Mass loss from OB-stars

Massive stars are critical agents in galactic evolution, both in the present and in the early Universe (e.g., re-ionization and first enrichment). Mass loss is a key process, which modifies chemical profiles, surface abundances, and luminosities. Furthermore, mass loss has to be understood quantitatively in order to describe and predict massive star evolution in a correct way. The standard theory to describe hot, massive star winds is based on radiative line-driving, and has been proven to work successfully in most evolutionary phases (OB-stars, A-supergiants, and LBVs in their “quiet” phase). Also for the pivotal Wolf-Rayet (WR) stadium, line-driving is still the most promising acceleration mechanism (Gräfener and Hamann, 2005, 2008).

In this review, we summarize fundamental predictions of the theory, as well as corresponding observational evidence, and subsequently concentrate on two urgent problems that challenge our understanding of line-driven winds, the so-called weak-wind problem and wind clumping. We concentrate on the winds from “normal” OB-stars in all evolutionary phases (for corresponding results and problems regarding WR-winds and additional material, see the contributions by Hamann and Hillier, this volume).

To be efficient, radiative line-driving requires a large number of photons, i.e., a high luminosity $L$. Since $L\propto\mbox{$T_{\rm eff}$}^{4}\mbox{$R_{\ast}$}^{2}$, not only OB-supergiants, but also hot dwarfs and A-supergiants undergo significant mass loss via this mechanism. Typical mass-loss rates are of the order of $\dot{M}$ $\approx$ 0.1 … 10 $\cdot 10^{-6}\,M_{\odot}{\rm yr}^{-1}$, with terminal velocities $v_{\infty}$ $\approx$ 200 … 3,000 ${\rm km}\,{\rm s}^{-1}$. Another prerequisite is the presence of a multitude of spectral lines, with high interaction probabilities, close to flux maximum, implying that the strength of line-driven winds should strongly depend on metallicity.

Pioneering work on this subject was performed by Lucy and Solomon (1970) and Castor, Abbott & Klein ((Castor et al., 1975), “CAK”), where the latter still builds the theoretical foundation of our present understanding. Improvements with respect to a quantitative description and first applications were provided by Friend and Abbott (1986) and Pauldrach et al. (1986), whereas recent reviews on the topic have been published by Kudritzki and Puls (2000) and Puls et al. (2008).

Using these scaling relations, a fundamental prediction for line-driven winds becomes apparent if one calculates the so-called modified wind-momentum rate,

and accounts for the fact that $\alpha^{\prime}$ is of the order of 2/3. Then the wind-momentum rate becomes independent on mass and $\Gamma$, and can be expressed in terms of the wind-momentum luminosity relation (WLR), discovered first by Kudritzki et al. (1995),

with slope $x=1/\alpha^{\prime}$ and offset $D$, which depends on $N_{\rm eff}$ and thus on metallicity $z$ and spectral type. Originally, it was proposed to exploit the WLR for measuring extragalactic distances on intermediate scales (up to the Virgo cluster), but nowadays the relation is mostly used to test the theory itself (see below).

The most frequently cited theoretical wind models (stationary, 1-D, homogeneous) are those from Vink et al. (2000, 2001). Based on the Monte-Carlo approach developed by Abbott and Lucy (1985), they allow multi-line effects to be considered. In these models, the mass-loss rate is derived (iterated) from global energy conservation, whilst the ($\beta$-) velocity field is pre-described and the NLTE rate equations are treated in a simplified way. Pauldrach (1987) and Pauldrach et al. (1994, 2001), on the other hand, obtain a consistent hydrodynamic solution by integrating the (modified) CAK equations based on a rigorous NLTE line-force using Sobolev line transfer. Moreover, Krtička and Kubát (2000, 2001, 2004, 2009) and Krtička (2006) solve the equation of motion by means of a NLTE, Sobolev line-force, including a more-component description of the fluid (accelerated metal ions plus H/He) that allows them to consider questions regarding drift-velocities, non-thermal heating, and ion decoupling. Also, Kudritzki (2002) (see also Kudritzki et al. (1989)) provides an analytic “cooking recipe” for mass-loss rate and terminal velocity, based on an approximate NLTE treatment, and Gräfener and Hamann (2005, 2008) obtain self-consistent solutions (applied to WR winds) by means of a NLTE line-force evaluated in the comoving frame (see Mihalas et al. (1975, 1976a, 1976b, 1976c) and Hamann, this volume). Finally, Lucy (2007a, b) and Müller and Vink (2008) derive the wind-properties from a regularity condition at the sonic point, in contrast to most other solutions that invoke a singularity condition at the CAK-critical point of the wind (see comments by Owocki, this volume).

