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Table A.1

Conditions at crossover when the total mass is twice the mass in H+He gas in the envelope Mxy and also (by definition) twice the combined mass in heavy metals in the core Mcore and envelope MZ,env.

r ṀPeb EoS simpars speb Mcore Mcross MZ,env Mxy tcross txy r0.05 Zdc Figure ref.
au M⊕ yr−1 cm M⊕ M⊕ M⊕ M⊕ Myr Myr R⊕
0.2 10−4 1.85 20.7 8.48 10.3 0.10 0.067 30.4 0.51 8, 11
0.2 10−4 0.1 1.72 34.3 15.4 17.2 0.17 0.11 54.0 0.50 11
0.2 10−5 ideal 1.56 13.1 5.02 6.51 0.66 0.68 19.0 0.52 8
0.2 10−5 ideal rec. 1.67 16.5 6.60 8.24 0.83 1.13 19.4 0.51
0.2 10−5 2.03 15.2 5.53 7.63 0.76 0.36 20.1 0.52 8, 9, 10, 11, 13
0.2 10−5 rec. 2.12 19.6 7.71 9.81 0.98 0.72 22.1 0.51 10, 12
0.2 10−5 III8 2.03 14.4 5.10 7.23 0.81 0.48 18.4 0.52 12
0.2 10−5 III6 2.03 11.9 3.91 5.96 1.02 1.23 14.1 0.54 12
0.2 10−5 III4 2.04 7.83 1.92 3.87 5.28 11.4 7.62 0.60 12
0.2 10−5 ideal ∞ 32.3 64.6 0.0 32.3 3.23 0.56 3.82 1.00
0.2 10−5 ∞ 14.6 28.8 0.0 14.2 1.45 0.061 2.93 1.00 9, 10
0.2 10−5 1.0 2.03 15.1 5.51 7.53 0.75 0.36 19.8 0.52 11
0.2 10−5 0.1 1.75 17.2 6.82 8.64 0.86 0.37 22.3 0.51 11, 12, 13
0.2 10−5 III8 0.1 1.75 15.0 5.73 7.51 0.90 0.49 19.0 0.52 12
0.2 10−5 III6 0.1 1.75 11.9 4.19 5.96 1.11 1.31 13.8 0.54 12
0.2 10−5 III4 0.1 1.75 7.90 2.21 3.95 5.68 11.4 7.66 0.60 12
0.2 10−6 ideal 1.77 9.54 3.03 4.74 4.80 3.24 12.4 0.53 6, 7, 8
0.2 10−6 ideal rec. 1.96 12.1 4.10 6.07 6.06 5.66 12.9 0.51
0.2 10−6 2.20 11.2 3.38 5.58 5.58 1.85 13.0 0.54 5, 6, 7, 8, 10, 11, 13
0.2 10−6 rec. 2.38 14.7 4.99 7.36 7.37 3.94 14.6 0.51 10
0.2 10−6 III8 2.20 11.1 3.31 5.61 5.71 1.96 12.8 0.54
0.2 10−6 III6 2.20 10.6 3.09 5.33 5.97 2.58 12.0 0.55
0.2 10−6 III4 2.21 8.03 1.76 4.06 9.84 10.9 7.75 0.59
0.2 10−6 n 2.19 11.0 3.33 5.44 5.52 1.96 12.9 0.54
0.2 10−6 ideal S 1.34 7.90 2.64 3.92 3.98 3.34 13.0 0.52 8
0.2 10−6 S 1.50 9.16 3.11 4.55 4.61 2.42 14.6 0.53 8
0.2 10−6 ideal ∞ 14.5 28.8 0.0 14.3 14.5 2.28 2.92 1.00
0.2 10−6 ∞ 8.84 17.6 0.0 8.80 8.83 0.54 2.48 1.00 10
0.2 10−6 1.0 2.20 11.2 3.38 5.57 5.58 1.84 13.0 0.54 11
0.2 10−6 0.1 2.22 11.2 3.40 5.56 5.62 1.86 13.1 0.54 11
0.2 10−6 0.01 1.72 20.5 8.43 10.3 10.1 3.95 22.2 0.50 11
0.2 10−7 ideal 1.92 7.21 1.69 3.60 36.1 13.8 8.44 0.55 8
0.2 10−7 ideal rec. 2.21 9.26 2.40 4.66 46.1 25.7 8.98 0.51
0.2 10−7 2.39 8.41 1.81 4.21 42.0 8.17 8.69 0.57 8, 10, 11
0.2 10−7 rec. 2.67 11.0 2.90 5.48 55.7 20.6 9.76 0.53 10
0.2 10−7 ideal ∞ 7.20 14.3 0.0 7.15 71.7 10.0 2.31 1.00
