LIFE: Formation-Flying Capabilities for Exoplanet Discovery with Nulling Interferometry

Introduction
One of the main goals of extrasolar planet science is the detailed characterisation of atmospheric properties of Earth-like exoplanets in the hopes of assessing their habitability and identifying potential biosignature gases. At the same time, these observations would enhance the understanding of the diversity of planetary bodies, making a statistical prediction of the occurrence of conditions supporting life as we know it possible [1]. Currently available methods, like transit spectroscopy, high-contrast ground-based imaging or microlensing, cannot be reliably employed to analyse the planets of most interest. The space based Large Interferometer for Exoplanets (LIFE) mission has thus been proposed to fill in these gaps through the use of a system of satellites in formation flight.

Mission Concept
The mission employs the principle of nulling interferometry to suppress the target star’s light, as proposed by Bracewell [2], and receive the photon flux directly from the planet. LIFE would analyse the mid-infrared (MIR) spectra 6.0 - 16 μm , allowing for characterisation of biosignature gases like methane (CH4) and nitrous oxide (N2O) at 7.7 and 7.8 μm respectively, as well as more precise determination of the exoplanet’s radius and temperature [1]. The current interferometer design is a double Bracewell interferometric nuller arranged in an “Emma X-array” configuration, which combines two pairwise nulls to generate a deeper and broader null [3]. To detect and characterise a given planet, this configuration is rotated around the line-of-sight (LOS) vector such that off-axis sources (exoplanets) are modulated against the on-axis star and background sources, such as exozodiacal dust and other stray light. Given the high angular resolution (~0.01’’)  requirement necessary to resolve exoplanets from their host stars and extremely low photon fluxes constraining minimum telescope mirror sizes, the LIFE mission would ideally require baselines of up to 600 meters, only realistically achievable through a formation flying satellite concept [3,4]. Such a setup would also allow for baseline optimisation per target, for instance to maximise the detection yield of planets in the habitable zone (HZ). The satellite formation would orbit the Sun-Earth Lagrange point L2, one of the system’s gravitational equilibrium points, largely chosen based on its favourable dynamical environment for formation flying and the thermal stability necessary for cryogenic missions [4].
The LIFE mission builds on findings of both NASA’s TPF-I and ESA’s Darwin studies, which converged on very similar baseline designs. It also benefits from developments in optical and formation flying technologies (e.g. the Proba-3 demonstrator), advances in atmospheric modelling, and most importantly, a more complete understanding of the occurrence rate of Earth-sized planets in the HZ of Sun-like stars from NASA's Kepler mission and subsequent analyses [4]. The star target catalogue for LIFE will also benefit significantly from findings of the upcoming ESA’s Plato mission.

Research Objectives 
The formation flying design for LIFE must simultaneously satisfy stringent and deeply coupled requirements spanning optics, science and astrodynamics. These include frequent reconfigurations, continuous rotation of the array around the LOS, maintaining optical path difference (OPD) control at the centimetre level with negligible drift, and formation stability over periods of up to 40 days to enable detailed atmospheric characterisation [4]. Satisfying all of these simultaneously, while remaining within realistic mission cost bounds, is the central challenge that this work addresses, and is one not fully resolved by previous studies.
This work therefore presents a systems-level analysis of formation flying for nulling interferometry missions, evaluating LIFE as a case study. It aims to quantify how mission parameter choices such as orbit selection, formation size, allowable drift, error margins, and array rotation rate, affect the mission’s ΔV cost and scientific yield (the number and quality of characterisable star systems). Target selection (and ordering) strategies are considered as part of this broader trade-off. 

Methodology 
The analysis examines formation behaviour both in the absence of control and under continuous control schemes maintaining the required formation geometry. This is carried out in both the circular restricted 3-body problem (CR3BP) and a full ephemeris model, to evaluate the fidelity of the preliminary analysis in predicting mission capabilities. From this, preferential orbital regimes, optimised target selection strategies, and formation reconfiguration and maintenance techniques are identified, with example observing scenarios proposed.

References
[1] Quanz S. P. et al, (2022) Exp Astron 54, 1197–1221.
[2] Bracewell R. N. (1978) Nature 274, 780–781.
[3] Lay O. P. & Dubovitsky S. (2004) Proc. SPIE 5491, 874. 
[4] Glauser A. M. et al, (2024) Proc. SPIE 13095, 130951D.