Planetary heat flow measurements

Axel Hagermann

Abstract

The year 2005 marks the 35th anniversary of the Apollo 13 mission, probably the most successful failure in the history of manned spaceflight. Naturally, Apollo 13's scientific payload is far less known than the spectacular accident and subsequent rescue of its crew. Among other instruments, it carried the first instrument designed to measure the flux of heat on a planetary body other than Earth. The year 2005 also should have marked the launch of the Japanese LUNAR-A mission, and ESA's Rosetta mission is slowly approaching comet Churyumov-Gerasimenko. Both missions carry penetrators to study the heat flow from their target bodies. What is so interesting about planetary heat flow? What can we learn from it and how do we measure it?

Not only the Sun, but all planets in the Solar System are essentially heat engines. Various heat sources or heat reservoirs drive intrinsic and surface processes, causing ‘dead balls of rock, ice or gas’ to evolve dynamically over time, driving convection that powers tectonic processes and spawns magnetic fields. The heat flow constrains models of the thermal evolution of a planet and also its composition because it provides an upper limit for the bulk abundance of radioactive elements. On Earth, the global variation of heat flow also reflects the tectonic activity: heat flow increases towards the young ocean ridges, whereas it is rather low on the old continental shields.

It is not surprising that surface heat flow measurements, or even estimates, where performed, contributed greatly to our understanding of what happens inside the planets. In this article, I will review the results and the methods used in past heat flow measurements and speculate on the targets and design of future experiments.

Keywords:

1. What does planetary heat flow tell us?

All bodies in the Solar System exchange thermal energy with their environment by a variety of processes. They also produce and store energy internally. Therefore, an investigation of the surface energy balance shows us how planets generate, store and exchange heat.

(a) Why planetary heat flow?

In a simplistic world, all bodies in the Solar System receive energy from the Sun and re-emit it into space. However, planets are more than mere dead spheres whose effective surface energy balance is zero; if this were the case, our planetary system would be no more than a collection of inert spheres circling around the Sun, each at an equilibrium temperature that corresponds to its solar distance. The only bodies that may to a first approximation be classified as ‘dead’ are the asteroids.1 Planets (i.e. large bodies in hydrostatic equilibrium) and also comets can be thought of as heat engines because they convert one form of energy into another. Comets use solar energy to sublime gases and eject gas and dust. Thermal processes in planets are slightly more complicated. Internal heat can come from retained energy (the heat left over from accretion of the planet), potential energy (heat released during differentiation of the body), radioactive energy (heat released during radioactive decay), latent heat (mainly heat from crystallization), ohmic heat (released when electric currents flow) and dissipation (mainly of orbital and rotational energy). On the surface of the Earth, there are also complicated exchange processes among surface, vegetation and the atmosphere. Since any of these processes can contribute to a planet's surface heat flow, measurements suffer from an inherent ambiguity. The reason why comets are mentioned and asteroids explicitly excluded from the previous discussion is that a cometary experiment will be included in this presentation of ‘planetary’ heat flow measurements, since the MUPUS experiment presents the state-of-the-art in the field in terms of technology and scientific purpose.

(b) Lessons learned from surface heat flow measurements

Before looking at the techniques used in heat flow measurement in the next section, the lessons learned so far from measurements (or estimates) of planetary surface heat flow are outlined by giving a number of examples.

(i) Earth

Earth is certainly the planet best known and most thoroughly investigated. The global mean of terrestrial heat flow is 87 mW m−2, with a mean of 65 mW m−2 flowing through the continents and a mean of 101 mW m−2 through the oceans (Pollack et al. 1993). In 1954, Bullard noted that the heat flow through the floor of the Atlantic was higher than expected and came to the conclusion that ‘either the rocks in the first 100 km beneath the oceans are much more radioactive than has been assumed, or heat is transported from deep in the mantle by convection.’

