## Abstract

High-resolution optical spectra of 57 Galactic B-type supergiant stars have been analysed to determine their rotational and macroturbulent velocities. In addition, their atmospheric parameters (effective temperature, surface gravity and microturbulent velocity) and surface nitrogen abundances have been estimated using a non-local thermodynamic equilibrium grid of model atmospheres. Comparisons of the projected rotational velocities have been made with the predictions of stellar evolutionary models and in general good agreement was found. However, for a small number of targets, their observed rotational velocities were significantly larger than predicted, although their nitrogen abundances were consistent with the rest of the sample. We conclude that binarity may have played a role in generating their large rotational velocities. No correlation was found between nitrogen abundances and the current projected rotational velocities. However, a correlation was found with the inferred projected rotational velocities of the main-sequence precursors of our supergiant sample. This correlation is again in agreement with the predictions of single star evolutionary models that incorporate rotational mixing. The origin of the macroturbulence and microturbulent velocity fields is discussed and our results support previous theoretical studies that link the former to subphotospheric convection and the latter to non-radial gravity mode oscillations. In addition, we have attempted to identify differential rotation in our most rapidly rotating targets.

## 1 INTRODUCTION

The spectra of early-type stars are affected by a variety of non-thermal velocity fields. Those present in the photosphere are often designated as microturbulence (see e.g. Gies & Lambert 1992; Daflon, Cunha & Butler 2004; Simón-Díaz et al. 2006) and macroturbulence (see e.g. Howarth et al. 1997; Ryans et al. 2002). Microturbulence is associated with distance scales smaller than the mean free path of a photon, while macroturbulence is associated with longer distance scales. Recently, the former has been linked with the presence of subsurface convection fields (Cantiello et al. 2009) driven by the opacity of iron group elements, whilst the latter may be a manifestation of the large number of non-radial gravity-mode stellar oscillations (Aerts et al. 2009) present in the stellar photosphere.

Stellar rotation also significantly affects early-type stellar spectra and particularly for main-sequence objects can dominate the broadening of the metal absorption lines (see e.g. Gray 1976, 2008). Rotation may play a key role in the evolution of early-type stars (see e.g. Maeder & Meynet 2001) and in long-duration gamma-ray bursts (Woosley & Heger 2006). In turn, this has stimulated several recent studies (Wolff, Edwards & Preston 1982; Abt, Levato & Grosso 2002; Strom, Wolff & Dror 2005; Huang & Gies 2006; Martayan et al. 2006; Wolff, Strom & Dror 2007; Hunter et al. 2008a) of stellar rotation in both field and cluster stars and in different metallicity environments. However, recently both slowly rotating stars with relatively high nitrogen abundance and rapidly rotating stars with relatively low nitrogen abundances (Hunter et al. 2008b, 2009) have been identified in the Very Large Telescope – Fibre Large Array Multi Element Spectrograph (VLT-FLAMES) survey of massive stars (Evans et al. 2005). Hence, other mechanisms as well as rotation may be important for mixing nucleosynthetically processed material to the surface, as discussed by Brott et al. (2009).

In this paper, we present high-resolution and high-signal-to-noise spectra of a sample of 57 Galactic B-type supergiant stars, and use these data to further investigate the relationship between rotation and mixing, in addition to testing the predictions of theoretical models. We also characterize the microturbulent and macroturbulent velocity fields present in our sample and compare these with the theoretical studies of Cantiello et al. (2009) and Aerts et al. (2009), respectively. We have also attempted to make the first identification of differential rotation in evolved massive stars.

## 2 OBSERVATIONS AND DATA REDUCTION

The observing list was initially developed to sample, as widely as possible, B-type supergiants of different spectral subtype. The availability of targets (in terms of spatial position and brightness) led to the early-B spectral types being better sampled than the later spectral types as can be seen from Table 1. However, even for the latter, most spectral subclasses contained at least one target. A number of targets were subsequently excluded from the analysis. In particular, four B9 supergiants (HD 94367, HD 96919, HD 111904, HD 158799) were found to have effective temperatures that were smaller than the lower limit of our model atmosphere grid. Additionally, eight targets (HD 74804, HD 99103, HD 75821, HD 76728, HD 101330, HD 152046, HD 68161, HD 53244) were found to have gravities that were significantly higher than supegiants of similar spectral types. Indeed, their logarithmic gravity estimates (3.0-3.5 dex) were similar to those found for B-type giants (see e.g. Vrancken et al. 2000) and they were therefore excluded.

Table 1

Observational details.

 Identifier Sp. type Exp. (s) S/N Ref. HD 77581a B0 Ia 716 430 4b HD 122879 B0 Ia 464 510 1 HD 149038 B0 Ia 119 470 1 HD 167264 B0 Iab 178 500 1 HD 164402 B0 Ib 258 550 1b HD 168021 B0 Ib 684 400 1b HD 115842 B0.5 Ia 321 480 1 HD 150898 B0.5 Ia 214 500 1 HD 152234 B0.5 Ia 190 450 1b HD 152667a B0.5 Ia 362 350 1 HD 94493a B0.5 Iab 1010 520 3 HD 64760 B0.5 Ib 62 480 1 HD 103779 B0.5 II 962 500 3 HD 155985 B0.7 Ib 486 480 2 HD 109867 B1 Ia 397 460 1 HD 152235 B1 Ia 424 420 1 HD 142758 B1 Ia 830 410 3 HD 148688 B1 Iae 170 380 1 HD 154090 B1 Ia 111 470 1 HD 152236 B1 Iape 98 440 1 HD 119646 B1 Ib-II 543 410 3 HD 125545 B1 Iab-Ib 1145 400 3 HD 150168 B1 Iab-Ib 229 390 1 HD 99857a B1 Ib 1220 400 3 HD 157246 B1 Ib 27 560 1 HD 93840a BN1 Ib 1640 410 2 HD 106343 B1.5 Ia 386 400 1 HD 148379 B1.5 Iape 173 400 1 HD 96248 BC1.5 Iab 528 420 2 HD 108002 B2 Ia-Iab 750 400 3 HD 52089 B2 II 5 430 1 HD 99953 B2 Iab-Ib 495 440 3 HD 93827a B2 Ib -II 6770 270 3 HD 111990 B2 Ib 647 400 3 HD 117024 B2 Ib 861 400 3 HD 165024 B2 Ib 37 510 1 HD 141318 B2 II 246 450 1 HD 92964 B2.5 Iae 178 440 1 HD 116084 B2.5 Ib 270 500 1 HD 75149 B3 Ia 192 440 1 HD 53138 B3 Iab 20 500 1 HD 51309 B3 II 70 520 1 HD 157038 B4 Ia 460 450 1 HD 159110 B4 Ib 1045 550 4 HD 79186 B5 Ia 126 440 1 HD 111973 B5 Ia 288 480 1 HD 58350 B5 Ia 12 440 1 HD 86440 B5 Ib 33 520 1 HD 164353 B5 Ib 49 520 1 HD 83183 B5 II 54 400 1 HD 74371 B6 Iae 155 440 1 HD 80558 B6 Iae 280 430 1 HD 105071 B6 Iab-Ib 428 510 1 HD 125288 B6 Ib 68 500 1 HD 91619 B7 Iae 359 460 1 HD 111558 B7 Ib 1007 450 3 HD 166937 B8 Iap 44 460 1b
 Identifier Sp. type Exp. (s) S/N Ref. HD 77581a B0 Ia 716 430 4b HD 122879 B0 Ia 464 510 1 HD 149038 B0 Ia 119 470 1 HD 167264 B0 Iab 178 500 1 HD 164402 B0 Ib 258 550 1b HD 168021 B0 Ib 684 400 1b HD 115842 B0.5 Ia 321 480 1 HD 150898 B0.5 Ia 214 500 1 HD 152234 B0.5 Ia 190 450 1b HD 152667a B0.5 Ia 362 350 1 HD 94493a B0.5 Iab 1010 520 3 HD 64760 B0.5 Ib 62 480 1 HD 103779 B0.5 II 962 500 3 HD 155985 B0.7 Ib 486 480 2 HD 109867 B1 Ia 397 460 1 HD 152235 B1 Ia 424 420 1 HD 142758 B1 Ia 830 410 3 HD 148688 B1 Iae 170 380 1 HD 154090 B1 Ia 111 470 1 HD 152236 B1 Iape 98 440 1 HD 119646 B1 Ib-II 543 410 3 HD 125545 B1 Iab-Ib 1145 400 3 HD 150168 B1 Iab-Ib 229 390 1 HD 99857a B1 Ib 1220 400 3 HD 157246 B1 Ib 27 560 1 HD 93840a BN1 Ib 1640 410 2 HD 106343 B1.5 Ia 386 400 1 HD 148379 B1.5 Iape 173 400 1 HD 96248 BC1.5 Iab 528 420 2 HD 108002 B2 Ia-Iab 750 400 3 HD 52089 B2 II 5 430 1 HD 99953 B2 Iab-Ib 495 440 3 HD 93827a B2 Ib -II 6770 270 3 HD 111990 B2 Ib 647 400 3 HD 117024 B2 Ib 861 400 3 HD 165024 B2 Ib 37 510 1 HD 141318 B2 II 246 450 1 HD 92964 B2.5 Iae 178 440 1 HD 116084 B2.5 Ib 270 500 1 HD 75149 B3 Ia 192 440 1 HD 53138 B3 Iab 20 500 1 HD 51309 B3 II 70 520 1 HD 157038 B4 Ia 460 450 1 HD 159110 B4 Ib 1045 550 4 HD 79186 B5 Ia 126 440 1 HD 111973 B5 Ia 288 480 1 HD 58350 B5 Ia 12 440 1 HD 86440 B5 Ib 33 520 1 HD 164353 B5 Ib 49 520 1 HD 83183 B5 II 54 400 1 HD 74371 B6 Iae 155 440 1 HD 80558 B6 Iae 280 430 1 HD 105071 B6 Iab-Ib 428 510 1 HD 125288 B6 Ib 68 500 1 HD 91619 B7 Iae 359 460 1 HD 111558 B7 Ib 1007 450 3 HD 166937 B8 Iap 44 460 1b

a Subsequently added to observing list as Howarth et al. (1997) found anomalously large line widths for spectral type.

b Listed as binary in SIMBAD online data base.

