Macroturbulent and rotational broadening in the spectra of B-type supergiants

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1 Mon. Not. R. Astron. Soc. 336, (2002) Macroturbulent and rotational broadening in the spectra of B-type supergiants R. S. I. Ryans, 1 P. L. Dufton, 1 W. R. J. Rolleston, 1 D. J. Lennon, 2 F. P. Keenan, 1 J. V. Smoker 1 and D. L. Lambert 3 1 Physics Department, Queen s University, Belfast BT7 1NN 2 Isaac Newton Group of Telescopes, Apartado de Correos 368, E-38700, Santa Cruz de La Palma, Canary Islands, Spain 3 Department of Astronomy, The University of Texas at Austin, Austin, TX , USA Accepted 2002 June 17. Received 2002 May 31; in original form 2002 April 16 ABSTRACT The absorption-line spectra of early B-type supergiants show significant broadening that implies that an additional broadening mechanism (characterized here as macroturbulence ) is present in addition to rotational broadening. Using high-resolution spectra with signal-to-noise ratios of typically 500, we have attempted to quantify the relative contributions of rotation and macroturbulence, but even with data of this quality significant problems were encountered. However, for all our targets, a model where macroturbulence dominates and rotation is negligible is acceptable; the reverse scenario leads to poor agreement between theory and observation. Additionally, there is marginal evidence for the degree of broadening increasing with line strength, possibly a result of the stronger lines being formed higher in the atmosphere. Acceptable values of the projected rotational velocity are normally less than or equal to 50 km s 1, which may also be a typical upper limit for the rotational velocity. Our best estimates for the projected rotational velocity are typically km s 1 and hence compatible with this limit. These values are compared with those predicted by single star evolutionary models, which are initially rapidly rotating. It is concluded that either these models underestimate the rate of rotational breaking or some of the targets may be evolving through a blue loop or are binaries. Key words: stars: early-type stars: fundamental parameters stars: rotation supergiants. 1 INTRODUCTION It has been known for some time that the absorption lines in the spectra of O-type stars always exhibit a significant amount of broadening (Conti & Ebbets 1977). A similar effect is found in the spectrum of supergiant (but not main-sequence) early and mid B-type stars (see, for example, the sample of stars considered by Lennon, Dufton & Fitzsimmons 1993). Howarth et al. (1997) investigated this effect by cross-correlating IUE spectra for nearly 400 early-type stars against that of τ Sco. For the O-type supergiants, the estimated projected rotational velocities (assuming that this was the dominant broadening mechanism) were always greater than 65 km s 1, while all but one of the supergiants with a spectral type earlier than B5 had values greater than or equal to 50 km s 1. Howarth et al. interpreted these results as unambiguous evidence that another important mechanism in addition to rotation must be present in these stars. For convenience, we will in future characterize this additional broadening as macroturbulence, although it could represent r.ryans@qub.ac.uk other phenomena such as outflows from the photosphere into a wind (Kudritzki 1992) The methodology used by Howarth et al. (1997) was not able to distinguish between the relative contributions of macroturbulence and rotation for any specific object. This is important as estimates of rotational velocities in early-type supergiants would help constrain their evolutionary history. Here we attempt to utilize very high-quality [both in terms of spectral resolution and signal-to-noise (S/N) ratio] spectra of B-type supergiants to investigate whether it is possible to constrain the relative magnitudes of these broadening mechanisms. 2 OBSERVATIONS AND REDUCTION PROCEDURES The observational data fall into two parts, and are discussed separately below. 2.1 McDonald observatory spectroscopy Spectroscopy of eight bright supergiants was undertaken from 1999 November 23 to 30 using the coudé echelle spectrograph C 2002 RAS

2 578 R. S. I. Ryans et al. (Tull et al. 1995) on the 2.7-m telescope at the McDonald Observatory, at a resolution of R = The targets were selected from the model atmosphere analysis of 46 supergiants of McErlean, Lennon & Dufton (1999) in order to cover as wide a range of spectral types as possible. Because of the intrinsic difficulty in distinguishing between different broadening mechanisms, we required that the spectra had signal-to-noise ratios in excess of 200. At the focal position providing R = , the spectrograph with its chargecoupled device (CCD) samples relatively small regions of the spectrum. Our spectra sample approximately 19 Å for 10 echelle orders with an interorder gap of about 90 Å. Hence stars were observed at a number of settings aimed at observing relatively strong isolated absorption lines. These settings were as follows. (i) The