Planetary dynamos in evolving cold gas giants | Astronomy & Astrophysics (A&A)

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Table D.1

Output quantities for the dynamo saturated states of all models of Table 1.

Model	N_ρ	E	Ra	Pm	Pr	Rm	Λ	E_mag	E_kin	f_dip	f_ohm	P_v	f_P(%)
1 M_J 0.2 Gyr	2.99	1.01 ⋅ 10⁻⁵	1.63 ⋅ 10⁹	1	1	1107	1.38	5.42 ⋅ 10⁶	3.44 ⋅ 10⁷	0.0271	0.235	2.123 ⋅ 10¹¹	2.4
1 M_J 0.4 Gyr	2.99	1.08 ⋅ 10⁻⁵	1.27 ⋅ 10⁹	1	1	956	0.99	3.8 ⋅ 10⁶	3.13 ⋅ 10⁷	0.028	0.197	1.49 ⋅ 10¹¹	0.45
1 M_J 0.5 Gyr	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	1	1	904	0.987	3.7 ⋅ 10⁶	2.56 ⋅ 10⁷	0.031	0.194	1.29 ⋅ 10¹¹	0.22
1 M_J 0.7 Gyr	2.99	1.12.10−5	1.05 ⋅ 10⁹	1	1	829	0.71	2.58 ⋅ 10⁶	2.54 ⋅ 10⁷	0.028	0.176	9.27 ⋅ 10¹⁰	0.31
1 M_J 1 Gyr	2.99	1.12.10−5	9.81 ⋅ 10⁸	1	1	734	0.649	2.31 ⋅ 10⁶	1.68 ⋅ 10⁷	0.030	0.172	7.36 ⋅ 10¹⁰	0.025
1 M_J 1.5 Gyr	2.98	1.15 ⋅ 10⁻⁵	8.78 ⋅ 10⁸	1	1	641	0.385	1.32 ⋅ 10⁶	1.22 ⋅ 10⁷	0.0267	0.141	5.42 ⋅ 10¹⁰	0.062
1 M_J 2.1 Gyr	2.99	1.18 ⋅ 10⁻⁵	7.87.10⁸	1	1	525	0.44	1.29 ⋅ 10⁶	8.61 ⋅ 10⁶	0.045	0.191	4.10 ⋅ 10¹⁰	0.066
1 M_J 2.8 Gyr	2.99	1.20 ⋅ 10⁻⁵	7.33.10⁸	1	1	439	0.490	1.52 ⋅ 10⁶	7.1 ⋅ 10⁶	0.104	0.216	3.32 ⋅ 10¹⁰	0.18
1 M_J 3.5 Gyr	2.99	1.21 ⋅ 10⁻⁵	6.71 ⋅ 10⁸	1	1	400	0.39	1.85 ⋅ 10⁶	6.16. 10⁶	0.114	0.207	2.93 ⋅ 10¹⁰	0.26
1 M_J 5 Gyr	2.99	1.23 ⋅ 10⁻⁵	6.22 ⋅ 10⁸	1	1	370	0.51	1.94 ⋅ 10⁶	4.89. 10⁶	0.130	0.232	2.32 ⋅ 10¹⁰	0.20
1 M_J 6.5 Gyr	2.98	1.28 ⋅ 10⁻⁵	5.52 ⋅ 10⁸	1	1	323	0.53	2.57 ⋅ 10⁶	4.40 ⋅ 10⁶	0.114	0.247	2.15 ⋅ 10¹⁰	0.079
1 M_J 10 Gyr	3.00	1.30 ⋅ 10⁻⁵	4.97−10⁸	1	1	274	0.558	2.08 ⋅ 10⁶	3.65 ⋅ 10⁶	0.130	0.250	1.51 ⋅ 10¹⁰	0.043