It needs to be said that oceanic values may often be biased because of hydrothermal circulation within the crust (e.g. Lister 1972), but in the following decades, measurements in the seafloor showed an increase in heat flow towards ocean ridges, an important piece of evidence for seafloor spreading and thereby plate tectonics (Sclater et al. 1981).

On the continents, the heat flow is not uniformly high. It is fairly uniform in old crustal regions, where it reflects the radiogenic heat produced in those rocks, mainly K, Th and U. In young crustal regions, heat flow is associated with volcanic or plutonic processes; it can vary by more than an order of magnitude over short distances in young crustal regions (Sclater et al. 1980).

(ii) Moon

Interpretation of surface heat flow is considerably less ambiguous on the Moon because of its lack of atmospheric and tectonic processes. The heat flow from the surface is thought to be directly related to the abundance of radiogenic elements, and thereby directly constrains models of its origin and evolution. Jaeger (1959) derived the lunar heat flow to be approximately 9.6 mW m−2, assuming radiogenic heat production at a chondritic rate. A few years later, Krotikov & Troitskiı̆ (1964) estimated 54.4 mW m−2 from Earth-based radio observations, thereby challenging the assumption of a chondritic composition of the Moon. After the first measurement in situ, Langseth et al. (1972) gave 33 mW m−2. Keihm & Langseth (1975) estimated a global heat flow of 30 mW m−2. They later revised the measurements at the Apollo 15 and 17 sites to yield 21 and 16 mW m−2, respectively. Langseth et al. (1976) assumed these two sites to be representative and derived a mean value of 18 mW m−2. Rasmussen and Warren (1985) and Warren and Rasmussen (1987) finally adjusted the Apollo 17 measurement for the effect caused by the measurement site being located near the highlands/mare boundary, resulting in a focusing of the heat flux, and a corrected value of 12 mW m−2, so the U content was less than half of what Langseth et al. (1976) had estimated. Two things can be learned from the history of lunar heat flow measurements. First, to be meaningful, heat flow measurements need to be carried out not in one, but in several, well-chosen locations. And second, we should never underestimate the wisdom of our elders—after all, Jaeger's estimate from 1959 had been surprisingly accurate.

(iii) Jupiter, Saturn and Io

Three bodies in the outer Solar System show how even crude estimates of surface heat flow can revolutionize models of planetary origin, evolution and state. Infrared observations by Aumann et al. (1969) implied that Jupiter emits 2.7 times more energy than it receives from the Sun. Graboske et al. (1975) and Hubbard (1977) managed to explain this excess flux as a release of Jupiter's heat of formation. Pollack et al. (1977) tried to explain Saturn's thermal emission in the same way, but their model fell short of the observed heat flux from Saturn. The difference was explained by helium differentiation, a process occasionally depicted as ‘Helium rain’ (Salpeter 1973; Stevenson & Salpeter 1977). Jupiter is not the only body of the Jovian system whose heat flow is unusual. The surface heat flow of its tiny moon Io is orders of magnitude higher than that of any other solid planetary body in the Solar System; its surface is shaped by infernal volcanic activity. Peale et al. (1979) showed how Io, locked in its slightly eccentric orbit by Laplace resonance, is kneaded in Jupiter's gravitational field and correctly predicted volcanism on Io. Morrison & Telesco (1980), Matson et al. (1981), Johnson et al. (1984), Veeder et al. (1994), Spencer et al. (2000) all estimate a minimal heat flow of around 2 W m−2, and Matson et al. (2001) give an upper bound of 13.5 W m−2, more than two orders of magnitude our terrestrial heat flux. With tidal dissipation as a primary heat source, Segatz et al. (1988) were able to develop models of Io's interior that could explain the observed heat flow values (figure 1).

Figure 1

Penetration of a periodic temperature variation into a half-space with thermal diffusivity κ=10−6 m2 s−1, the same order of magnitude as terrestrial rocks. The depth scale on the left ordinate corresponds to a period of 24 h, the scale on the right corresponds to a period of 365 days. Line numberings refer to temperatures every 4 h or every two months, respectively.