Figure 1

Estimated projected rotational velocities as a function of spectral type for the early B-type supergiants analysed by Howarth et al. (1997). The dashed line represents a subjective estimate of the upper limit for the part of the sample that are rotating relatively slowly.

Figure 1

Estimated projected rotational velocities as a function of spectral type for the early B-type supergiants analysed by Howarth et al. (1997). The dashed line represents a subjective estimate of the upper limit for the part of the sample that are rotating relatively slowly.

High-resolution (R≃ 48 000) spectra were obtained with the Fibre fed Extended Range Optical Spectrograph (FEROS; Kaufer et al. 1999) on the 2.2-m Max Planck Institut (MPI) European Southern Observatory (ESO) telescope at La Silla during a three-night observation run in 2005 April. Some preliminary observations had been obtained in 2004 July and December to test the feasibility of our analysis procedures (see Section 3), but due to their relatively low signal-to-noise-ratios (S/Ns), these have not been used in the current analysis. All spectra covered the wavelength range from 3600 to 9200 Å and were reduced using the reduction pipeline that runs under the midas environment (Kaufer et al. 1999).

The S/N for each spectrum was estimated by taking a normalized region of the continuum and finding the standard deviation, the S/N estimate being its reciprocal. This procedure was normally carried out in the region of 4500–4600 Å as this was compatible with the spectral lines used to estimate the projected rotational velocities (see Table 2). However, for spectral types later than B5, this region contained a significant number of strong lines and hence the region from 4700–4800 Å was adopted. As the S/N is expected to vary with wavelength, the estimates for several stars were measured in both regions with those from the 4700–4800 Å region being found to be approximately 5 per cent lower. Hence, the estimates for all stars of spectral type B6 or later have been scaled accordingly. Given that weak undetected absorption will lead to underestimates of the S/Ns, these estimates should only be taken as an approximate comparative guide to the quality of the spectra. All the targets are listed in the Table 1, together with exposure times and estimates of the S/Ns. Spectral types are taken in the first instance from the Bright Star Catalog (Hoffleit & Warren 1991), then from the IUE Atlas of B-Type Stellar Spectra (Walborn, Parker & Nichols 1995) and the University of Michigan Catalogue of Spectral Types Houk & Cowley (1975) and Reed (2003).

Table 2

Lines used to estimate the projected rotational velocities and macroturbulence for our targets.

 Species Wavelength (Å) N ii 3995.00 Si ii 4128.07 Si ii 4130.89 C ii 4267.00/4267.26 Mg ii 4481.13/4481.33 Si iii 4552.62 Si iii 4567.82 Si iii 4574.76 O ii 4590.97 O ii 4595.96/4596.18 N ii 4630.54 O ii 4661.63 He i 4713.15/4713.38
 Species Wavelength (Å) N ii 3995.00 Si ii 4128.07 Si ii 4130.89 C ii 4267.00/4267.26 Mg ii 4481.13/4481.33 Si iii 4552.62 Si iii 4567.82 Si iii 4574.76 O ii 4590.97 O ii 4595.96/4596.18 N ii 4630.54 O ii 4661.63 He i 4713.15/4713.38

For all stars in the sample, the equivalent widths (Wλ) of selected lines were estimated. The N ii line at 3995 Å was measured to estimate nitrogen abundances, whilst the silicon spectrum (Si ii 4128 Å, 4131 Å; Si iii 4552 Å, 4567 Å, 4574 Å; and Si iv 4116 Å) was used to constrain effective temperatures as described in Section 4. The continuum adjacent to each line was normalized using a second-order polynomial fit. For the slowly rotating stars (see Section 3.1) where macroturbulent broadening will generally dominate, a Gaussian was then fitted to the absorption line using a least-squares technique. For those stars with a relatively large projected rotational velocity (≈100 km s−1 or greater), the lineshape is dominated by rotation. In these cases, a profile shape appropriate to rotationally dominated broadening (with the value of ve sin i taken from Table 3– see Section 3.1) was used, and was generally found to give a better fit. Although the choice of profile is a possible source of error, we note that the equivalent width estimates of the stronger lines normally agreed to within 5 to 10 mÅ with those found by direct numerical integration over the profile. The estimates are presented in Table 4.

Table 3

Estimates of the projected rotational velocity, atmospheric parameters and nitrogen abundances. The ordering of targets follows that in Table 1.

Identifier ve sin i (km s−1σr (km s−1nr vt (km s−1σt (km s−1nt Teff (K) log g (cm s−2ξt (km s−1[M (M
HD 77581a 56 10 – – – 26 500 2.90 17 8.40 40b
HD 122879 55 80 27 200 2.90 14 8.37 40b
HD 149038 61 69 28 500 3.10 12 7.91 40b
HD 167264 83 66 27 500 3.05 16 7.96 30b
HD 164402a 46 56 28 100 3.25 13 7.55 30b
HD 168021a 48 58 26 900 3.10 15 7.81 25b
HD 115842 39 66 24 800 2.75 14 8.44 40
HD 150898 93 56 26 400 3.10 20 8.00 25b
HD 152234a 59 57 25 700 2.90 14 7.69 38b
HD 152667 139 – – – 26 000c 3.05 18 7.58 25b
HD 94493 97 60 23 500 2.95 14 8.02 24b
HD 64760 255 – – – 26 000c 3.25 22 7.89 23
HD 103779 40 60 25 000 3.00 12 8.07 25b
HD 155985 35 46 23 200 2.95 12 8.19 22
HD 109867 43 56 22 300 2.75 14 8.32 23
HD 152235 46 58 22 000 2.65 14 7.59 30
HD 142758 46 38 17 300 2.25 21 8.46 35
HD 148688 48 44 20 700 2.45 16 7.94 37
HD 154090 47 54 22 200 2.70 15 8.30 28
HD 152236 34 46 21 500d – – – –
HD 119646 35 26 17 600 2.50 21 7.93 20
HD 125545 65 53 20 800 2.75 17 7.70 22
HD 150168 129 55 12 24 800 3.15 13 8.26 20b
HD 99857 189 10 59 11 21 500c 2.95 16 7.20 18
HD 157246 269 11 – – – 21 500c 2.90 15 8.11 19
HD 93840 58 68 20 900 2.75 15 8.37 23
HD 106343 43 52 20 100 2.50 17 8.20 30
HD 148379 44 33 17 000 2.00 19 7.93 43
HD 96248 37 53 19 500 2.40 15 7.48 29
HD 108002 37 46 20 200 2.60 16 8.19 25
HD 52089 22 17 20 100 3.05 17 7.74 14
HD 99953 49 37 16 800 2.15 22 8.43 32
HD 93827 227 14 – – – 18 500c 2.70 20 7.86 17
HD 111990 34 30 16 500 2.40 18 8.12 20
HD 117024 55 25 16 500 2.55 24 7.62 12
HD 165024 98 35 18 500 2.70 18 8.23 17
HD 141318 30 32 18 300 2.90 15 8.13 13
HD 92964 36 28 15 600 2.00 22 8.60 30
HD 116084 40 35 16 200 2.25 23 8.09 23
HD 75149 30 34 15 900 2.20 20 8.43 24
HD 53138 35 23 15 400 2.15 18 8.22 24
HD 51309 22 20 15 600 2.40 18 8.23 17
HD 157038 38 41 15 700 2.00 14 8.97 32
HD 159110 13 19 700 3.20 12 7.36 12
HD 79186 39 10 36 15 100 2.00 14 8.39 35
HD 111973 36 28 16 000 2.30 19 8.04 21
HD 58350 32 25 14 500 2.10 18 8.16 23
HD 86440 17 15 14 600 2.55 20 7.59 13
HD 164353 18 14 15 100 2.50 21 7.78 14
HD 83183 19 – – – 14 900 2.50 20 7.42 14
HD 74371 31 30 13 400 1.90 20 7.85 24
HD 80558 41 17 13 000 1.70 24 8.66 30
HD 105071 29 17 12 200 1.85 20e 7.97 20
HD 125288 23 21 13 900 2.55 20e 7.67 10
HD 91619 31 25 13 100 1.70 18 8.36 31
HD 111558 26 10 21 12 100 2.00 20 8.08 17
HD 166937a 29 32 12 200 1.75 20 7.87 23
Identifier ve sin i (km s−1σr (km s−1nr vt (km s−1σt (km s−1nt Teff (K) log g (cm s−2ξt (km s−1[M (M
HD 77581a 56 10 – – – 26 500 2.90 17 8.40 40b
HD 122879 55 80 27 200 2.90 14 8.37 40b
HD 149038 61 69 28 500 3.10 12 7.91 40b
HD 167264 83 66 27 500 3.05 16 7.96 30b
HD 164402a 46 56 28 100 3.25 13 7.55 30b
HD 168021a 48 58 26 900 3.10 15 7.81 25b
HD 115842 39 66 24 800 2.75 14 8.44 40
HD 150898 93 56 26 400 3.10 20 8.00 25b
HD 152234a 59 57 25 700 2.90 14 7.69 38b
HD 152667 139 – – – 26 000c 3.05 18 7.58 25b
HD 94493 97 60 23 500 2.95 14 8.02 24b
HD 64760 255 – – – 26 000c 3.25 22 7.89 23
HD 103779 40 60 25 000 3.00 12 8.07 25b
HD 155985 35 46 23 200 2.95 12 8.19 22
HD 109867 43 56 22 300 2.75 14 8.32 23
HD 152235 46 58 22 000 2.65 14 7.59 30
HD 142758 46 38 17 300 2.25 21 8.46 35
HD 148688 48 44 20 700 2.45 16 7.94 37
HD 154090 47 54 22 200 2.70 15 8.30 28
HD 152236 34 46 21 500d – – – –
HD 119646 35 26 17 600 2.50 21 7.93 20
HD 125545 65 53 20 800 2.75 17 7.70 22
HD 150168 129 55 12 24 800 3.15 13 8.26 20b
HD 99857 189 10 59 11 21 500c 2.95 16 7.20 18
HD 157246 269 11 – – – 21 500c 2.90 15 8.11 19
HD 93840 58 68 20 900 2.75 15 8.37 23
HD 106343 43 52 20 100 2.50 17 8.20 30
HD 148379 44 33 17 000 2.00 19 7.93 43
HD 96248 37 53 19 500 2.40 15 7.48 29
HD 108002 37 46 20 200 2.60 16 8.19 25
HD 52089 22 17 20 100 3.05 17 7.74 14
HD 99953 49 37 16 800 2.15 22 8.43 32
HD 93827 227 14 – – – 18 500c 2.70 20 7.86 17
HD 111990 34 30 16 500 2.40 18 8.12 20
HD 117024 55 25 16 500 2.55 24 7.62 12
HD 165024 98 35 18 500 2.70 18 8.23 17
HD 141318 30 32 18 300 2.90 15 8.13 13
HD 92964 36 28 15 600 2.00 22 8.60 30
HD 116084 40 35 16 200 2.25 23 8.09 23
HD 75149 30 34 15 900 2.20 20 8.43 24
HD 53138 35 23 15 400 2.15 18 8.22 24
HD 51309 22 20 15 600 2.40 18 8.23 17
HD 157038 38 41 15 700 2.00 14 8.97 32
HD 159110 13 19 700 3.20 12 7.36 12
HD 79186 39 10 36 15 100 2.00 14 8.39 35
HD 111973 36 28 16 000 2.30 19 8.04 21
HD 58350 32 25 14 500 2.10 18 8.16 23
HD 86440 17 15 14 600 2.55 20 7.59 13
HD 164353 18 14 15 100 2.50 21 7.78 14
HD 83183 19 – – – 14 900 2.50 20 7.42 14
HD 74371 31 30 13 400 1.90 20 7.85 24
HD 80558 41 17 13 000 1.70 24 8.66 30
HD 105071 29 17 12 200 1.85 20e 7.97 20
HD 125288 23 21 13 900 2.55 20e 7.67 10
HD 91619 31 25 13 100 1.70 18 8.36 31
HD 111558 26 10 21 12 100 2.00 20 8.08 17
HD 166937a 29 32 12 200 1.75 20 7.87 23

