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Up: A catalog of rotational stars


Subsections

2 The observational program


2.1 The stellar sample


For this observing program we have selected all stars covering the spectral range from middle F to middle K of luminosity classes IV, III and II listed in "The Bright Star Catalog'' (Hoffleit & Jaschek [1982]; Hoffleit et al. [1983]) and in the list of supergiants compiled by Egret ([1980]), located north of declination zero degrees for the subgiant and giant stars, and north of declination -25 degrees for the bright giant stars. For the luminosity classes IV and III our sample is complete to apparent visual magnitude mv = 6.3 (e.g. Bahcall et al. [1981]), whereas for luminosity class II the sample is complete to apparent visual magnitude mv of about 8.0 (De Medeiros et al. [1999]). To have a better statistics in the spectral region of the Hertzsprung gap and for comparative purposes, we have added several dozen more of F5 to G5 stars of luminosity class III south of zero degrees from "The Bright Star Catalogue''. A systematic radial velocity survey of cool supergiant stars has been carried out in the northern and southern hemispheres for about 10 years (Burki & Mayor [1983]). This survey mostly devoted to a systematic study of binarity and variability will be used here to extend our research towards the Ib and Ib-II luminosity classes. For the latter luminosity classes the sample is complete to apparent visual magnitude mv of about 8.0 (De Medeiros et al. [1999]). With these criteria in hand we prepared a list of approximately 1960 stars. The total number for each luminosity class is:

1.
200 subgiant stars (classes IV and IV-V), in the spectral range F5 to K2.
2.
1100 giant stars (classes III and III-IV), in the spectral range F5 to K5.
3.
425 bright giant stars (classes II and II-III), in the spectral range F3 to K7.
4.
233 supergiant stars (classes Ib and Ib-II), in the spectral range F0 to K5.

In addition, a few dozen of G and K active evolved stars nearly brighter than mv = 8.0 and north of $-25^\circ$ from Fekel et al. ([1986]) and Fekel (1997), as well as 4 G5III stars from Alschuler ([1975]) have been added to the observing list for comparison purposes. Thus, some 2000 evolved stars were taken for observation, which were selected regardless of binarity characteristics, radial velocity variations or some peculiarity pointed out in the literature.

The large amount of data presently available allowed a detailed comparative analysis of the spectral classification. To check the different luminosity classes, the classifications of different authors for the classes IV, III, II and Ib were compared from data provided by the CDS "Centre de Données Stellaires'' of Strasbourg Observatory. Essentially we have adopted the classification given by the "Bright Star Catalogue'' for those stars with mv < 6.5, and by Jaschek (1978) for stars with mv > 6.5.


2.2 The observational method


The results presented in this catalog are based on the observations obtained with the CORAVEL spectrometer (Baranne et al. [1979]), where the spectrum of a given star is cross-correlated with an adequate mask located in the focal plane of the instrument. Three free parameters can be derived from the resulting cross-correlation function: position of the minimum, half-width at half-minimum and the cross-correlation area. These parameters are clearly related to the physical quantities: radial velocity, atmospheric velocity fields and, in some cases, stellar metallicity. The large majority of the observations presented here were carried out from March 1986 to May 1994, except for those stars having a larger time base. All stars north of declination $-25^\circ$, which represent approximately 80% of our program stars, were observed with the CORAVEL mounted on the Swiss 1-meter telescope at the Haute-Provence Observatory, Saint-Michel (France). The stars south of declination $-25^\circ$ have been measured with the southern CORAVEL at the Cassegrain focus of the 1.5 m Danish telescope at ESO La Silla (Chile).


   
Table 2: Comparison between CORAVEL and Gray's $v \sin i\ $ measurements for stars of luminosity classes II and Ib
HD $v \sin i\ $ $v \sin i\ $ remark
  (Gray) (COR)  
17506 6.8 5.8  
20902 17.9 16.8  
26630 7.4 8.8  
31398 3.5 3.8  
48329 7.1 8.8  
84441 4.2 5.7  
92125 4.7 7.7  
156283 3.7 1.3  
157999 3.2 4.2 SB
159181 7.3 10.7 SB
163770 3.4 6.3  
173009 6.5 5.1 SB
173764 5.2 7.8 SB
177249 5.2 5.0  
180809 3.6 3.5  
183912 3.0 1.4  
185758 5.2 7.1 SB
186791 3.2 3.8  
192876 6.2 7.3  
195295 6.4 9.5 SB
196725 0.0 2.9  
200905 1.6 3.5  
201223 5.6 7.9  
201251 3.1 6.3 SB
204075 6.2 7.6 SB
205349 6.7 6.4  
206731 6.2 5.2  
206778 6.5 6.0  
206859 5.7 6.1  
209750 6.7 7.8  
210745 7.8 8.0  
216206 5.8 5.4  
218356 3.9 4.4 SB
221861 7.8 7.9  
222047 7.1 6.4  
223173 4.1 4.2  
224165 3.9 2.6  


