tokens: which describes the adopted stellar mass ( M ), polar radius ( R p ), polar effective temperature ( T eff,p ), equatorial rotation velocity ( v e ) and inclination angle ( i ). For example, ‘m40r40t150v300i30’ is the case of M = 4.0 M ⊙ , R p = 4.0 R ⊙ , T eff,p = 15 000 K, v e = 300 km s −1 and i = 30°. (2) Polar radius (in R ⊙ ). (3) Equatorial radius (in R ⊙ ). (4) Polar effective temperature (in K). (5) Equatorial effective temperature (in K). (6) Mean effective temperature in K (which was derived by averaging the local effective temperature over the observed stellar disc while weighting according to the local continuum intensity). (7) Product of v e and sin i (in km s −1 ). (8) First-zero frequency of He 4471 (in Å − 1 ). (9) Ratio of to , where is the first-zero frequency of classical rotational broadening function (see, e.g. Gray 2005 ), which is related to v e sin i as (λ: wavelength, c : velocity of light). (10) First-zero frequency of Mg 4481 (in Å − 1 ). (11) Ratio of to . The wavelengths of the reference pseudo-continuum, necessary for reducing the normalized profile, were defined in almost the same way as in Section 4.1: Having found the critical wavelength λ* corresponding to the maximum level between these two lines, we set [, ] = [4471 − (λ* − 4471), λ*] and [, ] = [λ*, 4481 + (4481 − λ*)]. The Fourier transforms were then calculated for the resulting R (λ) profiles of He 4471 and Mg 4481 lines. Fig. 6 illustrates the behaviours of | f (σ)| as function of σ for the same selected cases as in Fig. 5 . The first-zero frequencies (σ 1 ) measured from the computed transforms are presented in Table 2 . Figure 6. Fourier transform amplitudes [| f (σ)|] plotted against σ, for the theoretical profiles of He 4471 (left-hand panels) and Mg 4481 (right-hand panels) computed for six representative models (same as those shown in Fig. 5 ). The upper panels (a) and (b) show the results for T eff,p = 12 000 K, while the lower panels (c) and (d) are for T eff,p = 15 000 K. 5 DISCUSSION 5.1 Characteristics of first-zero frequencies We first discuss the trend of theoretical σ 1 modelled in Section 4.2 . Since this quantity is expressed as σ 1 = 0.660/(λ v e sin i / c ) in the classical approximation, the projected rotational velocity (or the linewidth for the case of rotation-dominated broadening) plays the most significant role for determining σ 1 , though its precise value is affected also by the profile shape. The resulting values of σ 1 corresponding to the theoretical line profiles simulated on the gravity-darkened models are plotted against v e sin i in Fig. 7 , where the classical σ 1 versus v e sin i relation is depicted by a slanted solid line and the observed σ 1 values for six stars are indicated by horizontal dashed lines. Figure 7. The values of theoretical σ 1 , measured from the Fourier transforms of simulated spectra for gravity-darkened models, are plotted against v e sin i . The results for He 4471 (left-hand panels)
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