The influence of temperature-dependent thermal diffusivity on the conductive cooling rates of plutons and temperature-time paths in contact aureoles

Abstract

We explore the conductive cooling rates of plutons and temperature-time paths of their wall rocks using numerical methods that explicitly account for the temperature dependence of thermal diffusivity (α) and heat capacity (CP). We focus on α because it has the strongest influence on the temperature-dependence of thermal conductivity (k=ρ·CP·α) at high temperatures. Latent heats of crystallization are incorporated into the models as apparent CP's. Two sets of models are presented, one for a 50m thick basalt sill emplaced into rocks with diffusivity of the average crust, and one for a 5km wide and 2km thick granite pluton emplaced into dolostones. The sill's liquidus is 1230°C, the solidus 980°C, and the sill is emplaced into wall rocks that are at 150°C. The pluton's liquidus is 900°C, the solidus 680°C, and the pluton is emplaced into wall rocks with initial geothermal gradient of 30°C/km. The top of the pluton is at 3km depth. Incorporating appropriate α=f(T) into calculations can more than double the solidification times of intrusions in comparison with incorporating constant α of 1mm2·s−1 that is used in most petrologic heat transport models. The instantaneously emplaced basalt sill takes ~51a to completely solidify, whereas the granite pluton takes ~52ka to completely solidify. The solidification time is longer because of low thermal diffusivity of magma and because wall rocks become more insulating as temperature rises.In contact aureoles, maximum temperatures reached with α=f(T) are somewhat lower in comparison with α=1mm2·s−1; however, temperatures in inner aureoles stay elevated significantly longer with α=f(T), and consequently promote approach to mineralogical and textural equilibrium. The elevated temperature regime in inner aureoles enhances temperature gradients that may promote greater fluid fluxes if fluid pore pressures are controlled by temperatures. The results demonstrate the need to incorporate temperature-dependent transport properties of magmas and wall rocks into models of metamorphism and fluid flow in contact aureoles.