Stellar structure and evolution Pierre Hily-Blant 2017-18 April 25, 2018 IPAG pierre.hily-blant@univ-grenoble-alpes.fr, OSUG-D/306
10 Protostars and Pre-Main-Sequence Stars 10.1. Introduction 10 Protostars and Pre-Main-Sequence Stars Introduction Protostars Deuterium burning stage Hayashi contraction
10 Protostars and Pre-Main-Sequence Stars 10.1. Introduction 3 Summary of the previous episodes From molecular clouds to protostars Jeans criterium: a cloud of mass M > M J is unstable Pre-stellar cores embedded in molecular clouds: isothermal, Bonnor-Ebert sphere Density contrast above threshold: quasi-static, isothermal, contraction Central density too high: opacity increases, adiabiatic First Larson core in hydrostatic equilibrium Mass increases, H 2 dissociation: second, isothermal, collapse Second Larson core: adiabatic protostars hydrostatic equilibrium, surrounded by 1st core and infalling (supersonic) enveloppe
10 Protostars and Pre-Main-Sequence Stars 10.1. Introduction 4 Overview Not yet on the main-sequence Upper right corner: large radii, and low effective temperature Where to stars appear in the HR diagram? What path do they follow from protostars to MS? Time for protostars to reach the MS? What is the effect of accretion?
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars 10 Protostars and Pre-Main-Sequence Stars Introduction Protostars Deuterium burning stage Hayashi contraction
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars The main accretion phase 7 Structure of a protostar From a prestellar core to the protostar Prestellar core embedded in a molecular cloud Inside-out collapse and first Larson core 1st core: H 2 dissociation at T 2000 K, constant 1st core collapses (M increases isothermally)
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars The main accretion phase 8 Starting point: protostar in the main accretion phase Larson (1969) 2nd core in hydrostatic equilibrium: atomic hydrogen R 2 few R, M 2 10 3 0.1 M, ρ 2 10 2 g cm 3, T 2 few 10 4 K Mass grows fast by accretion of the envelope: main accretion phase Falling material free-fall (supersonic) When M env M : PMS
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars The main accretion phase 9 Protostars: mass accretion Initial condition: main accretion phase Initially: M = 0.1 M, R = 1.5, 2.5, 3.5 R Initial conditions quickly lost Constant accretion rate: Ṁ = 10 5 M yr 1 Protostar mass increases fast Final state: protostar M = M, R = 5R
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars The main accretion phase 10 Main accretion phase: energetics Supersonic infall on the protostar: R = 5R, M = 1 M v ff = (2GM /R ) 1/2 = 280 km s 1 (M / M ) 1/2 (R /5R ) 1/2 kinetic energy (grav.): radiation plus internal energy (heat + chemical changes) Ionization of H, He, and dissociation of H 2 : negligible Radiative losses are important (radius would be 10 TTauri) Moreover: T too low for nuclear ignition Conclusion: most of grav. energy goes into heat and radiation Partitioning: complicated problem; outcome is 50/50 L rad 1/2L acc = 30L (M/ M )(R /5R )(Ṁ/ 10 5 M yr 1 ) Duration: 10 5 yr
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars Protostellar radiation 11 Main accretion phase: infrared luminosity During this phase, contributions from nuclear fusion and quasi-static contraction in the core are L acc. protostar mass-gaining star with L L acc (IR) L acc 4πR 2 σt 4 eff T eff 8000K(Ṁ/ 10 5 M yr 1 ) 1/4 (M / M ) 1/4 (R /5R ) 3/4 Radiation escapes the cloud in the infrared (optically invisible, not in the HR diagram) R phot 10 AU, T phot 300 K
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars Protostellar radiation 12 Protostars envelope: temperature structure Central protostar: L = 26L M = 1 M, Ṁ = 2 10 6 M yr 1 Opacity gap (r = 0.2 AU, T d = 1500 K) κ d 4.8(T /300) 0.8 cm 2 /g (at T 100 600 K) ρ env Ṁr 3/2 /(4π 2GM Envelope: becomes optically thin to dust beyond T 300 K T phot 30 100 K and Wien s law, λ 30 100µm
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars Protostellar radiation 13 Infrared protostellar radiation
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars Protostellar radiation 14 Infrared protostellar radiation
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars Protostellar radiation 15 Infrared protostellar radiation
10 Protostars and Pre-Main-Sequence Stars 10.2. Protostars Protostellar radiation 16 Structure of a protostar Typical values for a M 1 M protostar outer envelope: 0.1 pc dust photosphere: 10 AU dust destruction front: 1 AU (T 1500K) protostar (2nd core): R 5R = 0.02 AU
