10. Rocky Planets, Mercury & Mars

Learning objectives: By the end of this lecture, you will be able to explain Mercury’s unusual spin-orbit resonance and metal-rich interior, reconstruct the geological history of Mars across its three main periods, derive the Jeans escape parameter and use it to explain which gases Mars loses by thermal escape, interpret the seismic structure of Mars from InSight data, and use Mercury and Mars as limiting cases that isolate the roles of planet size, distance, and timing in rocky-planet evolution.

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Slides: Download Lecture 10 (PDF)

10.1. Why Mercury and Mars together?

In Lecture 9 we examined Earth and Venus as a near-twin pair with similar mass but divergent surface conditions. Mercury and Mars represent limiting cases. They are extreme bodies that bracket Earth and Venus in size, heliocentric distance, volatile inventory, and dynamo longevity. Mercury is the smallest and densest terrestrial planet. It sits closest to the Sun, stripped of almost all volatiles. Mars has roughly half the diameter of Earth and sits at the outer edge of the habitable zone. It preserves a sedimentary and atmospheric record of a wetter, warmer past. Fig. 10.1 sets the four side by side.

Fig. 10.1 The four terrestrial planets at approximate relative scale. From left to right: Mercury, Venus, Earth, and Mars. Despite forming in the same protoplanetary disk, these worlds span a factor of about 18 in mass and have followed dramatically different evolutionary paths. Credit: NASA/JPL, public domain.

The lecture is divided into three parts. Part 1 examines Mercury as a metal-world case study, covering orbital dynamics, interior structure, surface morphology, polar volatiles, and the exosphere. Part 2 focuses on Mars, exploring its interior, geological periods, evidence for past water, and thermal atmospheric loss via the Jeans escape flux. Part 3 compares these extremes to show how size, heliocentric distance, and dynamo longevity govern planetary evolution and habitability.

10.2. Part 1: Mercury, the metal world

10.2.1. Mercury overview: the smallest, densest, closest

Mercury is a small planet with mass \(0.0553\,\Mearth\), mean radius \(0.3829\,\Rearth = 2440\ \mathrm{km}\), and bulk density \(5.43\ \mathrm{g\ cm^{-3}}\). Correcting for internal compression gives an uncompressed density (density corrected for internal pressure) of \(\sim 5.3\ \mathrm{g\ cm^{-3}}\). This is the highest value in the solar system, well above Earth’s \(\sim 4.0\ \mathrm{g\ cm^{-3}}\) [Solomon et al., 2018]. This density requires a much larger iron mass fraction than any other terrestrial planet (Fig. 10.2). How Mercury acquired so much iron is the iron-enrichment problem.

Fig. 10.2 Mercury’s internal structure inferred from MESSENGER gravity and libration data. The crust (\(\sim 30\)–\(50\ \mathrm{km}\)) and a thin silicate mantle (\(\sim 400\ \mathrm{km}\)) overlie a large core occupying \(\sim 83\%\) of Mercury’s radius. The core itself is layered: a possible thin solid Fe-S layer at the top of the core (the “FeS snow zone”), a liquid Fe-Ni-S outer core that sustains the planet’s weak global magnetic field, and an inferred but unresolved solid inner core. The radar libration measurement of Margot et al. [2007] established that the core is at least partially molten; the layer dimensions shown here follow the MESSENGER-era synthesis of Margot et al. [2018]. Course-original figure.

Mercury’s orbit is also extreme. The semi-major axis is \(a = 0.387\ \mathrm{AU}\) and the eccentricity \(e = 0.2056\), the highest of any planet. Distance to the Sun varies from \(0.307\ \mathrm{AU}\) at perihelion to \(0.467\ \mathrm{AU}\) at aphelion. Solar flux changes by more than a factor of two over a Mercurian year. This orbital eccentricity and tidal evolution drove the planet into its spin-orbit resonance. Mercury’s near-zero obliquity (about \(2\) arcminutes) keeps the rotation axis perpendicular to the orbital plane. This allows polar ice to survive close to the Sun.

10.2.2. Orbit and the 3:2 spin-orbit resonance

Mercury rotates once every \(58.65\) Earth days and orbits the Sun once every \(87.97\) Earth days. Radar observations in 1965 revealed a \(3:2\) spin-orbit resonance rather than synchronous rotation.

Tidal torques act on a planet’s permanent quadrupole moment (an equatorial bulge) most strongly at perihelion. In a \(3:2\) resonance, this bulge points Sunward at alternate perihelia. The capture probability during Mercury’s orbital evolution is \(\sim 55\%\) [Correia and Laskar, 2004].

Expanding the orbit-averaged torque in eccentricity Fourier components yields non-zero torque only when the spin (\(n_{\mathrm{spin}}\)) and orbital (\(n_{\mathrm{orb}}\)) frequencies satisfy:

(10.1)\[ \frac{n_{\mathrm{spin}}}{n_{\mathrm{orb}}} \;=\; 1 + \frac{p}{2}\, , \qquad p \in \mathbb{Z}\, . \]

The allowed states in (10.1) are \(1{:}1\) (\(p=0\)), \(3{:}2\) (\(p=1\)), and \(2{:}1\) (\(p=2\)). Resonance strength scales as a constant for \(1{:}1\), as \(e\) for \(3{:}2\), and as \(e^2\) for \(2{:}1\). With eccentricity \(e = 0.206\), the wide \(3{:}2\) resonance dominates.

Consequently, a solar day (time between local noons) lasts \(\sim 176\) Earth days, twice the orbital year. Longitudes \(0^\circ\) and \(180^\circ\) face the Sun at alternate perihelia. These hot poles reach peak temperatures of \(\sim 700\) K. Longitudes offset by \(90^\circ\) reach perihelion at midnight, reaching peak temperatures of \(\sim 570\) K.

Fig. 10.3 Mercury spin rate deviations from the resonant \(3/2\) rate measured by Earth-based radar speckle interferometry. The \(88\)-day forced libration amplitude (\(35.8 \pm 2\) arcseconds) is twice the solid-planet value, showing mantle decoupling from a liquid core. Reproduced from Margot et al. [2007], Fig. 3.

Mercury’s rotation also probes its interior through its forced libration in longitude over its \(88\)-day year. Earth-based radar measurements yielded a libration amplitude of \(35.8 \pm 2\) arcseconds (Fig. 10.3) [Margot et al., 2007]. This amplitude is roughly twice the value for a solid planet, confirming that the mantle decouples from a liquid outer core and carries only \(C_m/C \approx 0.5\) of the total moment of inertia, where \(C_m\) is the moment of inertia of the silicate shell alone. Fig. 10.4 shows the Monte Carlo distribution of \(C_m/C\) behind this statement.

Fig. 10.4 Histograms of best-fit values for the diagnostic moment-of-inertia ratio \(C_m/C\) (where \(C_m\) is the moment of inertia of the silicate mantle alone and \(C\) is the total moment of inertia, so \(C_m/C\) is the fraction of the total moment of inertia contributed by the mantle), drawn from \(10^5\) Monte Carlo draws on the measured libration amplitude and the gravity coefficient \(C_{22}\). Panel A uses the radar measurements alone, panel B adds the relation between the gravitational harmonic coefficients and the obliquity that holds in a Cassini state, which tightens the result. Each panel shows two histograms, for the two extremes of the plausible total moment of inertia adopted in 2007: \(C/MR^2 = 0.325\) in red and \(0.380\) in blue. Radio science with MESSENGER has since put \(C/MR^2 \approx 0.346\) between those two extremes, and that is the value used in the body text and in the interior structure inversion below. Every distribution peaks near \(C_m/C \approx 0.5\), far from the value of unity a fully solid Mercury requires, so the core must be decoupled and at least partly liquid. Reproduced from Margot et al. [2007], Fig. 4.

10.2.3. Interior: a giant iron core

Gravity and libration measurements yield a normalised moment of inertia \(C/MR^2 \approx 0.346\) [Margot et al., 2007]. As shown in Lecture 8, \(C/MR^2 < 0.4\) indicates that mass is concentrated toward the centre. While comparable to Earth’s \(0.331\), Mercury’s value implies a much thinner silicate shell around an unusually large metallic core. The core radius is approximately \(2020\ \mathrm{km}\), \(83\%\) of the planet’s radius. The mantle and crust are only \(420\ \mathrm{km}\) thick (\(17\%\)) (Fig. 10.5). By mass, the core represents roughly \(74\%\) of Mercury against \(32\%\) for Earth.

Fig. 10.5 Schematic representation of Mercury’s internal layering used in modern interior structure models from Margot et al. [2018]. From the centre outward, \(R_{\mathrm{ic}}\) is the inner solid core boundary, \(R_{\mathrm{oc}}\) separates the liquid outer core from the solid outer shell, \(R_{\mathrm{b}}\) marks the optional dense compositional layer at the base of the silicate mantle, and \(R_{\mathrm{m}}\) is the crust-mantle boundary. The radially varying densities of the inner and outer core (\(\rho_{\mathrm{ic}}(r)\) and \(\rho_{\mathrm{oc}}(r)\)) capture compression and composition effects with depth.

Gravity and libration data are consistent with a liquid outer core surrounding a small solid inner core. Its existence and size remain debated. Mercury also possesses an intrinsic dipolar magnetic field aligned with the rotation axis, with about \(1\%\) of Earth’s surface field strength. This field is powered by an active dynamo, the self-sustaining generation of a magnetic field by convective motion of an electrically conducting fluid. Sustaining convection after \(\sim 4.5\) Gyr of cooling requires that the core has not fully frozen. Thermal evolution models indicate that light elements such as sulfur, silicon, or carbon depress the freezing point and slow inner-core growth [Wicht and Heyner, 2017].