0.2 10−7 ∞ 5.42 10.9 0.0 5.45 54.2 4.19 2.11 1.00 10
0.2 10−7 1.0 2.39 8.41 1.81 4.21 42.0 8.19 8.69 0.57 11
0.2 10−7 0.1 2.39 8.37 1.81 4.17 42.0 8.25 8.65 0.57 11
1 10−4 2.07 13.6 4.65 6.84 0.067 0.021 19.2 0.55 8, 11
1 10−4 0.1 1.78 45.1 20.9 22.5 0.23 0.12 77.4 0.51 11
1 10−5 ideal 1.67 8.98 2.85 4.46 0.45 0.25 13.5 0.56 8
1 10−5 ideal rec. 1.76 11.7 4.02 5.88 0.58 0.40 16.7 0.52
1 10−5 2.13 10.2 2.95 5.11 0.51 0.12 12.9 0.57 8, 10, 11
1 10−5 rec. 2.24 12.6 4.10 6.22 0.63 0.21 15.9 0.54 10, 12
1 10−5 III8 2.13 10.0 2.89 4.97 0.51 0.14 12.5 0.58 12
1 10−5 III6 2.13 9.77 2.78 4.86 0.53 0.18 12.1 0.58 12
1 10−5 III4 2.13 8.01 1.83 4.04 0.70 0.47 8.89 0.62 12
1 10−5 ideal ∞ 11.0 22.2 0.0 11.2 1.10 0.074 2.67 1.00
1 10−5 ∞ 7.66 15.5 0.0 7.80 0.77 0.027 2.36 1.00 10
1 10−5 1.0 2.14 10.2 2.98 5.12 0.51 0.14 13.0 0.57 11
1 10−5 0.1 1.80 17.9 7.16 8.92 0.90 0.27 23.7 0.52 11, 12
1 10−5 III8 0.1 1.80 14.9 5.58 7.50 0.87 0.22 19.5 0.54 12
1 10−5 III6 0.1 1.81 11.9 4.09 5.97 0.83 0.20 14.9 0.57 12
1 10−5 III4 0.1 1.81 7.93 2.16 3.96 0.89 0.55 8.55 0.65 12
1 10−6 ideal 1.73 6.83 1.70 3.39 3.44 1.15 9.16 0.58 8
1 10−6 ideal rec. 1.87 8.79 2.53 4.39 4.40 2.13 11.5 0.54
1 10−6 2.21 7.69 1.66 3.82 3.87 0.82 8.72 0.61 8, 10, 11
1 10−6 rec. 2.34 9.98 2.60 5.05 4.93 1.04 11.3 0.55 10
1 10−6 ideal ∞ 6.51 13.1 0.0 6.60 6.51 0.39 2.24 1.00
1 10−6 ∞ 4.97 9.87 0.0 4.90 4.97 0.24 2.05 1.00 10
1 10−6 1.0 2.21 7.72 1.65 3.85 3.87 0.60 8.72 0.61 11
1 10−6 0.1 2.26 8.67 2.05 4.37 4.31 0.64 10.2 0.59 11
1 10−6 0.01 1.78 21.6 8.93 10.8 10.7 3.52 25.7 0.51 11
1 10−7 ideal 1.73 5.20 0.89 2.58 26.2 5.54 6.26 0.62 8
1 10−7 ideal rec. 1.93 6.77 1.48 3.36 34.1 10.9 8.02 0.56
1 10−7 2.25 5.84 0.63 2.95 28.9 2.31 5.55 0.69 8, 10, 11
1 10−7 rec. 2.45 7.78 1.43 3.90 38.8 4.79 7.84 0.59 10
1 10−7 ideal ∞ 3.90 7.72 0.0 3.83 38.9 2.96 1.89 1.00
1 10−7 ∞ 3.25 6.54 0.0 3.29 32.5 1.82 1.78 1.00 10
1 10−7 1.0 2.25 5.85 0.64 2.96 28.9 2.32 5.57 0.68 11
1 10−7 0.1 2.25 5.76 0.64 2.86 29.0 2.67 5.54 0.69 11
5 10−4 2.03 8.91 2.45 4.43 0.045 0.011 11.3 0.63 8, 11
5 10−4 0.1 1.80 47.6 21.9 23.9 0.24 0.10 81.1 0.52 11
5 10−5 ideal 1.60 5.86 1.31 2.95 0.29 0.078 7.98 0.65 8
5 10−5 ideal rec. 1.68 7.44 2.03 3.73 0.37 0.13 10.6 0.58
5 10−5 2.07 6.44 1.17 3.20 0.32 0.035 7.00 0.70 8, 10, 11
5 10−5 rec. 2.14 8.27 2.00 4.13 0.41 0.088 9.84 0.61 10, 12
5 10−5 III8 2.07 6.40 1.16 3.17 0.32 0.030 6.96 0.70 12
5 10−5 III6 2.07 6.44 1.15 3.23 0.33 0.027 6.93 0.70 12
