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Register a new userTEE, a simple estimator for the precision of eclipse and transit minimum times
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Hans J. Deeg
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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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Transiting exoplanets provide access to data to study the mass-radius relation and internal structure of extrasolar planets. Long-period transiting planets allow insight into planetary environments similar to the Solar System where, in contrast to hot Jupiters, planets are not constantly exposed to the intense radiation of their parent stars. Observations of secondary eclipses additionally permit studies of exoplanet temperatures and large-scale exo-atmospheric properties. We show how transit and eclipse probabilities are related to planet-star system geometries, particularly for long-period, eccentric orbits. The resulting target selection and observational strategies represent the principal ingredients of our photometric survey of known radial-velocity planets with the aim of detecting transit signatures (TERMS).
We present 33 transit minimum times of 20 transiting planets discovered by the CoRoT mission, which have been obtained from ground-based observations since the missions end in 2012, with the objective to maintain the ephemeris of these planets. Twelve of the observed planets are in the CoRoT fields near the galactic center and the remaining eight planets are in the fields near the anticenter. We detect indications for significant transit timing variations in the cases of CoRoT 3b, 11b, 13b, 27b. For two more planets (CoRoT 18b and 20b) we conclude that timing offsets in early follow-up observations led to ephemeris in discovery publications that are inconsistent with timings from follow-up observations in later epochs. In the case of CoRoT-20b, this might be due to the influence from a further non-transiting planet. We also note that a significant majority (23 of 33) of our reported minimum times have negative O-C values, albeit most of them are within the expected uncertainty of the ephemeris.
Observations of the Earthshine off the Moon allow for the unique opportunity to measure the large-scale Earth atmosphere. Another opportunity is realized during a total lunar eclipse which, if seen from the Moon, is like a transit of the Earth in front of the Sun. We thus aim at transmission spectroscopy of an Earth transit by tracing the solar spectrum during the total lunar eclipse of January 21, 2019. Time series spectra of the Tycho crater were taken with the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) at the Large Binocular Telescope (LBT) in its polarimetric mode in Stokes IQUV at a spectral resolution of 130000 (0.06 AA). In particular, the spectra cover the red parts of the optical spectrum between 7419-9067 AA . The spectrographs exposure meter was used to obtain a light curve of the lunar eclipse. The brightness of the Moon dimmed by 10.75 mag during umbral eclipse. We found both branches of the O$_2$ A-band almost completely saturated as well as a strong increase of H$_2$O absorption during totality. The deep penumbral spectra show significant excess absorption from the NaI 5890 AA doublet, the CaII infrared triplet around 8600 AA, and the KI line at 7699 AA in addition to several hyper-fine-structure lines of MnI and even from BaII. The detections of the latter two elements are likely due to an untypical solar center-to-limb effect rather than Earths atmosphere. The absorption in CaII and KI remained visible throughout umbral eclipse. A small continuum polarization of the O$_2$ A-band of 0.12% during umbral eclipse was detected at 6.3$sigma$. No line polarization of the O$_2$ A-band, or any other spectral-line feature, is detected outside nor inside eclipse. It places an upper limit of $approx$0.2% on the degree of line polarization during transmission through Earths atmosphere and magnetosphere.
When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model optimization and posterior sampling. Here we describe a general-purpose symplectic integrator for arbitrary orbital architectures, including those with close encounters, which we have recast to maintain numerical stability and precision for small step sizes. We compute the derivatives of the N-body coordinates and velocities as a function of time with respect to the initial conditions and masses by propagating the Jacobian along with the N-body integration. For the first time we obtain the derivatives of the transit times with respect to the initial conditions and masses using the chain rule, which is quicker and more accurate than using finite differences or automatic differentiation. We implement this algorithm in an open source package, NbodyGradient.jl, written in the Julia language, which has been used in the optimization and error analysis of transit-timing variations in the TRAPPIST-1 system. We present tests of the accuracy and precision of the code, and show that it compares favorably in speed to other integrators which are written in C.
Recently, we introduced PLanetary Atmospheric Tool for Observer Noobs (PLATON), a Python package that calculates model transmission spectra for exoplanets and retrieves atmospheric characteristics based on observed spectra. We now expand its capabilities to include the ability to compute secondary eclipse depths. We have also added the option to calculate models using the correlated-$k$ method for radiative transfer, which improves accuracy without sacrificing speed. Additionally, we update the opacities in PLATON--many of which were generated using old or proprietary line lists--using the most recent and complete public line lists. These opacities are made available at R=1000 and R=10,000 over the 0.3--30 um range, and at R=375,000 in select near IR bands, making it possible to utilize PLATON for ground-based high resolution cross correlation studies. To demonstrate PLATONs new capabilities, we perform a retrieval on published HST and Spitzer transmission and emission spectra of the archetypal hot Jupiter HD 189733b. This is the first joint transit and secondary eclipse retrieval for this planet in the literature, as well as the most comprehensive set of both transit and eclipse data assembled for a retrieval to date. We find that these high signal-to-noise data are well-matched by atmosphere models with a C/O ratio of $0.66_{-0.09}^{+0.05}$ and a metallicity of $12_{-5}^{+8}$ times solar where the terminator is dominated by extended nanometer-sized haze particles at optical wavelengths. These are among the smallest uncertainties reported to date for an exoplanet, demonstrating both the power and the limitations of HST and Spitzer exoplanet observations.
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