Also regarding the predicted metallicity dependence, the various results agree satisfactorily (note that the $z$-dependence of $v_{\infty}$ is rather weak):

In the last decade, various spectroscopic NLTE analyses of hot stars and their winds have been undertaken, in the Galaxy and in the Magellanic Clouds, in the UV, in the optical, and in a combination of both. For a compilation of these publications (without Galactic Center objects and objects analyzed within the flames survey of massive stars, see below), see Tables 2 and 3 in Puls (2008), to be augmented by the UV-Pv investigation of Galactic O-stars by Fullerton et al. (2006), the UV+optical analysis of Galactic O-dwarfs by Marcolino et al. (2009), and the optical analysis of LMC/SMC O-stars by Massey et al. (2009). Most of this work has been performed by means of 1-D, line-blanketed, NLTE, atmosphere/spectrum-synthesis codes allowing for the presence of winds, in particular cmfgen (Hillier and Miller (1998)), wm-basic (Pauldrach et al. (2001)), and fastwind (Puls et al. (2005)).

Observations confirm the “velocity-part” of this picture, at least qualitatively. For stars with $T_{\rm eff}$$\geq$ 23 kK, the observed ratio is  $\approx$ 3, whereas it decreases gradually towards cooler temperatures, reaching values of $\approx$ 1.3…1.5 for stars with $T_{\rm eff}$$\leq$ 18 kK (Evans et al., 2004; Crowther et al., 2006; Markova and Puls, 2008). With respect to the predicted increase in $\dot{M}$, however, the situation is different. As shown by Markova and Puls (2008), the mass-loss rates of B-supergiants below the observed bi-stability jump ($T_{\rm eff}$$<$ 22 kK) actually decrease or at least do no change. This is a first indication that there are still problems in our understanding of line-driven winds.

Regarding the last objective, Mokiem et al. (2006, 2007b) analyzed a total of $\sim 60$ O- and early B-stars in the SMC and LMC, by means of fastwind and using a genetic algorithm (Mokiem et al., 2005). The results were combined by Mokiem et al. (2007a) with data from previous investigations, to infer the metallicity dependence of line-driven mass-loss based on a significant sample of stars. Using mean abundances of $z=0.5\ \mbox{$z_{\odot}$}$ (LMC) and $z=0.2\ \mbox{$z_{\odot}$}$ (SMC), a metallicity dependence of $\mbox{$v_{\infty}$}\propto(z/\mbox{$z_{\odot}$})^{0.13}$, and a correction for clumping effects (see below) following Repolust et al. (2004), they derived an empirical relation

with rather narrow confidence intervals. This result is consistent with theoretical predictions, both from line-statistics (Puls et al., 2000) and from hydrodynamic models (see above).

The results as summarized above imply that line-driven mass loss seems to be basically understood, though certain problems need further consideration. In particular, from early on there were indications that the (simple) theory might break down for low-density winds. E.g., Chlebowski and Garmany (1991) have derived mass-loss rates for late O-dwarfs that are factors of ten lower than expected. By means of UV-line diagnostics, Kudritzki et al. (1991) and Drew et al. (1994) have derived mass-loss rates for two BII stars that are a factor of five lower than predicted, and Puls et al. (1996) have shown that the wind-momentum rates for low-luminosity dwarfs and giants ($\log L/L_{\odot}<$ 5.3) lie well below the empirical relation for “normal” O-stars.

