ldtk: Limb Darkening Toolkit Parviainen, H.; Aigrain, S.
Monthly Notices of the Royal Astronomical Society,
11/2015, Volume:
453, Issue:
4
Journal Article
Peer reviewed
Open access
We present a python package ldtk that automates the calculation of custom stellar limb-darkening (LD) profiles and model-specific limb-darkening coefficients using the library of phoenix-generated ...specific intensity spectra by Husser et al. The aim of the package is to facilitate analyses requiring custom generated LD profiles, such as the studies of exoplanet transits – especially transmission spectroscopy, where the transit modelling is carried out for custom narrow passbands – eclipsing binaries, interferometry, and microlensing events. First, ldtk can be used to compute custom LD profiles with uncertainties propagated from the uncertainties in the stellar parameter estimates. Secondly, ldtk can be used to estimate the LD-model-specific coefficients with uncertainties for the most common LD models. Thirdly, ldtk can be directly integrated into the log posterior computation of any pre-existing modelling code with minimal modifications. The last approach can be used to constrain the LD model parameter space directly by the LD profile, allowing for the marginalization over the LD parameter space without the need to approximate the constraint from the LD profile using a prior.
We analyzed three years of data from the Kepler space mission to derive rotation periods of main-sequence stars below 6500 K. Our automated autocorrelation-based method detected rotation periods ...between 0.2 and 70 days for 34,030 (25.6%) of the 133,030 main-sequence Kepler targets (excluding known eclipsing binaries and Kepler Objects of Interest), making this the largest sample of stellar rotation periods to date. In this paper we consider the detailed features of the now well-populated period-temperature distribution and demonstrate that the period bimodality, first seen by McQuillan et al. in the M-dwarf sample, persists to higher masses, becoming less visible above 0.6 M sub(middot in circle). We show that these results are globally consistent with the existing ground-based rotation-period data and find that the upper envelope of the period distribution is broadly consistent with a gyrochronological age of 4.5 Gyr, based on the isochrones of Barnes, Mamajek, & Hillenbrand and Meibom et al. We also performed a detailed comparison of our results to those of Reinhold et al. and Nielsen et al., who measured rotation periods of field stars observed by Kepler. We examined the amplitude of periodic variability for the stars with detection rotation periods, and found a typical range between ~950 ppm (5th percentile) and ~22,700 ppm (95th percentile), with a median of ~5600 ppm. We found typically higher amplitudes for shorter periods and lower effective temperatures, with an excess of low-amplitude stars above ~5400 K.
We present a new, simple method to predict activity-induced radial velocity (RV) variations using high-precision time series photometry. It is based on insights from a simple spot model, has only two ...free parameters (one of which can be estimated from the light curve) and does not require knowledge of the stellar rotation period. We test the method on simulated data and illustrate its performance by applying it to MOST/SOPHIE observations of the planet host star HD 189733, where it gives almost identical results to much more sophisticated but highly degenerate models, and synthetic data for the Sun, where we demonstrate that it can reproduce variations well below the m s−1 level. We also apply it to quarter 1 data for Kepler transit candidate host stars, where it can be used to estimate RV variations down to the 2-3 m s−1 level, and show that RV amplitudes above that level may be expected for approximately two-thirds of the candidates we examined.
