209:
1534:, relating the pressure, opacity and energy generation rate to other local variables appropriate for the material, such as temperature, density, chemical composition, etc. Relevant equations of state for pressure may have to include the perfect gas law, radiation pressure, pressure due to degenerate electrons, etc. Opacity cannot be expressed exactly by a single formula. It is calculated for various compositions at specific densities and temperatures and presented in tabular form. Stellar structure
237:
251:
223:
69:
3743:
20:
3754:
1798:
135:, which do not establish a steep temperature gradient. Thus, radiation dominates in the inner portion of solar mass stars. The outer portion of solar mass stars is cool enough that hydrogen is neutral and thus opaque to ultraviolet photons, so convection dominates. Therefore, solar mass stars have radiative cores with convective envelopes in the outer portion of the star.
1523:.) When the convection is not adiabatic, the true temperature gradient is not given by this equation. For example, in the Sun the convection at the base of the convection zone, near the core, is adiabatic but that near the surface is not. The mixing length theory contains two free parameters which must be set to make the model fit observations, so it is a
166:. In the CNO cycle, the energy generation rate scales as the temperature to the 15th power, whereas the rate scales as the temperature to the 4th power in the proton-proton chains. Due to the strong temperature sensitivity of the CNO cycle, the temperature gradient in the inner portion of the star is steep enough to make the core
1777:, important improvements have to be made in order to remove uncertainties which are linked to the limited knowledge of transport phenomena. The most difficult challenge remains the numerical treatment of turbulence. Some research teams are developing simplified modelling of turbulence in 3D calculations.
1785:
The above simplified model is not adequate without modification in situations when the composition changes are sufficiently rapid. The equation of hydrostatic equilibrium may need to be modified by adding a radial acceleration term if the radius of the star is changing very quickly, for example if
1424:
1225:
967:
1101:
103:
and continues to rise if it is warmer than the surrounding gas; if the rising parcel is cooler than the surrounding gas, it will fall back to its original height. In regions with a low temperature gradient and a low enough
1293:. This treats the gas in the star as containing discrete elements which roughly retain the temperature, density, and pressure of their surroundings but move through the star as far as a characteristic length, called the
671:
811:
1004:(which usually escape the star without interacting with ordinary matter) per unit mass. Outside the core of the star, where nuclear reactions occur, no energy is generated, so the luminosity is constant.
505:. Although LTE does not strictly hold because the temperature a given shell "sees" below itself is always hotter than the temperature above, this approximation is normally excellent because the photon
95:
Convection is the dominant mode of energy transport when the temperature gradient is steep enough so that a given parcel of gas within the star will continue to rise if it rises slightly via an
1314:
574:
1557:, a solution of these equations completely describes the behavior of the star. Typical boundary conditions set the values of the observable parameters appropriately at the surface (
1542:
based on the tabulated values. A similar situation occurs for accurate calculations of the pressure equation of state. Finally, the nuclear energy generation rate is computed from
3594:
1475:
998:
1786:
the star is radially pulsating. Also, if the nuclear burning is not stable, or the star's core is rapidly collapsing, an entropy term must be added to the energy equation.
1764:
448:
1521:
475:
2052:
Mueller, E. (July 1986), "Nuclear-reaction networks and stellar evolution codes – The coupling of composition changes and energy release in explosive nuclear burning",
527:
332:
1272:
1248:
1127:
1716:
1677:
1642:
704:
419:
390:
361:
1607:
1581:
869:
843:
883:
724:
495:
1954:
Rauscher, T.; Heger, A.; Hoffman, R. D.; Woosley, S. E. (September 2002), "Nucleosynthesis in
Massive Stars with Improved Nuclear and Stellar Physics",
1017:
1538:(meaning computer programs calculating the model's variables) either interpolate in a density-temperature grid to obtain the opacity needed, or use a
3784:
1007:
The energy transport equation takes differing forms depending upon the mode of energy transport. For conductive energy transport (appropriate for a
170:. In the outer portion of the star, the temperature gradient is shallower but the temperature is high enough that the hydrogen is nearly fully
600:
185:
The lowest mass main sequence stars have no radiation zone; the dominant energy transport mechanism throughout the star is convection.
746:
3789:
2209:
3626:
2203:
1419:{\displaystyle {{\mbox{d}}T \over {\mbox{d}}r}=\left(1-{1 \over \gamma }\right){T \over P}{{\mbox{d}}P \over {\mbox{d}}r},}
3601:
2920:
2181:
2101:
276:
1550:
to compute reaction rates for each individual reaction step and equilibrium abundances for each isotope in the gas.
2233:
Stellar atmospheres: A contribution to the observational study of high temperature in the reversing layers of stars
1524:
1308:, meaning that the convective gas bubbles don't exchange heat with their surroundings, mixing length theory yields
3313:
498:
3606:
3243:
3227:
2262:
2212:
a FORTRAN 90 software derived from
Eggleton's Stellar Evolution Code, a web-based interface can be found here
1285:
The case of convective energy transport does not have a known rigorous mathematical formulation, and involves
532:
3653:
3520:
1275:
3636:
3587:
3562:
2855:
194:
3577:
3557:
1774:
1432:
2940:
267:
of stellar structure is the spherically symmetric quasi-static model, which assumes that a star is in a
3779:
3641:
3572:
3542:
49:
of the star. Different classes and ages of stars have different internal structures, reflecting their
976:
3648:
3525:
3502:
3084:
2533:
2528:
2523:
2518:
2513:
2508:
2791:
2665:
2300:
2196:
1721:
424:
3567:
3318:
3117:
3027:
2987:
2969:
2895:
2466:
2392:
1492:
581:
453:
132:
1220:{\displaystyle {{\mbox{d}}T \over {\mbox{d}}r}=-{3\kappa \rho l \over 64\pi r^{2}\sigma T^{3}},}
3728:
3708:
3480:
3475:
3373:
3268:
3217:
3022:
3012:
2685:
2483:
2451:
2342:
2325:
2110:
Kennedy, Dallas C.; Bludman, Sidney A. (1997), "Variational
Principles for Stellar Structure",
731:
42:
512:
308:
3582:
3552:
3547:
3537:
3465:
3253:
2419:
1767:
1257:
1233:
1117:
In the case of radiative energy transport, appropriate for the inner portion of a solar mass
108:
to allow energy transport via radiation, radiation is the dominant mode of energy transport.