The last investigation illuminated an immediate problem arising for low-density winds. For $\mbox{$\dot{M}$}<(5{\ldots}1)\cdot 10^{-8}$ $M_{\odot}{\rm yr}^{-1}$, the conventional mass-loss indicator, H_α, becomes insensitive, and only upper limits for $\dot{M}$ can be derived (for a recent illustration of this problem, see (Marcolino et al., 2009)). Instead, unsaturated UV resonance lines (C iv, Si iv, C iii) might be used to obtain actual values for $\dot{M}$ (e.g., (Martins et al., 2004; Puls et al., 2008; Marcolino et al., 2009)).

By means of such UV-diagnostics, strong evidence has accumulated that a large number of late type O-dwarfs (and a few giants of intermediate spectral type) have mass-loss rates that are factors of 10 to 100 lower than corresponding rates from both predictions and extrapolations of empirical WLRs. In particular, such weak winds have been found in the Magellanic Clouds (O-dwarfs in NCG 346 (LMC): Bouret et al. (2003); extremely young O-dwarfs in N81 (SMC): Martins et al. (2004)) and in the Milky Way (O-dwarfs and giants: Martins et al. (2005); late O-dwarfs: Marcolino et al. (2009)).

Two points have to be stressed. (i) Until now, it is not clear whether all or only part of the late type dwarfs are affected by this problem. (ii) The derived UV mass-loss rates are not very well constrained, since they might be contaminated²²2via a modified ionization equilibrium. from X-rays embedded in the wind (due to shocks, see next Section). The higher the X-ray emission, the weaker the lines, and the higher the actual mass-loss rates (see Figs. 19 and 20 in Puls et al. (2008)). However, to “unify” the present, very low, $\dot{M}$-values with “normal” mass-loss rates by invoking X-rays, unrealistically high X-ray luminosities would be required (Marcolino et al., 2009).

The weak-wind problem is a prime challenge for the radiative line-driven wind theory. Martins et al. (2004) investigated a variety of candidate processes (e.g., ionic decoupling, shadowing by photospheric lines, curvature effects of velocity fields), but none of those turned out to be strong enough to explain the very low mass-loss rates that seem to be present. At the end of this review, we will return to this problem.

During the last years, overwhelming direct and indirect evidence has accumulated that one of the standard assumptions of conventional wind models, homogeneity, needs to be relaxed. Nowadays the winds are thought to be clumpy, consisting of small scale density inhomogeneities, where the wind matter is compressed into over-dense clumps, separated by an (almost) void inter-clump medium (icm). Details on observations and theory can be found in the proceedings of a recent workshop, “Clumping in hot star winds” (Hamann et al., 2008).

Theoretically, such inhomogeneities are considered related to structure formation due to the line-driven (“de-shadowing”) instability, a strong instability inherent to radiative line-driving (cf. Owocki, this volume). Time-dependent hydrodynamic models allowing for this instability to operate have been developed by Owocki and coworkers (1-D:(Owocki et al., 1988; Runacres and Owocki, 2002, 2005); 2-D:(Dessart and Owocki, 2003, 2005)) and by Feldmeier (Feldmeier, 1995; Feldmeier et al., 1997), and show that the wind, for $r\mathrel{\mathchoice{\vbox{\offinterlineskip\halign{\hfil$\displaystyle#$\hfil\cr>\cr\sim\cr}}}{\vbox{\offinterlineskip\halign{\hfil$\textstyle#$\hfil\cr>\cr\sim\cr}}}{\vbox{\offinterlineskip\halign{\hfil$\scriptstyle#$\hfil\cr>\cr\sim\cr}}}{\vbox{\offinterlineskip\halign{\hfil$\scriptscriptstyle#$\hfil\cr>\cr\sim\cr}}}}1.3\mbox{$R_{\ast}$}$, develops extensive structure consisting of strong reverse shocks separating slower, dense material from high-speed rarefied regions in between. Such structure is the most prominent and robust result from time-dependent modeling, and the basis for our interpretation and description of wind clumping. Within the shocks, the material is heated to a couple of million Kelvin, and subsequently cooled by X-ray emission (which has been observed by all X-ray observatories), with typical X-ray luminosities $L_{\rm X}/L_{\rm bol}\approx 10^{-7}$ (for newest results, see Sana et al. (2006)).