He I line at 4713 Å, which also covered the C II line at 4267 Å. (ii) The O II lines at 4590 and 4596 Å, which also covered the O II lines at 4415 and 4417 Å (although these were sometimes blended together). (iii) The Si II lines at 4128 and 4132 Å, which also covered the C II lines at 3918 and 3921 Å. (iv) The Si III lines at 4567 and 4574 Å, which also covered the lines of Mg II at 4481 Å and O II at 4661 Å. The actual choice of regions was governed by which features were likely to be strong with, for example, the Si III and Si II regions being observed in early and late B-type stars, respectively. The spectra were reduced to a one-dimensional format using the NOAO IRAF package (Tody 1993). The procedures were effectively identical to those used for observations with this facility by Lehner et al. (2000), where more details can be found. Observations were also taken of the sharp-lined main-sequence star γ Peg and these were reduced in an identical manner. After reduction the spectra were transferred into the STARLINK DIPSO package (Howarth et al. 1998) for further analysis. The normalization of the spectra is critical for accurately delineating the line profiles. This was achieved in two stages. First, the blaze profile was estimated by fitting polynomials (typically of order eight to ten, with the shape of the fits being effectively independent of the actual order chosen) to the continuum in the spectra of γ Peg. The supergiant spectra were then rectified using these polynomials. Although not normalized, the continuum of the processed spectra appeared to have no significant structure. The orders were then normalized using low-order polynomial fits to the continuum regions. The observational data are summarized in Table 1, where the spectral regions are designated by the major features observed, the signal-to-noise ratios are taken from the central order and the spectral types are taken from McErlean et al. (1999). 2.2 William Herschel Telescope spectroscopy The McDonald data were supplemented with observations of four supergiants obtained using the UES spectrograph on the William Herschel Telescope (WHT) on 2001 June 2/3. These data have a lower spectral resolution of approximately , but this should be sufficient to adequately sample the line profiles. The spectra provide near complete coverage from 3800 to 6700 Å, while the reduction of these data again followed standard methods as, for example, discussed by Trundle et al. (2001). Spectra of the sharplined star, γ Peg, were again obtained and used for the preliminary rectification of the supergiant continua. The choice of lines extracted as before depended on the atmospheric parameters of the Table 1. Summary of the McDonald Observatory observational data. Star Spectral type Region S/N ratio HD 2905 BC0.7 Ia He I 700 Si III 600 HD B1 Iab He I 275 Si III 250 HD B9 Ia Mg II 600 Si II 700 HD B1 Ib He I 500 Si III 600 HD B8 Ia Mg II 800 Si II 400 HD B4 Iab He I 250 Si II 250 HD B0.5 Ia He I 275 O II 300 Si III 400 HD B2 Ia Si III 250 Table 2. Summary of the WHT observational data. Star Spectral type S/N ratio HD B1.5 Ib 340 HD B0.2 Ia 625 HD B2 Ib 670 HD B8 Ib 500 targets, but included lines of He I at 4713 and 5876 Å, C II at 3918, 3920, 4267, 5055, 5047, 6578 and 6582 Å, N II at 3995, 4237, 4241 and 4630 Å, O II at 4317, 4319, 4590, 4596 and 4661 Å, Mg II at 4481 Å, Si II at 4128 and 4132 Å, and Si III at 4552, 4567 and 4574 Å. The observational data are summarized in Table 2 with the estimated signal-to-noise ratio. 3 ANALYSIS AND RESULTS In this section, we discuss both the method of analysis and the results obtained. In the course of the investigations it was found that the techniques we needed to apply changed as our appreciation of the data grew, and this is reflected in the following discussion. 3.1 Outline of method Initially we investigated matching observation and theory using both the intrinsic profiles and their Fourier transforms. The latter method has been used extensively in, for example, estimating rotational velocities in late-type stars (e.g. Gray 1989; Gray & Baliunas 1997). However, our tests showed that working in Fourier space yielded no significant advantages (see Section 4) and hence this approach was not pursued. Our analysis technique was, in principle, straightforward. We measured the equivalent widths (W λ ) of the lines of interest in each star, and generated theoretical profiles of the same strength using the atmospheric parameters and non-lte models of McErlean et al. (1999). We then calculated macroturbulent (v m ) and rotational broadening (v sin i) functions for an appropriate range of values of v m and v sin i at high velocity resolution (0.02 km s 1 ) and convolved these with the theoretical line profile (see Fig. 1). For rotational broadening we used the function discussed by Gray