5 10−5 III4 2.07 6.23 1.05 3.11 0.33 0.047 6.62 0.71 12
5 10−5 ideal ∞ 4.97 10.0 0.0 5.04 0.50 0.024 2.05 1.00
5 10−5 ∞ 4.07 8.04 0.0 3.98 0.41 0.023 1.91 1.00 10
5 10−5 1.0 2.09 7.25 1.57 3.59 0.37 0.044 8.32 0.67 11
5 10−5 0.1 1.91 18.1 7.07 9.09 0.90 0.31 23.9 0.52 11, 12
5 10−5 III8 0.1 1.91 14.7 5.43 7.31 0.86 0.21 19.5 0.54 12
5 10−5 III6 0.1 1.92 11.7 3.96 5.80 0.80 0.15 14.9 0.59 12
5 10−5 III4 0.1 1.93 7.95 2.04 3.98 0.64 0.066 8.80 0.70 12
5 10−6 ideal 1.55 4.07 0.51 2.01 2.06 0.17 4.75 0.74 8
5 10−6 ideal rec. 1.68 5.49 1.08 2.74 2.76 0.63 7.08 0.63
5 10−6 2.01 4.63 0.30 2.32 2.31 0.071 4.17 0.81 8, 10, 11
5 10−6 rec. 2.17 6.09 0.86 3.07 3.03 0.31 6.20 0.68 10
5 10−6 ideal ∞ 2.87 5.75 0.0 2.87 2.87 0.18 1.70 1.00
5 10−6 ∞ 2.49 4.95 0.0 2.47 2.49 0.15 1.62 1.00 10
5 10−6 1.0 2.01 4.69 0.32 2.36 2.33 0.14 4.22 0.80 11
5 10−6 0.1 2.22 7.59 1.57 3.80 3.79 0.38 8.59 0.64 11
5 10−6 0.01 1.89 21.1 8.76 10.5 10.6 3.38 25.4 0.52 11
5 10−7 ideal 1.35 3.00 0.15 1.50 15.0 0.85 3.08 0.83 8
5 10−7 ideal rec. 1.59 4.00 0.41 2.00 20.0 2.41 4.51 0.70
5 10−7 1.52 3.07 0.021 1.53 15.4 1.01 2.14 0.94 8, 10, 11
5 10−7 rec. 2.02 4.42 0.18 2.22 22.0 0.84 3.70 0.80 10
5 10−7 ideal ∞ 1.68 3.34 0.0 1.66 16.8 1.29 1.43 1.00
5 10−7 ∞ 1.55 3.08 0.0 1.54 15.4 1.04 1.39 1.00 10
5 10−7 1.0 1.52 3.07 0.021 1.53 15.4 1.01 2.14 0.94 11
5 10−7 0.1 1.64 3.32 0.040 1.64 16.8 1.01 2.46 0.91 11

Notes. The first five columns indicate the parameters: the distance from the star sets the boundary conditions (see Table 1) the pebble accretion rate, the equation of state (ideal else real), the pebble opacity given in terms of the pebble size (else, no pebble opacity). Additional parameters in the simpars column denote rec.: simulations including entropy advection, where the outer boundary is reduced by 50% (see text); IIIX: phase III simulation, in which the total mass in solids is limited to X M⊕ ; ∞: an infinite saturation pressure, ensuring all solids make it to the core and there is vapor in the envelope; n: including radionuclide heating; S: using the Stull LV-curve instead of the Kraus. The table further lists: the masses (core, total, vapor, and H+He) at crossover, the time of crossover tcross, the H+He growth time txy at this point, the radius r0.05 where the metal fraction has dropped to 5%, and the average metallicity Zdc of the said dilute core.

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