a Classified as binary in SIMBAD.

b In ambiguous region of HR diagram that can lead to ambiguous mass estimates.

c Large ve sin i precludes use of silicon ionization balance and ve sin i estimates supplemented with those from He lines.

d Gravity is too low to be analysed with tlusty grid.

e Si iii lines too weak to reliably estimate the microturbulence.

Table 4

Equivalent widths (in mÅ) for selected metal lines. The ordering of targets follows Table 1. The letter B indicates a blend of lines.

 Identifier N ii 3995 Si iv 4116 Si ii 4129 Si ii 4131 Si iii 4553 Si iii 4568 Si iii 4575 HD 77581 155 475 435 365 195 HD 122879 105 455 305 230 115 HD 149038 60 460 230 175 85 HD 167264 75 460 270 200 95 HD 164402 50 345 270 210 110 HD 168021 85 365 300 245 125 HD 115842 165 395 405 345 195 HD 150898 155 370 325 250 125 HD 152234 80 380 350 295 160 HD 152667 85 B 495 400 230 HD 94493 205 190 375 310 180 HD 64760 170 B 410 330 155 HD 103779 165 255 345 285 165 HD 155985 235 165 375 315 195 HD 109867 280 180 425 355 215 HD 152235 125 230 495 425 270 HD 142758 385 85 555 470 305 HD 148688 210 200 550 480 305 HD 154090 285 190 470 400 245 HD 152236 470 95 500 435 275 HD 119646 235 40 380 315 185 HD 125545 200 135 505 425 270 HD 150168 230 230 385 330 195 HD 99857 95 B 405 330 200 HD 157246 290 B 460 375 255 HD 93840 350 105 420 345 215 HD 106343 330 115 465 385 235 HD 148379 240 40 430 365 230 HD 96248 140 95 465 395 240 HD 108002 315 115 450 380 235 HD 52089 200 55 350 295 190 HD 99953 375 60 460 380 235 HD 93827 225 B 390 325 210 HD 111990 215 20 275 215 130 HD 117024 130 20 330 270 160 HD 165024 300 55 405 340 215 HD 141318 220 30 310 250 160 HD 92964 345 25 365 300 180 HD 116084 240 30 370 305 180 HD 75149 285 140 170 255 200 115 HD 53138 200 155 180 230 175 105 HD 51309 120 150 160 165 125 70 HD 157038 340 170 190 300 250 155 HD 159110 95 65 65 195 150 90 HD 79186 195 155 170 210 160 95 HD 111973 190 150 170 230 180 105 HD 58350 150 190 195 155 115 65 HD 86440 60 165 175 85 55 25 HD 164353 100 175 185 130 90 50 HD 83183 55 175 185 75 45 20 HD 74371 80 205 215 115 80 45 HD 80558 105 200 205 95 65 35 HD 105071 55 250 255 65 35 15 HD 125288 50 170 175 60 30 15 HD 91619 135 200 210 110 80 45 HD 111558 55 305 315 50 30 15 HD 166937 50 250 260 60 40 20
 Identifier N ii 3995 Si iv 4116 Si ii 4129 Si ii 4131 Si iii 4553 Si iii 4568 Si iii 4575 HD 77581 155 475 435 365 195 HD 122879 105 455 305 230 115 HD 149038 60 460 230 175 85 HD 167264 75 460 270 200 95 HD 164402 50 345 270 210 110 HD 168021 85 365 300 245 125 HD 115842 165 395 405 345 195 HD 150898 155 370 325 250 125 HD 152234 80 380 350 295 160 HD 152667 85 B 495 400 230 HD 94493 205 190 375 310 180 HD 64760 170 B 410 330 155 HD 103779 165 255 345 285 165 HD 155985 235 165 375 315 195 HD 109867 280 180 425 355 215 HD 152235 125 230 495 425 270 HD 142758 385 85 555 470 305 HD 148688 210 200 550 480 305 HD 154090 285 190 470 400 245 HD 152236 470 95 500 435 275 HD 119646 235 40 380 315 185 HD 125545 200 135 505 425 270 HD 150168 230 230 385 330 195 HD 99857 95 B 405 330 200 HD 157246 290 B 460 375 255 HD 93840 350 105 420 345 215 HD 106343 330 115 465 385 235 HD 148379 240 40 430 365 230 HD 96248 140 95 465 395 240 HD 108002 315 115 450 380 235 HD 52089 200 55 350 295 190 HD 99953 375 60 460 380 235 HD 93827 225 B 390 325 210 HD 111990 215 20 275 215 130 HD 117024 130 20 330 270 160 HD 165024 300 55 405 340 215 HD 141318 220 30 310 250 160 HD 92964 345 25 365 300 180 HD 116084 240 30 370 305 180 HD 75149 285 140 170 255 200 115 HD 53138 200 155 180 230 175 105 HD 51309 120 150 160 165 125 70 HD 157038 340 170 190 300 250 155 HD 159110 95 65 65 195 150 90 HD 79186 195 155 170 210 160 95 HD 111973 190 150 170 230 180 105 HD 58350 150 190 195 155 115 65 HD 86440 60 165 175 85 55 25 HD 164353 100 175 185 130 90 50 HD 83183 55 175 185 75 45 20 HD 74371 80 205 215 115 80 45 HD 80558 105 200 205 95 65 35 HD 105071 55 250 255 65 35 15 HD 125288 50 170 175 60 30 15 HD 91619 135 200 210 110 80 45 HD 111558 55 305 315 50 30 15 HD 166937 50 250 260 60 40 20

## 3 DATA ANALYSIS

### 3.1 Projected rotational velocities

The use of Fourier transforms to estimate projected rotational velocities (ve sin i) from stellar spectra was first proposed by Carroll (1933), and more recently has been discussed by Gray (1976, 2008), Reiners & Schmitt (2002) and Royer (2005). The applicability of this methodology specifically to OB-type stars has been considered by Simón-Díaz et al. (2006). In essence, the Fourier transform technique is predicated on the convolution theorem, whereby when an observed spectrum is transformed into the Fourier domain, the convolution of the intrinsic spectrum with the rotational, macroturbulent and instrumental profiles becomes a multiplication of the corresponding Fourier transforms. Furthermore, as only the rotational profile is expected to have zeroes in its Fourier transform at low frequencies, these will appear in the total transform, thereby allowing the projected rotational velocity to be estimated.

The position of the first zero for a solidly rotating body is inversely proportional to the projected rotational velocity (see e.g. Gray 1976, 2008); this relationship will form the basis for our estimates of the projected rotational velocities. A more sophisticated analysis, such as that discussed by Reiners (2003) shows that differential rotation, limb darkening, the angle of inclination and gravity darkening can all alter the line profile, and hence its Fourier transform. However, these effects should not significantly affect the position of the first zero, particularly for stars with an equatorial velocity, v < 200 km s−1 which is appropriate to most of our sample. Furthermore, the main diagnostic of these secondary effects – namely the ratio of the first and second zeroes in the Fourier transform, (q1/q2)– was only measurable for stars which had significant rotational broadening. Such objects will have large equatorial velocities and are discussed further in Section 5.6.

As discussed in Section 2, there is additional broadening present in the spectrum of early-type supergiants (Howarth et al. 1997; Ryans et al. 2002; Simón-Díaz et al. 2006), which is normally designated as macroturbulence. This will also affect the line profile in the Fourier domain, acting to decrease the amplitude of the sidelobes. While the precise nature of this broadening is not fully understood, if it can be approximated by, for example, a Gaussian it should not affect the position of the first zero in the Fourier transform. Recently, Aerts et al. (2009) simulated the effects of non-radial gravity mode oscillations on the observed line profile. In particular, they find that on occasions this can lead to an underestimation of the projected rotational velocity and we discuss this further in Section 5.