10.2.4. Why is Mercury so iron-rich?

Mercury has a core mass fraction of \(\sim 74\%\), compared to \(32\%\) for Earth and Venus and \(24\%\) for Mars [Margot et al., 2018]. Three hypotheses have been proposed:

1. Selective condensation in the inner solar nebula. Hot inner-disc temperatures could condense Fe-Ni metal before silicates. Modern models find no steep gradient at \(0.4\) AU.

2. Vapour and aerosol stripping by the early Sun. Solar luminosity or stellar winds could evaporate the silicate mantle. MESSENGER data show volatile enrichment (Na, S, K) [Solomon et al., 2018] (Fig. 10.6). This is in tension with the thermal-stripping hypothesis.

Fig. 10.6 (a) Global maps of Mg/Si (left) and Al/Si (right) elemental ratios on Mercury’s surface, derived from four years of MESSENGER X-Ray Spectrometer measurements by Nittler et al. [2020]. White contours mark the High-Mg Region (HMR), the Caloris Basin (CB), the Northern Smooth Plains, and the Low-Mg Northern Smooth Plains (LM-NSP). (b) A higher-resolution Mg/Si zoom around the Gaudi and Stieglitz craters within the Low-Mg Northern Smooth Plains (LM-NSP), showing that compositional variations exist on small spatial scales as well. Mercury’s surface is volatile-element rich and does not match the expectations of a planet that lost its silicate mantle by thermally driven evaporation, undermining the strongest version of the vaporisation-stripping hypothesis for Mercury’s iron enrichment.

3. One or more giant impacts. Late collisions could strip the silicate mantle, leaving a metallic core. Smoothed-particle hydrodynamics simulations (modeling fluids as particles) show impacts reproduce the core fraction [Chau et al., 2018]. However, single impacts occur in well below \(1\%\) of dynamical histories (Fig. 10.7). This favours multiple impacts [Franco et al., 2022].

Fig. 10.7 Final mass distribution of remnant bodies at the end of N-body integrations of inner-solar-system formation, plotted against semi-major axis, for six different surface density profile slopes (\(x = 0.5\) to \(5.5\)). Open circles are larger (\(> 0.3\,\Mearth\)) bodies, crosses are smaller ones, and solid triangles mark the masses of the actual terrestrial planets in our solar system. Reproducing a Mercury-mass body in the right orbital location with the observed iron enrichment occurs in well below \(1\%\) of all trial histories. From Franco et al. [2022], Fig. A1.

We cannot yet decide between these mechanisms. BepiColombo data will test whether volatile abundances match single-impact or multiple-impact scenarios.

10.2.5. A weak, offset dynamo

Mercury’s magnetic dipole is aligned with the rotation axis within \(\sim 1^\circ\). Yet it is offset northward from the geometric centre by \(479 \pm 6\ \mathrm{km}\), roughly \(20\%\) of the planetary radius [Anderson et al., 2012]. The equatorial surface dipole strength is only \(\sim 200\ \mathrm{nT}\) (about \(1\%\) of Earth’s value), far weaker than a naive extrapolation of the magnetic Reynolds number criterion from Lecture 4 would suggest (the criterion only tells us that a dynamo can operate, not how strong its surface field will be).

Fig. 10.8 Mollweide maps of the radial magnetic field at the surface of Mercury (top) compared with two of Wicht and Heyner [2017]’s numerical dynamo models (CW3, middle, and CW4, bottom) that incorporate a thermally stratified outer core layer. The hemispheric asymmetry of the radial field, with positive equatorial flux (yellow/orange) concentrated in the southern hemisphere and weaker, opposite-sign flux in the north (blue), is the surface signature of the dipole that is offset \(\sim 480\) km northward of the planetary centre: the southern surface lies closer to the magnetic-pole end of the dipole and therefore samples a stronger field. Models with a stably stratified upper core can reproduce both the weakness and the asymmetry of the observed field.

Two mechanisms explain these features: a thermally stratified outer layer at the top of the liquid core, in which heat is carried by conduction rather than convection, and a stable inner core boundary that introduces a north-south asymmetry. Numerical simulations combining these ingredients reproduce both the weakness and offset of the field [Wicht and Heyner, 2017] (Fig. 10.8).

10.2.6. The surface: ancient cratering, smooth plains, lobate scarps, and hollows

Mercury’s heavily cratered surface resembles the lunar highlands. A thick blanket of regolith, the loose layer of fragmented impact debris, covers it. Global topography (Fig. 10.9) reveals distinct features that record the planet’s thermal and geological history.

Fig. 10.9 Global topographic measurement coverage of Mercury from the MESSENGER Mercury Laser Altimeter (MLA) projected on a Hammer equal-area map. The northern hemisphere is densely covered by direct laser altimetry; topographic relief on Mercury spans roughly \(10\ \mathrm{km}\) from the lowest to highest points measured. Image courtesy NASA/JHUAPL/Carnegie Institution; reproduced from Zuber et al. [2012].

The smooth plains are large, lightly cratered volcanic regions that resemble lunar maria. These flood-basalt provinces were emplaced between \(\sim 3.7\) and \(\sim 3.9\) billion years ago. That is near the end of the late heavy bombardment, an early period of elevated impact flux. Large-scale effusive volcanism on Mercury ceased after about \(3.5\) Ga [Solomon et al., 2018].

The lobate scarps are long, sinuous cliffs produced by thrust faults. The faults accommodate global contraction as Mercury’s interior cooled. Mapping of these scarps indicates a total radial contraction of \(5\) to \(7\ \mathrm{km}\) [Byrne et al., 2014]. Small, unweathered scarps crosscut young craters. Tectonic contraction is therefore ongoing today [Watters et al., 2016]. Mercury is the only planet besides Earth currently known to host active tectonic deformation.

The Caloris basin (\(\sim 1550\ \mathrm{km}\) in diameter) is one of the largest impact basins in the solar system. Its interior is filled by smooth plains and deformed by ridges and graben, down-dropped crustal blocks bounded by faults. Seismic waves from the Caloris impact were focused at the antipodal point to produce jumbled “weird terrain”. The Moon’s Imbrium and South Pole-Aitken basins show similar antipodal focusing.

The hollows are shallow, flat-floored bright depressions found on crater walls, peaks, and floors [Blewett et al., 2011]. They likely form through the loss of volatile compounds from the upper crust. Solar heating, micrometeorite gardening, and ion sputtering drive the loss. Their fresh appearance indicates that hollow formation actively modifies the surface today.

These surface features record early differentiation and heavy cratering, widespread effusive volcanism ending around \(3.5\) Ga, sustained global contraction, and ongoing modification by tectonics and volatile loss.

10.2.7. Polar volatiles: ice on the hottest planet

In 1991, radar observations from the Arecibo and Goldstone telescopes revealed polarisation-inverting echoes inside Mercury’s polar craters. Such echoes are characteristic of water ice. Between 2011 and 2015, the MESSENGER spacecraft confirmed these deposits directly (Fig. 10.10). Topography from the Mercury Laser Altimeter showed that polar crater floors are permanently shadowed. Because of Mercury’s nearly zero obliquity, they never receive direct sunlight [Paige et al., 2013].

Fig. 10.10 Mercury’s north polar region in polar projection (latitude \(\sim 65^\circ\)N to the pole), from Neumann et al. [2013] Fig. 1. (A) MLA topography (colour scale in km above the reference sphere), showing the cratered high-northern-latitude terrain with several impact craters visible along the polar circle. (B) MLA \(1064\)-nm surface reflectance on the same polar projection (colour scale \(0\) to \(0.10\)). Dark spots (low reflectance, red markers) are located inside permanently shadowed crater floors. (C) Biannual-average insolation at the surface, expressed as a percentage of the 1 AU solar constant. The darkest regions coincide with the low-reflectance spots in panel B: the crater floors receive essentially zero direct sunlight year-round. (D) Biannual maximum illumination temperature, again showing permanently cold regions coinciding with the anomalously dark reflectance in B. The spatial coincidence of low reflectance, zero insolation, and low temperature is interpreted as evidence that Mercury’s permanently shadowed crater floors host surface-near volatiles: a thin lag of organic-rich material (responsible for the low 1064-nm reflectance) overlying a water-ice deposit. Combined with MESSENGER neutron-spectrometer evidence of hydrogen enrichment at the same craters [Lawrence et al., 2013], this establishes Mercury as a rocky body that retains cold-trapped volatiles despite its proximity to the Sun. From Neumann et al. [2013].

Mercury hosts an estimated \(\sim 10^{16}\) to \(10^{18}\ \mathrm{g}\) of polar water across \(\sim 5\times10^4\ \mathrm{km^2}\) of permanently shadowed terrain [Lawrence et al., 2013]. In a cold trap, water molecules delivered by comets, asteroids, or interior dehydration wander via ballistic hops and freeze onto crater floors at \(\sim 100\ \mathrm{K}\).

10.2.8. Exosphere and magnetosphere

Mercury has a surface-bounded exosphere. Its column density is so low that gas particles follow ballistic trajectories without colliding before hitting the surface or escaping. Its composition includes atomic Na, K, Ca, Mg, H, and He. These atoms are released from the surface by solar wind sputtering (energetic ions knocking atoms loose near magnetic cusps), micrometeorite impact vaporisation (releasing volatiles from the regolith), photon-stimulated desorption by ultraviolet sunlight, and thermal desorption of volatile species.

