava-ocean planet model -

The Kepler mission has made an important observation, the first detection of photons from a terrestrial planet by observing its phase curve (Kepler-10b). This opens a new field in exoplanet science: the possibility to get information about the atmosphere and surface of rocky planets, objects of prime interest. In this letter, we apply the Lava-ocean model to interpret the observed phase curve. The model, a planet with no atmosphere and a surface partially made of molten rocks, has been proposed for planets of the class of CoRoT-7b, i.e. rocky planets very close to their star (at few stellar radii). Kepler-10b is a typical member of this family. It predicts that the light from the planet has an important emission component in addition to the reflected one, even in the Kepler spectral band. Assuming an isotropical reflection of light by the planetary surface (Lambertian-like approximation), we find that a Bond albedo of \sim50% can account for the observed amplitude of the phase curve, as opposed to a first attempt where an unusually high value was found. We propose a physical process to explain this still large value of the albedo. The overall interpretation can be tested in the future with instruments as JWST or EChO. Our model predicts a spectral dependence that is clearly distinguishable from that of purely reflected light, and from that of a planet at a uniform temperature.Comment: Accepted in ApJ Letters, 17 pages, 3 figure

CoRoT: harvest of the exoplanet program

One of the objectives of the CoRoT mission is the search for transiting extrasolar planets using high-precision photometry, and the accurate characterization of their fundamental parameters. The CoRoT satellite consecutively observes crowded stellar fields since February 2007, in high-cadence precise photometry; periodic eclipses are detected and analysed in the stellar light curves. Then complementary observations using ground-based facilities allows establishing the nature of the transiting body and its mass. CoRoT has acquired more than 163,000 light curves and detected about 500 planet candidates. A fraction of them (5%) are confirmed planets whose masses are independently measured. Main highlights of the CoRoT discoveries are: i) the variety of internal structures in close-in giant planets, ii) the characterisation of the first known transiting rocky planet, CoRoT-7 b, iii) multiple constraints on the formation, evolution, role of tides in planetary systems.Comment: Icarus, in press, special issue on Exoplanet

A 5MJup5M_\text{Jup} Non-Transiting Coplanar Circumbinary Planet Around Kepler-1660AB

Over a dozen transiting circumbinary planets have been discovered around eclipsing binaries. Transit detections are biased towards aligned planet and binary orbits, and indeed all of the known planets have mutual inclinations less than $4.5^{\circ}$. One path to discovering circumbinary planets with misaligned orbits is through eclipse timing variations (ETVs) of non-transiting planets. Borkovits et al. (2016) discovered ETVs on the 18.6 d binary Kepler-1660AB, indicative of a third body on a $\approx 236$ d period, with a misaligned orbit and a potentially planetary mass. Getley et al. (2017) agreed with the planetary hypothesis, arguing for a $7.7M_{\rm Jup}$ circumbinary planet on an orbit that is highly misaligned by $120^{\circ}$ with respect to the binary. In this paper, we obtain the first radial velocities of the binary. We combine these with an analysis of not only the ETVs but also the eclipse depth variations. We confirm the existence of a $239.5$ d circumbinary planet, but with a lower mass of $4.87M_{\rm Jup}$ and a coplanar orbit. The misaligned orbits proposed by previous authors are definitively ruled out by a lack of eclipse depth variations. Kepler-1660ABb is the first confirmed circumbinary planet found using ETVs around a main sequence binary.Comment: Resubmitted to MNRAS following positive referee repor

Trends in Frailty and Its Association With Mortality:Results From the Longitudinal Aging Study Amsterdam, 1995-2016

The aim of this study was to investigate trends in frailty and its relationship with mortality among older adults aged 64-84 years across a period of 21 years. We used data from 1995 to 2016 from the Longitudinal Aging Study Amsterdam. A total of 7,742 observations of 2,874 respondents in the same age range (64-84 years) across 6 measurement waves were included. Frailty was measured with a 32-item frailty index, with a cutpoint of ≥0.25 to indicate frailty. The outcome measure was 4-year mortality. Generalized estimating equation analyses showed that among older adults aged 64-84 years the 4-year mortality rate declined between 1995 and 2016, while the prevalence of frailty increased. Across all measurement waves, frailty was associated with 4-year mortality (odds ratio = 2.79, 95% confidence interval: 2.39, 3.26). There was no statistically significant interaction effect between frailty and time on 4-year mortality, indicating a stable association between frailty and mortality. In more recent generations of older adults, frailty prevalence rates were higher, while excess mortality rates of frailty remained the same. This is important information for health policy-makers and clinical practitioners, showing that continued efforts are needed to reduce frailty and its negative health consequences