A&A 386, 1019-1027 (2002)
DOI: 10.1051/0004-6361:20020349
M. A. Urbaneja1 - A. Herrero1,2 - R. P. Kudritzki3 - F. Bresolin3 - L. J. Corral1 - J. Puls4
1 - Instituto de Astrofísica de Canarias, 38200 La Laguna,
Tenerife, Spain
2 -
Departamento de Astrofísica, Universidad de La Laguna,
Avda. Astrofísico Francisco Sánchez, s/n, 38071 La Laguna, Spain
3 -
Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive,
Honolulu, Hawaii 96822, USA
4 -
Universitäts-Sternwarte München, Scheinerstr. 1, 81679 München,
Germany
Received 7 February 2002 / Accepted 4 March 2002
Abstract
We present terminal velocities of M 33 B-supergiants, obtained
from STIS HST spectra
as part of our programme to investigate the Wind Momentum -
Luminosity Relationship (WLR) in the Local Group.
Terminal velocities are derived from their N V,
C IV, and Si IV resonance lines in UV spectra. Comparing with
IUE spectra of Galactic B-supergiants we found evidence
of low metallicity in three of our objects.
The terminal velocities are consistent with the corresponding values of Galactic
stars, except for B-133. For this
star we find a very large
and a red Si IV
component deeper than the blue one, that might be an indication
of binarity. The average ratio
between terminal and turbulent wind velocities is 0.25,
well above the value found for Galactic stars.
Key words: stars: atmospheres - stars: early-types - stars: supergiants - stars: fundamental parameters - stars: winds, outflows - galaxies: individual: M 33
The Wind Momentum-Luminosity Relationship (WLR, Kudritzki et al. 1995; Puls et al. 1996, for recent reviews see Kudritzki 1998 and Kudritzki & Puls 2000) offers the very attractive opportunity to derive the stellar luminosity directly from the analysis of the observed spectrum, provided that the wind is radiatively driven. Accurate individual stellar distances can then be obtained if the apparent magnitude and extinction are known. This method, that has been extensively described elsewhere (see for example the reviews cited above), can be potentially applied to individual stars up to distances of 10-20 Mpc, reaching the Virgo and Fornax clusters with accuracies as low as 0.1 mag, using present day telescopes and techniques (McCarthy et al. 1997; Kudritzki et al. 1999).
However, accurate application of the method requires previous
calibrating work, as the WLR depends on the stellar metallicity
and the spectral type (Puls et al. 1996; Kudritzki et al. 1999).
Thus observation and analysis of stars of
different spectral type and metallicity at known distances are
crucial to calibrate the method before applying it.
Ident | Ident | ![]() |
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V | Spectral | Obs. | Exp. | S/N |
IFM93 | HS80 | mag | Type | Date | time(s) | |||
0900 |
01 33 44.7 | 30 36 18 | 17.3 | B0-B1 I | Jul.-8-00 | 5193 | 24 | |
0785 | 110-A | 01 33 41.0 | 30 22 37 | 16.1 | B1 Ia+ | Aug.-7-99 | 5201 | 29 |
B-38 | 01 33 00.8 | 30 35 05 | 16.7 | B1 Ia | Sep.-5-00 | 5205 | 30 | |
0515 | B-133 | 01 33 29.0 | 30 47 44 | 17.6 | B1.5 Ia | Aug.-5-99 | 5205 | 30 |
1733 | B-526 | 01 34 15.9 | 30 33 46 | 17.6 | B2.5 I | Dec.-11-00 | 5201 | 15 |
1137 | 01 33 53.1 | 30 35 28 | 16.7 | B3 I | Jul.-9-00 | 5205 | 15 |
For this reason we have started in our group a number of programs aimed at calibrating the WLR for different stars in different environments within the Local Group (Puls et al. 1996; McCarthy et al. 1997; Kudritzki et al. 1999; Herrero et al. 2001).
In the present paper, we analyze STIS HST UV spectra of M 33 B-supergiants. Our analysis is primarily aimed at obtaining the wind terminal velocities, needed to calculate the WLR, that will be determined after the analysis of the optical spectrum.
