25 years of progress in modeling stellar winds

Transcription

1 Universität Kiel September 2001 Gaining Insight into Stellar Atmospheres International Workshop in the honor of the 80 th birthday of Prof. Dr. Kurt Hunger 25 years of progress in modeling stellar winds Wolf-Rainer Hamann Berlin Kiel Potsdam with: Werner Schmutz Ulf Wessolowski Gerhard Dünnebeil Eberhard Schwarz Ekkehard Baum Klaus Hempe Uwe Leuenhagen Lars Koesterke Götz Gräfener Achim Feldmeier

2 25 years of progress... Linearization: v = s t here: t = 25 years, i.e. v progress = status(2001) - status(1976) 25 yr v progress > ε??? Forthcoming chapters: Stellar wind modeling 1976 Stellar wind modeling 2001 Future tasks

3 Wolf-Rayet Stars Discovery 1867 by C. Wolf & G. Rayet Letter to the Academie Francaise : 3 Stars with bright and broad emission lines in Cygnus ( 8 mag) Wolf-Rayet Spectrum (Example): Normalized Flux WR138 = HD A o = 1500 km/s He II λ/a o For comparison: main-sequence star of similar temperature Normalized Flux Lac (O9 V) λ/a o Known today: about 227 (massive) WR stars in our Galaxy Early interpretation as stars with strong mass outflow (Menzel 1929; Beals 1929)

4 Stellar winds in the mid 70 s Upcoming UV satellites (COPERNICUS ; IUE ): All bright O stars showing P-Cygni profiles VLA (1979- ): all bright O stars show radio emission Stellar winds are common for early-type stars! Status of spectral modeling Spherically-symmetric expansion Velocity law to be given Ionization structure: to be assumed (constant) Formation of single lines, pure scattering, two-level atom Sobolev approximation ( narrow line limit ) Progress: co-moving frame transfer, Doppler broadening, doubletts Cf. static, plane-parallel non-lte models at that time Complete-linearization technique Hydrogen + helium, 10 lines Radiative equilibrium spurious temperature stratification No models existing that time for Wolf-Rayet spectra

5 The "Standard Model" for expanding atmospheres Basic assumptions Spherically-symmetric expansion Stationarity & homogeneity Radiative equilibrium temperature structure T(r) Models for the purpose of spectral analyses Velocity law: (ad-hoc, no HD) v(r) = (1-1 v8 r )β mostly with β = 0.8 (O) or 1.0 (WR) Mass-loss rate Ṁ = free parameter Terminal wind velocity = free parameter v8 Hydrodynamically consistent models Driving force: radiation pressure (mainly on spectral lines) Stationary solution of the hydrodynamic equations For O stars established (Munich); for WR stars in progress (Potsdam) Time-dependent HD with schematic radiation transfer (O stars only)

6 The Kiel/Potsdam Code for expanding atmospheres Radiation transfer Co-moving frame (CMF) formulation Moment equations solved as difference scheme Method of Variable Eddington Factors Angle-dependent radiation transfer solved by integration along Short Characteristics (which guarantees J ν > 0) Non-LTE statistical equilibrium He, H, C, N, O... (optionally) implemented Typically: 250 levels, 1000 lines; maximum (?): 500 levels, 3000 lines Iron Line Blanketing Iron-group elemts (Fe, Ni, Co, Ti...) represented by one "generic ion" Full inclusion of Kurucz data (e.g lines) Superlevel concept Solution technique Accelerated Lambda Iteration (ALI) Radiative equilibrium / flux conservation by temperature correction method (Unsöld-Lucy)

7 Iron line blanketing in expanding atmospheres The problem: ~10 5 levels, ~10 7 lines Method: superlevels with non-lte population relative LTE population assumed within each superlevel level energy / 10 3 cm log (Σ g i per 100 cm -1 ) Example: Fe V (+ Ni V+...) In contrast to static atmospheres: Rad. transfer is coupled in frequency (expansion redshifts!) No re-ordering of frequencies allowed Solution by brute force : all opacities in their proper place levels (colors: total / even parity) Combined into 19 superlevels σ LU /10 15 cm Superline cross section for transition between superlevels λ/a o (from Gräfener et al. 2001)