3 Broadening in the spectra of B-type supergiants 579 Figure 1. A demonstration of the approach used to determine v m and v sin i. Theoretical profiles (panel 1) are convolved with broadening profiles (panel 2 the Gaussian profile is v m and the other profile is v sin i). The convolved theoretical profile is compared with the observational data (panel 3). (1992) with a limb-darkening coefficient of 0.6 tests showed that the results were insensitive to this choice. For the turbulent broadening, we assumed a Gaussian distribution of velocities. The resulting spectrum was then compared with the observational data and the sum of the squares of the differences computed, giving us a measure of the quality of the fit at each point in (v m, v sin i) space. These data were then plotted as contour maps and gridded surfaces (see Fig. 2), allowing us (in theory) to identify the optimal values of (v m, v sin i). We had initially hoped that the resulting maps of fit quality would indicate a unique point in the parameter space, allowing easy identification of the optimal value of (v m, v sin i). In practice, although there was an optimal solution this may not be well constrained, as can be seen from Fig. 2. Since the purpose of this project was to place limits on the contributions from macroturbulence and rotation we will discuss this problem in more detail. 3.2 Determination of parameter limits To illustrate the principles involved, we consider two cases representing the range of data available in our sample. For illustrative purposes we will consider simulated data, which eliminates some of the complications that we found with the actual observations (these are discussed in Section 3.3). For our best case, we took the 4567 Å Si III line in HD 24398, which was isolated, strong (W λ 330 må) and had a continuum signal-to-noise ratio in excess of 500. The worst case was the 3919/3921 ÅCII doublet in HD , with two partly blended lines, each having W λ 100 m Å and a continuum S/N ratio of around 150. For each line we convolved the appropriate non-lte model profile with representative values of (v m, v sin i) determined from initial analysis of the observational data. The continuum S/N ratio was then reduced to the appropriate value by adding random noise. Fig. 3 shows the test spectra and the resulting surface plots of the goodness of fit for each. Instead of a single well-defined point, we see a plateau of fitting parameters. A single minimum point could be identified in each case and this was consistent with the values of (v m, v sin i) adopted initially. However, it was unclear how much confidence could be placed in such solutions. Clearly, it was desirable to establish limits on the likely values of (v m, v sin i). Our initial approach was to trace isochrones of fitting probabilities on the contour plots. At each point on the isochrone we compared the Figure 2. A sample of the contour and surface plots of the goodness-of-fit parameter in (v m, v sin i) space. The darker bands in the contour plot correspond to minima (and thus the best fits). No calibration scale is given as the plot is merely illustrative. The z-axis of the surface plot is inverted for clarity so that lower values (those representing a better fit) are at the top.

4 580 R. S. I. Ryans et al. Figure 3. Spectra and goodness-of-fit surface plots for the sample cases of simulations of the Si III 4567-Å line in HD (left) and the C II 3920-Å pair in HD (right). The plateau effect is clearly seen in both. As one would expect, for the case with better data the plateau is significantly narrower, indicating less uncertainty in the range of acceptable fits. observed and theoretical profiles, trying to determine the point at which the model profiles began to diverge significantly from the observational data. We found this to be a difficult and subjective process, and indeed it proved to be impossible to determine quantifiably a point at which the fits were no longer acceptable, forcing us to rely on a qualitative assessment of the fit. However, using this technique we were able to determine an initial range of acceptable (v m, v sin i) parameters for a given line, and these were plotted on diagrams such as those shown in Fig. 4. Several important results are observed in Fig. 4. First, the distribution shows that while a model with v sin i = 0 always provided an acceptable fit, one with v m = 0 was not acceptable. Secondly, we see that the distribution of points covers a relatively large range of values of v m and v sin i, with the range for v sin i being proportionally larger than for v m. These patterns were observed in all our observational data, and while they do suggest a significant contribution from macroturbulent broadening in all cases, they clearly did not assist in placing stringent limits on the value of v sin i. Finally, it is clear that the range of acceptable fits is larger for the case with the lower signal-to-noise ratio, which is as one would expect. 3.3 Initial results We will now review the results of our initial analysis of the data. Applying the above procedures, we identified the acceptable (v m, v sin i) locus for each line in the programme stars, and plotted these in the manner discussed. The resulting plots could be placed in one of two categories. (i) Stars that showed good agreement of the (v m, v sin i) loci between different lines HD 34085, HD 36371, HD 41117, HD (ii) Stars that showed an essentially continuous range of (v m, v sin i) loci, with some degree of overlap between results from different lines HD , HD 13854, HD 2905, HD 38771, HD 21291, HD , HD , HD

