We propose a novel method for estimating possible evolutionary stage on exoplanets based on the hypothesis that evolutionary rate is a linear function of cumulative carbon fixed on an entire planet.  We explore the implications of this hypothesis using spatially explicit climate simulations of TRAPPIST-1e, a tidally locked planet within the habitable zone of a red dwarf star ~40 light years away.  We estimate that Earth has cumulatively fixed ~9.4 e25 g C carbon, and TRAPPIST 1e (T1e) as an ocean world with 400 ppm CO₂ using photon energy of wavelengths 400 -1100 nm would need 22 Gy years to fix the same amount of carbon.  Since T1e's mean estimated age is 7.6 Gyr, we estimate it to be at a potential microbial, but not multicellular life stage.  We then apply this technique to 29 nearby exoplanets that may have the conditions suitable for harboring life and using 400-1100nm light, assuming a 30% continent ratio. We identify one planet that surpasses Earth’s cumulative NPP and which could have both multicellular and intelligent life and 5 planets at the potential multicellular stage.  Planets most likely to have higher cumulative NPP than Earth are also most likely to be dominated (more than Earth) by precipitation-limited ecosystems, like deserts or temperate ecosystems (versus boreal or tropical ecosystems).  Planets GJ1061c and K2-3D rank highest in cumulative productivity potential under a number of our scenarios because they are bigger, hotter, brighter, and older than other planets in the solar neighborhood.

2.1 T1e climate and NPP

We used simulated climatology data for T1e from the THAI experiment (Fauchez et al., 2021, 2020) as well as GCM simulated modern Earth climatology to estimate surface productivity for different atmosphere and surface composition scenarios.  For most results, we used the Met Office Unified Model (UM) model (Mayne et al., 2014) simulations (144 by 90 pixels) of the downwelling shortwave (SW) solar flux at surface (F_SW^down), time-average precipitation flux and surface temperature (TS) (downloaded from https://thai.emac.gsfc.nasa.gov/organization/thai on June 1, 2024).  We also compared these results to simulations from ExoCAM (Exoplanet Community Atmosphere Model - derived from the CAM4 NCAR model).   For most results, we used Hab 1 simulations of a single layer slab ocean covered planet with 400 ppm CO_2, but we also employed Hab 2 simulations which have an atmosphere of 1 bar of CO₂ averaged over between 10 and 100 orbits.  We used two models, UM and ExoCam, because they represent the endmembers of the THAI models in terms of planetary temperatures with ExoCAM producing the warmest climate and UM the coolest (Sergeev et al., 2022).   For Earth simulations, we used the community land model. NCAR’s CLM 4.0 (Oleson et al., 2010) monthly data averaged over 12 months (288 by 192 pixels) for atmospheric incident solar radiation (diagnostic name FSDS), 2-m air temperature (TSA) and atmospheric precipitation (RAIN). We specifically ran the model using compset F_2000_CN with details in (Doughty et al., 2018).

The above simulated climatologies of stellar radiation, temperature, and precipitation for both T1e and Earth were used to calculate NPP with the Miami model (Bernardi, 2006).  For each grid cell of the above datasets, we used the Miami model Equations 1-3 below to estimate NPP in units of grams of dry matter m^-2 yr^-1 as limited by temperature and precipitation:

Equation 1  = NPP_T = 3000 *(1 + exp(1.315 - .119 *T))^{^-1}

Equation 2 =  NPP_P = 3000 *(1 - exp(-0.000664 * P))

Equation 3 = NPP_final = min(NPP_T, NPP_P),

where T is temperature, P is precipitation, NPP_T is the NPP response to temperature, and NPP_P is the response to precipitation. The Miami model does not incorporate light limitation on NPP; however, light is critical for photosynthesis. To incorporate radiation levels into our NPP estimates, we used maps of downwelling stellar flux at the surface in W m^-2 (F_SW^down) and equations 4 and 5.  The NPP response was scaled by the grid point’s IPAR relative to the Earth average.  In other words, on Earth, the map of FSDS has an average of 158 W m^-2, and we incorporated spatially explicit maps of light for T1e by dividing each pixel’s FSDS first by 158 W m^-2, which normalizes the surface light flux by the amount used in Earth’s NPP calculations.  In other words, T1e light is a multiplier where, if light levels are greater than Earth’s FSDS average, NPP will increase linearly, and if less it will decrease linearly (we vary this assumption in a sensitivity study). 

