Phase curves, or the change in observed illumination of the planet as it orbits around its host star, help us to characterize their atmospheres. However, the variability of the host star can make their detection challenging. The presence of starspots, faculae, flares, and rotational effects introduce brightness variations that can hide other flux variations related to the presence of an exoplanet: ellipsoidal variation, Doppler boosting, and a combination of reflected light and thermal emission from the planet. Here we present a study to quantify the effect of stellar variability on the detectability of phase curves in the optical. In the first stage we simulated ideal data, with different white noise levels, and with cadences and total duration matching a quarter of the Kepler mission. We performed injection and recovery tests to evaluate the minimum number of planetary orbits that need to be observed in order to determine the amplitude of the phase curve with an accuracy of 15%. We also evaluate the effect of a simplistic stellar variability signal with low amplitude in order to provide strong constraints on the minimum number of orbits needed under these ideal conditions. In the second stage we applied these methods to data from Q9 of the Kepler mission, known for its low instrumental noise. The injection and recovery tests are performed on a selected sample of the less noisy stars in different effective temperature ranges. Even for the shortest explored planet period of 1 day, we find that observing a single orbit of the planet fails to detect accurately more than 90% of the inserted amplitude. The best recovery rates, close to 48%, are obtained after 10 orbits of a 1 day period planet with the largest explored amplitude of 150 ppm. The temperature range of the host stars providing better recovery ratios is 5500 K < Teff < 6000 K. Our results provide guidelines to selecting the best targets in which phase curves can be measured to the greatest accuracy, given the variability and effective temperature of its host star, which is of interest for the upcoming TESS, CHEOPS, and PLATO space missions.
The Evolutionary Properties on Solitary Solutions of Nonlinear Evolution Equations
