winds from ob stars: a two-component scenario? - IOPscience

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The Astrophysical Journal, 637:506–517, 2006 January 20 # 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.

WINDS FROM OB STARS: A TWO-COMPONENT SCENARIO? D. J. Mullan Department of Physics and Astronomy, University of Delaware, Newark, DE 19716; [email protected]

and W. L. Waldron L-3 Communications Government Services, Inc., Largo, MD 20774-5370; [email protected] Received 2005 July 21; accepted 2005 September 22

ABSTRACT X-ray spectroscopy of several OB stars with massive winds has revealed that many X-ray line profiles exhibit unexpectedly small blueshifts and are almost symmetric. Moreover, the hottest X-ray lines appear to originate closest to the star. These properties appear to be inconsistent with the standard model of X-rays originating in shocked material in line-driven spherically symmetric winds. Here we raise the question, can the X-ray line data be understood in terms of a two-component wind? We consider a scenario in which one component of the wind is a standard line-driven wind that emerges from a broad range of latitudes centered on the equator. The second component of the wind emerges from magnetically active regions in extensive polar caps. The existence of such polar caps is suggested by a recent model of dynamo action in massive stars. We describe how the two-component model is consistent with a variety of observational properties of OB star winds. Subject headinggs: stars: early-type — stars: magnetic fields — stars: winds, outflows Online material: color figures

in several stars ( Ori, Ori, 1 Ori C). With regard to line widths, the observed HWHM values are in some cases found to be significantly smaller than the wind terminal speed (WC02). To date, the smallest HWHMs for an early-type star are those observed in Sco (B0 V): there the HWHMs are found to be essentially identical to the (narrow) HWHMs observed in latetype stars (Cohen et al. 2003). (In late-type stars, mass-loss rates are so small that X-ray lines are likely to originate in coronal loops, rather than in a wind.) Moreover, it is possible to obtain information on the radial distances at which certain X-ray emission lines are emitted by using the f /i emission line ratios from He-like ions (where f and i represent the forbidden and intercombination lines, respectively). To understand this diagnostic, we note that in a collisionally dominated plasma, Gabriel & Jordan (1969) showed that the f /i line ratio is density sensitive because the relative populations of the various energy levels involved are highly dependent on the collisional rates. In fact, this density sensitivity has proven to be a very useful diagnostic in studies of the solar corona. However, in the presence of a strong UV radiation field, radiative effects can significantly alter the populations of certain levels. In particular, the UV radiation enhances the f to i transition rates, resulting in a depopulation of the f-level and an increased population of the i-levels. As a result, the f /i ratio at a particular density can be seriously altered (Blumenthal et al. 1972). The alterations in f /i depend on the UV mean intensity J (r) ¼ 4W (r) H (TeA ), where H is the surface radiation predicted by a model atmosphere (with effective temperature TeA ) at a frequency that can deplete the forbidden line population, and the geometric dilution factor at radial distance r is W (r) ¼ 0:5f1 ½1 (R /r)2 0:5 g (Waldron & Cassinelli 2001; Kahn et al. 2001). Applying this formalism to Ori, Waldron & Cassinelli (2001) found that the line radiation from the cooler ions (e.g., O vii and Ne ix) originates quite far from the star, at radial emitting distances re (cool) ranging from 5R to 12R. Such radial emitting distances are

1. INTRODUCTION Before the launch of the high-resolution X-ray spectrometers on Chandra (HETGS) and on XMM-Newton (RGS), predictions of OB stellar wind models (including radiatively driven shocks distributed throughout the wind) suggested that X-ray emission lines in OB star winds should be highly asymmetric and significantly blueshifted (e.g., MacFarlane et al. 1991). The velocity amplitude of the blueshift (as measured by the peak of the line) was predicted to approach the terminal speed of the wind v1 in optically thick winds (cf. also Owocki & Cohen 2001). The main reason for this line profile behavior is that in optically thick environments, the redward emission on the receding portion of the wind suffers greater attenuation than the blueward emission. In general, the resulting line widths (HWHM) were expected to be very broad (comparable to the terminal speed of the wind), and since these HWHMs were expected to be correlated with the wind density, the observed HWHMs should exhibit a range of values. Furthermore, since shock heating increases with speed, the emission from the hottest ions was expected to occur in regions where the velocity jump across a shock would be as large as possible, i.e., in the fastest part of the wind, at great distances from the star. 1.1. Empirical Questions about the Wind Shock Model X-ray spectroscopic observations now indicate that some of these predictions do not seem to work well in many of the stars that have been observed (Waldron & Cassinelli 2001; Miller et al. 2002; Cohen et al. 2003; Waldron et al. 2004). For example, Waldron & Cassinelli (2002, hereafter WC02), in an early summary of Chandra observations of O stars, found that, with the exception of one particular O supergiant ( Pup: spectral type O4 If; Cassinelli et al. 2001; Kahn et al. 2001), the observed X-ray lines failed to exhibit significant blueshifts. The amplitudes of the empirical blueshifts are found to be 0:2v1 506

WINDS FROM OB STARS: TWO-COMPONENT SCENARIO? consistent with material that has been heated to 2–4 MK by shock heating in the wind. However, the emission sources for the hotter ions (Mg xi and Si xiii) were found to be located sequentially closer to the star. The Mg xi emission (formed at 6 MK) appears to arise between 3R and 4R , and the Si xiii emission (formed at 10 MK) was found to originate very close to the star: the radial emitting distance re (hot) is within 0.1R* of the surface. For Si xiii, the distance hot from the stellar surface to the X-ray–emitting region [hot /R ¼ re (hot) 1] is at least 1 order of magnitude smaller than the equivalent distance for O vii [cool /R ¼ re (cool) 1]. Similar conclusions have also been found by analyzing the f /i ratio in other O stars (Cassinelli et al. 2001; Miller et al. 2002; Waldron et al. 2004). Comparison of the f /i formation radii with the expected temperatures associated with the maximum He-like ionic emissions suggests that the X-ray temperatures within the wind increase inward toward the stellar surface. Better temperature constraints can be obtained by using H-like to He-like line emission ratios as discussed by Miller et al. (2002). Cassinelli et al. (2003) and Waldron (2005), using the results for several OB stars, have compared the temperatures derived from H-like to He-like line ratios with the radii derived from the f /i ratios; they conclude that the temperature derived from X-ray lines increases as one moves inward toward the star. The reliability of the numerical value of re for any ion in a hot star wind depends on how reliably the H spectrum is known at the appropriate frequency. For different lines, H lies at energies that are in some cases longward (e.g., O vii) and in other cases shortward (e.g., Si xiii) of the Lyman edge. Longward of the Lyman edge, H is (in principle) accessible to observations and is therefore known fairly well. However, shortward of the edge, information on H can only be obtained from model atmosphere calculations. As a result, re (hot) is subject to greater uncertainty than re (cool). If it turns out that errors in modeling the spectrum of (say) Ori at wavelengths shortward of the Lyman edge are significant, then the relative numerical value inferred for re ( hot) could change. However, the errors in the spectrum would have to be large in order to eliminate the order of magnitude (or more) difference between cool and hot cited above. Although the numerical values may be uncertain, we assume in this paper that hot < cool is a reliable result. In a recent study, Waldron et al. (2004) studied another O supergiant that is similar in spectral type to Pup: Cyg OB2 No. 8A (spectral type O5.5 If ). Since Cyg OB2 No. 8A is believed to have a stellar wind that is faster and at least twice as massive as that from Pup, the X-ray emission lines from Cyg OB2 No. 8A were expected to display even more significant line asymmetry and larger blueshifts than those observed in Pup. However, Waldron et al. (2004) found that these expectations were not fulfilled. On the contrary, the X-ray emission lines in Cyg OB2 No. 8A were found to be in agreement with the majority of other OB X-ray lines; the lines are essentially symmetric and unshifted. Furthermore, the hottest X-ray lines from Cyg OB2 No. 8A were again found to be formed deep in the wind, close to the star. In theoretical work aimed at understanding the Chandra data, Owocki & Cohen (2001) computed synthetic line profiles for X-rays that are emitted by parameterized models of hot-star winds. In an extensive survey of various combinations of wind parameters, Owocki & Cohen noted that X-ray line profiles that have ‘‘little asymmetry and blueshift are difficult to reconcile with a simple wind outflow that includes attenuation by the wind and stellar core.’’ We note that the wind models used by