Solar radiation pressure sweeps neutral sodium antisunward into a comet-like sodium tail observable from Earth. Ground-based and MESSENGER observations show that this tail varies with orbital phase and solar wind conditions. This makes it a tracer of space-weather coupling.

Mercury possesses a compact magnetosphere, the smallest in the solar system, with its subsolar magnetopause only \(\sim 1.5\) Mercury radii from the centre (Fig. 10.11).

Fig. 10.11 Equatorial cross-section of Mercury’s compact magnetosphere. The standoff distance is only about 1.5 Mercury radii and the magnetotail is correspondingly short. Reconnection at the dayside magnetopause and in the tail is fast and frequent compared to Earth. Reproduced from Wicht and Heyner [2017].

10.2.9. Mission history at Mercury

Mariner 10 flew past Mercury three times in 1974 and 1975. The mission discovered Mercury’s intrinsic magnetic field and revealed its heavily cratered surface. The MESSENGER mission transformed our understanding of the planet during its orbital phase from 2011 to 2015, returning orbital imaging of major geologic structures such as the Caloris basin (Fig. 10.12).

Fig. 10.12 The Caloris basin on Mercury, \(\sim 1550\ \mathrm{km}\) in diameter, imaged in enhanced colour by NASA’s MESSENGER spacecraft. Caloris is one of the largest and best-preserved multi-ring impact basins in the solar system; the orange interior plains are smooth volcanic deposits emplaced after the impact, while the surrounding annulus shows ejecta and concentric ring structures. The basin’s antipode on Mercury contains chaotic “weird terrain” thought to have formed from the focused seismic shock of the same event. Credit: NASA/Johns Hopkins APL/Carnegie Institution of Washington, public domain.

MESSENGER data established Mercury’s offset dipole, polar ice deposits, hollows, global contraction, and unexpectedly high volatile content. BepiColombo will enter orbit in late 2026 to constrain core structure, refine polar ice inventories, and test origin scenarios through surface volatile abundances.

10.3. Part 2: Mars, the watery past

10.3.1. Mars overview: half Earth, one tenth the mass

Mars is the second-smallest planet, with a mass of \(0.107\,\Mearth\), radius of \(0.532\,\Rearth = 3389\ \mathrm{km}\), and mean density of \(3.93\ \mathrm{g\ cm^{-3}}\). The orbit sits near the outer edge of the conservative habitable zone of Lecture 13. The semi-major axis is \(a = 1.524\ \mathrm{AU}\) and the eccentricity \(e = 0.0934\). The atmosphere is thin (\(\sim 6\ \mathrm{mbar}\) surface pressure) and dominated by \(\mathrm{CO_2}\). The global mean surface temperature is near \(210\ \mathrm{K}\). Mars has two small natural satellites, Phobos and Deimos.

Compared to Mercury and Venus, Mars has an Earth-like day length (\(24\) h \(37\) min) and a current obliquity of \(25.19^\circ\) (close to Earth’s \(23.4^\circ\)). The result is Earth-like seasons. However, resonance with planetary perturbations causes Martian obliquity to oscillate chaotically on \(\sim 100\) Myr timescales between near-zero and over \(60^\circ\). This drives periodic ice ages. Although cold, dry, and uninhabitable today, early Mars hosted abundant liquid water for at least \(\sim 100\) Myr, perhaps episodically for a billion years. Mars offers the best preserved record of an Earth-like planet losing its atmosphere and drying out. This makes it an essential target for astrobiology. Mariner 4 returned the first close-up view of that surface in 1965 (Fig. 10.13).

Fig. 10.13 The first close-up image of another planet’s surface: Mariner 4, 15 July 1965. Mariner 4 returned 21 frames during the brief Mars encounter, of which this is one of the most reproduced. The heavily cratered, Moon-like terrain visible here decisively ended speculation about Martian canals and surface vegetation. Credit: NASA/JPL.

10.3.2. Phobos and Deimos: the twin moons

Because Phobos orbits faster than Mars rotates, tidal torques pull it inward (\(1.8\ \mathrm{cm/yr}\)) toward disruption within \(30\) to \(50\) Myr. Deimos, by contrast, recedes. Both moons are dark, primitive-looking rubble piles. Phobos has a low bulk density of \(1.89 \pm 0.05\ \mathrm{g\ cm^{-3}}\), which implies high porosity [Kuramoto et al., 2022].

The captured asteroid hypothesis matches their primitive spectra. Capturing circular orbits, however, is dynamically difficult. The giant-impact debris hypothesis produces their orbits from an impact disc (Fig. 10.14) Hyodo et al. [2017]. However, it predicts a Mars-mantle composition.

Fig. 10.14 Two snapshots of entropy gain (in \(\mathrm{J\,K^{-1}\,kg^{-1}}\)) from a smoothed-particle hydrodynamics simulation of a Borealis-scale giant impact onto early Mars by Hyodo et al. [2017], at \(t = 0.17\ \mathrm{h}\) (left, immediately post-impact) and \(t = 20\ \mathrm{h}\) (right, after the debris disc has expanded). The impact drives an entropy increase of \(\sim 1500\ \mathrm{J\,K^{-1}\,kg^{-1}}\) in the disc material and ejects a circumplanetary disc containing both impactor and Martian-mantle material. Disc fragments collide at \(1\)–\(5\ \mathrm{km\,s^{-1}}\) and grind down to \(\sim 100\ \mu\)m grains, providing the building blocks from which Phobos and Deimos may subsequently accrete. Two panels selected from the original 4 columns \(\times\) 4 rows grid (composition, temperature, entropy, pressure across four times).

The Martian Moons eXploration (MMX) mission will sample Phobos to test these models [Kuramoto et al., 2022].

Fig. 10.15 shows the planned quasi-satellite orbits of MMX around Phobos.

Fig. 10.15 Planned observation orbits for the JAXA MMX spacecraft around Phobos, drawn in a Phobos-fixed frame with Phobos at the centre, the \(xy\) plane taken as the Phobos orbital plane and the \(x\) axis pointing away from Mars. Top: the five quasi-satellite orbits confined to the \(xy\) plane, from QSO-H at about \(200\ \mathrm{km}\) along \(y\) down to QSO-Lc at a few tens of kilometres; the low orbits support the sampling phase. Bottom: one three-dimensional quasi-satellite trajectory, at the QSO-M effective radius and an inclination of \(45^\circ\), which carries the spacecraft over the whole surface rather than over the equatorial band alone. Reproduced from Kuramoto et al. [2022], Fig. 3.

10.3.3. Mars’ interior: the InSight revolution

Before in situ seismology, orbital gravity and topography [Smith et al., 2001] gave crustal thickness maps through isostatic compensation, and the moment of inertia \(C/MR^2 \approx 0.364\) (Lecture 8) indicated a smaller relative core than Earth’s; the InSight seismometer, deployed in 2018, then recorded over a thousand marsquakes.

Fig. 10.16 Detection of core-reflected \(S\) waves (\(ScS\)) in InSight marsquake recordings, adapted from Fig. 1 of Stähler et al. [2021]. (a) Transverse-component seismogram of event S0173a (top) and the stacked envelope of six marsquakes (bottom) against time relative to the \(ScS\) arrival predicted for a core radius of \(1830\) km; for S0173a, \(ScS\) arrives about \(350\) s after the direct \(S\) wave. (b) Energy in a \(10\) s window around the predicted \(ScS\) arrival for each of \(5000\) interior models against the core radius of the model, normalised here from the minimum to the peak of the fitted curve; the peak pins the core-mantle boundary at \(r_{\mathrm{core}} \approx 1830\ \mathrm{km}\). Axes and arrival labels added for this course.

From core-reflected shear waves (\(ScS\)), Stähler et al. [2021] measured a core radius of \(1830 \pm 40\ \mathrm{km}\) (Fig. 10.16). Reanalyses [Khan et al., 2023, Samuel et al., 2023] reinterpret this reflection as the top of a \(150 \pm 15\ \mathrm{km}\) thick molten silicate layer, revising the metallic core radius to \(\sim 1650\) to \(1675\ \mathrm{km}\) and its density upward to \(\sim 6500\ \mathrm{kg\,m^{-3}}\) (Lecture 8). Detecting \(ScS\) waves indicates a liquid outer core, as fluids do not transmit shear waves, and the low density of the 2021 core solution (\(5.7\) to \(6.3\ \mathrm{g\ cm^{-3}}\); \(\sim 6.5\) for the smaller 2023 core) requires light elements dissolved in the iron.

In a planet of radius \(R\), direct shear waves cannot cross the liquid core of radius \(r_{\mathrm{core}}\). The straight-ray limit for a ray grazing the core yields:

(10.2)\[ \cos\!\left(\frac{\Delta_{\max}}{2}\right) \;=\; \frac{r_{\mathrm{core}}}{R}\, . \]

Setting \(r_{\mathrm{core}} = 1830\ \mathrm{km}\) and \(R = 3389\ \mathrm{km}\) gives \(\Delta_{\max} \approx 115^\circ\). Quakes beyond \(115^\circ\) fall into a shadow zone where only reflected \(ScS\) waves reach InSight (Fig. 10.17). Stähler et al. [2021] combined \(ScS\) arrival times and the direct-\(S\) cutoff to constrain \(r_{\mathrm{core}}\) to \(\pm 40\ \mathrm{km}\).

