ory based on low polar temperatures) be- cause most of the crater floor would be in perpetual shadow. REFERENCESANDNOTES 1. For circularly polarized transmission, the polar- ized echo is the component returned in the circu- lar polarization orthogonal to the transmitted sense; the depolarized echo is the component returned in the same polarization sense. The polarized echo is normally dominated by quasi- specular reflection from large planar facets in the near-subradar region. The depolarized echo can be associated with diffuse reflection from wave- length-scale roughness elements, multiple scat- tering, or subsurface scattering in icy regoliths. 2. S. Zohar and R. M. Goldstein, Astron. J. 79, 85 (1 974) 3. P. E. Clark, M. A. Leake, R. F. Jurgens, in Mercury, F. Vilas, C. R. Chapman, M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1988), pp. 77- 100. 4. A radar target is said to be "overspread" when the product & of its rotational Doppler bandwidth B and delay depth T exceeds unity. Conventional delay-Doppler mapping uses a repetitive code with a cycle time greater than T. Because the sampling interval for the spectral (Doppler) anal- ysis is equal to the code cycle time, the echo from an overspread target will be aliased in Doppler. Mercury is overspread by up to 75% at S-band wavelengths and 270% at X-band wavelengths. 5. M. A. Slade, B. J. Butler, D. 0. Muhleman, Sci- ence 258, 635 (1 992). 6. J. K. Harmon, M. P. Sulzer, P. J. Perillat, J. F. Chandler, lcarus 95, 153 (1992). 7. The decoding for a given delay b ~ n is done by multiplication of the echo signal by an appropri- ately lagged replica of the transmitted code. The uncorrelated product of the cone and the echo from other delays constitutes a random "clutter" that adds to the total noise background. For more on this coding technique, see M. P. Sulzer [Radio Sci. 21 , 1033 (1 986)] 8. R. M. Goldstein, Science 168, 467 (1970). 9. G. H. Pettengill and T. W. Thompson, lcarus 8, 457 (1 968). 10. T. W. Thompson, Moon 10, 51 (1974). 11. D. 0. Muhleman, B. J. Butler, A. W. Grossman, M. A. Slade, Science 253, 1508 (1991). 12. S. H. Zisk, G. H. Pettengill, G. W. Catuna, Moon lo, 17 (1 974) 13. J. K. Harmon, D. B. Campbell, D. L. Bindschadler, J. W. Head, I. I. Shapiro, J. Geophys. Res. 91, 385 (1 986). 14. K. P. Klaasen, Icarus 28, 469 (1976). 15. M. E. Davies, S. E. Dwornik, D. E. Gault, R. G. Strom, Atlas of Mercury (National Aeronautics and Space Administration, Washington, DC, 1978). 16. R. M. Killen, A. E. Potter, T. H. Morgan, Icarus85, 145 (1 990) 17. B. Ha~ke, ibid. 88. 407 (1990). 18. A. L. road foot, Rev. ~ e o ~ h i s . Space Phys. 14, 625 (1 976) 19. D. A. Paige, S. E. Wood, A. R. Vasavada, Science 258, 643-(1992). 20. A. Crespo, R. Velez, J. Cruz, A. Vazquez, P. Perillat, M. Dryer, M. Sulzer, and J. Chandler provided support for the Arecibo obse~ations. We thank the authors of the companion papers (D. Paige, S. Wood, A. Vasavada, B. Butler, and D. Muhleman) for communicating some of their results to us before publication. Part of the re- search described above was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA) The National Astronomy and Ionosphere Center (Arecibo Observatory) is operated by Cornell Uni- versity under a cooperative agreement with the National Science Foundation and with support from NASA. 29 May 1992; accepted 20 July 1992 The Thermal Stability of Water Ice at the Poles of Mercury David A. Paige,* Stephen E. Wood, Ashwin R. Vasavada Recent radar observations of Mercury have revealed the presence of anomalous radar reflectivity and polarization features near its north and south poles. Thermal model cal- culations show that, despite Mercury's proximity to the sun, the temperatures of flat, low-reflectivity surfaces at Mercury's poles are not expected to exceed 167 kelvin. The locations of the anomalous polar radar features appear to be correlated with the locations of large, high-latitude impact craters. Maximum surface temperatures in the permanently shadowed regions of these craters are expected to be significantly colder, as low as 60 kelvin in the largest craters. These results are consistent with the presence of