Early Atmosphere: How Single Cells Changed the Sky

Biology lens: the invention that changed the planet

Life is old. It dates back to before 3.5 to 3.8 billion years ago, or even earlier 1. But for a long time, life did not produce free oxygen. That changed with oxygenic photosynthesis: it uses sunlight to split water, gains energy and reducing power from it, and releases oxygen as a waste product. Woodward Fischer and colleagues call it the most important metabolic innovation in Earth’s history. It freed life from the limited supply of chemical energy sources, greatly increased global productivity – and its waste gas changed the atmosphere and oceans for good 3.

The organisms that invented it were cyanobacteria, single-celled bacteria that still live in oceans and lakes today. When exactly they appeared is debated. Carbon isotopes and structures resembling filaments of cyanobacteria in stromatolites – layered rocks built by microbial mats – are consistent with cyanobacteria by 3.2 to 2.7 billion years ago 1. Fischer and colleagues, by contrast, read the geological and biological records as showing that oxygenic photosynthesis first appeared only in the early Paleoproterozoic, shortly before oxygen rose – a relatively late invention in Earth’s history 3.

Oxygen also opened new paths for life. Once it was available, aerobic respiration – burning food with oxygen – and new biochemical pathways could evolve, and with them much of the richness of modern biology, including complex many-celled life 3. Even before the atmosphere filled with oxygen, lakes and shallow seas inhabited by photosynthesising microbes may have been local “oxygen oases” 1.

Physics lens: a faint Sun, a greenhouse and an open lid

A Sun that grows brighter. As a star like the Sun burns hydrogen in its core, the core contracts and heats up, and the Sun becomes brighter. According to Douglas Gough, this slow brightening is an inevitable consequence of Newtonian physics and of how nuclear reactions depend on density, temperature and composition 5. Models of stellar evolution give a solar input about 25 % lower than today for the early Earth 5.

The faint young Sun paradox. Earth’s temperature is set by a balance: the sunlight it absorbs must equal the heat it radiates. With a quarter less sunlight and all other conditions as today, the early Earth would have been completely frozen for its first two billion years 5. Carl Sagan and George Mullen pointed this out in 1972: with today’s albedo and atmospheric composition, global mean temperatures would have been below the freezing point of seawater until less than 2.3 billion years ago – contrary to geological evidence 6. Rocks from the Archean show liquid water and life 5.

The greenhouse solution. Most explanations invoke more greenhouse gases – carbon dioxide, methane or ammonia – which let sunlight in but absorb part of the heat radiated by the ground and send it back down 5. Sagan and Mullen proposed a few parts per million of ammonia 6. Today’s estimates favour carbon dioxide and methane, whose concentrations were sufficient to offset the fainter Sun 1. Still, every proposed solution has its difficulties, and the problem cannot be regarded as completely solved 5.

Ultraviolet light without a shield. Today the ozone layer in the stratosphere absorbs most of the Sun’s short-wavelength ultraviolet light. Ozone forms from oxygen, so the Archean, with almost no oxygen, had no ozone layer. Short-wavelength UV reached the lower atmosphere and broke up volcanic sulfur dioxide molecules 1. This photochemistry left an unusual fingerprint – a mass-independent fractionation of sulfur isotopes – in rocks older than about 2.45 billion years. It disappears between 2.45 and 2.09 billion years ago, when oxygen rose 7. Physics of light thus dates a biological revolution.

An open lid. Light gases can escape from the top of the atmosphere into space. Catling and Zahnle conclude from xenon isotopes that hydrogen escaped rapidly through the Archean – and that this substantial loss of hydrogen helped to oxidise the Earth 1.

Mathematics lens: the temperature of a planet and the speed of a molecule

Radiation balance. A planet absorbs sunlight on its cross-section πR² and radiates heat from its whole surface 4πR². By the Stefan–Boltzmann law, a body at temperature T radiates σT⁴ per square metre. Setting absorbed equal to emitted energy gives

with the solar constant S ≈ 1361 W/m², the albedo A ≈ 0.3 (the fraction of sunlight reflected) and σ = 5.67 · 10⁻⁸ W/(m² K⁴). The result is 255 K, about −18 °C – the temperature of an Earth without greenhouse effect. The actual average is about 288 K; the difference of 33 K is the warming by greenhouse gases today.

A fainter Sun. Because T grows only with the fourth root of the sunlight, 25 % less sunlight lowers the temperature by a factor of 0.75^1/4 ≈ 0.93 – from 255 K to about 237 K. Small as it seems, this drop of 18 K is enough to push a planet like ours below freezing, unless its greenhouse is stronger.

