A&A 393, 897-911 (2002)
DOI: 10.1051/0004-6361:20020943
F. Royer1,2 - S. Grenier2 - M.-O. Baylac2 - A. E. Gómez2 - J. Zorec3
1 - Observatoire de Genève, 51 chemin des Maillettes, 1290 Sauverny, Switzerland
2 - GEPI/CNRS FRE 2459, Observatoire de Paris, 5 place Janssen, 92195 Meudon Cedex, France
3 - CNRS, Institut d'Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
Received 25 February 2002 / Accepted 19 June 2002
Abstract
This work is the second part of the set of measurements of
for A-type stars, begun by Royer et al. (2002). Spectra of 249 B8 to F2-type stars
brighter than V=7 have been collected at Observatoire de
Haute-Provence (OHP). Fourier transforms of several line profiles in the range 4200-4600 Å are used to derive
from the frequency of the first zero. Statistical analysis of the sample indicates that measurement error mainly depends on
and this relative error of the rotational velocity is found to be about 5% on average.
The systematic shift with respect to standard values from Slettebak et al. (1975), previously
found in the first paper, is here confirmed. Comparisons with data
from the literature agree with our findings:
values from
Slettebak et al. are underestimated and the relation between both
scales follows a linear law
.
Finally, these data are combined with those from the previous paper
(Royer et al. 2002), together with the catalogue of Abt & Morrell (1995). The
resulting sample includes some 2150 stars with homogenized rotational velocities.
Key words: techniques: spectroscopic - stars: early-type - stars: rotation
This paper is a continuation of the rotational velocity study of A-type stars, initiated in Royer et al. (2002, hereafter Paper I). The main goals and motivations are described in the previous paper. The sample of A-type stars described and analyzed in this work is the counterpart of the one in Paper I, in the northern hemisphere.
In short, it is intended to produce a homogeneous sample of measurements of
projected rotational velocities (
)
for the spectral interval of A-type stars, and this without using any
preset calibration.
This article is structured in a way identical to the precedent, except for
an additional section (Sect. 5) where data from this paper, the previous one and the catalogue of
Abt & Morrell (1995) are gathered, and the total sample is discussed in statistical terms.
Spectra were obtained in the northern hemisphere with the AURÉLIE spectrograph (Gillet et al. 1994) associated with the 1.52 m telescope at Observatoire de Haute-Provence (OHP), in order to acquire complementary data to HIPPARCOS observations (Grenier & Burnage 1995).
The initial programme gathers early-type stars for which
measurement is needed. More than 820 spectra have been collected for
249 early-type stars from January 1991 to May 1994. As shown in
Fig. 1, B9 to A2-type stars represent the major part of the
sample (70%). Most of the stars are on the main sequence and only
about one fourth are classified as more evolved than the luminosity
class III-IV.
These northern stars are brighter than the magnitude V=7. Nevertheless, three
stars are fainter than this limit and do not belong to the
HIPPARCOS Catalogue (ESA 1997). Derivation of their magnitude from TYCHO observations
turned out to be: HD 23643 V=7.79, HD 73576 V=7.65 and HD 73763 V=7.80. These
additional stars are special targets known to be Scuti stars.
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Figure 1: Distribution of the spectral type for the 249 programme stars. |
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AURÉLIE spectra were obtained in three different spectral ranges (Fig. 2):
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Figure 2:
Observed spectra of Vega are displayed for the different spectral ranges: top panel, range ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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The method adopted for
determination is the computation of
the first zero of Fourier transform (FT) of line profiles
(Carroll 1933; Ramella et al. 1989). For further description of the method applied
to our sample, see Paper I.
The different observed spectral range induces some changes,
which are detailed below.
The normalization of the spectra was performed using MIDAS: the continuum has been determined
visually, passing through noise fluctuations. The procedure is much
like the normalization carried out in Paper I, except for a different spectral window.
For the ranges
and
,
the influence of the
Balmer lines is important, and their wings act as non negligible
contributions to the difference between true and pseudo-continuum, over
the major part of the spectral domain, as shown in Paper I.
On the other hand, the
range is farther from H
.