In addition our study constitutes, together with a similar study of B-supergiants in M 31 (Bresolin et al. 2002), the largest homogeneous sample of stars analyzed in the UV beyond the Milky Way and the Magellanic Clouds (see Prinja & Crowther 1998, for a recent list), and an important increase in the total number of analyzed B-supergiants, in particular those with large intrinsic brightness (bright magnitudes are of course still a primary selection criteria for our extragalactic targets). The group of early B-supergiants is particularly important for the spectral type dependence of the WLR. Between O9 and B3, two jumps are observed in the WLR, one between O9 and B0 and another between B1 and B1.5, while the WLR for B-supergiants between B1.5 and B3 is not well understood in terms of the radiatively driven wind theory, as wind momenta lower than expected are derived for the analyzed Galactic stars (Kudritzki et al. 1999).
In Sect. 2 we show the observations of the spectra, that are described in Sect. 3. Section 4 presents the analysis of the UV profiles, while in Sect. 5 we discuss the individual aspects found for each star. In Sect. 6 we present the discussion of the results and the conclusions.
Observations were made with the HST STIS, using the GL140 grating which provides a resolution from 310 to 210 km s-1 in the wavelength range from 1150 to 1700 Å. We used a 02 wide slit, which is recommended for optimizing the spectral purity. Table 1 gives our list of objects and other details of the observations.
There are two spectra for each star. We merged these two spectra after checking their relative displacement by cross-correlating them.
Merged stellar spectra are corrected for the relative
velocity between stars and observer. This is done by measuring
the displacement from rest wavelength of metal lines that are purely
photospheric. There are a few photospheric lines that
could in principle be used in the observed spectral range
(Prinja 1990). They are difficult to identify in all spectra.
Thus, after inspection of the spectra,
we decided to use the
Si III doublet at
1500.24, 1501.19 Å, because it
is the only one that can be clearly identified in all spectra.
The spectral resolution does not allow us to resolve
both components of the Si III doublet. We use as rest wavelength
that of a
composed line centered at
1500.72 Å. Because of the
small signal to noise ratio of the spectra, we
decided to correct one of the spectra of higher quality and then refer the
others to this one. We selected the spectrum of M 33-0900 for that purpose.
Once the M 33-0900 spectrum had been shifted so that the Si III line
was at rest wavelentgh, we checked this correction with the position
of other strong interstellar lines (see f.e. Prinja 1990), as these
are probably produced by the interstellar medium close to M 33-0900.
We can see in Fig. 1 that the shifted interstellar lines
are at their expected rest wavelengths.
To correct the other spectra we cross-correlated them with the corrected
spectrum of M 33-0900. To avoid possible biases, strong P-Cygni profiles
have been masked
before correlations (see Howarth et al. 1997).
For M 33-1137 and M 33-B-526, the stars with lowest SN spectrum,
the cross-correlation function does not present a well defined maximum.
Checking the strong interstellar lines present in the spectra (Si II
1260.40, 1526.70) we found good
concordance between all spectra, excluding M 33-1137 and M 33-B-526.
We decided to shift both spectra until the position of their
interstellar lines agree with those of other spectra.
Special care was taken in the
case of M 33-B-526, as the unshifted spectrum shows several lines
in the vicinity of the rest wavelength of the intestellar lines.
After having shifted the spectra we rectified the continuum by tracing a polynomial through a number of selected continuum points chosen iteratively, in the same way as described in Herrero et al. (2001).
After all the above corrections have been performed, we finally obtained the spectra displayed in Fig. 1.
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Figure 1: The observed rectified UV spectra. From top to bottom: M 33-0900, M 33-110-A, M 33-B-38, M 33-B-133, M 33-B-526 and M 33-1137. Relative fluxes have been arbitrarily displaced in ordinates for the sake of clarity. The main IS lines are marked at the top, and below we have indicated the rest wavelengths of the most important stellar lines. |
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One of the difficulties of stellar analyses in M 33 is the large possible variation in metallicity, that complicates the interpretation of the spectrum. Thus in Fig. 2 we show a comparison of the N V, Si IV and C IV lines of the M 33 stars with Galactic stars of similar spectral classification. Their identifications and spectral types are given in Table 2.
The Galactic UV spectra have been taken
from the INES IUE archive, and have been degraded from the
original high resolution to the lower resolution of our M 33 HST spectra.
We emphasize that we have taken the rectification points of the
M 33 stars as a guide to rectify the IUE spectra in the same way.
