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Table B.2

Model parameters for non-irradiated planets of various masses.

Mp   (MJ) Age (Gyr) R0,p   (RJ) T  eff   (K) P  c   (M Bar) T  c   (K) ρ  c   (kg/m3) n κn k2
Analytic Numeric
0.35 0.05 1.1579 235.6 2.87 15 324. 1016. 0.913 0.681 0.568 0.428
0.35 0.10 1.0923 194.6 3.26 13 566. 1109. 0.868 0.694 0.598 0.478
0.35 0.50 0.9934 118.4 4.05 9698. 1292. 0.801 0.715 0.645 0.578
0.35 1.00 0.9801 93.4 4.18 9142. 1326. 0.792 0.718 0.651 0.594
0.35 5.00 0.9501 58.9 4.50 7758. 1402. 0.771 0.725 0.667 0.631
0.5 0.05 1.1730 280.9 5.40 19 045. 1394. 0.946 0.670 0.547 0.445
0.5 0.10 1.1112 234.8 6.06 16 765. 1507. 0.897 0.686 0.579 0.495
0.5 0.50 1.0165 140.2 7.47 12 120. 1742. 0.838 0.704 0.618 0.578
0.5 1.00 0.9961 108.4 7.91 10 950. 1811. 0.834 0.705 0.621 0.595
0.5 5.00 0.9682 62.4 8.53 9160. 1918. 0.824 0.708 0.628 0.624
0.6 0.05 1.1809 302.0 7.67 21 971. 1670. 0.987 0.658 0.522 0.443
0.6 0.10 1.1233 254.0 8.51 19 377. 1795. 0.936 0.674 0.553 0.490
0.6 0.50 1.0292 153.9 10.44 13 816. 2067. 0.869 0.694 0.597 0.571
0.6 1.00 1.0063 120.0 11.06 12 332. 2146. 0.861 0.697 0.602 0.591
0.6 5.00 0.9775 66.7 12.01 10 196. 2278. 0.856 0.698 0.606 0.616
0.7 0.05 1.1842 322.0 10.44 25 065. 1945. 1.021 0.648 0.501 0.440
0.7 0.10 1.1313 271.9 11.50 22 040. 2090. 0.974 0.662 0.529 0.484
0.7 0.50 1.0390 166.9 14.00 15 781. 2398. 0.901 0.684 0.576 0.562
0.7 1.00 1.0155 129.9 14.79 13 766. 2492. 0.887 0.688 0.585 0.583
0.7 5.00 0.9849 71.0 16.13 11 251. 2644. 0.882 0.690 0.589 0.607
0.8 0.05 1.1857 339.9 13.64 28 043. 2218. 1.044 0.641 0.488 0.439
0.8 0.10 1.1360 285.7 14.98 24 692. 2374. 1.003 0.654 0.512 0.478
0.8 0.50 1.0466 178.8 18.13 17 626. 2728. 0.929 0.676 0.558 0.553
0.8 1.00 1.0224 139.5 19.22 15 272. 2846. 0.912 0.681 0.568 0.574
0.8 5.00 0.9903 76.1 20.96 12 243. 3022. 0.903 0.684 0.575 0.599
0.9 0.05 1.1864 355.5 17.22 30 999. 2469. 1.057 0.637 0.480 0.438
0.9 0.10 1.1393 297.1 18.84 27 295. 2641. 1.021 0.648 0.501 0.475
0.9 0.50 1.0525 189.6 22.83 19 399. 3048. 0.952 0.669 0.543 0.546
0.9 1.00 1.0272 148.9 24.30 16 774. 3191. 0.933 0.674 0.555 0.567
0.9 5.00 0.9946 82.0 26.53 13 201. 3402. 0.921 0.678 0.563 0.592
1.0 0.05 1.1873 369.1 21.02 33 873. 2696. 1.061 0.636 0.478 0.440
1.0 0.10 1.1419 306.5 23.04 29 826. 2897. 1.030 0.645 0.496 0.474
1.0 0.50 1.0576 199.5 27.98 21 165. 3357. 0.970 0.663 0.532 0.540
1.0 1.00 1.0316 157.6 29.88 18 218. 3528. 0.951 0.669 0.544 0.560
1.0 5.00 0.9980 87.0 32.77 14 132. 3779. 0.936 0.673 0.553 0.585
1.2 0.05 1.1902 397.7 29.16 39 189. 3127. 1.051 0.639 0.484 0.445
1.2 0.10 1.1467 328.1 32.22 34 685. 3384. 1.032 0.645 0.495 0.475
1.2 0.50 1.0666 216.9 39.33 24 692. 3949. 0.992 0.657 0.519 0.530
