2 Stellar parameters

$\omega$ Ori has sometimes been classified as a Herbig Be star, (e.g. Thé et al. 1994) but the small IR excess is consistent with free-free emission rather than circumstellar dust (Hillenbrand et al. 1992). Moreover, it shows wind activity typical of classical Be stars of the same spectral type (Grady et al. 1996) and no X-ray emission has been detected for this star (Zinnecker & Preibisch 1994). Therefore, $\omega$ Ori is considered as a classical Be star, as most researchers agree. Its radial velocity is $V_{\rm rad} = 21.8$ km s^-1 (Duflot et al. 1995).

For an appropriate modeling of the rotational and pulsational phenomena, knowledge of the stellar parameters is essential. We compiled the most reliable data and attempted a critical evaluation of the various numbers using the usual astronomical formulae and the BCD (Barbier-Chalonge-Divan) spectrophotometric system (Zorec & Briot 1991).

The distance to the star is not well constrained by Hipparcos parallax measurements (see Table 1), but much stronger limits are put by $\omega$ Ori's undisputed membership of the Orion OB1a association (e.g. Brown et al. 1994) located at $380 \pm 50$ pc, which we adopt as the distance to the star.

 

 

Table 1: Stellar parameters for $\omega$ Ori (HD 37490, HR 1934). First column: derived from the usual astrophysical formulae. Second column: derived from the BCD (Barbier-Chalonge-Divan spectrophotometric system) classification taking into account rapid rotational and evolutionary effects, with formal errors.

		BCD
Spectral Type	B2-3IIIe	B2III
$V_{\rm rad}$ (km s-1)	21.8
V	4.55 $\pm$ 0.1	4.58
B-V	-0.1 $\pm$ 0.01
AV	0.32 $\pm$ 0.05
$D_{\rm Hipparcos}$ (pc)	500 +570-330
$D_{\rm Ori OB1a}$ (pc)	380 $\pm$ 50	370 $\pm$ 58
MV	-3.67 $\pm$ 0.39	-3.43 $\pm$ 0.28
$M_{\rm bol}$	-5.57 $\pm$ 0.49	-5.3 $\pm$ 0.37
log(L/$L_{\odot}$)	4.12 $\pm$ 0.20	4.03 $\pm$ 0.15
log $T_{\rm eff}$		4.306 $\pm$ 0.016
logg		3.48 $\pm$ 0.03
$R/R_{\odot}$	9.35 +12.66-6.89	6.84 $\pm$ 0.25
$M/M_{\odot}$	9.91 +19.50-5.04	8.02 $\pm$ 0.25
$v_{\rm crit}$ (km s-1)	450 +542-373
i ($^{\circ}$)	35 +52-25	32 $\pm$ 15
vsini (km s-1)	179 $\pm$ 4	175 $\pm$ 20
$f_{\rm rot}$ (c d-1)	0.66 +0.91-0.48	0.79 +1.65-0.49

One way to calculate the radius is to estimate the effective temperature, $T_{\rm eff}$, from the spectral type and the luminosity L from the visual magnitude, distance, extinction and bolometric correction (see Table 1). The spectral type as given by several sources varies between B2IIIe, B3IIIe and B2IVe. Ballereau et al. (1995) gives B2-3IIIe, which we adopt here.

$T_{\rm eff}$ and logg are determined with the BCD method by deriving the photospheric spectrophotometric BCD parameters of the star ($\lambda_1$, D_*). $\lambda_1$ gives the mean spectral position of the Balmer discontinuity and is a sensitive indicator of the stellar surface gravity, whereas D_* is a measure of the Balmer jump and a diagnostic of the stellar effective temperature. With these two parameters, we can determine the MK spectral type, the absolute magnitude M_V and the absolute bolometric magnitude $M_{\rm bol}$. They all fit with the parameters determined earlier (see Table 1). This method also gives the effective temperature log $T_{\rm eff} = 4.306 \pm 0.016$ and the surface gravity $\log g = 3.48 \pm 0.03$.

Below we argue that the most likely value of $v\sin i$ is 179 km s^-1 (see Sect. 5.3). For such a star several corrections would apply, in particular in relation to the rotational deformation of the star and gravity darkening. Therefore the established parameters represent an average photosphere which corresponds to the observed hemisphere of the star deformed by rotation. The real parameters of the star are related to these observed parameters by functions of the stellar mass, angular velocity ratio $\omega$, inclination angle i of the rotational axis and stellar age (Zorec et al. 2002, see also Sect. 2 in Floquet et al. 2000a).

These relations are solved using the evolutionary tracks of Schaller et al. (1992). We obtain $\omega = 0.83 ~\omega_{\rm c}$, where $\omega_{\rm c}$ is the critical angular velocity, and $i = 32^{\circ} \pm 15$. This yields $R_{\rm e} = 8.24 ~R_{\odot}$ for the equatorial radius and $M = 8.02 ~M_{\odot}$, for the mass, implying a mean radius of $R = 6.84 ~R_{\odot}$. The radius and mass derived from the usual formulae are given in Table 1 and agree with the ones derived from the BCD classification within the errors. We can compute the critical velocity $v_{\rm crit}$ at which the star could rotate without breaking up and using the value of $\omega$, we obtain $i = 35^{\circ}$. These two determinations of the inclination angle are consistent with the low inclination angle ( $i = 30^{\circ} \pm 5$) deduced from the calculations of Poeckert & Marlborough (1976) from polarimetric measurements.

From $i = 35^{\circ}$ and our determination of $v\sin i = 179$ km s^-1, we obtain $f_{\rm rot} = 0.66$ c d^-1. Using $i = 32^{\circ}$ and the corresponding radius as determined from the BCD method, which takes into account rapid rotational and evolutionary effects, and using $v\sin i = 175$ km s^-1, we find $f_{\rm rot} = 0.79$ c d^-1. Therefore, we consider 0.73 c d^-1 as the best estimate of the stellar rotational frequency. The uncertainty, however, is still large, as shown in Table 1, where the minimum and maximum values of the two determinations are given, taking into account the extremes of all the errors.

Figure 1: Long-term evolution of the normalized H$\alpha$ intensity of $\omega$ Ori. Data are taken from Andrillat & Fehrenbach (1982), Balona et al. (2001), Banerjee et al. (2000), Bopp & Dempsey (1989), Buil (2001), Dachs et al. (1981), Doazan et al. (1991), Hanuschik et al. (1996), Oudmaijer & Drew (1999), Sonneborn et al. (1988), Srinivasan (1996), this paper and unpublished data obtained from TBL (France) in 2000, NTT (ESO) and 1.52m/FEROS (ESO) in 2000/2001.