Light on T1e has a different stellar spectrum and spectral flux compared to our Sun-Earth, so we then converted FSDS to planet-specific incident photosynthetically active radiation (IPAR), in the spectral ranges of either 400-700 nm or 400-1100 nm.  We used estimates from Kiang et al 2007 for the estimated photon flux density for planets relative to Earth (Kiang et al., 2007a).  They calculated a cloudless Earth as having a solar noon photosynthetic photon flux density (PPFD) of 11 e²⁰ photons m^-2 s^-1 for 400-700 nm and we compare this to the simulated M5V planet (for low O₂) which had a PPFD for 400-700 nm of 1.5 e²⁰ photons m^-2 s^-1 for terrestrial surfaces, 1.4 e²⁰ photons m^-2 s^-1 for under 5 cm water and 1.1 e²⁰ photons m^-2 s^-1for under 100 cm of water.  Using light from 400-1100 nm, the M5V planet has PPFD₁₁₀₀ of 16.9 e²⁰ photons m^-2 s^-1for terrestrial surfaces, 9.9 e²⁰ photons m^-2 s^-1under 5 cm water and 1.5 e²⁰ photons m^-2 s^-1under 100 cm water.  For instance, in equation 4, we estimated that a M5V planet in the terrestrial regions will have a ratio of 1.5/11 or 14% of the usable light as Earth between 400-700 nm and 17/11 or 150% of the usable light as Earth between 400-1100 nm.  Due to high uncertainty, we varied these numbers by 20% in a sensitivity study.  We scaled planetary NPP as a function of planetary continental cover fraction, C_frac (0.3 like Earth or 0 for an ocean world).  Light in the red and near-infrared does not transmit well through water, and we approximated the ocean photon flux for 400-700nm as a weighted average of 50% water at 5cm with 1.4 e²⁰ (9.9 for 400-1100nm) photons m^-2 s^-1 and 50% at 100 cm with 1.1 e²⁰ (1.5 for 400-1100nm) photons m^-2 s^-1 (varied in a sensitivity study).

We then scaled this value, which is valid for the M5V planet to T1e and other exoplanets.  The top of atmosphere stellar flux for the M5V planet in Kiang et al 2007 was 1135 W/m².  The top-of-atmosphere simulated Earth solar constant is 1361 W/m² (Prša et al., 2016).  In our equation, we used the ratio of the planet solar flux relative to Earth, S_p relative to the M5V planet in Kiang et al (2007).  For instance, Trappist-1e has a solar flux ratio to Earth of S_p = 0.65 (Agol et al., 2021), such that T1e is 65% of 1361 W m^-2, or 885 W m^-2. Therefore, T1e NPP was scaled by 885/1135 or a ratio of 0.78 to the generic M5V planet.     

Equation 4 – NPP _{400-700 nm} = NPP_final(i,j) *(IPAR(i,j) /158)* ((1.5/11)* C_frac + (((1.4+1.1)/2)/11)*(1- C_frac)) *((S_p *1361)/1135)

Equation 5 – NPP _{400– 1100 nm}  = NPP_final(i,j) *(IPAR₁₁₀₀(i,j) /158)* ((16.9/11)* C_frac + (((9.9+1.5)/2)/11)*(1- C_frac)) *((S_p *1361)/1135)

We quantified light-, temperature-, and precipitation-limited regions on Earth and on exoplanets following Nemani et al. (2003).  We used equation 3 from the Miami model to determine temperature- and precipitation-limited regions, but employed the approach of Nemani et al., 2003 to estimate that warm wet regions with high cloud cover are light limited.  For Earth, from the CLM we determined light limited regions have surface temperature T>15 Celsius, precipitation P>1500 mm yr^-1, and cloud cover >60%, roughly following Nemani et al 2003.  For exoplanets, instead of cloud cover, we used a light threshold of 200 W m^-2.  In equation 6, we show whether each pixel is light, temperature or precipitation limited (respectively, logical, Light_lim, Precip_lim, Temp_lim). 

Equation 6 – if T>15 & P>1500 & F_SW^down <200 W m^-2 then Light_lim

elseif NPP_T> NPP_P then Precip_lim

else Temp_lim

2.2 T1e evolutionary stage

We then summed total planetary NPP for both Earth and T1e in Pg C yr^-1. The dataset for the CLM Earth simulation from Doughty et al 2018 is just for land and we estimate current terrestrial NPP on Earth to be ~53 Pg C yr^-1which is close to more complex models like CASA, estimating the annual terrestrial NPP at 56.4 Pg C yr^-1.  The Miami model does not calculate oceanic NPP and we estimate an additional oceanic NPP based on CASA of 48.5 Pg C yr^-1for a total of 101.5 Pg C yr^-1 (versus 104.9 Pg C yr^-1 from CASA).   C_frac above is to estimate continental fraction on exoplanets. On Earth we multiply the average per area NPP by the total surface area of the Earth which is 5.1×10¹⁴ m². On T1e, we calculate the surface area based on the planetary radius.  