1.2 1.00 1.0396 173.3 42.28 21 047. 4173. 0.975 0.662 0.529 0.550
1.2 5.00 1.0037 96.0 46.87 15 917. 4513. 0.960 0.666 0.538 0.574
1.5 0.05 1.1974 437.2 43.27 46 493. 3761. 1.019 0.648 0.502 0.456
1.5 0.10 1.1541 362.0 48.34 41 254. 4096. 1.016 0.650 0.504 0.479
1.5 0.50 1.0768 238.7 59.61 29 797. 4811. 0.998 0.655 0.515 0.524
1.5 1.00 1.0496 193.9 64.49 25 342. 5108. 0.989 0.658 0.520 0.541
1.5 5.00 1.0103 108.2 72.65 18 523. 5584. 0.976 0.661 0.528 0.563
1.8 0.05 1.2044 467.7 59.79 53 447. 4405. 0.994 0.656 0.517 0.465
1.8 0.10 1.1613 392.9 67.23 47 612. 4816. 0.999 0.655 0.514 0.484
1.8 0.50 1.0853 257.2 83.49 34 881. 5679. 0.997 0.655 0.515 0.521
1.8 1.00 1.0575 211.6 90.76 29 639. 6049. 0.993 0.656 0.518 0.535
1.8 5.00 1.0157 119.2 103.42 21 166. 6665. 0.984 0.659 0.524 0.556
2.1 0.05 1.2098 493.7 79.29 60 248. 5071. 0.980 0.660 0.526 0.471
2.1 0.10 1.1680 420.3 89.18 54 147. 5542. 0.989 0.658 0.521 0.487
2.1 0.50 1.0920 272.9 111.54 39 939. 6568. 0.996 0.656 0.516 0.518
2.1 1.00 1.0639 227.4 121.62 33 971. 7009. 0.995 0.656 0.517 0.530
2.1 5.00 1.0199 129.6 139.84 23 851. 7773. 0.988 0.658 0.521 0.550
3.0 0.05 1.2203 578.7 156.52 83 329. 7108. 0.980 0.660 0.526 0.480
3.0 0.10 1.1803 488.6 176.70 74 971. 7806. 0.989 0.658 0.520 0.490
3.0 0.50 1.1031 316.3 225.68 55 401. 9414. 1.006 0.652 0.510 0.510
3.0 1.00 1.0756 266.8 246.76 47 633. 10 073. 1.009 0.652 0.508 0.518
3.0 5.00 1.0264 158.3 290.80 32 425. 11 396. 1.009 0.652 0.509 0.534
5.0 0.05 1.2306 746.7 437.22 134 158. 12 207. 1.038 0.643 0.491 0.477
5.0 0.10 1.1855 620.1 509.10 121 231. 13 722. 1.053 0.638 0.483 0.479
5.0 0.50 1.1058 401.2 671.34 92 480. 16 920. 1.076 0.631 0.469 0.485
5.0 1.00 1.0775 333.8 741.09 80 859. 18 218. 1.081 0.630 0.467 0.489
5.0 5.00 1.0226 214.3 900.43 54 736. 21 064. 1.085 0.629 0.464 0.498
8.0 0.05 1.2338 986.7 1202.57 222 136. 20 971. 1.140 0.612 0.434 0.453
8.0 0.10 1.1759 804.3 1468.06 201 343. 24 340. 1.159 0.607 0.425 0.452
8.0 0.50 1.0854 516.0 2028.59 154 227. 30 946. 1.178 0.601 0.415 0.452
8.0 1.00 1.0568 428.1 2248.11 135 487. 33 390. 1.179 0.601 0.414 0.454
8.0 5.00 1.0018 278.2 2740.70 94 044. 38 622. 1.175 0.602 0.416 0.461
10.0 0.05 1.2355 1131.0 1940.74 286 246. 27 042. 1.191 0.598 0.408 0.439
10.0 0.10 1.1682 924.2 2439.07 259 634. 32 036. 1.206 0.593 0.401 0.438
10.0 0.50 1.0703 582.7 3458.94 198 170. 41 464. 1.217 0.590 0.395 0.437
10.0 1.00 1.0415 482.5 3839.83 174 150. 44 787. 1.215 0.591 0.396 0.439
10.0 5.00 0.9873 313.6 4676.54 121 844. 51 786. 1.206 0.593 0.400 0.445
13.0 0.05 1.2413 1330.1 3355.37 388 856. 35 933. 1.243 0.583 0.383 0.422
13.0 0.10 1.1605 1099.6 4390.75 352 475. 43 831. 1.249 0.581 0.379 0.421
13.0 0.50 1.0501 684.2 6502.34 268 237. 58 583. 1.247 0.581 0.380 0.422
