{ "run": { "code": "Castro 26.01", "geometry": "2-D axisymmetric r-z (coord_sys=1)", "domain_cm": { "prob_lo": [ 0, -60000.0 ], "prob_hi": [ 60000.0, 30000.0 ] }, "amr": { "max_level": 2, "ref_ratio": 2, "level_dx_cm": [ 234.375, 117.188, 58.594 ], "level_dims": [ [ 256, 384 ], [ 512, 768 ], [ 1024, 1536 ] ], "CPPR_L2": 85 }, "eos": "external/Microphysics/EOS/tillotson_ezero_cs (granite Tillotson; zero-point energy, adiabatic sound speed, eos_p_cav=1e6 dyn/cm2)", "riemann": "HLLC (2)", "slurm_job": 84, "nodes": "hpc6a-48xl", "ranks": 16, "steps": 1275, "wall_s": 143.96, "t_final_s": 0.05, "exit_code": 0, "outputs": { "small_plotfiles": 251, "small_plot_per_s": 0.0002, "full_plotfiles": 26, "plot_per_s": 0.002, "checkpoints": 4 } }, "impact": { "diameter_m": 100, "radius_a_cm": 5000, "velocity_km_s": 18, "rho_impactor": 2.7, "rho_target": 2.7, "impactor_mass_g": 1413700000000.0, "impactor_mass_on_grid_g": 1412532000000.0, "KE_erg": 2.288301e+24, "KE_reference_erg": 2.29e+24 }, "peak_state": { "pressure_GPa": 385.694, "analytic_GPa": 391.419, "error_percent": -1.463, "plotfile": "spk2d_00074", "t_s": 0.000409564, "r_cm": 849.609375, "z_cm": -205.078125, "rho_at_peak": 6.0456, "density_ratio": 2.30781, "density_ratio_analytic": 2.2662, "density_error_percent": 1.84, "method": "elementwise per-cell maximum accumulated over all 251 spk2d_* snapshots on a single level-2 covering grid (1024x1536)" }, "decay": { "law": "P = P0 (R/r_ic)^-n", "r_ic_cm": 7210.0, "fits": { "med": { "n": 1.999352511929951, "n_err": 0.05658232349012372, "P0": 342.5104939858613, "R2": 0.9912669465249613, "nb": 13.0, "lo": 3.0, "hi": 7.5 }, "vw": { "n": 1.8240977910232328, "n_err": 0.0909060988377189, "P0": 224.4833683289205, "R2": 0.9734064264026924, "nb": 13.0, "lo": 3.0, "hi": 7.5 }, "mx": { "n": 2.661460268797521, "n_err": 0.09813094176062681, "P0": 1400.6330107393137, "R2": 0.985266084404739, "nb": 13.0, "lo": 3.0, "hi": 7.5 }, "p999": { "n": 2.662574564043744, "n_err": 0.09656419897166335, "P0": 1397.5027991960712, "R2": 0.9857379197598489, "nb": 13.0, "lo": 3.0, "hi": 7.5 } }, "adopted": { "statistic": "median per radial bin", "n": 1.999352511929951, "n_err": 0.05658232349012372, "R2": 0.9912669465249613, "P0_GPa": 342.5104939858613, "window": [ 3.0, 7.5 ], "n_bins": 13 }, "window_note": "Prescribed window was 3<=R/a<=20, but the shock front reaches only R/a=7.54 (99th pct of shocked cells) by t=0.05 s. Fitting to R/a=20 includes unshocked rock sitting at the 0.0486 GPa baseline and inflates n to ~6.3 -- an artefact, not physics.", "published": { "central": 2.0, "bracket": [ 1.44, 3.0 ], "comparison": "measured n=1.999+-0.057 is within 0.05% of the literature central value 2.0 and comfortably inside the 1.44-3.0 bracket" }, "sensitivity_to_statistic": { "median": 1.999352511929951, "volume_weighted": 1.8240977910232328, "bin_max": 2.661460268797521, "window_3_to_7_median": 2.0603091516046423, "note": "Bin-max and 99.9th-percentile statistics coincide (n=2.66) and are steeper than the median (n=2.00). Both remain inside the published bracket, so the choice of statistic does not drive the conclusion. Mass-weighted quantities use the median/volume-weighted statistic; the bin maximum tracks the single hottest cell on the front and is shown only as a sensitivity." }, "cadence_bias": { "front_motion_cells_between_outputs": 5.4, "bound_at_r_ic_percent": 9, "bound_at_46GPa_isobar_percent": 3, "effect_on_n": -0.063, "direction": "n is biased LOW (measured shallower than truth): the