Module 0: Early Earth & the Hadean Eon

The stage for life's emergence was set during the Hadean eon (4.56–4.0 Gya), a chaotic period of magma oceans, giant impacts, and an atmosphere radically different from today's. This module reconstructs the physical environment of early Earth: from accretion and differentiation of the iron core, through the Moon-forming Theia collision, to the Late Heavy Bombardment and the formation of the first oceans. Evidence comes from zircon crystals older than any surviving rock, and the earliest known microfossils, the Strelley Pool stromatolites at 3.48 Gya.

0.1 Formation of the Earth

The Solar System condensed from a collapsing fragment of a molecular cloud roughly 4.567 billion years ago. Canonical CAI (calcium-aluminium inclusion) ages from primitive chondrites place the start of planetary formation at 4.5672 ± 0.0006 Gya. Earth itself accreted from planetesimals in the inner protoplanetary disk within \(\sim 30\text{-}100\) Myr of that reference.

Gravitational accretion and Safronov growth

Planetesimals (~km-scale bodies) collide and merge under mutual gravity. In the runaway-growth regime the largest embryo absorbs nearby smaller bodies at a rate set by gravitational focusing:

\[ \frac{dM}{dt} = \pi R^2 \, \rho_\text{disk} \, v_\text{rel} \left(1 + \frac{v_\text{esc}^2}{v_\text{rel}^2}\right) \]

where \(v_\text{esc} = \sqrt{2GM/R}\) is the embryo's escape speed and \(v_\text{rel}\) is the relative velocity of accretors. When \(v_\text{esc} \gg v_\text{rel}\), the Safronov number \(\Theta = (v_\text{esc}/v_\text{rel})^2\) greatly exceeds unity and growth is super-linear in mass.

Differentiation and the iron catastrophe

Accretion delivered enough kinetic energy to melt the growing proto-Earth. Denser iron-nickel alloys sank through the silicate mantle under the Rayleigh-Taylor instability, releasing gravitational potential energy:

\[ \Delta E_\text{diff} \approx \frac{3GM_\oplus^2}{5R_\oplus} \cdot f_\text{Fe} \approx 1.5 \times 10^{31}\;\text{J} \]

enough to raise the planet's temperature by roughly 2000 K, completing melting and establishing a global magma ocean. Siderophile (“iron-loving”) elements including Ni, Co, Pt, and Au partitioned into the core; lithophiles (Mg, Si, Al, Ca) stayed in the silicate mantle. The resulting core mass fraction of 0.325 matches both modern seismology and cosmochemical constraints from chondrite abundances.

The Theia impact and Moon formation

A Mars-sized body (Theia) is thought to have struck the proto-Earth at \(\sim 4.51\) Gya. SPH simulations by Canup & Asphaug (2001) show that a low-velocity oblique impact can launch a disk of molten silicate from which the Moon condenses within \(\sim 100\) yr. Evidence supporting this scenario includes:

Identical oxygen-isotope ratios between terrestrial and lunar samples (\(\delta^{17}\text{O}\) agreement to within 5 ppm)
Iron-depleted lunar bulk composition (consistent with a post-core-formation collision)
Angular momentum of the Earth-Moon system matching a single grazing impact
The Moon's thick anorthositic highlands, interpreted as magma-ocean flotation crust

0.2 Early Atmosphere & Oceans

The original hydrogen-helium nebular envelope was stripped within a few Myr by the T-Tauri wind of the young Sun. The secondary atmospherethat replaced it was outgassed from the interior during volcanic activity and delivered by impacting volatile-rich planetesimals from beyond the snow line.

