One of the major gaps in our understanding of stellar physics is the role of angular momentum in the formation and early life of a star. Two problems of great interest are the transport of angular momentum in collapsing interstellar clouds and the subsequent braking of young stars during the PMS contraction. Accurate rotational velocities of young stars are essential for further progress in these areas. Also, the knowledge of the behaviour of the distribution of rotational velocities as a function of the spectral type puts important constraints on models of the stellar angular momentum evolution and provides information on what physical process controls the rotational velocity across the HR diagram.

Different methods have been developed to calculate rotational velocities, all of them relying, to some extent, on the geometrical technique, suggested originally by Shajn & Struve (1929), that relates line profiles and line widths to the apparent rotational velocity, $v \sin i$ . Until the advent of solid-state detectors about two decades ago, most of the rotational velocities were determined by measurements of one or two relatively strong lines. The method consisted in identifying a particular point on the line profile (usually the full width at half maximum) and calibrating this parameter in terms of a rotational standard. Although helpful in identifying older sources of $v \sin i$ measurements, catalogues such as those of Bernacca & Perinotto (1970) and Uesugi & Fukuda (1982) pose serious problems because they attempt to combine observations that have different resolutions obtained with a variety of techniques.

Table 6: Results of the spectral classification and projected rotational velocities. The values of $v \sin i$ are given in km s^-1.
Star Type of star Spectral type Previous classifications $v \sin i$ $v \sin i$

