Thermal evolution is at the origin of all dynamics inside a planet. In terms of approximations including parameterizing the stagnant-lid convection heat transfer in Mercury’s mantle and representing the temperature distribution in Mercury’s liquid core by an adiabat, a one-dimensional finite difference model with core-mantle coupling is established in this study to investigate Mercury’s thermal evolution since its core began to solidify. Based on observational data and previous research, this article focuses on analyzing the influence of the solidification mode of Mercury’s core and the radioactive heat generation in Mercury’s mantle on the internal temperature and heat flow evolution of Mercury, laying a foundation for studying the origin of Mercury’s magnetic field. The numerical modeling results indicate that the thermal evolution of outward solidification of Mercury’s core cannot explain the observed magnetic field of Mercury. Based on a previous estimate of the thickness of a stable conductive layer in the upper region of Mercury’s core, the thermal evolution model with inward core solidification predicts that the current solid outer core of Mercury has an age older than 2.8 Ga, while the heat flow through the current liquid inner core of Mercury is between 0.8 and 0.4 TW. The low intensity of the observed Mercury’s magnetic field is a combined result of the low heat flow through the liquid inner core and the magnetic shielding effect of the solid outer core.
[1] Turcotte D L, Schubert G. Geodynamics[M]. 3th ed. Cambridge: Cambridge University Press, 2014.
[2] Schubert G, Turcotte D L, Olson P. Mantle convection in the earth and planets[M]. Cambridge: Cambridge University Press, 2001.
[3] Driscoll P, Bercovici D. On the thermal and magnetic histories of earth and venus: influences of melting, radioactivity, and conductivity[J]. Physics of the Earth and Planetary Interiors, 2014, 236: 36-51. DOI: 10.1016/j.pepi.2014.08.004.
[4] Zhang N, Parmentier E M, Liang Y. A 3-D numerical study of the thermal evolution of the Moon after cumulate mantle overturn: the importance of rheology and core solidification[J]. Journal of Geophysical Research: Planets, 2013, 118(9): 1789-1804. DOI: 10.1002/jgre.20121.
[5] Grott M, Breuer D, Laneuville M. Thermo-chemical evolution and global contraction of mercury[J]. Earth and Planetary Science Letters, 2011, 307(1-2): 135-146. DOI: 10.1016/j.epsl.2011.04.040.
[6] Breuer D, Hauck S A, Buske M, et al. Interior evolution of mercury[J]. Space Science Reviews, 2007, 132(2): 229-260. DOI: 10.1007/s11214-007-9228-9.
[7] Christensen U R. A deep dynamo generating Mercury’s magnetic field[J]. Nature, 2006, 444(7122): 1056-1058. DOI: 10.1038/nature05342.
[8] Guervilly C. Fingering convection in the stably stratified layers of planetary cores[J]. Journal of Geophysical Research: Planets, 2022, 127(11): e2022JE007350. DOI: 10.1029/2022JE007350.
[9] Li Q, Sun T, Zhang Y G, et al. Atomic transport properties of liquid iron at conditions of planetary cores[J]. The Journal of Chemical Physics, 2021, 155(19): 194505. DOI: 10.1063/5.0062081.
[10] Edgington A L, Vočadlo L, Stixrude L, et al. The top-down crystallisation of Mercury’s core[J]. Earth and Planetary Science Letters, 2019, 528: 115838. DOI: 10.1016/j.epsl.2019.115838.
[11] Stanley S, Bloxham J, Hutchison W E, et al. Thin shell dynamo models consistent with Mercury’s weak observed magnetic field[J]. Earth and Planetary Science Letters, 2005, 234(1-2): 27-38. DOI: 10.1016/j.epsl.2005.02.040.
[12] Buffett B A, Huppert H E, Lister J R, et al. On the thermal evolution of the Earth’s core[J]. Journal of Geophysical Research: Solid Earth, 1996, 101(B4): 7989-8006. DOI: 10.1029/95JB03539.
[13] Williams Q. Bottom-up versus top-down solidification of the cores of small solar system bodies: constraints on paradoxical cores[J]. Earth and Planetary Science Letters, 2009, 284(3-4): 564-569. DOI: 10.1016/j.epsl.2009.05.019.
[14] Hauck S A II, Margot J L, Solomon S C, et al. The curious case of Mercury’s internal structure[J]. Journal of Geophysical Research: Planets, 2013, 118(6): 1204-1220. DOI: 10.1002/jgre.20091.
[15] Glassmeier K H, Auster H U, Motschmann U. A feedback dynamo generating Mercury’s magnetic field[J]. Geophysical Research Letters, 2007, 34(22): L22201. DOI: 10.1029/2007GL031662.
