4 Rotational velocities data

4.1 Results

 

 

Table 5: (extract) Results of the measurements. Only the 15 first stars are listed below. The whole table is available electronically at the CDS. Description of the columns is detailed in the text.

HD	HIP	Spect. type		$\sigma$	#	Remark
			( )
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).

4.1.1 SB2 systems

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.

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 for both components. The three others a), c), e) have low differential Doppler shift ($\le$60  ) which makes all the lines blended. No has been determined for these objects.

Figure 8: The three following SB2 stars have been observed twice, in $\Lambda _1$ (upper panels) and $\Lambda _3$ (lower panels): a) HD 79763 at HJD 2449025, b) HD 98353 at HJD 2448274, c) HD 119537 at HJD 2449025, d) HD 79763 at HJD 2449365, e) HD 98353 at HJD 2449413, f) HD 119537 at HJD 2449415. SB2 nature of these objects is not detected in $\Lambda _1$ spectral range, and the derived is a "combined'' broadening. The triple system HD 98353 is observed close to conjunction, and lines remain blended. For HD 79763 d) and HD 119537 f), the difference in radial velocity is large enough to measure separately the rotational velocities.

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 $\Delta V_{\rm r}$computed from a few lines in the spectrum.

 

 

Table 6: Results for stars seen as SB2. Rotational velocities are given for each component when measurable. $\Delta V_{\rm r}$ stands for the difference in radial velocity between the two components. Dash indicates a non possible measurement (either for or $\Delta V_{\rm r}$).

HD	HIP	Spect. type			$\Delta V_{\rm r}$	Fig.
			( )		( )
			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

• 110 Tau (HD 35189) is highly suspected to be a spectroscopic binary due to its spectra taken in the $\Lambda _1$ domain. As it can be seen in Fig. 7a, core of the lines is double in most cases, corresponding to a difference in radial velocity of about 37  . However, this case does not allow the measurement of the projected rotational velocity.
• $\beta$ Aur (HD 40183) is a well known early A-type eclipsing binary of Algol type. The derived corresponds well with the values of Nordström & Johansen (1994) (respectively 33 and 34  ) that indicate synchronous rotation. Knowing the time of minimum from Johansen & Sørensen (1997):
  
  $${\rm HJD}_{\rm min} = 2431076.7269 + 3.96004732~ E,$$
  
  
  where E is an integer of phases, and the Julian date of observation (HJD 2449413.3301), the phase is equal to 0.4.
• HD 42035 has no indication of any binary status in the literature and it is flagged as a photometrically constant star from HIPPARCOS data. Nevertheless the observed line profiles in its spectrum tend to suggest that it is composite. The cross-correlation function (CCF) of the observed spectrum with a synthetic one ( $\ensuremath{T_{\rm eff}} = 10~000$ K, $\ensuremath{\log g} =4.0$, $\ensuremath{v\sin i} =5$  ) has been computed. This CCF is not characteristic of a single star, and it is perfectly fitted by the sum of two Gaussian components centered at 26 and 34  respectively and whose FWHM are 30 and 120  . This indicates that the system is composed of a low star and a faster rotator.
• HD 79763 is known as a SB2 system whose orbital period is P=15.986 d (Batten et al. 1989). Using the spectrum in $\Lambda _3$ range (Fig. 8d), the difference in radial velocity is sufficient to estimate of both components.
• 55 UMa (HD 98353) is a triple system for which components are early A-type stars. Using tomographic separation, Liu et al. (1997) estimate the of each of them: $30\pm 4$  , $45\pm 5$  , $55\pm 5$  . Knowing the orbital parameters: P=2.5538380 d and $T_{\rm minRV} = 2~449~602.588$ (Horn et al. 1996) for the close pair, our spectra correspond to phases $\phi=0.99$ (Fig. 8b, HJD 2448274.6233) and $\phi=0.02$ (Fig. 8e, HJD 2449413.5500). This means that both observations were unfortunately made close to opposition, and the difference in radial velocity is not large enough to see separated lines. The measured corresponds to a blend.
• HD 119537 is indicated as SB in the Bright Star Catalogue (Hoffleit & Jaschek 1982) and was not detected as a double-lined system with the spectrum collected at ESO, within the context of the southern sample (Grenier et al. 1999; Royer et al. 2002). The rotational velocity derived in Paper I is $13\pm 1$  , whereas it equals 23.9  in Ramella et al. (1989). The spectrum in the $\Lambda _3$ domain displays evidence of SB2 nature and Fig. 8f shows perfectly the faint lines around Ti II 4501, Fe II 4508 and Ti II 4515 which are usually well isolated in a single star with such a spectral type.
• HD 181470 is a close binary system first detected by speckle observations by Miura et al. (1993) and later confirmed by Hartkopf et al. (2000). The measured separation is $\rho= 0\hbox{$.\!\!^{\prime\prime}$ }13$ with a magnitude difference $\Delta m= 1.6\pm 0.2$. In the observed spectrum, the difference in radial velocity is large: 229  .
• HD 203439 is known as a spectroscopic binary system in Batten et al. (1989).
• HD 203858 is a known spectroscopic binary. Abt & Morrell (1995) do not see the two components of the system and give a which is likely overestimated, 70  , because of blend due to binarity. In this case, the components are well separated and each is measured.

