5 Line activity

5.1 Observations

5.1.1 H$\alpha$ line

HD 127972 showed H$\alpha$ emission intensity strengthening from 1996 through 2000 and a slight fading in 2001; this last was accompanied by increased central absorption. The average H$\alpha$ emission line profiles observed in the 1996, 1997, 1998, 2000 and 2001 epochs are shown in Fig. 11. This pattern of H$\alpha$ line profiles variation resembles that displayed by the star in the 1987-1993 period (Hanuschik et al. 1996), but in the opposite sense. Putting both patterns together, a kind of cyclic emission variation of about 6-7 years appears.

From 34 H$\alpha$ emission line profiles obtained from Mar. 12 to Mar. 23, 2000, a rapid cyclic variability of the V/R emission peak intensity ratio (Fig. 12) and a rough increase, followed by a rapid decrease in the separation of the emission peaks, was observed (Fig. 13). The total peak separation change is not greater than 15 km s^-1. Let us note also that the highest peak separation corresponds to the highest V/R value. After this maximum, the V/R ratio and the peak separation decreased. These changes were accompanied by a general wiggling of the line emission profile, characterized by a noticeable pulling down of the whole blue emission wing that produced the observed V/R decreasing ratio. This drop of the emission intensity on the blue side of the emission line profile was followed by an increase of the red wing, but of much smaller amplitude. The maximum intensity changes in the blue wing were $\Delta I \sim 0.1$ (I is the intensity normalized to the local continuum) and they were produced in the spectral region from $V \sim -350$ to -800 km s^-1, while the intensity variation in the remaining profile was $\Delta I \sim 0.05$. Transient sharp absorption spikes were also observed far out in the wings.

5.1.2 He  I 6678 line

Each epoch corresponding to four season-averaged H$\alpha$ emission line profiles shown in Fig. 11 is also characterized by a different spectral extent of the He  I 6678 lpv. Figure 14 displays the mean absolute deviations of the lpv across the He  I 6678 line profile, as defined by Walker (1991). It can be seen in this figure that the wavelength interval showing profile variability systematically widens from 1996 through 2000. The wavelength interval where the variability of highest significance extends beyond the $V\sin i$ limit, from roughly $\pm$390 km s^-1 in 1997 to about $\pm$450 km s^-1 in 2000. This behavior was also observed in other Be stars and in particular in $\lambda$ Eri by Kambe et al. (1993 and references therein).

 

 

Table 5: Fundamental parameters of $\eta$ Cen.

$\lambda_1 =$	$51.4 \pm 1.5$ Å
D* =	$0.159 \pm 0.017$ dex
$T_{\rm eff}(\lambda_1,D_*) =$	$20455 \pm 946$ K
$\log g(\lambda_1,D_*) =$	$3.80 \pm 0.07$ dex
$\log L(\lambda_1,D_*)/L_{\odot} =$	$3.753 \pm 0.155$ dex
$R(\lambda_1,D_*)/R_{\odot} =$	$6.00 \pm 0.61$
$T_{\rm eff}^f =$	$20560\pm 600$ K
$\theta\times10^{8} =$	$0^r\!\!.279\pm0.003$
$(f = L/4\pi d^2)\times10^{5} =$	$1.975\pm0.049$
$\log L^f/L_{\odot} =$	$3.742\pm 0.080$ dex
$R^f/R_{\odot} =$	$5.86\pm 0.55$
$V\sin i$ in km s-1 =	310	370	$\pm$ 44
$\omega =$ $\Omega/\Omega_{\rm c} =$	0.86	0.90	$\pm$ 0.10
$M/M_{\odot} =$	8.5	8.7	$\pm$ 1.1
$R_{\rm e}(\omega)/R_{\odot} =$	6.2	6.3	$\pm$ 0.8
i =	66o	70o	$\pm$ 12o
$R_{\rm o}/R_{\odot} =$	5.3	5.2	$\pm$ 0.8
t/108 yr =	0.199	0.178	$\pm$ 0.035
$\nu_{\rm r}$ in c/d =	1.12	1.24	$\pm$ 0.18
$V_{\rm c}$ in km s-1 =	485	494	$\pm$ 55
$\nu_{\rm c}$ in c/d =	1.34	1.39	$\pm$ 0.18

