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Table 1.

Initial parameters and results for our ideal MHD simulations.

Run Σ0 Tc0 {Tmid} ± σTmid {Teff} ± σTeff {β} α ± σα qsurface ζ fconv H/R tavg
Net Flux SimulationsB0 = 8G
Upper branch
439F 540 75000 76708 ± 3497 11869 ± 1121 120079 0.046 ± 0.014 81 2.07E-4 0.003 4.78E17 1.38E17 3.46E-2 700
437F 174 50000 48009 ± 1578 8218 ± 424 30236 0.055 ± 0.009 48 2.97E-4 0.012 1.10E17 8.26E16 2.74E-2 600
442F 113 34500 38085 ± 3389 7520 ± 339 17177 0.078 ± 0.017 52 6.43E-4 0.10 7.56E16 8.90E16 2.43E-2 600
456F 80 35000 26024 ± 4367 6989 ± 310 9571 0.144 ± 0.040 81 8.47E-4 0.28 5.83E16 1.39E17 2.02E-2 600
457F 70 30000 R R R R R R R R R R 200
Lower branch
401F 200 11000 R R R R R R R R R R 600
435F 191 5000 13751 ± 638 5656 ± 302 14202 0.067 ± 0.013 70 1.89E-3 0.59 2.80E16 1.21E17 1.46E-2 600
436F 150 9000 9238 ± 573 4544 ± 274 7817 0.089 ± 0.025 37 3.74E-3 0.21 1.37E16 6.33E16 1.20E-2 600
465F 116 6000 3925 ± 300 3681 ± 228 3839 0.156 ± 0.027 34 4.28E-3 0.22 8.06E15 5.84E16 7.83E-3 600
434F 93 5000 3290 ± 163 3240 ± 183 2563 0.186± 0.034 31 4.37E-3 0.26 5.52E15 5.40E16 7.17E-3 600
477F 70 3000 3005 ± 172 3044 ± 181 1591 0.275 ± 0.063 31 1.01E-2 0.32 5.15E15 5.37E16 6.81E-3 600
476F 50 2500 2416 ± 121 2653 ± 150 939 0.354 ± 0.060 30 1.25E-2 0.25 3.33E15 5.22E16 6.12E-3 600
Net Flux SimulationsB0 = 2G
Upper branch
439F 540 75000 75531 ± 2228 11541 ± 785 1954988 0.040 ± 0.009 377 1.28E-4 0.003 4.10E17 3.93E16 3.44E-2 600
437F 174 50000 44748 ± 3496 7965 ± 384 478899 0.047 ± 0.015 256 1.21E-4 0.08 8.60E16 1.81E16 2.64E-2 600
442F 113 34500 34349 ± 5792 7386 ± 327 263340 0.078 ± 0.027 264 2.66E-4 0.20 6.67E16 2.75E16 2.32E-2 600
452F 100 30000 28530 ± 4463 7064 ± 293 207469 0.097 ± 0.025 322 3.06E-4 0.37 5.62E16 3.37E16 2.11E-2 600
454F 90 28000 R R R R R R R R R R 150
Middle branch
415F 360 14000 14194 ± 298 5913 ± 402 552927 0.046 ± 0.018 X X 0.81 4.32E16 X 1.49E-2 600
413F 340 10000 12259 ± 127 5230 ± 243 380814 0.041 ± 0.011 X X 0.61 2.50E16 X 1.38E-2 600
411F 320 4500 9840 ± 113 4140 ± 419 291836 0.037 ± 0.012 X X 0.74 1.39E16 X 1.24E-2 600
Lower branch
409F 300 4000 4973 ± 842 3497 ± 156 187517 0.028 ± 0.010 74 8.84E-4 0.31 4.69E15 7.72E15 8.78E-3 1500
407F 280 4000 3450 ± 71 2996 ± 137 128410 0.028 ± 0.009 63 2.75E-4 0.16 2.46E15 6.61E15 7.31E-3 600
404F 230 3500 3465 ± 92 3053 ± 147 106544 0.039 ± 0.014 85 6.70E-4 0.15 2.93E15 8.85E15 7.32E-3 600
403F 220 3500 3230 ± 70 2925 ± 135 94363 0.038 ± 0.011 67 4.44E-4 0.09 2.31E15 6.99E15 7.07E-3 600
401F 200 4000 2728 ± 142 2672 ± 137 74292 0.035 ± 0.009 49 1.94E-4 0.03 1.43E15 5.10E15 6.51E-3 600
465F 116 3000 2176 ± 98 2371 ± 130 37650 0.051 ± 0.011 50 3.91E-4 0.03 9.97E14 5.20E15 5.80E-3 600
434F 93 2500 2021 ± 107 2243 ± 144 28981 0.055 ± 0.014 41 4.96E-4 0.03 7.69E14 4.34E15 5.60E-3 600
477F 70 2000 1885 ± 44 2097 ± 125 21167 0.065 ± 0.012 45 9.96E-4 0.03 6.47E14 4.78E15 5.42E-3 600
Net Flux SimulationsB0 = 0, 8 G
Upper branch
439F 540 75000 73173 ± 3826 10731 ± 1269 12025687 0.032 ± 0.013 2116 8.09E-5 0.001 3.17E17 3.53E16 3.38E-2 600
437F 174 50000 47560 ± 3365 8367 ± 528 3068497 0.054 ± 0.017 1121 1.52E-4 0.019 1.06E17 1.87E16 2.73E-2 900