fractional peak underestimate is larger at small radius (9%) than at the 46 GPa isobar (3%), which flattens the fitted slope by about 0.06 -- comparable to the 0.057 statistical uncertainty." }, "isobar_crossings_R_over_a": { "46_GPa": 3.96, "56_GPa": 3.61, "119_GPa": 2.437, "579_GPa": null } }, "isobaric_core": { "measured_over_a": 1.462, "measured_volweighted_over_a": 1.197, "predicted_over_a": 1.442, "plateau_P_GPa": 354.54, "method": "intersection of the fitted outer power law with the near-field plateau (max of the median-per-bin profile inside R/a<0.5)", "empirical_departure_over_a": { "95pct": 0.334, "90pct": 0.502, "80pct": 0.867 }, "agreement": "measured 1.462 a vs predicted 1.442 a = +1.4%" }, "melt_vapour": { "weighting": "dV = 2*pi*r*dx^2 (axisymmetric); mass = rho_init*dV over cells whose PEAK pressure exceeds the threshold; ambient rho<1e-2 excluded", "thresholds_GPa": { "incipient_melt": 46, "complete_melt": 56, "incipient_vaporisation": 119, "complete_vaporisation": 579 }, "measured": { "incipient_melt": { "mass_g": 30729000000000.0, "impactor_masses": 21.737, "cells": 85782 }, "complete_melt": { "mass_g": 23660000000000.0, "impactor_masses": 16.736, "cells": 72939 }, "incipient_vaporisation": { "mass_g": 7783400000000.0, "impactor_masses": 5.506, "cells": 36227 }, "complete_vaporisation": { "mass_g": 0.0, "impactor_masses": 0.0, "cells": 0 } }, "predicted": { "melt_impactor_masses": 28, "melt_range": [ 10, 30 ], "vapour_impactor_masses": 9, "vapour_range": [ 5, 10 ], "complete_vaporisation": "none" }, "agreement": "melt 21.7 vs predicted 28 (inside the 10-30 range); vapour 5.5 vs 9 (at the low edge of 5-10); complete vaporisation zero in both -- confirmed, peak 385.7 GPa < 579 GPa", "sensitivity_rho_at_peak_weighting": { "incipient_melt": 39.354, "complete_melt": 30.977, "incipient_vaporisation": 10.963, "note": "Weighting by density AT the time of peak (Eulerian) instead of rho_init raises every figure ~1.8x because shocked cells are compressed. The Lagrangian rho_init weighting is the correct one for 'how much material was shocked above X'; the Eulerian variant bounds the choice." }, "cavitation_contamination_audit": { "result": "clean", "dense_gate": "rho > 2.0 g/cm3 at the time of peak", "cells_shocked_with_rho_at_peak_below_gate": 0, "cells_shocked_total": 70718, "max_abs_difference_between_gated_and_raw_peak_field_GPa": 0.0, "expanded_branch_cells_above_46GPa": 1, "expanded_branch_mass_fraction_above_46GPa": 9.27e-06, "mass_fraction_in_singleton_components_above_46GPa": 0.000459, "conclusion": "The density gate is a strict no-op on shocked material: all 70718 cells whose peak pressure exceeds 3x the ambient baseline were compressed (rho>2.0) at the moment of their peak, and the gated and ungated peak fields are bit-identical there. The melt/vapour budget carries no cavitation contamination -- verified, not assumed." }, "convergence": { "last_cell_to_cross_46GPa_t_s": 0.024033, "last_cell_to_cross_119GPa_t_s": 0.015017, "max_R_over_a_above_46GPa": 5.06, "note": "The melt and vapour budgets are CONVERGED, not truncated by the 0.05 s window: no cell crossed 46 GPa after t=0.024 s, less than half way through the run." }, "hemispherical_crosscheck": { "melt_46GPa_impactor_masses": 30.51, "complete_melt_56GPa": 22.71, "vapour_119GPa": 7.33, "note": "2/3*pi*R^3*rho_0 with R from the measured n=2.00 fit. Exceeds the directly integrated masses by ~40% because the real isobar is not a hemisphere centred on the impact point -- it is flattened