8 Basic Accelerated Lambda Iteration (ALI) The Non-LTE Problem - fully coupled in space and frequency: J = radiation field S = source function n = population numbers Λ = operator, representing formally the linear mapping S J FS P = matrix of transition rates, containing frequency integrals over J Rad. Transfer - spatial coupling - J FS = S(n OLD ) Λ Rate Eqs. - frequency coupling - n NEW P(J NEW ) = b Normal Lambda Iteration: J FS J NEW Accelerated Lambda Iteration: J NEW = J FS + Λ * [ S(n NEW ) - S(n OLD ) ] Λ * = Approximate Lambda Operator (ALO) Sufficiently simple for being incorporated into Rate Eqs. Accurate enough for large optical depth τ >> 1 May simplify (or neglect) the spatial coupling Rate Eqs. include feedback from the new pop. numbers n

9 Clumping in "first approximation" Assumptions Clump density enhanced by a factor D > 1 (compared to a smooth model with same mass-loss rate) D constant over the whole atmosphere (justified??) Interclump medium: void volume filling factor f V = D -1 Clumps have small size (compared to the photon s free path) Consequences main spectral features are (nearly) invariant if D 1/2 Ṁ = constant higher clumping compensates for lower mass-loss rate Electron-scattering line wings become weaker with clumping Detailed profile fits indicate: D = Empirical mass-loss rates are scaled down Br 24 versus model series with different clumping = 950 km/s log L/L = T = 40 kk * D v log {Ṁ / M yr -1 )} Normalized Flux 2 1 N V 4-3 N III He II 4-3 Observation D = 1 Model D = 4 Model D = 16 Model λ/a o

10 = 950 km/s, log L/L = 5.35, T * = 40 kk, log {Ṁ / (M yr -1 )} = X N = 0.8%, X C = 0.01% v8 Br 24 (WN 7) 4 Observation Model (D = 4) He II + H I He II He II + H I N V H I He II N IV H I C IV He I N IV N V N III He II λ / A o Normalized Flux

11 T * /kk WN model grids Contour plots: Lines of constant eq. width Labels: W λ in A o log (R t /R ) N III 4640 N classification lines Grid: = 1600 km/s v8 log (R t /R ) N IV 4058 Discrete symbols: analyzed WN stars (color: LMC, b/w: Gal.) log (R t /R ) N V log (T * /K)

12 WC spectra: consistent fits only with clumping and blanketing Example: WR 111 (WC5) (Gräfener et al., submitted) = 2200 km/s, log L/L = 5.45, T * = 85 kk, log {Ṁ / (M yr -1 )} = (D=10), He/C/O = 51/45/04 (mass v8 Observation Model Model Continuum He II C IV Lα i.s. C III He II 6-4 C III C III C IV C III / C IV He II 4-3 He II 5-3 O IV C IV 5-4 C III O V C III C III log F λ [erg s -1 cm -2 A o -1 ] Iron forest (Fe V, Fe VI) Pseudo continuum log λ / A o

13 Empirical HRD for Wolf-Rayet stars Existing analyses: LMC: 15 WN (Crowther et al. 1995, 1997), 18 WN (Hamann & Koesterke 2000), 5 WC (Gräfener et al. 1998) Galaxy: 62 WN (Hamann & Koesterke 1998), 3 WC (Dessart et al. 2000) 6.5 T * /kk log (L /L ) M 40 M 25 M 5.0 He-ZAMS WNL WNE-w WNE-s WC H-ZAMS log (T * /K) LMC Galactic H no H H no H

14 Radiation driven wind theory Pioneering paper: Castor, Abbott & Klein (1975) Radiation pressure on numerous metal lines Coupling to passive H, He by collisions (Coulomb) Line force in Sobolev approximation For the whole sample of lines, parameterized as g rad ~ ( dv dr )α Limits: α = 0 if all lines optically thin α = 1 if all lines optically thick O stars: α = 0.8 Stationary solution of the equation of motion After important refinements (Kudritzki, Puls, Pauldrach...) Good reproduction of observed O star winds, namely: Ṁ, v Scaling wind momentum - luminosity Scaling mass loss - metallicity 8 Are Wolf-Rayet winds radiation-driven, too? Not enough radiative force within CAK-type modeling Several CAK approximations break down for very dense winds Expected scalings not confirmed observationally