Reducing vs weakly reducing: the Miller-Urey question

Stanley Miller's 1953 spark-discharge apparatus used a strongly reducing mixture of CH₄, NH₃, H₂, and H₂O (after Urey's theoretical suggestion). In the 1980s Kasting and Walker argued that, by the time geology began, the atmosphere was only weakly reducing: dominantly CO₂, N₂, and H₂O with trace CO and H₂. The degree of reducing character is quantified by the redox buffer of the upper mantle, set by FeO/Fe₂O₃ equilibria roughly one log-unit above the QFM (quartz-fayalite-magnetite) buffer:

\[ 3\,\text{Fe}_2\text{SiO}_4 + \text{O}_2 \rightleftharpoons 2\,\text{Fe}_3\text{O}_4 + 3\,\text{SiO}_2 \]

Hydrogen escape

Light gases (H₂, He) escape the atmosphere via Jeans and hydrodynamic mechanisms. The Jeans escape flux for species of mass \(m\) at the exobase is:

\[ \Phi_\text{J} = \frac{n v_T}{2\sqrt{\pi}} (1 + \lambda) e^{-\lambda}, \quad \lambda = \frac{GM_\oplus m}{k_B T_\text{exo} r_\text{exo}} \]

For the hot extended early atmosphere \((T_\text{exo} \gtrsim 3000\,\text{K})\)hydrogen could escape at the diffusion-limited flux of roughly \(10^{13}\,\text{cm}^{-2}\text{s}^{-1}\). This “late venting” gave Earth its irreversibly weakly-reducing character within a few tens of Myr.

Ocean formation: zircon evidence

The Jack Hills detrital zircons from Western Australia preserve \(\delta^{18}\text{O}\) values up to +7.4‰, consistent with crystallisation from magmas that had interacted with liquid water at low temperature. Wilde et al. (2001) reported a zircon with U-Pb age 4.404 ± 0.008 Gya — evidence that surface liquid water existed within ~150 Myr of Earth formation. The Cool Early Earth hypothesis (Valley 2002) thus replaced the long-standing picture of a persistently molten Hadean.

\[ t = \frac{1}{\lambda_{238}}\ln\!\left(\frac{{}^{206}\text{Pb}^\star}{{}^{238}\text{U}} + 1\right), \quad \lambda_{238} = 1.551\times10^{-10}\,\text{yr}^{-1} \]

0.3 The Late Heavy Bombardment

Apollo lunar samples show a pronounced spike in impact melt ages between 4.1 and 3.8 Gya. This Late Heavy Bombardment (LHB), or “lunar cataclysm”, is thought by many workers to reflect a destabilisation of the outer Solar System (the Nice model) in which Jupiter and Saturn passed through a 2:1 mean motion resonance, scattering Kuiper-belt and asteroid-belt bodies into the inner Solar System. Recent work questions the LHB as a discrete event, favouring a smoothly declining tail; we present both views.

Energy delivered to Earth

A body of mass \(m\) impacting at speed \(v\) delivers kinetic energy \(E = \tfrac{1}{2} m v^2\). For a typical main-belt asteroid (\(v \sim 18\) km/s) the equivalent TNT yield is

\[ E = \tfrac{1}{2}\,m\,v^2 \approx 1.6 \times 10^{14} \left(\frac{m}{10^9\,\text{kg}}\right)\,\text{J} \]

Cumulative LHB energy is estimated at \(\sim 10^{25}\) J — enough to boil away the upper ocean if delivered uniformly. Sleep et al. (1989) showed that the largest LHB impactors could have sterilised the surface by driving surface temperatures above the thermal death point of even the most robust thermophiles (~400 K sustained for decades).

Implications for life's timing

If LHB sterilisation was global, life must either have:

Originated after LHB, leaving \(\sim 300\) Myr before 3.48 Gya stromatolites
Retreated into deep subsurface refugia and re-colonised the surface afterwards
Originated during LHB in protected hydrothermal settings
Been re-seeded from Mars or elsewhere via lithopanspermia (see Module 5)

0.4 Earliest Evidence of Life

The oldest widely accepted biogenic signatures include:

Isua (Greenland, 3.83 Gya): graphite inclusions with \(\delta^{13}\text{C} \approx -25\,\permil\) consistent with biological carbon fixation (Mojzsis et al. 1996; contested).
Nuvvuagittuq (Quebec, 3.77-4.28 Gya): putative hematite filaments interpreted as iron-oxidising microbe remnants (Dodd et al. 2017).
Strelley Pool (Pilbara, 3.48 Gya): laminated conical stromatolites with clear microbial mat textures (Allwood et al. 2006) — the oldest widely accepted macroscopic biogenic structures.
Apex Chert (3.465 Gya): filamentous microfossils reinterpreted (Schopf et al. 2018) as biogenic after initial controversy.