4.2 Comparison with existing data

   
4.2.1 South versus North

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.

 

 

Table 7: Comparison of the computed for the stars in common in the northern and southern samples (N $\equiv$ this work, S $\equiv$ Paper I). CFF is a flag indicating the shape of the cross-correlation function carried out by Grenier et al. (1999) using the ECHELEC spectra (0: symmetric and Gaussian peak, 4: probable double, 5: suspected double, 6: probable multiple system).

HD	Sp. type	CCF	$\ensuremath{v\sin i} _{{\rm N}}$	$\sigma_{{\rm N}}$	$\ensuremath{v\sin i} _{{\rm S}}$	$\sigma_{{\rm S}}$
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 ( $FWHM{\scriptstyle [{\rm\AA}]} \approx 0.025~\ensuremath{v\sin i} {\scriptstyle [\ensuremath{{\rm km}~{\rm s}^{-1}} ]}$), the low limit of  is:

$$\ensuremath{v\sin i} _{\rm lim} = {1\over 0.025}~ FWHM_{\rm inst} = {1\over 0.025}~ {\lambda\over R},$$ (4)

where R is the power of resolution, and $\lambda$ the considered wavelength. For ECHELEC spectra ( $R\approx 28~000$) this limit is 6.4  at 4500 Å, whereas for AURÉLIE data ( $R\approx 16~000$), it reaches 11.3  . These limits correspond to the "rotational velocity'' associated with the FWHMof the instrumental profile. There is no doubt that in Fourier space, the position of the first zero of a line profile dominated by the instrumental profile is rather misleading and the effective lowest measurable may be larger. This effect explains the discrepancy found for slow rotators, i.e. HD 27962 and HD 72660 in Table 7. The determination using AURÉLIE spectra is 5  larger than using ECHELEC spectra. The two stars are slow rotators for which has already been derived using better resolution. HD 27962 is found to have $\ensuremath{v\sin i} =12$ and 11  by Varenne & Monier (1999) and Hui-Bon-Hoa & Alecian (1998) respectively. HD 72660 has a much smaller , lower than the limit due to the resolution of our spectra: 6.5  in Nielsen & Wahlgren (2000) and 6  in Varenne (1999).

Second of all, one other difference lies in the observed spectral domain. HD 198001 has no observation in the $\Lambda _3$ domain using AURÉLIE, so that $\ensuremath{v\sin i} _{{\rm N}}$ in Table 7 is not derived on the basis of the Mg II line. The overestimation of $\ensuremath{v\sin i} _{{\rm N}}$ 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:

$$\ensuremath{v\sin i} _{\rm S} = 1.05{\scriptstyle\pm 0.04}~\ensuremath{v\sin i} _{\rm N}-0.2{\scriptstyle\pm 1.5}.$$ (5)

Although common data are very scarce, they seem to be consistent. It suggests that both data sets can be merged as long as great care is taken for cases detailed above, i.e. extremely low rotators, high rotators with no from Mg II line, spectroscopic binaries.

   
4.2.2 Standard stars

Figure 9: Comparison of data for the 163 common stars between this work and Abt & Morrell (1995). The solid line stands for the one-to-one relation.

