Thermodynamic properties of $\mathrm{MgSiO}{}_3$ at super-Earth mantle conditions

Recent discoveries of terrestrial exoplanets distant from our solar system motivate laboratory experiments that provide insight into their formation and thermal evolution. Using laser-driven shock wave experiments, we constrain high-temperature and high-pressure adiabats and the equation of state of ${\mathrm{MgSiO}}_3$, a dominant mantle constituent of terrestrial exoplanets. Critical to the development of a habitable exoplanet is the early thermal history, specifically the formation and freezing of the magma ocean and its role in enabling convection in the mantle and core. We measure the adiabatic sound speed and constrain the melt transition along the Hugoniot and find that the adiabats and melt boundary of silicate magmas are shallower than predicted. This suggests that small changes in the temperature of a super-Earth mantle would result in rapid melting and solidification of nearly the entire mantle.

Figure 1

Experimental target design. (a) Target design used for sound speed measurements. (b) Target design used in the decaying shock wave experiments. Layers are not drawn to scale.

Figure 2

Typical VISAR data obtained in order to determine the ${\mathrm{MgSiO}}_3$ sound speed is shown. (a) The raw VISAR data illustrating a two-section target where the shock velocity in a quartz witness and ${\mathrm{MgSiO}}_3$ sample are measured simultaneously. (b) The shock-front velocity determined from (a). (c) By mapping the fluctuations from the ${\mathrm{MgSiO}}_3$ sample onto the quartz witness, we determine out perturbations within the witness are Doppler shifted in the sample, enabling extraction of the sample sound speed. The relative difference in the Doppler shift ($\frac{\mathrm{\Delta }{t}_S}{\mathrm{\Delta }{t}_R}$) determines the ${\mathrm{MgSiO}}_3$ Eulerian sound speed.

Figure 3

Eulerian sound speed measurements (red points) along the ${\mathrm{MgSiO}}_3$ principal Hugoniot are compared with DFT principal Hugoniot calculations [15] (black dashed line), gas-gun Hugoniot sound speed measurements [13] (blue circles), DAC measurements [14], and theoretical isentropic bulk velocities and isentropic shear velocities [16]. The reduction in sound speed of these measurements, when compared to the DAC data [13] are indicative of a loss in shear strength due to melt.

Figure 4

Experimentally determined enstatite principal Hugoniot data are shown. The experimental measurements from this work are shown as red circles, Luo et al. [11] as black circles, Akins et al. [12] as green circles, and a reanalysis of the Spaulding et al. [7] as the blue circles. We find that a linear fit represents these data and the linear $U_s\text{−}{U}_p$ fit is shown as the black dashed line.

Figure 5

The experimental VISAR and SOP data from a single experiment (s77778). (a) The experimental raw (top) and analyzed (bottom) spatially resolved shock-velocity data. The VISAR diagnostic produces a sinusoidal spatial modulation on the image where Doppler shifts in a probe laser reflected off of the shock front appear as displacement of the fringes record in the streak record. The displacement of these fringes is directly related to the shock velocity. (b) The experimental raw (top) and analyzed (bottom) spatially resolved thermal emission from the shock front. A change in the thermal-emission decay slope of the enstatite sample is observed at $\sim 9.3$ ns and is not observed in the quartz witness.

Figure 6

The observed thermal temperature as a function of pressure for four experiments is shown as the green, red, purple, and blue lines. The two-segment fit is shown as the black line and the extrapolation of each segment is shown as the black dashed line.

Figure 7

Radiation hydrocode decaying shock-wave simulations were performed to examine the observed “kink” in thermal emission. (a) The pressure and temperature of the shock front (blue) and last fluid element to remain in the liquid phase (red) are plotted versus time. Three times ($T_1$, $T_2$, and $T_3$) are examined. (b) The shock front (blue), last fluid element (red), and the melt line (black dashed) are shown. The times from (a) illustrates how the shock-front pressure and fluid temperature can be convolved to produce a kink in the thermal emission (cyan line) that occurs at the onset of melt.

Figure 8

The continuous measure of the enstatite principal Hugoniot temperature versus pressure is shown as the red shaded region and the onset of melt is indicated by the red point. Our measured temperature pressure path is in good agreement with recent DFT simulations (dot-dashed blue line) [8] for the liquid phase. Our Simon fit for the melt boundary (black line) is compared with predictions [15, 26, 27] and the measured bridgmanite/post-perovskite phase boundary [28]. The pressure constraints that we place upon melt is shown as the yellow shaded region, indicating that our inferred liquidus melting point is consistent with other observations.

Figure 9

Liquid silicate pressure-temperature phase diagram compared with core-mantle boundary super-Earth masses [29]. The enstatite Hugoniot melt point (red circle) and the proposed melt boundary (black solid line) extrapolated to high pressure (black line) are compared with previous silicate melt predictions [30] and high-pressure silicate melt data [31]. The pressure constraints that we place upon melt are shown as the yellow shaded region. Predicted liquid isentropes (red-yellow solid lines) for different initial potential temperatures are shown. The mantle adiabats are nearly parallel to the melt boundary, indicating that for a small change in potential energy, super Earths would undergo a drastic rheological transition.