Photosynthetic exergy I. Thermodynamic limits for habitable-zone planets

Abstract

Photosynthesis is central to Earth's biosphere and a prime candidate for sustaining complex life on habitable exoplanets, yet a thermodynamically consistent treatment of the work potential of stellar radiation at planetary surfaces is still lacking. We develop a radiative-thermodynamic framework that quantifies the maximum useful work extractable for a given star-planet configuration and yields exergy-based bounds on photosynthetic power and long-wavelength absorption cutoffs. From these we derive kinetically constrained red limits for high-$ΔG$ photochemistry and apply them to Earth-like planets receiving the same bolometric flux from FGK and M blackbody hosts, computing thresholded photon supplies and truncated exergy fluxes below a photosystem II red limit. For such planets the constraints confine single-photon oxygenic photosynthesis to near-infrared bands around Solar-type stars and to somewhat bluer wavelengths around late M dwarfs. Integrated over the stellar spectrum, the thresholded photon supply and truncated exergy available to drive a photosystem water-oxidation step are larger by factors $\sim 5$ around FGK hosts than around $T_\star\approx 3000$~K M dwarfs. For the Solar-Earth system, the exergy-based upper bound on O$_2$ production exceeds the observed O$_2$ throughput by several orders of magnitude, consistent with Earth's photosynthetic efficiencies. Cool M dwarfs suffer a double penalty: fewer photons above threshold and a lower shortwave exergy fraction, yielding systematically tighter ceilings on high-$ΔG$ photosynthesis than around FGK stars. Our framework provides upper limits on photosynthetically harvestable power on habitable-zone planets and enables comparisons of photosynthetic potential across exoplanetary systems, and can be extended to multi-band photosystems.

Figures (3)

• Figure 1: Single-photon $\lambda$ limits for a PSII-like high-$\Delta G$ step around a Sun-like host at $T_{\rm env}=288$ K. The curve shows the maximum useful work per photon, $W_{\max}(\lambda)$; the shaded region marks where the required per-photon free energy exceeds $W_{\max}$ and is therefore thermodynamically forbidden. Horizontal lines indicate the benchmark requirement $\Delta G$ and the augmented requirement $\Delta G + A$; vertical lines mark the corresponding $\lambda$ limits: the purely energetic limit $\lambda_{\max}^{(E)}$, the exergy-corrected limit $\lambda_{\max}(0)$, and the exergy- and rate-constrained limit $\lambda_{\max}(A)$.
• Figure 2: Spectral flux and exergy at the top of the atmosphere for three blackbody models, all normalized to the same bolometric flux $F_{\rm bol}=1361\,{\rm W\,m^{-2}}$. Solid curves show $F_{\rm TOA,\lambda}$ and dashed curves $\eta_{\rm ex} F_{\rm TOA,\lambda}$. The vertical line marks a PSII-like threshold at $\lambda_{\rm thr}=690$ nm, illustrating how the short-wavelength band available for high-$\Delta G$ photochemistry shrinks for M-type hosts.
• Figure 3: Normalised photon and exergy upper limits for a high-$\Delta G$ reaction as a function of stellar effective temperature. We assume Earth analogues at fixed $F_{\rm bol}=1361\,{\rm W\,m^{-2}}$, $T_{\rm env}=288$ K and a PSII-like threshold $\lambda_{\rm thr}=690$ nm, with blackbody stellar spectra, no atmosphere, and only photons with $\lambda<\lambda_{\rm thr}$ included. The blue curve shows the thresholded photon rate $\dot N_{\gamma,{\rm eff}}/\dot N_{\gamma,{\rm eff},\odot}$; the orange curve the truncated exergy flux $\dot E^{(<\lambda_{\rm thr})}_{\rm area}/ \dot E^{(<\lambda_{\rm thr})}_{\rm area,\odot}$; both normalised to a Sun-like host.