Fig. 10.17 Schematic interior of Mars constrained by InSight seismic observations (Stähler et al. [2021]). The \(1830 \pm 40\ \mathrm{km}\) discontinuity reflects shear waves, but reanalyses [Khan et al., 2023, Samuel et al., 2023] place the metallic core beneath a \(150 \pm 15\ \mathrm{km}\) molten silicate layer at radius \(1650\)–\(1675\ \mathrm{km}\).

Seismic velocity inversions indicate a \(\sim 500\ \mathrm{km}\) thick lithosphere over a cool upper mantle [Khan et al., 2021]. Crustal thickness beneath InSight is \(20 \pm 5\ \mathrm{km}\) or \(39 \pm 8\ \mathrm{km}\), depending on which seismic discontinuity marks the base of the crust; the corresponding global mean crustal thickness is \(24\) to \(38\ \mathrm{km}\) or \(39\) to \(72\ \mathrm{km}\), in both cases thinner under the northern lowlands and thicker under the southern highlands [Knapmeyer-Endrun et al., 2021].

These observations establish a silicate mantle extending to \(\sim 1560\ \mathrm{km}\) depth and a liquid metallic core. Without a solid inner core to drive compositional convection, Mars lacks a modern dynamo.

The \(^{182}\mathrm{Hf}\)-\(^{182}\mathrm{W}\) chronometer shows that Mars differentiated within \(\sim 2\) to \(4\ \mathrm{Myr}\) of CAI formation, far faster than Earth’s \(\sim 30\) to \(100\ \mathrm{Myr}\) accretion [Kruijer et al., 2017]. Mars is therefore a planetary embryo, a protoplanet that stopped growing before consolidating into a full-sized terrestrial planet, and this rapid formation is consistent with its small core fraction and short-lived dynamo.

Fig. 10.18 Present-day crustal thickness models of Mars from gravity, topography, and InSight seismic constraints (Plesa et al. [2022]). Global mean thickness ranges from \(40.6\ \mathrm{km}\) (thin end-member a, \(31\ \mathrm{km}\) at InSight) to \(71.4\ \mathrm{km}\) (thick end-member c, \(49\ \mathrm{km}\) at InSight).

Thermal models indicate that Mars is in a stagnant-lid regime, where an immobile lithosphere encloses a slowly convecting mantle and heat escapes by conduction (Fig. 10.18 and Fig. 10.19) [Plesa et al., 2022] (Lecture 3). Radioactive heat-producing elements (uranium, thorium, and potassium) are concentrated in the crust. The mantle is correspondingly depleted. This explains why core cooling halted the early dynamo while volcanic activity persisted into the recent past.

Fig. 10.19 Cut-away renderings of the present-day mantle convection pattern in three thermal-evolution models of Mars. The dark red sphere is the core, the orange surfaces are the hot upwellings, and the outer shell shows the surface topography. All three models use the same crust, of mean thickness \(61.3\ \mathrm{km}\) and density \(2800\ \mathrm{kg\,m^{-3}}\), and differ only in core radius: \(1500\ \mathrm{km}\) in a, \(1700\ \mathrm{km}\) in b, and \(1850\ \mathrm{km}\) in c. Only the largest core agrees with the InSight core-radius estimate. The larger the core, the more numerous and the smaller the plumes and downwellings become, which is hard to reconcile with building the crustal dichotomy by mantle convection alone and so favours an impact origin for it. Reproduced from Plesa et al. [2022], Fig. 10a-c; the mantle temperature-variation slices of the original are not shown.

Planetary thermal evolution is characterized by the Urey number, the ratio of internal radiogenic heat production to total surface heat loss:

(10.3)\[ \mathrm{Ur} \;\equiv\; \frac{H_{\mathrm{rad}}}{Q_{\mathrm{surf}}}\, . \]

For Mars, the modern radiogenic heat production is \(H_{\mathrm{rad}} \sim 2.5 \times 10^{12}\ \mathrm{W}\). Thermal models [Plesa et al., 2022] estimate a global surface heat loss of \(Q_{\mathrm{surf}} \approx 20 \times 10^{-3}\ \mathrm{W\,m^{-2}} \times 1.45 \times 10^{14}\ \mathrm{m^2} \approx 3 \times 10^{12}\ \mathrm{W}\). Evaluating the ratio yields:

\[ \mathrm{Ur}_{\mathrm{Mars}} \;\sim\; \frac{2.5 \times 10^{12}}{3 \times 10^{12}} \;\approx\; 0.8\, , \]

With a value below unity, Mars is losing heat slightly faster than radioactive decay deposits it, but its cooling rate is substantially slower than Earth’s (\(\mathrm{Ur}_\oplus \approx 0.3\) to \(0.5\)).

10.3.4. Mars’ geological periods: Noachian, Hesperian, Amazonian

Mars is divided into three major geological periods (each subdivided into epochs) based on impact crater density [Hartmann and Neukum, 2001], compiled globally by Tanaka et al. [2014] (Fig. 10.20); translating crater counts to absolute ages requires model corrections because the Martian impact rate differs from the Moon’s (Fig. 10.21).

Fig. 10.20 Global geologic map of Mars from the chronostratigraphic mapping of Tanaka et al. [2014], in a Robinson projection. Noachian units (red and brown shades) dominate the southern highlands; Hesperian units (greens and blues) cover the northern lowlands and large volcanic provinces; Amazonian units (yellows and tans) include the youngest volcanic and polar deposits. The dichotomy between the heavily cratered south and the smoother north is the dominant first-order feature.

Fig. 10.21 Correlation chart of the map units in the global geologic map of Mars by Tanaka et al. [2014]. Columns separate the major terrain categories (lowland, impact, polar, basin, volcanic, apron, transition, highland) and rows correspond to the Amazonian, Hesperian, and Noachian periods, each split into early, middle, and late epochs except the Hesperian, which has only an early and a late epoch. Each box spans the age range of one map unit. The numbers on the right give the crater densities that define the epoch boundaries: the number of craters larger than 1, 5, and 16 km per \(10^6\) km\(^2\). The decline in the number and extent of new units from the Noachian to the Amazonian records the slowing of resurfacing on Mars and is a key constraint on its thermal and atmospheric evolution. Image credit: USGS (public domain).

The Noachian period (\(\sim 4.1\) to \(\sim 3.7\) Ga) is the oldest, preserved in the heavily cratered southern highlands. It hosted an active core dynamo. Most water-related features formed then: valley networks, open-basin lakes, and clay minerals.

The Hesperian period (\(\sim 3.7\) to \(\sim 3.0\) Ga) is marked by widespread volcanism and catastrophic outflow channels. Surface chemistry shifted from clay-forming to sulfate-forming environments as the dynamo shut off and the atmosphere thinned.

The Amazonian period (\(\sim 3.0\) Ga to present) covers two thirds of Mars’ history with minimal geological activity. Surfaces exhibit low crater densities, cold and dry conditions, and sporadic Tharsis volcanism within the last \(1\) Gyr.

Across these periods, surface renewal fell by over an order of magnitude. Liquid water was concentrated in the Noachian.

10.3.5. Mars surface highlights: dichotomy, Tharsis, Olympus, Valles

Mars’ topography [Smith et al., 2001] is dominated by two large-scale geological features. The first is the hemispheric dichotomy, a \(\sim 6\)-km elevation difference between the cratered southern highlands and the smooth northern lowlands. An exogenic giant impact excavating the elliptical Borealis basin (\(\sim 10\,600 \times 8\,500\ \mathrm{km}\)) is the leading explanation for the thinner northern crust [Andrews-Hanna et al., 2008], though degree-1 mantle convection remains a competing hypothesis.

The second feature is Tharsis, a continent-sized volcanic province covering roughly a quarter of Mars’ surface and standing several kilometres above the datum. Tharsis hosts the solar system’s largest volcanoes, including Olympus Mons, a shield volcano rising \(\sim 21.3\ \mathrm{km}\) above the datum (\(\sim 22\ \mathrm{km}\) above surrounding plains) with a base diameter of roughly \(600\ \mathrm{km}\) (Fig. 10.22).

Fig. 10.22 Olympus Mons on Mars, the largest volcano in the solar system, seen from above in this Viking Orbiter colour mosaic. The shield volcano has a base diameter of \(\sim 600\ \mathrm{km}\) and a summit elevation of \(\sim 21\ \mathrm{km}\) above the Mars datum. The caldera complex at the summit (centre) contains multiple nested collapse craters formed by episodic magma withdrawal. The steep basal escarpment (up to \(6\ \mathrm{km}\) high) is visible as the sharp boundary encircling the edifice. Olympus Mons grew to this immense size because Mars lacks plate tectonics: the volcanic source remained fixed beneath the lithosphere for billions of years. Credit: NASA/JPL/USGS, public domain.

These volcanoes grew to enormous sizes for two reasons. First, without plate tectonics, a stationary mantle plume delivers magma to the same location for hundreds of millions of years, building a single massive structure rather than a chain of separate volcanoes as on Earth. Second, Mars’ lower gravity (\(g = 3.71\ \mathrm{m\,s^{-2}}\), \(\sim 38\%\) of Earth’s) allows the lithosphere to support larger topographic loads before flexing downward.

Enormous lithospheric stresses from Tharsis opened Valles Marineris, a canyon system on its eastern flank. It stretches \(\sim 4000\ \mathrm{km}\) along the equator and is up to \(200\ \mathrm{km}\) wide and \(7\ \mathrm{km}\) deep. Despite resembling fluvial canyons like the Grand Canyon, Valles Marineris is fundamentally a tectonic rift.