Isotopic biosignatures

Biological carbon fixation preferentially incorporates the lighter \({}^{12}\text{C}\)over \({}^{13}\text{C}\), producing a measurable isotopic fractionation \(\Delta\) typical of 20-30‰:

\[ \delta^{13}\text{C} = \left(\frac{R_\text{sample}}{R_\text{PDB}} - 1\right) \times 1000\,\permil, \quad R = \frac{{}^{13}\text{C}}{{}^{12}\text{C}} \]

Organic carbon in Archean sediments clusters near \(-25\,\permil\), strongly depleted relative to the carbonate reservoir near \(0\,\permil\). This offset is the signature of rubisco-mediated or acetyl-CoA pathway carbon fixation.

0.5 Heat Flow & Radiogenic Power

The Hadean Earth released three to five times more heat per unit area than the modern planet. This high heat flow determined mantle viscosity, the style of tectonics (or its absence), and the longevity of the global magma ocean. Four heat sources contributed:

Accretional heat: conversion of kinetic energy of infalling planetesimals — roughly \(2.5 \times 10^{32}\) J total, largely retained in the first 10-50 Myr.
Core-formation energy: gravitational potential energy released by iron descending through silicate (\(\sim 1.5 \times 10^{31}\) J).
Radiogenic heating: \({}^{26}\text{Al}\)(\(t_{1/2} = 717\) kyr) dominated the first few million years; long-lived\({}^{40}\text{K}\), \({}^{232}\text{Th}\), \({}^{235}\text{U}\), \({}^{238}\text{U}\)then took over.
Tidal heating: the early Moon orbited at \(\sim 1/16\) its present distance, producing tides ~4000 times stronger.

The radiogenic heat production per unit mass of bulk silicate Earth at time \(t\)is:

\[ H(t) = \sum_i X_i H_i \exp\!\left(-\frac{\ln 2}{t^{(i)}_{1/2}}\,t\right) \]

where \(X_i\) is the mass fraction of isotope \(i\) and \(H_i\) is its specific heat-release rate. Integrating over the Hadean gives bulk radiogenic power that declined from roughly \(\sim 100\) TW at 4.5 Gya (short-lived \({}^{26}\text{Al}\)-dominated) to about 30-40 TW by 3.8 Gya.

Urey ratio and mantle convection

The Urey ratio \(\mathrm{Ur} = H/Q\) compares internal radiogenic production \(H\) to total surface heat flow \(Q\). Today \(\mathrm{Ur} \approx 0.35\); during the Hadean it approached unity, requiring vigorous “squishy-lid” or stagnant-lid convection before plate tectonics could stabilise in the Archean.

Python: Hadean Thermal & Atmospheric Evolution

This simulation models the surface temperature history of the Hadean Earth from 4.56 to 3.5 Gya, combining post-accretion exponential cooling, a CO₂-H₂O greenhouse bump, and a re-heating spike from the Late Heavy Bombardment. The companion panel tracks partial pressures of H₂, CH₄, NH₃, CO₂, H₂O and N₂ as the atmosphere transitioned from strongly reducing to weakly reducing.