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Owocki & Cohen are assumed to be spherically symmetric. In this paper, we argue that this assumption should be relaxed. Ignace & Gayley (2002), in a discussion of the observed lack of asymmetry in X-ray lines, have suggested that the degree of line asymmetry may be reduced by resonance line scattering. However, Ignace & Gayley based their work on Sobolev theory, which relies on a smooth velocity gradient. If X-rays are indeed coming from shocks in a wind, then the local velocity gradient will likely be highly nonmonotonic. 1.2. What about Magnetic Effects? In the context of the present paper, it is especially noteworthy that the hottest X-ray lines are formed closer to the star than the cooler lines. This contradicts the expectations of the standard wind shock model. In view of these results, we are led to consider magnetic effects, first of all from an empirical point of view and subsequently on the basis of theoretical arguments. The idea that magnetically confined hot plasma may exist in OB stars has been in the literature for two decades. Cassinelli (1985) proposed this idea on the basis of an early study of X-ray spectral lines (observed with the Einstein SSS instrument): those lines suggested the presence of a hot (T ¼ 15 MK) component in the O supergiant Ori. Cassinelli (1985) argued that if the temperature of the hottest X-ray gas exceeds an ‘‘escape temperature’’ (derived from coronal wind theory; in Ori, the escape temperature is 7 MK), then the material must be confined somehow. Magnetic fields were considered a natural candidate for confinement. The same star ( Ori) was subsequently observed with Chandra (Waldron & Cassinelli 2001), and again the possibility of magnetic confinement arose in the interpretation of the hottest X-ray component. The presence of hot components in many of the Orion OB stars has been remarked on by Schulz et al. (2003), and also in the main-sequence star Sco by Cohen et al. (2003). Moreover, among early-type stars in Orion (i.e., those earlier than spectral type B4), all but two of the stars have been found to have a hot component in their X-ray spectra (Stelzer et al. 2005). The presence of hot components in so many OB stars invites consideration of widespread magnetic confinement. Significantly, Schulz et al. (2003), in a study of the ‘‘signatures of magnetically confined plasmas’’ among young stars in Orion, have found that these signatures are more prominent in certain stars than in others, perhaps depending on the age of the star. Schulz et al. (2003) suggest explicitly that ‘‘magnetic confinement provides an additional source of X-rays.’’ However, in 1985 and for many years afterward, the concept that magnetic fields are present on the surface of an OB star was not widely accepted. Empirically, there had been no field detections, and theoretically, it was not clear how magnetic fields might originate in OB stars. Recently, the empirical difficulties have been alleviated somewhat with the direct detection of magnetic fields on one O star and on four B stars (Donati et al. 2001, 2002; Neiner et al. 2003a, 2003b, 2003c). The Zeeman data for these five stars suggest that the magnetic field is a global dipole in each of the stars. Even with these detections, however, it is still unclear how widespread magnetic fields really are among O and B stars. For example, Schulz et al. (2003) list Ori (in their Table 4) as a star with ‘‘No Magnetic Fields,’’ even though this is the star in which Cassinelli (1985) and Waldron & Cassinelli (2001) inferred the presence of magnetic confinement. In this regard, a question that was raised by Shorlin et al. (2002) is relevant. In the context of A stars, Shorlin et al. asked, do 5% have ‘‘large-scale ordered fields. . .while the others are nonmagnetic? Or do some (or all) of the others have magnetic

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fields, but fields that are of a different nature than those in the classical magnetic Ap stars?’’ For example, might the fields in some A stars (and by implication also in hotter stars) be arranged in many localized regions (such as in solar-type stars) rather than in a global dipole? The answer to this question now appears to be affirmative for at least one object: the Ap star 53 Cam, with field strengths up to 25 kG, has been shown (Kochukhov et al. 2004) to have a highly complex field on its surface, with multiple local enhancements in field strength, including both poloidal and toroidal components. In order to address their own question, Shorlin et al. (2002) undertook a ‘‘highly sensitive search for magnetic fields in B, A, and F stars.’’ There were only a few detections. In most cases, only upper limits on longitudinal fields were reported in a sample of 74 stars. The upper limits were quite stringent, typically 10–20 G. The B stars in their sample are of most interest to us here. Among a sample of 17 B stars, only one (a chemically peculiar star) had a 3 detection of a longitudinal field Blong . Two of the stars were detected at the 1 –2 level. Fourteen stars (>80%) were not detected in Blong even at the level of 1 ¼ 22 G. If there are indeed fields with magnitudes of a few hundred gauss on these B stars (comparable to those reported by Donati et al. 2001 and by Neiner et al. in four B stars), the geometries of the fields must be quite complex, leading to strong cancellation in the longitudinal field. The B star results of Shorlin et al. lead us to ask the following question: is it possible that only a minority of OB stars have global dipole fields while most OB stars have complex magnetic geometries? In this paper, we raise this latter possibility because of some recent work on dynamo activity in hot stars. Moreover, interest in complex magnetic fields is especially timely in view of the results of Kochukhov et al. (2004): these authors observed in all four Stokes parameters, rather than only the longitudinal field, and so were able to extract more information about the magnetic field than Shorlin et al. (2002). In x 2 we discuss how magnetic fields with complex geometries may be created in certain OB stars. We use this complexity as the basis for the scenario that we propose in x 3 for a two-component stellar wind. A discussion of the scenario with regards to the effects on X-ray line profiles appears in x 4. Further empirical considerations that provide support for our two-component scenario are presented in x 5. 2. MAGNETIC FIELDS IN OB STARS In the present context, the key aspect of our proposed scenario has to do with the spatial distribution of magnetic fields on the surface of an OB star in which a dynamo is at work. First we discuss the origins and expected strengths of magnetic fields on such OB stars. Then we present our picture of how we expect the geometrically distributed magnetic fields to be structured. 2.1. Origins We confine our attention here to stars in which a dynamo is at work. We recognize that there are some hot stars where the fields may be fossils (e.g., the Ap/Bp stars; cf. Mullan 1973; Moss 1989). Some of those fields may be structured in global dipole geometry, but we do not consider such stars here. In the context of dynamo activity in hot stars, Spruit (1999, 2002) has suggested that in regions of a rotating star where the gas is convectively stable, dynamo action may operate as a result of an instability in the magnetic field itself. Specifically, he has suggested that an instability that was first discussed by Tayler (1957) in the context of a laboratory plasma and later in

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the context of stars (Tayler 1973) may operate in nonconvective zones of rotating stars. By assuming that the dynamo is driven by this ‘‘Tayler instability’’ and assuming also that the dynamo settles into a stage of marginal instability, Spruit (2002) derived expressions for the strength of the field, both azimuthal (toroidal) and radial (poloidal) components, as a function of the local shear and the local Brunt-Vaïsa¨la¨ frequency. (The latter, NBV ¼ g½d/dP (d/dP)ad 1/2 , is a measure of how stable the gas is against convection.) Spruit’s formalism refers to any system where convectively stable material exists. Application of the formalism to the problem of mixing in hot stars has been reported by Maeder & Meynet (2003). Combining the Spruit formalism with buoyancy theory, Mullan & MacDonald (2005, hereafter MM05) studied the properties of magnetic fields that are generated in their models of rotating massive stars. In the context of the present paper, it is important to stress certain aspects of the models that were used for rotating massive stars. We also wish to stress why the Spruit-Tayler dynamo leads to the model we consider here. 2.2. Models of Rotating Massive Stars The rotating star models that entered into the MM05 dynamo work had been reported previously by MacDonald & Mullan (2004, hereafter MM04). The models assume that the angular velocity is uniform on spherical shells. Diffusion equations were used to model the mixing of elements, as well as the redistribution of angular momentum. Mass loss was included, using standard estimates of radiative-driven mass-loss rates for hot star winds. Angular momentum loss was treated using the magnetic stellar wind formalism of Barnes et al. (2001): this formalism includes a parameter Nw (the ‘‘wind index’’), which represents the geometry of the magnetic fields in the wind. The numerical value of Nw can range from 37 to 2, denoting completely dipolar and radial fields, respectively. In the hot star models (MM04), Nw was set to 1.5, representing the mixed character of the magnetic fields in the wind, neither purely dipole nor purely radial; this parameterization allows for the fact that the wind escapes with different efficiency from different parts of the surface. Ud-Doula & Owocki (2002) used an MHD model to demonstrate how the line-driven wind from a star with one particular field geometry (a global dipole field) indeed has a mixed field structure, essentially radial (open) near the poles and dipolar (closed) near the equator. Even if the field on any given star is not a global dipole but has higher order structure on the surface (as we argue below is the case on certain OB stars), the results of ud-Doula & Owocki (2002) are useful: the physical nature of the interaction between magnetic fields and a wind inevitably means that the wind will be able to escape more freely from certain areas of the surface than from others. As a result, the magnetic structure on such a star will have a mixed character. This suggests that the choice Nw ¼ 1:5 (intermediate between 37 and 2) in the work of MM04 is a plausible way to parameterize the mixed character (neither purely dipolar nor purely radial) of mass loss from OB stars with magnetic fields on the surface. Of course, it is highly idealized to assume that a unique value of Nw applies to all stars. Each star will probably have a different value. For example, stars with strong (or weak) fields are expected to tend toward the dipolar (or radial) limit of Nw (37 or 2). Also, stars with strong wind driving (i.e., high luminosity) will likely generate more nearly radial fields (Nw ! 2) than stars where the wind driving is weak. In any given star, the condition as to how influential the wind is in opening up the field can be

