Table 1.
Initial parameters and results for our ideal MHD simulations.
Run | Σ0 | Tc0 | {Tmid} ± σTmid | {Teff} ± σTeff | {β} | α ± σα | qsurface | ζ | fconv |
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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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