1 M_J 1 Gyr	2.30	1.23 ⋅ 10⁻⁵	7.92−10⁸	1	1	1092	1.87	3.07 ⋅ 10⁶	1.48 ⋅ 10⁷	0.0057	0.283	8.74 ⋅ 10¹⁰	0.18
	3.68	1.08 ⋅ 10⁻⁵	1.10 ⋅ 10⁹	1	1	461	0.172	1.38 ⋅ 10⁶	1.54 ⋅ 10⁷	0.053	0.101	5.10 ⋅ 10¹⁰	0.31
	4.58	1.05 ⋅ 10⁻⁵	1.20 ⋅ 10⁹	1	1	301	0.072	1.37 ⋅ 10⁶	1.58 ⋅ 10⁷	0.041	0.066	3.83 ⋅ 10¹⁰	0.43

0.3 M_J 5 Gyr	1.10	3.61 ⋅ 10⁻⁵	3.18 ⋅ 10⁷	1	1	213	0.48	1.49 ⋅ 10⁵	8.3 ⋅ 10⁵	0.030	0.28	9.9 ⋅ 10⁸	4.4
0.7 M_J 5 Gyr	2.98	1.37 ⋅ 10⁻⁵	4.01 ⋅ 10⁸	1	1	213	0.300	1.41 ⋅ 10⁶	2.55 ⋅ 10⁶	0.131	0.305	5.31 ⋅ 10⁹	0.033
2 M_J 5 Gyr	2.98	1.12 ⋅ 10⁻⁵	1.24 ⋅ 10⁹	1	1	1032	3.14	1.03 ⋅ 10⁷	1.82 ⋅ 10⁷	0.055	0.358	2.26 ⋅ 10¹¹	0.90
4 M_J 5 Gyr	2.98	1.08 ⋅ 10⁻⁵	2.49 ⋅ 10⁹	1	1	2203	14.0	3.57 ⋅ 10⁷	5.98 ⋅ 10⁷	0.0041	0.526	1.020 ⋅ 10¹²	15

1 M_J 0.5 Gyr	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	0.5	1	514	0.41	3.0 ⋅ 10⁶	3.2 ⋅ 10⁷	0.076	0.228	1.335 ⋅ 10¹¹	0.16
	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	2	1	1790	1.93	3.50 ⋅ 10⁶	2.47 ⋅ 10⁷	0.0045	0.218	1.32 ⋅ 10¹¹	5.4
	2.98	1.08 ⋅ 10⁻⁵	1.22.10⁹	4	1	3250	5.30	4.86.10⁶	2.27 ⋅ 10⁷	0.00204	0.331	1.40 ⋅ 10¹¹	53
	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	0.5	0.5	1190	2.11	1.50 ⋅ 10⁷	8.10 ⋅ 10⁷	0.020	0.292	5.78 ⋅ 10¹¹	6
	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	1	0.5	2050	4.11	1.46.10⁷	7.16. 10⁷	0.00934	0.332	5.66 ⋅ 10¹¹	11
	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	1	2	454	0.213	8.7 ⋅ 10⁵	7.62.10⁶	0.073	0.127	2.84 ⋅ 10¹⁰	0.086
	2.98	1.08 ⋅ 10⁻⁵	1.22 ⋅ 10⁹	2	2	803	0.803	1.63 ⋅ 10⁶	6.12.10⁶	0.054	0.180	3.07 ⋅ 10¹⁰	0.22