13 metal spectral lines were considered for each star, as listed in Table 2. Four of the lines used are in close doublets or triplets with separations of 0.25 Å or less (corresponding to a velocity of approximately 15 km s−1), which is less than the typical broadening from macroturbulence and rotation. Indeed, in all these cases, the features appeared as single lines. Hydrogen and diffuse helium lines, although strong and well observed, were not normally considered, as although the Fourier technique should be capable of separating rotational broadening from that due to linear Stark effect, the approximation of line broadening as a convolution of unrelated effects may become unreliable (Heinzel 1978). An exception was made for two targets (HD 64760 and HD 152667) with large projected rotational velocities, where the metal lines were poorly observed and/or blended; for these targets, the diffuse neutral helium lines at 3819 and 4026 Å were also considered.

Spectra were analysed using procspec, an unpublished package of idl routines for manipulating spectra. The lines listed in Table 2 were normalized using a polynomial that had been fitted to the adjacent continuum. Whilst the amount of continuum considered should be minimized to reduce the noise in the Fourier domain, tests showed that the projected rotational velocity estimates were not significantly affected by this factor.

Each line was then assigned a ranking between 1 and 5 to reflect its reliability (relative to the other lines for that star). Factors considered were the quality of the spectrum, degree of symmetry in the line, the presence of cosmic rays, confidence in the normalisation procedure and the intrinsic strength of the line. Lines that were in the top two quality ranking bins for each star were Fourier transformed using the procedure discussed by Simón-Díaz & Herrero (2007). Those that gave a transform with a clearly identifiable first zero were then used to estimate the projected rotational velocity. An illustrative example of this procedure can be seen in Fig. 2. For each star, the number, mean and standard deviations of these estimates of the projected rotational velocity are summarized in Table 3.

Figure 2

An example of the Fourier transform methodology for the C ii 4267 Å line in HD 117024. The topmost panel shows the observed line profile, normalized to the continuum. The centre panel shows the Fourier transform of this line. The bottom panel shows the same Fourier transform, but with two theoretical Fourier transforms overplotted, one with no macroturbulence (red line), and one with a Gaussian macroturbulent velocity of 50 km s−1 (blue line). The value of ve sin i which gave the best fit to this line was 53 km s−1.

Figure 2

An example of the Fourier transform methodology for the C ii 4267 Å line in HD 117024. The topmost panel shows the observed line profile, normalized to the continuum. The centre panel shows the Fourier transform of this line. The bottom panel shows the same Fourier transform, but with two theoretical Fourier transforms overplotted, one with no macroturbulence (red line), and one with a Gaussian macroturbulent velocity of 50 km s−1 (blue line). The value of ve sin i which gave the best fit to this line was 53 km s−1.

### 3.2 Macroturbulence

Macroturbulence was originally introduced as an additional velocity field to improve the agreement between observed metal line profiles of supergiants and those calculated using model atmospheres (see e.g. Howarth et al. 1997; Ryans et al. 2002; Simón-Díaz et al. 2006). Macroturbulence is postulated to be a velocity field characterized by a length-scale longer than the mean free path of a photon (as opposed to microturbulence). Recent work by Aerts et al. (2009) has suggested a physical explanation for macroturbulence, in term of the pulsation of stars due to non-radial gravity-mode oscillations. These authors considered pulsational models for a B1-type supergiant, with comparable atmospheric parameters to those found in this paper and found that the additional line broadening simulated a macroturbulence consistent with those found observationally. Additionally, the pulsations could lead to errors in the values estimated for projected rotational velocities, and we return to this in Section 5.4.

We have estimated macroturbulences for all the stars in our sample by assuming that the magnitude of the velocity field follows a Gaussian distribution. Clearly, given the work of Aerts et al., this assumption may not be valid. However, the estimates will still be useful in characterizing how the excess broadening varies with spectral type and in many cases where macroturbulence dominates the line broadening, the observed profiles appeared to be well approximated by a Gaussian function.

Our procedure was to consider the lines tabulated in Table 2 (excluding the neutral helium line) and to optimize the agreement between theoretical and observed profiles. Intrinsic spectra were extracted from our tlusty grid using the grid point closest to our estimated atmospheric parameters and an elemental abundance that gave an equivalent width similar to that observed – typically differences were less than 10 per cent. The theoretical profile was then scaled, so that the two equivalent widths were the same. The theoretical profile was convolved with a rotational broadening function using the values of the projected rotational velocity listed in Table 3 and then with Gaussian profiles to represent the macroturbulence. For each line, an estimate of the macroturbulence was found by minimizing the sum of the square of the residuals with the mean, standard deviation and number of the estimates being listed in Table 3. Note that we have defined the macroturbulence as the (half-) width of the Gaussian profile. These values are discussed further in Section 5.4.

## 4 ATMOSPHERIC PARAMETERS

Atmospheric parameters and nitrogen abundances have been estimated from non-local thermodynamic equilibrium (LTE) model atmosphere grids generated using the codes tlusty and synspec (Hubeny 1988; Hubeny & Lanz 1995; Hubeny, Heap & Lanz 1998; Lanz & Hubeny 2007). Details of the methods adopted can be found in Hunter et al. (2007) while a more detailed discussion of the grids can be found in Ryans et al. (2003) and Dufton et al. (2005).1 Hence, only a brief summary will be given here with further details available as discussed above.

Four model atmosphere grids have been calculated for metallicities correponding to a Galactic metallicity of [Fe/H]= 7.5 dex, and metallicities of 7.2, 6.8 and 6.4 dex to represent the Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC) and lower metallicity material, respectively. For each of these grids, non-LTE models have been calculated for effective temperatures ranging from 12 000 to 35 000 K, in steps of no more than 2 500 K, surface gravities ranging from 4.5 dex down to the Eddington limit, in steps of no more than 0.25 dex and for microturbulences of 0, 5, 10, 20 and 30 km s−1. Assuming that the light elements (C, N, O, Mg and Si) have a negligible effect on line-blanketing and the structure of the stellar atmosphere, models were then generated with the light element abundance varied by +0.8, +0.4, −0.4 and −0.8 dex about their normal abundance at each point on the tlusty grid. Theoretical spectra and equivalent widths were then calculated based on these models. Photospheric abundance estimates for approximately 200 absorption lines at any set of atmospheric parameters covered by the grid can then be calculated by interpolation between the models via simple idl routines. The reliability of the interpolation technique has been verified by Ryans et al. (2003).

As the estimation of the atmospheric parameters is interrelated, it was necessary to use an iterative approach, as follows:

• Initial estimates of the effective temperature (Teff) and gravity (log g) were obtained from the spectral type and the calibration of Crowther, Lennon & Walborn (2006).

• The microturbulence (ξt) was estimated from the Si iii triplet at 4552–4574 Å.

• The effective temperature was re-estimated from the silicon ionization equilibrium.

• Surface gravity was re-estimated from the Balmer line profiles.

• The last three steps were iterated until the estimates converged.

Further details of this approach are given below.

### 4.1 Effective temperature

For the hotter targets with spectral types earlier than B3, the Si iii to Si iv ionization balance was used, whilst for the later spectral types the Si ii to Si iii ionization balance was considered. The very high quality of the observational data implies that the random errors should be small and normally less than 1000 K. Systematic errors due to, for example, errors in the adopted atomic data or in the physical assumptions were more difficult to quantify. However, Dufton et al. (2005) compared atmospheric parameters found for SMC supergiants using the approach adopted here with those found for two stars by Trundle et al. (2004). The latter utilized the unified code fastwind (Santolaya-Rey, Puls & Herrero 1997; Herrero, Puls & Najarro 2002; Repolust, Puls & Herrero 2004). The two approaches yielded similar estimates of the effective temperature (agreeing to 500 K for one star and 2000 K for the other), hence an error estimate of ±1 000 K would appear to be appropriate. The values of the other atmospheric parameters from the two codes were also in good agreement; log g to within 0.1 dex, microturbulence to within 3 km s−1 and nitrogen abundance to within 0.2 dex.

Five targets (HD 152667, HD 64760, HD 99857, HD 157246, HD 93827) had large projected rotational velocities that precluded the observation of two ionization stages of silicon. In these cases, the effective temperature was taken to be that implied by the spectral type and then the other atmospheric parameters were estimated as discussed below.

### 4.2 Surface gravity

The logarithmic surface gravity (log g) of each star was estimated by fitting the observed hydrogen Balmer lines with theoretical profiles. In order to minimize the effects of the stellar wind, relative high-order lines in the series (Hγ and Hδ) were normally considered. Automated procedures have been developed to fit model spectra in our tlusty model atmosphere grid to the observed spectra, with contour maps displaying the region of best fit. With an effective temperature estimate being available (from the methods described above), it was a straightforward matter to estimate the gravity.

Hunter et al. (2007) have discussed the errors associated with this procedure and estimate a typical random error of ±0.1 dex. Given that our observational data is generally of a higher quality than their Magellanic Cloud spectroscopy, this would appear to be a conservative error estimate to adopt here. Systematic errors due to, for example, uncertainties in the line broadening or assumption in the model atmosphere calculations could be significant, although the gravity estimates from the tlusty grid and fastwind calculations discussed in Dufton et al. (2005) agreed to within 0.1 dex. Hence, an error estimate of ±0.2 dex would therefore appear to be a conservative estimate.

### 4.3 Microturbulence

The microturbulence is normally derived by removing any systematic dependence of the abundance estimates on line strength found from lines of a specific ion. For B-type stars, the O ii ion is often considered (e.g. Gies & Lambert 1992; Daflon et al. 2004; Hunter et al. 2005; Simón-Díaz et al. 2006) as its rich spectrum should improve its reliability. However, the analysis is complicated by the lines arising from different multiplets, making any estimate susceptible to errors in the adopted atomic data or in the magnitude of non-LTE effects. In order to remove these uncertainties, a single O ii multiplet can be used. However, the number of lines is then drastically reduced, whilst the O ii spectrum is weak or unobservable for spectral types later than B3.

