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Wind models for O
Wind models for O-type stars T. L. Hoffmann & A. W. A. Pauldrach, University of Munich email: [email protected], [email protected] http://www.usm.uni-muenchen.de/people/adi/adi.html Abstract Spectral analysis of hot stars requires adequate model atmospheres which take into account the effects of NLTE and radiation-driven winds properly. Here we present significant improvements of our approach in constructing detailed atmospheric models and synthetic spectra for O-type stars. The most important ingredients of our models with regard to a realistic description of stationary winds are: • A sophisticated and consistent description of line blocking and blanketing that renders the line blocking influence on the ionizing fluxes in identical quality as the synthetic high-resolution spectra, as well as properly accounting for the line blanketing effect in the energy balance. • A consistent determination of the radiative line acceleration and solution of the hydrodynamics. • A considerably improved and enhanced atomic data archive providing the basis for a detailed multilevel NLTE treatment of the metal ions (from C to Zn) and an adequate representation of line blocking and the radiative line acceleration. • Inclusion of EUV and X-ray radiation produced by cooling zones originating from shock-heated matter. This new tool not only provides a method for O-star diagnostics (whereby physical constraints on the properties of stellar winds, stellar parameters, and abundances can be obtained via a comparison of observed and synthetic spectra), but also allows the astrophysically important information about the ionizing fluxes of these stars to be determined. Description of Method Comparison with observations Determining stellar parameters The basis for our approach in constructing detailed atmospheric models for hot luminous stars is the concept of homogeneous, stationary, and spherically symmetric radiation-driven winds, where the expansion of the atmosphere is due to scattering and absorption of radiation by Doppler-shifted metal lines. From the large sample of Galactic stars for which mass loss rates and stellar parameters have been determined by Puls et al. (1996) we have selected a representative subsample to compare against our model calculations. The parameters are listed in Table 1. Computing the wind dynamics consistently permits not only the determination of wind parameters from given stellar parameters, but, conversely, makes it possible to obtain the stellar parameters from the observed UV spectrum alone. The basic procedure for determining the stellar parameters from the observed UV spectrum is outlined in Figure 8. (Sν − I ν )κν = µ ∑ n j (R ji + C ji ) + nκ (Rκ i + Cκ i ) j≠i model with consistent dynamics ∂I ν 1 − µ 2 ∂I ν + ∂r r ∂µ T guess new stellar parameters terminal velocity vs. temperature mass loss rate vs. temperature 4000 κνK ν 100 3500 ni Energy equation 3000 10 2500 2000 1500 FIGURE 1. — Overview of the physics of radiation-driven winds. 1000 500 Puls et al. 1996 our models 0 25000 30000 35000 40000 45000 50000 Puls et al. 1996 our models 0.01 25000 55000 30000 35000 line force continuum force temperature Spectrum (formal solution) ni (r), χν , ην , v(r) H νem ⇒ N IV S VI P IV N IV C III N III line and continuum spectrum O VI S IV PV C III N III Si III N V C III 1 0.5 950 Si III 1000 N V C III 1050 1100 O IV OV 1150 1200 1250 SV C IV Si IV 0 900 2 1300 Si III 1000 N V C III 1050 O IV 1100 OV 1150 1200 1250 SV C IV 1500 1550 Si IV logg = 4.0 R = 25 R = 20 1300 1 R = 15 1.5 profile 1.5 950 1 0.5 1 0.5 0 1200 2 1250 1300 C IV 1350 1400 He II 1450 1500 1550 0 1200 2 1600 N IV 1250 1300 1350 1400 1450 0 1600 1000 He II 1 1 0.5 0.5 1550 1600 1650 1700 wavelength 1750 1800 1850 0 1500 1900 1550 1600 1650 HD 93129A − model 5000 6000 1700 wavelength 1750 1800 1850 FIGURE 9. — Consistent terminal velocities and mass loss rates for a grid of 40000 K models with radii from 15 to 25 R and log g from 3.4 to 4.0. 