   
Table 3: Comparison between CORAVEL and Fekel's $v \sin i\ $ measurements for stars of luminosity classes IV, III and II
HD $v \sin i\ $ $v \sin i\ $ remark
  (Fekel) (COR)  
1833 18.2 16.3 SB
9746 9.0 8.7  
10909 3.0 2.7 SB
12929 1.8 1.0 SB
17144 21.3 18.9  
23249 0.6 1.0  
25893 5.2 5.1  
26162 2.2 1.0  
28591 28.8 27.2 SB
31993 33.4 31.1  
32357 13.1 11.5 SB
33021 0.7 2.0  
37160 0.4 1.0  
37824 14.9 13.1 SB
39743 9.5 9.8 SB
61421 4.9 6.1 SB
62345 2.8 1.6  
66141 2.5 1.1  
69267 4.0 2.1  
71369 3.4 4.3 SB
80953 4.0 1.2 SB
81410 27.1 26.1 SB
82210 5.9 5.5  
82328 6.4 8.3 SB?
94481 2.4 2.8  
95689 3.2 1.6 SB
104979 2.5 1.4 SB
106225 31.3 28.8 SB
107328 4.0 1.3  
113226 3.2 2.3  
113996 3.2 1.8  
120136 14.8 15.4 SB?
121107 15.8 14.5  
124570 4.1 5.6  
124897 3.3 1.0  
126868 15.7 14.4 SB?
136202 4.3 4.8  
142091 0.6 1.0 SB
142980 2.2 1.0 SB
144284 27.7 28.0 SB
145148 0.6 1.0  
148856 3.0 4.8 SB
150680 3.9 4.8 SB
160538 6.7 7.2 SB
161096 2.5 1.0  
161239 6.0 5.9  
161797 1.2 1.7 SB?
173009 6.4 5.1 SB
173920 8.4 8.0  
175225 2.2 1.0 SB?
176095 11.6 13.2  
180809 3.9 3.5  
181809 4.2 5.1 SB
182572 2.6 1.7  
185510 19.6 16.0 SB
185758 6.0 7.1 SB


 
Table 3: continued
HD $v \sin i\ $ $v \sin i\ $ remark
  (Fekel) (COR)  
188512 1.4 1.2  
188947 1.8 1.0  
196524 41.2 49.8 SB
196755 2.7 3.3  
197964 2.9 1.0  
197989 2.0 1.4 SB
198149 0.6 1.4  
203251 46.5 44.8 SB
208110 5.2 3.3 SB
212943 1.0 1.0  
213389 35.7 34.4 SB
215648 7.8 7.9  
216489 28.2 25.6 SB
217188 4.2 3.0 SB
218153 28.9 27.1 SB

As a rule, we tried to obtain two observations for each program star, separated by approximately one-year intervals, searching for spectroscopic variability. Several new spectroscopic binaries were discovered and, for some stars, the radial velocity variations have been followed up with a suitable cadence to derive the orbital elements. These data will be published in a separate paper which will deal with the spectroscopic binary stars in this program. The radial velocities are derived from a one-Gaussian-curve fitted to the correlation dip obtained with CORAVEL. However, for stars with very wide dips, mostly F stars exhibiting high rotation rates, a parabola is fitted. For double-lined spectroscopic binaries, radial velocities are derived through a fit with two Gaussians. The integration time for a CORAVEL observation in the present survey was typically 5 minutes for the bright stars later than the spectral type G0 and 15 minutes for the earlier ones. For some faint stars, namely mv > 10, as well as blended double-lined spectroscopic binaries, moderate or high rotators, the integration time was typically 15 to 20 minutes.


