4.2. Thermal History of Mars
 We may apply our estimates of elastic lithosphere thickness Te to elucidate the thermal history of Mars. For each region or feature discussed above we convert Te to estimates of mean lithospheric thermal gradient and heat flux q. We then compare our results with those of previous workers and evaluate trends with respect to the age of each feature. A summary of our findings is given in Table 3.
Table 3. Summary of Thermal Gradient and Heat Flux Estimates
|Feature||Surface agea||Te, km||Thermal gradient, K/km||Heat flux, mW/m2||Lwin||l range for fit||Load densityb ρl, kg/m3||Bottom loading, f|
|Hellas south rime,h||H-N||<25||>9||>22||15||18–45||2900||0|
|Hellas south rime,i||H-N||60–200||3.5–11||13–30||15||18–45||2900||0.3–0.6|
|Hellas west rime,h||H-N||<15||>13||>32||15||18–45||2900||0|
|Terra Cimmeriae,h|| || || || || || || || |
|Arabia Terrae,h|| || || || || || || || |
 We convert Te to using the strength envelope formalism of McNutt . The heat flux q can then be estimated from , where k is the mean thermal conductivity, appropriately weighted for the proportion of crust (k = 2.5 W m−1 K−1) and mantle (k = 4.0 W m−1 K−1) in the lithosphere. The thermal gradient is estimated by determining the thickness Tm of an elastic-plastic plate with the same bending moment and curvature as the elastic plate of thickness Te [McNutt, 1984]. The mechanical lithosphere thickness, Tm, is always equal to or greater than Te, by an amount that increases with increasing plate curvature. The conversion to Tm requires assumptions regarding the strain rate, rock friction law, and ductile strength of the lithosphere. This conversion can be expressed in graphical form as a chart: given Te and plate curvature, Tm and can be read from the chart. We use charts of the type shown in Figures 5 and 6 of Solomon and Head . The low-pressure friction law of Byerlee  defines the brittle portion of the strength envelope; the ductile portion is given by flow laws for olivine [Goetze, 1978; Evans and Goetze, 1979] and diabase [Caristan, 1982], respectively. We assume strain rates between 10−19 and 10−16 s−1, corresponding to the accumulation of 1% strain in 3 billion and 3 million years, respectively. Crustal thickness is assumed to be 50 km (Table 1) [Zuber et al., 2000; Zuber, 2001]. For regions with Te comparable to this value, we calculate and q for both olivine and diabase flow laws. Plate curvature is calculated directly from the second derivative of modeled lithospheric deflections, for models with the bounding values of Te for each feature (Table 3, third column). We use the maximum curvature associated with a given feature [e.g., McNutt, 1984]. Solomon and Head  discussed the uncertainties involved in this procedure.
 Our results are shown in Figure 14. The five subdivisions of the vertical axes in Figure 14 indicate the approximate surface age of a load feature, as given in the second column of Table 3. The horizontal axes in Figure 14 give the thermal gradient (Figure 14a) and heat flux q (Figure 14b). A horizontal bar delimits the range of and q for each feature or region. Arrows at the end of a bar indicate the absence of an upper bound for the relevant parameter.
Figure 14. Lithospheric thermal gradient dT/dz (in K/km) and heat flux q (in mW/m2) versus surface age for several regions on Mars. Three of the age subdivisions correspond to the Noachian, Hesperian, and Amazonian epochs (in order of decreasing age); the remaining two are used to identify features that exhibit surface unit ages spanning two epochs (see also Table 3). Within a given age subdivision, vertical positions give an approximate indication of the relative surface ages of features, based on crater counts [e.g., Plescia and Saunders, 1979; Neukum and Hiller, 1981] and geologic mapping [e.g., Scott and Tanaka, 1986; Greeley and Guest, 1987], although the development of a given pair of features may have overlapped in time. (a) Lithospheric thermal gradients based on Te estimates in this paper. (b) Heat fluxes based on Te estimates in this paper.
Download figure to PowerPoint
 We may compare our estimates of lithospheric thermal gradient and heat flow with those of earlier workers. Solomon and Head  concluded that substantial variations in thermal gradient and heat flux were present during the Amazonian epoch, because of the large inferred differences in Te between Olympus Mons (and “Tharsis” in general) and the Tharsis Montes found by Comer et al. . Such variations are not consistent with the new Te estimates for features with Amazonian-aged surfaces given in Table 3. It is now clear that the low Te estimates for Tharsis Montes reported by Comer et al.  were the result of an incorrect interpretation of graben, now known to lie on the flanks of the edifices on the basis of MGS altimetry, as due to flexural stresses in the lithosphere. Instead, the extensional stress state required to form flank graben is likely caused by either edifice sliding or spreading [McGovern and Solomon, 1993] or intrusion and uplift [McGovern et al., 2001; Montési, 2001]. Estimates of Te from a purely flexural interpretation of Tharsis Montes flank graben will be biased to low values, such that the flexural wavelength is sufficiently low to predict a maximum extensional stress on the flank. Of the Te estimates given by Comer et al.  and used by Solomon and Head , MGS observations indicate that only those for Olympus Mons and the Isidis basin are likely to be valid. The former estimate was based on the absence of load-induced graben, while the latter estimate was based on the positions of the basin-encircling graben beyond the edge of the mascon load.