In order to maintain consistency throughout the analysis, we have instead estimated the microturbulence from the Si iii triplet of lines at 4552–4574 Å, which is observed in all our spectra. As these lines are from the same multiplet, errors arising from the oscillator strengths and non-LTE effects should be negligible and this method has been used previously by e.g. Dufton et al. (2005) and Vrancken et al. (1997, 2000). For two stars (HD 105071, HD 125288), the Si iii lines were too weak to usefully constrain the microturbulence. For these cases a value of 20 km s−1 was adopted, which is compatible with the estimates for other supergiants of similar spectral type.

### 4.4 Nitrogen abundances

In early B-type stars, there is a relatively rich N ii spectra with singlet transitions at 3995 and 4447 Å and triplet multiplets at 4601–4643, 4780–4819 and 4994–5007 Å. Here, we have estimated nitrogen abundances solely from the feature at 3995 Å. This choice was based on the following considerations:

• This feature is amongst the strongest N ii lines in the optical spectrum and is unblended. As such, it could be measured in effectively all our targets (see Table 4).

• The other lines and multiplets were either not observable over the full range of spectral and/or suffered from blending.

• The use of only one feature will inevitably increase the random error in the estimate and may lead to systematic errors. In the case of the former, the abundance estimates listed in the Table 3 have a range of over 1 dex, which is larger than our estimated random error discussed below. Additionally, the nitrogen abundances will depend on the amount of nucleosynthetically processed material mixed from the core to the photosphere. Hence, the relative rather than the absolute abundances will be important for investigating this phenomena.

The nitrogen abundance estimates from the line at 3995 Å were obtained using our grid of tlusty models and the methodology discussed e.g. in Hunter et al. (2007).

To investigate the magnitude of the errors in these abundances, we have also deduced nitrogen abundance from the other N ii lines listed above for six stars covering the range of spectral types (and hence effective temperatures present in our sample). These are summarized in Table 5, where to ease comparison we have also listed the estimates obtained from the N ii line at 3995 Å, which were taken directly from Table 3. As can be seen, there is no systematic differences between the two sets of estimates with the differences being compatible with the standard deviations found from the abundances estimates from the other features. Hence, we do not believe that our choice of a single feature has introduced significant systematic errors. The standard deviations in Table 5 range from ±0.11 to 0.17 dex and will represent at least in part the random errors in the abundance determinations. Also, there may be systematic differences in the estimates from different multiplets which will contribute to the standard deviations of the corresponding estimates. Hence, we adopt a random error of ±0.15 for the estimates in Table 3. We believe that this may be conservative as the feature at 3995 Å is stronger and does not suffer from the blending affecting some other feature. As well as random errors, there could be additionally systematic errors due to, for example, errors in the atmospheric parameters. These have been extensively discussed by Hunter et al. (2007) and vary depending on the strength of the feature and on the adopted atmospheric parameters. Typically, such errors are of the order of 0.1–0.2 dex (but on occasions can be larger). Here, we will adopt a typical error in our nitrogen abundance estimates of the order of 0.2 dex.

Table 5

Nitrogen abundances estimated form the feature at 3995 Å (N3995) and from other N ii lines (No) for six targets covering the range of effective temperatures of our sample. For the latter the standard deviation (σ) and number (n) of the individual estimates are also listed.

 Star Teff N3995 No σ n HD 115842 24 800 8.44 8.28 0.17 8 HD 155985 23 200 8.19 8.12 0.17 12 HD 108002 20 200 8.19 8.12 0.14 12 HD 142758 17 300 8.46 8.50 0.13 12 HD 79186 15 100 8.39 8.43 0.11 12 HD 80558 13 000 8.55 8.54 0.14 12
 Star Teff N3995 No σ n HD 115842 24 800 8.44 8.28 0.17 8 HD 155985 23 200 8.19 8.12 0.17 12 HD 108002 20 200 8.19 8.12 0.14 12 HD 142758 17 300 8.46 8.50 0.13 12 HD 79186 15 100 8.39 8.43 0.11 12 HD 80558 13 000 8.55 8.54 0.14 12

### 4.5 Masses

Masses for the stars in our sample were estimated by comparing our effective temperatures and surface gravities estimates with those predicted from the evolutionary tracks from the Geneva group models (Meynet & Maeder 2003). All the stars in our sample were found to lie in a region between approximately 10 M and 40 M.

As can be seen from Fig. 3, the evolutionary tracks in our pseudo-HR diagram loop back on themselves for values of log Teff greater than 4.3 dex and log g greater than 2.8 dex. This increases the uncertainty in the determination of mass for stars in this region of the diagram, as a degeneracy in log g versus Teff is introduced. This uncertainty is mitigated by the fact that the stars in this region all have masses between 20 and 40 M and the behaviour of evolutionary models in this mass range is quite similar.

Figure 3

Estimated effective temperatures and surface gravities for our sample, plotted against the Geneva group evolutionary tracks (Meynet & Maeder 2003). Each track is identified by an integer which is the initial mass in solar masses (M). The number in brackets refers to the mass of the model at an effective temperature Teff= 4.1, note that the mass of the models changes by less than 0.2 M between the loop back at the upper left and this point.

Figure 3

Estimated effective temperatures and surface gravities for our sample, plotted against the Geneva group evolutionary tracks (Meynet & Maeder 2003). Each track is identified by an integer which is the initial mass in solar masses (M). The number in brackets refers to the mass of the model at an effective temperature Teff= 4.1, note that the mass of the models changes by less than 0.2 M between the loop back at the upper left and this point.

At higher temperatures and lower gravities, the tracks are closer together, leading to larger errors in the mass estimates, with the relative error being approximately 15 per cent. Compounding this problem, stars with high rotational velocities are likely to exhibit gravity darkening in accordance with Von Zeipel's theorem (Von Zeipel 1924a,b), and if these stars are pole on, significant errors can be made in estimating their effective temperature (Gillich et al. 2008). These uncertainties in effective temperature will in turn increase the uncertainty in mass. Based on these factors, we have adopted a conservative uncertainty in mass of ±20 per cent, which corresponds to an uncertainty of 2 M at the lower end of our mass range and 8 M at the upper end.

## 5 RESULTS AND DISCUSSION

### 5.1 Comparison with previous rotational velocity estimates

There are several studies of projected rotational velocities that have targets in common with our sample (see e.g. Penny 1996; Abt et al. 2002; Simón-Díaz & Herrero 2007). It is encouraging that Simón-Díaz & Herrero deduced from a similar methodology to that used here a value of 73 ± 4 km s−1 for HD 167264. This is in reasonable agreement with our estimate of 83 ± 3 km s−1 (our error estimate for the mean is based on the standard deviation of the sample and assuming that the errors are normally distributed). Kaufer, Prinja & Stahl (2002) have found ve sin i to be 265 ± 5 km s−1 for HD 64760, which is again in good agreement with our measured value of 255 km s−1. It is also encouraging that Kaufer et al. did not use the Fourier method to obtain this result, but rather rotationally broadened a model spectral line to match the Si iii line at 4552 Å. Unfortunately, we had no targets in common with the sample of Markova & Puls (2008), who also used a Fourier technique to measure rotational and macroturbulent velocities. We note, however, that within their limited sample, the trends in both rotational and macroturbulent velocity mirror that of our targets.

The only study that has sufficient overlap to allow a meaningful statistical comparison is that of Howarth et al. (1997) and in Fig. 4 the two sets of estimates are compared for 42 stars, with spectral types from B0 to B5. The cross-convolution method of Howarth et al. generally leads to larger estimates. For the slowly rotating stars (where our estimates are less than 70 km s−1), there is a systematic difference of approximately 30 km s−1 (with a standard deviation of 10 km s−1). We ascribe this difference to the effect of macroturbulence, which was not explicitly included in the estimates of Howarth et al. For the stars rotating with intermediate projected velocities between 70 and 140 km s−1, we find good agreement between the values obtained from the cross-correlation and Fourier transform methods; the average difference between the results of the two techniques is 8 km s−1 with a standard deviation of 8 km s−1. For the four most rapidly rotating stars, HD 64760, HD 157246, HD 99857 and HD 93827, the Fourier transform estimates are higher by typically 30 km s−1 from those using the cross-correlation method. We would expect our estimates to be secure as the line profiles are now dominated by rotational broadening and the zeros in the Fourier transform are well observed. It is possible that the difference between our values and those of Howarth et al. is due to gravity darkening. For rapidly rotating stars, we expect to see a temperature gradient across the star, with the poles being hotter than the equator Von Zeipel (1924a,b). This could lead to Howarth et al. finding lower values for ve sin i, as their UV spectra are preferentially sampling the hot, slowly rotating, poles over the cooler and rapidly rotating equator.

Figure 4

Comparison of the projected rotational velocities for stars common to both Howarth et al. (1997) and this paper. The effects of macrotubulence, which is not explicitly included in the former can be clearly seen.

Figure 4

Comparison of the projected rotational velocities for stars common to both Howarth et al. (1997) and this paper. The effects of macrotubulence, which is not explicitly included in the former can be clearly seen.

### 5.2 Comparison with evolutionary models

Our estimated projected rotational velocities are plotted against spectral type in Fig. 5, with the majority of stars lying on a locus from approximately 60 km s−1 at B0 to 30 km s−1 at B9. This decrease in projected rotational velocity at later spectral type is in accordance with evolutionary models, as discussed below. However, there are a number of early-B type supergiants that appear to have anomalously high projected rotational velocities for their spectral type and these will be further discussed in Section 5.3.

Figure 5

Projected rotational velocities as a function of spectral type. The six additional targets that were selected as they were suspected to have a high projected rotational velocity have been identified.

Figure 5

Projected rotational velocities as a function of spectral type. The six additional targets that were selected as they were suspected to have a high projected rotational velocity have been identified.