1 M_J 1 Gyr	2.99	1.12.10⁻⁵	9.81 ⋅ 10⁸	0.5	1	440	0.25	1.81 ⋅ 10⁶	2.4 ⋅ 10⁷	0.093	0.153	7.57 ⋅ 10¹⁰	0.061
	2.99	1.12 ⋅ 10⁻⁵	9.81 ⋅ 10⁸	2	1	1360	1.31	2.33 ⋅ 10⁶	1.45 ⋅ 10⁷	0.0088	0.186	7.57 ⋅ 10¹⁰	1.36
	2.99	1.12.10⁻⁵	9.81 ⋅ 10⁸	4	1	2460	3.52	3.17 ⋅ 10⁶	1.25 ⋅ 10⁷	0.00236	0.230	7.98 ⋅ 10¹⁰	20.9
	2.99	1.12 ⋅ 10⁻⁵	9.81 ⋅ 10⁸	0.5	0.5	918	0.95	6.6.10⁶	8.7 ⋅ 10⁷	0.0141	0.213	3.08 ⋅ 10¹¹	0.65
	2.99	1.12.10⁻⁵	9.81 ⋅ 10⁸	1	0.5	164	2.07	7.2.10⁶	7.1−10⁷	0.0081	0.245	3.18 ⋅ 10¹¹	1.54
	2.99	1.12 ⋅ 10⁻⁵	9.81 ⋅ 10⁸	1	2	310	0.221	9.1 ⋅ 10⁵	3.83 ⋅ 10⁶	0.124	0.162	1.461 ⋅ 10¹⁰	0.037
	2.99	1.12 ⋅ 10⁻⁵	9.81 ⋅ 10⁸	2	2	570	0.73	1.45 ⋅ 10⁶	3.13 ⋅ 10⁶	0.073	0.203	1.593 ⋅ 10¹⁰	0.084

1 M_J 10 Gyr	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	0.5	1	157	0.252	2.01 ⋅ 10⁶	5.0 ⋅ 10⁶	0.333	0.219	1.89 ⋅ 10¹⁰	0.024
	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	2	1	532	1.11	2.04 ⋅ 10⁶	3.30 ⋅ 10⁶	0.062	0.250	1.55 ⋅ 10¹⁰	0.070
	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	4	1	1100	1.77	1.59 ⋅ 10⁶	3.18 ⋅ 10⁶	0.0139	0.220	1.63 ⋅ 10¹⁰	3.87
	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	0.5	0.5	368	0.634	4.29 ⋅ 10⁶	1.87•10⁷	0.088	0.271	8.113 ⋅ 10¹⁰	0.23
	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	1	0.5	699	1.40	4.78 ⋅ 10⁶	1.71 ⋅ 10⁷	0.0456	0.281	8.49 ⋅ 10¹⁰	0.072
	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	1		135	0.128	5.13 ⋅ 10⁵	7.78.10⁵	0.301	0.177	3.14 ⋅ 10⁹	0.0068
	3.00	1.30 ⋅ 10⁻⁵	4.97 ⋅ 10⁸	2	2	257	0.473	8.8 ⋅ 10⁵	6.76 ⋅ 10⁵	0.085	0.251	3.36 ⋅ 10⁹	0.069

4 M_J 0.5 Gyr	4.60	8.37 ⋅ 10⁻⁶	6.50 ⋅ 10⁹	1	1	1460	4.4	7.28 ⋅ 10⁷	1.250 ⋅ 10⁸	0.0058	0.374	2.39 ⋅ 10¹²	3.6
4 M_J 1 Gyr	4.58	8.98 ⋅ 10⁻⁵	5.02 ⋅ 10⁹	1	1	1130	3.3	5.26 ⋅ 10⁷	8.47 ⋅ 10⁷	0.00768	0.353	1.542 ⋅ 10¹²	0.63
4 M_J 10 Gyr	4.60	1.06 ⋅ 10⁻⁵	2.42 ⋅ 10⁹	1	1	554	1.1	1.61 ⋅ 10⁷	2.48 ⋅ 10⁷	0.0051	0.256	3.28 ⋅ 10¹¹	0.054

Notes. Specifically we show, for all of them, the input nondimensional numbers (E and Ra fixed as in Table 1, and the Prandtl numbers Pm, Pr), and the diagnostics: Λ, E_mag (in code units), E_kin (in code units), dipolarity f_dip, Ohmic fraction f_ohm, buoyancy power P_ν, power imbalance f_P. The values are time-averaged. The typical standard deviations, here omitted for the sake of space, are shown as error bars in Figs. 5, 9.

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