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characterized (see ud-Doula & Owocki 2002) by a dimension˙ v1 ), less ‘‘wind magnetic confinement parameter’’ (=B2eq R2 /M which characterizes the ratio between magnetic field energy density and kinetic energy density of the wind. Based on the parameter, it appears that in a star such as Sco, the wind is so weak that a field of only 10–20 G may be sufficient to ‘‘close off ’’ significant areas of the surface. On the other hand, in Pup, the wind is so strong that a field of 100 G or more will be needed to interfere significantly with the wind outflow. And even in a given star, the conditions may change during evolution. The complexity of the spatial structures of magnetic fields on the surface of a hot star depends on a competition between wind driving and magnetic confinement. The ram pressure associated with the wind tends to open up magnetic loops that attempt to extend far from the star. The opening up is expected to occur near a radial distance where the Alfveń speed and the wind speed are comparable. Beyond such a location (the ‘‘Alfveń radius,’’ RAlf ), closed loops would find it difficult to exist. A combination of weak fields and/or strong winds would lead to small RAlf . (The parameter introduced by ud-Doula & Owocki [2002] is relevant in this context.) An upper limit on the scale height of magnetic loops in OB stars is set by the length difference RAlf R . If this difference is small, then the surface of a star with a dynamo would likely consist of many small localized magnetic loops. By analogy with the Sun, we might say that there are many ‘‘active regions’’ on the surface of such a star. In contrast, in a star with strong field and weak wind (e.g., the Ap stars), larger loops could survive, and the field might be organized on a more global scale. In x 5.2, we return to estimates of the upper limits of loop lengths in massive stars where a dynamo is operative. Thus, in a more complete study, we should allow for a feedback loop in which each star is allowed to evolve with the value of Nw that is appropriate at each stage of evolution. Such modeling would take us far beyond the exploratory study we are reporting here. MM04 followed the evolution of the internal angular velocity profile inside rotating stars of 10 and 50 M from the pre– main-sequence phase until the termination of the main-sequence phase of evolution. The angular velocity profiles served as input to the Spruit formalism in order to calculate the dynamo magnetic fields inside the star. The results indicate the presence of radial fields up to a few kilogauss in strength, and even stronger azimuthal fields. 2.3. Surface Field Strength and Polarity Building on earlier work on the topic of magnetic buoyancy (MM04), MM05 demonstrated that the dynamo-generated fields inside their model OB stars could be buoyed up to the surface. Although the numbers are very rough, MM05 suggested that the surface fields created in this manner could have strengths of hundreds of gauss. These estimates of surface field strengths appear to overlap with empirical field strengths that have been reported on certain massive stars (Donati et al. 2001, 2002). However, this overlap (which cannot be relied on until more detailed modeling is done) is not essential to the present paper. Here we are more concerned with the spatial structure of the field rather than with the field strength. Is there an overall polarity to the stellar field? In this area, the Spruit-plus-buoyancy model does not make any clear predictions, since individual field elements that are buoyed up to the surface may emerge with a mixture of polarities. This is important in the context of the present paper because the proximity of radial fields of opposite polarity is a condition for the for-

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mation of closed loops. In our model, when such loops form on small length scales, they serve as a source of hot X-rays at small radial distances (see x 3.2). The question is, do such loops form all over the star’s surface, or are certain portions of the surface preferred? The answer to this question is key to our understanding of the overall magnetic properties of a star. Recall that in the Sun, the dynamogenerated fields (such as those in spots) do not emerge uniformly over the surface: they emerge preferentially at low latitudes, between the equator and latitudes of 35 (e.g., Bray & Loughhead 1979, p. 243). We now turn to a consideration of the latitudinal distribution of fields in the context of OB stars. 2.4. Magnetic and Nonmagnetic Areas of Stellar Surface In the present context, more important than the overall strength of the surface field is the distribution of the field on the surface of the star. To appreciate this point, it is worthwhile to recapitulate certain aspects of the instability that is at the heart of the dynamo proposed by Spruit (1999, 2002). In the original papers by Tayler (1957, 1973), the general problem that was being addressed was the following: is it possible that there are instabilities that depend more on the topology of the magnetic field, rather than on the strength of the field? This question first arose in the context of attempts to produce controlled fusion in the laboratory. For this case, most configurations in which a plasma is confined by a magnetic field had been found to be unstable. Tayler’s 1957 paper was set in the context of a laboratory plasma pinch. In such a pinch, where the geometry is essentially cylindrical (with coordinates r, , z), Tayler found that a purely toroidal field [i.e., B ¼ (0; B ; 0)] is indeed unstable, no matter how weak the field is. The instabilities are driven by forces that are associated with the field itself (curvature, gradient, and pressure). Various modes of instability can be represented by perturbations that are proportional to eim . The mode m ¼ 0 gives rise to a ‘‘sausage’’ instability, requiring displacements of gas along the axis. The mode m ¼ 1 gives rise to a ‘‘kink’’ instability, which involves displacements that are mainly perpendicular to the axis. The paper of Tayler (1973) moved beyond the laboratory case and applied the instability analysis to the case of a star containing a toroidal field. In contrast to the case of a pinch, gravity now enters the analysis, and the system is so complex that ‘‘it is difficult to draw general conclusions’’ about the instability of the star as a whole. However, Tayler points out that, rather than focusing on the global picture, it is worthwhile to pay attention to localized regions, to see whether there are local instabilities at work. In particular, he pointed out that near the axis of the star, ‘‘the field configuration resembles that of a cylindrical gas discharge,’’ although with the important proviso that gravity is now also at work. The effects of gravity tend to suppress the m ¼ 0 modes. The reason is that the axial displacements associated with m ¼ 0 now must do work against gravity. (Tayler was considering the case of a star where the material is stable against convection: in the present paper, we are also interested in such a case.) However, the m ¼ 1 kink modes, with motions that are mainly perpendicular to the axis, do not need to work (much) against gravity, as long as we stay close to the axis. In such a case, the toroidal field (which can be seen as consisting of ‘‘stacks of loops concentric with the axis’’; Spruit 2002) responds to a kink by having the loops ‘‘slip’’ horizontally relative to each other. In a graphic image, Spruit (2002) refers to this as a ‘‘process similar to the accidental slippage of disks in the spinal column of bipedal vertebrates.’’