[16] Tian Z L, Zuber M T, Stanley S. Magnetic field modeling for Mercury using dynamo models with a stable layer and laterally variable heat flux[J]. Icarus, 2015, 260: 263-268. DOI: 10.1016/j.icarus.2015.07.019.
[17] Spohn T. Physics of terrestrial planets and moons: an introduction and overview[M]//Treatise on Geophysics (Second Edition). Amsterdam: Elsevier, 2015: 1-22. DOI: 10.1016/b978-0-444-53802-4.00165-2.
[18] Davaille A, Jaupart C. Transient high-Rayleigh-number thermal convection with large viscosity variations[J]. Journal of Fluid Mechanics, 1993, 253: 141-166. DOI: 10.1017/S0022112093001740.
[19] Ogawa M. Evolution of the interior of Mercury influenced by coupled magmatism‐mantle convection system and heat flux from the core[J]. Journal of Geophysical Research: Planets, 2016, 121(2): 118-136. DOI: 10.1002/2015JE004832.
[20] Moresi L N, Solomatov V S. Numerical investigation of 2D convection with extremely large viscosity variations[J]. Physics of Fluids, 1995, 7(9): 2154-2162. DOI: 10.1063/1.868465.
[21] Reese C, Solomatov V S, Baumgardner J R, et al. Stagnant lid convection in a spherical shell[J]. Physics of the Earth and Planetary Interiors, 1999, 116(1-4): 1-7. DOI: 10.1016/S0031-9201(99)00115-6.
[22] Date A W. Introduction to computational fluid dynamics[M]. New York: Cambridge University Press, 2005.
[23] Davis G B, Hill J M. A moving boundary problem for the sphere[J]. IMA Journal of Applied Mathematics, 1982, 29(1): 99-111. DOI: 10.1093/imamat/29.1.99.
[24] Hauck S A, Dombard A J, Phillips R J, et al. Internal and tectonic evolution of mercury[J]. Earth and Planetary Science Letters, 2004, 222(3-4): 713-728. DOI: 10.1016/j.epsl.2004.03.037.
[25] Roberts J H, Barnouin O S. The effect of the Caloris impact on the mantle dynamics and volcanism of Mercury[J]. Journal of Geophysical Research: Planets, 2012, 117(E2): E02007. DOI: 10.1029/2011JE003876.
[26] Michel N C, Hauck S A II, Solomon S C, et al. Thermal evolution of Mercury as constrained by MESSENGER observations[J]. Journal of Geophysical Research: Planets, 2013, 118(5): 1033-1044. DOI: 10.1002/jgre.20049.
[27] Knibbe J S, van Westrenen W. The thermal evolution of Mercury’s Fe-Si core[J]. Earth and Planetary Science Letters, 2018, 482: 147-159. DOI: 10.1016/j.epsl.2017. 11.006.
[28] McDonough W F, Yoshizaki T. Terrestrial planet compositions controlled by accretion disk magnetic field[J]. Progress in Earth and Planetary Science, 2021, 8(1): 1-12. DOI: 10.1186/s40645-021-00429-4.
[29] Peplowski P N, Evans L G, Hauck S A II, et al. Radioactive elements on Mercury’s surface from MESSENGER: implications for the planet’s formation and evolution[J]. Science, 2011, 333(6051): 1850-1852. DOI: 10.1126/science.1211576.
[30] Padovan S, Tosi N, Plesa A C, et al. Impact-induced changes in source depth and volume of magmatism on Mercury and their observational signatures[J]. Nature Communications, 2017, 8: 1945. DOI: 10.1038/s41467-017-01692-0.
[31] Stacey F D, Loper D E. The thermal boundary-layer interpretation of D″and its role as a plume source[J]. Physics of the Earth and Planetary Interiors, 1983, 33(1): 45-55. DOI: 10.1016/0031-9201(83)90006-7.
[32] Davies G F. Ocean bathymetry and mantle convection: 1. Large-scale flow and hotspots[J]. Journal of Geophysical Research: Solid Earth, 1988, 93(B9): 10467-10480. DOI: 10.1029/JB093iB09p10467.
[33] Sleep N H. Hotspots and mantle plumes: some phenomenology[J]. Journal of Geophysical Research, 1990, 95(B5): 6715-6736. DOI: 10.1029/JB095iB05p06715.
[34] Lay T, Hernlund J, Buffett B A. Core-mantle boundary heat flow[J]. Nature Geoscience, 2008, 1(1): 25-32. DOI: 10.1038/ngeo.2007.44.
