Waste Heat Approximation for Understanding Dynamic Compression in Nature and Experiments

Abstract:

Energy dissipated during dynamic compression quantifies the residual heat left in a planet due to impact and accretion, as well as the deviation of a loading path from an ideal isentrope. Waste heat ignores the difference between the pressure–volume isentrope and Hugoniot in approximating the dissipated energy as the area between the Rayleigh line and Hugoniot (assumed given by a linear dependence of shock velocity on particle velocity). Strength and phase transformations are ignored: justifiably, when considering sufficiently high dynamic pressures and reversible transformations. Waste heat mis-estimates the dissipated energy by less than 10-20 percent for volume compressions under 30-60 percent.

Specific waste heat (energy per mass) reaches 0.2-0.3 c₀² at impact velocities 2-4 times the zero-pressure bulk sound velocity (c₀), its maximum possible value being 0.5 c₀². As larger impact velocities are implied for typical orbital velocities of Earth-like planets, and c₀² ≈ 2-30 MJ/kg for rock, the specific waste heat due to accretion corresponds to temperature rises of about 3-15 x 10³ K for rock: melting accompanies accretion even with only 20-30 percent waste heat retained. Impact sterilization is similarly quantified in terms of waste heat relative to the energy required to vaporize H₂O (impact velocity of 7-8 km/s, or 4.5-5 c₀, is sufficient).

Waste heat also clarifies the relationship between shock, multi-shock and ramp loading experiments, as well as the effect of (static) pre-compression. Breaking a shock into 2 steps significantly reduces the dissipated energy, with minimum waste heat achieved for two equal volume compressions in succession. Breaking a shock into as few as 4 steps reduces the waste heat to within a few percent of zero, documenting how multi-shock loading approaches an isentrope. Pre-compression, being less dissipative than an initial shock to the same strain, further reduces waste heat. Multi-shock (i.e., high strain-rate) loading of pre-compressed samples may thus offer the closest approach to an isentrope, and therefore the most extreme compression at which matter can be studied at the “warm” temperatures of planetary interiors.