Astrophysics and Space Science DOI 10.1007/s•••••-•••-••••-• Stellar winds from hot low-mass stars W.-R. Hamann1 c Springer-Verlag •••• Abstract Stellar winds appear as a persistent fea- on the track from the Asymptotic Giant Branch (AGB) ture of hot stars, irrespective of their wide range to the white dwarf cooling sequence. Extreme helium of different luminosities, masses, and chemical com- (EHe) stars and subdwarf-O (sdO) stars are further position. Among the massive stars, the Wolf-Rayet types of low-mass stars which are found to display signs types show considerably stronger mass loss than the of mass-loss. Their evolutionary origin is attributed to O stars. Among hot low-mass stars, stellar winds are binarity (Saio and Jeffery 2002; Heber 2009). seen at central stars of planetary nebulae, where again Prototype for an O-type star with mass loss is the O5 the hydrogen-deficient stars show much stronger winds supergiant ζ Puppis. Striking evidence for the stellar than those central stars with “normal” composition. wind comes from the P-Cygni profiles of resonance lines We also studied mass-loss from a few extreme helium in the UV (cf. Fig. 2, left panel). However, these pro- stars and sdOs. Their mass-loss rate roughly follows the files are often saturated and therefore not sensitive for same proportionality with luminosity to the power 1.5 a precise determination of the mass-loss rates. The op- as the massive O stars. This relation roughly marks tical spectrum shows mostly “normal” absorption lines, a lower limit for the mass loss from hot stars of all while Hα is in emission (cf. Fig. 2, right panel). Mass- kinds, and provides evidence that radiation pressure on spectral lines is the basic mechanism at work. For T / kK certain classes of stars the mass-loss rates lie signifi- eff 100 50 20 10 5 2 cantly above this relation, for reasons that are not yet 7 fully understood. Mass-loss from low-mass stars may 6 WR OB LBV affect their evolution, by reducing the envelope mass, 40 M and can easily prevent diffusion from establishing atmo- 5 spheric abundance patterns. In close binary systems, their winds can feed the accretion onto a companion. 4 EHe L CSPN / Keywords Stellar winds – mass loss L 3 sdO log 2 White Dwarf ZAMS 1 Introduction: winds from hot stars 1 Hot stars of various types lose mass through stellar winds (see Fig.1). Massive stars lose mass as O or 0 1 M B-type stars (OB), Luminous Blue Variables (LBV), or Wolf-Rayet (WR) stars, before they finally explode as 5 4 supernova. Among low-mass stars, central stars of plan- log Teff / K etary nebulae (CSPNe) show stellar winds. They are Fig. 1 Location of various types of hot stars (see text) with mass loss in the Hertzsprung-Russell-Diagram (HRD). W.-R. Hamann The Zero Age Main Sequence (ZAMS) is indicated together 1Institut f¨ur Physik und Astronomie, Universit¨at Potsdam, Ger- with evolutionary tracks for a massive (40 M⊙) star and a many low-mass (1 M⊙) star. 2 2.0 C IV 1.2 α He II 14-5 He II 6-4 H 1.5 1.1 1.0 1.0 Normalized Flux 0.5 Observation 0.9 Model 0.0 1520 1540 1560 1580 6500 6550 6600 o o λ / A λ / A Fig. 2 Observed spectrum (blue) of ζ Puppis around the C iv resonance doublet (left frame) and Hα (right frame), and a model fit (red-dotted) calculated with the Potsdam Wolf-Rayet (PoWR) model atmosphere code. loss rates from O stars are most conveniently deter- After some minor modifications, this theory can well mined from fitting this line with model calculations. explain the observed mass loss from OB stars like, e.g., However, as the Hα emission is powered from the re- ζ Puppis. combination cascade, it depends on the degree of small- The highest mass-loss rate that can be achieved by scale inhomogeneity which is poorly known (Hamann, the Castor, Abbott, and Klein (1975) theory is obvi- Feldmeier, and Oskinova 2008). Empirical mass-loss ously reached when the momentum from all photons is rates decrease when “micro-clumping” is taken into ac- transferred to the wind, i.e. M˙ v∞ = L/c. The winds count. Mass-loss rates derived from (preferably un- of Wolf-Rayet stars, however, are often even stronger saturated) UV resonance lines do not suffer from this and exceed this so-called single-scattering limit. In or- problem since their opacity depends linearly on den- der to drive the strong WR winds, multiple scattering sity. However, it was shown by Oskinova, Hamann, must be taken into account. Adequate hydrodynamical and Feldmeier (2007) that inhomogeneities on larger models for WR