Gemini/GMOS Transmission Spectroscopy of the Grazing Planet Candidate WD 1856+534 b

WD 1856+534 b is a Jupiter-sized, cool giant planet candidate transiting the white dwarf WD 1856+534. Here, we report an optical transmission spectrum of WD 1856+534 b obtained from ten transits using the Gemini Multi-Object Spectrograph. This system is challenging to observe due to the faintness of the host star and the short transit duration. Nevertheless, our phase-folded white light curve reached a precision of 0.12%. WD 1856+534 b provides a unique transit configuration compared to other known exoplanets: the planet is 8× larger than its star and occults over half of the stellar disk during mid-transit. Consequently, many standard modeling assumptions do not hold. We introduce the concept of a “limb darkening corrected, time-averaged transmission spectrum” and propose that this is more suitable than ( R p , λ / R s ) 2 for comparisons to atmospheric models for planets with grazing transits. We also present a modified radiative transfer prescription. Though the transmission spectrum shows no prominent absorption features, it is sufficiently precise to constrain the mass of WD 1856+534 b to be >0.84 M J (to 2σ confidence), assuming a clear atmosphere and a Jovian composition. High-altitude cloud decks can allow lower masses. WD 1856+534 b could have formed either as a result of common envelope evolution or migration under the Kozai–Lidov mechanism. Further studies of WD 1856+534 b, alongside new dedicated searches for substellar objects around white dwarfs, will shed further light on the mysteries of post-main-sequence planetary systems.

Thomson Scattering in the Lower Corona in the Presence of Sunspots

Polarized scattered light from low (few tens of megameter altitudes) coronal transients has been recently reported in Solar Dynamics Observatory/Helioseismic and Magnetic Image (HMI) observations. In a classic paper, Minnaert (1930) provided an analytic theory of polarization via electron scattering in the corona. His work assumed axisymmetric input from the photosphere with a single-parameter limb-darkening function. This diagnostic has recently been used to estimate the free-electron number and mass of HMI transients near the solar limb, but it applies equally well to any coronal material, at any height. Here we extend his work numerically to incorporate sunspots, which can strongly effect the polarization properties of the scattered light in the low corona. Sunspot effects are explored first for axisymmetric model cases, and then applied to the full description of two sunspot groups as observed by HMI. We find that (1) as previously reported by Minnaert, limb darkening has a strong influence, usually increasing the level of linear polarization tangential to the limb; (2) unsurprisingly, the effects of the sunspot generally increase at the lower scatterer altitudes, and increase the larger the sunspot is and the closer to their center the scatterer subpoint is; (3) assuming the Stokes Q > 0 basis to be tangential to the limb, sunspots typically decrease the Stokes Q/I polarization and the perceived electron densities below the spotless case, sometimes dramatically; and (4) typically, a sizeable non-zero Stokes U/I polarization component will appear when a sunspot’s influence becomes non-negligible. However, that is not true in rare cases of extreme symmetry (e.g., scattering mass at the center of an axisymmetric sunspot). The tools developed here are generally applicable to an arbitrary image input.

Modelling of Planetary Gravitational Microlensing Events

<p>This thesis describes and develops procedures for the generation of theoretical lightcurves that can be used to model gravitational microlensing events that involve multiple lenses. Of particular interest are the cases involving a single lens star with one or more orbiting planets, as this has proven to be an effective way of detecting extrasolar planets. Although there is an analytical expression for microlensing lightcurves produced by single lensing body, the generation of model lightcurves for more than one lensing body requires the use of numerical techniques. The method developed here, known as the semi-analytic method, involves the analytical rearrangement of the relatively simple ‘lens equation’ to produce a high-order complex lens polynomial. Root-finding algorithms are then used to obtain the roots of this ‘lens polynomial’ in order to locate the positions of the images and calculate their magnifications. By running example microlensing events through the root-finding algorithms, both the speed and accuracy of the Laguerre and Jenkins-Traub algorithms were investigated. It was discovered that, in order to correctly identify the image positions, a method involving solutions of several ‘lens polynomials’ corresponding to different coordinate origins needed to be invoked. Multipole and polygon approximations were also developed to include finite source and limb darkening effects. The semi-analytical method and the appropriate numerical techniques were incorporated into a C++ modelling code at VUW (Victoria University of Wellington) known as mlens2. The effectiveness of the semi-analytic method was demonstrated using mlens2 to generate theoretical lightcurves for the microlensing events MOA-2009-BLG-319 and OGLE-2006-BLG-109. By comparing these theoretical lightcurves with the observed photometric data and the published models, it was demonstrated that the semi-analytic method described in this thesis is a robust and efficient method for discovering extrasolar planets.</p>

Modelling of Planetary Gravitational Microlensing Events

<p>This thesis describes and develops procedures for the generation of theoretical lightcurves that can be used to model gravitational microlensing events that involve multiple lenses. Of particular interest are the cases involving a single lens star with one or more orbiting planets, as this has proven to be an effective way of detecting extrasolar planets. Although there is an analytical expression for microlensing lightcurves produced by single lensing body, the generation of model lightcurves for more than one lensing body requires the use of numerical techniques. The method developed here, known as the semi-analytic method, involves the analytical rearrangement of the relatively simple ‘lens equation’ to produce a high-order complex lens polynomial. Root-finding algorithms are then used to obtain the roots of this ‘lens polynomial’ in order to locate the positions of the images and calculate their magnifications. By running example microlensing events through the root-finding algorithms, both the speed and accuracy of the Laguerre and Jenkins-Traub algorithms were investigated. It was discovered that, in order to correctly identify the image positions, a method involving solutions of several ‘lens polynomials’ corresponding to different coordinate origins needed to be invoked. Multipole and polygon approximations were also developed to include finite source and limb darkening effects. The semi-analytical method and the appropriate numerical techniques were incorporated into a C++ modelling code at VUW (Victoria University of Wellington) known as mlens2. The effectiveness of the semi-analytic method was demonstrated using mlens2 to generate theoretical lightcurves for the microlensing events MOA-2009-BLG-319 and OGLE-2006-BLG-109. By comparing these theoretical lightcurves with the observed photometric data and the published models, it was demonstrated that the semi-analytic method described in this thesis is a robust and efficient method for discovering extrasolar planets.</p>