Python

script.py83 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Thermal evolution of the Hadean Earth
# Simple 1-D conductive cooling model with impact heating flux

fig, axes = plt.subplots(1, 2, figsize=(16, 7), facecolor='#03120a')
fig.subplots_adjust(wspace=0.35)

# ---- Panel 1: Surface temperature over Hadean eon ----
ax1 = axes[0]
ax1.set_facecolor('#061a0d')

t_Gyr = np.linspace(4.56, 3.8, 500)   # Hadean window
# Magma ocean crystallises quickly; simplify as exponential cooling + LHB bump
T_eq = 255.0                          # equilibrium blackbody temp at 1 AU, no atmosphere (K)
T_hot = 2000.0                        # magma ocean surface
tau = 0.05                            # cooling time constant (Gyr)
# Time since formation
dt = 4.56 - t_Gyr
T_base = T_eq + (T_hot - T_eq) * np.exp(-dt / tau)
# Greenhouse kick (CO2+H2O atmosphere)
greenhouse = 80.0 * np.exp(-(dt - 0.05)**2 / 0.15**2)
# Late Heavy Bombardment 4.1 - 3.8 Gya
lhb = 400.0 * np.exp(-((t_Gyr - 4.0)**2) / 0.06**2)
T_surface = T_base + greenhouse + lhb

ax1.plot(t_Gyr, T_surface, color='#34d399', lw=2.5, label='Surface T (model)')
ax1.axhline(373, color='#fbbf24', ls='--', lw=1.2, alpha=0.75, label='Water boils (1 atm)')
ax1.axhline(273, color='#60a5fa', ls='--', lw=1.2, alpha=0.75, label='Water freezes')
ax1.axvspan(4.1, 3.8, alpha=0.15, color='#f97316', label='Late Heavy Bombardment')
ax1.axvspan(4.56, 4.45, alpha=0.15, color='#dc2626', label='Magma ocean')

ax1.invert_xaxis()
ax1.set_xlabel('Time (Gya)', color='#6ee7b7', fontsize=11)
ax1.set_ylabel('Surface Temperature (K)', color='#6ee7b7', fontsize=11)
ax1.set_title('Hadean Earth: Thermal Evolution\n(Cooling + Greenhouse + LHB Reheating)',
              color='#a7f3d0', fontsize=12, fontweight='bold')
ax1.legend(fontsize=8, labelcolor='#a7f3d0', facecolor='#061a0d', edgecolor='#10b981')
ax1.tick_params(colors='#6ee7b7')
ax1.grid(True, alpha=0.2, color='#10b981')
for sp in ax1.spines.values(): sp.set_edgecolor('#10b981')

# ---- Panel 2: Atmospheric composition evolution ----
ax2 = axes[1]
ax2.set_facecolor('#061a0d')

t2 = np.linspace(4.56, 3.5, 400)
dt2 = 4.56 - t2
# Relative partial pressures (log arbitrary units)
H2  = 0.3 * np.exp(-dt2 / 0.08)                 # escape to space
CH4 = 0.08 * np.exp(-dt2 / 0.2)                  # photolysis
NH3 = 0.04 * np.exp(-dt2 / 0.1)                  # rapid UV destruction
CO2 = 20 - 18 * np.exp(-dt2 / 0.5)               # outgassing accumulation
H2O = 5 + 40 * np.exp(-dt2 / 0.4)                # steam -> ocean condensation down-drop
N2  = 0.5 + 0.5 * (1 - np.exp(-dt2 / 0.3))       # outgassed, stable

ax2.semilogy(t2, H2, color='#60a5fa', lw=2, label='H2 (escape)')
ax2.semilogy(t2, CH4, color='#f97316', lw=2, label='CH4 (reducing component)')
ax2.semilogy(t2, NH3, color='#a78bfa', lw=2, label='NH3 (UV-destroyed)')
ax2.semilogy(t2, CO2, color='#6ee7b7', lw=2.5, label='CO2 (outgassed)')
ax2.semilogy(t2, H2O, color='#22d3ee', lw=2, label='H2O (condensing)')
ax2.semilogy(t2, N2,  color='#fbbf24', lw=2, label='N2')

