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

NLTE wind models of A supergiants

Jiˇ r´ ı Krtiˇ cka1 Jiˇ r´ ı Kub´ at2

1Masaryk University Brno, Czech Republic 2Astronomical 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
• verlooked 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
• ccupation 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

µ∂I(r,ν,µ) ∂r + 1 − µ2 r ∂I(r,ν,µ) ∂µ = η − χI(r,ν,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 ¯ Jij = (1 − β)Sij + βcIc,

• ¯

Jij = ∞

0 dν

1

−1 dµ φij(ν)I(r,ν,µ) is the mean

intensity, φij(ν) is the line profile

• Ic is the specific intensity of star,

β = 1

2

1

−1 dµ 1−e−τµ τµ

, βc = 1

2

1

µ∗ dµ 1−e−τµ τµ

, µ∗ =

• 1 − R2

∗/r21/2,

• source function Sij = ηij/χij.

IAU Symposium No. 224 “The A-Star Puzzle”, Poprad, Slovakia, July 8-13, 2004 – p. 6

Statistical equilibrium equations

Occupation number Ni of atoms in the state i is given by the solution of

• j=i

NjPji − Ni

• j=i

Pij = 0.

• Pij 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 Pij

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 dr

• r2ρvr
• = 0 ⇒ ˙

M = 4πr2ρvr = const.

• ρ is the wind density
• vr 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

vr dvr dr = grad − g − 1 ρ d dr

• a2ρ
• g is the gravity acceleration
• a is the isothermal sound speed
• grad = grad

lines + grad el

is the radiative acceleration grad

lines = 8π

ρc2 vr r

• lines

νHc 1

µc

dµ µ

• 1 + σµ2

1 − e−τµ

IAU Symposium No. 224 “The A-Star Puzzle”, Poprad, Slovakia, July 8-13, 2004 – p. 10

Hydrodynamic equations

• energy equation

3 2vrρda2 dr + a2ρ r2 d dr

• r2vr
• = Qrad
• Qrad 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

Teff = 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

Teff = 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

Teff = 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

20 40 60 80 100 120 140 160 1 2 3 4 5 vr [km s-1] r/R*

• bserved terminal velocity →

HD 12953

5500 6000 6500 7000 7500 8000 8500 9000 9500 10000 10500 1 2 3 4 5 T [K] 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