We present an analytic model to estimate the capabilities of space missions dedicated to the search for biosignatures in the atmosphere of rocky planets located in the habitable zone of nearby stars. Relations between performance and mission parameters, such as mirror diameter, distance to targets, and radius of planets, are obtained. Two types of instruments are considered: coronagraphs observing in the visible, and nulling interferometers in the thermal infrared. Missions considered are: single-pupil coronagraphs with a 2.4m primary mirror, and formation-flying interferometers with 4x0.75m collecting mirrors. The numbers of accessible planets are calculated as a function of {eta}Earth. When Kepler gives its final estimation for {eta}Earth, the model will permit a precise assessment of the potential of each instrument. Based on current estimations, {eta}Earth=10% around FGK stars and 50% around M stars, the coronagraph could study in spectroscopy only ~1.5 relevant planets, and the interferometer ~14.0. These numbers are obtained under the major hypothesis that the exozodiacal light around the target stars is low enough for each instrument. In both cases, a prior detection of planets is assumed and a target list established. For the long-term future, building both types of spectroscopic instruments, and using them on the same targets, will be the optimal solution because they provide complementary information. But as a first affordable space mission, the interferometer looks the more promising in terms of biosignature harvest.

Cone search capability for table J/ApJ/808/194/table8 (M stars for 1yr observations with a 4x0.75m interferometer)

Cone search capability for table J/ApJ/808/194/table9 (FGK stars for 4yr observations with a 4x0.75m interferometer)

Cone search capability for table J/ApJ/808/194/table2 (Integration times divided by c for FGK stars)

Cone search capability for table J/ApJ/808/194/table3 (Possible target list for a 2.4m coronagraph)

Cone search capability for table J/ApJ/808/194/table7 (Integration times divided by d for G stars)