ax2.invert_xaxis()
ax2.set_xlabel('Time (Gya)', color='#6ee7b7', fontsize=11)
ax2.set_ylabel('Relative partial pressure (log, arbitrary)', color='#6ee7b7', fontsize=11)
ax2.set_title('Hadean Atmospheric Composition\nReducing -> Weakly Reducing Transition',
              color='#a7f3d0', fontsize=12, fontweight='bold')
ax2.legend(fontsize=8, labelcolor='#a7f3d0', facecolor='#061a0d', edgecolor='#10b981', ncol=2)
ax2.tick_params(colors='#6ee7b7')
ax2.grid(True, which='both', alpha=0.2, color='#10b981')
for sp in ax2.spines.values(): sp.set_edgecolor('#10b981')

fig.suptitle('Hadean Earth: Thermal & Atmospheric Evolution 4.56-3.5 Gya',
             color='#a7f3d0', fontsize=14, fontweight='bold')

plt.savefig('output.png', bbox_inches='tight', facecolor=fig.get_facecolor(), dpi=120)
plt.close()
print('Hadean thermal/atmosphere simulation complete.')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Python: Zircon U-Pb Concordia & LHB Flux

Panel 1 plots the U-Pb concordia curve (\({}^{206}\text{Pb}^\star/{}^{238}\text{U}\) vs.\({}^{207}\text{Pb}^\star/{}^{235}\text{U}\)) with the oldest known terrestrial zircon (4.374 Gyr Jack Hills grain) highlighted. Panel 2 reconstructs the declining-tail impact flux with an LHB spike at 3.95 Gya; cumulative energy delivery is sufficient to boil the upper ocean repeatedly.

Python

script.py82 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Zircon U-Pb dating: Pb/U isochron approach
# 238U -> 206Pb (lambda1 = 1.55e-10 /yr)
# 235U -> 207Pb (lambda2 = 9.85e-10 /yr)

lam1 = 1.55125e-10  # per year
lam2 = 9.8485e-10   # per year

t = np.linspace(0, 4.6e9, 1000)  # years
r_206 = np.exp(lam1 * t) - 1
r_207 = np.exp(lam2 * t) - 1

# Concordia curve: 207Pb*/235U vs 206Pb*/238U
fig, axes = plt.subplots(1, 2, figsize=(16, 7), facecolor='#03120a')
fig.subplots_adjust(wspace=0.35)

ax1 = axes[0]
ax1.set_facecolor('#061a0d')
ax1.plot(r_207, r_206, color='#34d399', lw=2.5, label='Concordia curve')

# Mark key ages
mark_ages_Gyr = [0.5, 1.0, 2.0, 3.0, 4.0, 4.4]
for t_mark_Gyr in mark_ages_Gyr:
    t_mark = t_mark_Gyr * 1e9
    x = np.exp(lam2 * t_mark) - 1
    y = np.exp(lam1 * t_mark) - 1
    ax1.scatter(x, y, color='#fbbf24', s=55, zorder=6, edgecolor='white', linewidth=1.1)
    ax1.annotate(f'{t_mark_Gyr:.1f} Gyr', (x, y), xytext=(8, -12),
                 textcoords='offset points', color='#fbbf24', fontsize=9)

# Jack Hills oldest zircon (4.374 Gyr)
t_jh = 4.374e9
x_jh = np.exp(lam2 * t_jh) - 1
y_jh = np.exp(lam1 * t_jh) - 1
ax1.scatter(x_jh, y_jh, color='#f472b6', s=130, zorder=7, marker='*',
            edgecolor='white', linewidth=1.2, label='Jack Hills zircon (4.374 Gyr)')

ax1.set_xlabel('207Pb*/235U', color='#6ee7b7', fontsize=11)
ax1.set_ylabel('206Pb*/238U', color='#6ee7b7', fontsize=11)
ax1.set_title('U-Pb Concordia Diagram\nOldest Terrestrial Zircons',
              color='#a7f3d0', fontsize=12, fontweight='bold')
ax1.legend(fontsize=9, labelcolor='#a7f3d0', facecolor='#061a0d', edgecolor='#10b981')
ax1.tick_params(colors='#6ee7b7')
ax1.grid(True, alpha=0.2, color='#10b981')
for sp in ax1.spines.values(): sp.set_edgecolor('#10b981')