2700:
2213:
2065:
2022:
1686:
1647:
1612:
3723:
3621:
3611:
3460:
3428:
3222:
3017:
3002:
2315:
2161:
2129:
2061:
2018:
1973:
1928:
1816:
1290:
1111:
962:{\displaystyle {{\mbox{d}}l \over {\mbox{d}}r}=4\pi r^{2}\rho (\epsilon -\epsilon _{\nu })}
2218:
1679:, there is no mass inside the center of the star, as required if the mass density remains
680:
395:
366:
337:
76:
Different layers of the stars transport heat up and outwards in different ways, primarily
8:
3183:
3166:
2837:
2739:
2562:
1586:
1560:
1554:
848:
822:
736:
50:
3323:
2165:
2133:
1977:
1932:
3718:
3679:
3631:
3616:
3530:
3470:
3393:
3303:
3273:
3263:
3207:
3129:
2820:
2456:
2255:
2145:
2119:
2034:
2008:
1963:
1279:
709:
529:, is much smaller than the length over which the temperature varies considerably, i.e.
480:
81:
62:
3669:
3067:
3047:
2847:
2631:
2619:
2446:
2426:
2380:
2362:
2330:
2177:
2097:
1531:
587:
96:
72:
The different transport mechanisms of high-mass, intermediate-mass and low-mass stars
46:
3154:
2149:
2038:
3497:
3450:
3400:
3388:
3366:
3361:
3288:
3248:
3195:
2977:
2900:
2875:
2769:
2690:
2414:
2375:
2137:
2026:
1981:
1936:
1251:
105:
3684:
3487:
3356:
3200:
3171:
3112:
3107:
2982:
2710:
2675:
2609:
2555:
2550:
2495:
2305:
1953:
1543:
1478:
1096:{\displaystyle {{\mbox{d}}T \over {\mbox{d}}r}=-{1 \over k}{l \over 4\pi r^{2}},}
167:
85:
2156:
Weiss, Achim; Hillebrandt, Wolfgang; Thomas, Hans-Christoph; Ritter, H. (2004),
3746:
3512:
3351:
3178:
3149:
3124:
3057:
2746:
2614:
2500:
2402:
2292:
2282:
506:
179:
159:
2030:
3773:
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3007:
2830:
2801:
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2397:
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2347:
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1539:
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1118:
264:
208:
112:
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3433:
3383:
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3278:
3161:
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3102:
3072:
3062:
2997:
2880:
2825:
2806:
2786:
2764:
2756:
2599:
2592:
2431:
2352:
2335:
1811:
1803:
268:
3674:
3346:
3338:
3328:
3308:
3283:
3212:
3134:
2890:
2865:
2860:
2774:
2734:
2695:
2660:
2643:
2638:
2310:
2232:
2124:
1999:
Moya, A.; Garrido, R. (August 2008), "Granada oscillation code (GraCo)",
1968:
1773:
Although nowadays stellar evolution models describe the main features of
1008:
288:
236:
175:
89:
68:
1680:
250:
222:
3258:
2955:
2928:
2905:
2885:
2870:
2722:
2626:
2604:
2582:
2577:
2441:
1904:
1286:
292:
171:
139:
123:
119:
77:
38:
1919:
Iglesias, C. A.; Rogers, F. J. (June 1996), "Updated Opal
Opacities",
666:{\displaystyle {{\mbox{d}}P \over {\mbox{d}}r}=-{Gm\rho \over r^{2}}}
302:(exploiting the assumed spherical symmetry), one considers the matter
3445:
3293:
3077:
3042:
3037:
3032:
2992:
2945:
2935:
2729:
2705:
2680:
2587:
2538:
2471:
2461:
2436:
2409:
2385:
2320:
2225:
1486:
1305:
1301:
1298:
1001:
198:
163:
131:), including the Sun, hydrogen-to-helium fusion occurs primarily via
3438:
3139:
2813:
2572:
2545:
2141:
1985:
1940:
816:
284:
272:
152:
2013:
3713:
3188:
2950:
2717:
2670:
2653:
2648:
2567:
1289:
in the gas. Convective energy transport is usually modeled using
591:
303:
100:
806:{\displaystyle {{\mbox{d}}m \over {\mbox{d}}r}=4\pi r^{2}\rho .}
3703:
3691:
2910:
2796:
2237:(1925) by Cecilia Payne-Gaposchkin, Cambridge: The Observatory.
2092:
Hansen, Carl J.; Kawaler, Steven D.; Trimble, Virginia (2004),
590:
within the star is exactly balanced by the inward force due to
502:
280:
156:
148:
874:
Considering the energy leaving the spherical shell yields the
1121:
star and the outer envelope of a massive main sequence star,
734:. The cumulative mass increases with radius according to the
19:
2155:
1918:
3052:
2271:
1644:, meaning the pressure at the surface of the star is zero;
34:
3753:
1797:
497:
from the center of the star. The star is assumed to be in
3418:
594:. This is sometimes referred to as stellar equilibrium.
24:
2240:
1527:
theory rather than a rigorous mathematical formulation.
1401:
1389:
1334:
1322:
1147:
1135:
1037:
1025:
903:
891:
766:
754:
620:
608:
458:
2206:, stellar evolution and structure Fortran source code
1724:
1718:, the total mass of the star is the star's mass; and
1689:
1650:
1615:
1589:
1563:
1495:
1435:
1317:
1260:
1236:
1130:
1020:
979:
886:
851:
825:
749:
712:
683:
603:
535:
515:
501:(LTE) so the temperature is identical for matter and
483:
456:
427:
398:
369:
340:
311:
2091:
1888:
1876:
1859:
1847:
1835:
1793:
1998:
819:
the mass continuity equation from the star center (
2221:(some of them including rotational induced mixing)
1758:
1710:
1671:
1636:
1601:
1575:
1515:
1469:
1418:
1266:
1242:
1219:
1095:
992:
961:
863:
837:
805:
718:
698:
665:
568:
521:
489:
469:
442:
413:
384:
355:
326:
2082:
188:
3771:
2172:Zeilik, Michael A.; Gregory, Stephan A. (1998),
2158:Cox and Giuli's Principles of Stellar Structure
2109:
1906:An introduction to Modern Stellar Astrophysics
1871:This discussion follows those of, e. g.,
147:), the core temperature is above about 1.8Ă—10
2256:
2176:(4th ed.), Saunders College Publishing,
2171:
1872:
33:models describe the internal structure of a
2051:
706:is the cumulative mass inside the shell at
421:, and energy generation rate per unit mass
2263:
2249:
1000:is the luminosity produced in the form of
2174:Introductory Astronomy & Astrophysics
2123:
2012:
1967:
1912:
363:, total pressure (matter plus radiation)
138:In massive stars (greater than about 1.5
37:in detail and make predictions about the
3785:Stellar astronomy classification systems
2219:Geneva Grids of Stellar Evolution Models
1947:
1903:Ostlie, Dale A. and Carrol, Bradley W.,
1899:
1897:
1766:, the temperature at the surface is the
569:{\displaystyle \lambda \ll T/|\nabla T|}
115:star depends upon the mass of the star.
67:
53:makeup and energy transport mechanisms.
18:
3772:
178:radiation. Thus, massive stars have a
2244:
1894:
871:) yields the total mass of the star.
228:Mass inside a given radius in the Sun
174:, so the star remains transparent to
99:. In this case, the rising parcel is
2228:database of stellar evolution tracks
2083:Kippenhahn, R.; Weigert, A. (1990),
450:in a spherical shell of a thickness
287:vary with radius; two represent how
2160:, Cambridge Scientific Publishers,
1889:Hansen, Kawaler & Trimble (2004
1877:Hansen, Kawaler & Trimble (2004
1860:Hansen, Kawaler & Trimble (2004
1848:Hansen, Kawaler & Trimble (2004
1836:Hansen, Kawaler & Trimble (2004
1470:{\displaystyle \gamma =c_{p}/c_{v}}
13:
1780:
555:
277:first-order differential equations
14:
3801:
2190:
1485:in the gas. (For a fully ionized
56:
3752:
3742:
3741:
1796:
993:{\displaystyle \epsilon _{\nu }}
249:
235:
221:
207:
118:In stars with masses of 0.3–1.5
2085:Stellar Structure and Evolution
2045:
499:local thermodynamic equilibrium
2001:Astrophysics and Space Science
1992:
1882:
1865:
1853:
1841:
1829:
1734:
1728:
1699:
1693:
1660:
1654:
1625:
1619:
956:
937:
693:
687:
562:
551:
437:
431:
408:
402:
379:
373:
350:
344:
321:
315:
214:Temperature profile in the Sun
189:Equations of stellar structure
61:For energy transport refer to
1:
3790:Stellar astrophysics concepts
3654:Timeline of stellar astronomy
1822:
845:) to the radius of the star (
586:the outward force due to the
1759:{\displaystyle T(R)=T_{eff}}
443:{\displaystyle \epsilon (r)}
111:The internal structure of a
7:
3314:Hertzsprung–Russell diagram
1789:
1516:{\displaystyle \gamma =5/3}
470:{\displaystyle {\mbox{d}}r}
300:stellar structure equations
263:The simplest commonly used
256:Pressure profile in the Sun
10:
3806:
3228:Kelvin–Helmholtz mechanism
2096:(2nd ed.), Springer,
2076:
2054:Astronomy and Astrophysics
1873:Zeilik & Gregory (1998
1011:), the energy equation is
242:Density profile in the Sun
192:
3737:
3662:
3511:
3409:
3337:
3236:
3093:
2968:
2846:
2755:
2491:
2482:
2361:
2291:
2278:
2270:
2031:10.1007/s10509-007-9694-2
1956:The Astrophysical Journal
1304:, when the convection is
1276:Stefan–Boltzmann constant
275:. It contains four basic
162:occurs primarily via the
3607:With multiple exoplanets
1775:color–magnitude diagrams
737:mass continuity equation
579:First is a statement of
522:{\displaystyle \lambda }
327:{\displaystyle \rho (r)}
195:Mass–luminosity relation
2393:Asymptotic giant branch
2210:EZ to Evolve ZAMS Stars
2199:retrieved November 2009
2066:1986A&A...162..103M
2023:2008Ap&SS.316..129M
1909:, Addison-Wesley (2007)
1553:Combined with a set of
1267:{\displaystyle \sigma }
1243:{\displaystyle \kappa }
582:hydrostatic equilibrium
3729:Tidal disruption event
3218:Circumstellar envelope
2452:Luminous blue variable
1760:
1712:
1711:{\displaystyle m(R)=M}
1673:
1672:{\displaystyle m(0)=0}
1638:
1637:{\displaystyle P(R)=0}
1603:
1577:
1530:Also required are the
1517:
1471:
1420:
1268:
1244:
1221:
1097:
994:
963:
865:
839:
807:
732:gravitational constant
720:
700:
667:
570:
523:
491:
471:
444:
415:
386:
357:
328:
73:
27:
3254:Effective temperature
2112:Astrophysical Journal
1921:Astrophysical Journal
1768:effective temperature
1761:
1713:
1674:
1639:
1604:
1578:
1518:
1472:
1421:
1269:
1245:
1222:
1098:
995:
964:
866:
840:
808:
721:
701:
668:
571:
524:
492:
472:
445:
416:
387:
358:
329:
273:spherically symmetric
71:
23:Cross-section of the
22:
3724:Planet-hosting stars
3602:With resolved images
3573:Historical brightest
3503:Photometric-standard
3429:Solar radio emission
3223:Eddington luminosity
3003:Triple-alpha process
2941:Thorne–Żytkow object
2316:Young stellar object
1817:Standard solar model
1722:
1687:
1648:
1613:
1587:
1561:
1493:
1433:
1315:
1291:mixing length theory
1258:
1234:
1128:
1112:thermal conductivity
1018:
977:
884:
849:
823:
747:
710:
699:{\displaystyle m(r)}
681:
601:
533:
513:
481:
454:
425:
414:{\displaystyle l(r)}
396:
385:{\displaystyle P(r)}
367:
356:{\displaystyle T(r)}
338:
309:
279:: two represent how
133:proton–proton chains
3548:Highest temperature
3319:Color–color diagram
3184:Protoplanetary disk
2988:Proton–proton chain
2666:Chemically peculiar
2166:2004cgps.book.....W
2134:1997ApJ...484..329K
1978:2002ApJ...576..323R
1933:1996ApJ...464..943I
1602:{\displaystyle r=0}
1576:{\displaystyle r=R}
1555:boundary conditions
1546:experiments, using
864:{\displaystyle r=R}
838:{\displaystyle r=0}
3553:Lowest temperature
3304:Photometric system
3274:Absolute magnitude
3208:Circumstellar dust
2821:Stellar black hole
2457:Stellar population
2343:Herbig–Haro object
1875:, §16-1–16-2) and
1756:
1708:
1669:
1634:
1599:
1573:
1532:equations of state
1513:
1467:
1416:
1405:
1393:
1338:
1326:
1280:Boltzmann constant
1264:
1240:
1217:
1151:
1139:
1093:
1041:
1029:
990:
959:
907:
895:
861:
835:
803:
770:
758:
716:
696:
663:
624:
612:
566:
519:
487:
467:
462:
440:
411:
382:
353:
324:
295:vary with radius.
86:thermal conduction
82:radiative transfer
74:
63:Radiative transfer
28:
16:Structure of stars
3780:Stellar astronomy
3767:
3766:
3670:Substellar object
3649:Planetary nebulae
3068:Luminous red nova
2978:Deuterium burning
2964:
2963:
2447:Instability strip
2427:Wolf-Rayet nebula
2381:Horizontal branch
2326:Pre-main-sequence
2204:Yellow CESAM code
2094:Stellar Interiors
2087:, Springer-Verlag
1548:reaction networks
1411:
1404:
1392:
1383:
1368:
1344:
1337:
1325:
1212:
1157:
1150:
1138:
1088:
1063:
1047:
1040:
1028:
913:
906:
894:
776:
769:
757:
719:{\displaystyle r}
661:
630:
623:
611:
588:pressure gradient
490:{\displaystyle r}
461:
97:adiabatic process
31:Stellar structure
3797:
3759:Stars portal
3757:
3756:
3745:
3744:
3401:Planetary system
3324:Strömgren sphere
3196:Asteroseismology
2917:Black hole star
2489:
2488:
2415:Planetary nebula
2376:Red-giant branch
2265:
2258:
2251:
2242:
2241:
2186:
2168:
2152:
2127:
2125:astro-ph/9610099
2106:
2088:
2070:
2069:
2060:(1–2): 103–108,
2049:
2043:
2042:
2016:
2007:(1–4): 129–133,
1996:
1990:
1989:
1971:
1969:astro-ph/0112478
1951:
1945:
1944:
1916:
1910:
1901:
1892:
1886:
1880:
1869:
1863:
1857:
1851:
1845:
1839:
1833:
1806:
1801:
1800:
1765:
1763:
1762:
1757:
1755:
1754:
1717:
1715:
1714:
1709:
1678:
1676:
1675:
1670:
1643:
1641:
1640:
1635:
1608:
1606:
1605:
1600:
1582:
1580:
1579:
1574:
1540:fitting function
1525:phenomenological
1522:
1520:
1519:
1514:
1509:
1476:
1474:
1473:
1468:
1466:
1465:
1456:
1451:
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1423:
1422:
1417:
1412:
1410:
1406:
1402:
1398:
1394:
1390:
1386:
1384:
1376:
1374:
1370:
1369:
1361:
1345:
1343:
1339:
1335:
1331:
1327:
1323:
1319:
1273:
1271:
1270:
1265:
1249:
1247:
1246:
1241:
1226:
1224:
1223:
1218:
1213:
1211:
1210:
1209:
1197:
1196:
1180:
1166:
1158:
1156:
1152:
1148:
1144:
1140:
1136:
1132:
1102:
1100:
1099:
1094:
1089:
1087:
1086:
1085:
1066:
1064:
1056:
1048:
1046:
1042:
1038:
1034:
1030:
1026:
1022:
999:
997:
996:
991:
989:
988:
968:
966:
965:
960:
955:
954:
933:
932:
914:
912:
908:
904:
900:
896:
892:
888:
876:energy equation:
870:
868:
867:
862:
844:
842:
841:
836:
812:
810:
809:
804:
796:
795:
777:
775:
771:
767:
763:
759:
755:
751:
725:
723:
722:
717:
705:
703:
702:
697:
672:
670:
669:
664:
662:
660:
659:
650:
639:
631:
629:
625:
621:
617:
613:
609:
605:
575:
573:
572:
567:
565:
554:
549:
528:
526:
525:
520:
496:
494:
493:
488:
476:
474:
473:
468:
463:
459:
449:
447:
446:
441:
420:
418:
417:
412:
391:
389:
388:
383:
362:
360:
359:
354:
333:
331:
330:
325:
253:
239:
225:
211:
88:is important in
47:future evolution
3805:
3804:
3800:
3799:
3798:
3796:
3795:
3794:
3770:
3769:
3768:
3763:
3751:
3733:
3658:
3627:Milky Way novae
3563:Smallest volume
3507:
3488:Radial velocity
3411:
3405:
3357:Common envelope
3333:
3232:
3201:Helioseismology
3172:Bipolar outflow
3113:Microturbulence
3108:Convection zone
3089:
2983:Lithium burning
2970:Nucleosynthesis
2960:
2842:
2751:
2478:
2357:
2306:Molecular cloud
2287:
2274:
2269:
2193:
2184:
2104:
2079:
2074:
2073:
2050:
2046:
1997:
1993:
1952:
1948:
1917:
1913:
1902:
1895:
1887:
1883:
1870:
1866:
1858:
1854:
1846:
1842:
1834:
1830:
1825:
1802:
1795:
1792:
1783:
1781:Rapid evolution
1744:
1740:
1723:
1720:
1719:
1688:
1685:
1684:
1649:
1646:
1645:
1614:
1611:
1610:
1609:) of the star:
1588:
1585:
1584:
1562:
1559:
1558:
1544:nuclear physics
1505:
1494:
1491:
1490:
1481:, the ratio of
1479:adiabatic index
1461:
1457:
1452:
1446:
1442:
1434:
1431:
1430:
1400:
1399:
1388:
1387:
1385:
1375:
1360:
1353:
1349:
1333:
1332:
1321:
1320:
1318:
1316:
1313:
1312:
1282:is set to one.
1259:
1256:
1255:
1254:of the matter,
1235:
1232:
1231:
1205:
1201:
1192:
1188:
1181:
1167:
1165:
1146:
1145:
1134:
1133:
1131:
1129:
1126:
1125:
1081:
1077:
1070:
1065:
1055:
1036:
1035:
1024:
1023:
1021:
1019:
1016:
1015:
984:
980:
978:
975:
974:
950:
946:
928:
924:
902:
901:
890:
889:
887:
885:
882:
881:
850:
847:
846:
824:
821:
820:
791:
787:
765:
764:
753:
752:
750:
748:
745:
744:
711:
708:
707:
682:
679:
678:
655:
651:
640:
638:
619:
618:
607:
606:
604:
602:
599:
598:
561:
550:
545:
534:
531:
530:
514:
511:
510:
482:
479:
478:
457:
455:
452:
451:
426:
423:
422:
397:
394:
393:
368:
365:
364:
339:
336:
335:
310:
307:
306:
298:In forming the
271:and that it is
261:
260:
259:
258:
257:
254:
245:
244:
243:
240:
231:
230:
229:
226:
217:
216:
215:
212:
201:
191:
145:
142:
129:
126:
59:
17:
12:
11:
5:
3803:
3793:
3792:
3787:
3782:
3765:
3764:
3762:
3761:
3749:
3738:
3735:
3734:
3732:
3731:
3726:
3721:
3716:
3711:
3706:
3701:
3696:
3695:
3694:
3689:
3688:
3687:
3682:
3666:
3664:
3660:
3659:
3657:
3656:
3651:
3646:
3645:
3644:
3639:
3629:
3624:
3619:
3614:
3609:
3604:
3599:
3598:
3597:
3592:
3591:
3590:
3580:
3575:
3570:
3565:
3560:
3558:Largest volume
3555:
3550:
3545:
3535:
3534:
3533:
3528:
3517:
3515:
3509:
3508:
3506:
3505:
3500:
3495:
3490:
3485:
3484:
3483:
3478:
3473:
3463:
3458:
3453:
3448:
3443:
3442:
3441:
3436:
3431:
3426:
3415:
3413:
3407:
3406:
3404:
3403:
3398:
3397:
3396:
3391:
3386:
3376:
3371:
3370:
3369:
3364:
3359:
3354:
3343:
3341:
3335:
3334:
3332:
3331:
3326:
3321:
3316:
3311:
3306:
3301:
3296:
3291:
3286:
3281:
3276:
3271:
3269:Magnetic field
3266:
3261:
3256:
3251:
3246:
3240:
3238:
3234:
3233:
3231:
3230:
3225:
3220:
3215:
3210:
3205:
3204:
3203:
3193:
3192:
3191:
3186:
3179:Accretion disk
3176:
3175:
3174:
3169:
3159:
3158:
3157:
3155:Alfvén surface
3152:
3150:Stellar corona
3147:
3142:
3137:
3127:
3125:Radiation zone
3122:
3121:
3120:
3115:
3105:
3099:
3097:
3091:
3090:
3088:
3087:
3082:
3081:
3080:
3075:
3070:
3065:
3060:
3050:
3045:
3040:
3035:
3030:
3025:
3020:
3015:
3010:
3005:
3000:
2995:
2990:
2985:
2980:
2974:
2972:
2966:
2965:
2962:
2961:
2959:
2958:
2953:
2948:
2943:
2938:
2933:
2932:
2931:
2926:
2923:
2915:
2914:
2913:
2908:
2903:
2898:
2893:
2888:
2883:
2878:
2873:
2863:
2858:
2852:
2850:
2844:
2843:
2841:
2840:
2835:
2834:
2833:
2823:
2818:
2817:
2816:
2811:
2810:
2809:
2804:
2794:
2784:
2783:
2782:
2772:
2767:
2761:
2759:
2753:
2752:
2750:
2749:
2747:Blue straggler
2744:
2743:
2742:
2732:
2727:
2726:
2725:
2715:
2714:
2713:
2708:
2703:
2698:
2693:
2688:
2683:
2678:
2673:
2663:
2658:
2657:
2656:
2651:
2646:
2636:
2635:
2634:
2624:
2623:
2622:
2617:
2612:
2602:
2597:
2596:
2595:
2590:
2585:
2575:
2570:
2565:
2560:
2559:
2558:
2553:
2543:
2542:
2541:
2536:
2531:
2526:
2521:
2516:
2511:
2505:Main sequence
2503:
2498:
2492:
2486:
2484:Classification
2480:
2479:
2477:
2476:
2475:
2474:
2469:
2459:
2454:
2449:
2444:
2439:
2434:
2429:
2424:
2423:
2422:
2420:Protoplanetary
2412:
2407:
2406:
2405:
2400:
2390:
2389:
2388:
2378:
2373:
2367:
2365:
2359:
2358:
2356:
2355:
2350:
2345:
2340:
2339:
2338:
2333:
2328:
2323:
2313:
2308:
2303:
2297:
2295:
2289:
2288:
2286:
2285:
2279:
2276:
2275:
2268:
2267:
2260:
2253:
2245:
2239:
2238:
2229:
2222:
2216:
2207:
2200:
2192:
2191:External links
2189:
2188:
2187:
2182:
2169:
2153:
2142:10.1086/304333
2118:(1): 329–340,
2107:
2102:
2089:
2078:
2075:
2072:
2071:
2044:
1991:
1986:10.1086/341728
1962:(1): 323–348,
1946:
1941:10.1086/177381
1911:
1893:
1881:
1864:
1852:
1840:
1827:
1826:
1824:
1821:
1820:
1819:
1814:
1808:
1807:
1791:
1788:
1782:
1779:
1753:
1750:
1747:
1743:
1739:
1736:
1733:
1730:
1727:
1707:
1704:
1701:
1698:
1695:
1692:
1668:
1665:
1662:
1659:
1656:
1653:
1633:
1630:
1627:
1624:
1621:
1618:
1598:
1595:
1592:
1583:) and center (
1572:
1569:
1566:
1512:
1508:
1504:
1501:
1498:
1483:specific heats
1464:
1460:
1455:
1449:
1445:
1441:
1438:
1427:
1426:
1415:
1409:
1397:
1382:
1379:
1373:
1367:
1364:
1359:
1356:
1352:
1348:
1342:
1330:
1263:
1239:
1228:
1227:
1216:
1208:
1204:
1200:
1195:
1191:
1187:
1184:
1179:
1176:
1173:
1170:
1164:
1161:
1155:
1143:
1104:
1103:
1092:
1084:
1080:
1076:
1073:
1069:
1062:
1059:
1054:
1051:
1045:
1033:
987:
983:
971:
970:
958:
953:
949:
945:
942:
939:
936:
931:
927:
923:
920:
917:
911:
899:
860:
857:
854:
834:
831:
828:
814:
813:
802:
799:
794:
790:
786:
783:
780:
774:
762:
715:
695:
692:
689:
686:
675:
674:
658:
654:
649:
646:
643:
637:
634:
628:
616:
564:
560:
557:
553:
548:
544:
541:
538:
518:
507:mean free path
486:
477:at a distance
466:
439:
436:
433:
430:
410:
407:
404:
401:
381:
378:
375:
372:
352:
349:
346:
343:
334:, temperature
323:
320:
317:
314:
255:
248:
247:
246:
241:
234:
233:
232:
227:
220:
219:
218:
213:
206:
205:
204:
203:
202:
190:
187:
143:
140:
127:
124:
58:
57:Heat transport
55:
15:
9:
6:
4:
3:
2:
3802:
3791:
3788:
3786:
3783:
3781:
3778:
3777:
3775:
3760:
3755:
3750:
3748:
3740:
3739:
3736:
3730:
3727:
3725:
3722:
3720:
3719:Intergalactic
3717:
3715:
3712:
3710:
3707:
3705:
3702:
3700:
3699:Galactic year
3697:
3693:
3690:
3686:
3683:
3681:
3678:
3677:
3676:
3673:
3672:
3671:
3668:
3667:
3665:
3661:
3655:
3652:
3650:
3647:
3643:
3640:
3638:
3635:
3634:
3633:
3630:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3596:
3593:
3589:
3586:
3585:
3584:
3581:
3579:
3578:Most luminous
3576:
3574:
3571:
3569:
3566:
3564:
3561:
3559:
3556:
3554:
3551:
3549:
3546:
3544:
3541:
3540:
3539:
3536:
3532:
3529:
3527:
3524:
3523:
3522:
3519:
3518:
3516:
3514:
3510:
3504:
3501:
3499:
3496:
3494:
3493:Proper motion
3491:
3489:
3486:
3482:
3479:
3477:
3474:
3472:
3469:
3468:
3467:
3464:
3462:
3459:
3457:
3456:Constellation
3454:
3452:
3449:
3447:
3444:
3440:
3437:
3435:
3432:
3430:
3427:
3425:
3424:Solar eclipse
3422:
3421:
3420:
3417:
3416:
3414:
3410:Earth-centric
3408:
3402:
3399:
3395:
3392:
3390:
3387:
3385:
3382:
3381:
3380:
3377:
3375:
3372:
3368:
3365:
3363:
3360:
3358:
3355:
3353:
3350:
3349:
3348:
3345:
3344:
3342:
3340:
3336:
3330:
3327:
3325:
3322:
3320:
3317:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3295:
3292:
3290:
3287:
3285:
3282:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3241:
3239:
3235:
3229:
3226:
3224:
3221:
3219:
3216:
3214:
3211:
3209:
3206:
3202:
3199:
3198:
3197:
3194:
3190:
3187:
3185:
3182:
3181:
3180:
3177:
3173:
3170:
3168:
3165:
3164:
3163:
3160:
3156:
3153:
3151:
3148:
3146:
3143:
3141:
3138:
3136:
3133:
3132:
3131:
3128:
3126:
3123:
3119:
3116:
3114:
3111:
3110:
3109:
3106:
3104:
3101:
3100:
3098:
3096:
3092:
3086:
3083:
3079:
3076:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3056:
3055:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3008:Alpha process
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2989:
2986:
2984:
2981:
2979:
2976:
2975:
2973:
2971:
2967:
2957:
2954:
2952:
2949:
2947:
2944:
2942:
2939:
2937:
2934:
2930:
2927:
2924:
2922:
2919:
2918:
2916:
2912:
2909:
2907:
2904:
2902:
2899:
2897:
2894:
2892:
2889:
2887:
2884:
2882:
2879:
2877:
2874:
2872:
2869:
2868:
2867:
2864:
2862:
2859:
2857:
2854:
2853:
2851:
2849:
2845:
2839:
2836:
2832:
2829:
2828:
2827:
2824:
2822:
2819:
2815:
2812:
2808:
2805:
2803:
2800:
2799:
2798:
2795:
2793:
2790:
2789:
2788:
2785:
2781:
2780:Helium planet
2778:
2777:
2776:
2773:
2771:
2770:Parker's star
2768:
2766:
2763:
2762:
2760:
2758:
2754:
2748:
2745:
2741:
2738:
2737:
2736:
2733:
2731:
2728:
2724:
2721:
2720:
2719:
2716:
2712:
2709:
2707:
2704:
2702:
2701:Lambda Boötis
2699:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2677:
2674:
2672:
2669:
2668:
2667:
2664:
2662:
2659:
2655:
2652:
2650:
2647:
2645:
2642:
2641:
2640:
2637:
2633:
2630:
2629:
2628:
2625:
2621:
2618:
2616:
2613:
2611:
2608:
2607:
2606:
2603:
2601:
2598:
2594:
2591:
2589:
2586:
2584:
2581:
2580:
2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2557:
2554:
2552:
2549:
2548:
2547:
2544:
2540:
2537:
2535:
2532:
2530:
2527:
2525:
2522:
2520:
2517:
2515:
2512:
2510:
2507:
2506:
2504:
2502:
2499:
2497:
2494:
2493:
2490:
2487:
2485:
2481:
2473:
2470:
2468:
2467:Superluminous
2465:
2464:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2421:
2418:
2417:
2416:
2413:
2411:
2408:
2404:
2401:
2399:
2396:
2395:
2394:
2391:
2387:
2384:
2383:
2382:
2379:
2377:
2374:
2372:
2371:Main sequence
2369:
2368:
2366:
2364:
2360:
2354:
2351:
2349:
2348:Hayashi track
2346:
2344:
2341:
2337:
2334:
2332:
2329:
2327:
2324:
2322:
2319:
2318:
2317:
2314:
2312:
2309:
2307:
2304:
2302:
2299:
2298:
2296:
2294:
2290:
2284:
2281:
2280:
2277:
2273:
2266:
2261:
2259:
2254:
2252:
2247:
2246:
2243:
2236:
2234:
2230:
2227:
2223:
2220:
2217:
2214:
2211:
2208:
2205:
2201:
2198:
2195:
2194:
2185:
2183:0-03-006228-4
2179:
2175:
2170:
2167:
2163:
2159:
2154:
2151:
2147:
2143:
2139:
2135:
2131:
2126:
2121:
2117:
2113:
2108:
2105:
2103:0-387-20089-4
2099:
2095:
2090:
2086:
2081:
2080:
2067:
2063:
2059:
2055:
2048:
2040:
2036:
2032:
2028:
2024:
2020:
2015:
2010:
2006:
2002:
1995:
1987:
1983:
1979:
1975:
1970:
1965:
1961:
1957:
1950:
1942:
1938:
1934:
1930:
1926:
1922:
1915:
1908:
1907:
1900:
1898:
1890:
1885:
1878:
1874:
1868:
1861:
1856:
1849:
1844:
1837:
1832:
1828:
1818:
1815:
1813:
1810:
1809:
1805:
1799:
1794:
1787:
1778:
1776:
1771:
1770:of the star.
1769:
1751:
1748:
1745:
1741:
1737:
1731:
1725:
1705:
1702:
1696:
1690:
1682:
1666:
1663:
1657:
1651:
1631:
1628:
1622:
1616:
1596:
1593:
1590:
1570:
1567:
1564:
1556:
1551:
1549:
1545:
1541:
1537:
1533:
1528:
1526:
1510:
1506:
1502:
1499:
1496:
1488:
1484:
1480:
1462:
1458:
1453:
1447:
1443:
1439:
1436:
1413:
1407:
1395:
1380:
1377:
1371:
1365:
1362:
1357:
1354:
1350:
1346:
1340:
1328:
1311:
1310:
1309:
1307:
1303:
1300:
1296:
1295:mixing length
1292:
1288:
1283:
1281:
1277:
1261:
1253:
1237:
1214:
1206:
1202:
1198:
1193:
1189:
1185:
1182:
1177:
1174:
1171:
1168:
1162:
1159:
1153:
1141:
1124:
1123:
1122:
1120:
1119:main sequence
1115:
1113:
1109:
1090:
1082:
1078:
1074:
1071:
1067:
1060:
1057:
1052:
1049:
1043:
1031:
1014:
1013:
1012:
1010:
1005:
1003:
985:
981:
951:
947:
943:
940:
934:
929:
925:
921:
918:
915:
909:
897:
880:
879:
878:
877:
872:
858:
855:
852:
832:
829:
826:
818:
800:
797:
792:
788:
784:
781:
778:
772:
760:
743:
742:
741:
740:
738:
733:
729:
713:
690:
684:
656:
652:
647:
644:
641:
635:
632:
626:
614:
597:
596:
595:
593:
589:
585:
583:
577:
558:
546:
542:
539:
536:
516:
508:
504:
500:
484:
464:
434:
428:
405:
399:
392:, luminosity
376:
370:
347:
341:
318:
312:
305:
301:
296:
294:
290:
286:
282:
278:
274:
270:
266:
252:
238:
224:
210:
200:
196:
186:
183:
181:
177:
173:
169:
165:
161:
158:
154:
150:
146:
136:
134:
130:
121:
116:
114:
113:main sequence
109:
107:
102:
98:
93:
91:
87:
83:
79:
70:
66:
64:
54:
52:
48:
44:
40:
36:
32:
26:
21:
3622:White dwarfs
3612:Brown dwarfs
3595:Most distant
3543:Most massive
3521:Proper names
3481:Photographic
3434:Solar System
3412:observations
3339:Star systems
3162:Stellar wind
3145:Chromosphere
3118:Oscillations
3094:
2998:Helium flash
2848:Hypothetical
2826:X-ray binary
2765:Compact star
2600:Bright giant
2353:Henyey track
2331:Herbig Ae/Be
2231:
2197:opacity code
2173:
2157:
2115:
2111:
2093:
2084:
2057:
2053:
2047:
2004:
2000:
1994:
1959:
1955:
1949:
1924:
1920:
1914:
1905:
1884:
1867:
1855:
1843:
1831:
1812:Scale height
1804:Stars portal
1784:
1772:
1552:
1547:
1535:
1529:
1428:
1294:
1284:
1229:
1116:
1107:
1105:
1006:
972:
875:
873:
815:
735:
727:
676:
580:
578:
299:
297:
269:steady state
262:
184:
137:
120:solar masses
117:
110:
94:
90:white dwarfs
75:
60:
30:
29:
3675:Brown dwarf
3451:Circumpolar
3329:Kraft break
3309:Color index
3284:Metallicity
3244:Designation
3213:Cosmic dust
3135:Photosphere
2901:Dark-energy
2876:Electroweak
2861:Black dwarf
2792:Radio-quiet
2775:White dwarf
2661:White dwarf
2311:Bok globule
1850:, Tbl. 1.1)
1009:white dwarf
817:Integrating
289:temperature
176:ultraviolet
3774:Categories
3637:Candidates
3632:Supernovae
3617:Red dwarfs
3476:Extinction
3264:Kinematics
3259:Luminosity
3237:Properties
3130:Atmosphere
3028:Si burning
3018:Ne burning
2956:White hole
2929:Quasi-star
2856:Blue dwarf
2711:Technetium
2627:Hypergiant
2605:Supergiant
1823:References
1287:turbulence
1278:, and the
293:luminosity
193:See also:
182:envelope.
168:convective
78:convection
39:luminosity
3568:Brightest
3466:Magnitude
3446:Pole star
3367:Symbiotic
3362:Eclipsing
3294:Starlight
3095:Structure
3085:Supernova
3078:Micronova
3073:Recurrent
3058:Symbiotic
3043:p-process
3038:r-process
3033:s-process
3023:O burning
3013:C burning
2993:CNO cycle
2936:Gravastar
2472:Hypernova
2462:Supernova
2437:Dredge-up
2410:Blue loop
2403:super-AGB
2386:Red clump
2363:Evolution
2321:Protostar
2301:Accretion
2293:Formation
2014:0711.2590
1927:: 943–+,
1862:, §2.2.1)
1838:, §5.1.1)
1497:γ
1487:ideal gas
1437:γ
1366:γ
1358:−
1306:adiabatic
1302:ideal gas
1299:monatomic
1262:σ
1238:κ
1199:σ
1186:π
1175:ρ
1172:κ
1163:−
1075:π
1053:−
1002:neutrinos
986:ν
982:ϵ
952:ν
948:ϵ
944:−
941:ϵ
935:ρ
922:π
798:ρ
785:π
648:ρ
636:−
556:∇
540:≪
537:λ
517:λ
429:ϵ
313:ρ
199:Polytrope
180:radiative
164:CNO cycle
51:elemental
3747:Category
3642:Remnants
3538:Extremes
3498:Parallax
3471:Apparent
3461:Asterism
3439:Sunlight
3389:Globular
3374:Multiple
3299:Variable
3289:Rotation
3249:Dynamics
3140:Starspot
2814:Magnetar
2757:Remnants
2573:Subgiant
2546:Subdwarf
2398:post-AGB
2150:16835178
2039:16150778
1790:See also
1297:. For a
285:pressure
153:hydrogen
144:☉
128:☉
45:and the
3714:Gravity
3663:Related
3583:Nearest
3531:Chinese
3379:Cluster
3352:Contact
3189:Proplyd
3063:Remnant
2951:Blitzar
2925:Hawking
2881:Strange
2831:Burster
2787:Neutron
2740:Extreme
2691:He-weak
2336:T Tauri
2162:Bibcode
2130:Bibcode
2077:Sources
2062:Bibcode
2019:Bibcode
1974:Bibcode
1929:Bibcode
1891:, §5.1)
1879:, §7.1)
1477:is the
1274:is the
1252:opacity
1250:is the
1110:is the
730:is the
592:gravity
503:photons
304:density
172:ionized
106:opacity
101:buoyant
3704:Galaxy
3692:Planet
3680:Desert
3588:bright
3526:Arabic
3347:Binary
3167:Bubble
2891:Planck
2866:Exotic
2802:Binary
2797:Pulsar
2735:Helium
2696:Barium
2639:Carbon
2632:Yellow
2620:Yellow
2593:Yellow
2432:PG1159
2180:
2148:
2100:
2037:
1681:finite
1429:where
1230:where
1106:where
973:where
677:where
281:matter
160:fusion
157:helium
84:, but
41:, the
3709:Guest
3513:Lists
3394:Super
3048:Fusor
2921:Black
2906:Quark
2886:Preon
2871:Boson
2807:X-ray
2723:Shell
2676:Ap/Bp
2578:Giant
2496:Early
2442:OH/IR
2272:Stars
2226:BaSTI
2146:S2CID
2120:arXiv
2035:S2CID
2009:arXiv
1964:arXiv
1536:codes
265:model
151:, so
43:color
3384:Open
3279:Mass
3103:Core
3053:Nova
2946:Iron
2896:Dark
2706:Lead
2686:HgMn
2681:CEMP
2610:Blue
2583:Blue
2501:Late
2283:List
2224:The
2202:The
2178:ISBN
2098:ISBN
726:and
291:and
283:and
197:and
155:-to-
80:and
35:star
3685:Sub
3419:Sun
2838:SGR
2615:Red
2588:Red
2138:doi
2116:484
2058:162
2027:doi
2005:316
1982:doi
1960:576
1937:doi
1925:464
25:Sun
3776::
2718:Be
2671:Am
2654:CH
2649:CN
2568:OB
2563:WR
2144:,
2136:,
2128:,
2114:,
2056:,
2033:,
2025:,
2017:,
2003:,
1980:,
1972:,
1958:,
1935:,
1923:,
1896:^
1683:;
1489:,
1183:64
1114:.
576:.
509:,
92:.
65:.
2911:Q
2730:B
2644:S
2556:B
2551:O
2539:M
2534:K
2529:G
2524:F
2519:A
2514:B
2509:O
2264:e
2257:t
2250:v
2235:,
2215:.
2164::
2140::
2132::
2122::
2068:.
2064::
2041:.
2029::
2021::
2011::
1988:.
1984::
1976::
1966::
1943:.
1939::
1931::
1752:f
1749:f
1746:e
1742:T
1738:=
1735:)
1732:R
1729:(
1726:T
1706:M
1703:=
1700:)
1697:R
1694:(
1691:m
1667:0
1664:=
1661:)
1658:0
1655:(
1652:m
1632:0
1629:=
1626:)
1623:R
1620:(
1617:P
1597:0
1594:=
1591:r
1571:R
1568:=
1565:r
1511:3
1507:/
1503:5
1500:=
1463:v
1459:c
1454:/
1448:p
1444:c
1440:=
1414:,
1408:r
1403:d
1396:P
1391:d
1381:P
1378:T
1372:)
1363:1
1355:1
1351:(
1347:=
1341:r
1336:d
1329:T
1324:d
1215:,
1207:3
1203:T
1194:2
1190:r
1178:l
1169:3
1160:=
1154:r
1149:d
1142:T
1137:d
1108:k
1091:,
1083:2
1079:r
1072:4
1068:l
1061:k
1058:1
1050:=
1044:r
1039:d
1032:T
1027:d
969:,
957:)
938:(
930:2
926:r
919:4
916:=
910:r
905:d
898:l
893:d
859:R
856:=
853:r
833:0
830:=
827:r
801:.
793:2
789:r
782:4
779:=
773:r
768:d
761:m
756:d
739::
728:G
714:r
694:)
691:r
688:(
685:m
673:,
657:2
653:r
645:m
642:G
633:=
627:r
622:d
615:P
610:d
584::
563:|
559:T
552:|
547:/
543:T
485:r
465:r
460:d
438:)
435:r
432:(
409:)
406:r
403:(
400:l
380:)
377:r
374:(
371:P
351:)
348:r
345:(
342:T
322:)
319:r
316:(
149:K
141:M
125:M
122:(
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