Correcting the effect of stellar spots on ARIEL transmission spectra II. The limb darkening effect

This paper is part of an effort to correct the transmission spectra of a transiting planet orbiting an active star. In Paper I (Cracchiolo et al. 2020) we have demonstrated a methodology to minimize the potential bias induced by unocculted star spots on the transmission spectrum, assuming a spot model parameterized by filling factor and temperature. In this work we introduce the limb darkening effect, therefore the position of the spot in the stellar disk and the impact parameter of the transiting planet now play a key role. The method is tested on simulations of planetary transits of three representative kinds of planetary systems, at ARIEL resolution. We find that a realistic treatment of the limb darkening is required to reliably estimate both the spots parameters and the transmission spectrum of the transiting planet. Furthermore, we show that the influence of the spots on the retrieval of the planetary transmission spectrum is significant for spots close to the center of the star, covering a fraction greater than 0.05 and with a temperature contrast greater than 500 K, and that for these cases our method can confidently extract the transmission spectrum and the impact parameter of the transiting planet for both cases of occulted and not occulted spots, provided that we have an accurate characterization of the stellar parameters and a reliable simulator of the instrument performances.

Restoring the top-of-atmosphere reflectance during solar eclipses: a proof of concept with the UV absorbing aerosol index measured by TROPOMI

During a solar eclipse the solar irradiance reaching the top of the atmosphere (TOA) is reduced in the Moon shadow. The solar irradiance is commonly measured by Earth observation satellites before the start of the solar eclipse and is not corrected for this reduction, which results in a decrease in the computed TOA reflectances. Consequently, air quality products that are derived from TOA reflectance spectra, such as the ultraviolet (UV) absorbing aerosol index (AAI), are distorted or undefined in the shadow of the Moon. The availability of air quality satellite data in the penumbral and antumbral shadow during solar eclipses, however, is of particular interest to users studying the atmospheric response to solar eclipses. Given the time and location of a point on the Earth's surface, we explain how to compute the obscuration during a solar eclipse, taking into account wavelength-dependent solar limb darkening. With the calculated obscuration fractions, we restore the TOA reflectances and the AAI in the penumbral shadow during the annular solar eclipses on 26 December 2019 and 21 June 2020 measured by the TROPOMI/S5P instrument. We compare the calculated obscuration to the estimated obscuration using an uneclipsed orbit. In the corrected products, the signature of the Moon shadow disappeared, but only if wavelength-dependent solar limb darkening is taken into account. We find that the Moon shadow anomaly in the uncorrected AAI is caused by a reduction of the measured reflectance at 380 nm, rather than a colour change of the measured light. We restore common AAI features such as the sunglint and desert dust, and we confirm the restored AAI feature on 21 June 2020 at the Taklamakan Desert by measurements of the GOME-2C satellite instrument on the same day but outside the Moon shadow. No indication of local absorbing aerosol changes caused by the eclipses was found. We conclude that the correction method of this paper can be used to detect real AAI rising phenomena during a solar eclipse and has the potential to restore any other product that is derived from TOA reflectance spectra. This would resolve the solar eclipse anomalies in satellite air quality measurements in the penumbra and antumbra and would allow for studying the effect of the eclipse obscuration on the composition of the Earth's atmosphere from space.

Forward modelling of Kepler-band variability due to faculae and spots

Variability observed in photometric lightcurves of late-type stars (on timescales longer than a day) is a dominant noise source in exoplanet surveys and results predominantly from surface manifestations of stellar magnetic activity, namely faculae and spots. The implementation of faculae in lightcurve models is an open problem, with scaling typically based on spectra equivalent to hot stellar atmospheres or assuming a solar-derived facular contrast. We modelled rotational (single period) lightcurves of active G2, K0, M0 and M2 stars, with Sun-like surface distributions and realistic limb-dependent contrasts for faculae and spots. The sensitivity of lightcurve variability to changes in model parameters such as stellar inclination, feature area coverage, spot temperature, facular region magnetic flux density and active band latitudes is explored. For our lightcurve modelling approach we used actress, a geometrically accurate model for stellar variability. actress generates 2-sphere maps representing stellar surfaces and populates them with user-prescribed spot and facular region distributions. From this, lightcurves can be calculated at any inclination. Quiet star limb darkening and limb-dependent facular contrasts were derived from MURaM 3D magnetoconvection simulations using ATLAS9. 1D stellar atmosphere models were used for the spot contrasts. We applied actress in Monte Carlo simulations, calculating lightcurve variability amplitudes in the Kepler band. We found that, for a given spectral type and stellar inclination, spot temperature and spot area coverage have the largest effect on variability of all simulation parameters. For a spot coverage of $1{{\ \rm per\ cent}}$, the typical variability of a solar-type star is around 2 parts-per-thousand. The presence of faculae clearly affects the mean brightness and lightcurve shape, but has relatively little influence on the variability.