Previous work

HD 23362 CTT K5 IIIm K2 V, K2 6 $\pm$ 1

HD 23680 CTT G5 IV G5

HD 31293 97 $\pm$ 20 80 $\pm$ 5⁽¹⁵⁾

HD 31648 HAeBe A5 Vep A3ep+sh, A3ep+sh, A2 102 $\pm$ 5 80⁽¹⁾

HD 34282 HAeBe A3 Vne A2 Ve+sh, A0e, A0 129 $\pm$ 11

HD 34700 ETT G0 IVe G0 V 46 $\pm$ 3

HD 58647* HAeBe B9 IVep A0 IVe, B9 II-IIIe, B9e 118 $\pm$ 4

HD 109085 Vega F2 V F2 V, F3 V, F2 III-IV 68 $\pm$ 2 51⁽²⁾, 81⁽³⁾

HD 123160* CTT K5 III G5 V, K5 7.8 $\pm$ 0.5 9 $\pm$ 1⁽⁴⁾

HD 141569 HAeBe A0 Vev A0 Ve, B9.5 Ve, B9e 258 $\pm$ 17 236 $\pm$ 9⁽⁴⁾

HD 142666 HAeBe A8 Ve A7 V, A8 V, A8 Ve 72 $\pm$ 2 70 $\pm$ 2⁽⁴⁾

HD 142764 Vega K7 V K5 7.8 $\pm$ 1.5

HD 144432 HAeBe A9 IVev A7 Ve, A9/F0 V, A7 Ve 85 $\pm$ 4 74 $\pm$ 2⁽⁴⁾, 73⁽⁵⁾

HD 150193 HAeBe A2 IVe A2 Ve, A1 V, A1 Ve

HD 158352 MS A8 Vp A7/8 V+sh, A8 Vsh

HD 163296 HAeBe A1 Vepv A3 Vep+sh, A1 V, A0-A2 133 $\pm$ 6 120⁽⁶⁾

HD 179218 HAeBe A0 IVe B9/A0 IV/Ve, B0e

HD 190073 HAeBe A2 IVev B9/A0 Vp+sh, A0 IV esh

HD 199143 MS F6 V F6 V 155 $\pm$ 8

HD 203024 MS A5 V Ae

HD 233517 CTT K5 III K2, A2 16 $\pm$ 1 15⁽⁷⁾, 17.6⁽¹⁹⁾

HR 10 Ash A0 Vn A2 V-A5 V, A6 Vn 294 $\pm$ 9 $^{\dag }$ 220⁽⁸⁾, 195⁽⁹⁾

HR 26 A MS B9 Vn B9 Vn, B8.5 Vnn 266 $\pm$ 5 275⁽¹⁰⁾

HR 26 B PTT K0 V G5 Ve

HR 419 162 $\pm$ 14

HR 1847 Vega B5 V B7 IIIe

HR 2174* Vega A2 Vnv A3 Vn, A1 IV-sh, A3 V 252 $\pm$ 7

HR 4757 A MS B9.5 V B9.5 V 239 $\pm$ 7 205⁽¹¹⁾

HR 4757 B PTT K2 V K0 V, K2 Ve, K1 V 5.7 $\pm$ 0.7

HR 5422 A MS A0 V A0 V, B9.2p, B9 Vp 7.4 $\pm$ 0.3 14⁽¹²⁾, 20⁽¹³⁾

HR 5422 B PTT K0 V K1 V

HR 9043 Vega A5 Vn A5 V, A3 Vn 205 $\pm$ 18 210⁽⁸⁾

AS 442 HAeBe B8 Ve B8e

BD+31 643 Vega B5 V B5, B5 V 162 $\pm$ 13 $^{\dag }$

MWC 297* HAeBe B1 Ve O9e, Be, B1.5, 09

BM And CTT K5 Ve K5 V

$\lambda$ Boo Vega A1 V A0 Vpsh, A0p 129 $\pm$ 7 100⁽¹⁴⁾

VX Cas HAeBe A0 Vep A0/3e, A0, A3, A0e 179 $\pm$ 18

BH Cep ETT F5 IIIev A/F5 Ve, F5 IVvar 98 $\pm$ 3

BO Cep CTT F5 Ve F2e, F2e

SV Cep HAeBe A2 IVe A0e, A 206 $\pm$ 13

49 Cet Vega A4 V A3 V, A1 V 186 $\pm$ 4

24 CVn Ash A4 V A5 V, A4 V, A5.5 A 173 $\pm$ 4 145⁽³⁾, 160⁽¹⁾

V1685 Cyg HAeBe B2 Ve B2 Ve+sh, B2, B2 Ve

V1686 Cyg* HAeBe A4 Ve G2 V, A0 V, A7 V

R Mon HAeBe B8 IIIev B0e, B.., B2

VY Mon* HAeBe A5 Vep B9/A0e, B8, B-A

51 Oph HAeBe B9.5 IIIe A0 V, B9.5 Ve,A0 II-III(e) 256 $\pm$ 11 $^{\dag }$ 267⁽⁴⁾

KK Oph HAeBe A8 Vev B3, B-Ae, A5 Ve, A6 177 $\pm$ 13 $^{\dag }$

T Ori HAeBe A3 IVev A3/4e, A3, B9, A5 e 175 $\pm$ 14 130 $\pm$ 20⁽¹⁵⁾

BF Ori HAeBe A2 IVev A5/6 IIIe+sh, A5e, A6e 37 $\pm$ 2 100⁽¹⁵⁾

CO Ori ETT F7 Vev F9/G Ve, F9: e, F8 65 $\pm$ 4 48 $\pm$ 15⁽¹⁶⁾

HK Ori* ETT G1 Ve A5, A4, G:ep, B8/A4ep

NV Ori ETT F6 IIIev F0/8 IVe, F 4/0 III,V 81 $\pm$ 8 80 $\pm$ 7⁽¹⁵⁾

RY Ori ETT F6 Vev F6/Gep, F8:pe 66 $\pm$ 6

**Table 6:** continued.
Star	Type of star	Spectral type	Previous classifications	$v \sin i$	$v \sin i$
					Previous work
UX Ori	HAeBe	A4 IVe	A3e, A2/3 IIIe, A1-3IIIe	215 $\pm$ 15	175⁽¹⁷⁾, 70 $\pm$ 6⁽¹⁵⁾
V346 Ori	HAeBe	A2 IV	F1:III:e, A5 III:e
V350 Ori	HAeBe	A2 IVe	A5e, A0
XY Per	HAeBe	A2 IV	B6/A5e, B6, A2 II+B6e	217 $\pm$ 13
VV Ser*	HAeBe	A0 Vevp	A2e, B1-3e:, B1/3e/A2:	229 $\pm$ 9 $^{\dag }$
17 Sex	Ash	A0 V	A1 V, A1 Vsh, A5	259 $\pm$ 13 $^{\dag }$	180⁽³⁾
CQ Tau	ETT	F5 IVe	F2:e, A8 IV/F2 IVe	105 $\pm$ 5	110 $\pm$ 20⁽¹⁵⁾
CW Tau*	CTT	K3 Ve	K3, K5 V:e
DK Tau	CTT	K5 Ve	M0 V:e, K7 V, K7
DR Tau*	CTT	K5 Vev	K4 V:e
RR Tau*	HAeBe	A0 IVev	F:e, A2 II-IIIe, B8ea	225 $\pm$ 35 $^{\dag }$