# ---- Panel 2: Impact flux during LHB ----
ax2 = axes[1]
ax2.set_facecolor('#061a0d')

t_Gyr = np.linspace(4.5, 3.5, 500)
# Declining smooth-accretion flux
base = 1.5 * np.exp(-(4.5 - t_Gyr) / 0.4)
# LHB spike
spike = 8 * np.exp(-(t_Gyr - 3.95)**2 / 0.04**2)
flux = base + spike

ax2.semilogy(t_Gyr, flux, color='#f97316', lw=2.5)
ax2.fill_between(t_Gyr, 0.001, flux, alpha=0.25, color='#f97316')
ax2.axvspan(4.1, 3.8, alpha=0.15, color='#dc2626', label='Late Heavy Bombardment')
ax2.axhline(1, color='#60a5fa', ls='--', lw=1, label='Steady-state flux (modern normalized)')

ax2.invert_xaxis()
ax2.set_xlabel('Time (Gya)', color='#6ee7b7', fontsize=11)
ax2.set_ylabel('Impact flux (relative, log)', color='#6ee7b7', fontsize=11)
ax2.set_title('Impact Flux on Early Earth\nAccretion tail + LHB spike',
              color='#a7f3d0', fontsize=12, fontweight='bold')
ax2.legend(fontsize=9, labelcolor='#a7f3d0', facecolor='#061a0d', edgecolor='#10b981')
ax2.tick_params(colors='#6ee7b7')
ax2.grid(True, which='both', alpha=0.2, color='#10b981')
for sp in ax2.spines.values(): sp.set_edgecolor('#10b981')

fig.suptitle('Dating the Hadean: U-Pb Concordia & Bombardment Flux',
             color='#a7f3d0', fontsize=14, fontweight='bold')
plt.savefig('output.png', bbox_inches='tight', facecolor=fig.get_facecolor(), dpi=120)
plt.close()
print('U-Pb concordia and LHB flux simulation complete.')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

References

Wilde, S.A., Valley, J.W., Peck, W.H. & Graham, C.M. (2001). Evidence from detrital zircons for the existence of continental crust and oceans on the Earth 4.4 Gyr ago. Nature, 409, 175-178.
Canup, R.M. & Asphaug, E. (2001). Origin of the Moon in a giant impact near the end of the Earth's formation. Nature, 412, 708-712.
Sleep, N.H., Zahnle, K.J., Kasting, J.F. & Morowitz, H.J. (1989). Annihilation of ecosystems by large asteroid impacts on the early Earth. Nature, 342, 139-142.
Gomes, R., Levison, H.F., Tsiganis, K. & Morbidelli, A. (2005). Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets. Nature, 435, 466-469.
Mojzsis, S.J. et al. (1996). Evidence for life on Earth before 3800 million years ago. Nature, 384, 55-59.
Allwood, A.C., Walter, M.R., Kamber, B.S., Marshall, C.P. & Burch, I.W. (2006). Stromatolite reef from the Early Archaean era of Australia. Nature, 441, 714-718.
Valley, J.W. (2002). A cool early Earth? Geology, 30, 351-354.
Catling, D.C. & Kasting, J.F. (2017). Atmospheric Evolution on Inhabited and Lifeless Worlds. Cambridge University Press.
Zahnle, K. et al. (2007). Emergence of a habitable planet. Space Science Reviews, 129, 35-78.
Dodd, M.S. et al. (2017). Evidence for early life in Earth's oldest hydrothermal vent precipitates. Nature, 543, 60-64.
Hazen, R.M. (2012). The Story of Earth. Penguin.
Schopf, J.W., Kitajima, K., Spicuzza, M.J., Kudryavtsev, A.B. & Valley, J.W. (2018). SIMS analyses of the oldest known assemblage of microfossils. PNAS, 115, 53-58.

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