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The material near the axis is always subject to the Tayler instability. But as we move away from the axis to lower latitudes, the m ¼ 1 mode becomes harder to drive. The reason is that as the latitude decreases, motions that are perpendicular to the axis involve increasingly large components that are locally in the vertical direction: gravity makes it increasingly difficult for such motions to occur. Whether or not the instability occurs at a given location depends on the latitudinal gradient of field strength. Quantitatively, in the context of spherical geometry, an extension of Tayler’s work by Goossens et al. (1981) indicates that the instability occurs at latitude provided that the following conditions are satisfied. For the m ¼ 0 mode, cos @=@( ln B2 = sin2 ) > 0. For the m ¼ 1 mode, @=@( ln B2 sin cos ) > 0. Spruit (1999) points out that in the case in which B is due to the winding up of an initially uniform field parallel to the axis, the m ¼ 0 mode is stable at all latitudes, but the m ¼ 1 mode is unstable at certain parts of the star. Specifically, the m ¼ 1 mode is unstable throughout ‘‘caps’’ that extend from both poles down to latitudes of 45 . This result is key to the present paper. In fact, the ‘‘polar caps’’ may extend over even larger areas of the star if one takes into account the finite dimensions of buoyant flux ropes or if conditions were such that the magnetic fields were in a ‘‘strong field limit’’ (see MM05). Although the word ‘‘cap’’ often has a connotation of covering only a small area, this is not the case here: the polar caps in a Tayler-unstable star are expected to occupy a large percentage of the total surface area. Thus, if Tayler instability is at work in a particular OB star, as MM05 suggest, we are led to an image of that star’s surface that is structured on a macroscopic scale: there are large polar caps surrounding north and south poles, and there is an extensive equatorial ‘‘band.’’ Figure 1 shows a simple schematic diagram of the distribution of these regions on the OB star’s surface. The use of the terms ‘‘cap’’ and ‘‘band’’ becomes obvious from a visual inspection of the geometric shapes of those regions in Figure 1. The caps are conically shaped and symmetric about the polar axis. The band is a wedge-shaped region between the two polar caps, is symmetric about the stellar equator, and encircles the star. The long-dashed lines in Figure 1 denote the boundaries between the polar caps and the equatorial band. Because of the nature of the Tayler instability, the magnetic properties of the polar caps and the equatorial band are expected to be significantly different from each other. On the one hand, the caps are regions where magnetic fields rise from time to time to the surface. In view of what is known about magnetic fields on the surface of the Sun, we expect that the dynamo in an OB star will lead to the formation of a number of looplike structures at any particular instant of time (as in Fig. 1). In the Sun, as magnetic flux tubes rise through the convection zone, the turbulent motions lead to significant distortion of the field: this gives rise to a characteristic fragmented or ‘‘shredded’’ appearance of the fields in solar active regions (cf. Fig. 8-13 of Foukal 1990). In OB stars, the dynamo-generated flux tubes approach the surface of the star by rising up through nonconvective gas. This may allow flux tubes to have a ‘‘neater’’ appearance on the surface of an OB star than in the Sun. As time goes on, the loops in the polar caps of an OB star are likely to be dynamically active when local conditions are appropriate, e.g., when a newly emerging loop collides with an old one or when a previously closed loop opens up due to over-

Fig. 1.—Simple pictorial of the two-component wind of a massive star. A line-driven wind escapes unimpeded from a broad band centered on the equator. Polar caps contain loops of magnetic flux that appear from time to time as the dynamo generates new flux; these loops impede (but do not entirely suppress) the outflow of wind from the polar caps. The loops also trap material that is raised to high temperatures as a result of shock heating (see x 3.2). [See the electronic edition of the Journal for a color version of this figure.]

loading with hot material. On the other hand, the equatorial band is, in this scenario, expected to be devoid of magnetic fields. As Figure 1 suggests, the caps and the band do not occupy vastly different fractional areas of the stellar surface. In fact, to zeroth order, both regimes occupy comparable areas of the surface. Thus, other things being equal, both regimes are expected to contribute equally weighted observational signatures. In theory, the magnetic poles and the rotation poles are expected to be aligned in the Spruit-Tayler dynamo. However, experience with astrophysical magnetic fields, especially in the Sun and planets, indicates that the magnetic axis and rotation axis often do not coincide precisely. We suggest that a similar situation may also arise in an OB star, especially with caps that extend over (essentially) one-half of the stellar surface. At any instant of time, each polar cap is not expected to be uniformly covered with magnetic loops. Instead, just as in the latitude ranges on the Sun where dynamo fields emerge, there are expected to be areas where the field is strong (‘‘active regions’’) and other areas where the field is weaker. As a result, suppose that a large and strong magnetic loop appears in one of the polar caps at a certain time: such a loop could temporarily dominate the magnetic signature of that polar cap during the lifetime of the loop. We suggest that when such a magnetic OB star is viewed from Earth, the effect will be to resemble a field structure that amounts to an oblique magnetic rotator, at least during the lifetime of a strong loop. As a result, axial rotation (on timescales that are short compared to loop lifetime) may serve to bring into view different magnetic structures at different rotational phases. We return to the oblique rotator in x 5.4. 2.5. Magnetic Polar Caps: Large-Scale Properties It may be that global effects could impose an overall predominant polarity on one polar cap and the opposite polarity on the other cap, enough to make the star appear to have a (weak) global dipole. This is apparently what happens in the Sun (a star to which Spruit [2002] applies his dynamo theory). At any given time, apart from a year or so near maximum activity, the coronal hole that surrounds the Sun’s north pole has a

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well-defined large-scale polarity, which is opposite to that of the coronal hole surrounding the Sun’s south pole. In the course of an activity cycle, the large-scale polarity undergoes reversal. Newly emerging toroidal flux creates bipolar active regions with strong local fields. During the course of one 11 yr cycle, magnetic fields in the trailing edges of active regions diffuse slowly toward the poles, canceling out the previous polar cap fields and reversing the polarity of the global dipole (for a discussion, see, e.g., Foukal 1990, p. 388). However, the appearance of a large-scale dipole in the Sun is true only in a statistical sense and not in a strict physical sense: the polar coronal holes are not monolithic in their magnetic structure. Instead, small-scale magnetic fields of mixed polarity are also present in coronal holes (e.g., Judge & Pietarila 2004). In fact, small-scale structures inside coronal holes contribute significantly to some of the most important coronal dynamics, especially with regards to the origin of the solar wind (Hassler et al. 1999). If OB stars contain many small loops in their polar caps, individual loops would probably not be detectable by magnetic measurements. But there might still be a residual global field. In the case of the Sun, observations of the ‘‘Sun as a star’’ (e.g., from the Wilcox Solar Observatory) do indeed reveal a global dipole with an 11 yr cycle, but the amplitude of the polar field is only 2 G. Individual magnetic elements on the solar surface have fields that are much stronger, some tens of gauss when observed at the highest angular resolution (0B1; e.g., Berger et al. 2004). If such fields occur in small-scale structures in polar regions, the observed polar field of 2 G represents cancellation by 1 order of magnitude or more. Moreover, when the polar fields are reversing, the statistical nature of the process means that at certain time intervals (lasting up to a year or so around maximum), both polar caps may exhibit the same net polarity. If dynamos in OB stars generate small-scale closed loops in polar caps, as we suggest here, the large-scale field strengths that would be susceptible to Zeeman observations of the star might also be expected to be subject to significant cancellation. Therefore, if individual loops had fields of a few hundred gauss, the ‘‘global’’ field strength might be weaker than this by 1 order of magnitude or more. This could lead to ‘‘polar’’ fields of the order of 10 G or less. If polar caps with many small-scale closed loops are a common feature of O and B stars, this could explain why most OB stars are not observed to have detectable fields. The few stars that have been detected (Donati et al. 2001, 2002; Neiner et al. 2003a, 2003b, 2003c) with strong global fields may be stars where the fields are not generated by dynamos: they may be fossils. Is there a way to distinguish between dynamo-generated fields and fossil fields? One sure signature of dynamo activity would be polarity reversal in a particular star. No estimates have yet been made of the periods of activity cycles in a Spruit-Tayler dynamo. 3. PROPOSAL FOR THE SPATIAL STRUCTURE OF WINDS FROM OB STARS Let us explore the effects that the scenario proposed in Figure 1 would have on the wind from a hot star. The primary hypothesis of this paper is the following: the wind from an OB star in which a Spruit-Tayler dynamo operates consists of two distinct regimes (see Fig. 1), (1) an equatorial wind band and (2) polar cap winds. The dynamics of each regime are different. We now discuss the wind structures from these two regimes and how they are expected to alter the observed X-ray emission.