ABSTRACT We present a consistent optimal estimation retrieval analysis of 10 hot Jupiter exoplanets, each with transmission spectral data spanning the visible to near-infrared wavelength range. Using ...the NEMESIS radiative transfer and retrieval tool, we calculate a range of possible atmospheric states for WASP-6b, WASP-12b, WASP-17b, WASP-19b, WASP-31b, WASP-39b, HD 189733b, HD 209458b, HAT-P-1b, and HAT-P-12b. We find that the spectra of all 10 planets are consistent with the presence of some atmospheric aerosol; WASP-6b, WASP-12b, WASP-17b, WASP-19b, HD 189733b, and HAT-P-12b are all fit best by Rayleigh scattering aerosols, whereas WASP-31b, WASP-39b and HD 209458b are better represented by a gray cloud model. HAT-P-1b has solutions that fall into both categories. WASP-6b, HAT-P-12b, HD 189733b, and WASP-12b must have aerosol extending to low atmospheric pressures (below 0.1 mbar). In general, planets with equilibrium temperatures between 1300 and 1700 K are best represented by deeper, gray cloud layers, whereas cooler or hotter planets are better fit using high Rayleigh scattering aerosol. We find little evidence for the presence of molecular absorbers other than H2O. Retrieval methods can provide a consistent picture across a range of hot Jupiter atmospheres with existing data, and will be a powerful tool for the interpretation of James Webb Space Telescope observations.
ABSTRACT
In recent years, Gaussian Process (GP) regression has become widely used to analyse stellar and exoplanet time-series data sets. For spotted stars, the most popular GP covariance function is ...the quasi-periodic (QP) kernel, whose hyperparameters of the GP have a plausible interpretation in terms of physical properties of the star and spots. In this paper, we test the reliability of this interpretation by modelling data simulated using a spot model using a QP GP, and the recently proposed quasi-periodic plus cosine (QPC) GP, comparing the posterior distributions of the GP hyperparameters to the input parameters of the spot model. We find excellent agreement between the input stellar rotation period and the QP and QPC GP period, and very good agreement between the spot decay time-scale and the length scale of the squared exponential term. We also compare the hyperparameters derived from light and radial velocity (RV) curves for a given star, finding that the period and evolution time-scales are in good agreement. However, the harmonic complexity of the GP, while displaying no clear correlation with the spot properties in our simulations, is systematically higher for the RV than for the light-curve data. Finally, for the QP kernel, we investigate the impact of noise and time-sampling on the hyperparameters in the case of RVs. Our results indicate that good coverage of rotation period and spot evolution time-scales is more important than the total number of points, and noise characteristics govern the harmonic complexity.
We have analysed 10 months of public data from the Kepler space mission to measure rotation periods of main-sequence stars with masses between 0.3 and 0.55 M. To derive the rotational period, we ...introduce the autocorrelation function and show that it is robust against phase and amplitude modulation and residual instrumental systematics. Of the 2483 stars examined, we detected rotation periods in 1570 (63.2 per cent), representing an increase of a factor of ∼30 in the number of rotation period determination for field M dwarfs. The periods range from 0.37 to 69.7 d, with amplitudes ranging from 1.0 to 140.8 mmag. The rotation period distribution is clearly bimodal, with peaks at ∼19 and ∼33 d, hinting at two distinct waves of star formation, a hypothesis that is supported by the fact that slower rotators tend to have larger proper motions. The two peaks of the rotation period distribution form two distinct sequences in period-temperature space, with the period decreasing with increasing temperature, reminiscent of the Vaughan-Preston gap. The period-mass distribution of our sample shows no evidence of a transition at the fully convective boundary. On the other hand, the slope of the upper envelope of the period-mass relation changes sign around 0.55 M, below which period rises with decreasing mass.
We present k2sc (K2 Systematics Correction), a python pipeline to model instrumental systematics and astrophysical variability in light curves from the K2 mission. k2sc uses Gaussian Process ...regression to model position-dependent systematics and time-dependent variability simultaneously, enabling the user to remove both (e.g. for transit searches) or to remove systematics while preserving variability (for variability studies). For periodic variables, k2sc automatically computes estimates of the period, amplitude and evolution time-scale of the variability. We apply k2sc to publicly available K2 data from Campaigns 3–5 showing that we obtain photometric precision approaching that of the original Kepler mission. We compare our results to other publicly available K2 pipelines, showing that we obtain similar or better results, on average. We use transit injection and recovery tests to evaluate the impact of k2sc on planetary transit searches in K2 Pre-search Data Conditioning data, for planet-to-star radius ratios down to R
p/R
* = 0.01 and periods up to P = 40 d, and show that k2sc significantly improves the ability to distinguish between true and false detections, particularly for small planets. k2sc can be run automatically on many light curves, or manually tailored for specific objects such as pulsating stars or large amplitude eclipsing binaries. It can be run on ASCII and FITS light-curve files, regardless of their origin. Both the code and the processed light curves are publicly available, and we provide instructions for downloading and using them. The methodology used by k2sc will be applicable to future transit search missions such as TESS and PLATO.
