One of the mission design drivers for PLATO is assuring the detectability of planets with the size of the Earth around stars with the size of the Sun in 1-year period orbits. For the P1 sample (< 34 ppm in 1 hour), the SNR of a single transit for an Earth-Sun analogue is 9 and 13 when integrating 2 transits. It is generally considered that a SNR>10 guarantees the detectability of 100% of the transit signals (see Fressin et al. 2013, based on studies by Jenkins et al. 1996, 2010). A third transit event is beneficial to confirm the consistency of previous observations.

With a nominal mission duration of 4 years there are two possibilities for the observing strategy (see above):

• to observe 2 consecutive fields in a Long-Duration Observation Phase of 2 year duration each towards different directions on the sky, guaranteeing typically 2, and only in some favourable cases 3, transit events for planets in the HZ of Sun-like stars. This scenario is labelled (2+2) and is our baseline.
• to observe 1 field in a Long-Duration Observation Phase of 3 years duration, guaranteeing 3 transit events for planets in the HZ of Sun-like stars, followed by a step-and-stare phase with several pointings of few months each. The step-and-stare phase allows us to obtain large statistics of short period planets in different regions of the Galaxy. We have considered 6 pointings of 2 months duration. This scenario is labelled (3+1).

The mission is being designed for an in-orbit lifetime of 6.5 years and a mission duration of up to 8 years is possible. If a mission extension is granted beyond the nominal science operations of 4 years, the additional time could be used, e.g., for the following scenario: 2 long-pointings with durations between 2 and 3 years plus a step-and-stare phase with a total duration of 1 year. This scenario is labelled (3+2+1).

The expected planet yields resulting from these 3 scenarios is given in the table below.

The planet yield is the result of the stellar population observed, the planet occurrence rate, the geometric transit probability, the observing strategy, and the detection efficiency:

• We consider here only the P1 and P5 samples, dwarf and sub-giant stars of spectral types between F5 and K7. PLATO can also detect transiting planets around giant stars, as Kepler did and TESS will do (see, for example, Lillo-Box et al. 2016; Campante et al. 2016), but here we concentrate on the planet yield for the solar-like samples.
• The planet occurrence rate and the geometric transit probability are imposed by nature and do not depend on instrument performance. The planet occurrence rates are taken from Fressin et al. (2013), except in the habitable zone. The planet occurrence rate in the habitable zone is still highly debated in the literature. Values found today range from 2% to 100% of solar-like stars hosting planets with the size of the Earth (up to super-Earths) in the HZ (see Winn & Fabrycky 2015 and references therein; Batalha 2014; Burke et al. 2015; Traub 2016, etc.). We consider a representative average value of 40% occurrence for Earth and super-Earth sized planets in the habitable zone for the P1 and P5 samples, but we also provide in Table 7.1the values considering the expected range (2% to 100%) for the yield of small planets in the HZ around V£11 stars. It must be understood that there are large uncertainties in these estimations. On the one side the statistical uncertainties in the planet occurrence rates, and on the other side systematic uncertainties related to our limited knowledge on the actual stellar parameters of the populations observed. These have a strong influence on the stellar insolation on top of the atmosphere and hence on the planetary energy balance. It is realistic to consider that the different biases will contribute to a typical uncertainty in the planet yield of transit surveys up to 50% (see Sullivan et al. 2015), if not larger. It will take observations by PLATO to constrain this value significantly better.
• The observing strategies considered have been discussed above.
• The detection efficiency depends on the transit depth, hence the radius ratio between planet and star, and the noise level in the light curve. It is different for the P1 sample, which is both magnitude and noise limited (V≤11, NSR<34 ppm in 1h), and for the P5 sample, only magnitude limited (V≤13):
  • For the LOP fields, we will take as benchmark the detection of an Earth-sized planet around a solar-like star in 1 year period orbit, which is about 80 ppm depth and 13h duration.
    • For P1 sample (<34 ppm in 1h) the detection efficiency is assumed to be 100%.
    • For P5 sample the detection efficiency of Neptune-sized and giant planets is assumed to be 100%. For planets smaller than 2 Earth radii we set a stricter limit. The detectability of small planets is 50% for the light curves with less than 80 ppm noise in 1h and 0% elsewhere, which is conservative.
  • For the step-and-stare phases we consider detection of planets up to 30 days orbital period. Single transit events of planetary objects will also be detected (see Osborn et al. 2016 and references therein), but we will not consider them further here. For the P1 sample the detection efficiency is assumed to be 100%. For the P5 sample, Neptune-sized and giant planets have 100% detection efficiency and small planets 50% efficiency if the NSR<80 ppm in 1h and 0% elsewhere.

