The anticipated high accuracy of planet parameters for PLATO demands a correspondingly high accuracy of stellar parameters. Planetary radii are measured as ratio to stellar radii, planet masses require knowledge of stellar mass and finally the age of a planetary system is deduced from the age of the host star. We therefore first demonstrate that PLATO can achieve the required stellar parameter accuracy and then discuss the corresponding planet parameters below.
Stellar parameters
The accuracy which can be obtained for the seismic determination of the ages, masses, and radii of solar-like stars has been assessed in Phase B1 taking into account the instrument noise budget. Involving a team of asteroseismologists, theoretical calculations, numerical simulations and a blind test (‘hare-and-hounds exercise’) have been performed to estimate the accuracy of stellar parameters that can be achieved today.
Relative random error (equivalent 1σ precision) for the age of the reference stars as a function of the apparent magnitude for 28 telescopes (filled dots) and 24 telescopes (open dots) for 2 years continuous observations.
The drawing on the right side shows the relative age uncertainty for a solar-like star (V=10) at 6 Gyrs with end of life (EOL) instrument performance for 28 N-cameras (previous design) and 24 N-cameras (nominal design). At V=10, the age uncertainty for the reference star amounts to <10%. These estimations consider only statistical uncertainties. There are systematic uncertainties that need to be evaluated on a case by case basis. However, available information from Gaia, PLATO lessons learned on stellar models, and ground-based facilities will certainly lead to a reduction of those systematic uncertainties. We have not considered systematic uncertainties for the theoretical calculations, but we do have considered them in the hare-and-hounds exercise.
Results of seismic modelling for Hare-and-Hound exercise: relative differences for the stellar masses against radii on the left and stellar ages against masses on the right. The dashed box corresponds to the requirements specified for PLATO: 10% in stellar mass and 1% in stellar radius for a ‘Sun’ with V=10. Each colour corresponds to the results of one modeller.
Planet parameters
The transit depth provides the planet-to-stellar radius ratio. The scientific requirement for PLATO is to provide a radius accuracy of 3% for a G0V star of V=10, which means that the radius ratio needs to be obtained with 2% uncertainty. Whether this accuracy can be achieved has been studied with simulations of realistic noise-to signal ratios with 24 N-cameras EOL, including random and systematic noise sources. It is necessary to take the transit duration and number of observed transits into account, because the transit depth is measured from averaging several points, and multiple transits can be averaged to increase the SNR. We do not include the impact of stellar activity as we are testing instrument performance.
Uncertainty in the absolute planet radius as a function of the V magnitude of the reference star with 24 N-Cameras, EOL. The benchmark performance of 3% uncertainty is shown with a horizontal dashed line.
The drawing on the right side shows the expected uncertainty in the absolute planetary radius of an Earth-sized planet orbiting a G0V star as a function of the visual magnitude of the host star and the number of transits observed. For the calculation of the uncertainties, we assumed that a central (i.e. zero impact parameter) transit of an Earth-sized planet occurs around a quiet G0V star whose limb darkening law is known. The stellar density is assumed to be derived by asteroseismology, so the scaled semi-major axis (a/Rstar) is known to 2% accuracy, while the stellar radius is known to 1%. It can be seen that, for the benchmark case of an Earth around the Sun, two transits are enough to achieve the required planetary radius accuracy for a V=10 mag star. For planets with shorter orbital periods more transits can be observed, improving the final accuracy. Larger planets will produce a larger signal for the same amount of transits, hence improving the final accuracy in the planetary radius.
The second important planet parameter relevant to characterise the planet mean density and hence constrain bulk compositions is the planetary mass. The mass is derived from ground-based follow-up observations obtained by high-resolution spectroscopy. We consider here only planets orbiting stars brighter than V=11, since for fainter objects such ground-based observations get too time consuming to be obtained on a larger sample.
The possible mass accuracy depends critically on instrumental and astrophysical noise. For an instrument like ESPRESSO at the VLT (ESO) the estimated performances are in the range of 1‒10 cm/s, with 7 cm/s being the most frequently given estimate.
Planetary mass precision achievable for the inner edge of the optimistic HZ, as a function of the host star’s spectral type. The solid lines denote the median precision, while the shaded bands encompass the 1-sigma regions. Colours correspond to different input planet masses: 2ME (blue); 3ME (red); 5ME (green); 10ME (purple); MNep (turquoise), and MJ (yellow). The horizontal, dashed line denotes the PLATO science requirement of 10% for a G0V star.
The drawing on the left side shows the estimated mass precision for a range of stellar types with planets orbiting at the inner edge of the HZ. With the assumed ESPRESSO performance of 7 cm/s the required mass precision can be reached for (super-)Earths orbiting quiet solar-like stars. The final mass precision will of course be dependent on the actual performance of the ESPRESSO instrument. Intuitively, one may expect the radial velocity semi-amplitude to scale with stellar and planet mass, and orbital period, so that the lowest mass planets around the highest mass stars in the longest period orbits are the most difficult to detect.
A planet with 1 ME orbiting in the HZ of a solar type star represents one of the most difficult configurations to be encountered by PLATO. For this we have assumed a realistic observation strategy with yearly gaps in observation due to visibility and poor weather conditions. Other configurations (higher planet mass and/or shorter orbital periods) will be easier to solve. The final modelling strategy employed will be dictated by the actual performance of ESPRESSO, which will be known more than 5 years in advance of the PLATO launch in 2026.
References
PLATO – Revealing habitable worlds around solar-like stars
Definition Study Report, ESA-SCI(2017)1, April 2017
platomission.com 