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3.1. Equatorial Wind Band This region consists of a band extending to 45 on either side of the equator. There are no magnetic fields and therefore no obstacles to ion flow. In this band, the radiative line force is unhindered, and the resulting stellar wind will have the typical characteristics that are associated with heavy mass loss. In particular, radiative-driven wind shocks will develop and produce a distribution of X-ray emission. However, a major difference from the standard model is that the observational characteristics of the X-ray emission will now vary depending on the observer’s viewing angle; i.e., how does the line of sight (LOS) intersect with the band? 3.2. Polar Cap Winds In the polar caps, the individual magnetic loops that may exist at any instant of time are expected to inhibit the easy outflow of ionized material. In particular, the ions that are responsible for the line-driving forces are not permitted to expand freely. As a result, the wind from the polar caps should be more or less inhibited, depending on how effective the loops are at interfering with the line-driving forces. This leads us to expect that the overall mass-loss rate (per unit area) from the polar caps will be less than the rate (per unit area) from the equatorial band. The existence of closed field lines on a certain part of the surface of an OB star is reminiscent of the MHD modeling by ud-Doula & Owocki (2002). Those authors computed how a global dipole field interferes with the outflow of line-driven wind from a hot star: one of the outcomes is the presence of shock-heated material on closed magnetic loops. In the next subsection, we compare and contrast in some detail our model and the work of ud-Doula & Owocki. For now, we note that if we were to take a local view, each closed magnetic loop in the polar cap of an OB star might be considered as a localized (buried) dipole. How does this local dipole interfere with wind outflow? No detailed answer is yet available. However, one result that may be transferred immediately from ud-Doula & Owocki is the presence of hot gas on closed loops: radiative driving of material up along the legs of a loop leads to shock heating, whether the loops are small or large. Thus, we expect the closed loops in the polar caps of Figure 1 to contain hot gas, specifically, gas that is hot enough to excite emission of S xv and Si xiii. Moreover, recalling the (global) parameter of ud-Doula & Owocki (2002), it seems physically plausible that with appropriate modifications, a local (=magnetic energy density/kinetic energy density) may be defined in such a way as to be pertinent to the conditions that pertain in the vicinity of a local dipole. From this perspective, loops in the polar caps with strong fields are expected to be more capable of impeding wind outflow than weak field loops. Thus, an individual loop is expected to interfere with a greater or lesser amount of material for a certain amount of time. Material that is confined to a polar cap loop will be shock heated and will produce hard X-rays in the same way as ud-Doula & Owocki (2002) discuss for the global dipole. However, in contrast to ud-Doula & Owocki’s model, where the magnetic field is static, the loops in our polar cap model are intrinsically time-dependent because of dynamo action. In particular, new fields are continually emerging. Such emerging flux will inevitably interact from time to time with preexisting loops and undergo magnetic reconnection. Two consequences follow. First, magnetic energy that is released in reconnection events will cause local heating (as in solar flares). This provides

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a source of magnetic heating in OB stars over and above the shock heating that occurs on closed loops. Second, material that has hitherto been confined to a local loop now has access to open fields: such material is released from confinement. With the opening up of an individual loop, the bursty release of previously impeded ions would serve as a natural source of material for a discrete absorption component in the wind (Mullan 1984). We return to this topic in x 5.3. 3.3. Comparison and Contrast with a Different Example of a Two-Component Wind The star 1 Ori C is an example of a two-component wind that has some overlap with the type we consider here but also has significant differences. Zeeman observations suggest that 1 Ori C has a global dipole field with a polar strength of 1.1 kG (Donati et al. 2002). The star is very young, and it is possible that the field is a fossil from the time of star formation. If this is true, the star differs from the type of object in which we are interested in this paper. 1 Ori C has been the subject of X-ray studies by two groups of Chandra investigators (Schulz et al. 2001, 2003; Gagne´ et al. 2005). There is a very broad range of temperatures associated with the X-ray–emitting material, from a few MK up to as much as 60 MK (Schulz et al. 2003). Most X-ray lines have velocity widths (200–500 km s1) that are much narrower than v1 . However, two lines (due to O viii and Fe xvii) are significantly broader (700–900 km s1), and the O viii line is blueshifted (Schulz et al. 2003). Significantly, the two broadest lines are emitted by relatively cool material. Gagne´ et al. (2005) conclude that ‘‘the two broader lines could represent cooler plasma formed by the standard wind instability process.’’ In order to understand the great width of the O viii line, Schulz et al. (2003) conclude that the line must be formed ‘‘near the terminal velocity of the wind,’’ at about 7 stellar radii from the photosphere. Thus, it appears that one component of the X-rays in 1 Ori C can be understood in the context of a ‘‘standard’’ wind model. On the other hand, as far as the remaining (narrow) lines are concerned, Gagne´ et al. (2005) show that they can be fitted ‘‘surprisingly well’’ by a two-dimensional MHD magnetospheric wind model. This model includes a wind that escapes at high speed from the polar caps but is impeded in the equatorial regions by closed loops of a global dipole field. (An earlier version of this model was reported by ud-Doula & Owocki [2002], although the latter did not include an energy equation, so temperatures were not known.) The closed loops near the equator lead to collisions of upward accelerating plasma from both footpoints. As a result, shock heating leads to hot gas that is trapped on loops. This material, which cannot expand freely in the wind, gives rise to narrow X-ray lines. Gagne´ et al. (2005) also use the f, i, and r line ratios to show that the hottest lines (due to S xv) are formed at heights of 0.2R –0.5R above the stellar surface. These are presumably the heights of the topmost closed loops. The similarities with the model in the present paper are clear: in one part of the star, wind escapes freely, while in other locations, the outflow is impeded by closed field lines. In both models, hot material is associated with closed loops, while the cooler lines are emitted by freely escaping wind. The heights of the uppermost closed field lines are a few tenths of R , consistent with estimates that we provide in x 5.2. The differences are also clear: in our model, the wind escapes freely from the equatorial region, whereas Gagne´ et al. have the wind escaping freely from the polar regions. In our model, many small magnetic loops interfere with the polar flow,

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whereas Gagne´ et al. use a global dipole field to impede the equatorial flow. In our model, the hottest X-rays emerge from the polar caps, whereas in the model of Gagne´ et al., the equatorial loops are the site of the hottest X-rays. In our model, the magnetic field is time-dependent, including reconnection events to provide extra heating and bursty release of material, whereas Gagne´ et al. have a static field. To be sure, the global dipole field in certain (rotating) stars may also release material from time to time: Townsend & Owocki (2005) refer to such an event as ‘‘breakout’’ and suggest that it may explain the occurrence of flares in magnetic Bp stars. But in the Townsend-Owocki work, breakout occurs as a result of centrifugal forces acting on material that has accumulated above a critical mass; in the model we consider (see Fig. 1), loops in polar caps will not be subject to significant centrifugal forces. We consider it more likely that the loops in Figure 1 will open up as a result of reconnection. 4. DISCUSSION The major aspect of our proposal is the large-scale and systematic departure of OB star winds from spherical symmetry. In particular, an observer who views from a direction near to either pole will see a quite different regime from one who views from near-equatorial directions. 4.1. The Near-equatorial View An equatorial observer can see the full expansion effects of the wind directed along the line of sight. With the equatorial band extending to 45 on either side of the equator, the wind in projection will obscure some 70% of the surface. Thus, the view of the star in X-rays will be dominated by the emission from the wind band. As a result, we expect to see significant blueshifted and asymmetric line profiles. Polar caps may be observable to some extent, although there will be some obscuration of the view because of the wind equatorial band. To the extent that these glimpses of the polar caps are negligible, the use of a spherically symmetric wind model would be expected to work best in the limit of equatorial viewing. We suggest that Pup is in this category. X-rays created by wind shocks are expected to be distributed throughout the wind, with the most energetic lines arising from the outer wind region where the wind speed is larger. 4.2. The Near-polar View Here we are looking right down into the polar caps where the magnetic loops are most plentiful. In this case, we expect to see hard X-rays caused by magnetic activity in loops that lie close to the stellar surface. Moreover, from this perspective, we see two components of the wind: a weak wind from the polar cap and a strong wind in the equatorial plane. From the perspective of a pole-on view, the dominant wind component (in the equatorial band) lies close to the plane of the sky. Therefore, the dominant wind flow is essentially perpendicular to our line of sight. As a result, line emission from this flow would not be expected to display any significant blueshifts or redshifts. We suggest that Sco is in this category. (We note that Cohen et al. [2003] have also pointed out, on the basis of the observed rotational velocity, that Sco may be a pole-on star.) However, since the equatorial band is wedge-shaped with a finite spreading angle, there are finite projected flow components toward and away from the observer. Hence, the observed width (or HWHM) of lines that are emitted by the wind is determined by the opening angle of the equatorial band. For example, with an opening angle of the order of 45 , the maximum