stars have been successfully computed scale (“macroclumping”) can affect these lines, this (Gr¨afener and Hamann 2005, 2008), thus demonstrat- time leading to under-estimating the mass-loss rates. ing that WR winds can also be radiation-driven. Hot star winds are driven by the radiation field. Stel- lar radiation is intercepted by spectral lines, where the photons deliver their momentum hν/c. As the wind ac- ν celerates to the terminal wind velocity v∞, the spectral L ∆ν = ν0 v∞ / c line becomes Doppler-shifted and sweeps up the radi- Lν0 ation over the whole frequency band ∆ν = ν0 v∞/c. Hence the momentum that is intercepted by one opti- cally thick line per time is Lν0 ∆ν/c, which is of the 2 order of L v∞/c for a line frequency at about the flux ≈ L Lν0 ν0 maximum (cf. Fig. 3). This intercepted momentum rate can be compared with the mechanical momentum car- Specific Luminosity ν0 ried by the wind per time, M˙ v∞. Thus, one optically ν thick line drives a mass-loss of M˙ = L/c2 – interestingly Frequency the same rate by which the star must convert mass into Fig. 3 Line driving of a stellar wind. Due to the Doppler energy to sustain its luminosity L. shift, one single optically thick line sweeps up all radiation In a seminal paper, Castor, Abbott, and Klein (1975) within the frequency interval ∆ν. When the line frequency have shown that for a mixture of optically thick and ν0 is located at about the flux maximum, the specific lumi- thin lines the hydrodynamic equation has a stationary nosity Lν0 is of the order of L/ν0. This allows to estimate solution with the mass-loss rate M˙ as its eigenvalue. the mass-loss driven by one single line (see text). Stellar winds 3 2 Mass loss from hot stars 123 40 82 -4.0 116 107 2.1 Model atmospheres 91 75 100 124 130 36 110 62 78 6 16 Mass-loss becomes manifest in the stellar spectrum. 85 24 120 55105 156 131 Thin winds may only affect a few UV resonance lines 84 89 158 )] -4.5 74 63115 -1 37 87 that become asymmetrically broadened; in stronger 67 18 108 yr 61 71 149 34 winds, these broadened, blue-shifted absorptions are ac- 7 1 54 35 M 94 20 companied by a red-shifted emission feature (P-Cygni / ( 49 44 Ç -5.0 51 28 profile), while in very dense winds the whole line spec- M 129 138 trum may appear in emission (Wolf-Rayet types). In log [ 46 order to determine the mass-loss rates, adequate mod- 2 els must be compared to the observation. Such mod- -5.5 3 els are provided by the Potsdam Wolf-Rayet (PoWR) 152 ζ Pup model atmosphere code (Hamann and Gr¨afener 2004, and references therein). This code solves the non-LTE radiative transfer in -6.0 5.5 6.0 6.5 a spherically symmetric expanding atmosphere. Mass- log (L /L ) loss rate and wind velocity are free parameters of the models. Wind inhomogeneities (“clumping”) are ac- Fig. 4 Mass-loss rates versus luminosity for massive stars. counted for in a first-order approximation, assuming O-stars are represented by the prototype ζ Puppis, while the that optically thin clumps fill a volume fraction fV values for other O stars roughly follow the blue-dashed line. while the interclump space is void. Thus the matter The other points refer to Wolf-Rayet stars (labelled by their 1 WR catalog numbers), where the red (dark) filled symbols density in the clumps is higher by a factor D = f − , V are “late” WN subtypes and the green (light) symbols rep- compared to an un-clumped model with the same pa- resent “early” subtypes. The dashed lines are tentative fits rameters. The proper values for this clumping contrast with the same slope 1.5 for either groups. is highly debated (see Hamann, Feldmeier, and Oski- nova 2008). Detailed model atoms of the most relevant elements 2.2 Massive stars (H, He, C, N, O, Si) are taken into account in our models. Typically, 400 non-LTE levels and 5000 line Empirical mass-loss rates have been determined for a transitions are explicitely treated. Additionally, about multitude of O-stars. In Fig. 4 they are represented 105 energy levels and 107 line transitions of iron and by the prototype ζ Puppis, while the values for other other iron-group elements are approximately included O stars roughly follow the (blue) dashed line with the ˙ ∝ using the “superlevel” approach. In addition to Doppler slope log M 1.5log L. The Galactic Wolf-Rayet stars of the nitrogen sequence (i.e. WN types) have com- broadening from thermal motion and microturbulence, prehensively analyzed by Hamann, Gr¨afener, and Lier- radiation damping and pressure broadening are ac- mann (2006).