In order to quantify the alteration of continuum due to Balmer lines
wings and blends of spectral lines, a grid of synthetic spectra of
different effective temperatures (10 000, 9200, 8500 and 7500 K) and
different rotational broadenings, computed from Kurucz' model
atmosphere (Kurucz 1993), is used to calculate the differences between
the true continuum and the pseudo-continuum. The pseudo-continuum is
represented as the highest points in the spectra. The differences
are listed in Table 1, for different spectral 20 Å
wide sub-ranges. This table is a continuation of the similar one in
Paper I, considering the spectral range 4200-4500 Å.
![]() ![]() |
central wavelength (Å) | |||||
(K,
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4510 | 4530 | 4550 | 4570 | 4590 | |
Data for wavelengths shorter than 4500 Å | ||||||
are given in Table 1 of Paper I | ||||||
10 000, | 10 | 0.0005 | 0.0003 | 0.0002 | 0.0000 | 0.0000 |
10 000, | 50 | 0.0008 | 0.0003 | 0.0003 | 0.0002 | 0.0003 |
10 000, | 100 | 0.0011 | 0.0005 | 0.0016 | 0.0005 | 0.0013 |
9200, |
10 | 0.0010 | 0.0006 | 0.0006 | 0.0006 | 0.0006 |
9200, | 50 | 0.0017 | 0.0008 | 0.0010 | 0.0012 | 0.0012 |
9200, | 100 | 0.0023 | 0.0012 | 0.0027 | 0.0012 | 0.0051 |
8500, |
10 | 0.0017 | 0.0012 | 0.0010 | 0.0010 | 0.0010 |
8500, | 50 | 0.0030 | 0.0020 | 0.0022 | 0.0025 | 0.0020 |
8500, | 100 | 0.0042 | 0.0027 | 0.0062 | 0.0030 | 0.0093 |
7500, |
10 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 |
7500, | 50 | 0.0032 | 0.0023 | 0.0036 | 0.0045 | 0.0032 |
7500, | 100 | 0.0059 | 0.0050 | 0.0149 | 0.0059 | 0.0181 |
Put end to end, the spectra acquired with AURÉLIE cover a spectral
range of almost 500 Å. It includes that observed with ECHELEC in
Paper I. The choice of the lines for the determination of the
in Paper I is thus still valid here. Moreover, in addition to this
selection, redder lines were adopted in order to benefit from the
larger spectral coverage.
The complete list of the 23 lines that are candidate for
determination is given in Table 2.
range | wavelength | element | range |
4215.519 | Sr II | ||
4219.360 | Fe I | ||
4226.728 | Ca I | ||
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4227.426 | Fe I | |
4235.936 | Fe I | ||
4242.364 | Cr II | ||
4261.913 | Cr II | ![]() |
|
4404.750 | Fe I | ||
4415.122 | Fe I | ||
4466.551 | Fe I | ||
4468.507 | Ti II | ||
4481 .126 .325 | Mg II ![]() |
||
4488.331 | Ti II | ||
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4489.183 | Fe II | |
4491.405 | Fe II | ||
4501.273 | Ti II | ||
4508.288 | Fe II | ||
4515.339 | Fe II | ||
4520.224 | Fe II | ||
4522.634 | Fe II | ||
4563.761 | Ti II | ||
4571.968 | Ti II | ||
4576.340 | Fe II |
Wavelength of both components are indicated for the magnesium doublet line.