RY Tau	ETT	F8 IIIev	F8 V:e, K1 IV, G5e, K7	55 $\pm$ 3	52⁽¹⁸⁾
PX Vul	ETT	F3 Ve	F0 V:e, F0, F5
WW Vul	HAeBe	A2 IVe	A3e, A0/3 Ve, A0, A1e	220 $\pm$ 22
LkH $\alpha$ 200	CTT	K3 Ve	K1 V, Ke, dK0
LkH $\alpha$ 234	HAeBe	B5 Vev	B5.7e, B5/7, B9/A0e, A7
LkH $\alpha$ 262*	CTT	M1 IIIe	K?, M0

Notes to Table 6: The meanings of the lower case suffixes are: "e'' emission lines, "v'' variable spectrum, "p'' peculiar spectrum (presence of non-standard components), "n'' broad or weak lines in the spectrum, "m'' unexpected lines from metals or metal lines with unusually large strengths. The abbreviations in Col. 2 mean: CTT (classical T Tauri), ETT (early T Tauri), HAeBe (Herbig Ae/Be), MS (main sequence), PTT (Post-T Tauri) and Ash (A-shell star). The stars marked with an asterisk (*) have been classified with an error of about five spectral subtypes because they present peculiar spectra, too many diffuse interstellar bands or veiling. In Sect. 4.6 we give particular details on these stars.

A blank in Col. 5 means that the star was not observed with the WHT, furthermore no determination of $v \sin i$ was feasible. The symbol $\dag$ indicates that $v \sin i$ has been obtained using only the Mg II 4481 Å line. References to $v \sin i$ in Col. 6: (1) Jaschek et al. (1988); (2) Wolff & Simon (1997); (3) Abt & Morrel (1995); (4) Dunkin et al. (1997); (5) Fekel (1997); (6) van den Ancker et al. (1998); (7) Jasniewicz et al. (1999); (8) Welsh et al. (1998); (9) Lecavelier des Etangs et al. (1997); (10) Ghosh et al. (1999); (11) Baade (1989); (12) Ramella et al. (1989); (13) Millward & Walker (1985); (14) Paunzen et al. (1999); (15) Böhm & Catala (1995); (16) Fernández & Miranda (1998); (17) Grady et al. (1996); (18) Petrov et al. (1999); (19) Balachandran et al. (2000).

In this paper, we make use of the technique proposed by Gray (1992). In short, the method is based on the relation between $v \sin i$ and the frequencies where the Fourier transform of the rotational profile reaches a relative minimum: the dominant term in the Fourier transform of the rotational profile is a first-order Bessel function that produces a series of relative minima at regularly spaced frequencies (Fig. 7). Unlike the above-mentioned methods which require the building up of a calibration library of rotational velocities, Gray's method provides a direct measurement of $v \sin i$ . Moreover, it also allows the differentiation of rotation from other potential competing broadening sources such us, for instance, macroturbulence in late-type stars. Projected rotational velocities, in km s^-1, calculated using the high resolution spectra taken with the WHT are given in Col. 5 of Table 6; results from previous work are shown in Col. 6. Metallic lines of photospheric origin covering the full wavelength range and whose main source of broadening is rotation were used in this analysis.

Projected rotational velocities were not calculated for two stars of our sample: DR Tau and HK Ori (Fig. 8). DR Tau shows, in the range covered by the WHT observations, a spectrum of complex nature characterized by the absence of absorption photospheric features caused by a high degree of veiling, whereas HK Ori is a visual and spectroscopic binary showing a composite spectrum where the contribution of a companion classified as a T Tauri star is superimposed (Corporon & Lagrange 1999) (see Sect. 4.6).