1900 2 N IV S VI P IV N IV C III N III O VI S IV PV C III N III Si III N V C III N IV S VI P IV N IV C III N III 1.5 O VI S IV PV C III N III Si III N V C III Teff = 40000, logg = 3.4, R = 15 1.5 1 2 N IV S VI P IV N IV C III N III O VI S IV PV C III N III Si III N V C III Teff = 40000, logg = 3.4, R = 20 1.5 1 2 N IV S VI P IV N IV C III N III 1 0.5 950 Si III 1000 N V C III 1050 1100 O IV OV 1150 1200 Si IV SV 1250 C IV Si III 1.5 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 Si IV SV 1250 1 0.5 Si III C IV 1250 1300 C IV 1350 1400 He II 1450 1500 1550 1300 1600 1650 1700 wavelength 1750 1800 1850 0 1500 1900 1200 1250 SV C IV 1350 1400 1450 1500 1550 He II N IV 1550 1600 1650 1700 wavelength 1800 1850 1250 1300 1350 1400 He II 1450 1500 1550 1600 HD 66811 − model O VI S IV PV C III N III Si III N V C III N IV S VI P IV N IV C III N III 1 O VI S IV PV C III N III Si III 950 Si III 1000 N V C III 1050 1100 O IV OV 1150 1200 Si IV SV 1250 1600 N IV S VI P IV N IV C III N III 1650 O VI C IV Si III 1.5 N V C III 1050 O IV 1100 OV 1150 1200 Si IV SV 1700 wavelength 1750 1800 1850 1 1250 1300 C IV 1350 1400 He II 1450 1500 1550 S IV PV C III N III Si III 1300 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 Si IV 1250 N IV 1400 1450 1500 1 0.5 1550 1600 He II 1350 1400 1650 1700 wavelength 1750 1800 1850 He II S IV PV Si III 1550 1600 N IV S VI P IV N IV C III N III 1600 N IV S VI P IV N IV C III N III 1 1650 1700 wavelength 1750 1800 1850 1900 1650 1700 wavelength 1750 1800 1850 Si III 1000 N V C III 1050 1100 O IV OV 1150 1200 1250 O VI S IV PV C III N III Si III SV C IV Si IV O VI S IV PV C III N III Si III N V C III 1000 N V C III 1050 O IV 1100 OV 1150 1200 1250 profile SV C IV Si IV 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 Si IV 1250 1250 1300 C IV 1350 1400 He II 1450 1500 1550 1600 1650 1700 wavelength 1250 1300 1800 1850 1350 1400 He II S IV PV 1550 1600 Si III PV C III N III Si III He II 1550 1600 N V C III N V C III 1600 1750 1800 1850 1900 N IV 1650 O VI 1700 wavelength S IV PV C III N III Si III N V C III 1 1000 1050 O IV 1100 OV 1150 1200 1250 SV C IV Si IV 0.5 1300 0 900 2 Si III 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 1600 1750 1800 1850 1900 Si IV 1250 1300 1.5 1250 1300 1350 1400 He II 1450 1500 1550 1 0.5 1600 0 1200 2 N IV 1250 1300 C IV 1350 1400 He II N IV 1.5 1 1550 1600 1650 1700 wavelength 1750 1800 1850 0.5 1900 0 1500 1550 1600 O VI S IV PV C III N III Si III N V C III 1650 1700 wavelength Teff = 40000, logg = 3.7, R = 25 2 N IV S VI P IV N IV C III N III 1700 wavelength 1800 1850 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 Si IV 1250 PV C III N III Si III N V C III 0.5 1300 0 900 2 Si III 1 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 1600 1750 1800 1850 1900 Si IV 1250 1300 1.5 1250 1300 1350 1400 He II 1 0.5 1600 0 1200 2 N IV 1250 1300 C IV 1350 1400 He II N IV 1.5 0.5 1900 S IV 1 0 900 2 0 1200 2 1750 O VI 1.5 1 0 1500 1550 1600 1650 1700 wavelength 1750 1800 1850 0.5 1900 0 1500 1550 1600 O VI S IV PV C III N III Si III N V C III 1650 1700 wavelength Teff = 40000, logg = 4.0, R = 20 2 N IV S VI P IV N IV C III N III 1450 1500 1550 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 Si IV 1250 1600 1650 1700 wavelength 1750 1800 1850 1900 N IV S VI P IV N IV C III N III O VI S IV C III N III Si III C III N