5 Broadening in the spectra of B-type supergiants 581 Figure 4. Plot of the range of (v m, v sin i) pairs that produce acceptable fits for simulations of the Si III 4567-Å line in HD and the C II 3920-Å pair in HD Each point is marked with a. An example of each of these results is shown in Fig. 5, from which it is clear that all the (v m, v sin i) pairs form curves with similar shapes. From these we can measure the largest acceptable value of turbulent velocity (designated vm 0 ), which corresponds to v sin i = 0; the (v m, v sin i) which provides the best fit and the largest acceptable value of v sin i (which will of course be associated with a non-zero value of v m ). We summarize this information in Table 3. Several important points can be seen from these results. As mentioned previously, we see that a v sin i = 0 solution is always within the range of acceptable fits, while a v m = 0 solution is rarely acceptable. We also see that while any individual line will indicate a relatively tight range (of the order of 10 km s 1 ) of acceptable values of v m, the range of v sin i values is much larger typically 0 50 km s 1. We believe that these systems are dominated by macroturbulence, so it is not surprising that the magnitude of the smaller contribution is harder to estimate, but it is clearly desirable to further constrain the range of likely values, and this will be further considered in Section 3.4. The results from the first group of stars those showing good convergence of results from each line considered are easily understood. Of more immediate concern are those from the other group, where we see a continuum of results in (v m, v sin i) space. Our initial suspicion was that this effect was the result of an error in the normalization or reduction of the spectra. This would lead to an incorrect determination of the continuum level, in turn altering the width of the absorption profiles and thus to an incorrect (v m, v sin i) loci. As explained in Section 2 these data were high-, or ultrahigh-resolution echelle spectra, and blaze removal was a difficult process, so the existence of continuum level errors would not be entirely surprising, despite the care taken to avoid Figure 5. Plots showing typical results from our initial fitting procedures. The top pane shows HD 24398, representing those stars with excellent agreement between the (v m, v sin i) loci measured for all the observed lines. The lower pane shows HD 38771, which had a wider range of (v m, v sin i) loci with some overlap between the results from each line. For clarity the results from some lines have been excluded where these overlapped with others. them. There were two ways to test this hypothesis as discussed below. Our first step was to take a representative theoretical line (the Si III 4567-Å profile considered earlier), and vary the equivalent width of the input model profile by ±10 per cent (chosen to represent what we believe to be a plausible worst case ) to gauge the effect of incorrectly measuring this quantity (and FWHM) caused by continuum placement errors. For this case we found that the predicted value of v 0 m varied by ±5 kms 1 from that for the unscaled case. A repeat of the procedure with the lower-quality C II 3920 Å profile (discussed in Section 2) showed comparable variations. We then proceeded to vary the continuum level in the test profiles by combining the spectrum with a low-order polynomial, chosen to represent some hypothetical residual blaze profile. When we rectified the observed spectra, there appeared to be no residual structure in the continuum, so that any remaining element of the blaze profile must be small. We therefore chose polynomials that just began to cause a noticeable structure in the continuum. For both the Si III 4567-Å and C II 3920-Å line simulations, we found that a variation in the predicted v 0 m of the order of 5 km s 1 might be caused without leading to excessive structure in the continuum. Our second test for evidence of incorrect continuum placement was to plot the offset from the mean of the values of v 0 m measured for each line as a function of the equivalent width. If there was a systematic error in normalization then, for example, the wings of