Therefore, the extra absorption seen redwards of the Si IV
and C IV profiles in some Galactic stars are probably
an effect of metallicity. Furthermore these extra
absorptions are consistent with the profiles indicating a lower
metallicity in the M 33 stars. The N V comparison is strongly
affected by the different L
absorptions.
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Figure 2: Comparison of the N V (left), Si IV (middle) and C IV (right) lines in the M 33 (full line) and Galactic (dashed line) stars. From top to bottom: M 33-0900 and HD 154090; M 33-110-A and HD 148688; M 33-B-38 and HD 148688; M 33-B-133 and HD 38711; M 33-B-526 and HD 198487; M 33-1137 and HD 51309. Spectral clssifications are given in Table 2. Relative fluxes have been arbitrarily displaced in ordinates for the sake of clarity. Galactic spectra have been degraded to the M 33 HST resolution. |
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M 33-0900 has Si IV and C IV profiles that are very similar to those of HD 154090. Although N V is stronger in M 33-0900, the star looks normal for its spectral type.
This is not the case for M 33-110-A, which in comparison to HD 148688 displays very weak Si and C lines. Moreover considering the luminosity effect we would expect for Si IV, the difference is even larger. This is consistent with the low Si and O abundances derived by Monteverde et al. (2000). Thus we can expect a low metallicity for 110-A, also consistent with the higher continuum level redwards from Si IV and C IV. The N V profile is again stronger than in the comparison star. The slopes of the blue wings of both the Si and C lines are smaller than in HD 148688. This will be interpreted during the fit procedure as a larger dispersion velocity. Finally we shall mention the broad absorption in the C IV blue wing that becomes more apparent due to the low absorption in this line. This additional absorption is present in both individual M 33-110-A spectra and can be clearly indentified in Fig. 3 where we show a comparison of the C IV line in 110-A and in B-38. We have used this figure as a guide in fitting the C IV line in 110-A.
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Figure 3: Comparison of the C IV line in M 33-110-A (solid line) and M 33-B-38 (dashed line). |
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M 33-B-38, for which Monteverde et al. (2000) again derive low O and Si abundances, has also been compared with HD 148688. Similar comments as for 110-A are applicable, although effects are less extreme and the N V profile in this case is marginal (as in the Galactic star).
This has previously been observed and
analized by Bianchi et al. (1996) and was later reanalyzed by Prinja & Crowther (1998).
Both used the same HST GHRS spectrum, which looks like ours,
including the lower slope in the blue wings as compared to Galactic
stars (see Fig. 4 from Bianchi et al. 1996).
Bianchi et al. (1996) find a narrow absorption feature (narrow absorption
component, NAC) at a
blueshifted velocity of 1250 km s-1,
which is close to the edge velocity determined by
Prinja & Crowther (1998), 1225 km s-1. Interestingly, we also find evidence of
a NAC at the same velocity, which may indicate that this is a more
permanent feature.
M 33-B-133 shows the most puzzling spectra. The red component of the Si IV doublet is deeper than the blue one, which cannot be explained by the theory. The effect is due neither to noise nor to variability, as it is present in the same form in both individual spectra of M 33-B-133. We see numerous features in the C IV profile that could be interpreted as NACs. From them, only the absorptions at 250, 585 and 1990 km s-1 show both components. None of these NACs, however, seems strong enough to explain the red component of Si IV.
This is not the only remarkable feature in the spectrum of M 33-B-133.
This object has been classified by
Monteverde et al. (2000) as B1.5 Ia, and is compared with HD 152236
(B1.5 Ia+)
in Fig. 2. We see that the profiles are quite different.
In fact, the spectrum of B-133 resembles more that of
Ori (HD 38771), a B0.5 Ia star, although a comparison
of the optical spectra excludes such an early spectral type for
M 33-B-133.
Another possibility is a blend with the spectrum of a hotter star.
This is supported by the resemblance of the spectra of B-133 and
Ori, and by the data in Table 1. Note that there
B-133 has a larger S/N than would be expected from a comparison
of its visual magnitude and spectral type with those of the
other stars. Thus, although a particular set of circumstances
is required because the B1.5 supergiant dominates the blue
spectrum, it is not impossible that a hotter companion of type
O9.5-B0.5 is dominating the UV spectrum. If this is the case
the apparent strong
red component of the Si IV doublet would be the
main contribution of the B1.5 star in the UV spectrum.