 There are further differences between our results and those of Solomon and Head  and other workers. Given a wide range of inferred values for heat flux and thermal gradient for features with Amazonian-aged surfaces, and moderate-to-low inferred values for pre-Amazonian structures (such as Alba Patera, the Elysium rise, and the Isidis basin), no clear temporal trend in these quantities was found by Comer et al. . In contrast, we find a general trend of decreasing values of and q with the surface age of a feature (Figure 14). The moderate flux inferred for the southern Hellas rim and the low heat flux inferred for Valles Marineris (Figure 14b), as well as for Isidis by Solomon and Head , nonetheless suggest significant spatial heterogeneity in thermal gradient and heat flow prior to the Amazonian.
 Our results may be compared and contrasted to those of other studies that have used MGS gravity and topography data. Our upper bounds on q at Valles Marineris are inconsistent with the lower bound of 20 mW/m2 reported by Anderson and Grimm . Poor resolution of older gravity and topography solutions and the use of a purely spatial-domain method for estimating Te by Anderson and Grimm  may account for the difference. In contrast, estimates of at Valles Marineris by Schultz and Lin , obtained from forward models of deformation due to normal faulting and small measured footwall uplifts, yield an upper bound of 10 K/km, broadly consistent with our results. Our estimates of at Olympus Mons and the Tharsis Montes are also generally lower than the 7–10 K/km range for central Tharsis found by Arkani-Hamed . The model gravity calculations of Arkani-Hamed  did not take into account finite-amplitude effects (see Appendix C); the dense buried loads at Tharsis volcanoes inferred by Arkani-Hamed  are likely artifacts of this choice. Such loads allow models with lower Te to fit the observed gravity, resulting in higher heat flux estimates. Several of our Te estimates for individual features in Tharsis, Valles Marineris, and Elysium differ significantly from estimates given by McKenzie et al.  for the regions enclosing them. This is likely because admittance signals from these features are diluted by averaging with signals from other features contained within the broad areas used by McKenzie et al. . In contrast, the relatively compact localization windows used in this study enable us to isolate the admittance signatures of individual features (volcanoes, chasm segments, etc.) from those of their surroundings, allowing us to gather both more refined and more numerous estimates of Te. Nonetheless, our results confirm earlier suggestions, based on admittance analysis of MGS gravity and topography data for limited numbers of regions [Zuber et al., 2000; McKenzie et al., 2002], that the lithosphere of Mars has thickened and the planet has cooled with time.
 Estimates of Te for the ancient southern uplands have further implications for the early (Noachian) thermal and magnetic history of Mars. The topography of the cratered uplands and the Hellas basin was Airy compensated, or nearly so, at the time of formation (Figures 11, 13). However, such topography will tend to decay with time due to ductile flow in the lower crust [e.g., Zuber et al., 2000; Nimmo and Stevenson, 2001], a process facilitated by high temperatures. The fact that this topography was preserved to the present implies that after the topography formed the lithosphere cooled sufficiently rapidly to arrest lower crustal flow (and remained cool thereafter). A relatively rapid decline in heat flow in the early history of Mars is consistent with predictions of thermal history models (with parameterized mantle convection) based on a decline in radiogenic heating with time [e.g., Stevenson et al., 1983; Schubert et al., 1992]. The mechanical lithosphere thickness Tm defines the depth to an isotherm in the lithosphere near 550–600°C, depending on strain rate [McNutt, 1984]. This isotherm is close to the Curie temperature for common magnetic minerals. It has been argued that magnetic anomalies observed in Terrae Cimmeria and Sirenum suggest a depth extent of magnetization of several tens of kilometers [Connerney et al, 1999; Nimmo, 2000], although this figure depends on the assumed value for specific magnetization. Such a depth extent significantly exceeds estimates for Te at Terrae Cimmeria and Sirenum at the time the present gravity/topography relationship was established. Either magnetization postdated that time by an amount sufficient for significant cooling and thickening of the lithosphere, or values of specific magnetization higher than typically assumed must be postulated.