To date, the radial velocity (RV) method has been one of the most productive techniques for detecting and confirming extrasolar planetary candidates. Unfortunately, stellar activity can induce RV ...variations which can drown out or even mimic planetary signals – and it is notoriously difficult to model and thus mitigate the effects of these activity-induced nuisance signals. This is expected to be a major obstacle to using next-generation spectrographs to detect lower mass planets, planets with longer periods, and planets around more active stars. Enter Gaussian processes (GPs) which, we note, have a number of attractive features that make them very well suited to disentangling stellar activity signals from planetary signals. We present here a GP framework we developed to model RV time series jointly with ancillary activity indicators (e.g. bisector velocity spans, line widths, chromospheric activity indices), allowing the activity component of RV time series to be constrained and disentangled from e.g. planetary components. We discuss the mathematical details of our GP framework, and present results illustrating its encouraging performance on both synthetic and real RV data sets, including the publicly available Alpha Centauri B data set.
We present a large sample of stellar rotation periods for Kepler Objects of Interest, based on three years of public Kepler data. These were measured by detecting periodic photometric modulation ...caused by star spots, using an algorithm based on the autocorrelation function of the light curve, developed recently by McQuillan, Aigrain & Mazeh (2013). Of the 1919 main-sequence exoplanet hosts analyzed, robust rotation periods were detected for 737. Comparing the detected stellar periods to the orbital periods of the innermost planet in each system reveals a notable lack of close-in planets around rapid rotators. It appears that only slowly spinning stars with rotation periods longer than 5-10 days host planets on orbits shorter than 2 or 3 days, although the mechanism(s) that lead(s) to this is not clear.
The hot Jupiter HD 189733b is the most extensively observed exoplanet. Its atmosphere has been detected and characterized in transmission and eclipse spectroscopy, and its phase curve measured at ...several wavelengths. This paper brings together the results of our campaign to obtain the complete transmission spectrum of the atmosphere of this planet from UV to infrared with the Hubble Space Telescope, using the STIS, ACS and WFC3 instruments. We provide a new tabulation of the transmission spectrum across the entire visible and infrared range. The radius ratio in each wavelength band was re-derived, where necessary, to ensure a consistent treatment of the bulk transit parameters and stellar limb darkening. Special care was taken to correct for, and derive realistic estimates of the uncertainties due to, both occulted and unocculted star spots.
The combined spectrum is very different from the predictions of cloud-free models for hot Jupiters: it is dominated by Rayleigh scattering over the whole visible and near-infrared range, the only detected features being narrow sodium and potassium lines. We interpret this as the signature of a haze of condensate grains extending over at least five scaleheights. We show that a dust-dominated atmosphere could also explain several puzzling features of the emission spectrum and phase curves, including the large amplitude of the phase curve at 3.6 μm, the small hotspot longitude shift and the hot mid-infrared emission spectrum. We discuss possible compositions and derive some first-order estimates for the properties of the putative condensate haze/clouds. We finish by speculating that the dichotomy between the two observationally defined classes of hot Jupiter atmospheres, of which HD 189733b and HD 209458b are the prototypes, might not be whether they possess a temperature inversion, but whether they are clear or dusty. We also consider the possibility of a continuum of cloud properties between hot Jupiters, young Jupiters and L-type brown dwarfs.
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