In order to quantify effects of blends in the selected lines for later
spectral types, we use the skewness of synthetic line profiles, as in
Paper I. The same grid of synthetic spectra computed using Kurucz'
model (Kurucz 1993), is used. Skewness is defined as
,
where mk is moment of kth order equal to
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||||
line | (
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10 000 | 9200 | 8500 | 7500 |
Data for wavelengths shorter than 4500 Å | |||||
are given in Table 3 of Paper I | |||||
Ti II 4501 | 10 | -0.05 | -0.06 | -0.07 | -0.12 |
50 | -0.02 | -0.03 | -0.04 | -0.04 | |
100 | -0.03 | -0.04 | -0.05 | -0.07 | |
Fe II 4508 | 10 | 0.01 | 0.01 | 0.01 | 0.02 |
50 | -0.00 | -0.00 | -0.00 | -0.00 | |
100 | -0.01 | -0.02 | -0.03 | -0.05 | |
Fe II 4515 | 10 | 0.00 | -0.00 | -0.01 | -0.06 |
50 | 0.02 | 0.02 | 0.01 | -0.04 | |
100 | 0.01 | 0.01 | 0.02 | 0.03 | |
Fe II 4520 | 10 | 0.01 | 0.01 | 0.01 | -0.01 |
50 | 0.00 | 0.00 | -0.00 | -0.01 | |
100 | -0.17 | -0.19 | -0.23 | -0.30 | |
Fe II 4523 | 10 | -0.06 | -0.06 | -0.06 | -0.05 |
50 | -0.01 | -0.01 | -0.01 | 0.01 | |
100 | -0.12 | -0.09 | -0.01 | 0.08 | |
Ti II 4564 | 10 | 0.04 | 0.04 | 0.05 | 0.06 |
50 | 0.01 | 0.02 | 0.04 | 0.06 | |
100 | 0.03 | 0.04 | 0.08 | 0.16 | |
Ti II 4572 | 10 | -0.00 | -0.00 | -0.01 | -0.02 |
50 | 0.01 | 0.00 | -0.01 | -0.09 | |
100 | 0.01 | 0.01 | -0.00 | -0.04 | |
Fe II 4576 | 10 | 0.01 | 0.01 | 0.02 | 0.05 |
50 | 0.00 | 0.00 | 0.01 | 0.01 | |
100 | 0.01 | 0.02 | 0.04 | 0.07 |
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Figure 3:
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Figure 4: Simulation of the doublet width behavior: FWHM of the sum of two Gaussian lines (separated with 0.2 Å) as a function of the FWHM of the components. |
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The comparison between the rotational velocity derived from the weak
lines and the one derived from the magnesium doublet was already
approached in Paper I. It is here of an increased importance since the
Mg II line is not present in all spectra (i.e. and
spectral ranges). Figure 3 shows
this comparison between
and
using AURÉLIE data. The deviation from the
one-to-one relation (solid line) in the low velocity part of the diagram
is due to the intrinsic width of the doublet. This deviation is
simulated by representing the Mg II doublet as the sum of two
identical Gaussians separated by 0.2 Å. The full-width at half
maximum (FWHM) of the simulated doublet line is plotted in
Fig. 4 versus the FWHM of its single-lined components.
The relation clearly deviates from the one-to-one relation for single
line FWHM lower than 0.6 Å. Using the rule of thumb from Slettebak et al. (1975, hereafter SCBWP):
,
this value corresponds to
.
This limit coincides with what is observed in
Fig. 3. For higher velocities
(
),
becomes
larger than
.
A linear regression
gives:
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Figure 5:
The average number of measured lines (running average
over 30 points) is plotted as a function of the mean
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The number of measurable lines among the 23 listed in
Table 2 varies from one spectrum to another according
to the wavelength window, the rotational broadening and the
signal-to-noise ratio. The number of measured lines ranges from 1 to 17 lines. The
range offers a large number of candidate lines.
Figure 5 shows the variation of this number with
(solid line).
Rotational broadening starts to make the number of lines decrease
beyond about 70
.
Nevertheless additional lines in the spectral
domain redder than 4500 Å makes the number of lines larger than in the
domain collected with ECHELEC (Paper I; dotted line). Whereas with
ECHELEC the number of lines decreases with
from 30
to
reach only one line (i.e. the Mg II doublet) at 100
,
the number
of lines with AURÉLIE is much sizeable: seven at 70
,
still
four at 100
and more than two even beyond 150
.
In Fig. 6, the differences between the individual
values from each measured line in each spectrum and the
associated mean value for the spectrum are plotted as a function of
.
In the same way the error associated with the
has been estimated
in Paper I, a robust estimate of the standard deviation is computed
for each bin of 70 points. The resulting points (open grey circles in
Fig. 6) are adjusted with a linear least squares fit
(dot-dashed line). It gives:
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Figure 6:
Differences between individual
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The slope is lower with AURÉLIE data than with ECHELEC
spectra (Paper I):
% against
%. This trend can be explained by the average number of lines for the computation of
the mean
.
In the velocity range from 15 to 180
,
the number
of measured lines (Fig. 5) is on average 2.4 times larger with AURÉLIE than
with ECHELEC, which could lower the measured dispersion by a factor of
.
