  Phosphine could be a key molecule in the understanding of exotic chemistry
happening in (exo)planetary atmospheres. While it has been detected in the
Solar System's giant planets, it has not been observed in exoplanets yet. In
the exoplanetary context however it has been theorized as a potential
biosignature molecule. The goal of our study is to identify which illustrative
science cases for PH3 chemistry are observable with a space-based mid-infrared
nulling interferometric observatory like the LIFE (Large Interferometer For
Exoplanets) concept. We identified a representative set of scenarios for PH3
detections in exoplanetary atmospheres varying over the whole dynamic range of
the LIFE mission. We used chemical kinetics and radiative transfer calculations
to produce forward models of these informative, prototypical observational
cases for LIFEsim, our observation simulator software for LIFE. In a detailed,
yet first order approximation it takes a mission like LIFE: (i) about 1h to
find phosphine in a warm giant around a G star at 10 pc, (ii) about 10 h in H2
or CO2 dominated temperate super-Earths around M star hosts at 5 pc, (iii) and
even in 100h it seems very unlikely that phosphine would be detectable in a
Venus-Twin with extreme PH3 concentrations at 5 pc. Phosphine in concentrations
previously discussed in the literature is detectable in 2 out of the 3 cases
and about an order of magnitude faster than comparable cases with JWST. We show
that there is a significant number of objects accessible for these classes of
observations. These results will be used to prioritize the parameter range for
the next steps with more detailed retrieval simulations. They will also inform
timely questions in the early design phase of a mission like LIFE and guide the
community by providing easy-to-scale first estimates for a large part of
detection space of such a mission.