2. Methods, missions and measurements

In a homogeneous and isotropic medium of thermal conductivity λ, heat flows in the direction of decreasing temperature −∇T. The vectorEmbedded Image(2.1)is the heat flux density vector.2 If we approximate the surface of a terrestrial planet as a homogeneous and isotropic half-space, the heat flux density vector is perpendicular to the surface. As pointed out in §1, the Sun contributes to a planet's surface energy balance. This contribution is periodic because of the planets' rotation and revolution around the Sun. If the surface temperature of a body is subject to a sinoidal temperature variation of amplitude T0 and period Π, the temperature as a function of time t and depth z takes the formEmbedded Image(2.2)where κ is the thermal diffusivity, i.e. the quotient of λ and heat capacity ρc. This means that the thermal influence of insolation is attenuated with depth and also experiences a time lag, resulting in a heat wave penetrating into the ground. The longer the period of the surface temperature variation, the deeper the surface heat wave will penetrate. The penetration depthEmbedded Image(2.3)is the depth at which the temperature variation has been damped to 1/e of the surface amplitude. On Earth, zp is usually of the order of several centimetres for the diurnal heat wave and a few metres for the annual heat wave. Equation (2.1) shows that two parameters need to be measured in order to obtain the heat flow: thermal conductivity λ and temperature gradient ∂T/∂z. Equation (2.3) shows that at shallow depths, usually of the order of zp, measurements are likely to reflect external contributions to the surface heat flow, whereas measurements far below the penetration depth zp usually represent internal contributions.

(a) The first planetary heat flow measurements

Quite naturally, Earth had to be the first planet whose heat flow was investigated and, to a certain extent, most methods used to determine planetary heat flow have been applied on Earth. The late Edward Bullard pioneered, and for many decades dominated this field, be it on the seafloor or on the continents. His 1954 paper on the flux of heat through the floor of the Atlantic Ocean is well known and it gives a fascinating overview of experimental and theoretical methods used for penetrator heat flow measurements. Bullard published results of heat flow measurements as early as 1939, using boreholes in South Africa (Bullard 1939). Here, the temperature was measured to a depth of more than 3000 m. Thermal conductivity was recovered very precisely from drill cores. Boreholes enable us to carry out temperature measurements at great depth, thereby escaping the influence of diurnal, annual and even secular variations in the Earth's surface temperature. The possibility of precisely determining thermal conductivity from core samples eliminates the need for high-precision thermal property measurements in situ.

As illustrated in equation (2.2), measurements at shallow depth are usually dominated by a heat wave of some period. This means that borehole measurements can be used to recover the long-term history of the Earth's surface temperature; one can reconstruct the surface temperature history from the temperatures measured in the borehole, which are essentially only a damped and lagged representation of the surface temperature signal (Shen & Beck 1991; Wang 1992). In the darkness of the bottom of the oceans, diurnal or annual temperature variations do not exist. Therefore, it is not necessary to drill deeply in order to escape periodic temperature waves. As operations at large depths need to be automated, seafloor measurements usually involve simple yet very effective techniques to measure both thermal gradient and thermal conductivity. The constraints of simplicity and effectiveness are exactly the same as in space sciences, which might explain why Bullard's 1954 paper is probably the most influential in terms of planetary heat flow measurements. His penetrator was approximately 5 m long and 2.7 cm in diameter, with one temperature sensor at the front-end, one at the rear-end and a recording unit at the very top. Revelle & Maxwell (1952) had already used Bullard's penetrator in the Pacific before, but Bullard was the one to give a detailed description of his design, including the mathematical methods to analyse the data. He not only measured thermal conductivity of sediment samples in the laboratory, but also inferred the thermal properties of the sediment from the cooling curve of the penetrator. Later, Christoffel & Calhaem (1969) and Lister (1970) introduced a heated penetrator probe to measure sediment conductivity in situ together with the thermal gradient. Previously, accurate measurements of sediment thermal properties had been obtained from sediment cores, e.g. by von Herzen & Maxwell's (1959) needle probe method (figure 2).

