NLTE wind models of A supergiants cka 1 Ji Krti r at 2 Ji Kub - PowerPoint PPT Presentation

NLTE wind models of A supergiants cka 1 Jiˇ ı Krtiˇ r´ at 2 Jiˇ ı Kub´ r´ 1 Masaryk University Brno, Czech Republic 2 Astronomical Institute, Ondˇ rejov, Czech Republic IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 1

Stellar wind of A supergiants • similar properties as stellar wind of OB stars • accelerated by the absorption of radiation mainly in the resonance lines of C, N, O or Fe • the domain of A supergiants seems to be overlooked by wind theorists up to now IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 2

NLTE models of stellar wind (Krtiˇ cka & Kubát 2004) • spherically symmetric stationary wind models • radiative force calculated using level occupation numbers obtained from the solution of statistical equilibrium equations • wind density, velocity and temperature calculated as the solution of hydrodynamic equations • enable prediction of ˙ M , v ∞ IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 3

Process of model calculation radiative transfer equation IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 4

Process of model calculation radiative transfer equation NLTE equations IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 4

Process of model calculation radiative transfer equation NLTE equations IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 4

Process of model calculation radiative transfer equation NLTE equations hydrodynamic equations IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 4

Process of model calculation radiative transfer equation NLTE equations hydrodynamic equations IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 4

Continuum radiative transfer + 1 − µ 2 µ∂I ( r,ν,µ ) ∂I ( r,ν,µ ) = η − χI ( r,ν,µ ) , ∂r r ∂µ • wind motion neglected • I ( r,ν,µ ) is the specific intensity of radiation • µ = cos θ is the direction cosine, ν is the frequency • χ ( r,ν,µ ) , η ( r,ν,µ ) are the emissivity and absorption coefficients • solution obtained using Feautrier method IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 5

Line radiative transfer Solution using Sobolev approximation ¯ J ij = (1 − β ) S ij + β c I c , � ∞ � 1 • ¯ J ij = 0 d ν − 1 d µ φ ij ( ν ) I ( r,ν,µ ) is the mean intensity, φ ij ( ν ) is the line profile • I c is the specific intensity of star, � 1 � 1 − 1 d µ 1 − e − τµ µ ∗ dµ 1 − e − τµ β = 1 , β c = 1 , τ µ τ µ 2 2 ∗ /r 2 � 1 / 2 , � 1 − R 2 µ ∗ = • source function S ij = η ij /χ ij . IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 6

Statistical equilibrium equations Occupation number N i of atoms in the state i is given by the solution of � � N j P ji − N i P ij = 0 . j � = i j � = i • P ij are rates of all processes that transfer an atom from a given state i to state j , • radiative excitation and deexcitation, radiative ionization and recombination and corresponding collisional processes contribute to P ij IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 7

Included ionization states H I - II He I - III C I - IV N I - IV O I - IV Ne I - IV Na I - III Mg II - IV Al I - V Si II - V S II - V Ar III - IV Ca II - IV Fe II - V Ni II - V • model atoms are taken mostly from TLUSTY code (Hubeny & Lanz 1992, 1995) • the original set is extended using data from Opacity Project and Iron Project IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 8

Hydrodynamic equations • continuity equation d = 0 ⇒ ˙ r 2 ρv r M = 4 πr 2 ρv r = const. � � d r • ρ is the wind density • v r is the radial velocity IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 9

Hydrodynamic equations • equation of motion d v r d r = g rad − g − 1 d a 2 ρ � � v r ρ d r • g is the gravity acceleration • a is the isothermal sound speed • g rad = g rad lines + g rad is the radiative el acceleration � 1 lines = 8 π v r � 1 − e − τ µ � g rad 1 + σµ 2 � � � νH c d µ µ ρc 2 r µ c lines IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 10

Hydrodynamic equations • energy equation 2 v r ρ d a 2 d r + a 2 ρ 3 d = Q rad r 2 v r � � r 2 d r • Q rad is the radiative heating/cooling calculated using the thermal balance of electrons method (Kubát et al. 1999) IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 11

Stellar wind of HD 12953 • A1Iae supergiant with parameters T eff = 9 100 K, R = 145 R ⊙ and M = 9 . 7 M ⊙ (Kudritzki et al. 1999) IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 12

Stellar wind of HD 12953 • A1Iae supergiant with parameters T eff = 9 100 K, R = 145 R ⊙ and M = 9 . 7 M ⊙ (Kudritzki et al. 1999) • observed wind mass-loss rate is M = 4 . 3 × 10 − 7 M ⊙ year − 1 and observed wind ˙ terminal velocity is v ∞ = 150 km s − 1 (Kudritzki et al. 1999) IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 12

Stellar wind of HD 12953 • A1Iae supergiant with parameters T eff = 9 100 K, R = 145 R ⊙ and M = 9 . 7 M ⊙ (Kudritzki et al. 1999) • observed wind mass-loss rate is M = 4 . 3 × 10 − 7 M ⊙ year − 1 and observed wind ˙ terminal velocity is v ∞ = 150 km s − 1 (Kudritzki et al. 1999) • calculated wind parameters are M = 1 . 3 × 10 − 7 M ⊙ year − 1 and ˙ v ∞ = 140 km s − 1 IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 12

Wind model of HD 12953 160 10500 observed terminal velocity → 10000 140 9500 120 9000 100 8500 v r [km s -1 ] T [K] 80 8000 7500 60 7000 40 6500 HD 12953 20 6000 0 5500 1 2 3 4 5 1 2 3 4 5 r/R * r/R * IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 13

Conclusions • we presented NLTE code which is capable to calculate wind models of A supergiants, • predicted wind parameters agree relatively well with observed parameters of HD 12953, • model improvements are necessary (e.g. consistent radiative transfer, inclusion of X-rays, etc.) • more model testing is necessary. IAU Symposium No. 224 “The A-Star Puzzle” , Poprad, Slovakia, July 8-13, 2004 – p. 14