We model the ascent and eruption of lunar mare basalt magmas with new data on crustal

48 We model the ascent and eruption of lunar mare basalt magmas with new data on crustal 49 thickness and density (GRAIL), magma properties, and surface topography, morphology and 50 structure (Lunar Reconnaissance Orbiter). GRAIL recently measured the broad spatial variation 51 of the bulk density structure of the crust of the Moon. Comparing this with the densities of lunar 52 basaltic and picritic magmas shows that essentially all lunar magmas were negatively buoyant 53 everywhere within the lunar crust. Thus positive excess pressures must have been present in 54 melts at or below the crust-mantle interface to enable them to erupt. The source of such excess 55 pressures is clear: melt in any region experiencing partial melting or containing accumulated 56 melt, behaves as though an excess pressure is present at the top of the melt column if the melt is 57 positively buoyant relative to the host rocks and forms a continuously interconnected network. 58 The latter means that, in partial melt regions, probably at least a few percent melting must have 59 taken place. Petrologic evidence suggests that both mare basalts and picritic glasses may have 60 been derived from polybaric melting of source rocks in regions extending vertically for at least a 61 few tens of km. This is not surprising: the vertical extent of a region containing inter-connected 62 partial melt produced by pressure-release melting is approximately inversely proportional to the 63 acceleration due to gravity. Translating the ~25 km vertical extent of melting in a rising mantle 64 diapir on Earth to the Moon then implies that melting could have taken place over a vertical 65 extent of up to 150 km. If convection were absent, melting could have occurred throughout any 66 region in which heat from radioisotope decay was accumulating; in the extreme this could have 67 been most of the mantle. 68 The maximum excess pressure that can be reached in a magma body depends on its 69 environment. If melt percolates upward from a partial melt zone and accumulates as a magma 70 reservoir, either at the density trap at the base of the crust or at the rheological trap at the base of 71 the elastic lithosphere, the excess pressure at the top of the magma body will exert an elastic 72 stress on the overlying rocks. This will eventually cause them to fail in tension when the excess 73 pressure has risen to close to twice the tensile strength of the host rocks, perhaps up to ~10 MPa, 74 allowing a dike to propagate upward from this point. If partial melting occurs in a large region 75 deep in the mantle, however, connections between melt pockets and veins may not occur until a 76 finite amount, probably a few percent, of melting has occurred. When interconnection does 77 occur, the excess pressure at the top of the partial melt zone will rise abruptly to a high value, 78 again initiating a brittle fracture, i.e. a dike. That sudden excess pressure is proportional to the 79 vertical extent of the melt zone, the difference in density between the host rocks and the melt, 80 and the acceleration due to gravity, and could readily be ~100 MPa, vastly greater than the value 81 needed to initiate a dike. We therefore explored excess pressures in the range ~10 to ~100 MPa. 82 If eruptions take place through dikes extending upward from the base of the crust, the mantle 83 magma pressure at the point where the dike is initiated must exceed the pressure due to the 84 weight of the magmatic liquid column. This means that on the nearside the excess pressure must 85 be at least ~19  9 MPa and on the farside must be ~29  15 MPa. If the top of the magma body 86 feeding an erupting dike is a little way below the base of the crust, slightly smaller excess 87 pressures are needed because the magma is positively buoyant in the part of the dike within the 88 upper mantle. Even the smallest of these excess pressures is greater than the ~10 MPa likely 89 maximum value in a magma reservoir at the base of the crust or elastic lithosphere, but the 90 values are easily met by the excess pressures in extensive partial melt zones deeper within the 91 mantle. Thus magma accumulations at the base of the crust would have been able to intrude 92 dikes part-way through the crust, but not able to feed eruptions to the surface; in order to be 93