Figure 2

Bullard's penetrator. The eye used for extracting the probe is visible on top of the cylinder housing the temperature recording equipment. Bullard (1954).

Penetrators require the ocean floor to be covered with soft sediments. An alternative applicable on impenetrably hard surfaces is the pillow or blanket method as described by Johnson & Hutnak (1996) or Kinoshita (1996). Here, the ground is covered with a thick blanket and the thermal gradient is measured within the blanket whose thermal properties are known.

Experimental methods similar to those presented above have been used in another context, namely in the investigation of meteorological processes, where the diurnal heat wave is not an unwanted distortion but the focus of scientific interest (e.g. Staley & Gerhardt 1957). A small and very simple penetrator-like device was also used by Lehmann (1952) for investigating the heat exchange between soil and atmosphere, and a method similar to the blanket set-up is the plate method described by Dunkle (1940). In contrast to the blanket, however, this method requires a plate to be inserted horizontally into the soil.

After the failure of Apollo 13, the first successful measurement of lunar heat flow was carried out during the Apollo 15 mission. Two further experiments were launched on Apollo 16 and 17, with a technical failure ending the former and only the latter delivering scientific data. The two heat flow sites of Apollo 15 and 17 were Hadley Rille and Taurus Littrow, respectively. The Apollo experiment was a mixture of a penetrator and a borehole experiment: the astronauts first drilled a hole and then emplaced a long rod into the hole cased by the fibreglass borestem. The rod consisted of two identical sections, each 50 cm long, each with two differential thermometers, with further thermocouples on the cable connecting the probe to the electronics unit. Conductivity measurements were made using heaters that surrounded the outer gradient bridge sensors. Each experiment consisted of two probes placed a few metres apart. Originally, Langseth's et al. (1970) intention was to place the probes at the bottom of 3 m deep boreholes, but this depth could not be reached for technical reasons (e.g. Langseth et al. 1972). Because of the long time-scales of the experiment, the influence of short-term temperature variations at the surface could be reduced drastically by Fourier filtering (Langseth et al. 1976; figure 3).

Figure 3

Schematic of the lunar heat flow probe (after Langseth et al. 1972).

For the decades to come, there were no other planetary missions that measured heat flow in situ. The ambiguity in the Apollo data reported by Warren & Rasmussen (1987) highlights that the results of lunar measurements are highly location dependent. Without further heat flow measurements at other locations on the Moon we will not be able to constrain its total heat flux reliably, a caveat already pointed out by Langseth et al. (1976). Yoshida et al. (2001) show how heat flow measurements at further locations, together with surface thorium abundances derived from gamma-ray spectrometer data (Lawrence et al. 2000), can help to constrain the total abundance of radioactive elements in the Moon. The Japanese mission LUNAR-A was designed with the open questions about the Moon in mind (Mizutani 1995).

3. Latest planetary heat flow measurements

The LUNAR-A mission consists of two penetrators and an orbiter and is scheduled to arrive at the Moon within the next few years. Just like in ocean floor measurements, the term penetrators is used for penetrating probes. Penetrators in space missions, however, are quite different in design. Usually, planetary penetrators are autonomous spacecraft and are by no means as long and slender as the Bullard-type probe (Surkov et al. 2001). The LUNAR-A penetrators (figure 4) will be about 80 cm long and 15 cm in diameter and will be emplaced into the lunar regolith directly from orbit. After release from the orbiter, a rocket motor will cancel the orbital velocity. Then the attitude will be changed so that the penetrator impacts the lunar surface nose first at a velocity of about 300 m s−1. Each penetrator is an autonomous system with an antenna, batteries, a seismometer and a heat flow experiment. The heat flow experiment consists of five absolute and eleven relative temperature sensors. Five of the temperature sensors can also serve as thermal conductivity sensors because they are located under a small copper disk whose response to a finite heating pulse of known power and length is measured. Because of their high impact velocity, the penetrators will penetrate to a depth of more than 1 m, thereby escaping the influence of the diurnal temperature fluctuations near the surface (Mizutani et al. 2003).