6 582 R. S. I. Ryans et al. Table 3. Maximum value of macroturbulence (vm 0 ) corresponding to v sin i = 0 for all the lines analysed in each programme star. Also listed are the (v m, v sin i) pair giving the best fit between theory and observation and our initial estimates of the maximum possible projected rotational velocities (with corresponding values of v m ). Star Line W λ (m Å) S/N ratio vm 0 (v m, v sin i) (Å) Best fit Maximum HD 2905 Si III , 3 54, 62 Si III , 11 54, 68 O II , 1 52, 64 Si III , 22 57, 53 Si III , 22 46, 62 O II , 18 34, 64 C II , 20 22, 70 Mg II , 38 17, 68 HD Si III , 15 43, 59 Si III , 11 43, 55 O II , 13 37, 58 Mg II , 7 27, 58 HD He I , 15 26, 27 Mg II , 5 23, 34 C II , 5 21, 24 Si II , 3 15, 28 Si II , 28 8, 32 O II , 8 10, 25 C II , 6 15, 21 HD C II , 10 29, 50 Si III , 19 35, 42 Si III , 7 33, 42 Mg II , 22 29, 47 O II , 4 36, 40 HD Mg II , 3 31, 30 Si II , 15 21, 40 O II , 8 21, 34 Si II , 15 26, 32 O II , 10 28, 24 C II , 10 18, 30 C II , 4 20, 28 HD Si II , 41 18, 48 Si II , 32 21, 41 C II 3919/ , 36 18, 46 HD O II , 5 44, 76 Si III , 5 57, 53 Si III , 9 46, 62 O II , 21 34, 65 O II 4415/ , 53 26, 66 Mg II , 52 17, 68 HD Si III , 3 32, 47 Si III , 24 32, 50 Mg II , 18 21, 56 O II , 9 28, 47 HD C II 6578/ , 24 39, 54 C II 6578/ , 3 40, 56 Si III , 9 40, 50 N II , 13 41, 43 O II , 30 29, 59 Si III , 47 27, 55 Si III , 48 30, 57 Si III , 15 39, 51 Si III , 20 39, 53 O II 4316/ , 10 37, 53 Si III , 52 26, 60 C II , 14 30, 60 C II , 47 34, 59 N II , 8 36, 54 Mg II , 9 35, 47 Table 3 continued Star Line W λ /må S/N ratio vm 0 (v m, v sin i) (Å) Best fit Maximum N II , 8 35, 50 N II , 2 33, 53 C II 3919/ , 4 38, 55 C II 3919/ , 4 45, 49 HD C II , 57 39, 71 C II , 59 41, 74 Mg II , 3 51, 64 Si III , 3 49, 70 Si III , 6 59, 71 Si III , 71 39, 80 Si III , 3 62, 73 Si III , 14 66, 60 O II 4590/ , 66 64, 71 HD C II 6578/ , 10 36, 44 C II , 21 24, 53 C II , 41 30, 48 Si III , 3 33, 41 C II 3919/ , 7 26, 45 C II 3919/ , 20 26, 45 N II , 3 28, 40 Mg II , 14 28, 41 Mg II , 8 28, 41 O II 4317/ , 14 28, 36 Si III , 9 33, 34 O II , 16 32, 34 Si III , 6 28, 37 Si III , 4 34, 37 Si III , 3 34, 36 O II , 11 33, 36 N II , 14 33, 35 O II , 19 23, 39 HD Mg II , 21 26, 37 Mg II , 18 24, 38 C II , 11 18, 41 C II , 9 17, 42 Si II , 9 25, 31 Si II , 5 25, 31 C II 3919/ , 11 20, 29 C II 3919/ , 10 21, 30 the stronger lines might be more affected, narrowing the profiles and leading to a general underestimation of the maximum value of v m. We would then see a trend for the stronger lines to have below average vm 0 values. Fig. 6 shows that there is no such relationship in our data indeed, we appear to see the opposite. The gradient of the best-fitting line (shown) is ± km s 1 m Å 1, which is significant at the 3σ level. This implies that there was a systematic increase in the width of the stronger lines. It is possible that this trend may be a result of there being more than one value of v m within the star, with the stronger lines being formed higher in the atmosphere and subject to a different v m. However, from Fig. 6, it can be seen that the majority of the line scatter lies within a band of approximately ±5 kms 1, which is consistent with the above error estimates. Additionally observations of the same absorption line in adjacent echelle orders can yield estimates of vm 0 (see Table 3) differing by up to 10 km s 1. Hence it may be possible to explain most if not all of the observed scatter in vm 0 as being a function of the inherent uncertainties in the process. We also considered the possibility that the initial theoretical profiles deduced from the non-lte model atmosphere calculations

7 Broadening in the spectra of B-type supergiants 583 Offset (km s -1 ) Equivalent Width (må) Figure 6. Offset from the mean value of vm 0 for each line as a function of the line strength, and a straight line fit to the data. were inappropriate. Indeed, during the analysis we found that the He I feature at 5585 Å was consistently indicating larger values of v 0 m than the other lines in a given star. This line was therefore excluded from consideration, since it seems probable that the natural broadening of this (intrinsically wide) line was not properly replicated in our models. To ensure no other line was unduly biasing our results, we created the plot shown in Fig. 7. This shows the mean offset from the average value of v m for the star on a line-by-line basis. None of the lines featured in the plot show significant evidence for an unusual spread of offsets. We have also investigated the effects of possible errors in our adopted atmospheric parameters. For example, we have adopted the estimates of the effective temperature, gravity and microturbulent velocities (together with a Gaussian velocity distribution) of McErlean et al. (1999). Additionally, we have adopted a normal helium abundance, although enhanced helium abundances have been found for early-type supergiants (see, for example, Voels et al. 1989; Herrero et al. 1992; Smith & Howarth 1994). However, more recent studies (for example, McErlean, Lennon & Dufton 1998; Smith & Howarth 1998; Villamariz et al. 2002) yield normal helium abun- 20 dances estimates when the effects of microturbulence are properly included. Indeed, McErlean et al. (1999) found no evidence for anomalous helium abundances in any of the targets considered here. However, to test the sensitivity of our results to these adopted values we have undertaken test calculations for the Si III 4567-Å line in HD 24398, where we have changed the effective temperature by ±2000 K, the logarithmic