The brightening Sun. Gough’s formula describes the luminosity L at time t after the Sun’s birth, with today’s age t_☉ = 4.57 billion years 5:

At the Sun’s birth (t = 0) this gives 1/1.4 ≈ 71 % of today’s value; four billion years ago, about 74 %. Except for the first roughly 0.2 billion years, the formula agrees very well with detailed models 5.

Why hydrogen escapes. In a gas at temperature T, a molecule of mass m moves on average with the speed

where k = 1.38 · 10⁻²³ J/K is the Boltzmann constant. For an assumed temperature of 1,000 K in the upper atmosphere, a hydrogen atom moves at about 5.0 km/s, an oxygen molecule – 32 times heavier – at only about 0.88 km/s. Earth’s escape velocity is 11.2 km/s. Neither speed reaches it on average, but the fastest hydrogen atoms in the gas do, again and again – so over geological time hydrogen leaks away, while oxygen and nitrogen stay.

Computer science lens: a climate model in thirty lines

How cold would the early Earth have been with today’s atmosphere? The program below combines Gough’s formula for the brightening Sun with the radiation balance of the mathematics lens and a simple model of the greenhouse effect: a single “grey” layer of air that absorbs a fixed fraction of the heat radiated by the ground and sends half of it back down. The model is calibrated to today’s 288 K and then kept unchanged as the Sun grows brighter. Albedo, today’s temperature and the one-layer greenhouse are simplifying assumptions, not a real climate model.

import numpy as np
import matplotlib.pyplot as plt

SOLAR_CONSTANT = 1361.0   # sunlight reaching Earth today (W/m²)
ALBEDO = 0.30             # fraction of sunlight reflected, assumed constant
SIGMA = 5.670e-8          # Stefan–Boltzmann constant (W/m²/K⁴)
SUN_AGE = 4.57            # age of the Sun (billion years)
T_TODAY = 288.0           # mean surface temperature of Earth today (K)
FREEZING = 273.15         # freezing point of water (K)


def luminosity(ago):
    """Brightness of the Sun relative to today, 'ago' billion years ago (Gough's formula)."""
    t = SUN_AGE - ago
    return 1 / (1 + 0.4 * (1 - t / SUN_AGE))


def bare_temperature(ago):
    """Temperature (K) of an Earth without greenhouse effect: absorbed sunlight = emitted heat."""
    absorbed = SOLAR_CONSTANT * luminosity(ago) * (1 - ALBEDO) / 4
    return (absorbed / SIGMA) ** 0.25


def surface_temperature(ago, emissivity):
    """One-layer 'grey' atmosphere: it absorbs the fraction 'emissivity' of the heat radiation
    from the ground and sends half of it back down, so T_surface = T_bare · (2 / (2 − ε))^(1/4)."""
    return bare_temperature(ago) * (2 / (2 - emissivity)) ** 0.25


# Calibrate the atmosphere so that it gives today's 288 K, then keep it unchanged.
emissivity_today = 2 - 2 * (bare_temperature(0) / T_TODAY) ** 4
print(f"today: {bare_temperature(0):.0f} K without greenhouse effect, "
      f"{T_TODAY:.0f} K with it (emissivity {emissivity_today:.2f})")
print("billion years ago   Sun   with today's atmosphere")
for ago in [4.0, 3.0, 2.4, 2.0, 1.0, 0.0]:
    surface = surface_temperature(ago, emissivity_today)
    print(f"{ago:17.1f}   {luminosity(ago) * 100:3.0f} %   {surface - 273.15:6.1f} °C")

ages = np.linspace(4.0, 0, 401)
surface = surface_temperature(ages, emissivity_today)
if (surface < FREEZING).any():
    print(f"with today's atmosphere the oceans would freeze before "
          f"{ages[surface < FREEZING].min():.1f} billion years ago")
else:
    print("with today's atmosphere the oceans would never freeze")
needed = 2 - 2 * (bare_temperature(4.0) / FREEZING) ** 4
more_or_fewer = "more" if needed > emissivity_today else "fewer"
print(f"4.0 billion years ago, liquid water needed an emissivity of {needed:.2f} instead of "
      f"{emissivity_today:.2f} – {more_or_fewer} greenhouse gases than today")