442F 113 35000 31312 ± 6879 7273 ± 316 1561523 0.082 ± 0.025 1099 2.51E-4 0.27 6.22E16 1.83E16 2.21E-2 800
452F 100 30000 R R R R R R R R R R R
Middle branch
415F 360 5000 10123 ± 245 4259 ± 187 2117377 0.031 ± 0.009 X X 0.83 1.41E16 X 1.26E-2 600
Lower branch
411F 320 4000 3480 ± 101 3002 ± 112 1140102 0.024 ± 0.008 148 1.89E-4 0.15 2.71E15 2.48E15 7.35E-3 1200
409F 300 3500 3623 ± 54 3093 ± 135 911231 0.029 ± 0.009 202 4.41E-4 0.18 3.08E15 3.38E15 7.48E-3 600
407F 280 3000 3508 ± 92 3026 ± 113 814922 0.032 ± 0.011 212 6.30E-4 0.19 2.93E15 3.54E15 7.37E-3 1000
405F 250 2500 3209 ± 131 2864 ± 155 665472 0.038 ± 0.017 338 8.89E-4 0.14 2.60E15 5.64E15 7.07E-3 600
404F 230 2000 2810 ± 118 2626 ± 131 540606 0.035 ± 0.010 152 7.82E-4 0.1 1.72E15 2.55E15 6.62E-3 600
403F 220 3500 2788 ± 512 2689 ± 312 531776 0.035 ± 0.014 165 2.51E-4 0.05 1.73E15 2.75E15 6.57E-3 1500
401F 200 3500 2716 ± 92 2667 ± 129 462249 0.037 ± 0.010 155 2.35E-4 0.04 1.55E15 2.60E15 6.48E-3 600
465F 116 3000 1954 ± 92 2170 ± 135 224681 0.035 ± 0.009 93 1.57E-4 0.01 6.01E14 1.56E15 5.50E-3 600
434F 93 2000 1878 ± 45 2037 ± 146 175993 0.039 ± 0.011 99 3.59E-4 0.02 5.16E14 1.65E15 5.41E-3 600
477F 70 2000 1806 ± 18 1877 ± 106 130298 0.041 ± 0.007 98 3.74E-4 0.02 3.81E14 1.63E15 5.31E-3 600
Net Flux Simulationsβ ≈ 104
Upper branch
439F 540 79000 82633 ± 3629 13426 ± 1143 12166 0.077 ± 0.020 33 X 0.01 8.53E17 5.73E17 3.59E-2 950
442F 113 34500 39219 ± 2659 7767 ± 444 12732 0.086 ± 0.018 46 X 0.07 8.83E16 1.10E17 2.48E-2 600
452F 100 34500 37777 ± 2428 7523 ± 388 12122 0.093 ± 0.021 55 X 0.11 7.72E16 1.15E17 2.4E-2 600
454F 90 34500 30721 ± 6055 7200 ± 369 10793 0.110 ± 0.034 55 X 0.17 6.48E16 1.05E17 2.18E-2 600
456F 80 34500 29261 ± 4841 7221 ± 346 10470 0.128 ± 0.033 71 X 0.20 6.18E16 1.21E17 2.14E-2 550
Lower branch
434F 93 1976 2392 ± 70 2608 ± 116 7168 0.099 ± 0.015 34 X 0.05 1.68E15 1.58E16 6.11E-3 600
434F_β12000 93 1976 2109 ± 38 2376 ± 101 13450 0.067 ± 0.009 46 X 0.03 9.94E14 1.07E16 5.74E-3 600
477F 70 1976 3065 ± 193 2967 ± 148 9063 0.104 ± 0.019 73 X 0.05 1.96E15 2.56E16 6.92E-3 600
Net Flux Simulationsβ ≈ 103
Upper branch
439F 540 79000 93180 ± 13750 19550 2791 0.424 ± 0.126 36 X 0.06 5.35E18 6.56E18 3.82E-2 300
442F 113 50000 49332 ± 6163 12031 ± 1274 637 0.444 ± 0.082 44 X 0.04 6.02E17 1.23E18 2.78E-2 520
452F 100 45000 45917 ± 4835 11569 ± 1167 490 0.469 ± 0.101 45 X 0.07 5.27E17 1.09E18 2.68E-2 380
Lower branch
434F 93 4500 11915 ± 4413 5993 ± 529 1051 0.315 ± 0.097 61 X 0.88 4.84E16 2.98E17 1.36E-2 500
Net Flux Simulationsβ ≈ 102
Upper branch
442F 113 34500 31015 ± 9461 10821 ± 2124 101.9 0.850 ± 0.191 32 X X 8.03E17 3.78E18 2.20E-2 200
Lower branch
434F 93 2000 5926 ± 2007 4609 ± 662 153.1 0.774 ± 0.280 32 X X 5.32E16 7.41E17 9.62E-3 200

Notes.Σ0 is the initial surface density in g cm−2, Tc0 the initial midplane temperature in K, and H/R0 where H is the corresponding scale height. Brackets are for quantities averaged over tavg (given in local orbits) with σ the associated standard deviation. R signals simulations with runaway heating or cooling.

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