gravity by ±0.3 dex, the microturbulent velocity by ±5 kms 1 and have also doubled the helium-tohydrogen abundance ratio. In all cases, the goodness-of-fit surfaces were effectively identical to that shown in Fig. 3. Hence we conclude that the theoretical unbroadened profiles that we adopted were adequate for our needs. Given that our data analysis methods or adopted model profiles may not explain all of the variation in our estimates of vm 0, we considered other possibilities. First, the use of a convolution with a simple v sin i profile might incorrectly describe the effects of stellar rotation for some of our sample stars. More sophisticated methods are available (see, for example, Howarth & Smith 2001), which integrate the specific intensity over the surface of the star and allow for variations in the effective temperature and gravity. Additionally these authors consider the effects of differential rotation. The effect of rotation is generally to produce lower temperatures and gravities at the equator than at the pole. Numerical tests show that particularly the change in temperature could effect the relative contributions of the polar and equatorial regions to an absorption-line profile. For example, consider an ion, for which the maximum in the absorption-line strengths occurs at an effective temperature, which is higher than that of the stellar mean effective temperature. The cooler equatorial region would then make a smaller contribution to the absorption line, leading to an underestimation of the projected rotational velocity. We have investigated whether this effect could be important as follows. For each line in each star we have calculated the fractional change in the equivalent width for an arbitrary decrease in the effective temperature of 1000 K. and plotted these values in Fig. 8 against the offset from vm 0. If the spread in the estimates for v0 m arose from variations in the temperature across the stellar surface a positive correlation between these quantities would be expected. As can be seen no significant correlation has been found, indicating that the approximation of using a convolution with a simple rotational broadening function may be valid Offset (km s -1 ) v m offset (km s -1 ) Å Mg II 4130Å Si II 4713Å He I 3920Å C II 4267Å C II 6580Å C II 3995Å N II 4591Å O II 4661Å O II 4552Å Si III 4567Å Si III 4575Å Si III -10 Figure 7. Offset from the mean value of vm 0 for each line observed in more than three stars considered on a line-by-line basis, allowing us to search for systematic errors owing to inadequate line models. Lines are ordered according to the temperature at which they reach their peak strength, from lowest (left) to highest (right) Fractional change in W λ Figure 8. Offset from the mean value of vm 0 for each line as a function of the sensitivity of the equivalent width to the adopted effective temperature.

8 584 R. S. I. Ryans et al. A second possibility is that our stellar sample may have previously undetected (presumably cooler) companion stars. Then, the contribution of the companion object would only have a significant effect on the cooler lines observed in the composite spectra. The x-axis in Fig. 7 is ordered according to the effective temperature at which the ions reach their peak strength (in terms of their absorption-line spectrum), and we find no evidence in these data for a relationship between the range of offsets and these effective temperatures. Finally, it is possible that our stronger lines are affected by stellar wings, which would be expected to lead to a broadening of the profile in the blue wing. We have looked carefully for asymmetries in our line profiles but have been unable to identify any significant effects. Indeed, all the strong lines are very well fitted by Gaussian profiles, indicating that they are symmetric and indirectly implying that the representation of macroturbulence by a Gaussian velocity field is a reasonable assumption. Hence we conclude that the origin of these variations in linewidth is still unclear. 3.4 Revised results In order to obtain more satisfactory limits on the acceptable parameter space, we initiated a second phase to the process. Using the initial analysis to locate the loci of the best (v m, v sin i) pairs, we took our model profiles for selected lines, degraded them to the appropriate S/N ratio, and applied broadening profiles corresponding to a selection of the most likely (v m, v sin i) values. We processed these synthesized models with our fitting routine, and compared the resulting quality-of-fit surfaces with those from the observational Figure 9. A comparison of the fitting contours obtained for the observed 4267-Å CII line in HD to those from the theoretical 4267-Å line profile broadened using likely (v m, v sin i) pairs. It is clear that the v sin i = 50 km s 1 model produces fitting contours different in shape from the observed spectrum, but no clear difference exists for the other values of v sin i. We therefore conclude that a limit of v sin i 40 km s 1 can be deduced for this case.