In general, our results agree with those found in previous work. There are, however, some cases where clear discrepancies are apparent. Figure 9 shows those stars for which our $v \sin i$ values are clearly discrepant with previous determinations. In all cases our values produce better fits to the observations. Also, in some other cases, the blending is so severe that only one spectral line, Mg II 4481 Å, can be used to determine the rotational velocity. These objects are labelled with " $\dag$ '' in Table 6. The Mg II 4481 Å doublet is considered an ideal indicator in these cases as it is free of strong pressure broadening and yet is strong enough that the rotation-broadened profile can be easily measured. Moreover, the large rotational broadening means that the 0.20 Å splitting of the doublet is not a problem.

$\begin{figure} \par\includegraphics[width=5.5cm,clip]{MS1324f10a.eps}\hspace*{1c... ...eps}\hspace*{1cm} \includegraphics[width=5.5cm,clip]{MS1324f10d.eps}\end{figure}$

Figure 10: Influence of the intrinsic profile of blended features on the Fourier transform. The observed spectrum (solid line) is compared to a synthetic spectrum (dotted line) with similar physical parameters ( $T_{\rm eff}$ , $\log g$ , [M/H]) and $v\sin i=0$ . Assumed line edges are also displayed. Top panel: the contribution of the intrinsic profile lies at high frequencies and thus does not affect the $v \sin i$ determination. Bottom panel: in this case the intrinsic profile produces a spurious minimum in the Fourier transform which may lead to a wrong $v \sin i$ determination.

5.1 Estimated uncertainties

Limb darkening: According to Eq. (17.12) of Gray (1992), one of the uncertainties in the calculation of $v \sin i$ comes from the limb-darkening law. In this work, a linear law with $\epsilon=0.6$ has been assumed. Following Díaz-Cordovés & Giménez (1992), the difference in the total emergent flux between the linear and the quadratic laws is less than 5% in the range of temperatures of our programme stars. Moreover, the dependence of $\epsilon$ with wavelength is also negligible: according to Díaz-Cordovés et al. (1995), we expect a variation in $\epsilon$ of 0.55 $\leq$ $\epsilon$ $\leq$ 0.85 in our range of temperatures, gravities and wavelengths. Solano & Fernley (1997) demonstrated that such a variation implies, in the worst case, a change in $v \sin i$ of less than 5%.

Continuum placement: The determination of the local continuum is another unavoidable source of error: a displacement in the continuum level can change the line profile, especially the wings, and thus distort the shape of the Fourier transform, modifying the position of its zeroes. Many objects in our sample have broad line profiles typical of high $v \sin i$ values. In this case, the continuum placement cannot be set by simply connecting the highest points in the observed spectrum since this would produce an underestimation of the equivalent widths. This problem was solved by defining the "true'' continuum level as that of a synthetic spectrum of physical parameters similar to those of the observed object.

Blending: The high $v \sin i$ values of many of the stars of our sample make it very difficult to apply the method to isolated lines. Blended features were used instead. A careful inspection using synthetic spectra was performed to avoid contamination in the Fourier domain due to the intrinsic profile of the blended features (Fig. 10).

Sampling frequency: Another limiting factor in the calculation of $v \sin i$ is the sampling frequency. Defining this frequency as $\sigma = 0.5/\Delta \lambda$ and considering the spectral resolution quoted in Sect. 3, a minimum value of $\approx$ 6 km s^-1 can be achieved. Hence, for stars with $v \sin i$ lower than this value it is not possible to calculate a proper value of $v \sin i$ but only an upper limit (Table 6).