2.3 The $v \sin i\ $measurements


Although the CORAVEL spectrometer has been initially developed for measuring high-precision radial velocities of late-type stars, Benz & Mayor ([1981], [1984]) have shown that accurate $v \sin i\ $measurements for dwarf stars could be deduced from the correlation function of this instrument.


   
Table 4: Comparison between CORAVEL and Alschuler's (1975) $v \sin i\ $measurements for giant stars
HD ST $v \sin i\ $ $v \sin i\ $
    (COR) (Alschuler)
5137 G5III 2.0 22
97561 G5III 3.8 21
127742 G5III 5.9 26
210264 G5III 5.0 27

The general procedure and calibration outlined by Benz & Mayor ([1984]) was applied here to determine the projected rotational velocities for the present stellar sample. A comparison with the $v \sin i\ $values determined by Fourier transform analysis of the lines, allows an estimation of the effects of macroturbulence acting on stars of different luminosity classes. This procedure enables us to determine, if necessary, a correction for each luminosity class to apply to the rotational velocities derived from the standard calibration established by Benz & Mayor ([1984]). Let us recall that the Fourier transform technique is the only direct method to deduce both rotation and macroturbulence (e.g. Gray 1989).

In order to accomplish this study we compare firstly our $v \sin i\ $measurements with those determined by Gray & Nagar ([1985]) and Gray ([1989]) for the subgiant and giant stars. Table 1 gives the stars with their rotational velocity values measured respectively by CORAVEL and Gray for these luminosity classes. A least-squares fit to the data yields the following relations:

Classes IV and III:
$v \sin i\ $(COR) = -1.15 + 1.18 $v \sin i\ $(Gray)
$ \sigma (\Delta $$v \sin i\ $) = 1.3 km s-1

where $ \sigma (\Delta $$v \sin i\ $) is the rms of the rotational velocity differences. This comparison shows the excellent agreement between CORAVEL $v \sin i\ $values and those of Gray. Furthermore, this comparison between CORAVEL $v \sin i\ $and those derived by the Fourier transform of a line profile by D. Gray clearly demonstrates that the original $v \sin i\ $calibration by Benz & Mayor ([1984]) is valid from luminosity classes V to III. Taking into account the median error on Gray's measurements ( $\epsilon_{v \sin i}$(Gray) = 0.55 km s-1 for the classes V, IV and III) we have a good estimation for the CORAVEL external precision of $\epsilon_{v \sin i} = 0.8~{\mathrm{km~s}}^{-1}$, such an external precision being valid for bright stars of luminosity classes V to III. Up to magnitude 10 or 11 and typical integration time, photon noise adds very little to this typical uncertainty. For luminosity classes II and Ib/Ib-II the increase of the macroturbulence imposes to adapt a new calibration for the width of the correlation dip if we are to obtain reliable $v \sin i\ $values. In the original calibration, the parameter $\sigma_{\mathrm{o}}$ is the characteristic width of the cross-correlation dip of a solar-type star without rotational broadening. Using the light of the sun reflected by minor planets Benz & Mayor ([1981]) have derived $\sigma_{\mathrm{o}} =
6.88 \pm 0.03$ km s-1 for the luminosity class V. From the $v \sin i\ $values measured by Gray & Toner ([1986], [1987]) for bright giants and Ib supergiants we can derive $\sigma_{\mathrm{o}}$ as a function of the luminosity classes. The value of $\sigma_{\mathrm{o}}$ is 7.16 and 7.98 km s-1 respectively for the bright giants (luminosity class II) and the supergiants of luminosity class Ib/Ib-II (de Medeiros [1990]).

The $v \sin i\ $values listed in Table 2 have been derived from the cross-correlation dips using the Benz & Mayor ([1984]) calibration, where the $\sigma_{\mathrm{o}}$ parameter is a function of the luminosity class. A least-squares fit of the data gives:

Classes II and Ib:
$v \sin i\ $(COR) = 1.45 + 0.86 $v \sin i\ $(Gray)
$ \sigma (\Delta $$v \sin i\ $) = 1.4 km s-1.

These results show an excellent agreement between CORAVEL $v \sin i\ $measurements and those from Gray, also for the luminosity classes II and Ib/Ib-II.