9 Broadening in the spectra of B-type supergiants 585 Table 4. Median values and upper limits for the projected rotational velocities deduced for each programme star, together with predicted rotational velocities (v pred ) for an initial rotational velocity of 300 km s 1 estimated from Meynet & Maeder (2000). Star Spectral v sin i v pred type Median Limit (km s 1 ) (km s 1 ) HD B9 Ia HD B8 Ia HD B8 Ib HD B4 Iab HD B2 Ia HD B2 Ib HD B1.5 Ib HD B1 Ib HD B1 Iab HD 2905 BC0.7 Ia HD B0.2 Ia HD B0.5 Ia data. We found that this approach permitted us to put a better limit on the maximum value of v sin i, since there were clear shifts in the form of the surfaces as v sin i increased relative to v m. This is best understood graphically, and is illustrated in Fig. 9, with the corresponding limits being summarized in Table 4. We have already listed in Table 3 the (v m, v sin i) pair that yielded the optimal fit with each absorption feature considered. Additionally our simulations have shown that the fitting procedure recovered the correct values for these quantities. Inspection of Table 3 indicates that for most targets, there is good reasonably good agreement between the estimates of the projected rotational velocities deduced from different lines. Only for HD and HD are a wide range of estimates obtained, implying that for these stars, there are additional uncertainties that have not been incorporated in our simulations. Indeed, we note that these are the two hottest stars in our sample. However, for other targets, we have calculated the median value (to reduce the effect of single extreme values) and also list these in Table 4. We believe that these provide our best estimates of the projected rotational velocities, but that they should be treated with considerable caution. 4 DISCUSSION AND CONCLUSIONS As will be apparent from the previous sections, the disentanglement of the effects of rotation and macroturbulence is difficult and has only been partially achieved in the current investigation. This is particularly the case when trying to estimate the contribution of one mechanism when the other mechanism appears to dominate. However, it has been possible to show that rotation by itself provides poor agreement between observation and theory (confirming the results of previous workers, for example, Howarth et al. 1997). Previous studies (for example, Slettebak et al. (1975); Conti & Ebbets 1977; Howarth et al. 1997) have deduced projected rotational velocities for stars in our sample. It is difficult to compare our results directly with these studies as we find a pure rotational model unsatisfactory. If we compare our values for a pure macroturbulence model (vm 0 ) with the values deduced by Howarth et al. for nine stars in common, our results are systematically smaller by per cent. We interpret this as evidence that the two studies are consistent but that we have used different parameters to characterize the width of the lines. This is supported by, for example, the results presented in Fig. 3, where values of vm 0 of approximately 44 and 29 km s 1 would map on to projected rotational velocities of approximately 58 and 38 km s 1. It has been possible to provide best estimates for, and put limits, on the contribution of rotation and these have been summarized in Table 4. Apart from two objects, er limits for the projected rotational velocity are v sin i 50 km s 1, while our best estimates are typically km s 1. Given that for random orientations of the rotation axis large values of sin i are more likely, these probably also represent reasonable estimates of (and limits to) the typical rotational velocity. Grids of models (see, for example, Heger & Langer 2000; Meynet & Maeder 2000) have been generated that follow the evolution of rapidly rotating stars with mass loss. For example, Meynet & Maeder discuss the evolution of stars with initial masses ranging from 9 to 40 M and an initial rotational velocity of 300 km s 1. Using the effective temperatures and luminosities of McErlean et al. (1999), we can use these evolutionary models to predict the current expected rotational velocities of our targets, and these are tabulated in Table 4. These predictions have been linearily interpolated from fig. 13 of Meynet & Maeder and will have uncertainties of typically 10 km s 1. There will be additional uncertainties owing to errors in the atmospheric parameters of approximately the same magnitude. Finally, there is no reason to believe that our targets had initial rotational velocities of 300 km s 1, whilst our observed values are of the projected rotational velocity (and on occasions sin i will be small). However, even with these caveats it is striking that the predicted rotational velocities are in all cases larger than even our upper limits for v sin i and in some cases the differences are large. In turn, this could be interpreted as evidence that the models are underestimating the rate of rotational braking. A direct comparison with the results of Heger & Langer is more difficult but again their results seem to indicate that the rate of rotational braking near the main sequence is relatively small. Another explanation of this discrepancy is that some of our targets are evolving back from the red supergiant phase (on a blue loop ). The results of Heger & Langer (2000) indicate that the rotational velocities at this stage will be relatively small and consistent with our observed