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HWHM of a wind-dominated line will be of the order of 0.7 times the terminal speed. With regard to the asymmetry of an X-ray wind line formed in the equatorial band, the geometry ensures that the line asymmetry will certainly be less than in the case of a spherically symmetric wind; depending on the optical thickness of the line of sight through the equatorial band of wind, the line asymmetry may in fact be small. With regard to the ‘‘temperature’’ of the X-rays in a polar view, our favorable viewing angle allows us to see the component that is confined in the closed loops in the polar cap region. To the extent that certain X-rays from these loops predominate over X-rays from the wind from such a star, the profiles of the loop X-ray lines in such a star may resemble lines in solar-like stars (where loops dominate the X-ray emission). In this regard, we consider it noteworthy that Cohen et al. (2003) have reported line widths in Sco that are comparable to those in latetype active stars. We speculate that magnetic activity is the source of hot X-rays in the polar caps; i.e., magnetic loops are the source of the hottest X-ray emission (e.g., S xv, Si xiii). The confined nature of the emission on such hot loops guarantees that this emission is located at small radial distances, as Waldron and Cassinelli (2001) first suggested for the star Ori. (We return below to estimate how small these radial distances are expected to be.) In view of the MHD modeling reported by Gagne´ et al. (2005), we expect that material that is trapped on closed loops may display a mixture of upflows and downflows. This would contribute to symmetric line broadening if loops dominate the X-ray flux. 4.3. X-Ray Line Profiles in a Two-Component Wind One of us has developed a code to compute X-ray line profiles emitted by a two-component wind (Waldron 2001). The code builds on the spherically symmetric work of Owocki & Cohen (2001), where sources of X-ray–emitting material are distributed throughout a circumstellar volume with emissivity k (r; ): here k is the observer’s wavelength, r is the radial location of the emitters, and ¼ cos1 is the angle between the line of sight and the local radial direction. The X-ray luminosity is obtained by integrating over direction and radius, including attenuation by continuum absorption in the wind: Z

1

Z

1

Lk 1

dr r 2 k ( ; r)e( ; r) :

R

Owocki & Cohen show how the optical depth is to be evaluated along any particular line of sight. The radial variation of density is determined by the velocity profile: for a steady ˙,M ˙ /r 2 v(r). A common choice for v(r) is mass-loss rate M the standard ‘‘-law’’: v(r) ¼ v1 (1 R /r) . With this choice of velocity profile, the smaller is, the more rapid is the acceleration of the wind. In the present work, we use a -law for each of the two components of the wind but with different values of in each component. The emissivity depends on the square of the density of the local material: k ( ; r) 2 . In the work of Owocki & Cohen (2001), is assumed to be spherically symmetric; i.e., is a function of r only. Here we allow not only for radial variations of density but also for variations of the density as a function of colatitude ; i.e., we adopt ¼ (r; ). The latitudinal variation of density is assigned as follows. At high latitudes, in the region

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Fig. 2.—Line profiles seen by an observer viewing a two-component wind from the pole-on direction. Abscissa: Ratio of velocity along the line of sight VLOS to the terminal velocity of the wind. Three sizes of the polar cap are used as indicated by the variable p , which are shown in the inset measured in degrees of colatitude. For all models, the equatorial wind has w ¼ 0:8, the polar wind has p ¼ 1:5, and the ratio of polar to equatorial density p /w has the value 0.1. [See the electronic edition of the Journal for a color version of this figure.]

between the pole and colatitude p , the wind is characterized by a density p at the inner radius and a velocity law with ¼ p . At low latitudes, from the equator up to latitude 90 p , the wind is characterized by a density w at the inner radius and a velocity law with ¼ w . In any particular model, we prescribe the ratio p /w ¼ (say) 0:5. Since the poles are regions where the wind outflow is impeded, we consider it physically plausible to assume that p /w is likely to be less than 1. Our choices of w and p are guided by the different physical conditions in the two components of the wind. In the equatorial band, we assign w ¼ 0:8, appropriate for the rapid (unimpeded) acceleration of a line-driven wind (cf., e.g., Cohen et al. 2003 for the case of Sco.) In the polar caps, we assign larger values to p (from 1.5 to 5), indicating that the polar cap winds accelerate more slowly, due to the inhibiting effects of the magnetic loops. For each volume element, an appropriate X-ray continuum optical depth is calculated based on the requested line of sight. This allows the resulting line profiles to be computed for different viewing angles relative to the pole and relative to the equatorial band. Detailed results of this code will be presented in a forthcoming paper. For the calculations to be reported here, we have chosen to use the relevant stellar parameters associated with Pup to define our wind density and velocity law, i.e., R ¼ 16:5 R , v1 ¼ ˙ ¼ 2:4 ; 106 M yr1 (Lamers & Leitherer 2200 km s1, and M 1993). The adopted X-ray wind absorption cross sections are discussed in Waldron et al. (2004). The primary goal of this exploratory paper is to demonstrate how the geometric effects of a two-component wind can alter X-ray emission line profiles produced from a wind distribution of X-ray sources. Hence, we are not concerned with specific X-ray characteristics such as temperature. Instead, we assume that throughout the winds in the polar region and equatorial band the X-ray temperature is the same and constant (the same assumption as used by Owocki & Cohen). In addition, our model does not include any X-ray contributions from the magnetic loops: we model only the emission from the outflows. In this study we confine our attention to a single set of examples as shown in Figure 2.

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The profiles in Figure 2 refer to a pole-on observer who is observing a star where the polar wind has a mass flux of 0.1 times the equatorial mass flux. For the polar wind, this case has p ¼ 1:5. With these choices, the code predicts that when the polar cap extends down to colatitude p ¼ 45 (see Fig. 2, black line), the line profile peaks at a blueshift of 0.4v1 . And if the polar cap extends down to p ¼ 60 (a possibility for the Tayler dynamo in certain cases; see MM05), the line profile (see Fig. 2, light gray line) peaks at a blueshift of 0.2v1 . In the limit of p ! 90 , the equatorial wind band becomes more and more confined to a thin disk. When such a disk is viewed from the polar direction, the X-ray lines appear unshifted, narrow, and symmetric (see Fig. 2, dark gray line). Note that the profiles in Figure 2 refer to X-rays that are emitted by sources distributed throughout the wind. They do not include the effects of X-ray emission from hot loops in the polar caps. However, if such loops are present, we expect them to contribute to the X-ray line profile at zero velocity, further reducing the overall line shift and also reducing the asymmetry. The line profiles predicted by our two-component code are more consistent with the properties of many lines observed in hot stars, i.e., symmetric and almost unshifted (WC02), than are the predictions of the standard model. To be sure, this improvement comes at the expense of extra parameters (viewing angle, ratio of polar to equatorial mass fluxes) that are not yet well known. If the only information we had on hot star winds were provided by X-ray spectroscopy, it might be difficult to choose between the standard model and the model we propose here. However, information from other sources is also available. We now turn to an examination of these. 5. ADDITIONAL ASPECTS OF A TWO-COMPONENT WIND In this section, we touch on a number of topics that appear to provide support for the scenario of a two-component wind. 5.1. X-Ray Variability: Limits of Detectability Our model is based on the presence of hot magnetic loops on certain parts of the surface. However, an essential aspect of our model is that these loops are not permanent structures, any more than loops in the Sun are permanent. On the contrary, the constant interplay of magnetic forces (which vary in time due to dynamo action, including newly emerging flux) and line-driven winds suggests that magnetic loops, which are closed structures for a certain period of time, will eventually open up, releasing material into the wind. Are there observable consequences of such openings? To answer that, we note that the MHD model of ud-Doula & Owocki (2002) demonstrates that material that is influenced by magnetic fields in an OB star behaves in a manner that is highly time dependent. Some material is channeled into a hot shockheated disk of outflowing wind, while other shock-heated material eventually drains back down onto the star. As another indication of the time-dependent behavior that accompanies interactions between fields and material in hot stars, we can refer to recent work by Townsend & Owocki (2005). These authors consider the case of a global dipole field interacting with a wind in a rotating Bp star ( Ori E) that is known to undergo X-ray flares (Groote & Schmitt 2004). In that star, Townsend & Owocki suggest that the flares are associated with ‘‘breakout events,’’ which occur when the mass accumulated in the closed magnetic loops becomes so large that centrifugal forces win out over the magnetic tension. During a breakout