If changes in the non-rotational part of the line broadening are not detected for the luminosity class V to III ( $\sigma_{\mathrm{o}}$ = 6.88 km s-1), the variation is important for classes II to Ib/Ib-II with a $\Delta\sigma_{\mathrm{o}}$ = 0.83 km s-1. The adopted constant value of $\sigma_{\mathrm{o}}$ by luminosity class will probably add some noise to our $v \sin i\ $measurements as a result of the discreetness of luminosity classes. However, the external comparison of Fourier transform $v \sin i\ $and cross-correlation $v \sin i\ $shows that the mean square difference is always about 1.3 to 1.4 km s-1, independently of the luminosity class. From this comparison we can conclude that for cool bright stars the cross-correlation and Fourier transform techniques give $v \sin i\ $measurements with an equivalent precision of about 1 km s-1 and present the same lower limit for a significant detection. The Fourier transform technique has the advantage to allow the distinction between the rotation and macroturbulence effects on line profiles, but unfortunately this method requires very high signal-to-noise ratio and is therefore applicable only to bright stars. The cross-correlation technique does not allow separation between rotation and macroturbulence but has the advantage to be applicable to faint stars. The signal-to-noise ratio is sufficiently high to analyse accurately the line profile of stars down to about magnitude 14. Experience has shown that on a 1.5-meter telescope, using the CORAVEL spectrometer, such a method gives $v \sin i\ $values for stars of magnitude 11, within a few minutes, and for stars of magnitude 14, within an hour, with a precision of 1 km s-1.

We have carried out a similar comparison between CORAVEL $v \sin i\ $values and those obtained by Fekel et al. ([1986]) for chromospherically active stars and Fekel ([1997]) for normal stars. Table 3 gives the list of the stars with their $v \sin i\ $values measured respectively with CORAVEL and then by Fekel and collaborators for the luminosity classes IV, III and II. The relationship between $v \sin i\ $(COR) and $v \sin i\ $(Fekel) is given by:

$v \sin i\ $(COR) = -0.37 + 0.99 $v \sin i\ $(Fekel)

with a rms of the velocity difference of about 1.4 km s-1.

The correlation between the $v \sin i\ $values determined respectively by CORAVEL and Fekel is clearly as good as that between CORAVEL and Gray. However, one should be careful here because Fekel has calibrated his rotational velocity measurements by using $v \sin i\ $data from D. Gray and co-workers.

As we have already recalled, prior to the determination of rotational velocities by cross-correlation and Fourier transform techniques a few studies employed somewhat low or moderate spectral resolution to the $v \sin i\ $measurements. In general, the lowest limit of such measurements was set by the spectral resolution. We have observed a few stars in common with some of those studies, which allow a comparison showing clearly that there is no sense to combine $v \sin i\ $values obtained by cross-correlation or Fourier transform techniques with those measured by poor or moderate resolution techniques. This is true at least for $v \sin i\ $values smaller than about 25 km s-1, as we can see from Table 4 which shows a comparison between CORAVEL and Alschuler ([1975]) $v \sin i\ $values.


2.4 Errors

The radial-velocity uncertainty is derived from an instrumental error quadratically added to the photon noise and the scintillation noise, estimated from observational parameters (Baranne et al. [1979]). At least for the low rotators, which represent the great majority of our sample, the radial-velocity measurements present a precision better than 0.30 km s-1 (see Duquennoy et al. [1991]). With an increase of $v \sin i\ $the uncertainty on the radial velocity increases as a consequence of the decrease of the cross-correlation dip contrast and the increase of its width.