values. However, it is not clear whether at least for our hotter targets, the blue loops will obtain a sufficiently high temperature. Additionally, both the grids of models discussed above are for single-star evolution and we cannot exclude additional effects owing to some of our targets being binaries. We note that several investigations have found a difference in masses deduced from stellar atmospheric parameters and distances (often called spectroscopic masses ) and those from evolutionary models (see, for example, Herrero et al. 1992; Vrancken et al. 2000). Indeed, McErlean et al. (1999) found some evidence for such a mass discrepancy in their large sample of supergiants from which our targets were drawn. This provides additional evidence that existing single-star evolutionary models may not completely explain the observed properties of early-type giants and supergiants. Finally, we consider how the constraints on the maximum rotational velocity might be improved. One attractive possibility would be to Fourier transform the observed spectra and then compare with theoretical results. The convolutions would then become simple multiplications of the corresponding Fourier transforms. We have experimented with this technique, but for the current observational data set we found that it did not yield any improvement in the estimates of the macroturbulence or rotational velocity. Additionally,

10 586 R. S. I. Ryans et al. it is not possible to gain a mutliplexing advantage by taking the Fourier transform of a spectral region containing several lines, as the wavelength shifts lead to frequency-dependent complex exponentials being present in the components, corresponding to different lines. It would therefore appear that the best way to improve the constraints will be by obtaining spectra with an even better S/N ratio. It will be equally important to ensure that the spectral response of the spectrograph is either relatively wavelength independent, or sufficiently well characterized that a reliable normalization is possible. Our principal conclusions may be summarized as follows. (i) For all of our targets, a model where macroturbulence dominates and rotation is negligible is acceptable. (ii) In contrast, models dominated by rotation provide unsatisfactory fits. (iii) There is marginal evidence for the degree of broadening increasing with line strength. It is unclear whether this is an artefact of the analysis procedure or possibly the result of the stronger lines being formed higher in the atmosphere where the macroturbulence could be greater. (iv) The maximum acceptable value of the projected rotational velocity is typically 50 km s 1 (and in some cases smaller), and given that for random orientations of the rotation axis large values of sin i are preferred, this is also a realistic limit for the rotational velocity. Our best estimates of the projected rotational velocity are normally in the range km s 1 and hence are consistent with this limit. (v) Rotational velocities for our targets deduced from evolutionary models of single stars with large initial velocities are generally larger than those observed. Although there are several uncertainties, this may imply that these models may underestimate the rate of rotational breaking or that some of the targets are evolving through a blue loop or are binaries. ACKNOWLEDGMENTS We are grateful for discussion with Neil McErlean who originally suggested this project and to the referee, Professor Andre Maeder, for useful comments on an earlier draft of this paper. JVS, RSIR and WRJR acknowledge funding from the UK Particle Physics and Astronomy Research Council (PPARC). REFERENCES Conti P.S., Ebbets D., 1977, ApJ, 170, 325 Gray D.F., 1989, 347, 1021 Gray D.F., 1992, The Observation and Analysis of Stellar Photospheres. Cambridge Univ. Press, Cambridge Gray D.F., Baliunas S.L., 1997, ApJ, 475, 303 Heger A., Langer N., 2000, ApJ, 544, 1016 Herrero A., Kudritzki R.P., Vilchez J.M., Kunze D., Butler K., Haser S., 1992, A&A, 261, 209 Howarth I.D., Smith K.C., 2001, MNRAS, 327, 353 Howarth I.D., Siebert K.W., Hussain G.A.J., Prinja R.A., 1997, MNRAS, 284, 265 Howarth I.D., Murray J., Mills D., Berry D.S., 1998, Starlink User Note 50.21, CCLRC/Rutherford Appleton Laboratory Kudritzki R.P., 1992, A&A, 266, 395 Lehner N., Dufton P.L., Lambert D.L., Ryans R.S.I., Keenan F.P., 2000, MNRAS, 314, 199 Lennon D.J., Dufton P.L., Fitzsimmons A., 1993, A&AS, 97, 559 McErlean N.D., Lennon D.J., Dufton P.L., 1998, A&A, 329, 631 McErlean N.D., Lennon D.J., Dufton P.L., 1999, A&A, 349, 553 Meynet G., Maeder A., 2000, A&A, 361, 101 Slettebak A., Collins G.W., Boyce P.B., White N.M., Parkinson T.D., 1975, ApJS, 29, 137 Smith K.C., Howarth I.D., 1994, A&A, 290, 868 Smith K.C., Howarth I.D., 1998, MNRAS, 299, 1146 Tody D., 1993, in Hanisch R.J., Brissenden R.J.V., Barnes J., eds, ASP Conf. Ser. Vol. 53, Astronomical Data Analysis Software & Systems. Astron. Soc. Pac., San Francisco, p. 173 Trundle C., Dufton P.L., Rolleston W.R.J., Ryans R.S.I., Lennon D.J., Lehner N., 2001, MNRAS, 328, 291 Tull R.G., MacQueen P.J., Sneden C., Lambert D.L., 1995, PASP, 107, 251 Villamariz M.R., Herrero A., Becker S.R., Butler K., 2002, A&A, 388, 940 Voels S.A., Bohannan B., Abbott D.C., Hummer D.G., 1989, ApJ, 340, 1073 Vrancken M., Lennon D.J., Dufton P.L., Lambert D.L., 2000, A&A, 358, 639 This paper has been typeset from a TEX/LATEX file prepared by the author.