13.0 1.00 1.0203 559.1 7258.53 234 464. 63 563. 1.243 0.583 0.383 0.423
13.0 5.00 0.9677 361.2 8837.13 166 014. 73 551. 1.231 0.586 0.388 0.429
17.0 0.05 1.5180 1963.5 2728.85 566 417. 27 110. 1.258 0.578 0.375 0.403
17.0 0.10 1.2104 1460.9 6602.33 518 481. 52 312. 1.287 0.570 0.362 0.405
17.0 0.50 1.0308 829.1 12 389.70 373 005. 83 468. 1.270 0.575 0.370 0.408
17.0 1.00 0.9989 672.8 13 988.06 325 053. 91 373. 1.264 0.577 0.373 0.410
17.0 5.00 0.9441 421.3 17 311.92 230 449. 107 176. 1.253 0.580 0.378 0.415
20.0 0.05 1.3776 1899.6 5422.33 663 050. 42 143. 1.301 0.566 0.356 0.396
20.0 0.10 1.1891 1528.5 9683.22 607 482. 64 873. 1.303 0.566 0.355 0.397
20.0 0.50 1.0200 903.9 17 617.27 446 001. 101 492. 1.281 0.572 0.365 0.401
20.0 1.00 0.9827 731.4 20 350.09 387 102. 113 070. 1.275 0.574 0.368 0.403
20.0 5.00 0.9291 458.3 25 212.93 276 207. 132 824. 1.265 0.576 0.372 0.407
25. 0.05 1.5200 2127. 5 955. 815 455. 40 447. 1.287 0.570 0.362 0.395
25. 0.10 1.2578 1787. 12 709. 795 339. 71 202. 1.304 0.565 0.354 0.396
25. 0.50 1.0257 1044. 28 841. 590 541. 131 050. 1.305 0.565 0.354 0.389
25. 1.00 0.9800 837. 34 513. 512 744. 149 997. 1.300 0.566 0.356 0.390
25. 5.00 0.9131 521. 45 516. 364 680. 184 780. 1.293 0.568 0.359 0.393
30. 0.05 1.4417 2251. 10 697. 1031 299. 57 276. 1.302 0.566 0.355 0.395
30. 0.10 1.2210 1942. 21 054. 1009 122. 94 918. 1.324 0.560 0.346 0.386
30. 0.50 1.0186 1178. 44 101. 755 593. 164 995. 1.324 0.560 0.345 0.379
30. 1.00 0.9639 951. 55 015. 657 633. 194 894. 1.321 0.560 0.347 0.380
30. 5.00 0.8894 587. 75 828. 465 898. 248 448. 1.319 0.561 0.347 0.382
35. 0.05 1.4087 2355. 16 000. 1248 903. 71 920. 1.315 0.562 0.349 0.391
35. 0.10 1.2392 2087. 27 668. 1218 128. 108 155. 1.342 0.555 0.338 0.375
35. 0.50 1.0140 1338. 62 590. 941 772. 199 702. 1.344 0.554 0.337 0.371
35. 1.00 0.9501 1089. 81 296. 823 309. 243 366. 1.343 0.554 0.337 0.371
35. 5.00 0.8678 653. 117 258. 573 154. 321 847. 1.346 0.554 0.336 0.372
40. 0.05 1.4201 2460. 20 626. 1456 790. 81 371. 1.331 0.558 0.342 0.384
40. 0.10 1.2789 2220. 32 737. 1421 580. 114 919. 1.359 0.550 0.330 0.365
40 0.50 1.0115 1477. 84 607. 1156 557. 234 911. 1.362 0.549 0.329 0.363
40. 1.00 0.9389 1211. 114 372. 1016 621. 295 137. 1.364 0.548 0.328 0.363
40. 5.00 0.8479 721. 173 644. 687 696. 406 412. 1.372 0.546 0.325 0.363
45. 0.05 1.4571 2550. 23 906. 1644 054. 85 812. 1.344 0.554 0.337 0.378
45. 0.10 1.3266 2341. 36 613. 1617 554. 118 015. 1.373 0.546 0.325 0.357
45. 0.50 1.0104 1587. 109 823. 1394 789. 269 944. 1.379 0.544 0.322 0.356
45. 1.00 0.9293 1312. 154 381. 1233 338. 349 384. 1.384 0.543 0.320 0.356
45. 5.00 0.8296 797. 246 867. 810 090. 500 992. 1.397 0.539 0.314 0.355