toward the free surface and truncated where the shock vents upward." }, "discrepancy_attribution": "Measured melt (21.7 m_i) and vapour (5.5 m_i) both fall BELOW the Phase-0 central predictions (28, 9) while remaining inside the published ranges. Attribution, in order of size: (1) GEOMETRIC -- the prediction assumed hemispherical isobars about the impact point; the measured isobars are truncated by the free surface. The hemispherical cross-check using the SAME measured n overpredicts by 40% (30.5 vs 21.7 m_i), which alone accounts for the melt shortfall. (2) PHYSICAL/EOS -- Tillotson has no explicit phase boundaries, latent heat or vapour dome, so mapping a pressure threshold to a phase is approximate. The Phase-0 reference itself flags 46/56 GPa as firm but 119/579 GPa as order-of-magnitude derived; ANEOS would place the vapour threshold differently, and the vapour figure is correspondingly the less trustworthy of the two. (3) NUMERICAL -- the finite output cadence biases every peak LOW (bounded at 3% at the 46 GPa isobar), and at n=2 a 3% pressure underestimate is ~1.5% in isobar radius and ~5% in enclosed mass. Resolution is not a limiting factor (CPPR=85 at level 2). The 0.05 s window is NOT a cause: the budget converged at t=0.024 s. 2-D axisymmetry is exact for this vertical impact and contributes no error." }, "excavation": { "cavity_criterion": "connected component of {rho < 0.1*rho_0, z<0, R<400 m} that touches the symmetry axis at the surface; depth = max downward extent, radius = max radial extent", "at_t_end": { "t_s": 0.05, "depth_m": 168.5, "radius_m": 144.1, "diameter_m": 288.3, "volume_cm3": 5391700000000.0, "depth_over_radius": 1.169, "depth_m_rho50_criterion": 205.4, "radius_m_rho50_criterion": 150.0 }, "trend": "Both dimensions increase monotonically to the final output, so 168.5 m depth and 144.1 m radius are LOWER BOUNDS on the transient cavity, not the transient cavity. Depth grows faster than radius over 15-50 ms (aspect ratio passes 1.0 at ~17 ms and reaches 1.17), i.e. the cavity deepens more than it widens during the coupling phase; the radial spreading that produces the final bowl happens later, in the gravity-driven regime this run does not reach.", "fraction_of_scaling_transient_diameter_percent": 16.3, "ejecta": { "criterion_primary": "solid (rho>=1e-2) material above z=0 with v_z>0", "mass_g": 13698000000000.0, "impactor_masses": 9.69, "criterion_1kms": { "mass_g": 13007000000000.0, "impactor_masses": 9.2, "note": "v_z>1 km/s, z>-200 m" }, "above_lunar_escape": { "v_esc_cm_s": 238000.0, "mass_g": 685530000000.0, "impactor_masses": 0.485, "status": "LOWER BOUND -- material is still accelerating at t=0.05 s and the ejecta curtain has not detached" }, "boundary_loss_comparison": { "mass_g": 8121000000.0, "impactor_masses": 0.0057, "note": "Boundary loss is 84x smaller than the above-escape mass, so escape is a genuine flow property and not a domain-size artefact. Boundary loss is the only figure that is a hard lower bound on total escaping mass." }, "curtain": "A coherent inverted-cone ejecta curtain IS resolved from t~4 ms onward: an outward-inclined sheet of rho ~ 0.01-1 g/cm3 rooted at the cavity rim, visible in panels (g)-(l) of the snapshot figure and throughout the animation. Peak upward velocity at t=0.05 s is 5.17 km/s, above the 2.38 km/s lunar escape speed." }, "velocity_field": "At t=0 the only motion is the impactor's 18 km/s descent. By 2 ms the flow has turned over into the canonical excavation pattern -- downward-and-outward beneath the cavity floor, outward-and-upward at the rim. Peak upward velocity falls from 20.3 km/s at 2 ms to 5.2 km/s at 50 ms as the driving shock weakens." }, "energy_budget": { "total_energy_t0_erg": 2.539414e+24, "total_energy_final_erg": 2.552254e+24, "drift_percent_final": 0.506, "max_abs_drift_percent": 0.5221, "drift_percent_to_29ms": 0.105, "numerical_error_budget_percent": 0.5, "kinetic_energy_t0_erg": 2.288301e+24, "kinetic_energy_final_erg": 9.6046e+23, "kinetic_fraction_remaining": 0.4197, "domain_mass_net_change_percent": -0.0019, "boundary_mass_loss_g": 8121000000.0, "boundary_mass_loss_impactor_masses": 0.0057, "note": "58% of the initial kinetic energy has become internal energy by t=0.05 s -- the irreversible shock heating that produces the melt and vapour. Quote 0.5% as the numerical error budget on any integrated quantity.", "verification_gates": { "planar_1D_gate_percent": 0.086, "HLLC_vs_two_shock_percent": 0.1 } }, "analysis_finding_cavitation": { "title": "With a cavitation-regularized Tillotson EOS the global pressure maximum is not a reliable late-time diagnostic", "evidence": "At the final output (t=0.05 s) the domain-wide maximum pressure is 36.90 GPa -- a 2.5x RISE over the previous output's 14.62 GPa, interrupting 24 consecutive outputs of monotonic decay. That maximum is a single cell out of 1,572,864 (rho=1.197 g/cm3 = 0.44 rho_0, on the crater wall) sitting in the cavitation-regularized expanded branch where eos_p_cav fires; only one cell in the whole domain exceeds 20 GPa at that time. The density-gated maximum over rho>2.0 g/cm3 at the same instant is 13.77 GPa and the dense 99.9th percentile is 13.16 GPa -- both continuing the decay trend smoothly.", "recommendation": "Peak-pressure statistics from a cavitation-regularized Tillotson run must be density-gated (or taken as a high percentile within dense material). A raw global max is single-cell-noise dominated once the shock weakens and will bias any decay fit. This analysis gates at rho > 2.0 g/cm3 and reports the median-per-bin statistic; the coupling-phase peak of 385.694 GPa is unaffected because it occurs at t=4.1e-4 s in strongly compressed rock (rho=6.05 g/cm3 = 2.24 rho_0)." }, "crater_scaling_NOT_A_CASTRO_OUTPUT": { "D_transient_km": 1.766, "d_transient_km": 0.62, "D_final_km": 2.21, "D_final_range_km": [ 1.52, 2.35 ], "crater_type": "simple", "Y_range_dyn_cm2": [ 10000000.0, 1000000000.0 ], "regime": "gravity-dominated (marginal: strength supplies ~1/3 of resistance)", "simple_to_complex_transition_km": [ 15, 20 ], "coefficients": { "K1": 0.095, "K2": 0.257, "mu": 0.55, "nu": 0.33, "Y_MPa": 10, "rho_kg_m3": 3200, "material": "Hard Rock" }, "coefficient_provenance": "VERIFIED IN THIS SESSION: read directly from Singer et al. (2020) Table S1, 'Hard Rock' row (arXiv:2008.10132 p.41; JGR Planets 125(8) e2019JE006313; doi 10.1029/2019JE006313). Singer's footnote states these values come from a website maintained by K. Holsapple downloaded in 2013 and are similar to Holsapple (1993), Holsapple & Housen (2007) and Housen & Holsapple (2011). The supplement also confirms the interpolating form is Holsapple (1993) eq. 18.", "why_not_simulated": "Castro is an inviscid compressible hydrodynamics code. It has NO deviatoric strength, NO damage model, NO porosity/compaction model and NO acoustic fluidisation. The final crater diameter is set by exactly those neglected processes, so 2.21 km is a pi-group scaling result and not a Castro output." } }