water ice, because at temperatures lower than 112 kelvin, water ice should be stable to evaporation over time scales of billions of years. O v e r the past three decades, a circumstan- tial case has developed for the possible stability of water ice deposits in high-lati- tude, permanently shadowed regions on the moon (1-3). but there is no definitive , ,. observational evidence for their existence. The possibility that water ice could be cold-trapped at the poles of Mercury has also been suggested (4). The new 3.5-cm (5) and 12.6-cm (6) radar observations of Mercury motivate detailed consideration of the thermal state of the vlanet's oolar re- gions as well as the long-term sources and sinks of water and other volatiles (7). Here we report the results of thermal model calculations that suggest that water ice could be stable to evaporation on Mercury in regions where anomalous radar reflectiv- ity and polarization features are observed. Using a thermal model, we have calcu- lated the temperatures of flat surfaces on Mercury as a function of latitude, longi- tude, and season. Because of Mercury's 312 resonant rotation rate and eccentric orbit, the distribution of incident solar radiation is a complicated function that repeats every 2 years (8). Because of the planet's proxim- ity to the sun, the finite angular size of the sun's disk (9) and solar limb darkening are taken into account when the sun's disk intersects the local horizon. Near Mercury's poles, the distribution of incident solar radiation is sensitive to the orientation of the planet's rotation axis relative to its orbital plane. Recent Arecibo radar obser- vations show that Mercury's obliquity is less than lo (6). Dynamical models predict that the most stable configuration of Mercury's spin axis corresponds to Cassini State 1, in which the spin axis is displaced slightly away from the orbit normal vector in a direction that is coplanar with the solar system normal vector and the orbit normal Department of Earth and Space Sciences, University of California, Los Angeles, Los Angeles, CA 90024. *To whom correspondence should be addressed. vector (10). The magnitude of this displace- ment is determined by the differences in the principal moments of inertia (10). Based on Mariner 10 gravity data (1 I), the present obliquity of Mercury is likely to be 10.05" (10). In our model, the' Cassini State 1 configuration is assumed; in it, northern spring equinox occurs at the ascending node of Mercury's orbit relative to the solar system plane (12). The present value of o, the angle between the ascending node and peri- helion, is approximately 29. lo (13). Because Mercury lacks an appreciable atmosohere. we determined the temoera- tures of flat surfaces using only the net effects of solar and infrared radiation and thermal conduction. Ground-based observations and Mariner 10 data have shown that the aver- age thermal and reflectance properties of the surface of Mercury are similar to those of the moon (14, 15). In our model, the solar reflectance of the surface was assumed to be 0.15 and the emissivity of the surface was assumed to be 0.90.. At each latitude and longitude, the model solves the one-dimen- sional heat diffusion equation using the bulk thermal properties of lunar soil, including the expected variation of thermal conductiv- ity and heat capacity with temperature (16). In accordance with the results of models for the thermal history of Mercury's interior, the present surface heat flow rate was assumed to be 0.020 W/m2 (17). The general results of the model calculations were consistent with those of earlier studies in that daytime sur- face temperatures were close to being in instantaneous radiative equilibrium and nighttime surface temperatures were deter- mined by the combined effects of thermal inertia and heat flow (8, 14). Maps of model-calculated, biannual maximum and average temperatures for flat surfaces in the north polar region of Mer- cury (Fig. 1, A and B) show strong longi- tudinal dependence. Because noon at peri- helion occurs alternately at longitudes of O" and 180°, polar isotherms tend to be elon- SCIENCE VOL. 258 23 OCTOBER 1992 643