We used a Kolmogorov–Smirnov (K–S) test to compare the distribution of rotational velocities in our Galactic supergiant sample, with that found for supergiants in the SMC by Dufton et al. (2006). While the sample of Dufton et al. is small, with only 13 stars, the K–S test indicates that at the 0.05 significance level, the distributions are the same, with a measured D statistic of 0.29. From this, we conclude that there is no evidence for any dependence of the current rotational velocities on initial metallicity, although this result must be qualified by again stressing the relatively small sample sizes, and the additional uncertainty introduced by the unknown value of sini.

From a theoretical perspective, the dependence of surface rotational velocity on metallicity is not straightforward. As discussed in Meynet & Maeder (2005), both mass loss and the internal coupling between core and envelope affect the surface equatorial velocity. Lower metallicity reduces mass-loss rates (and hence the loss of angular momentum from the star), but it also lowers the efficiency of the transport of angular momentum to the surface. Hence, as the metallicity changes, there are two competing mechanisms that to some extent cancel each other out.

Using the models of Meynet & Maeder (2003, 2005), we compared two 25 M models with initial velocities of 300 km s−1 and Z= 0.02 and 0.04 (D25z20S3A and D25z40S3, respectively). The higher metallicity model was found to have a rotational velocity that was ∼15 km s−1 lower at log Teff= 4.35, and ∼5 km s−1 lower at log Teff= 4.1. Such small differences are consistent with the cumulative frequency plot discussed above. The 40 M models (D40z08S3, D40z20S3A and D40z40S3) show a larger spread of equatorial velocities for a given temperature. For example, at a temperature of log Teff= 4.2, the low-metallicity model (Z= 0.008) has v= 37 km s−1, the solar metallicity model has v= 43 km s−1 and the high-metallicity model (Z= 0.040) has v= 66 km s−1. Scaling these values to account for average projection, the spread in projected rotational velocities is ∼20 km s−1. From this, we conclude that while differences in metallicity may increase the scatter of measured values when compared with evolutionary models, these are unlikely to be large enough to be observable when comparing the distribution and mean of rotational velocities for the SMC B supergiants of Dufton et al. (2006) to our Galactic sample. Furthermore, we can discount different metallicities as an explanation for our most rapidly rotating stars, as discussed in Section 5.3.

The projected rotational velocities for all our targets have been plotted against their effective temperature estimates (from Table 3) in Fig. 6, together with the predictions of the evolutionary models of Meynet & Maeder (2003) for Galactic metallicities. To aid the comparison, the observational data set has been subdivided into four initial mass ranges. The models used for the comparison are D09z20S3A, D12z20S3A, D215z20S3A, D20z20S3A, D25z20S3A and D40z20S3A, which have Z= 0.02, an initial equatorial rotational velocity of 300 km s−1 and masses from 9 M to 40 M; the theoretical rotational velocities have been scaled by a factor of π/4 to convert them to an average projected rotational velocity assuming a random orientation of axes (Chandrasekhar & Münch 1950).

Figure 6

Projected rotational velocities and effective temperatures for all stars, plotted against the evolutionary tracks of Meynet & Maeder (2003). Note that the rotational velocities from the evolutionary tracks have been scaled by π/4 to account for projection, apart from the red dotted line in the second panel that displays the evolution of a star with an initial mass of 15 M. Stars (which have had their masses estimated as described in Section 4.5) have been binned accordingly into four mass ranges 9 M < M < 15 M, 16 M < M < 20 M, 21 M < M < 25 M and 26 M < M < 40 M. These mass bins were chosen so as to facilitate comparison with the available evolutionary models.

Figure 6

Projected rotational velocities and effective temperatures for all stars, plotted against the evolutionary tracks of Meynet & Maeder (2003). Note that the rotational velocities from the evolutionary tracks have been scaled by π/4 to account for projection, apart from the red dotted line in the second panel that displays the evolution of a star with an initial mass of 15 M. Stars (which have had their masses estimated as described in Section 4.5) have been binned accordingly into four mass ranges 9 M < M < 15 M, 16 M < M < 20 M, 21 M < M < 25 M and 26 M < M < 40 M. These mass bins were chosen so as to facilitate comparison with the available evolutionary models.

In general, there is good agreement between observation and theory, both in the magnitude of the projected rotational velocities and a decrease as one moves to lower effective temperature or later spectral type. The agreement is particularly encouraging for the higher mass stars with initial mass estimates of >20 M. For the two lower mass cohorts, the agreement is less convincing. For example, the projected rotational velocity estimates for our lowest mass sample (9–15 M) appear to be systematically lower than predicted. This discrepancy would be ameliorated if the initial stellar masses had been underestimated but as discussed in Section 4.5, these estimates should be reliable to within 2 M. Another possibility is that the projected rotational velocities have been systematically underestimated. Aerts et al. (2009) simulated the effects of non-radial gravity-mode oscillations on the spectral line profiles of an early B type supergiant and found that this could lead to an underestimate of the rotational velocity found by our methodology. Although this would again improve agreement with theory, it would not explain why the effect is only found in the lowest mass cohort. Additionally, the simulations indicate that the underestimation only occurs in some cases and hence do not currently explain the systematic nature of the discrepancy. It should be noted that the simulations of Aerts et al. are for one set of atmospheric parameters (Teff= 18 200 K; log g= 3.05) and an extension to other spectral types would be useful. Hence we conclude that supergiants with initial masses in the range 9–15 M would appear to have lower rotational velocities than are predicted by the evolutionary models. For supergiants with initial masses of 16–20 M, the agreement is good apart from a small number of targets that appear to be rotating more rapidly and which are discussed further in Section 5.3.

We also note that the decrease in rotational velocities seen at spectral type B1 corresponds to the position of the bistability jump (Vink, de Koter & Lamers 1999), where wind properties change from a fast wind with standard mass-loss rates to a slower wind with higher mass-loss rates. It has been suggested (Vink 2008) that the bistability jump may be accompanied by bistability braking, where increased mass loss at spectral type B1 removes sufficient angular momentum from the system to account for a dramatic decrease in rotational velocities. Our results for the 20 to 25 M cohort, as illustrated in Fig. 6, provide some tentative support for this rapid decrease in rotational velocity, with three or four targets appearing to lie in this phase.

### 5.3 Rapid rotators

For the purposes of this discussion, ‘rapid rotators’ refers to four targets HD 157246, HD 93827, HD 99857 and HD 165024 that have larger projected rotational velocities than predicted by the evolutionary models (see Fig. 6). Of these, HD 165024 should be considered as a marginal case; if its mass estimate was reduced from 17 to 12 M, then it would not be classed as rapidly rotating. However, it was decided to include this in the sample of rapid rotators that would be examined in more detail for clues as to a different evolutionary history.

It should be noted that these rapidly rotating objects appear to be relatively rare with only four identified in our complete sample. Indeed six targets were pre-selected based on them having anomalously large projected rotational velocities estimates for their spectral type in the analysis of Howarth et al. Excluding these stars, there are 51 targets in our sample, with two having measured projected rotational velocities that appear to be significantly larger than the mean for their spectral type, viz. HD 157246, HD 165024. Thus, we find that approximately 4 per cent of our sample are anomalously rapid rotators. This is broadly consistent with the identification of only one rapid rotator in the sample of Dufton et al. (2006) of 13 SMC supergiants. Note that we may have underestimated the fraction of supergiants that are rapid rotators, as some of our sample could be observed pole-on. However, as discussed by Hunter et al. (2007), the probability of observing such objects is low due to the nature of the sine function. For example, only 13 percent of our targets will have a value of sin i less than 0.5, assuming a random orientation of the rotation axis. Hence, we consider that within the constraints of our sample size, our estimate of the fraction of anomalously rapid rotators among our targets is reasonable and that it is certainly small.

There are at least three channels by which these stars could have reached their current evolutionary state:

• They had extremely high rotational velocities on the main sequence, and have spun down normally as they evolved.

• They have not spun down as much as most other stars as they became supergiant stars.

• They had a moderate velocity on the main sequence but have experienced an additional source of angular momentum that has allowed them to maintain their rotational velocity.

The first two channels appear implausible as for the first, a very high main-sequence rotational velocity is required, whilst for the second, it is unclear what mechanism would have inhibited their spin down. Indeed, for models in this mass range, the increase in mass loss due to the bistability jump naturally leads to a decrease in the rotational velocity.

This leaves the possibility that these stars have an additional source of angular momentum. A plausible scenario would involve binarity and mass transfer (Koenigsberger 2003; Langer et al. 2003; Langer et al. 2008; Meibom, Mathieu & Stassun 2007). The SIMBAD online astronomical data base was checked to see if any of the four rapid rotators were listed as spectroscopic binaries (see Fig.3). None of the targets were so classified, and in the absence of the time-resolved spectra that could indicate binarity from radial velocity variations, the spectral lines in the rapid rotators were re-examined but no evidence was found for any asymmetry that might imply the presence of a binary companion. This is not in itself evidence that these are single stars, as the luminous nature of B-supergiants would make the detection of fainter binary companions difficult.

In addition to these three scenarios, we must also consider the possibility that the models used are simply not appropriate for these objects. It would be surprising if this was the case, however, as the agreement between theory and observation is excellent for most of our sample, and there is nothing particularly unusual about the observed properties of our rapid rotators (besides their large ve sin i) that would lead us to suspect that the models are not applicable.

### 5.4 Velocity fields

The atmospheres of early-type supergiants appear to contain significant velocity fields. These are often characterized as microturbulence (estimated in Section 4.3) and macroturbulence (estimated in Section 3.2). The former is incorporated into the line opacity profile and hence directly influences the strength of the metal line, whilst the latter is normally modelled by including additional broadening via a convolution of the theoretical line profile. Assuming that these effects are indeed caused by velocity fields, they represent the extremes of velocity fields with different scalelengths in the stellar atmosphere.