As shown in Fig. 1, the distribution of spectral types is mainly
concentrated towards late-B and early-A stars, so that a variation of
the precision as a function of the spectral type would not be very
significant.
On the other hand, as the observed spectral domain is not always the
same, this could introduce an effect due to the different sets of
selected lines, their quantity and their quality in terms of
determination. For each of the three spectral domains, the residuals,
normalized by
(Eq. (3)), are centered
around 0 with a dispersion of about 1 taking into account their error
bars, as shown in Table 4. This suggests that no effect due
to the measurement in one given spectral range is produced on the
derived
.
Spectral range |
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HD | HIP | Spect. type |
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# | Remark |
(
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||||||
905 | 1086 | F0IV | 35 | 1 | 6 | |
2421 | 2225 | A2Vs | 14 | 1 | 9 | |
2628 | 2355 | A7III | 21 | 2 | 9 | |
2924 | 2565 | A2IV | 31 | 2 | 16 | |
3038 | 2707 | B9III | 184 | - | 1 | |
4161 | 3572 | A2IV | 29 | 2 | 9 | |
4222 | 3544 | A2Vs | 38 | 2 | 17 | |
4321 | 3611 | A2III | 25: | 4 | 14 | SS |
5066 | 4129 | A2V | 121 | - | 1 | |
5550 | 4572 | A0III | 16 | 3 | 5 | |
6960 | 5566 | B9.5V | 33 | 4 | 7 | |
10293 | 7963 | B8III | 62 | - | 1 | |
10982 | 8387 | B9.5V | 33 | 3 | 3 | |
11529 | 9009 | B8III | 36 | 4 | 8 | |
11636 | 8903 | A5V... | 73 | 2 | 11 |
In total, projected rotational velocities were derived for 249 B8 to F2-type stars, 86 of which have no rotational velocities in Abt & Morrell (1995).
The results of the
determinations are presented in
Table 5 which contains the following data: Col. 1
gives the HD number, Col. 2 gives the HIP number, Col. 3
displays the spectral type as given in the HIPPARCOS catalogue
(ESA 1997), Cols. 4, 5, 6 give respectively the derived value of
,
the associated standard deviation and the corresponding number
of measured lines (uncertain
are indicated by a colon), Col. 7 presents possible remarks about the spectra: SB2 ("SB'') and
shell ("SH'') natures are indicated for stars showing such feature in
these observed spectra, as well as the reason why
is uncertain - "NO''
for no selected lines, ``SS'' for variation from spectrum to spectrum
and "LL'' for variation from line to line (see Appendix A).
Nine stars are seen as double-lined spectroscopic binary in the data
sample. Depending on the
of each component, their difference
in Doppler shift and their flux ratio, determination of
is
impossible in some cases.
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Figure 7:
Part of the spectra are displayed for the six SB2 stars that
have been observed only once: a) HD 35189, b) HD 40183,
c) HD 42035, d) HD 181470, e) HD 203439, f)
HD 203858. Three of them are well separated b), d), f), allowing
measurement of
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Figure 8:
The three following SB2 stars have been observed twice, in
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Table 6 displays the results for the stars in our sample which
exhibit an SB2 nature. Spectral lines are identified by
comparing the SB2 spectrum with a single star spectrum. Projected
rotational velocities are given for each component when measurable, as
well as the difference in radial velocity
computed from a few lines in the spectrum.
HD | HIP | Spect. type |
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Fig. | |
(
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(
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|||||
A | B | |||||
35189 | 25216 | A2IV | - | 37 | 7a | |
40183 | 28360 | A2V | 37 | 37 | 127 | 7b |
42035 | 29138 | B9V | see text | 12: | 7c | |
79763 | 45590 | A1V | 29 | - | 8a | |
34: | 21: | 67 | 8d | |||
98353 | 55266 | A2V | 44 | 8b | ||
34 | 64: | 8e | ||||
119537 | 67004 | A1V | 20: | - | 8c | |
17 | 18 | 98 | 8f | |||
181470 | 94932 | A0III | 15 | 20 | 229 | 7d |
203439 | 105432 | A1V | - | 56 | 7e | |
203858 | 105660 | A2V | 14 | 15 | 106 | 7f |
Fourteen stars are common to both the southern sample from Paper I and the northern one studied here. Matching of both determinations allows us to ensure the homogeneity of the data or indicate variations intrinsic to the stars otherwise. Results for these objects are listed in Table 7.
