Line doubling phenomena

The most important observationnal characteristic of BWVul is the presence of two line doubling phenomena which occur at each velocity discontinuity. Figure represents a series of spectra before and affter the stillstand.

  

Figure: Spectra of the $\lambda \lambda$4553 Siiii line for the night August 1$^{\rm st}$, 1994. The pulsation phase $\varphi$ is given on the right of each spectrum. The left column concerns spectra obtained during the first velocity discontinuity (maximum inward atmospheric motion), whereas the right column displays spectra during the second discontinuity (maximum outward velocity). The spectra are computed in the stellar rest frame (see text), the vertical line representing the laboratory wavelength

To interpret these line profiles, it is important to compute the spectra in the stellar rest frame i.e., the systemic velocity $\gamma$ of the star must be calculated. This is usually done by an integration of the velocity curve over one pulsation period. But this supposes that the shape of the radial velocity curve is well determined i.e., the number of spectra is large enough. Because at some phases a line doubling appears, three kind of velocities can be measured. First, when they are visible, we can fit each line component (the blueshifted and the redshifted ones) by a gaussian to obtain their velocity (Figurea) or a single gaussian fit over the whole profile whatever its shape (Figureb).

  

Figure: Heliocentric radial velocity curves as a function of pulsation phase. a: Velocites associated respectively to the blue (dots) and the red (circles) line components. b: Mean velocity curve, obtained with a single gaussian fit over the whole profile whatever its shape. In both cases, the horizontal dashed line represents the $\gamma$-velocity axis

Contrary to the double gaussian fit, only the single one provides a mean velocity of the motion of the atmospheric layers. The physical meaning of this average velocity is weakly informative on the dynamics of the atmosphere. Thus, the $\gamma$-velocities which can be deduced from these three velocity curves (Figure ) are quite different. It is around -20km.s^-1 for the blue component, 4km.s^-1 for the red one and -11km.s^-1 for the whole profile. For the second night (August 8$^{\rm th}$), we respectively find -14km.s^-1, 1km.s^-1 and -10km.s^-1.

At phase $\varphi=0.55$, the Siiii line profile has the more symmetrical and narrow shape and hence can be interpreted as the phase of the largest atmospheric extension, when the velocity field within the line formation region may be negligeable. Thus, its associated radial velocity (- 7.6km.s^-1) can be considered as close to the systemic velocity. For the night August 8$^{\rm th}$, we obtained -10.8km.s^-1. Thus, we have assumed hereafter that the systemic velocity of BW Vul can be estimated by the average of these two evaluations over our two observation nights. The adopted value $-9.2\pm\,1.7$km.s^-1 was used to compute the spectra in the stellar rest frame. This value is not very different from the average (-10.5km.s^-1) of the $\gamma$-velocities for the whole profile.

Our spectra follow the same general pattern as previous observations. During the inward atmospheric motion, the profile becomes slightly asymmetric ($\varphi=0.67$) on the blue side and then more and more complex, until two components can be clearly distinguished ($\varphi=0.87$). In the meantime, the red component decreases until disappearing ($\varphi=0.96$). Note that the blue component is slightly redshifted until $\varphi=0.87$,while it is close to a zero-velocity at $\varphi=0.90$, 0.93 and 0.96. If the red component is considered alone, it seems to be more and more redshifted, regularly, during the whole spectra set. One can easily imagine a straight line joining the cores, at the different phases.

This behavior is similar after the stillstand, except that the doubling is not resolved and is much shorter (between $\varphi=1.04$ and 1.07). However, this time, the blue component is really blueshifted and the red one is at zero-velocity. Then, from $\varphi=1.10$ to $\varphi=1.16$, the profile is symmetric, and blueshifted. