Stellar Models ASTR 2110 Sarazin

Transcription

1 Stellar Models ASTR 2110 Sarazin

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3 Jansky Lecture Tuesday, October 24 7 pm Room 101, Nau Hall Bernie Fanaroff Observing the Universe From Africa

4 Trip to Conference Away on conference in the Netherlands next week. Molly Finn, TA, will be our guest lecturer

5 Stellar Models ASTR 2110 Sarazin

6 Five Equations dp dr = GM(r)ρ r 2 Hydrostatic equilibrium dm dr = 4πr2 ρ Mass dl dr = 4πr2 ερ Thermal equilibirum dt dr = min " $ # $ % $ 3κρ 1 64πσ r 2 T L(r) T P dp dr radiation convection P = ρkt µm p + P rad + P deg Equation of state Energy transport

7 Boundary Conditions Take radius r as independent variable P(r), T(r), ρ(r), L(r), M(r) 0 r R * Boundary Conditions: Center (r = 0): M(0) = 0, L(0) = 0 Surface (r = R * ): M(R * ) = M *, P(R * ) = 0, ρ(r * ) = 0 Two Problems: 4 differential equations, 5 boundary conditions What is R *?

8 Boundary Conditions Change independent variable to mass M r(m ), P(M ), T(M ), ρ(m ), L(M ), 0 M M * dm dr = dr 4πr2 ρ dm = 1 4πr 2 ρ dx dm = dx dr dr dm

9 Five (New) Equations dr dm = 1 4πr 2 ρ radius (formerly mass) dp dm = GM(r) Hydrostatic equilibrium 4πr 4 dl dm = ε Thermal equilibirum dt dm = min " $ # $ % $ 3κ 1 256π 2 σ r 4 T L(r) T P dp dm P = ρkt µm p + P rad + P deg Equation of state radiation convection Energy transport

10 Boundary Conditions Center (M = 0): r(0) = 0, L(0) = 0 Surface (M = M * ): P(M * ) = 0, ρ(m * ) = 0 Better! 4 differential equations 4 boundary conditions R * is derived

11 Vogt-Russell Theorem Necessary inputs: Mass of star M * Mean particle mass μ, opacity κ, energy production ε Depend on ρ, T, composition Vogt-Russell Theorem: Star is uniquely determined by mass M * & composition

12 Solar Model ρ c = 147 gm/cm 3 T c = 15 million K Burning hydrogen in core ~ 20% of radius Radiative zone ~ inner 85% of radius Convective zone ~ outer 15% of radius ρ (gm/cm 3 ) T (10 6 K)

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14 Main Sequence Choice of composition: Try mainly hydrogen and helium Surface of Sun and most other stars Interstellar gas è what stars form from Vary mass M * Reproduce main sequence (normal stars) All burning H in their cores Main Sequence = stars made of hydrogen burning H in their cores

15 Main Sequence high mass mass low mass

16 Hydrogen: Most abundant element Best nuclear fuel Burned first Main Sequence Stars spend most of life on main sequence, only leave it when they start to die

17 Sub-Stellar Objects Stars Brown Dwarfs Planets Mass M M M M M M M 78 M J 13 M J M 78 M J 13 M J Fusion? Burn H Later He, C, Burn D = 2 H deuterium Short time, then cool Degeneracy pressure No fusion Star M 100 M è blown apart by radiation pressure while forming?

18 Sub-Stellar Objects Define star as self-gravitating object which can fuse 1 H (normal hydrogen) M > M Define planet as self-gravitating object which never has any fusion? M M < = 13 M J Must planets be formed orbiting stars? Free floating planets? Brown dwarfs intermediate

19 Brown Dwarfs Never hot enough to fuse 1 H (normal hydrogen) Hot enough to fuse 2 H (deuterium), but 2 H (deuterium) rare (2 x 10-5 than of 1 H) Makes less energy Burn deuterium for a short time, then cool down Supported by electron degeneracy pressure Like white dwarfs Predicted in early 1960 s, discovered in 1994

20 Brown Dwarfs

21 Brown Dwarf Binary Brown dwarves have been found: In binaries With planets Formed just like stars(?)

22 Sub-Stellar Objects Stars Brown Dwarfs Planets Mass M M M M M M M 78 M J 13 M J M 78 M J 13 M J Fusion? Burn H Later He, C, Burn D = 2 H deuterium Short time, then cool Degeneracy pressure No fusion Star M 100 M è blown apart by radiation pressure while forming?