The microturbulent velocities deduced for our sample range from approximately 12 to 24 km s−1 (with two cases where no reliable estimate was possible). There is some evidence that the microturbulent velocity may be anticorrelated with the effective temperature but this result should be treated with caution for at least two reasons. Even with very high-quality data, there are significant random errors associated with the estimation of the microturbulence. For example, the estimate of the microturbulence for HD 150898 is 20 km s−1. However, arbitrarily decreasing the equivalent width of Si iii line at 4552 Å by 5 per cent, whilst increasing that for the line at 4575 Å by 5 per cent would decrease the estimate to 15 km s−1. Additionally, the microturbulence estimate can vary depending on the ionic species and the set of lines considered (see e.g. Vrancken et al. 1997, 2000; Simón-Díaz et al. 2006; Hunter et al. 2007). Indeed, Vrancken et al. reported differences of up to 9 km s−1 in the estimates obtained from different species. Additionally the strength of the Si iii triplet varies with spectral type leading to different degrees of saturation and hence of sensitivity to the microturbulence parameter.

Recently Cantiello et al. (2009) have discussed the obeservational consequences of subsurface convection zones in massive stars. These zones arise from peaks in the opacity (as a function of temperature) that arise from the ionization of helium and iron. The latter is found to be more prominent at higher luminosity and lower gravities corresponding in the HR diagram to the region occupied by O- and B-type supergiants. Using the analyses of Trundle et al. (2007) and Hunter et al. (2008a) of B-type stars observed in the ESO VLT-FLAMES survey of massive stars (Evans et al. 2005), Cantiello et al. find a correlation between the magnitudes of the convection velocities implied by their models and the estimated microturbulent velocities. In particular, objects with microturbulent velocities of more than 10 km s−1 are in a region of the HR diagram where the mean convective velocity within 1.5 pressure scaleheights of the upper boundary of the iron convection zone (〈vc〉) is greater than 2.5 km s−1.

All our targets lie in the region of the HR digram where the convection due to the iron opacity is pronounced. Indeed, as well as lying within the contour for 〈vc〉= 2.5 km s−1, they all lie within the contour for 3.75 km s−1 which was the largest mean convection velocity regime considered by Cantiello et al. For their Galactic sample, Cantiello et al. only considered nine stars with five of them having estimates of the microturbulent velocity in excess of 10 km s−1. For our sample, we have been able to estimate the microturbulent velocity in 54 (out of 57) targets. The large values deduced coupled with their position within the HR diagram support the conclusion of Cantiello et al. that there is a physical connection between subphotospheric convection and the small-scale stochastic velocity fields in early-type stars.

As discussed in Section 3.2, a macroturbulent velocity was introduced in order to allow for the excess broadening in the observational metal line profiles as has been found in other studies (see e.g. Howarth et al. 1997; Ryans et al. 2002). The velocity field was assumed to have a Gaussian distribution and in general this appeared to be consistent with the observations. Estimates were obtained for all but six of our targets. In four cases (HD 64760, HD 152667, HD 157246, HD 93827), the line profile is dominated by rotational broadening making the estimation of the relatively small macroturbulent component unreliable. One target, HD 83183, appeared to have a very small degree of macroturbulent broadening, possibly due to its having a luminosity class II. For the sixth target, HD 77581, the fits to the spectra were relatively poor and a reliable estimate was therefore not possible.

The errors for the macroturbulence quoted in Table 3 are the standard deviations of the estimates from individual features. As such, they do not include systematic errors and implicitly assume that there is a unique value for the macroturbulence. A potentially significant source of systematic error is the choice of the intrinsic absorption line profiles. These were taken from spectra calculated from our grid of non-LTE tlusty model atmospheres as described in Section 3.2. Tests using theoretical spectra from different grid points indicated that uncertainties in the values adopted for the effective temperature or surface gravity were unlikely to be significant. However, the choice of the microturbulence (the tlusty grid was calculated for values of 0, 5, 10, 20 and 30 km s−1) was more important as it is this parameter that effectively determines the shape of the theoretical line profile. Again tests showed that for the early B-type stars, the value adopted for the microturbulence had little effect of the macroturbulence estimates. This was because the former had values (10–20 km s−1) that were significantly smaller than the latter (typically 60 km s−1). In such cases, the intrinsic profile is relatively narrow compared with the macroturbulent broadening and hence its choice is not critical. However, for late B spectral types, the magnitudes of the microturbulence and macroturbulence become comparable and in this case the choice of the intrinsic line profile becomes more important.

For example, the grid point adopted for HD 51309 had a microturbulence of 20 km s−1 being the nearest value to the observational estimate of 18 km s−1. If instead we had adopted a microturbulence of 10 km s−1, our estimate for the macroturbulence would have increased from 20 ± 3 to 31 ± 5 km s−1. This result is not surprising as we are modelling the total broadening of the lines using micro- and macroturbulent velocity fields (together with a rotational component). A decrease or increase in magnitude of one field will inevitable anticorrelate with the estimate obtained for the other field. However, the uncertainty in the macroturbulence estimates for the later B spectral types may be larger than that implied by the statistical error estimates quoted in Table 3.

The estimates of the macroturbulent velocity show a decrease from approximately 70 km s−1 at a spectral type of B0 to approximately 20 km s−1 at a spectral type of B8. Two targets (HD 52089 and HD 159100) appear to have anomalously low estimates. However, these estimates will depend on the adopted microturbulences as discussed above. Additionally, both these objects have relatively large surface gravities for their effective temperature, together with lower estimated masses than most of our sample; hence, their lower estimates may reflect their different evolutionary status. The decrease of macroturbulence with effective temperature has been found previously by Ryans et al. (2002) for 11 Galactic supergiants and by Dufton et al. (2006) for 13 SMC supergiants. These results have also been plotted in Fig. 7, and in general the estimates obtained from all three studies are consistent.

Figure 7

Macroturbulent velocity estimates plotted against effective temperature estimates for all stars in our sample for which reliable estimates were obtained (marked +). Also shown are the estimates of Dufton et al. (2006) for Galactic supergiants (marked ×) and SMC supergiants (marked ⊙).

Figure 7

Macroturbulent velocity estimates plotted against effective temperature estimates for all stars in our sample for which reliable estimates were obtained (marked +). Also shown are the estimates of Dufton et al. (2006) for Galactic supergiants (marked ×) and SMC supergiants (marked ⊙).

Recently, Aerts et al. (2009) have provided a physical explanation for this excess broadening in terms of the non-radial gravity-mode oscillations in the stellar atmosphere. They simulate the effect of these oscillations on the profile of the Si iii line at 4552 Å in a B2 Ia type supergiant (Teff= 18 200 K; log g= 3.05). Additional broadening is found which is modelled by rotational broadening coupled with a Gaussian macroturbulent velocity field. For the former, the estimates can be lower than those of the models (as discussed in Section 5.2), whilst estimates of the macroturbulence velocity ranging from 0 km s−1 to approximately 50 km s−1 are found. This range is consistent with our observational estimates in Fig. 7 and additionally the range of values found in the simulations (due to the time dependent contribution of the different modes) may also at least partially explain the scatter found in our estimates, including the anomalously low estimates found for HD 52089 and HD 159100.

### 5.5 Nitrogen abundances

Rotation is generally considered to be crucial for developing theoretical models of massive star evolution as it can induce mixing of nucleosynthetically processed material from the stellar core into the photosphere (see e.g. Heger & Langer 2000; Meynet & Maeder 2000). Such models have been used to explain the ratio of blue to red supergiants (Maeder & Meynet 2001) and Wolf–Rayet populations at different metallicities (Meynet & Maeder 2005; Vink & de Koter 2005). A natural consequence of such mixing is an enhancement of nitrogen (together with smaller changes in the carbon, oxygen and helium abundances) at the stellar surface. Hence, nitrogen abundances are often used as an indicator of the amount of mixing, and in particular rotationally induced mixing, that has occurred (see e.g. Brott et al. 2009). However, recent results from the VLT-FLAMES survey Evans et al. (2005) have indicated that other mechanisms may affect mixing of material between the interior and the surface Hunter et al. (2008b, 2009).

We have estimated the surface nitrogen enhancement for our targets by comparing our nitrogen abundances with those found for Galactic B-type stars in the clusters NGC 3293 and NGC 4755 (Trundle et al. 2007). This study was chosen as it used the same grid of model atmospheres and methodology to that adopted here. To ensure consistency with our own results, we have only used their abundance estimates from the 3995 Å line, whilst to minimize the effects of mixing, we have only included stars of luminosity class VIII. A mean abundance of 7.47 ± 0.14 dex was obtained from a sample of 15 stars. This is slightly smaller than the mean abundance of 7.59 ± 0.19 dex found when all the nitrogen lines are considered but is consistent with the comparison of nitrogen abundances given in Table 5. In Fig. 8, the surface nitrogen abundance for our targets is plotted against projected rotational velocity, together with the base abundance deduced from the results of Trundle et al.

Figure 8

Surface nitrogen abundances versus projected rotational velocity. Solid line is base abundance for early B stars while on the main sequence, based on VLT-FLAMES data as discussed in text.

Figure 8

Surface nitrogen abundances versus projected rotational velocity. Solid line is base abundance for early B stars while on the main sequence, based on VLT-FLAMES data as discussed in text.

There would appear to be no correlation of nitrogen abundance with current projected rotational velocity. This is not surprising given the ambiguity arising from the unknown angle of inclination and more importantly the large change in rotational velocity that occurs when a star leaves the main sequence (as is apparent, for example, in the theoretical models shown in Fig. 6). We have attempted to allow for the latter effect by estimating the projected rotational velocity of the progenitor main-sequence object. We have assumed that all the main-sequence precursors have a typical surface gravity of 4.2 dex (Cox 2000); we note that the actual value adopted is not critical to our methodology. We have then assumed that the decrease in rotational velocity as a star leaves the main sequence is due solely to its increase in radius. Hence, we are assuming that the effects of mass loss in both decreasing the stellar moment of inertia and in removing angular momentum are negligible. In such circumstances, the radius will simply scale as the square root of the surface gravity and we can estimate the ratio of the main sequence to the current radius. Additionally, if we assume solid body rotation and that the stellar moment of inertia scales as the radius squared, we can estimate the ratio of the main sequence to the current projected rotational velocities and hence deduce estimates for the former.