III Si III N V C III Teff = 40000, logg = 4.0, R = 25 2 N IV S VI P IV N IV C III N III 1300 1350 1400 950 1000 N V C III 1050 O IV 1100 OV 1150 Si IV 1200 1250 SV C IV He II 0 1200 2 N IV 0 900 2 Si III 1250 1300 1350 He II 1400 1450 1500 1550 1650 1700 wavelength 1750 1800 1850 0 1500 950 1000 N V C III 1050 O IV 1250 1300 C IV 1350 1100 OV 1150 1200 SV C IV 1450 1500 1550 1600 1750 1800 1850 1900 Si IV 1400 He II 1250 1300 N IV 1.5 0.5 1900 N V C III 1 0 1200 2 1 1600 Si III 0.5 1600 N IV 1.5 1550 C III N III 1.5 C IV 1 PV 0.5 1300 1 0.5 1600 S IV 1 Si III 1.5 1250 O VI 1.5 0 900 2 1 0.5 PV PV 0.5 1300 1.5 1.5 1550 S IV 1 0 900 2 1600 N IV O VI 1.5 1 1550 1600 1650 1700 wavelength 1750 1800 1850 0.5 1900 0 1500 N V C III 1550 1600 1.5 1 1550 Teff = 40000, logg = 3.5, R = 25 0.5 1600 N IV 1650 HD 30614 − IUE C III N III S IV 1 0 1500 O VI 1300 C IV 1500 1.5 950 N V C III 2 N IV S VI P IV N IV C III N III 1.5 0 1500 1 C IV 0 1200 2 HD 30614 − model 2 1400 0.5 0 1500 1900 1250 1450 0.5 1900 1.5 Si III C IV 1750 1350 He II C IV 1550 1400 Teff = 40000, logg = 4.0, R = 15 1.5 0 1500 1350 2 N IV 1 1850 N IV S VI P IV N IV C III N III Si III 1300 N IV S VI P IV N IV C III N III 0.5 1800 1.5 1250 0.5 0 1200 2 1600 1750 0.5 1300 1 1 1 1300 Teff = 40000, logg = 3.7, R = 20 1.5 profile 0 1200 2 1700 wavelength 1300 1 0.5 O VI N IV S VI P IV N IV C III N III 0 1500 950 0.5 1.5 1650 1 0 1200 2 1.5 1 0.5 1250 2 0.5 Si III 1.5 1600 N V C III 1 0 900 2 1300 0 1200 2 2 0 1500 1.5 1 950 N V C III SV 1 0.5 1900 1.5 0.5 0 900 2 Si III 1200 0.5 1600 1.5 Si III 1550 1.5 0.5 1550 1 C IV N V C III 1500 1.5 0 900 2 HD 217086 − IUE C III N III 1550 C IV profile O VI 1450 N IV C IV 0 1200 2 N IV 0.5 N IV S VI P IV N IV C III N III C III N III 1150 Si IV 2 N IV 2 1.5 PV 1100 OV 1 0 900 2 1 0 1500 1900 1400 0.5 1600 1.5 HD 217086 − model 2 S IV 1050 O IV 1.5 Si III 1300 0.5 0 1500 N V C III 1600 1.5 1 0.5 1350 He II 1.5 1250 1 C IV 1550 1000 Teff = 40000, logg = 3.7, R = 15 C IV 1.5 1350 1300 0.5 1300 1 0 1500 1300 950 Teff = 40000, logg = 3.5, R = 20 1.5 1 1250 1250 N V C III 0.5 0 1200 2 1600 Si III 0 1500 0.5 0 1200 2 0 900 2 0.5 1900 O VI 0.5 1300 1.5 N IV S VI P IV N IV C III N III Si III 1.5 0.5 C IV 1 0 900 2 N V C III 1250 1250 SV 2 C IV 1000 1200 1.5 0 1200 2 950 1150 Si IV 1 1550 1.5 0 900 2 1300 1100 OV 1 C IV 0.5 0 900 2 1050 O IV 2 1.5 0.5 N V C III 1.5 1.5 2 N IV S VI P IV N IV C III N III 1 1000 Teff = 40000, logg = 3.5, R = 15 1900 HD 66811 − IUE 2 Teff = 40000, logg = 3.4, R = 25 N IV S VI P IV N IV C III N III 0 1200 2 N IV 1 0.5 N V C III 1 950 0.5 0.5 1.5 Si III 2 Si III 0 1500 1750 C III N III 1.5 0 900 2 1 1600 PV 0.5 1300 0.5 C IV 1 0.5 1550 1150 Si IV 1.5 1250 1.5 1 0.5 0 1500 1100 OV 1.5 C IV N IV 1.5 1050 O IV 1 0 1200 2 0 1200 2 1600 1000 0.5 1 0.5 0 1200 2 950 N V C III 1.5 1.5 S IV 1 0 900 2 1300 O VI 1.5 0.5 0 900 2 1300 profile 0 900 2 profile 4000 HD 93129A − IUE 2 1650 1700 wavelength 1 0.5 0.5 0 900 2 950 Si III 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 Si IV 1250 0 900 2 1300 Si III FIGURE 10. — Synthetic UV spectra of the above grid models. 950 1000 N V C III 1050 O IV 1100 OV 1150 1200 SV C IV 1450 1500 1550 1600 1750 1800 1850 1900 Si IV 1250 1300 1.5 profile 1.5 profile 3000 N IV 1.5 0 1500 FIGURE 2. — Schematic sketch of a model run. 2000 vinf (km/s) C IV 1.5 profile Z, ρ (r), v(r), Tg (r) R ij , C ij , χν , ην ⇒ N V C III 0.5 Of these, the NLTE model is by far the most computationally intensive, since it must consider consistently the effects of hundreds of thousands of Dopplershifted spectral lines on the radiation field, and consequently on the rate coefficients and the occupation numbers. To illustrate the