However, we could not reproduce the observed spectrum by combining IUE spectra of different spectral types without extra ad hoc assumptions (as arbitrary relative displacements), nor can we detect any clear indication of binarity in the HST WFPC2 images of B-133, or other features indicative of a companion in the blue and UV spectrum, and thus the suspected binary nature of B-133 remains unconfirmed.
M 33-B-526 displays lines very similar to those of HD 198487, in spite of its suspected binary nature from its appearance in the Keck I screen (McCarthy, private communication).
The C IV profile displays several absorption features redwards of the rest wavelength that could be interpreted as contributions from a companion star. However, their positions do not correspond to those of the doublet separation Thus we expect this to be the spectrum of a single star.
M 33-1137 has Si IV profiles that are clearly weaker than those of the selected Galactic counterpart, HD 51309. The C IV profile in M 33-1137 is clearly broader than in HD 51309, with a shallow slope in the blue wing. It displays additional absorptions that agree with the positions of the C IV components at -75 km s-1, thus clearly pointing to wind inhomogeneities. Weaker absorptions are compatible with components at -550 km s-1. Other absorptions cannot be clearly assigned to the C IV doublet, specially considering the low SNR. The N V feature is more evident in M 33-1137 than in the Galactic star. The observed spectrum points again to a lower metallicity in the M 33 star than in the Galactic comparison star.
Therefore the UV spectral morphology of the observed M 33 stars separates them in three groups: a group (particularly evident in Si IV) with lines weaker than their Galactic comparison stars (M 33-110-A, M 33-B-38 and M 33-1137), a second group with lines similar to their Galactic counterparts (M 33-0900 and M 33-B-526) and one star (M 33-B-133) showing peculiar profiles for its spectral type. In addition, the M 33 stars seem to have lower slopes in the blue wings, pointing to larger dispersion velocities. This is particularly clear in the first group of stars.
We use the method described by Haser (Haser 1995, see also Lamers et al. 1999) to analyse the UV P Cygni lines in order to derive wind
terminal velocities. We have also derived H I column densities towards
the M 33 stars by fitting the IS L
line, in the same way as
in Herrero et al. (2001) (see also Jenkins 1970; Bohlin 1975).
The values quoted in Table 2 for these column densities
are similar to those obtained for stars in our
Galaxy (see Fig. 2 of Shull & Van Steenberg 1985).
After continuum
rectification, we extract small regions of each spectrum centered
in our strategics doublets: N V
1238.819,
1242.798; Si IV
1393.73, 1402.73 and C IV
1548.191, 1550.761. In case of
discrepancies or difficulties, we give more weight to the
Si IV and C IV lines than to the N V one.
To get the wind terminal velocities we have to correct for the underlying photospheric components, which we do in an approximate way, by using IUE spectra of hot stars with weak winds (and projected rotational velocities as low as possible) as templates. These templates have been convolved with appropriate rotational profiles, to account for the individual stellar rotational speeds. We excluded N V from this procedure, as the corresponding spectra are noisy and do not show any features.
We selected a sample of Milky Way dwarfs with spectral types from O9V to B3V taken from the INES database. This covers the spectral type range of our M 33 stars. Selection of photospheric template and continuum rectification has a big impact when fitting emission peaks, but has little effect on the determined terminal velocities. The IUE spectra have been corrected for the relative velocity between stars and observer, in the same way as for M 33 stars. The stars used for the photospheric templates are specified in Table 2. Note that the profiles of interest are very weak in these stars, but even so the different metallicity may be a small source of error.
The velocity stratification is parameterized as a usual -law,
and we account for the wind turbulent velocity in the same manner
as described in (Haser 1995) and Herrero et al. (2001).
The indetermination in the exponent of the velocity field,
,
produces an additional uncertainty in the terminal velocities.
Table 2 gives the fit results with respect to the wind and turbulent velocities. The final fit to each line is shown in Figs. 4 and 5.
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Figure 4: Final fits for the three earliest stars of our sample. Lines are plotted from left to right (N V, Si IV, C IV) and stars from top to bottom in the same order as they are listed in the tables. |
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Figure 5: As Fig. 4, however for the three last stars in Table 1. |
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We briefly comment here on individual aspects of the analysis that could be of interest.