To test the validity of our approach, we considered the decrease in equatorial rotational velocity as the radius of a star increases, as predicted by the Geneva stellar evolutionary models. These tests indicated that our simplification was reasonable, with best agreement for the 20 M model. For this model, evolving from the main sequence (defined here as when the star has a surface gravity of 4.1 dex) to the supergiant phase when the star has a surface gravity of 2.9 dex, its rotational velocity decreases by a factor of 3.9, whilst its radius increases by a factor of 3.8. For more massive models, the agreement is less satisfactory, with a 25 M model increasing in radius by a factor of 3.8 as it moves from the main sequence to the supergiant stage, but decreasing its rotational velocity by a factor of 5.6. At lower masses the agreement is poorer, with a 15 M model increasing its radius by a factor of 4, while decreasing its rotational velocity by a factor of 2.7. These discrepancies are most likely due to mass loss, which we have ignored in our simplification. Furthermore, we have assumed solid body rotation, whereas in the more sophisticated Geneva models, the coupling between core and envelope and the changing size of the core will affect the transport of angular momentum within the star, and hence rotational velocity.

In Fig. 9, our nitrogen abundances are plotted against these main sequence projected rotational velocities (hencefore designated as ‘scaled projected rotational velocities’). We have excluded the four targets that we believe may have not been undergone normal single star evolution (see Section 5.3), but our conclusions would not be significantly affected if they were included. We also excluded HD 152236 as its surface gravity could not be measured, and HD 64760 as its scaled rotational velocity is unrealistically large. We emphasize that the scaled projected rotational velocities must be considered as subject to significant uncertainties given the approximations made. Additionally, they do not remove the ambiguity introduced by the unknown angle of inclination. However, we believe that they are useful as the large increase in radius is likely to be an important mechanism as the star evolves from the main sequence.

Figure 9

Surface nitrogen abundances versus estimated main-sequence projected rotational velocity. Also shown is a linear least-squares fit.

Figure 9

Surface nitrogen abundances versus estimated main-sequence projected rotational velocity. Also shown is a linear least-squares fit.

A correlation is now seen between the scaled projected rotational velocity and nitrogen abundance. A linear least-squares fit (shown in Fig. 6 as a solid line) implies an increase in nitrogen abundances of approximately 0.6 dex (i.e. a factor of 4) over our range of scaled projected rotational velocities. The slope of the fit is found to be (1.1 ± 0.3) × 10−3 dex km s−1, which is not consistent with a null result. Additionally, the asymptotic nitrogen abundance at low velocities of approximately 7.7 dex is in reasonable agreement with our baseline nitrogen abundance of 7.47 dex. Indeed, as some of the stars with low projected rotational velocities will have low angles of inclination (and hence relatively large projected velocities), a small positive offset from the baseline abundance would be expected. We used a Monte Carlo technique to try and test the validity of the correlation. The value of ve sin i was randomly varied within one standard deviation of the mean for each star, and nitrogen abundance and surface gravity varied by 0.2 and 0.1 dex, respectively, and a least-squares fit made to the data. For all iterations, a positive correlation between scaled ve sin i and nitrogen abundance was observed, with a nitrogen enhancement of between 0.3 and 0.6 dex. Based on these results, and within the limits of our approximations, there would appear to be a statistically significant correlation between inferred main-sequence rotational velocity and surface nitrogen abundance at the supergiant stage.

These results are consistent with stellar evolutionary calculations. For example, Heger & Langer (2000) discussed the evolution of a star with an initial mass of 20 M and an equatorial velocity of 206 km s−1. They find an increase of a factor of 2 or more in the surface nitrogen abundance at the end of core hydrogen burning. The Geneva group stellar evolution models (Meynet & Maeder 2000) also find similar nitrogen enhancements at the surface of rapidly rotating massive stars. For example, a 20 M model, rotating with an initial velocity of 200 km s−1, leads to an increase in the nitrogen to carbon ratio at the surface by a factor of 4; when the initial rotational velocity is increased to 300 km s−1, this increases to a factor of approximately 7 with most of the change arising from an enhanced nitrogen abundance. Given the uncertainties in the initial rotational velocities of our objects, we conclude that there is satisfactory agreement between our results and models of rotational mixing. However, our results cannot exclude the types of inconsistencies found by Hunter et al. (2008b) in their study of LMC B-type stars.

Although we have compared our results with single star evolutionary models, we note that in some cases the surface composition may also have been affected by binary star evolution. For example, while attempting to model the binary progenitor of SN 1993J, Stancliffe & Elridge (2009) found that a blue supergiant in a binary system could undergo a surface nitrogen enrichment of up to a factor of 10.

### 5.6 Differential rotation

The relatively simple Fourier transform analysis employed in this study is based on the assumption that stars rotate as a solid body. While observations of our own Sun have long demonstrated this to be false (e.g. Schou et al. 1998), it none the less remains an appropriate assumption when confronted with spectra of limited resolution and S/N. Reiners & Schmitt (2002) have modelled the dependence of the first (q1) and second (q2) zeroes in the Fourier transform of rotationally broadened spectral lines, and have established criteria for solar and antisolar-like differential rotation. Using this technique, differential rotation has been identified in A-type main-sequence stars by Reiners & Royer (2004).

Differential rotation has not, however, previously been observed in stars of comparable spectral type and luminosity class to our sample. We have therefore attempted to identify the signatures of differential rotation in our sample. Only the fast rotating stars were considered, as a large projected rotational velocity allows the reliable identification of more than one zero in the Fourier transform. Furthermore, the angle of inclination of the most rapidly rotating stars can be constrained, as vve sin i when i≃ 90°. This is important as pole-on rotation may mimic the characteristics of differential rotation in the Fourier transform of absorption lines.

For the majority of the targets, the second zero was indistinguishable from the high-frequency noise in the transform. However, for five targets [HD 152667 (), HD 64760 (), HD 139518 (), HD 100841 () and HD 157246 ()], the position of the second zero was measurable. Reiners & Schmitt give a value of q2/q1 > 1.83 as being indicative of antisolar-like differential rotation (where the poles rotate faster than the equator), and a value of q2/q1 < 1.72 for solar-like differential rotation. Hence, of these stars, only HD 157246 satisfied the criteria for differential rotation, and in Table 6 we summarize the measurements for this star. It is important to note, however, that the value of q2/q1 determined for HD 157246 is within a standard deviation of the threshold for differential rotation.

Table 6

Details of lines used for analysis of differential rotation in HD 157246.

 Species λ (Å) ve sin i q1 q2 He i 3819.61 264 0.194 0.359 1.85 N ii 3995.00 279 0.177 0.335 1.89 He i 4026.19 269 0.181 0.346 1.91 C ii 4267.00/4267.26 255 0.181 0.335 1.85 Mg ii 4481.13/4481.33 255 0.171 0.296 1.73 Si iii 4552.62 277 0.156 0.296 1.90 O ii 4661.63 279a 0.150 0.301 2.01 He i 4921.93 271 0.148 0.274 1.85
 Species λ (Å) ve sin i q1 q2 He i 3819.61 264 0.194 0.359 1.85 N ii 3995.00 279 0.177 0.335 1.89 He i 4026.19 269 0.181 0.346 1.91 C ii 4267.00/4267.26 255 0.181 0.335 1.85 Mg ii 4481.13/4481.33 255 0.171 0.296 1.73 Si iii 4552.62 277 0.156 0.296 1.90 O ii 4661.63 279a 0.150 0.301 2.01 He i 4921.93 271 0.148 0.274 1.85

a Poor quality line, hence q1 and q2 are uncertain.

While antisolar-like differential rotation has recently been observed by e.g. Strassmeir, Kratzwald & Weber (2003), from Doppler maps of a K2 giant, it is unclear what the physical mechanism behind this is. It has been proposed that meridional circulation, driven by a strong temperature gradient, could lead to antisolar-like differential rotation (Kitchatinov & Rüdiger 2004).

## 6 CONCLUSION

From a sample of more than 50 early-type supergiant stars, we find a range of rotational velocities that in general are in good agreement with evolutionary models. For four stars, we find a significant difference between their measured values and the expected rotational velocities for their current evolutionary status. These discrepancies cannot be explained in terms of projection effects and are unlikely to be caused by observational uncertainties, and we conclude that the most likely explanation for their behaviour is binarity. In addition to the projected rotational velocities, we have measured the macroturbulence and microturbulence in most of our targets. For the former, we find good agreement with the predictions of Cantiello et al. (2009) for convection driven by the opacity of iron group elements. The latter may be a manifestation of the large number of non-radial gravity-mode stellar oscillations (Aerts et al. 2009) present in the stellar photosphere and our results are consistent with their prediction for a B2 Ia supergiant.

We find a range of nitrogen abundances stretching from the Galactic B-type baseline abundance to an enhancement of more than 1 dex. No correlation of abundance is found with the current projected rotational velocity. However, a correlation is found with the estimated main-sequence projected rotational velocity and this is consistent with current evolutionary models for single rotating stars.

We have attempted to determine if there was any evidence of differential rotation in our sample, and find marginal evidence that one of our most rapidly rotating targets is undergoing antisolar-like differential rotation.

The authors thank Connie Aerts for her comments and advice on an early draft of this paper, and to Chris Evans for obtaining some preliminary observational data. We also thank Ines Brott and Jorick Vink for useful discussions. We thank the referee, Ian Howarth, for his insightful comments, and in particular the suggestion that gravity darkening may explain the discrepancies between the values of ve sin i found for rapidly rotating stars in this work, and with cross-correlation methods. This research has made use of NASA's Astrophysics Data System and the SIMBAD data base, operated at CDS, Strasbourg, France. This research was supported by a rolling grant awarded by the UK Science and Technology Facilities Council. MF is funded by the Northern Ireland Department of Employment and Learning.

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