The most important consequence of such optically thin clumps is a reduction of any $\dot{M}$ derived from $\rho^{2}$-dependent diagnostics (e.g., recombination based processes such as H_α or radio-emission), assuming smooth models, by a factor of $\sqrt{f}_{\rm cl}$. That there is a reduction is conceivable, since, under the assumptions made, the square of the over-density “wins” against the smaller absorbing/emitting volume. Thus, a lower $\dot{M}$ is sufficient to produce the same optical depths/emission measures as in smooth models.

Note, however, that in this scenario any $\dot{M}$ derived from $\rho$-dependent diagnostics (e.g., UV-resonance lines) remains uncontaminated, since in this case the over-density cancels against the smaller absorbing/emitting volume. Finally, it should be mentioned that a clumpy medium also affects the ionization equilibrium, due to enhanced recombination (e.g., (Bouret et al., 2005)).

Results from NLTE-spectroscopy allowing for micro-clumped winds are as follows. (i) Typical clumping factors are $f_{\rm cl}$$\approx$ 10…50, and clumping starts at or close to the wind base, the latter in conflict with theoretical predictions. Derived mass-loss rates are factors of 3 to 7 lower than previously thought (Crowther et al., 2002; Hillier et al., 2003; Bouret et al., 2003, 2005). In strong winds, the inner region is more clumped than the outer one ($f_{\rm cl}^{\rm in}\approx 4{\ldots}6\times f_{\rm cl}^{\rm out}$), and the minimum reduction of smooth H_α mass-loss rates is by factors between 2 and 3 (Puls et al., 2006).

If such large reductions in $\dot{M}$ were true, the consequences for stellar evolution and feed-back would be enormous. Note that an “allowed” reduction from evolutionary constraints is at most by a factor of 2 to 4 (Hirschi (2008)).

Oskinova et al. (2007) used a simple, quasi-analytic treatment of macro-clumping (still assuming a smooth velocity law) to investigate P v in parallel with H_α from $\zeta$ Pup. Whereas macro-clumping had almost no effect on H_α, since the transition is optically thin in the clumps, P v turned out to be severely affected. Thus, only a moderate reduction of the smooth mass-loss rate (factors 2 to 3) was necessary to fit the observations, consistent with the evolutionary constraints from above.

This model has been criticized by Owocki (2008), who pointed out that not only the distribution/optical thickness of the clumps is important, but also the distribution of the velocity field, since the interaction between photons and lines is controlled by the Doppler-effect. Also the “holes” in velocity space, due to the non-monotonic character of the velocity field, lead to an increased escape (thus, he called this process velocity-porosity = “vorosity”), whilst the different velocity gradients inside the clumps lead to an additional modification of the optical depth.