plt.rcParams["font.size"] = 13      # large type: the chart stays readable on a phone
fig, ax = plt.subplots(figsize=(6.4, 5.2), layout="constrained")
ax.axhspan(-60, 0, color="#dbe9f4")
ax.plot(ages, surface - 273.15, lw=2.5, label="today's atmosphere")
ax.plot(ages, bare_temperature(ages) - 273.15, "--", lw=1.8, label="no greenhouse effect")
ax.axvspan(2.4, 2.3, color="0.85")
ax.text(2.33, 22, "oxygen\nrises", color="dimgray", fontsize=11, ha="right")
ax.text(3.95, -16, "frozen oceans", color="steelblue", fontsize=11)
ax.set_xlim(4.0, 0)
ax.set_ylim(-60, 30)
ax.set_xlabel("billion years ago")
ax.set_ylabel("mean surface temperature (°C)")
ax.set_title("A fainter Sun would have frozen the early Earth")
ax.legend(loc="lower right")
plt.show()

• Open in Colab
• Download .py
• How to run this code

Output · what the code prints, re-run at every build

today: 255 K without greenhouse effect, 288 K with it (emissivity 0.78)
billion years ago   Sun   with today's atmosphere
              4.0    74 %     -6.0 °C
              3.0    79 %     -1.5 °C
              2.4    83 %      1.4 °C
              2.0    85 %      3.5 °C
              1.0    92 %      8.9 °C
              0.0   100 %     14.9 °C
with today's atmosphere the oceans would freeze before 2.7 billion years ago
4.0 billion years ago, liquid water needed an emissivity of 0.88 instead of 0.78 – more greenhouse gases than today

What the result teaches:

• With today’s air, the early Earth freezes. Four billion years ago the Sun reached 74 % of today’s brightness, and the model surface would have been −6.0 °C; it stays below freezing until 2.7 billion years ago. This contradicts the geological evidence of liquid water 5 – the faint young Sun paradox in numbers.
• More greenhouse was needed. To keep water liquid four billion years ago, the model atmosphere must absorb 88 % of the ground’s heat radiation instead of 78 % today – that is, it needed more greenhouse gases, in line with the high carbon dioxide and methane levels inferred for the Archean 1.
• The model is too simple to give dates. Sagan and Mullen found temperatures below freezing until less than 2.3 billion years ago 6; this model says 2.7. It ignores feedbacks: ice reflects more sunlight, which would cool the planet further, and water vapour adds to the greenhouse as it warms. The direction of the result is robust, the exact dates are not.

Two programming ideas are worth noticing:

• Calibrate, then predict. The program does not guess the greenhouse strength; it fits one parameter, the emissivity, so that the model reproduces today’s 288 K – and then asks what the same atmosphere would do under a fainter Sun.
• Search with a mask. ages[surface < FREEZING] keeps only the times at which the surface is frozen; its smallest value is the last frozen moment. Checking first whether any value is frozen avoids an error when there is none.

Try it yourself – each change takes one line:

• Set ALBEDO = 0.35, Sagan and Mullen’s value: the planet without greenhouse is colder (250 K), but after calibration the surface temperatures are exactly the same (−6.0 °C four billion years ago). Only the greenhouse needed changes, to an emissivity of 0.96 instead of 0.87 today.
• Halve the brightening by changing 0.4 to 0.2 in luminosity: the young Sun now reaches 85 % of today’s brightness, the oceans never freeze, and four billion years ago the model atmosphere even needs fewer greenhouse gases than today (emissivity 0.72).

today: 250 K without greenhouse effect, 288 K with it (emissivity 0.87)
billion years ago   Sun   with today's atmosphere
              4.0    74 %     -6.0 °C
              3.0    79 %     -1.5 °C
              2.4    83 %      1.4 °C
              2.0    85 %      3.5 °C
              1.0    92 %      8.9 °C
              0.0   100 %     14.9 °C
with today's atmosphere the oceans would freeze before 2.7 billion years ago
4.0 billion years ago, liquid water needed an emissivity of 0.96 instead of 0.87 – more greenhouse gases than today

today: 255 K without greenhouse effect, 288 K with it (emissivity 0.78)
billion years ago   Sun   with today's atmosphere
              4.0    85 %      3.5 °C
              3.0    88 %      6.1 °C
              2.4    90 %      7.7 °C
              2.0    92 %      8.9 °C
              1.0    96 %     11.8 °C
              0.0   100 %     14.9 °C
with today's atmosphere the oceans would never freeze
4.0 billion years ago, liquid water needed an emissivity of 0.72 instead of 0.78 – fewer greenhouse gases than today