Other notable features include Hellas Planitia, a \(2300\)-km-diameter, \(\sim 7\)-km-deep impact basin. It is the largest unambiguous impact crater on Mars.

10.3.6. Evidence for past water

Valley networks are branching channels in Noachian highlands formed by precipitation-fed runoff [Hynek et al., 2010]. Outflow channels are large scoured features carved during the Hesperian by catastrophic aquifer discharges.

Clay minerals (phyllosilicates) formed by aqueous alteration of basalt at near-neutral pH during the Noachian (Fig. 10.23). Bibring et al. [2006] divided Martian aqueous history into the clay-forming phyllosian (neutral pH), sulfate-rich theiikian (acidic, evaporative), and dry siderikian (Fig. 10.24).

Fig. 10.23 Global map of hydrated minerals on Mars from OMEGA/Mars Express. Top: detections only, on a black background. Bottom: the same detections overlaid on an MGS/MOLA altitude reference map. Red points mark phyllosilicate (clay) detections, blue points mark sulfate detections, and yellow points mark other hydrated minerals whose spectral signatures are not driven by metal-OH vibrations. Clays cluster preferentially in the Noachian southern highlands, consistent with neutral-pH aqueous alteration during the phyllosian stage. Sulfates are concentrated at lower-latitude and equatorial sites, consistent with later, drier, more acidic evaporative settings of the theiikian stage (Fig. 10.24). Reproduced from Bibring et al. [2006], Fig. 3.

Fig. 10.24 The three-stage aqueous history of Mars from OMEGA imaging-spectrometer mineralogy: phyllosian (clays, neutral wet), theiikian (sulfates, acidic), and siderikian (anhydrous ferric oxides, dry). The coloured band gives the dominant alteration product of each stage, the row above it the mineralogical era, and the row below the chronostratigraphic Noachian, Hesperian, and Amazonian divisions, whose boundaries are related to but distinct from the mineralogical ones. Two arrows point down into the short cross-hatched interval that separates the clays from the sulfates: a red one labelled surface volcanic activity near its start, and a blue one labelled Mars global change near its end. The figure therefore places the peak of volcanism and the global change of surface chemistry together, inside that one narrow interval. Reproduced from Bibring et al. [2006], Fig. 5.

Sulfate deposits record later acidic and evaporative settings at Meridiani Planum and Gale crater. Lakebed sediments and deltas at Jezero and Gale crater require standing water bodies that persisted for thousands of years [Grotzinger et al., 2014].

Fig. 10.25 summarises the spectral classes that record these aqueous settings.

Fig. 10.25 Summary of Mars surface compositional spectra from infrared remote sensing and rover instruments, compiled by Ehlmann and Edwards [2014]. The diversity of spectral classes (basalts, hydrated silicates, sulfates, carbonates, hematite, opaline silica) is evidence for a wide range of aqueous and igneous environments through Mars history.

In situ analysis by the Perseverance rover in Jezero crater provided ground truth for these mineralogical stages [Farley et al., 2022]. PIXL and SHERLOC instrument observations revealed that the crater-floor Séítah formation consists of igneous olivine cumulates altered by multiple episodes of liquid water to form carbonates and sulfates. Visible and near-infrared reflectance spectroscopy from orbit maps these alteration suites globally (Lecture 7).

Fig. 10.26 Global distribution of olivine on the Martian surface from TES and OMEGA spectroscopic mapping, projected over a topographic basemap with major regional features labelled (Acidalia, Arabia Terra, Utopia, Tharsis, Terra Meridiani, Isidis, Hellas, Terra Sirenum, Argyre, Elysium). Olivine-rich units (coloured pixels) cluster in the equatorial-to-southern band including impact-exposed terrain around Hellas, Isidis, and Terra Sirenum. Fresh olivine implies limited aqueous alteration, helping identify regions where water was rare or absent. From Ehlmann and Edwards [2014].

Mineralogical and topographic records indicate a warmer, wetter Noachian between \(\sim 3.8\) and \(3.6\) Ga, while the survival of unaltered olivine (Fig. 10.26) shows where liquid water did not reach. Conditions were colder and drier thereafter.

10.3.7. The early Mars climate puzzle

Valley networks indicate surface liquid water on early Mars despite \(25\%\) lower solar luminosity at \(4\) Ga (the faint young Sun problem; Lecture 9). A pure \(\mathrm{CO_2}\)-\(\mathrm{H_2O}\) atmosphere cannot close the gap: radiative-convective models give mean surface temperatures of about \(225\ \mathrm{K}\) or less, because \(\mathrm{CO_2}\) spectral windows stay open and the water-vapour feedback is weak at low temperature, and \(\mathrm{CO_2}\) ice clouds add little net warming [Wordsworth, 2016]. One proposed solution invokes reducing gases such as \(\mathrm{H_2}\) or \(\mathrm{CH_4}\), which warm the surface through collision-induced absorption (CIA) with \(\mathrm{CO_2}\) [Wordsworth et al., 2017]. The \(\mathrm{H_2}\) can come from volcanic outgassing, from serpentinisation (water-rock reactions altering ultramafic minerals), or from large impacts [Wordsworth et al., 2017, Wordsworth et al., 2021]. The “icy highlands” hypothesis proposes a cold baseline in which snow accumulates on the southern highlands, with repeated warm excursions that melt it (Fig. 10.27); in the phase diagram of steady climate states this is the cold and relatively dry quadrant (Fig. 10.28) [Kite, 2019, Wordsworth, 2016].

Fig. 10.27 Schematic of the “cold baseline with transient warm excursions” picture of the early Mars climate, drawn as an idealised cross-section from the northern lowlands (left) to the southern highlands (right). Under the faint young Sun a pure \(\mathrm{CO_2}\)-\(\mathrm{H_2O}\) atmosphere leaves the surface frozen, whereas episodic \(\mathrm{H_2}\) release adds collision-induced absorption and cloud warming that seasonally melts highland snow to carve valley networks during excursions lasting \(10^5\) to \(10^6\) yr. Course-original figure based on Wordsworth [2016], Wordsworth et al. [2017], Wordsworth et al. [2021], Kite [2019] and Kite and Conway [2024].

Fig. 10.28 Idealised two-dimensional phase diagram for the steady-state climate of early Mars under a denser atmosphere, with mean surface temperature on the horizontal axis and total surface \(\mathrm{H_2O}\) inventory on the vertical axis across four end-member regimes. The cold and relatively dry quadrant (bottom left), combined with episodic melting, best matches the geological evidence. Reproduced from Wordsworth [2016], Fig. 7.

Fluvial features shifted from Late Noachian and Early Hesperian valleys to Late Hesperian and younger alluvial fans (deposits where channels slow) at mid-latitudes (Fig. 10.29), indicating a transition from global to seasonal greenhouse warming (Fig. 10.30) [Kite et al., 2022].

Fig. 10.29 Changing spatial distribution of water-worn landforms on Mars. Top: early-stage valley networks, about \(3.6\) Ga and older (Late Noachian and Early Hesperian). Bottom: late-stage alluvial fans and deltas, \(3.5\) to \(3\) Ga and perhaps younger (Late Hesperian and Amazonian). Each feature is coloured by its elevation, from \(-6\) km (blue) to \(+6\) km (yellow). Grey marks the region excluded because the detection probability there is low or zero, and the elevation contours are spaced \(3\) km apart. The rover letters are C for Curiosity at Gale crater, P for Perseverance at Jezero crater, and T-1 for the Tianwen-1 rover Zhurong. Once the detection bias is corrected, the early features favour high ground, while the late ones lie lower and form bands at mid-latitude in both hemispheres. The control therefore passes from elevation to latitude, and that shift is what constrains the change in the greenhouse effect. Reproduced from Kite et al. [2022], Fig. 1.

Fig. 10.30 Graphical summary of the Kite et al. [2022] model for the climate evolution of Mars. Left: geographically idealised cross-sections of the two eras, with the early-stage valley networks (blue) cut into the highlands at about \(3.6\) Ga, and the late-stage alluvial fans (orange) confined to lower ground at \(3.5\) to \(3\) Ga; the grey subsurface band is the cryosphere. Right: the climate states of the model as a function of \(\mathrm{CO_2}\) loss (horizontal, from \(1000\) to \(10\) mbar) and loss of non-\(\mathrm{CO_2}\) warming (vertical, gray-gas column optical depth \(\tau\) from \(5\) down to \(0\)), with the present-day state marked at the bottom right. The bands run from warm and wet at the top, through warm lowlands with cold highlands, then cold and wet, to cold and dry at the bottom. The blue outline encloses the states that match the early era and the orange outline those that match the late era. The two can be connected with or without a change in \(p\mathrm{CO_2}\), but a decline in non-\(\mathrm{CO_2}\) radiative forcing is very probably required. Reproduced from Kite et al. [2022], Fig. 6.

Geological constraints indicate that early Mars climate fluctuated between cold baselines and wet episodes, with valley networks forming over \(10^4\) yr or longer [Kite, 2019, Kite and Conway, 2024].

10.3.8. Modern Mars: thin atmosphere, dust, and methane

Mars today has a \(\sim 6\ \mathrm{mbar}\) surface pressure, \(95\%\) \(\mathrm{CO_2}\), with traces of \(\mathrm{N_2}\), \(\mathrm{Ar}\), and \(\mathrm{O_2}\). The mean surface temperature is \(\sim 210\ \mathrm{K}\) and varies with latitude, season, and time of day.

