Large Interferometer For Exoplanets (LIFE): VI. Detecting rocky exoplanets in the habitable zones of Sun-like stars

Context. Identifying and characterizing habitable and potentially inhabited worlds is one of the main goals of future exoplanet direct-imaging missions. The number of planets within the habitable zone (HZ) that are accessible to such missions is a key metric to quantify their scientific potential, and it can drive the mission and instrument design. Aims. While previous studies have shown a strong preference for a future mid-infrared nulling interferometer space mission, such as LIFE, to detect planets within the HZ around M dwarfs, we here focus on a more conservative approach toward the concept of habitability and present yield estimates for two stellar samples consisting of nearby (d < 20 pc) Sun-like stars (4800 K <= T-eff <= 6300 K) and nearby FGK-type stars (3940 K <= T-eff <= 7220 K) accessible to such a mission. Methods. Our yield estimates are based on recently derived occurrence rates of rocky planets from the Kepler mission and our LIFE exoplanet observation simulation tool LIFEsim, which includes all main astrophysical noise sources, but no instrumental noise sources as yet. In a Monte Carlo-like approach, we marginalized over 1000 synthetic planet populations simulated around single and wide binary stars from our two samples. We use new occurrence rates for rocky planets that cover the entire HZ around FGK-type stars, marginalize over the uncertainties in the underlying occurrence rate model, present a parameter study investigating the dependence of the planet yield on different instrumental and astrophysical parameters, and estimate the number of detectable HZ planets that might indeed harbor liquid surface water. Results. Depending on a pessimistic or optimistic extrapolation of the Kepler results, we find that during a 2.5-yr search phase, LIFE could detect between similar to 10-16 (average) or similar to 5-34 (including 1 sigma uncertainties) rocky planets (0.5 R-circle plus <= R-p <= 1.5 R-circle plus) within the optimistic HZ of Sun-like stars and between similar to 4-6 (average) or similar to 1-13 (including 1 sigma uncertainties) exo-Earth candidates (EECs) assuming four collector spacecraft equipped with 2 m mirrors and a conservative instrument throughput of 5%. The error bars are dominated by uncertainties in the underlying planet occurrence rates and the extrapolation of the Kepler results. With D = 3.5 m or 1 m mirrors, the yield Y changes strongly, following approximately Y proportional to D-3/2. With the larger sample of FGK-type stars, the yield increases to similar to 16-22 (average) rocky planets within the optimistic HZ and similar to 5-8 (average) EECs, which corresponds to similar to 50% of the yield predicted for M dwarfs in LIFE paper I. Furthermore, we find that in addition to the mirror diameter, the yield depends strongly on the total throughput, but only weakly on the exozodiacal dust level and the accessible wavelength range of the mission. Conclusions. When the focus lies entirely on Sun-like stars, larger mirrors (similar to 3 m with 5% total throughput) or a better total throughput (similar to 20% with 2 m mirrors) are required to detect a statistically relevant sample of similar to 30 rocky planets within the optimistic HZ. When the scope is extended to FGK-type stars, and especially when M dwarfs are included, a significant increase in the number of detectable rocky HZ planets is obtained, which relaxes the requirements on mirror size and total throughput. Observational insight into the habitability of planets orbiting M dwarfs, for example, from the James Webb Space Telescope, is crucial for guiding the target selection and observing sequence optimization for a mission such as LIFE.