   
Table 6: Double-lined spectroscopic binary systems SB2 with evolved component
HD (B - V) ST
2436 1.58 K5III
5137 0.86 G5III
5516 0.94 G8IIIb
8357 0.87 G8IV
8949 1.12 K1III
13480 0.78 G5III+F5V
17904 0.41 FIV
18894 0.60 G0IV-V
18925 0.70 G8III+A2V
23838 0.76 G2III+F2:V
24546 0.41 F5IV
29104 0.74 G5II-III+A
31738 0.71 G5IV
32453 0.88 G5III
34029 0.90 G1III/K0III
37847 1.07 K2III
38751 1.01 G8IIIv
40084 1.23 G5III
41116 0.82 G7III
43358 0.46 F5IV:
46178 1.07 K0III
47415 0.53 F8IV
47703 0.49 F8III
56200 0.40 F4II
57364 1.08 K0II
58972 1.43 K3III
59148 1.11 K2III
59878 1.01 K0II-III+F
60318 1.01 K0III
63799 1.12 K1III
64235 0.41 F5IV
68461 0.89 G8III
73596 0.40 F5III
78418 0.66 G5IV-V
81873 1.04 K0III
82543 0.62 F7IV-V
92787 0.33 F5III
102509 0.55 G5III-IV+A7V
106677 1.14 K0III
109511 1.15 K2III
115781 1.14 K0III
122703 0.45 F5III
123999 0.54 F9IV
139862 0.94 G8II
151237 0.49 F8II
152830 0.34 F5II
155638 1.07 K0III
158614 0.72 G9IV-V
169268 0.34 F6III-IV
169689 0.92 G8III-IV+A
169985 0.50 G0III+A6V
171802 0.37 F5III
172088 0.55 F9IV
174881 1.18 K1II-III
178619 0.52 F5IV-V
179094 1.09 K1IV
182549 0.90 G6II


 
Table 6: continued
HD (B - V) ST
184398 1.16 K2II-IIIe
185151 1.25 K0III
185734 0.97 G8III-IV
192577 1.18 K2II+B3V
196753 0.98 K0II-III+A
198084 0.54 F8IV-V
201051 1.05 K0II-III
202447 0.53 G0III+A5V
206901 0.43 F5IV
210334 0.72 G2IV+K0III
212280 0.70 G0IV-V
218527 0.91 G8III-IV
283533 0.71 G0II


 
Table 7: Evolved stars with no CORAVEL dip
HD/BD ST
+01 1876 F5II
+20 4010 F8II
+33 3998 F4II
+37 4115 F4II
1671 F5III
4758 F5III
11443 F6IV
17918 F5III
23010 F5II
34658 F5II
36994 F5III
48737 F5III
55052 F5III-IV
72779 G0III
77601 F6II-III
84607 F4IV
104425 F6II
108722 F5III
110834 F6IV
144070 F5IV
159026 F6III
169985 G0III+A6V
192871 F3II
194708 F6III
203842 F5III
208177 F5IV
210459 F5III
215807 F5II
220657 F8III
254429 F8II
345740 F4II

Concerning the rotational velocities the external comparison with Fourier transform indicates an uncertainty of about 1.0 km s-1 for the CORAVEL $v \sin i\ $of bright stars. For fainter stars we evidently should take into account the contribution of the photon noise. Nevertheless, as most of our integrations are relatively long, about 10 minutes or more for faint stars, the scintillation noise is not dominant. Despite this point, we take into account these contributions by adopting

$\epsilon_{v \sin i} = \max \,\,
(\epsilon_{v \sin i},\, \epsilon_{\min ,\,v \sin i\,})$ (luminosity class)

where $\epsilon_{{\min ,\, v \sin i}}$ is determined from the rms of the different determinations and where $\epsilon_{{\min ,\, v \sin i}}$ is a lower limit depending on the luminosity class. For classes IV and III, the $\epsilon_{{\min ,\, v \sin i}}$ has been conservatively fixed to 1.0 km s-1. Independently of the excellent agreement of our $v \sin i\ $values with the Fourier transform $v \sin i\ $for bright giant and supergiant stars, with $ \sigma (\Delta $$v \sin i\ $) between 1.3 and 1.4 km s-1, we prefer to adopt a more pessimistic uncertainty for the luminosity classes II and Ib/Ib-II, with $\epsilon_{v \sin i}$ = 2.0 km s-1 for both luminosity classes, because it is not possible to define precisely what are the limits on rotation and macroturbulence. In this context, such limiting values should be considered only to set extreme boundaries on the errors, without any physical meaning. In fact, these uncertainties are adopted for the $v \sin i\ $values lower than 30 km s-1 independently of the luminosity class. For rotations above 30 km s-1 the measurement of the dip becomes difficult (see Benz & Mayor [1981]) and differences between the fitted Gaussian and such dip are observed. Consequently, the error for $v \sin i\ $measurements will be more important than those estimated in the discussion above. For these high rotators our best estimations indicate an uncertainty of about 10%, these errors representing the precision with which the Gaussian matches the observations.


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