Suspended dust heats the atmosphere by absorbing visible sunlight, driving winds that loft more dust. This positive feedback occasionally produces global dust storms that obscure the surface for weeks to months (Fig. 10.31).

Fig. 10.31 Mars before and during the 2018 global dust storm, as imaged by the Mars Reconnaissance Orbiter. The left panel shows clear atmospheric conditions with surface features visible; the right panel shows the planet almost completely obscured by wind-lofted mineral dust. The storm ultimately ended the Opportunity rover’s 15-year mission by blocking sunlight to its solar panels. Credit: NASA/JPL-Caltech/MSSS, public domain.

In the seasonal \(\mathrm{CO_2}\) cycle, roughly \(25\%\) of the atmospheric mass condenses onto the winter pole and sublimates back in spring.

Recurring slope lineae (RSL), once interpreted as briny water flows, are now explained by dry granular flows without liquid water.

Methane on Mars has a photochemical destruction lifetime of only \(\sim 300\) years. Curiosity reported background methane of \(\sim 0.4\) to \(0.7\ \mathrm{ppb}\) with occasional spikes, but the Trace Gas Orbiter found global upper limits of \(< 0.05\ \mathrm{ppb}\).

10.4. Blackboard derivation: The Jeans escape parameter

Blackboard derivation: The Jeans escape parameter on Mars

Goal: Compare the thermal energy of a molecule with its gravitational binding energy at the top of the atmosphere, and apply this to Mars to see why hydrogen is lost on geological timescales but \(\mathrm{CO_2}\) essentially is not.

Setup.

Consider a thin layer at the exobase, the altitude in the atmosphere where the mean free path of a gas molecule becomes comparable to the local atmospheric scale height. Above the exobase, the gas is collisionless: any molecule moving fast enough to escape simply leaves. We assume the gas at the exobase is in local thermal equilibrium at temperature \(T = T_{\mathrm{exo}}\).

Fig. 10.32 shows the exobase geometry: below it the gas is collisional, above it a molecule on an outward path either escapes or falls back, depending only on its speed.

Fig. 10.32 Setup sketch of the board derivation of the Jeans escape parameter: the planet, the exobase at radius \(r_{\mathrm{exo}}\) (dashed), a molecule faster than \(v_{\mathrm{esc}}\) that leaves on a straight path, and a slower molecule that falls back on a ballistic arc. Course-original figure.

For a molecule of mass \(m\), the most probable speed in the Maxwell-Boltzmann distribution is

\[ v_{\mathrm{th}} = \sqrt{\frac{2\,\kB\, T}{m}}\, , \]

and the escape velocity at the exobase radius \(r_{\mathrm{exo}}\) is

\[ v_{\mathrm{esc}} = \sqrt{\frac{2\,G\,M}{r_{\mathrm{exo}}}}\, , \]

where \(M\) is the planet mass.

Step 1: The escape parameter. We define the dimensionless escape parameter as the ratio of the gravitational potential energy at the exobase to the thermal energy per molecule:

(10.4)\[ \lambda \equiv \left(\frac{v_{\mathrm{esc}}}{v_{\mathrm{th}}}\right)^{\!2} = \frac{G\,M\,m}{\kB\,T\,r_{\mathrm{exo}}}\, . \]

With \(v_{\mathrm{th}} = \sqrt{2 \kB T / m}\) (the most-probable thermal speed) and \(v_{\mathrm{esc}}^2 = 2 G M / r_{\mathrm{exo}}\), the algebra collapses cleanly to the right-hand side. A molecule with kinetic energy comparable to \(\kB T\) is gravitationally bound when \(\lambda \gg 1\) and free to escape when \(\lambda \lesssim 1\).

Step 2: The Boltzmann factor.

A molecule escapes when its kinetic energy exceeds its binding energy at the exobase, \(G M m / r_{\mathrm{exo}} = \lambda\,\kB T\). In a gas in thermal equilibrium, the fraction of molecules with an energy above \(E \gg \kB T\) is dominated by the Boltzmann factor \(e^{-E/(\kB T)}\), so the fraction fast enough to escape scales as \(e^{-\lambda}\). Because \(\lambda\) is proportional to the molecular mass, a heavy molecule has a much larger \(\lambda\) than a light one at the same temperature, and the exponential turns this linear difference into many orders of magnitude.

Integrating the Maxwell-Boltzmann distribution over all upward-moving molecules faster than \(v_{\mathrm{esc}}\) gives the Jeans escape flux, named after James Jeans and introduced in Lecture 5 (equation (5.15), with \(v_{\mathrm{th}}/(2\sqrt{\pi}) = \sqrt{\kB T/(2\pi m)}\)); we state it without the integration:

(10.5)\[ \boxed{\,\Phi_J \;=\; n\,\sqrt{\frac{\kB T}{2\pi m}}\,(1+\lambda)\,e^{-\lambda}\,} \]

where \(n\) is the number density at the exobase. The thermal-speed prefactor and the factor \((1+\lambda)\) change slowly with \(\lambda\); the exponential decides which species escape.

Step 3: Application to Mars.

For Mars: \(M = 6.4\times 10^{23}\ \mathrm{kg}\), \(r_{\mathrm{exo}} \approx R_{\mathrm{Mars}} + 200\ \mathrm{km} \approx 3.6\times 10^6\ \mathrm{m}\), \(T_{\mathrm{exo}} \approx 270\ \mathrm{K}\) (modern; somewhat higher under solar storms). The escape velocity at the exobase is

\[ v_{\mathrm{esc}} = \sqrt{\frac{2\,(6.67\times 10^{-11})\,(6.4\times 10^{23})}{3.6\times 10^6}} \approx 4.9\ \mathrm{km/s}\, . \]

For atomic hydrogen, \(m = 1.67 \times 10^{-27}\ \mathrm{kg}\) and

\[ \lambda_H = \frac{G M m}{\kB T r_{\mathrm{exo}}} \approx \frac{(6.67 \times 10^{-11})(6.4 \times 10^{23})(1.67 \times 10^{-27})}{(1.38 \times 10^{-23})(270)(3.6 \times 10^6)} \approx 5.3\, . \]

So \(e^{-\lambda_H} \approx 5 \times 10^{-3}\), modest but significant. The most-probable thermal speed of atomic hydrogen at \(270\) K is \(v_{\mathrm{th}}^H = \sqrt{2 \kB T / m_H} \approx 2.1\) km/s, about \(43\%\) of \(v_{\mathrm{esc}}\), so a non-negligible fraction of the high-velocity tail of the Maxwell-Boltzmann distribution exceeds escape velocity. Hydrogen can escape Mars’ atmosphere by Jeans escape, and over geological timescales the cumulative loss is enormous.

For molecular hydrogen (\(\mathrm{H_2}\), \(m = 2\) amu) the escape parameter doubles: \(\lambda_{H_2} \approx 10.6\), \(e^{-\lambda} \approx 2.5 \times 10^{-5}\). Still escaping, but more slowly than atomic H.

For \(\mathrm{CO_2}\), with molecular mass \(44\) amu, the escape parameter is

\[ \lambda_{CO_2} = \frac{m_{CO_2}}{m_H}\,\lambda_H = 44 \times 5.3 \approx 230\, . \]

The exponential is then \(e^{-230} \approx 10^{-100}\), which is zero for any practical purpose. Mars cannot lose \(\mathrm{CO_2}\) by Jeans escape on any reasonable timescale. The same applies to nitrogen (\(\lambda \approx 150\), \(e^{-\lambda} \sim 10^{-65}\)), oxygen (atomic O: \(\lambda \approx 85\), \(e^{-\lambda} \sim 10^{-37}\); molecular \(\mathrm{O_2}\): \(\lambda \approx 170\)), and water vapour (\(\lambda \approx 95\), although \(\mathrm{H_2O}\) is photolysed in the upper atmosphere and lost as H plus O via different channels).

Lesson.

Jeans escape is selective. Light species (H, He, \(\mathrm{H_2}\), possibly \(\mathrm{D}\)) are stripped by thermal escape on Gyr timescales; heavy species (C, N, O, Ar, \(\mathrm{CO_2}\)) are essentially immune. If Mars has lost a substantial inventory of \(\mathrm{CO_2}\) over its history, the loss must have happened by non-thermal processes that bypass the Maxwell-Boltzmann velocity distribution entirely. We turn to those processes next.

A few comments on the derivation. The factor \((1+\lambda)\) in equation (10.5) arises because the flux weights each molecule by its speed: a speed class contributes to the flux in proportion to its speed. Without gravity (\(\lambda \to 0\)) the formula reduces to \(n\sqrt{\kB T/(2\pi m)}\), the kinetic-theory flux of molecules through an aperture; for \(\lambda \gg 1\) it falls as \(\lambda\,e^{-\lambda}\). Fig. 10.33 shows the Maxwell-Boltzmann distribution and the escaping tail above \(v_{\mathrm{esc}}\).

Fig. 10.33 Maxwell-Boltzmann speed distribution for atomic hydrogen at the exobase temperatures of Earth (\(T_\mathrm{exo} = 1000\ \mathrm{K}\), blue) and Mars (\(T_\mathrm{exo} = 270\ \mathrm{K}\), red). Dashed vertical lines mark the escape velocity \(v_\mathrm{esc}\) at the exobase of each planet: \(10.8\ \mathrm{km\,s^{-1}}\) at \(500\ \mathrm{km}\) altitude for Earth, and \(4.9\ \mathrm{km\,s^{-1}}\) at \(200\ \mathrm{km}\) altitude for Mars. Only molecules in the high-speed tail above \(v_\mathrm{esc}\) (shaded) contribute to Jeans escape; the exponential dependence of the tail area on \(\lambda = v_\mathrm{esc}^2 / v_\mathrm{th}^2\) explains why escape rates vary by orders of magnitude across species and bodies. Course-original figure.