Regarding the uncertainties in the determination of $V\sin i$ we can adopt, using the data in Table 5, $V_{\rm c}\sin i = 490\sin66^{\rm o}$ km s^-1 as the reference value for the projected critical rotational velocity. Then, the line activity that extends up to $\pm$450 km s^-1 could imply that the stellar layers where the He  I 6678 line is formed may be in critical rotation. However, this rotation is somewhat puzzling, because from the He  I 4471 line observed in April and May 2000 we obtained $V \sin i =310$ km s^-1 (Sect. 4.2). At least two explanations can be put forward for this discrepancy: 1) the main contributions to He  I 6678 and He  I 4471 lines come respectively from different atmospheric layers [as expected from the ratio of their respective oscillator strengths f(6678)/f(4471) =5.6], so that while the uppermost layers are accelerated to the critical rotational velocity, the lower ones would be left unscathed; 2) the contribution to the He  I 6678 line wings at velocities $V > \vert V\sin i\vert$ is due to exophotospheric or circumstellar material travelling at velocities up to $(v^2_{\rm radial}+v^2_{\rm tangential})^{1/2} \ga 450$ km s^-1. The first possibility recalls the scenario proposed by Osaki (1986) and Saio (1994), where the prograde NRP modes accelerate the outer stellar atmospheric equatorial layers up to the critical rotational velocity. These layers may give rise to mass loss and the NRP modes decrease in intensity as the mass dissipates in the extended envelope.

We studied the He  I 6678 lpv beyond the $V\sin i$ limit. In order to obtain the characteristic frequencies, the red and the blue sides of the line profiles were folded into a unique positive velocity scale. The periodograms that resulted for the periods 1996, 1997/1998 and 2000, and the respective diagrams of confidence levels of the signals found are shown in Fig. 15. In the confidence level estimations we excluded the points at V < 310 km s^-1. Since roughly in the interval $\pm400$ to $\pm500$ km s^-1 the emission shoulders seen in the line profiles are probably formed in the circumstellar regions, we can consider frequencies $\nu <$ $\nu_{\rm r}$ as due to circumstellar orbiting matter. If so, $\nu = 0.1\pm0.1$ c/d could represent a perturbation produced at distances 3.3 to 6.4R_* away from the star, depending on whether we consider Keplerian or angular momentum conservation rotation law respectively. From the diagrams of Fig. 15 we see that the signal $\nu =$ $0.1\pm0.1$ c/d disappears gradually from 1996 to 2000, as it would be overtaken by matter gathered elsewhere and with a more significant contribution to the line profile. On the contrary, the signal $\nu =$ $0.6\pm0.1$ c/d is ubiquitous and its significance grows from 1996 to 2000 (the confidence peaks must be regarded relative to each other only within a given diagram). It may correspond to perturbations centered from 1.3 to 2.0R_* in the CE, depending on the rotational law assumed. As emission in the H$\alpha$ line also grows from 1996 to 2000, we may consider there is an increasing amount of matter gathered in these CE regions. This picture seems to be confirmed by an increasing CE density derived using a simple model of the H$\alpha$ line emission presented in Sect. 5.2. The widening of the wavelength interval of lpv in the He  I 6678 line could be then associated with a period of increased mass ejection.

Figure 11: Average H$\alpha$ line profiles for the 1996, 1997, 1998, 2000 and 2001 epochs.

There is also the prevalent frequency $\nu =$ $1.5\pm0.1$ c/d that could be due to the central star, which as seen in Sect. 3.2. is quite outstanding in the data analyzed in the present paper.

Let us finally note that if $V\sin i$ actually changed from 310 to 450 km s^-1, this would represent a variation of only 14% in $\Omega/\Omega_{\rm c}$, while the 45% variation of $V \sin i =$ $R_{\rm e}(\Omega)\Omega\sin i$ is provided mainly by rotational stretching of the equatorial radius  $R_{\rm e}(\Omega)$.

5.2 Modeling

One of the most difficult questions relating to Be stars concerns their CE formation. It is then important to determine the relevant parameters that characterize the CE structure at each observed emission phase. This may help us to estimate the effects of stellar activity on the observed CE changes. In particular, if the apparently increasing activity detected in the He  I 6678 line from 1996 to 2000 also implied conspicuous mass ejections, the average density of the CE must have changed perceptibly, so that we can detect it by studying the emission in the H$\alpha$ line. In order to obtain a rough insight on the scale factors characterizing the CE structure, we use first physical principles and a simple representation of the envelope. From Sect. 4.2 it seems that $\eta$ Cen is seen nearly equator-on. We assume then that the CE is represented by a rotating cylindrical disc seen edge-on. It can also be simultaneously expanding or contracting. Since the main radiation transfer effects are controlled by the optical depth, which is an integrated quantity, the disc can be treated in a first approximation as a rotating/expanding (or contracting) ring with the same radial optical depth as the CE is thought to have (Floquet et al. 2000). The ring has a radius R and a total height $h = 2\times H$.