 

Planets with RV follow-up

The full characterisation of planets requires the additional determination of their mass via ground-based follow-up spectroscopy. This yield for fully characterised planets is therefore dependent on the availability of telescope resources and time spent to perform the follow-up observations.

We have done an exercise to dimension the telescope resources required to confirm and characterise planets detected by the PLATO mission through ground-based follow-up observations. For our benchmark case of the Earth around the Sun we take as a starting point the subsample of planets detected during the long-pointing phases orbiting stars brighter than V=11, because for fainter targets follow-up is not feasible on a large scale.

We also account for the impact of stellar activity further reducing the considered subsample to those planets orbiting quiet stars. First, we mitigate the impact of stellar activity on the RV signal by adopting a strategy reducing the impact of granulation and stellar oscillations (see Dumusque et al. 2011a, b). In this way, we also estimate the amount of resources devoted to each target depending on the planet mass, the orbital period, and the level of stellar activity. Secondly, for the most difficult cases, we devote resources only to the planets orbiting quiet stars. We estimate the fraction of quiet stars from simulations drawn from real HARPS asteroseismology data (for oscillations and granulation, i.e. for timescales up to ~1 day) and from the modelling of families of spots on the star surface for different spectral types and various level of stellar activities. We implicitly suppose here that there is no significant stellar noise with timescale between the rotational period of the star and 1 year. The distribution for stars in the solar neighbourhood drawn from the HARPS GTO volume-limited sub-sample shows that 24% of the stars have log(R’HK) < ‒5.0 (non-active Sun) and 50% are less active than the average Sun (log(R’HK) =‒4.9). Therefore, we reduce the sample of detections as follows:

• Super Earths:
  • In short periods (<85 days): 50% of the planets detected orbit quiet stars suitable for RV,
  • In long periods (>85 days): 25% of the planets detected orbit quiet stars suitable for RV,
  • Earths:
  • For all periods: 25% of the planets detected orbit quiet stars suitable for RV.

In our approach we devote follow up resources in small class telescopes (1‒2m) to culling of false positives with low precision spectroscopy and high resolution imaging and on-off photometry. Mid-class telescopes (4m) are devoted to high precision spectroscopy and only the most difficult cases (small planets at long orbital periods) will go to 8m class telescopes for Rossiter-McLaughlin (confirmation of planetary nature) and RV follow-up.

Using resources comparable to a large ESO program (55 nights per year at 8m class telescopes, 65 nights per year at 4m class telescopes), we have enough resources to obtain masses for 100 super Earths (9 of them with semi-major axis comparable to 1 au) and 22 Earth-sized planets (7 of them with semi-major axis comparable to 1 au) and some tens of Neptunes. We have not allocated resources to Jupiter-sized planets as we do not consider them the main science goal for this exercise. Using facilities in La Palma (32 nights per year) we could follow-up additional 52 super-Earths (including 5 with semi-major axis comparable to 1 au). For comparison, CoRoT has published RV values for 31 giant planets and for one small planet, the short period super-Earth CoRoT-7b. Kepler has published RV values for about 70 planets, 60 of them being giants and most in short period orbits. K2 has published additional RV measurements for about a dozen planets in short period orbits.

PLATO is therefore expected to provide a unique sample of fully characterised (radius, mass, age) sample of small planets.

 

 

References

PLATO – Revealing habitable worlds around solar-like stars
Definition Study Report, ESA-SCI(2017)1, April 2017