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event, ‘‘stressed magnetic field lines will reconnect and release significant quantities of energy.’’ This raises the question, does our model also predict X-ray flares each time a loop opens up? In principle, the answer is yes. In practice, with NL loops on the surface, the relative fluctuation in X-ray emission when one loop opens is expected to be of order ðNL Þ1/2. In the case of a global dipole, NL is essentially equal to 1, so the relative fluctuation is very large (100%): such a fluctuation would be readily detectable as a flare. We suggest that such is the case for the Bp star Ori E. In our model, NL may be large; e.g., in the case of the OB supergiants in Orion, Cassinelli & Swank (1983) interpret the presence of hot gas as evidence for a number of closed loops on the surface. They estimate that for Ori, NL may be in excess of 250. As a result, the relative fluctuation in X-ray intensity from a star when one loop opens up may be of the order of 6% or less. Depending on the signal-to-noise ratio, such a flare may not be obvious, especially if it is short lived. In stars where the number of loops is smaller, say NL ¼ 50 100, the relative X-ray fluctuation due to the opening of one loop would be expected to be larger, 10%–14%. In this context, we note that Cassinelli et al. (1983), in a study of X-rays from two early B supergiants ( Ori and Ori), reported some short-term variability in the fluxes. For Ori, over an observing period of 26 ks, the X-ray fluxes were found to vary between 0.45 and 0.27 counts s1. For Ori, the range was between 0.22 and 0.08 counts s1. To be sure, the error bars are large enough that the statistical significance of the variations is not large: in a test of the hypothesis that the flux remains constant on timescales of 100 s, the reduced 2 was found to be 1.13 and 1.16, respectively, for the two stars. In view of these values, the hypothesis that the stars actually remain constant in X-rays is supported at a confidence level of 90%. The fact that the confidence level is not as high as 99% (when it would be referred to as ‘‘highly significant’’ according to Taylor 1982, p. 231), or even as high as 95% (when it would be referred to as ‘‘significant’’ according to Taylor 1982), means that the possibility of variable X-ray fluxes from the two stars is not ruled out at a highly significant level, or even at a significant level. However, it is important to note that, because of the poor signal-to-noise ratio in the data obtained by Cassinelli et al., rather large variations in X-ray flux would have had to occur in order to be detected reliably: ‘‘variability on hourly time scales. . .would have been detected in our data’’ only if the amplitude had been ‘‘greater than 20%.’’ Cassinelli et al. could not have detected the events at the level of ðNL Þ1/2 6% 14% estimated above. More than a decade after Cassinelli & Swank (1983) inferred the presence of 250 loops on the surface of Ori, ROSAT (Ro¨ntgensatellit) was used to study X-ray variability in the same star with improved signal-to-noise ratio. Over a time period of 3 yr, the X-ray flux was found to vary between 1.43 and 1.72 counts s1 (Bergho¨fer & Schmitt 1994). Disregarding the highest point (which may have been due to an exceptionally strong shock propagating through the wind), the remaining data points span a range of 5% about the mean level. And in a more intensive study of a 1 day interval, Bergho¨fer & Schmitt also found X-ray flux that varied from 1.35 to 1.55 counts s1, i.e., 7% about the mean. The authors state that the ‘‘level of absolute variations in X-ray count rate is well below 10%.’’ Thus, the data do not rule out the existence of real variations at the 6% level, as we expect from ðNL Þ1/2 effects. With regard to the variations at the few percent level, Bergho¨fer et al. (1996) have reported a study of simultaneous

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variability in H and X-ray emissions from another O supergiant, Pup. The signal-to-noise ratio of their ROSAT data was better than that of the Einstein data reported in the earlier work by Cassinelli et al. (1983). They established that there is a correlation between the variations in H and those in X-rays, attributing the variations to modulations in wind density. For our purposes, the key point is that ‘‘the amplitudes of the observed X-ray variations are small and amount to only 6%.’’ Of course, it is probably coincidence that this observed amplitude is the same as the relative fluctuations predicted above for a different O supergiant ( Ori), but we note it anyway. With regard to the variability in the wind of Ori, some of this may be associated with variations in H at low velocities (Prinja et al. 2004); these variations are likely connected with pulsation. However, there are also high velocity changes in H (extending to blueward velocities of 300 km s1) for which pulsation is a less satisfactory explanation. We suggest that the high-velocity H features reported by Prinja et al. (2004) may be associated with the transient opening of magnetic loops, ejecting material into the wind. Apart from short-term variability, there is also a question of long-term variability. Cassinelli et al. (1983) reported that for Ori, the X-ray count rate in 1980 was 46% larger than it had been 11 months earlier. Various possibilities are explored for explaining such a large change in X-ray emission. Although Ori is classified in the SIMBAD database as a variable star, the amplitude of Hipparcos variability is very small: only 9 mmag, and these variations are not periodic (cf. Morel et al. 2004). Here we would like to suggest that dynamo activity akin to the cycle of solar activity may contribute to the long-term variation in X-ray flux in Ori. In the context of dynamo theory, it is also natural to suggest that the nonperiodic variations that occur on short timescales in the H equivalent width in this star (Morel et al. 2004) may be due to magnetic activity, e.g., opening of loops. 5.2. Loop Lengths The magnetic loops in the polar caps are expected to have a variety of lengths, depending on how close to each other loops of opposite polarity emerge on the surface. How short might the loops be? We note that Cassinelli & Swank (1983), in their study of the O supergiant Ori, have used a line of reasoning to estimate an average length of the X-ray–emitting loops on that star. They find that the loops have half-lengths of 0.13R. Such loops are expected to extend to vertical heights of the order of 0.1R above the photosphere. In fact, this very star also shows hot emission (Si xiii) that, when interpreted in terms of dilution factors, is found to be confined within about 0.1R of the photosphere (Waldron & Cassinelli 2001). Thus, it seems that the method used by Cassinelli & Swank (1983) to estimate loop sizes overlaps in an interesting way with the independent analysis of a very different data set by Waldron & Cassinelli (2001). At the large end of the loop size spectrum, we note that fields that emerge farther apart are expected to create larger loops. The largest loops are expected to be those that form from oppositely directed fields with maximum spatial separation. Since the Tayler dynamo operates in a polar cap, the maximum local separation would arise between loops that form at latitudes close to 45 but at longitudes that are separated by 180 . Such loops would be separated by almost 90 in latitude, with spatial separations of the order of (/2)R. Since loops are expected to rise to altitudes that are comparable to their footpoint separation, this leads us to expect that loops on OB stars where the

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Tayler dynamo is at work could extend to altitudes of the order of R , i.e., to radial distances of 1R –2R. From an empirical point of view, we note that according to analysis of the f/i/r line ratios in He-like ions, the hottest ions in certain stars (e.g., Si xiii in Sco) occur at radial distances of 1.1R –1.5R (Cohen et al. 2003). These distances are so close to the star that it is difficult to see how, in a standard model, the wind shocks could have large enough amplitude to heat the gas to 10 MK. On the other hand, radial distances of 1.1R –1.5R are entirely consistent with the Si xiii emission arising in loops with the sizes estimated above. 5.3. Discrete Absorption Components Discrete absorption components (DACs) are relatively narrow features that appear as transient enhanced absorptions in the blueshifted absorption wings of O and B stars (e.g., Kaper 1993). They are almost ubiquitous phenomena in O stars: among 203 O stars that were observed by IUE (International Ultraviolet Explorer) at high resolution, Kaper reports that DACs were observed in at least 160. One possible model for DACs involves the occurrence of corotating interacting regions (CIRs; Mullan 1984), in which parcels of wind are supposed to emerge with differing speeds from different regions of the star. In the presence of such speed differences on a rotating star, a faster stream is expected to overtake a slower stream and set up a pair of shocks in the wind. Absorption of light from the star by the material between the shocks gives rise to a DAC. Evidence in support of the CIR concept has been provided as a result of an extensive observing campaign with the IUE satellite (Prinja et al. 1995; St-Louis et al. 1995). Why the wind that emerges from different regions of the surface of a hot star should have different speeds was not specified in the original CIR paper. However, it was quickly realized (Mullan 1986) that magnetic fields might help in this regard. In the context of the present paper, the geometry we propose for the magnetic fields in a hot star (confined to the polar caps) allows us to envision how the magnetic field of a hot star could give rise to variable wind speeds from different portions of the surface. The wind that emerges from the polar caps (where magnetic fields interfere with the flow) is expected to have quite different properties from the wind in the equatorial band (where line driving occurs in an unimpeded manner). Specifically, the occurrence of dynamo-generated fields that emerge in the polar caps leads us readily to a proposal for transient structures in the wind. When a new flux rope emerges into the polar cap, one of two possibilities may occur. First, if it encounters a preexisting loop, reconnection may occur in an explosive manner, giving rise to a mass ejection. The mass and speed of the ejection would be determined by local conditions. As a second possibility, if the flux loop can survive long enough, the line-driving forces that are ubiquitous in hot stars may force the loop to evolve in the manner described by ud-Doula & Owocki (2002) for a global dipole. Eventually, the loop may be forced open by the buildup of heat in the loop. The material that eventually emerges as a transient stream in the wind would have properties that are determined by the properties of the original loop. We suggest that a DAC occurs when a mass ejection event from a recently emerged loop in one of the polar caps creates a CIR that happens to transit the disk of the star. Limits on the lateral extent of the DAC can be judged (at least qualitatively) from the fact that the discrete components are seen in absorption but essentially never in emission. They therefore must have