The terminal velocity of this star has also been determined by Bianchi et al. (1996) and Prinja & Crowther (1998). The first authors use an analysis method similar to the one employed here, and thus it is not surprising that our value agrees with their. Prinja & Crowther (1998) determine the terminal velocities of their stellar sample from the violet edges of the profiles and the NACs. The velocity they obtain for this star is much larger (1225 km s-1) than ours (730 km s-1) or the one by Bianchi et al. (about 700 km s-1). Our velocity would support the interpretation that what we have seen at 1250 km s-1 is actually not a NAC.
Bianchi et al. (1996) do not give the turbulent velocity of their stars.
We derive a very large value, 250 km s-1, nearly 35
of
.
We adopted a large -value, both to improve the
consistency between the Si IV and C IV fits, and to
improve the fit of the blue side of the red emission peak.
Ident | Spectral | Galactic | Spectral | log | ![]() |
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Type | Star | Type | N(H I) | |||||
M 33-0900 |
B0-B1 I | HD 154090 | B0.7 Ia | 20.85 | 950 | 170 | 50 | 1.0 |
M 33-110-A | B1 Ia+ | HD 148688 | B1 Ia | 21.15 | 800 | 200 | 50 | 1.0 |
M 33-B-38 | B1 Ia | HD 148688 | B1 Ia | 20.70 | 730 | 250 | 50 | 2.0 |
M 33-B-133 | B1.5 Ia | HD 152236 | B1.5 Ia+ | 20.97 | 2050 | 150 | 100 | 1.0 |
M 33-B-526 | B2.5 I | HD 198487 | B2.5Ia | 21.10 | 380 | 120 | 75 | 2.0 |
M 33-B-1137 | B3 Ia | HD 51309 | B3Ib | 20.85 | 750 | 250 | 100 | 2.0 |
We have used HD 39777 for phostospheric profiles, as in the case of M 33-110-A and M 33-B-38.
In spite of the low O and Si abundances derived by Monteverde et al. (2000)
for this star, its UV spectrum shows comparatively strong C IV
and Si IV P-Cygni profiles, indicating a strong and fast
wind (see Sect. 3).
The terminal velocity reaches 2050 km s-1. The turbulent
velocity is 150 km s-1, a modest 7.
This is the only star for which
we obtain a terminal velocity clearly above the galactic average
for its spectral type (taken from Kudritzki & Puls 2000),
thus challenging the low abundances or
the spectral classification (or both!).
The spectral type, however, should change from B1.5 to O9 in
order to have a terminal velocity close to the spectral
type average. This is completely ruled out from inspection of the optical
spectrum.
The fits displayed in Fig. 5 also show a behaviour
different from those of the other stars. N V is well fitted.
The fit of the
C IV profile is good in the bluest part of the wind
absorption profile but is bad in the rest of the profile.
Fortunately, the first one is the important part for determining
the terminal velocity. The unsatisfactory fit at low
wind velocities is cosmetically very dependent on the underlying
photospheric profile, and thus does not mean very much by itself,
but it would be consistent with the presence of additional
C IV absorption at low wind velocities.
We keep the low
value
as there is no need to increase
to improve the consistency
between C IV and Si IV.
However, the anomaly in Si IV indicated in the
preceding section, i.e., a stronger red component, can also
not be fitted and indicates an extra absorption at low
wind velocities. This uncertainty does not affect the determination
of the terminal and turbulent wind velocities, that have an
accuracy of
100 km s-1.
This does not solve the problem
referred to above. The star has a large
for its
spectral classification and a Si IV red component stronger
than the blue one. The first might be attributed to a case of
bi-stability (Pauldrach & Puls 1990), similar to that of P-Cygni in our Galaxy,
where the ratio of terminal velocity to escape velocity is larger.
This however does not explain the red Si IV component.
One possible solution to this puzzle is that we are looking at
a composite spectrum, B-133 being the star contributing to the
red component of Si IV (see Sect. 3).
If this is the case, we estimate its terminal wind velocity to be of the
order of 450 km s-1, but would expect to see extra absorption
in Si IV at low wind velocities.
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Figure 6:
The ![]() ![]() ![]() |
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It has been classified as B2.5I (Monteverde et al. 1996), from its optical spectrum. We used a B2.5V galactic star for the photospheric profiles (HD 44402, Z CMa).