The exobase concept is crucial. Collisions below the exobase scramble velocities and prevent the high-velocity tail from accumulating, so escape effectively only happens at and above the exobase. The exobase altitude itself is set by where the mean free path equals the scale height, which depends on temperature, composition, and gravity. For Mars the modern exobase sits about \(200\ \mathrm{km}\) above the surface; for Earth it is around \(500\)–\(700\ \mathrm{km}\).

Finally, the temperature \(T_{\mathrm{exo}}\) in the formula is the exospheric temperature, which is set primarily by absorption of solar EUV radiation in the upper atmosphere. The exospheric temperature varies with solar activity and was almost certainly much higher in the early solar system, when the young Sun emitted \(10\)–\(100\) times more EUV than today. Hydrogen escape from early Mars would therefore have been much faster than the modern formula gives. An early hydrogen-rich greenhouse (see above) could have lost its \(\mathrm{H_2}\) on a timescale of only a few tens of Myr.

10.4.1. Atmospheric escape and the loss of Mars’ atmosphere

Because Jeans escape removes only light species, heavier Martian volatiles escape through non-thermal channels [Jakosky et al., 2018], which include photochemical escape (dissociative reactions producing fast neutrals), ion escape (acceleration by the solar wind), and sputtering (knockout by impacting ions).

Fig. 10.34 Oxygen escape rates from Mars (in particles per second) for the four MAVEN-resolved channels (dissociative recombination, pick-up ions, ion outflow, and sputtering) extrapolated from present-day measurements back to \(\sim 3.5\) Ga using estimates of the past solar EUV flux. All four channels were one to two orders of magnitude higher in the early Hesperian than today; the pick-up loss has dropped most steeply over time. From Jakosky et al. [2018]. The integrated total atmospheric loss over \(\sim 4\) Gyr (combining the oxygen channels shown here with hydrogen, carbon, and nitrogen loss inferred from other MAVEN datasets and isotopic constraints) is summarised in the body text below.

Fig. 10.35 shows the seasonal variation of the hydrogen corona that feeds the hydrogen escape.

Fig. 10.35 H corona column density at Mars as a function of solar longitude over a Mars year. Hydrogen escape varies by an order of magnitude over the seasonal cycle, peaking near perihelion when the lower atmosphere is warmer and water vapour rises to higher altitudes where it is photolysed. From Jakosky et al. [2018].

Extrapolating escape rates across solar EUV history indicates Mars lost \(\sim 0.5\) to \(1\) bar of \(\mathrm{CO_2}\) and \(\sim 23\) m of water equivalent over \(4\) Gyr [Jakosky et al., 2018] (Fig. 10.34). Carbon isotope ratios independently require an early atmospheric pressure below \(\sim 1\ \mathrm{bar}\) [Hu et al., 2015] (Fig. 10.36).

Fig. 10.36 Reconstructed history of Martian carbon evolution since \(3.8\) Ga (the conventional Late Heavy Bombardment epoch adopted as the starting point of the model) from Hu et al. [2015], using the modern atmospheric \(^{13}\mathrm{C}/^{12}\mathrm{C}\) ratio and known carbonate constraints as boundary conditions. (a) Atmospheric \(\delta^{13}\mathrm{C}\) evolution, with the present-day Curiosity-MSL measurement marked at right; (b) sputtering and photochemical escape rates (cumulative totals: \(232\) mbar lost via sputtering, \(8.2\) mbar via photochemistry); (c) carbonate formation rate for two precipitation environments (open-water systems in blue, shallow-subsurface aquifers in red), with associated total carbonate masses; (d) reconstructed equivalent atmospheric surface pressure of free carbon (atmosphere plus polar caps plus regolith) for two solution families with initial pressures \(0.32\)–\(0.50\) bar (blue) and \(0.25\)–\(0.29\) bar (red); solid and dashed curves are the two carbonate precipitation environments of panel (c). The solutions imply a Late Noachian / Early Hesperian atmospheric pressure that is below \(\sim 1\ \mathrm{bar}\) for most of the parameter space (carbonate-conservative scenarios give \(\lesssim 0.3\ \mathrm{bar}\)), with an absolute upper bound of \(\sim 1.8\ \mathrm{bar}\) requiring extensive subsurface carbonate sequestration (\(5\ \mathrm{wt\%}\) globally in the top 500 m). The picture is consistent with the MAVEN-based escape budget but explicitly invokes the heavy-isotope enrichment of carbon as an independent constraint.

Atmospheric loss is regulated by the Martian dynamo, the internal process generating a global magnetic field, and after this magnetic shield collapsed, direct solar wind interaction may have driven efficient ion escape.

10.4.2. Mars magnetism and the death of the dynamo

Although Mars lacks a global magnetic field today, its southern highlands retain intense crustal magnetic anomalies. These are remanent fields acquired below the Curie temperature in an ancient dynamo [Acuña et al., 1999]. The fields exceed \(\sim 1500\ \mathrm{nT}\) at \(\sim 100\ \mathrm{km}\) altitude (Fig. 10.37) (Fig. 10.38). That is an order of magnitude stronger than Earth’s crustal anomalies.

Fig. 10.37 Map of the radial component of the magnetic field measured by Mars Global Surveyor MAG/ER instrument during low-altitude aerobraking and science-phasing orbits (periapsis \(\sim 100\)–\(200\ \mathrm{km}\)). Strong remanent crustal magnetisation (red and blue patches) is concentrated in the Noachian-aged southern highlands; the younger northern lowlands and the Hellas and Argyre impact basins are essentially demagnetised. From Acuña et al. [1999]. Courtesy NASA Goddard Space Flight Center.

Fig. 10.38 Polar stereographic projection of the radial component \(B_r\) of the Martian crustal magnetic field measured during low-altitude MGS orbits (periapsis \(\sim 100\)–\(200\ \mathrm{km}\); left, colour-saturated at \(\pm 1500\) nT) and the corresponding topographic basemap (right, greyscale), showing concentric latitude rings at \(60^\circ\), \(70^\circ\), \(80^\circ\) and longitude meridians at \(0^\circ\), \(90^\circ\mathrm{W}\), \(180^\circ\), \(270^\circ\mathrm{W}\). Strong Noachian-age remanent magnetisation appears as concentrated red and blue patches confined to one azimuthal sector; the rest of the polar cap and the basin-reset terrains are essentially demagnetised. The lack of crustal magnetisation across Hellas, Argyre, and the Borealis lowlands implies that the dynamo had switched off before those basins formed and reset their thermal state. From Acuña et al. [1999]. Courtesy NASA Goddard Space Flight Center.

The Hellas, Argyre, and Isidis impact basins (\(4.0\) to \(4.1\ \mathrm{Ga}\)) are demagnetised relative to surrounding terrain. Impact heating above the magnetite Curie temperature (\(\sim 850\ \mathrm{K}\)) erased crustal magnetisation after the dynamo died. This originally dated dynamo shutdown to \(4.1\) to \(3.9\ \mathrm{Ga}\) [Acuña et al., 1999].

Collapse of the magnetic shield exposed the upper atmosphere to the solar wind. Ion escape may then have accelerated and stripped \(\mathrm{CO_2}\) and water. Mars is the textbook case of a world where the loss of internal magnetism was followed by the loss of habitability.

10.4.3. Mars exploration: a brief history

Six decades of Mars exploration have transitioned from initial reconnaissance to sustained surface science. The Mariner 4 flyby (1965) showed a cratered, Moon-like world; Mariner 9 (1971) and Viking then revealed the giant volcanoes, canyons, and outflow channels. Orbital mapping by Mars Global Surveyor produced global topography [Smith et al., 2001] and crustal magnetic maps [Acuña et al., 1999], while Mars Odyssey, Mars Express Bibring et al. [2006], and Mars Reconnaissance Orbiter mapped subsurface ice and mineralogy. In situ exploration from Pathfinder, Spirit, and Opportunity to Curiosity [Grotzinger et al., 2014] and Perseverance (Fig. 10.39) confirmed past habitable environments, complemented by geophysics from InSight and surface exploration by Tianwen-1.

Fig. 10.39 First colour view of Mars from NASA’s Perseverance rover, taken from one of its hazard-avoidance cameras shortly after landing in Jezero crater on 18 February 2021. The rover’s shadow and parts of its body are visible in the foreground; the rocky plain ahead is part of an ancient lake-delta system that filled Jezero crater about 3.6 Ga ago, close to the Noachian-Hesperian boundary. Perseverance is caching rock and regolith samples for return to Earth via the Mars Sample Return campaign. Credit: NASA/JPL-Caltech.

10.4.4. Mars Sample Return and the question of biosignatures

Mars Sample Return (MSR) is the joint NASA-ESA campaign to retrieve rock samples cached by Perseverance at Jezero; its architecture and schedule are being rebaselined after the 2024 cost review. Returning samples to Earth allows terrestrial laboratory instruments to analyze materials selected for high astrobiological potential. The primary scientific goal is to determine whether the samples contain definitive biosignatures from past or present Martian life (Lecture 14). Even a confident negative result would tightly constrain models of the origin of life.