convergence of the NLTE model, Figure 3 shows the ionization fractions of N III, N IV, and N V vs. depth and iteration block number. The reliability of the NLTE model is indicated by the resulting flux conservation, which turns out to be on the 1% level for the converged model, as shown in Figure 3. Spherical NLTE model ni (r), H ν (r), T(r) gL (r), gC (r) Si III 1.5 0 900 2 • the computation of the synthetic spectrum. LTE continuum force LTE temperature C III N III profile ⇒ PV 1 profile Tg (r), gC (r) S IV profile ρ (r), v(r) LTE continuum opacities O VI 0.5 • the solution of the NLTE model (calculation of the radiation field and the occupation numbers), Spherical gray model logg = 3.5 logg = 3.7 profile • the solution of the hydrodynamics, . mass loss rate: M terminal velocity: v∞ logg = 3.4 10 2 N IV S VI P IV N IV C III N III profile ⇒ 55000 HD 93250 − IUE 2 1.5 profile density structure: ρ (r) velocity field: v(r) 50000 mass loss rate and terminal velocity vs. radius and gravity (Teff = 40000 K) HD 93250 − model line force: gL (k,α ,δ ) continuum force: gC (r) temperature: T(r) 45000 Teff (K) FIGURE 5. — Terminal velocities (left panel) and mass loss rates (right panel) of our sample stars compared with the values obtained by Puls et al. (1996). A complete model atmosphere calculation consists of three main blocks that interact with each other: Hydrodynamics 40000 Teff (K) profile The required physics (see Figure 1) are solved in a series of nested iteration cycles as illustrated in Figure 2. (A detailed description of the method is given in Pauldrach et al. 2001.) As a result of the solution of this system we obtain not only the synthetic spectra and ionizing fluxes (which can be used in order to determine stellar parameters and abundances via comparison with observed spectra), but also the hydrodynamical structure of the wind (thus, constraints on the mass loss rate and velocity field can be obtained). 1 0.1 Mdot (10−6 Msun/yr) 1 ⌠∞ 4πκν (J ν − Sν )dν ρ ⌡0 profile = This idea is not new (see, for example, Kudritzki et al. 1992); however, only now are the models beginning to reach a degree of sophistication that makes such a procedure useful in practice. An application of the method to O-type central stars of planetary nebulae is given by Pauldrach et al. 2004. To briefly illustrate the effect of a change in radius and gravity on the spectra and wind parameters, we have calculated a grid of models with consistent wind dynamics, using radii R from 15 to 25 R and surface gravities log g from 3.4 to 4.0 (at a temperature of Teff = 40000 K). The resulting mass loss rates and terminal velocities are plotted in Figure 9; the corresponding UV spectra are shown in Figure 10. profile 1 ρ Msun/yr) d de + pv dr dr −6 v * Mdot (10 ∑ niσiKκ Z,z,i vinf (km/s) κνK = observed UV spectrum yes FIGURE 8. — Determining stellar parameters through UV spectral analysis. Shock physics ρ2 Λν (v) 4πκ K-shell ionization fit okay? no stellar and wind parameters determined! SνS SνS = f synthetic UV spectrum profile ni guess stellar parameters (Teff , R, log g, Z) The results are very encouraging: not only do our models reproduce the observed terminal velocities to within 10% and the mass loss rates to within about a factor of 2 (see Figure 5), but at the same time also represent the observed UV spectra quite well (Figure 6). (Note, however, that the analysis by Puls et al. did not consider line blanketing; the sample has recently been reanalyzed taking this effect into account.) Radiative transfer Iν j≠i our models . M v∞ 10 3200 14 3200 7.5 2000 0.55 2600 2.6 1500 profile Rate equations ni ∑(R ij + C ij ) + ni (R iκ + C iκ ) + ni RKiκ * Puls et al. 1996 . M v∞ 