It has long been known that the source function $S_{\rm H\alpha}$ of the H$\alpha$line in B stars is strongly dominated by radiative ionization and recombination processes (Thomas 1965; Jefferies 1968). In a slab, as the one represented by the ring facing the central star, we can then use the following dependence of the source function with the optical depth (Mihalas 1978):

$$S_{\rm H\alpha}(\tau_{\rm o}) = \left\{\begin{array}{rl} \e... ...tau_{\rm o}^{1/2} & {\rm for\ \tau_o > 1,} \end{array} \right.$$ (4)

where $\tau_{\rm o}$ is the optical depth at the center of the H$\alpha$transition. For radiative fields around B stars, CE electron temperatures of the order of $T_{\rm e} \sim$ $0.8\times T_{\rm eff}$ and electron densities $N_{\rm e} \la$ 10¹³ cm^-3, it can be shown that:

 

$$\left. \begin{array}{rcl} \eta & \simeq & R_{3k}/A_{32} \\ B^* &... ...c{R_{3k}}{R_{2k}}\frac{R_{k2}}{R_{k3}} - 1 \bigr]^{-1} \\ \end{array}\right\},$$ (5)

where R_nk and R_kn are the radiative ionization and recombination rates to the n-atomic level respectively and A₃₂ is the spontaneous emission rate.

The wavelength-dependent H$~\alpha$ line optical depth was assumed to be:

$$\tau_{\lambda} = \tau_{\rm o}\Phi(\Delta\lambda)$$ (6)

where $\Phi$ is the Voigt function given in the approximation suggested by Dobrichev (1984) and recommended by Piskunov (1992). The wavelength displacement $\Delta\lambda$ is produced by the total velocity of the ring projected along the line of sight $\pm\mu V_{\rm r}\pm(1-\mu^2)^{1/2}V_{\Omega}$ [ $\mu = \cos$ (radial direction, line of sight)] where the signs are chosen according to the sector of the ring facing the observer and whether it concerns the front or rear part of the ring.

From (5) we see that the radiation field of the underlying star determines the value of the source function, so that $\eta^{1/2}B^* \simeq$ 0.05. The rotationally broadened photospheric absorption line profile is obtained using the flux $\rm H~\alpha$ calculated for $V \sin i = 0$ km s^-1 from Kurucz' codes and using the fundamental stellar parameters presented in Table 5. The fit of each observed mean $\rm H\alpha$ line profile (Fig. 11) is then obtained using R, H, $V_{\rm r}$, $V_{\Omega}$ and $\tau_{\rm o}$ as free parameters. $V_{\rm r}$ determines the eventual asymetry seen in the emission peaks. It was determined only for the 1996 line profile; in other cases we considered $V_{\rm r} = 0$ km s^-1. The separation of the emission peaks is determined mainly by $V_{\Omega}$, but it also depends on $\tau_{\rm o}$. The full width of the emission line on its half intensity and on the low side of wings approaching the continuum level is fixed by R and $\tau_{\rm o}$. For a given value of R, H and $\tau_{\rm o}$ determine the emission intensity in the peaks. The ratio H/R and $\tau_{\rm o}$ establish the depth of the central absorption. The fits thus obtained are shown in Fig. 16 (dashed lines) and the corresponding CE parameters are given in Table 6. We considered the 1998 H$\alpha$ emission line profile as essentially the same as in 1997, so we did not produce a fit for this line.

Figure 12: H$\alpha$ V/R ratio between Mar. 12 and Mar. 23, 2000.

Figure 13: H$\alpha$ peak separation between Mar. 12 and Mar. 23, 2000.

Figure 14: Time evolution of mean absolute deviations of line profile variations detected in He  I$\lambda$6678 Å in four periods, 1996, 1997, 1998 and 2000. Notice the increase of variability beyond the limits of $V\sin i$ from 1996 to 2000, in apparent correlation with the strengthening of emission in the H$\alpha$ line.