We note, however, that the profile-strength reduction presented in Fig. 1 corresponds to a “most favourable case”, using rather ideal parameters. Our investigations have shown how details on porosity, vorosity, and the icm, all are important for the formation of the line profiles. In fact, the strengths of similar profiles calculated from our pseudo 2-D hydrodynamic models are only reduced by $\approx 10\%$, because of insufficient vorosity inherent to structures from present time-dependent modeling (see also Owocki (2008)). Such a modest reduction is much lower than needed to alleviate the discrepancy discussed above. Also, as it turns out, the icm is a crucial parameter if to de-saturate intermediate strong lines and, at the same time, allowing the formation of the observed saturated profiles. Tests have shown that, with a void icm, the formation of saturated profiles is only possible if the average clump separation (controlling the porosity) is very small, but then the de-saturation of intermediate strong lines becomes marginal. Only by assuming an icm with sufficient density ($\approx 0.01\rho_{\rm smooth}$) we have been able to form saturated lines in parallel with de-saturated ones of intermediate strength. This finding is consistent with results from Zsargó et al. (2008), who pointed out that the icm is crucial for the formation of highly ionized species such as O vi.

Further details and results from our investigations will be given in a forthcoming paper (Sundqvist et al., in prep for A&A), including a systematic investigation of different key parameters and effects. Future plans include a comparison with emission lines, and the development of simplified approaches to incorporate porosity/vorosity effects into NLTE models.

In the preceeding paragraphs, we have argued that (i) mass-loss rates from unsaturated UV line-profiles are much lower than those from H_α or radio emission, and that (ii) this discordance might be mitigated by porosity/vorosity effects. Recall here that the mass-loss rates from weak winds discussed so far (Sect. 4) rely on the same UV-line diagnostics, and the question arises whether one encounters a similar problem, i.e., an under-estimation of the “true” mass-loss rates due to insufficient physics accounted for in the diagnostics. Thus, to clarify in how far the weak wind problem is a real one, independent diagnostics are required!

Already in 1969 Auer and Mihalas (1969), based on their first generation of NLTE, hot-star model atmospheres, predicted that the IR Br_α-line should show significant photospheric core emission, due to an under-population of its lower level ($n=4$) relative to the upper one ($n=5$), resulting from a very efficient decay channel $4\rightarrow 3$. Indeed, such core emission has meanwhile been observed in various weak wind candidates such as $\tau$ Sco (B0.2V), HD 36861 (O8III(f)), and HD 37468 (O9.5V) (Najarro, Hanson and Puls, in prep. for A&A). Recent simulations (Puls et al. (2008), Figs. 21/22) actually show that such photospheric + wind emission can fit the observations quite nicely, and that the core of Br_α is a perfect tracer for the wind density also for thinner winds (as opposed to H_α). Astonishingly, the height of the peak increases for decreasing $\dot{M}$, which is related to the onset of the wind, i.e., the density/velocity structure in the transition zone between photosphere and wind, and not due to radiative transfer effects. The higher the wind-density, the deeper (with respect to optical depth) this onset, which subsequently suppresses the relative under-population of $n=4$ due to efficient pumping from the hydrogen ground-state. Moreover, Br_α is only weakly affected by the presence of X-rays, and thus an ideal tool to infer very low mass-loss rates. From fits to the observations, it turns out that $\dot{M}$ is actually very low (of the order of $10^{-10}\mbox{$M_{\odot}{\rm yr}^{-1}$}$ for HD 37468, and even lower, if the wind-base were clumped). Thus, weak winds seem to be a reality!

What may then be the origin of weak winds? Krtička and Kubát (2009) argue that weak-winded stars display enhanced X-ray emission, maybe related to extended cooling zones because of the low wind density. Already Drew et al. (1994) pointed out that strong X-ray emission can lead to a reduced line acceleration, because of a modified ionization equilibrium, and since higher ions have fewer lines. Thus, weak-winded stars might be the result of strong X-ray emission. Let us now speculate whether such strong emission might be related to magnetic fields. Note that weak winds can be strongly affected by relatively weak $B$-fields, of the order of 40 Gauss according to the scaling relations provided by ud-Doula and Owocki (2002), which is below the present detection threshold. In this case then, colliding loops might be generated, which in turn generate strong and hard X-ray emission in the lower wind, which finally might influence the ionization and thus radiative driving. Future simulations coupling magneto-radiation-hydrodynamic wind codes with a self-consistent description of the line-acceleration will tell whether this mechanism might work.