Figure 4

Schematic of the LUNAR-A penetrator, essentially an autonomous spacecraft in its own right (after Mizutani et al. 2000).

Another heat flow experiment currently on course to its target body is MUPUS (Spohn et al. 1995). MUPUS is an experiment package proposed by MUPUS for the lander of ESA's Rosetta mission towards comet Churyumov-Gerasimenko. It comprises a penetrator with a heat flow probe approximately 40 cm long and 1 cm in diameter. The MUPUS penetrator consists of a slender probe made of carbon fibre-reinforced plastic with a bulky head (figure 5). Thermal sensors cover the full length of the probe, and the size of the sensors increases towards the tip. In passive mode, these sensors can be used as thermometers. In active mode they are heated while temperature is recorded, and the temperature response to heating can be used to infer the thermal properties of the surrounding material. If all sensors are heated simultaneously, the measurement of thermal conductivity resembles the transient hot wire method as described by, for example, van der Held & van Drunen (1949), and the thermal conductivity can be extracted very precisely from the heating curve (Banaszkiewicz et al. 1997). The bulky head of the MUPUS penetrator houses the instrument electronics and a hammering device that will emplace the penetrator in the cometary nucleus. Heat flow measurements on comets have a different motivation than those on other bodies in the Solar System. Heat flow from the interior of a cometary nucleus is almost certainly negligible, but the interaction between the Sun and the surface and near subsurface layers leads to the release of gas and dust that form the coma and tail. Therefore, the short-term evolution of the near-surface energy balance has to be studied and the method is more closely related to Lehmann's meteorological experiments at shallow depth than to the Bullard-type measurements. As the main focus of interest in cometary measurements is the near-surface processes, the penetrator can be short, but needs a high depth resolution near the surface (Seiferlin et al. 2001a).

Figure 5

The MUPUS penetrator. The sensors (cutaway) can be operated in either passive mode for temperature or active mode for thermal property measurements (after Seiferlin et al. 2001a).

The usage of the MUPUS penetrator is by no means limited to comets; it has also been tested in the field by Marczewski et al. (2004).

Because of the stringent requirements in terms of mass, volume and mechanical complexity, the design of planetary penetrators is often sub-optimal for heat flow measurements. The Bullard probe was a simple rod with a length/diameter ratio of almost 200. One problem that can be encountered in planetary heat flow measurements is the shunting of the thermal gradient by the short, fat, well-conducting penetrator in a medium of poor thermal conductivity. A precise thermal model is vital for an accurate measurement of the temperature gradient (Tanaka et al. 2000). The undisturbed temperature gradient can be recovered from the temperatures measured by mathematical means (Hagermann & Spohn 1999).

4. The future of planetary heat flow measurements

Of course, LUNAR-A and MUPUS are by no means the end in the development of heat flow probes for planetary missions. Spohn et al. (2001) have suggested a heat flow probe for the surface element of the ESA's BepiColombo mission. A small, self-propelled penetrator termed ‘mole’ would dig into Mercury's regolith to a depth of several metres and carry out a heat flow measurement. Currently, a landing on Mercury within the framework of BepiColombo seems improbable, but the ongoing development of the concept illustrates that the importance of planetary heat flow measurements in situ has been recognized. Studies have also been made to use a planetary lander as an analogue of a thermal blanket on Mars to investigate the interaction among solar irradiation, atmosphere and Martian soil (Seiferlin et al. 2001b).

If one takes a look at the future of planetary exploration, deep borehole measurements on other planets can probably be ruled out for quite a while, leaving a near-surface experiment, usually a penetrator of some sort. The blanket method seems indeed intriguing as it requires no mechanical insertion. The problem of the solar irradiation pumping energy into the blanket from above could be overcome by landing in permanently shaded regions like craters near the planetary poles, creating a stable environment similar to that on the seabed.