4.9 3250 22 3200 5.9 2250 ≤ 0.2 2550 5.2 1550 R 18 20 19 10 29 TABLE 1. — Parameters of the sample stars. Radii are in solar radii, mass loss rates in 10−6 M /yr, terminal velocities in km/s. ρ ,v ni log g 4.00 3.95 3.60 3.75 3.00 profile ρ ,v Teff 50500 50500 42000 40000 30000 profile grad = star HD 93250 HD 93129A HD 66811 (ζ Pup) HD 217086 HD 30614 (α Cam) Hydrodynamics . M = 4π r 2 ρ v dp 1 dv = − + grad − g v dr ρ dr nl n u ⌠ ∞ ⌠ +1 = gcont + ∑ f lu gl − I ν ( µ )φ (ν ) µ d µ dν gl gu ⌡0 ⌡−1 lines 1 0.5 1 0.5 0 1200 2 1250 1300 C IV 1350 1400 He II 0 1200 2 1600 N IV 1250 1300 C IV 1.5 1350 1400 He II N IV 1.5 1 For example, lowering the temperature of the model for α Cam to 29000 K and increasing the radius to 35 R to obtain a higher mass loss rate leads to a much better agreement with the observed spectrum, as shown in Figure 11 (shock radiation is also included in this model). 1 0.5 0.5 0 1500 1550 1600 1650 1700 wavelength 1750 1800 1850 0 1500 1900 1550 1600 1650 1700 wavelength Copernicus IUE model HD 30614 2 N IV S VI P IV N IV C III N III FIGURE 3. — Temperature (left), flux conservation (right), and ionization fractions of nitrogen (top) vs. depth and iteration block number for a 29000 K supergiant model. FIGURE 6. — Comparison of synthetic model spectra with observed spectra of stars with similar stellar parameters. For comparison with observations, a high-resolution synthetic spectrum is calculated from the converged model using the same radiative transfer routine as in the NLTE program. An example is shown in Figure 4. Discrepancies to the observed UV spectra can be eliminated by fine-tuning the stellar parameters (and the abundances), as explained in the next section. Figure 7 shows the UV spectrum of the α Cam model additionally incorporating shock radiation, as well as the corresponding EUV flux and a comparison with the ROSAT observations. O VI S IV PV C III N III Si III N V C III 1.5 1 0.5 0.01 1050 O IV 1100 OV 1150 1200 1250 SV C IV 1450 1500 1550 1600 1750 1800 1850 1900 Si IV 1300 S IV PV C III N III Si III N V C III 2 log Eddington flux (erg/s/cm /Hz) 0.002 1 300 400 500 600 700 800 0.5 900 0 900 2 0.008 0.006 Si III 950 1000 N V C III 1050 O IV 1100 OV 1150 Si IV 1200 1250 SV C IV 1300 1e−06 profile 0.002 1100 1200 1300 1400 1500 1600 0.008 0 1200 2 1.5 0.004 1 0.002 profile 0.5 1e−16 0 200 400 600 wavelength (Å) 800 1000 1900 2000 wavelength 2100 2200 2300 FIGURE 4. — Synthetic high-resolution spectrum computed for a 45000 K supergiant model. 0 1500 0 1500 1550 1600 1650 1700 wavelength HD 30614 / ROSAT 1250 1300 1350 He II 1400 1450 1500 1550 1600 N IV FIGURE 11. — Synthetic spectrum of a model for α Cam with Teff = 29000 K and R = 35 R compared with the observed Copernicus and IUE spectra. 0.1 0.01 0.001 References 0.0001 1800 N IV 1e−12 0.5 1700 1400 1 C IV 0.006 1350 He II 1 1e−14 Flux (counts/s/keV) 1000 1300 C IV 1e−10 1 0.5 1250 1.5 1e−08 1.5 0.004 0 1200 2 0.0001 O VI 1550 1600 1650 1700 wavelength 1750 1800 1850 1900 1e-05 0.1 1 Energy (keV) FIGURE 7. — UV spectrum of a model for α Cam including shocks (left), its EUV flux (right top), and a comparison with the observed ROSAT flux (right bottom). Kudritzki R.-P., Hummer D. G., Pauldrach A. W. A., et al., A&A 257, 655 (1992) Pauldrach A. W. A., Hoffmann T. L., Méndez R. H., A&A 419, 1111 (2004) Pauldrach A. W. A., Hoffmann T. L., Lennon M., A&A 375, 161 (2001) Puls J., Kudritzki R.-P., Herrero A., et al., A&A 307, 171 (1996) This poster was formatted with groff 1.19. 1.5 N IV S VI P IV N IV C III N III flux 1000 0.5 2 0.004 0 1600 950 N V C III 0.01 HD 30614 − model 0.006 0 900 0.01 Si III 1 HD 30614 − model 0.008 0 200 0.01 0 900 2 1.5
5.4 - 11.3 keV