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MULLAN & WALDRON

length scales that are a sizeable fraction of the stellar radius but not as large as several stellar radii (Kaper 1993, p. 26). This reinforces the idea that DACs emerge from relatively compact structures on the star rather than on a global scale. We have already pointed out that the loops in the polar caps of an OB star are expected to have an upper limit to their sizes, namely, about R . If the DACs originate in such loops, then they can readily have linear dimensions that are capable of explaining the optical properties of a DAC (i.e., strong absorption without significant emission). 5.4. Oblique Rotator As was pointed out above (x 2.4), dynamo operation in massive stars may give rise to magnetic fields, which, at any given time, are not exactly aligned with the rotation axis. When this happens, axial rotation will bring into view different magnetic poles at different rotational phases. In an oblique rotator, we expect that the hard X-rays (emerging from both polar caps) would peak twice per rotation. On the other hand, the soft X-rays (predominantly created by shocks in the distant wind band) would be dominated by the rotational period of the star, as in the CIR model (Mullan 1984). We suggest that this difference in behavior between hard X-rays and soft X-rays should be searched for in time-resolved X-ray data. In addition, in the context of DACs (see x 5.3), if these indeed originate in the polar caps, then our chances to observe a DAC (which must intercept the visible disk of the star) would depend on a favorable viewing angle between a magnetic polar cap and the line of sight. An oblique rotator would provide us with a favorable angle twice in each rotation. In this regard, we note that the recurrence timescales for DACs have been found, in certain stars (e.g., Per, 68 Cyg), to be one-half the rotation period (Kaper 1993, pp. 107, 128). Kaper interprets this behavior in the context of an oblique rotator model for the source of the DACs. 6. CONCLUSION In this paper, we speculate that winds from OB stars depart from spherical symmetry in a systematic way. We suggest that the winds consist of two components, each of which occupies a different range of latitudes. One component occupies a broad band centered on the equator, that is free of magnetic fields; in this band, line driving creates a ‘‘normal’’ wind. The second component consists of two extensive polar caps where closed magnetic loops impede (but do not completely suppress) the outflow of the line-driven wind. Each cap extends from the pole down to colatitudes of at least 45 . These caps are by no means small structures: the two caps occupy a combined area of the stellar surface that is comparable to the area of the equatorial wind band. Our scenario (involving magnetic fields confined to polar caps) is based on recent work (MM05) that models the operation of a certain type of dynamo (Spruit-Tayler) in convectively stable gas in rotating massive stars. In this model, magnetic fields appear on the surface preferentially in polar regions rather than in equatorial regions. We note that such a latitudinal distribution of magnetic fields is the opposite of the solar case. By modeling the X-ray line emission from the two-component wind, we have shown that the profiles of X-ray lines emitted by the winds of an OB star can be narrow, symmetric, and (almost) unshifted, especially when viewed nearly pole-on. This conclusion is of interest in the light of recent X-ray data that suggest that X-ray line profiles from certain massive stars do not exhibit the asymmetric and blueshifted shapes that are predicted by the theory of shock heating in spherically symmetric winds. This leads us to consider two limiting cases. On the one hand,

Vol. 637

stars with unshifted and symmetric lines are (we suggest) objects that are being viewed from near-polar directions ( Sco may belong to this category). On the other hand, when a star is viewed from a near-equatorial direction, the profiles of X-ray lines can be broad, asymmetric, and blueshifted as in the standard (spherically symmetric) model ( Pup may belong to this category). We envision that some of the fields in the polar caps form closed magnetic loops on which plasma is trapped. In the presence of line-driving forces, the material trapped in a loop is subject to shock heating (see ud-Doula & Owocki 2002). Many such loops may exist in each polar cap. We suggest that closed loops in the polar caps are the source of the hottest X-ray emissions (S xv, Si xiii) that have been detected in OB spectra: such emissions require a local temperature of the order of 20 MK and are believed to be emitted close to the star. (This is in contrast to the shock-heated wind model, where the hottest X-rays should originate in the fastest wind, i.e., far from the star.) We argue that the loop lengths that are expected in an OB star with a Spruit-Tayler dynamo are consistent with the small radial distances that have been inferred for the source regions of S xv and Si xiii emissions. The loops in the polar caps will be most readily observable in stars that are viewed from nearpolar directions (e.g., Sco). Emission from closed loops is expected to be subject to temporal variability when individual loops lose their stability. Such a loss of stability may arise through magnetic reconnection with newly emerging flux or through accumulation of excessive amounts of line-driven material. The opening of a loop is expected to be accompanied by energy release. In a star with NL loops in the polar caps, the fractional fluctuation in X-ray flux is expected to be of order ðNL Þ1/2. We suggest that the opening of a polar cap loop may provide a source of material for a transient discrete absorption component in the absorption wings of strong ultraviolet lines. Such DACs have been found to be nearly ubiquitous phenomena in the UV spectra of OB stars. Are there observational tests of the speculations we propose here? One test would become possible if there were a way to determine the inclination angle between the rotation axis and our line of sight: stars that are viewed in directions that are close to pole-on should have X-ray line profiles that are systematically less shifted and less asymmetric than stars that are viewed close to the equatorial plane. The cleanest test of our model would be detection of individual loops in the polar caps, separated by a field-free surface in the equatorial band. According to our model, it is not merely the longitudinal component of the field that should be small in the equatorial band; the magnitude of the field should also be small there. The observational difficulty of observing an individual magnetic loop depends on how large the individual loops on a given star actually are: if the loops are all TR in linear extent, then it will be difficult to measure the magnetic fields. The best chances for detection would be in stars where the combination of mass-loss rate and Alfveń speed leads to a large Alfveń radius RAlf (see x 2.2). Advances in ZeemanDoppler imaging (or other techniques; e.g., Kochukhov et al. 2004; J. F. Donati 2005, private communication) may eventually achieve enough spatial resolution to allow detection of loops in stars with the largest RAlf . Until such observations become possible, the model may be testable in a statistical sense, by comparing line profiles in a large sample of OB stars. With lower resolution, one may be limited to inferring the presence of magnetic polar caps as a whole. Because of cancellation effects, if each loop has an average field strength B, the overall field strength observed in each cap may be small, of order BðNL Þ1/2.

No. 1, 2006


We suggest that the smallness of this overall field may explain why most OB stars have not yet been detected magnetically. (The OB stars that have already been detected may be stars with strong fossil fields, where NL is of the order of 1.) Moreover, if dynamo activity is at work, the stellar field may reverse polarity from time to time. This would distinguish unambiguously between stars where the fields are fossil and stars where the fields are being actively generated.

517

We are grateful to an anonymous referee for prompt reports that offered detailed and constructive criticisms. D. J. M. acknowledges the support of NASA grants NAG5-11228 and NNG04GC75G. W. L. W. was supported in part by NASA contract NAS5-02054 and by NASA through Chandra Award GO56006A issued by the Chandra X-Ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060.

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winds from ob stars: a two-component scenario? - IOPscience

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