15 Are WN mass-loss rates correlated with luminosity? log (Ṁ /(M yr -1 )) log (L /L ) Empirical data: LMC stars ( Brey labels) Galactic stars (small, unlabeled) Dashed line: exponent = H H WNL WNE-w WNE-s Exponent 1.6 established for OB stars empirically Exponent 1.6 predicted for radiation-driven (OB star) winds No tight correlation for WN stars No better correlation if considering T * or X H dependence Which is the hidden parameter? X 88

16 Why there is no metallicity effect Galaxy versus LMC? Average LMC metallicity Z LMC 1 4 Z (?) Radiation driven wind theory: Ṁ ~ Z 1/2 Lines should scale with both, Ṁ and abundance Comparison of observed spectra spectroscopic twins! log L/L T / kk * log Ṁ WR 6 Br Br 12 (LMC) WR 6 (Gal.) 3 Lα (geocoronal) N V 2p-2s N IV 2p 3-2s 2 C IV He II 3-2 N IV 10 5 Iron Forest λ / A o Normalized Flux

17 WR winds: high Ṁ because of low CAK α Calculate model atmospheres with fixed β law Ṁ = free parameter Calculate a posteriori the available radiation force f rad Compare with CAK force multiplier : f rad ~ (Ṁ) α For a mean f rad consider the work Q ~ Integral f rad dr α = (cf. α 0.7 in O stars) the hotter T * (labels), the lower α WC model grid: log L/L = 5.3, v8 = 2000 km/s, β = 1, D = 10, Fe blanketing -0.2 α = kK 141kK log Q (work ratio) α = kK 71kK 63kK 126kK 112kK 100kK 89kK 56kK 50kK log Ṁ [M /yr]

18 Steps towards self-consistent HD models for WR stars Our model calculations allows for an a posteriori check of forces All multiple-scattering effects etc. consistently included Iron lines give main contribution to radiative force Stepwise recombination provides fresh line opacities Comparison of adopted acceleration versus radiative acceleration Model for WR152 (WN3-w): T * = 80 kk, log L/L =5.5, R t =12.6 R, D=4 log (acceleration / g grav ) Acceleration needed: v v + g grav Radiative acceleration f rad blanketed unblanketed -1.0 v v(r) / Accelerating force missing by a factor of (only! ) Possible reasons: Inconsistent velocity field desirable: self-consistent v(r) Clumping still underestimated (but: D reduces Ṁ and κ) Opacities still incomplete (Fe; neglected elements: Si, Mg...) Radiation pressure might be sufficient to drive WR winds

19 Non-stationary & structured stellar winds Observations: line profile variability, e.g.: ζ Puppis - IUE MEGA Campaign (Massa et al. 1995) Si IV resonance doublett: single observation - mean template 15 time [days] 10 5 DAC modulation λ / λ D Two types of periodic variations: Discrete Absorption Components (DACs): P = 5.21 days (rotation?) Modulations: period = 19.2 hours (no integer fraction!) Likely explanation (DACs??): Corotating Interaction Regions (CIRs) Surface structures (spots?) φ cor Azimuthal variation of wind velocity Collision of fast / slow winds Conservation of angular momentum Spiral pattern in the Corotating frame to observer

20 Stochastic variability Theory: Time-dependent HD models (still 1D, simplified RT) line-driven winds are dynamically unstable (Owocki, Feldmeier...) Observations: X-rays from shock-heated gas cf. recent high-resolution X-ray line spectra with CHANDRA Observations: line profile variability, e.g.: rel. time in t flight 10 5 λ/a o time [min] WR 135 (WC8) C III 5696 A o line: single observation - mean template --- Velocity-law fits (β=1) to wavelength drift 50 0 v λ in Doppler units of Future work: structured stellar winds Hydrodynamical modeling Radiative transfer modeling & spectral analyses The shown transparancies are available via anonymous ftp from: ftp.astro.physik.uni-potsdam.de cd pub/wrhamann File: kielworkshop.ps (7.2 MB - gzipped 0.8 MB)