Figure 10: Comparison between data from this work and from Slettebak et al. (1975). The solid line stands for the one-to-one relation. The 21 standard stars are plotted with error bar on both axes (see text). HD number of the stars that deviate most from the one-to-one relation are indicated and these stars are listed in Table 8 and detailed in Appendix B.

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:

$$\ensuremath{v\sin i} _{\rm this\;work} = 1.18{\scriptstyle\pm 0.04}~\ensuremath{v\sin i} _{\rm AM}+3.8{\scriptstyle\pm 0.8}.$$ (6)

Abt & Morrell use the standard stars of SCBWP to calibrate the relation FWHM- . There are 21 stars in common between our sample and these standard stars. Figure 10 displays the derived in this paper versus the from SCBWP for these 21 common stars. The solid line represents the one-to-one relation. A clear trend is observed: from SCBWP are on average 20% lower. A linear least squares fit carried out with GaussFit on these values makes the systematic effect explicit:

$$\ensuremath{v\sin i} _{\rm this\;work} = 1.11{\scriptstyle\pm... ...7}~\ensuremath{v\sin i} _{\rm SCBWP}+7.1{\scriptstyle\pm 1.7}.$$ (7)

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 $\ensuremath{v\sin i} <200~\ensuremath{{\rm km}~{\rm s}^{-1}}$ and 15% for $\ensuremath{v\sin i}\geq 200~\ensuremath{{\rm km}~{\rm s}^{-1}}$). Our error bars are derived from the formal error found in Sect. 3.3 (Eq. (3)).

   

Table 8: Highlight of the discrepancy between values from SCBWP and ours (standard deviation of our measurement is indicated; dash "-'' stands for only one measurement). Comparison with data from the literature for the twelve stars that exhibit the largest differences. are classified in three subgroups according to the way they are derived: by-product of a spectrum synthesis, frequency analysis of the lines profiles or infered from a FWHM- relation independent from SCBWP's one. Flags from HIPPARCOS catalogue are indicated: variability flag H52 (C: constant, D: duplicity-induced variability, M: possibly micro-variable, U: unsolved variable, -: no certain classification) and double annex flag H59 (O: orbital solution, G: acceleration terms, -: no entry in the Double and Multiple Systems Annex).

Name	HD	Sp. type	( )						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
$\gamma$ Gem	47105	A0IV	<10	15	${\scriptstyle\pm 1}$	11.2(1)	$10.2{\scriptstyle\pm 0.2}^{(2)}$, 19.0(3)		-	X
30 Mon	71155	A0V	125	161	${\scriptstyle\pm 12}$				C	-
$\beta$ UMa	95418	A1V	35	47	${\scriptstyle\pm 3}$	44.8(1), 39(4)	44.3(3)		-	-
$\theta$ Leo	97633	A2V	15	24	${\scriptstyle\pm 3}$	21(5), 22.1(1)	24(6), 27.2(3)	23(7)	-	-
$\gamma$ UMa	103287	A0V SB	155	178	${\scriptstyle\pm 9}$		$154{\scriptstyle\pm 4}^{(8)}$		M	-
$\alpha$ Dra	123299	A0III SB	15	25	${\scriptstyle\pm 2}$		27(9)		M	O
$\sigma$ Boo	128167	F3Vwvar	10	15	${\scriptstyle\pm 1}$	$7.5{\scriptstyle\pm 1}^{(10)}$	7.5(11)	7.8(12), 8.1(13)	-	-
$\alpha$ CrB	139006	A0V	110	139	${\scriptstyle\pm 10}$		$127{\scriptstyle\pm 4}^{(8)}$		U	O
$\tau$ Her	147394	B5IV	30	46	${\scriptstyle\pm 3}$		32(6)		P	-
$\alpha$ Lyr	172167	A0Vvar	<10	25	${\scriptstyle\pm 2}$	22.4(1), 23.2(14)	$23.4{\scriptstyle\pm 0.4}^{(16)}$, 24(6)		U	-
						$21.8{\scriptstyle\pm 0.2}^{(15)}$	29.9(3)
$\gamma$ Lyr	176437	B9III	60	72	${\scriptstyle\pm 2}$				M	-
$\epsilon$ Aqr	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.