50. 0.05 1.5084 2624. 26 059. 1812 465. 86 914. 1.353 0.552 0.333 0.372
50. 0.10 1.3661 2443. 40 788. 1816 290. 121 580. 1.382 0.544 0.321 0.352
50. 0.50 1.0105 1696. 137 864. 1657 050. 304 354. 1.394 0.540 0.316 0.350
50. 1.00 0.9212 1416. 201 021. 1473 950. 405 043. 1.401 0.538 0.313 0.350
50. 5.00 0.8133 877. 337 922. 939 025. 603 700. 1.420 0.533 0.305 0.347
55. 0.05 1.5706 2692. 27 233. 1961 060. 85 721. 1.362 0.549 0.329 0.366
55. 0.10 1.4046 2529. 44 642. 2 009 304. 124 155. 1.389 0.542 0.318 0.348
55. 0.50 1.0124 1807. 168 106. 1939 776. 336 623. 1.406 0.537 0.311 0.346
55. 1.00 0.9152 1523. 254 050. 1737 899. 460 099. 1.415 0.535 0.307 0.344
55. 5.00 0.7992 961. 449 023. 1078 605. 712 565. 1.440 0.528 0.297 0.340
60. 0.05 1.6344 2755. 28 052. 2098 173. 84 004. 1.371 0.547 0.325 0.361
60. 0.10 1.4394 2605. 48 560. 2198 748. 126 745. 1.394 0.540 0.316 0.345
60. 0.50 1.0028 2022. 210 699. 2180 116. 384 420. 1.412 0.535 0.308 0.342
60. 1.00 0.9044 1686. 322 274. 1968 043. 528 985. 1.427 0.531 0.303 0.340
60. 5.00 0.7871 1046. 576 706. 1239 622. 823 831. 1.455 0.524 0.291 0.334
65. 0.05 1.7083 2808. 28 001. 2215 973. 80 685. 1.379 0.544 0.322 0.356
65. 0.10 1.4891 2670. 50 342. 2363 839. 125 232. 1.400 0.538 0.313 0.341
65. 0.50 1.0113 2143. 242 171. 2453 178. 410 782. 1.421 0.533 0.305 0.339
65. 1.00 0.9040 1835. 384 628. 2244 926. 581 941. 1.438 0.528 0.298 0.336
65. 5.00 0.7792 1144. 713 179. 1456 962. 926 551. 1.465 0.521 0.288 0.330
70. 0.05 1.9273 2830. 21 154. 2211 446. 62 872. 1.407 0.537 0.310 0.334
70. 0.10 1.5424 2723. 51 330. 2516 482. 122 503. 1.407 0.537 0.310 0.337
70. 0.50 1.0258 2247. 267 457. 2738 379. 426 572. 1.426 0.531 0.303 0.336
70. 1.00 0.9137 1966. 430 915. 2558 262. 610 607. 1.443 0.527 0.296 0.332
70. 5.00 0.7785 1275. 830 427. 1812 842. 996 941. 1.466 0.521 0.287 0.328
75. 0.05 1.9854 2855. 21 758. 2324 345. 62 117. 1.415 0.534 0.307 0.332
75. 0.10 1.5863 2769. 53 086. 2670 747. 121 465. 1.412 0.535 0.309 0.334
75. 0.50 1.0459 2352. 285 273. 3027 221. 432 191. 1.427 0.531 0.302 0.334
75. 1.00 0.9304 2108. 461 523. 2903 894. 620 803. 1.443 0.527 0.296 0.331
75. 5.00 0.7962 1527. 873 708. 2288 897. 998 714. 1.466 0.521 0.287 0.326

Notes. For each planetary mass (Mp) and age, this table gives the spherical equilibrium radius (R0,p, RJ ≡ 7.1492 × 107 m), the effective temperature (T  eff), the central pressure (P  c), temperature (T  c) and density (ρ  c) along with the polytropic index (n), the dimensionless moment of inertia (κn, see Eq. (30)) and Love number (k2). k2 was derived both with our analytical formula (Eq. (42); analytic) and with a numerical method (see Appendix A; numeric).

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