23 Stellar Evolution ASTR 2110 Sarazin HR Diagram vs. Mass

24 Stellar Evolution Evolution = aging of stars 1. Massive stars evolve first L M 3 E nucl 0.008Mc 2 /10 fraction of mass in core t * E nucl / L M 2 O star, M ~ 30 M t * ~ years Sun, M = 1 M t * years M 0.8 M t * 1.4 x years = age of Universe Explains why in clusters, top of main sequence is missing

25 Stellar Evolution SUV: bigger gas tank, but won t drive as far before refueling

26 Stellar Evolution 1. Massive stars evolve first 2. Stars are not completely mixed, composition changes only at center Luminosity Or Absolute Mag mixed He real H Temperature

27 Stellar Evolution Stars start when fusion of H begins Protostars

28 Low Mass Star Take Sun, 1 M star A-B) Main Sequence, H-burning in core (V) 4H è He in core Mean mass μ increases k T c (GM/R) μ m p T c increases slowly L increases slowly G H MS A B E C F D

29 Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted Low Mass Star M G E F D MS A B C H

30 Low Mass Star Take Sun, 1 star A. Main Sequence, H-burning in core (V) B-C. Core H Exhausted (IV) Energy leaves core Core contracts Energy can t escape star quickly Total energy ~ constant Envelope expands T eff drops M G H MS A B E C F D

31 Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C. Degenerate He Core (III) Core ~ 10-2 ~ R earth Core, L = 0, dt/dr = 0 T ~ const. in core T c high T (edge of core) high H around core Low Mass Star M R H burning in shell around core

32 Low Mass Star Take Sun, 1 M star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) H, high T è high L P c very high è push out envelope Giant star, R ~ AU Shell hot, photosphere cool è convective envelope G H MS A B E C F D

33 Red Giant Stars

34 Red Giant Stars

35 Red Giant Stars

36 Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash T c è >10 8 K He starts to burn in core Degenerate è very rapid Core expands rapidly Envelope contracts Low Mass Star M G H MS A B E C F He Flash D

37 Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash E. Horizontal Branch He Core, H Shell Burning Like MS, but He Burning in Core H Burning in Shell High L Short Lifetime Low Mass Star M G H MS A B E C F D

38 Take Sun, 1 star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash E. Horizontal Branch He Core, H Shell Burning F. Asymptotic Giant Branch = Supergiant (I) Like giant, but Low Mass Star M H burning shell, He burning shell Inert carbon core G H MS A B E C F D

39 Take Sun, 1 Low Mass Star M star A. Main Sequence, H-burning in core (V) B. Core H Exhausted (IV) C-D. Red Giant = H Shell Burning (III) D. Helium Flash E. Horizontal Branch He Core, H Shell Burning F. Asymptotic Giant Branch = Supergiant (I) Never gets hot enough to burn C Star must die, but how?

40 Low Mass Star - Death G Asymptotic Giant Branch = Supergiant (I) Red supergiant Inert carbon/oxygen core E F D MS A B C H

41 M 8 M A) Main Sequence, H-burning in core (V) CNO burning of H Convective Core B) Red Supergiant (I) High Mass Star Core H exhausted, degenerate core, H shell burning Repeat for each fusion element up to Iron H è He è C è O è Fe

42 High Mass Star

43 High Mass Star

44 M 8 M A) Main Sequence, H-burning in core (V) CNO burning of H Convective Core B) Red Supergiant (I) High Mass Star Core H exhausted, degenerate core, H shell burning Repeat for each fusion element up to Iron H è He è C è O è Fe C) Ends as Red Supergiant, Inert Fe core, many burning shells

45 High Mass Star

46 M 8 M A) Main Sequence, H-burning in core (V) CNO burning of H Convective Core B) Red Supergiant (I) High Mass Star Core H exhausted, degenerate core, H shell burning Repeat for each fusion element up to Iron H è He è C è O è Fe C) Ends as Red Supergiant, Inert Fe core, many burning shells Fe è no fusion energy è Star must die

47 A) Main Sequence, H-burning in core (V) B) Red Supergiant (I) C) Ends as Red Supergiant, Inert Fe core, many burning shells Complication: High radiation pressure, very strong stellar winds Can lose a significant fraction of mass Wolf-Rayet (WR) stars: High Mass Star Entire envelope blown away Expose He or C or O cores (Still, Fe è no fusion energy è Star must die)

48 High Mass Star - Death A) Inert Fe core, many burning shells B) Either Red Supergiant or blue WR star