HD | Sp. type | CCF |
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27962 | A2IV | 0 | 16 | 2 | 11 | 1 |
30321 | A2V | 4 | 132 | 4 | 124 | - |
33111 | A3IIIvar | 6 | 196 | - | 193 | 4 |
37788 | F0IV | 0 | 29 | 1 | 33 | 4 |
40446 | A1Vs | - | 27 | 5 | 27 | 5 |
65900 | A1V | 0 | 35 | 3 | 36 | 2 |
71155 | A0V | 4 | 161 | 12 | 137 | 2 |
72660 | A1V | 0 | 14 | 1 | 9 | 1 |
83373 | A1V | 0 | 28 | - | 30 | 2 |
97633 | A2V | 0 | 24 | 3 | 23 | 1 |
98664 | B9.5Vs | - | 57 | 1 | 61 | 5 |
109860 | A1V | 5 | 74 | 1 | 76 | 6 |
193432 | B9IV | 0 | 24 | 2 | 25 | 2 |
198001 | A1V | 0 | 130 | - | 102 | - |
Instrumental characteristics differ from ECHELEC to AURÉLIE
data. First of all, the resolution is higher in the ECHELEC spectra,
which induces a narrower instrumental profile and allows the
determination of
down to a lower limit. Taking the calibration
relation from SCBWP as a rule of thumb (
), the
low limit of
is:
Second of all, one other difference lies in the observed spectral
domain. HD 198001 has no observation in the
domain using
AURÉLIE, so that
in Table 7 is not derived
on the basis of the Mg II line. The overestimation of
reflects the use of weak metallic lines instead the strong
Mg II line for determining rotational velocity.
Using the same ECHELEC data, Grenier et al. (1999) flagged the stars according to the shape of their cross-correlation function with synthetic templates. This gives a hint about binary status of the stars. Three stars in Table 7 are flagged as "probable binary or multiple systems'' (CCF: 4 and 6).
When discarding low rotators, probable binaries and data of HD 198001 that induce biases
in the comparison, the relation between the eight remaining points is fitted
using GaussFit by:
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Figure 9:
Comparison of
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Figure 10:
Comparison between
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A significant part of the sample is included in the catalogue of
Abt & Morrell (1995). The intersection includes 163 stars. The
comparison of the
(Fig. 9) shows that our determination is higher on average than
the velocities derived by Abt & Morrell (AM). The linear relation given by GaussFit is:
The relation is computed taking into account the error bars of both sources. The error bars on the values of SCBWP are assigned according to the accuracy given in their paper (10% for
and 15% for
). Our error bars are derived from the formal error found in Sect. 3.3 (Eq. (3)).
Name | HD | Sp. type |
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HIPPARCOS | ||||||
SCBWP | this work | depth 0pt height 0.4pt width 3.0cm literature depth 0pt height 0.4pt width 3.0cm | H52 | H59 | ||||||
spec. synth. | freq. analysis | FWHM | ||||||||
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47105 | A0IV | <10 | 15 |
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11.2(1) |
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- | X | |
30 Mon | 71155 | A0V | 125 | 161 |
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C | - | |||
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95418 | A1V | 35 | 47 |
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44.8(1), 39(4) | 44.3(3) | - | - | |
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97633 | A2V | 15 | 24 |
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21(5), 22.1(1) | 24(6), 27.2(3) | 23(7) | - | - |
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103287 | A0V SB | 155 | 178 |
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M | - | ||
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123299 | A0III SB | 15 | 25 |
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27(9) | M | O | ||
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128167 | F3Vwvar | 10 | 15 |
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7.5(11) | 7.8(12), 8.1(13) | - | - |
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139006 | A0V | 110 | 139 |
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U | O | ||
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147394 | B5IV | 30 | 46 |
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32(6) | P | - | ||
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172167 | A0Vvar | <10 | 25 |
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22.4(1), 23.2(14) |
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U | - | |
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29.9(3) | |||||||||
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176437 | B9III | 60 | 72 |
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M | - | |||
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198001 | A1V | 85 | 130 | - | 95(17), 108.1(1) | - | - |
(1) Hill (1995). | (6) Smith & Dworetsky (1993). | (11) Gray (1984). | (16) Gray (1980b). |
(2) Scholz et al. (1997). | (7) Fekel (1998). | (12) Fekel (1997). | (17) Dunkin et al. (1997). |
(3) Ramella et al. (1989). | (8) Gray (1980a). | (13) Benz & Mayor (1984). | |
(4) Holweger et al. (1999). | (9) Lehmann & Scholz (1993). | (14) Erspamer & North (2002). | |
(5) Lemke (1989). | (10) Soderblom (1982). | (15) Gulliver et al. (1994). |
The standard stars for which a significant discrepancy occurs between our values and those derived by SCBWP - i.e. their error box does not intersect with the one-to-one relation - have their names indicated in Fig. 10. They are listed with data from the literature in Table 8 and further detailed in Appendix B.