We then compare the summed NPP for this period on Earth and then estimate the time it would require T1e to match this.  The first evidence for life on Earth dates to ~3.7 billion years ago and then higher plants evolved ~700 million years ago, and therefore microbial photosynthesis dominated Earth for 3 billion years (William Schopf, 2011).  We calculate Earth’s NPP for the first 3 billion years at a lower photosynthetic efficiency that current.  Most photosynthesis does not occur in ideal conditions.  For the Archean ocean, ocean NPP could have been up to 40 times lower than the current ocean due to reductant limitations (KHARECHA et al., 2005) and the Proterozoic ocean was likely 10% of modern oceans NPP due to lower nutrient recycling, among other reasons (Laakso and Schrag, 2019).  Continental ratio would also have varied from almost a water world during the Archean to a lower continental ratio during the Proterozoic.  To incorporate the gradual increase in productivity from the Archean to the Phanerozoic, we use an efficiency of 0.025 for the first 1 GY (Archean) and 0.1 for the next 2 GY (Proterozoic).  After the first three billion years, if an exoplanet was still at the microbial life stage, we set the photosynthetic efficiency to 0.47 based on average ideal photosynthesis rates between anoxic and oxygenic photosynthesis (Ritchie et al., 2018).

If T1e matches the summed carbon fixed during the first 3 billion years of anoxgenic photosynthesis, it can move to higher efficiency photosynthesis (e.g. eq 5).  We then calculate higher efficiency photosynthesis (i.e. the standard Miami model without the Archean or Proterozoic multiplier) for 700 million years on Earth.  We then calculate how long each exoplanet requires to match Earth’s photosynthesis at the higher efficiency rate. We account for T1e’s estimated age (7.8 billion years) with the assumption that life originated close to the start of the planet’s history like Earth when calculating total carbon fixed and comparing it to Earth.  If the summed carbon fixed for T1e_microbial exceeds that of Earth (Eq 7), we define it as multicellular.  If the summed carbon fixed for T1e_microbial + T1e_{multicellular} exceeds that of Earth (Eq 8), we define it as intelligent.

Equation 7 = if (Ʃ NPP _{400– 1100 nm}  Earth_microbial  <  Ʃ NPP _{400– 1100 nm}  T1e_microbial) then T1e is multicellular

Equation 8 = if (Ʃ NPP _{400– 1100 nm}  Earth_microbial + Ʃ NPP _{400– 1100 nm}  Earth_{multicellular}) <  (Ʃ NPP _{400– 1100 nm}  T1e_microbial + Ʃ NPP _{400– 1100 nm}  T1e_{multicellular}) then T1e is intelligent

2.3 Other planets evolutionary stage

We then used NASA data (https://exoplanetarchive.ipac.caltech.edu/) organized in the Habitable Worlds Catalog (https://phl.upr.edu/hwc ) which has compiled a list of 29 Earth sized rocky planets (i.e., 0.5 < Planet Radius ≤ 1.6 Earth radii or 0.1 < Planet Minimum Mass ≤ 3 Earth masses) within the habitable zone of their host stars. This list has data on potential planet radius, irradiation, temperature, age and distance (Table 1). Since all the planets listed (except 2) orbit class M red dwarf stars, we use the stellar radiation, temperature and precipitation maps as a baseline for all planets. We then scale the stellar flux for each planet using the estimate of stellar radiation (S_p from Table 2 and Eq 5) from the Habitable Worlds Catalog (i.e. by (S_p *1361)/1135 from eq 5). We use the top-of-atmosphere irradiance as an estimate of clear-sky surface irradiance, neglecting planet to planet changes in atmospheric absorbance. For example, for each pixel we will take surface downwelling irradiance and weight it by the following function from eq 5: (S_p *1361)/1135.   We then calculate the cumulative NPP fixed for each of these 29 planets and compare this to Earth’s NPP at each evolutionary stage.  For example, if the exoplanet has less than Earth’s cumulative NPP from 700 million years ago we classify life stage as microbial, if it has Earth NPP >Earth from 700 million years ago but less than Earth current day (eq 7), we classify life stage as multicellular, if it has > Earth’s cumulative NPP from today we classify life stage as intelligent (eq 8).