5.2 Observed distribution of rotational velocities

The stellar angular momentum is known to change dramatically along the evolutionary sequence. This is particularly relevant for T Tauri stars for which a large angular momentum loss is expected during the early stages of the star formation, where rotational velocities might decrease from values near break-up, typical of protostars, to velocities in the range from less than 10 km s^-1 up to 30 km s^-1 with a mean value about 15 km s^-1 for a 1 $M_{\odot}$ T Tauri star (Vogel & Kuhi 1981). Within the T Tauri stars it is also possible to find statistically significant differences between classical (CTTs) and weak (WTTs) T Tauri stars in the sense that the latter rotate faster suggesting a different rotational evolution (Bouvier et al. 1993). These differences can be interpreted as an evidence of the spinning-up of the WTTs as they contract while CTTs are prevented from doing so by e.g. strong winds or magnetic coupling between the star and the inner accretion disk. Solar-mass ZAMS stars in young stellar clusters represent the subsequent step in the evolutionary scenario. Contrary to TTs, these stars exhibit a much larger range of $v \sin i$ , peaked at low velocities (typically 10 km s^-1) with a wide high-velocity tail up to 200 km s^-1 (Allain et al. 1996). The question of how to account for the rotational distribution of ZAMS stars starting from that of TTs is not well understood yet. Bouvier et al. (1993) proposed linking the observed rotational distribution of ZAMS stars with the two T Tauri subclasses: according to this, WTTs and CTTs would be the progenitors of the ZAMS fast and slow rotators respectively. Shortly after their arrival on the ZAMS, solar-type stars are then drastically braked and, at the age of the Hyades, (600 Myr) have rotation rates lower than 10 km s^-1 irrespective of the initial angular momentum (Endal & Sofia 1981).

The use of projected rotational velocities in the determination of the rotational properties of stars is limited by the unknown geometric effect included in $\sin i$ . Moreover, the number of $v \sin i$ determinations, too low for a statistically significant analysis, is an additional limiting factor in our study. Nevertheless, it is possible to interpret the observed distribution in a qualitative way. Figure 11 displays the rotational velocities of our program stars as a function of their spectral type as given in Table 6. For comparison, we have also plotted mean rotational velocities of B, A-type stars (solid line, Fukuda 1982), F, G-type stars (dotted line, Fekel 1997) and Be stars (dashed line, Steele et al. 1999) of luminosity class V. Two stars appear to be clearly discrepant in this figure: HR 5422 A (A0 V, $v \sin i$ = 7.4 km s^-1) and BF Ori (A2 IVev, $v \sin i$ = 37 km s^-1 ). HR 5422 A is a Am star in a double system (Ramella et al 1989) whereas the $v \sin i$ value of BF Ori is confirmed by the large number of data used in the analysis (four spectra in two different observing runs with 8, 12, 15 and 13 lines used respectively) which suggests that the low $v \sin i$ value may be due to an inclination effect.

One of the results that can be deduced from Fig. 11 is that the PMS stars tend to rotate faster than stars in the main sequence with similar spectral types. The qualitative behaviour in the overall distribution of $v \sin i$ for pre-main sequence and main sequence stars is similar, namely, rotation is large for early-type stars dropping rapidly through the F-stars region. In the main sequence stars, this behaviour is tied in with the appearance of convective envelopes and the magnetic brake generated by its interaction with rotation in the dynamo process. Dudorov et al. (1994) proposed a similar hypothesis for PMS stars where the sudden transition in spin rates at F-spectral types would also occur as a consequence of the onset of a magnetic field in the star envelopes. Figure 11 also confirms the basic conclusions from Finkenzeller (1985) concerning the distribution of the projected rotational velocities of Herbig Ae/Be stars: Herbig Ae/Be stars are depleted of slow rotators and rotate at intermediate velocities systematically more rapidly than T Tauri stars.

For F-G spectral types, a clear difference in $v \sin i$ between the PMS stars and their counterparts of luminosity class V can be deduced from Fig. 11. Concerning the B, A-types, there is a smooth transition in the PMS group from high $v \sin i$ values, typical of Be stars, to values lower than the average ones for objects of luminosity class V. This result fits nicely with the two scenarios proposed by Finkenzeller (1985) in which the further evolution of $v \sin i$ in PMS stars would depend on the relative strength of two opposite processes, namely, a speeding up due to a further contraction and the associated conservation of the angular momentum or a spin down due to a net angular momentum loss (e.g. by stellar winds). Depending of the leading mechanism, one could expect the formation of either a "normal'' B, A-type main sequence star or a rapidly rotating Be star.

5 The projected rotational velocities

5.1 Estimated uncertainties

5.2 Observed distribution of rotational velocities