Fig. 10.40 shows the campaign concept as a chain of handovers.

Fig. 10.40 Block diagram of the Mars Sample Return campaign concept. Perseverance collects and caches sample tubes at Jezero crater; a Sample Retrieval Lander delivers a Mars Ascent Vehicle, which launches the sample container into Mars orbit; an Earth Return Orbiter captures it and carries it to Earth for entry, landing, curation and laboratory analysis. The architecture and schedule are being rebaselined after the 2024 cost review, so the boxes show the concept, not a fixed design or dates. Course-original figure.

10.5. Part 3: Comparative payoff for terrestrial planet evolution

10.5.1. Mercury and Mars as opposite limiting cases

Mercury cooled rapidly close to the Sun, lost its volatiles and froze much of its core, yet keeps a thin liquid outer shell that sustains a weak dynamo. Mars cooled more slowly, sustaining an early dynamo and surface liquid water for \(\sim 700\) Myr before losing its dynamo and then its atmosphere.

Both bracket Earth and Venus on the scaling relations of Lecture 3 and Lecture 4:

• Cooling timescale scales as \(\tau \sim L^2/\kappa\) for diffusive heat loss with body size \(L\), so a factor of two smaller body cools four times faster.

• Atmospheric retention depends exponentially on the escape parameter \(\lambda \propto M / (T r_{\mathrm{exo}})\) from equation (10.4).

• Volatile inventory at formation depends on heliocentric distance across the ice line and volatile delivery from the outer disc (Lecture 2).

Mercury fails the first two scaling relations. Mars fails the second and third, as its mass cannot retain a thick atmosphere once its dynamo dies and ion escape takes over. Fig. 10.41 compares the interiors behind these scalings: Mercury’s oversized core against the small cores of Mars and the Moon.

Fig. 10.41 Cross-sections of the four terrestrial planets and Earth’s Moon, drawn to relative size. Crust (orange), silicate mantle (grey), and metallic core (red) are coloured uniformly across the bodies; Earth’s two-component core (solid inner / liquid outer) is shown explicitly. Mercury’s core occupies \(\sim 83\%\) of its radius and \(\sim 74\%\) of its mass, the largest core fraction of any terrestrial planet, while the Moon has only a small (\(\sim 330\ \mathrm{km}\) radius) partially molten core. Credit: NASA Solar System Exploration, public domain.

10.5.2. Size and distance set the trajectory

Size and distance from the central star primarily determine the long-term evolution of a rocky planet, and most properties, including interior structure, atmospheric composition, climate, and habitability, follow from these two parameters.

Size controls interior cooling rate, the dynamo heat budget, absolute radiogenic heating, and surface gravity (setting the escape parameter \(\lambda\)), whereas distance from the Sun controls equilibrium temperature, volatile delivery during accretion, stellar wind erosion, and early hot-phase dynamics.

This framework applies in Lecture 13 and Lecture 14 to exoplanets, where size and orbital distance are typically the only known parameters.

Fig. 10.42 places the inner solar system bodies in the plane of these two parameters.

Fig. 10.42 Schematic regime diagram of planet radius against heliocentric distance for Mercury, Venus, Earth, the Moon and Mars, plotted at their actual radii and orbital distances. The dashed line and the two shaded regions sketch qualitatively which bodies retain an atmosphere, and the arrow notes that dynamo lifetime also grows with size; neither is a calculated boundary. Larger bodies keep both for longer, smaller and hotter bodies lose both. Course-original figure.

10.5.3. The timing problem: dynamo lifetimes and habitability

The four rocky planets show distinct dynamo histories. Earth has an active dynamo sustained by compositional buoyancy, buoyancy released by inner-core crystallisation. Mercury has a weak dynamo sustained by partial core freezing and convection in a thin liquid shell. Mars had a dynamo for its first \(400\) to \(800\) Myr. It ceased between \(\sim 4.1\) Ga [Acuña et al., 1999] and \(\sim 3.7\) Ga: MAVEN found crustal fields as young as \(\sim 3.7\) Ga, which suggests a longer-lived or episodic dynamo [Mittelholz et al., 2020], and the demagnetised basins may reflect impact excavation or a reversing dynamo [Steele et al., 2024].

Venus lacks a detectable intrinsic field, and its dynamo history remains unknown (Lecture 9).

Dynamo longevity correlates with atmospheric retention and surface habitability. This correlation does not prove a causal link between dynamo longevity and habitability: MAVEN escape rates show that an unmagnetised Mars-sized planet loses its atmosphere on \(10^9\)-year timescales rather than through immediate collapse. However, a magnetic shield may suppress ion escape by up to an order of magnitude over Gyr timescales, but whether, and by how much, a magnetic field protects an atmosphere is debated.

Fig. 10.43 places the four dynamo histories on one time axis.

Fig. 10.43 Dynamo lifetimes of the rocky planets on one time axis. Earth’s dynamo is active and sustained by compositional buoyancy, Mercury’s weak dynamo by partial core freezing in a thin liquid shell (the onset of both is undated, hatched); Mars had a dynamo for its first 400 to 800 Myr, and crustal fields as young as about 3.7 Ga suggest a longer-lived or episodic dynamo; Venus has no detectable field and an unknown history. A magnetic shield may suppress ion escape by up to an order of magnitude over Gyr timescales (whether, and by how much, a field protects an atmosphere is debated), but an unmagnetised Mars-sized planet still loses its atmosphere on \(10^9\)-year timescales. Course-original figure.

10.5.4. What makes a rocky planet habitable?

Synthesising Lecture 9 and this lecture, a rocky planet requires four principal ingredients for long-term surface habitability:

1. Liquid water: maintaining surface water requires an adequate volatile inventory at formation, a suitable equilibrium temperature (or compensating greenhouse gases), and surface pressure high enough to prevent vacuum boiling.

2. Volatile recycling: active geology must exchange volatiles between the surface, atmosphere, and interior (such as via plate tectonics) so they are not permanently sequestered in a single reservoir.

3. Magnetic shielding: a global magnetic field mitigates stellar wind erosion; its quantitative role is debated, but the contrast between magnetised Earth and unmagnetised Mars is one of the strongest empirical cases that magnetism matters.

4. Climate stability: negative temperature feedbacks, notably the carbonate-silicate cycle (the Walker thermostat; [Walker et al., 1981]), regulate atmospheric \(\mathrm{CO_2}\) by accelerating silicate weathering at higher temperatures to cool the surface.

Earth satisfies all four ingredients, possessing global magnetic shielding (Fig. 10.44) alongside volatile recycling and climate stability feedbacks.

Fig. 10.44 Structure of Earth’s magnetosphere. The solar wind (orange arrows, arriving from the left) is deflected at the bow shock, and the shocked plasma flows around the planet through the magnetosheath. The magnetopause, where the solar-wind ram pressure balances the magnetic pressure of Earth’s field, stands at roughly \(10\,\Rearth\) on the dayside, while the nightside field is drawn out into the long magnetotail. This cavity shields the surface from most solar-wind particles and suppresses ion-pickup escape from the regions of closed field lines, in contrast to the open field lines at the poles that permit polar wind. Credit: ESA, CC BY-SA 3.0 IGO.

Venus and Mars each fail on at least two, and Mercury lacks volatiles and an atmosphere (Lecture 14).

10.5.5. Recent advances and upcoming missions

The premier upcoming milestone for comparative rocky-planet science is the arrival of the joint ESA/JAXA BepiColombo mission, scheduled for orbit insertion at Mercury in late 2026. Carrying the Mercury Planetary Orbiter and Mercury Magnetospheric Orbiter, the mission will map the planet’s offset magnetic field to test thin-shell dynamo models and measure forced librations to constrain the radius and state of the liquid core. Simultaneously, surface spectrometer mapping of volatile abundances, including potassium, sodium, and sulfur, will test giant-impact stripping against nebular condensation models, while radar and thermal instruments resolve the volatile inventory preserved in permanently shadowed polar craters.

10.6. Summary and takeaways

• Mercury and Mars are limiting cases for rocky-planet evolution. Mercury is too small, too close, and too volatile-poor. Mars is too small to retain its atmosphere once the dynamo died. Both bracket Earth and Venus on the parameters that matter most for long-term habitability: size, distance, dynamo longevity, atmospheric retention.

• Each of Mercury’s oddities points to a specific physical mechanism. The high uncompressed density requires non-standard formation, plausibly involving giant impacts. The persistent weak dynamo requires a thin convecting shell with thermal stratification. The polar ice survives because the obliquity is essentially zero. The lobate scarps and active faulting record ongoing global contraction.

• Mars preserves the geological record of an Earth-like planet that lost its habitability. The Noachian was wet enough to form valley networks, lakes, and clays; the Hesperian saw transitional, more acidic conditions and volcanic resurfacing; the Amazonian is cold and dry. The dynamo ceased around \(4.1\)–\(3.7\) Ga, and atmospheric loss to space accumulated to \(\sim 0.5\)–\(1\) bar of \(\mathrm{CO_2}\) and \(\sim 23\) m of water over geological time.

• The Jeans escape formula, equation (10.5), is selective. Light species escape; heavy species do not. Mars’ atmospheric loss is dominated by non-thermal (photochemical and ion-escape) processes, not by Jeans escape, except for hydrogen.

• Comparative planetology with the four rocky planets gives four independent natural experiments on the parameters governing planetary evolution, providing the baseline for evaluating rocky exoplanets in Lecture 13 and Lecture 14.

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