The derived terminal velocity is the
lowest in our sample and the UV spectrum shows only weak signs of mass loss.
However, the turbulence velocity is relatively high, with a
ratio
in excess of 0.3. This large value
is the result of a compromise between the fit of C IV
and that of Si IV. The first would allow a lower
turbulence, but then we cannot fit the second one.
Again, the value of
has to be large to favour
consistency between both doublets and a better fit to
C IV. However,
the terminal velocity is not seriously affected. The uncertainty
of both velocities is different now, being that of
100 km s-1 and that of
50 km s-1.
For the sum of both we have adopted
75 km s-1.
The Si IV doublet is mainly photospheric or in any case the wind has a small contribution. The fit to N V is poor.
The C IV is the main profile for deriving the parameters
of the velocity field. The low SNR of the spectra and the additional
absorptions described in the preceding section make the fit difficult.
We find the best fit at 750 km s-1, 250 km s-1 and 2.0
for ,
and
.
Again,
is larger than
the Galactic average from Kudritzki & Puls (2000), but now much more
moderately than for B-133.
The uncertainties are slightly larger
than those of the other fits, as already expected from the described
difficulties. We adopt
100 km s-1 for
,
and its sum.
In Fig. 6 we have plotted the derived against the stellar spectral types, together with parabolic
fits to the average values quoted by Kudritzki & Puls (2000) for
Galactic OB supergiants. The fits have been obtained by
joining OI and BIa supergiants on the one
hand and OII and BIb supergiants on the other.
We have also plotted lines that
indicate a 30
variation from the plotted average relations,
a usual scatter range (see Fig. 4 in Kudritzki & Puls 2000).
All M 33 B-supergiants
give us values that can be considered normal, except B-133.
We see no difference between the stars with
different suspected metallicities. This is in agreement with Puls et al. (2000)
(see also Vink et al. 2000) who have argued that the
terminal velocity (which depends on the slope of the line-strength distribution
function, )
is primarily controlled by the ratio of light ions vs. iron
group elements, because of the different line statistics. As long as this ratio
is roughly similar, the theoretical expected change of terminal velocity
(due to the "indirect"
effect, see Puls et al. 2000, Sect. 5.2) is much smaller than if this ratio would be changed. In particular if a
dense wind is present (as is the case for our supergiants) and this ratio
remains unchanged (which we have to assume for the moment), the effect is
expected to be very
small (see Puls et al. 2000, Fig. 27), since the effective
then remains roughly
constant. Only for thin winds and/or a significantly lower (general)
metallicity the effect should become observable.
We could not find a satisfactory explanation for B-133. While its terminal velocity is well above the average for its spectral type, it could still be accepted (even with the low metallicity derived by Monteverde et al. 2000) assuming for example a bi-stability phenomenon, were it not for the anomalous red component of the Si IV doublet. Assuming on the other hand that B-133 is actually producing the red Si IV component, its velocity would be much closer to the average of its spectral type. However, we could not reproduce the observed profiles without ad hoc hypothesis, nor find conclusive evidence of a binary nature.
Although three of our stars have been analyzed by Monteverde et al. (2000) we will postpone a discussion of the terminal velocities in terms of the stellar parameters, as new analyses of their optical spectra, now including mass-loss effects, are currently under way in our group together with a set of newly observed stars.
The wind turbulent velocities derived here are larger than the typical
10
(Kudritzki & Puls 2000) or the 14
found by Herrero et al. (2001),
reaching nearly 35
in the most extreme case.
Including B-133 we obtain 0.25 for the mean
ratio. This result is of the same order of that found by
Bresolin et al. (2002) in their analysis of M 31 B supergiants.
We tentatively attribute it for the moment
to the extreme character of
our objects, selected among the brightest supergiants in M 33,
and as a consequence are among the most luminous objects.
Finally, we have detected evidence of numerous NACs, confirming the wide presence of wind inhomogenities.
Acknowledgements
We would like to thank F. Najarro for very useful discussions during the stellar analyses. A.H. wants to acknowledge support for this work by the spanish DGI under proyect AYA2001-0436, the DGES under project PB97-1438-C02-01 and from the Gobierno Autonómico de Canarias under project PI1999/008. F.B. and J.P. acknowledge support from the German DLR, under grant RD-RX 50OR9909/2.