Homogeneity and size are two crucial characteristics of a sample, in a
statistical sense. In order to gather a
sample obeying these
two criteria,
derived in this paper and in Paper I can be
merged with those of Abt & Morrell (1995). The different steps consist of
first joining the new data, taking care of their overlap; then
considering the intersection with Abt & Morrell, carefully scaling
their data to the new ones; and finally gathering the complete homogenized sample.
Despite little differences in the observed data and the way
were derived for the two samples, they are consistent. The gathering
contains 760 stars. Rotational velocity of common stars listed in
Table 7 are computed as the mean of both values, weighted
by the inverse of their variance. This weighting is carried on when
both variances are available (i.e.
and
), except for low rotators and HD 198001, for
which
is taken as the retained value.
In order to adjust by the most proper way the scale from Abt & Morrell's data to the one
defined by this work and the Paper I, only non biased
should
be used. The common subsample has to be cleaned from spurious
determinations that are induced by the presence of spectroscopic binaries,
the limitation due to the resolution, uncertain velocities of high rotators with no
measurement of the Mg II doublet, etc.
The intersection gathers 308 stars, and Fig. 11 displays the comparison.
We have chosen to adjust the scaling from Abt & Morrell's data (AM) to
ours (I II) using an iterative linear regression with sigma clipping.
The least-squares linear fit is computed on the data, and the
relative difference
The 23 points rejected during the sigma-clipping iterations are
indicated in Fig. 11 by open symbols. They are listed
and detailed in Appendix C. Some of them are known as
spectroscopic binaries.
Moreover, using HIPPARCOS
data, nine of the rejected stars are indicated as "duplicity induced
variable'', micro-variable or double star.
Half a dozen stars are low
stars observed with AURÉLIE, and
the resolution limitation can be the source of the discrepancy
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Figure 11:
Comparison of
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The "cleaned'' intersection, gathering 285 stars, is represented in
Fig. 11 by filled circles. The solid line is the one-to-one relation and
the dashed line represents the relation given by the iterative linear fit:
Table 9 lists the 2151 stars in the total merged sample.
It contains the following data: Col. 1
gives the HD number, Col. 2 gives the HIP number, Col. 3
displays the spectral type as given in the HIPPARCOS catalogue
(ESA 1997), Col. 4 gives the derived value of
(uncertain
,
due to uncertain determination in either
one of the source lists, are indicated by a colon).
HD | HIP | Spect. type |
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(
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3 | 424 | A1Vn | 228 | 4 |
203 | 560 | F2IV | 170 | 4 |
256 | 602 | A2IV/V | 241 | 5 |
315 | 635 | B8IIIsp... | 81 | 4 |
319 | 636 | A1V | 59 | 5 |
431 | 760 | A7IV | 97 | 4 |
560 | 813 | B9V | 249 | 1 |
565 | 798 | A6V | 149 | 1 |
905 | 1086 | F0IV | 36 | 6 |
952 | 1123 | A1V | 75 | 4 |
1048 | 1193 | A1p | 28 | 4 |
1064 | 1191 | B9V | 128 | 1 |
1083 | 1215 | A1Vn | 233 | 4 |
1185 | 1302 | A2V | 128 | 4 |
1280 | 1366 | A2V | 102 | 4 |
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Figure 12:
Pie chart of the subsample membership of the stars in the
total
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The total sample is displayed in Fig. 13a, as a density
plot in equatorial coordinates. This distribution on the sky partly
reflects the distribution in the solar neighborhood, and the density
is slightly higher along the galactic plane (indicated by a dashed
line). Note that the cell in
equatorial coordinates with the highest density (around h,
)
in Fig. 13a corresponds to the
position of the Hyades open cluster. The lower density in the
southern hemisphere is discussed hereafter in terms of completeness
of the sample.