So far, all experiments mentioned require an apparatus of some sort to be brought down onto the surface of a planet, usually a task both costly and risky. Of course, the remote determination of planetary heat flow has also been attempted. Lunar heat flow estimates derived from ground-based radio observations were given by, for example, Baldwin (1961) and Krotikov & Troitskiı̆ (1964). Microwave measurements from planetary orbiters would eliminate the cost and risk of measurements in situ and provide global coverage. The physical concept behind this method is closely related to the skin effect: the longer the wavelength of an electromagnetic wave, the further it can penetrate the planetary regolith. If one increases the wavelength at which the microwave emission of a planetary surface is observed, deeper layers contribute larger fractions to the total emission. Therefore, the subsurface temperature gradient can be inferred from the variation of brightness temperature with wavelength. Keihm (1984) has assessed this method with lunar heat flow mapping in mind, but the method would be applicable to most bodies without dense atmospheres. Keihm also noted that knowledge of the regolith thermal properties is not sufficient for remote microwave measurements, but information on electrical and scattering properties is equally important. It is probably difficult to determine the subsurface scattering properties of planetary regolith without in situ measurements, but electric properties of planetary surfaces can be determined from orbit, e.g. using bistatic radar experiments (Nozette et al. 1996), so clearly further investigations are needed. Other proposals have been made to make heat flow measurements in the infrared range. Watson (1967) suggested that infrared measurements in permanently shadowed craters could be used to infer planetary heat flow, but Lachenbruch (1968) pointed out the obstacles to this idea.

What are the potential targets for future heat flow measurements? Clearly, the terrestrial planets Mercury, Mars and Venus spring to mind. Their surface heat flow is an important constraint on thermal evolution models (Spohn 1991).

Mars looks like a promising candidate for the next heat flow measurement in situ, with a ‘mole’ type penetrator experiment proposed within ESA's framework of Mars exploration. This investigation seems particularly valuable since the surface heat flow on Mars influences the presence of near-surface water ice deposits. Currently, two missions to Mercury are developed which focus entirely on remote sensing. We can deduce the abundance of radioactive elements on Mercury's surface from orbit, but what about the crust? The depth-dependent abundance of radioactive elements cannot be determined without a heat flow measurement. Would the impact of an in situ heat flow measurement be comparable to the early years of the Apollo era, when years of speculation on origin and evolution of the Moon were brought to an end? Unless we go there, we will never find out.

Our nearest neighbour, the Moon, certainly requires further attention. Will we, at some point, be able to drill deep into the crust and measure the temperature gradient in the boreholes like Bullard used to in 1939? Will we be able to drop dozens of penetrators to get global coverage of in situ heat flow data? We still need further heat flow data to identify the correlation between heat flow and abundance of radioactive elements. LUNAR-A will hopefully address part of this question. The processes leading to cometary coma formation can hopefully better be understood after the MUPUS measurements on comet Churyumov-Gerasimenko in 2014. And considering the long, but sparse history of planetary heat flow measurements, this should be worth the wait.

Acknowledgments

The author would like to express his gratitude to Hitoshi Mizutani for his ongoing support, encouragement and infectious enthusiasm, and also to John Zarnecki and Tilman Spohn for their support and critical reading of this manuscript. Over the years, various parts of the author's heat flow-related activities have been funded by the Alexander von Humboldt Foundation, JSPS, Monbusho, PPARC, DFG and DLR.

Footnotes

  • One contribution of 17 to a Triennial Issue ‘Astronomy and earth science’.

  • To be precise, asteroids are neither spherical nor are they strictly ‘dead’ in a thermal sense. Radioactive decay leads to endogenic heat production and asteroids can occasionally be rather active in terms of gas emission (Luu & Jewitt 1990).

  • The more common term heat flow is used as a synonym of ‘heat flux density’ in this article.

References

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