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Register a new userSystem Geometries and Transit / Eclipse Probabilities
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Kaspar von Braun
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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).
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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.
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.
The probability that an exoplanet transits its host star is high for planets in close orbits, but drops off rapidly for increasing semimajor axes. This makes transit surveys for planets with large semimajor axes orbiting bright stars impractical, since one would need to continuously observe hundreds of stars that are spread out over the entire sky. One way to make such a survey tractable is to constrain the inclination of the stellar rotation axes in advance, and thereby enhance the transit probabilities. We derive transit probabilities for stars with stellar inclination constraints, considering a reasonable range of planetary system inclinations. We find that stellar inclination constraints can improve the transit probability by almost an order of magnitude for habitable-zone planets. When applied to an ensemble of stars, such constraints dramatically lower the number of stars that need to be observed in a targeted transit survey. We also consider multiplanet systems where only one planet has an identified transit, and derive the transit probabilities for the second planet assuming a range of mutual planetary inclinations.
I present RoadRunner, a fast exoplanet transit model that can use any radially symmetric function to model stellar limb darkening while still being faster to evaluate than the analytical transit model for quadratic limb darkening by Mandel & Agol (2002). CPU and GPU implementations of the model are available in the PyTransit transit modelling package, and come with platform-independent parallelisation, supersampling, and support for modelling complex heterogeneous time series. The code is written in numba-accelerated Python (and the GPU model in OpenCL) without C or Fortran dependencies, which allows for the limb darkening model to be given as any Python-callable function. Finally, as an example of the flexibility of the approach, the latest version of PyTransit comes with a numerical limb darkening model that uses LDTk-generated limb darkening profiles directly without approximating them by analytical models.
We observed a transit of WASP-166 b using nine NGTS telescopes simultaneously with TESS observations of the same transit. We achieved a photometric precision of 152 ppm per 30 minutes with the nine NGTS telescopes combined, matching the precision reached by TESS for the transit event around this bright (T=8.87) star. The individual NGTS light curve noise is found to be dominated by scintillation noise and appears free from any time-correlated noise or any correlation between telescope systems. We fit the NGTS data for $T_C$ and $R_p/R_*$. We find $T_C$ to be consistent to within 0.25$sigma$ of the result from the TESS data, and the difference between the TESS and NGTS measured $R_p/R_*$ values is 0.9$sigma$. This experiment shows that multi-telescope NGTS photometry can match the precision of TESS for bright stars, and will be a valuable tool in refining the radii and ephemerides for bright TESS candidates and planets. The transit timing achieved will also enable NGTS to measure significant transit timing variations in multi-planet systems.
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