Except for a handful of stars, all belong to the HIPPARCOS catalogue. The
latter
is complete up to a limiting magnitude
which depends
on the galactic latitude b (ESA 1997):
![]() |
Figure 13:
a) Density of the
![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
The completeness of the northern part is 80% at V=6.5 mag. This reflects the completeness of the Bright Star Catalogue (Hoffleit & Jaschek 1982) from which stars from Abt & Morrell are issued. In the southern part, it can be seen that the distribution of magnitudes goes fainter, but the completeness is far lower and reaches 50% at V=6.5 mag. These numbers apply to the whole spectral range from B9 to F0-type stars, and they differ when considering smaller spectral bins. For the A1-type bin for instance, the completeness reaches almost 90% and 70% for the northern and southern hemispheres respectively, at V=6.5 mag.
The determination of projected rotational velocities is sullied with several
effects which affect the measurement. The blend of spectral lines tends to
produce an overestimated value of
,
whereas the lowering of the measured
continuum level due to high rotation tends to lower the derived
.
The solution lies in a good choice of candidate lines to measure the
rotational velocity. The use of the additional spectral range
4500-4600 Å, compared to the observed domain in Paper I, allows for the
choice of reliable lines that can be measured even in case of high
rotational broadening and reliable anchors of the continuum, for the
considered range of spectral types.
The
is derived from the first zero of Fourier transform of
line profiles chosen among 23 candidate lines according to the
spectral type and the rotational blending.
It gives resulting
for 249 stars, with a precision of about 5%.
The systematic shift with
standard stars from SCBWP, already
detected in Paper I, is confirmed in this work. SCBWP's values are
underestimated, smaller by a factor of 0.8 on average, according to
common stars in the northern sample. When joining both intersections
of northern and southern samples with standard stars from SCBWP, the
relation between the two scales is about
,
using these 52 stars in common.
This is approximately our findings concerning the catalogue made by
Abt & Morrell (1995). They derive their
from the calibration
built by SCBWP, and reproduce the systematic shift.
In the aim of gathering a large and homogeneous sample of projected
rotational velocities for A-type stars, the new data, from the present
paper and from Paper I, are merged with the catalogue of Abt &
Morrell. First, the
from the latter catalogue are statistically
corrected from the above mentioned systematic shift. The final sample contains
for 2151 B8- to F2-type stars.
The continuation of this work will consist in determining and
analyzing the
distributions of rotational velocities (equatorial and angular) for different sub-groups of spectral type,
starting from the
.
Acknowledgements
We insist on warmly thanking Dr. M. Ramella for having provided the programme of determination of the rotational velocities. We are also very grateful to Dr. R. Faraggiana for her precious advice about the analysis of the spectra. We would like to acknowledge Dr. F. Sabatié for his careful reading of the manuscript.
In a few cases, the selected lines are all discarded either from their
Fourier profile or from their skewness (Table 3). For
these stars, an uncertain value of
is derived from the lines
that should have been discarded. They are indicated by a colon and
flagged as "NO'' in Table 5. These objects are listed below. It is
worth noticing that none of them have spectra collected in
spectral range:
A few stars of the sample exhibit an external error higher than the
estimation carried on in Sect. 3.3. It can be the
signature of a multiple system.
The following stars have variable
from spectrum to spectrum
and are labeled as "SS'' in Table 5:
The common stars, among SCBWP's data and this sample, which
exhibit the largest differences in
between both studies, are
listed in Table 8. They are detailed below.
When merging the sample from Abt & Morrell (1995) with the new
measurements using Fourier transforms, common data are compared in
order to compute the scaling law between both samples. Aberrant points
are discarded using a sigma-clipping algorithm. These stars are listed
and discussed, and their
are indicated in
(
):