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 10 Protostars and Pre-Main-Sequence Stars Introduction Protostars Deuterium burning stage Hayashi contraction
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 18 Convection raise a cell fluid in grav. field: initial: subscript 0; upper location: subscript 1 if (ρ int ) 1 < (ρ ext ) 1, convection; if (ρ int ) 1 > (ρ ext ) 1 : stable quick, adiabatic rise: specific entropy s is constant If s(m) increasing function: (s int ) 1 < (s ext ) 1 pressure equilibrium: (p int ) 1 = (p ext ) 1 ( ρ/ s) p < 0: (ρ int ) 1 > (ρ ext ) 1 Condition for stability: s/ M > 0
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 19 Deuterium burning: convection M /R rises fast; T also rises (virial) When T reaches 10 6 K, D-burning sets in: 2 H + 1 H 3 He + γ + 5.5MeV Large opacity in the center: radiation can not evacuate the generated heat s/ M < 0, and s/ t > 0 Interior becomes convective Interior is heated by: accretion shock (3/4) and deuterium burning (1/4)
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 20 Deuterium burning: convective energy transport Luminosity is still dominated by accretion Deuterium burning contributes to internal heating Convection: fresh D from infalling envelope sustains D-burning steady-state: L D Ṁe D 12L e D = [D/H]X E D /m a 7.4 10 9 J/g M 0.2 M, T c > 10 6 K: rising hot, underdense, fluid Rate of D-burning T 11.8 : T constant, R and M varying accordingly R 3R (M/0.5 M )
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 21 End of deuterium burning values: M ( M ) Arrow: radiative barrier, M r = 1.7 M Note L crit the max. luminosity that can be transported radiatively If the internal luminosity L int > L crit : convective transport of heat L crit = 64πGM r σt 3 /3κ d ( T / P) s... we can show that L crit M 11/2 R 1/2 L int cst, while L crit increases sharply Where L int = L crit, radiative barrier: convection is lost no fresh D: L int decreases, convection stops everywhere
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 22 Towards hydrogen burning continuing collapse: D accumulates outside the radiative barrier central region: M /R rises fast, hence T M /R also rises T reaches 10 6 K in the D-shell: D-shell burning
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 23 Towards hydrogen burning (a) D burning in the center (b) L crit reaches L int : radiative barrier (c) Protostar + envelope: radiatively stable (d) D-shell burning: convection propagates outwards
10 Protostars and Pre-Main-Sequence Stars 10.3. Deuterium burning stage 24 Mass-radius evolution: summary Evolutionary path (time increases from left to right) First circle: Fully convective protostar Second circle: Radiative barrier Steep increase of R due to heating by D-burning L crit increases: convection and burning shell move outwards Eventually: star is (almost) fully radiatively stable L int 1L (M / M ) 11/2 (R /R ) 1/2
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 10 Protostars and Pre-Main-Sequence Stars Introduction Protostars Deuterium burning stage Hayashi contraction
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 26 Towards the MS: Hayashi and Henyey tracks
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 27 Hayashi contraction Accretion luminosity L acc 30 100L Temperature in the protostar T c 10 4 K
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 28 Energy transport PMS: L int < L Convective transport MS: L int = L Radiative equilibrium
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 29 Timescales τ KH = GM 2 /(R L )
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 30 Overview Hayashi track isothermal collapse of unstable pre-stellar core formation of a hydrostatic core + gaseous envelope density, hence opacity, increases in the envelope: L decreases interior is convective contraction, downwards, vertical: L decreases at constant T accretion phase: infalling envelope (M env M ) luminosity due to accretion (L accr = GM Ṁ /R ) outflows and circumstellar disks (angular momentum) τ KH R/c s : quasi-static contraction when M reaches its final mass: PMS
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 31 Overview Henyey track Radiative transport of the energy L decreases, (T ) decreases: radiative core Luminosity is due to contraction (R decreases) T increases (L = 4πR 2 σt 4 ) When T is large enough, hydrogen iginites, contraction halts PMS reaches the ZAMS
10 Protostars and Pre-Main-Sequence Stars 10.4. Hayashi contraction 32 Timescales τ KH = GM 2 /(R L )
10 Protostars and Pre-Main-Sequence Stars 10.5. Hayashi contraction 33 Bibliography Larson, R. B. 1969, MNRAS, 145, 271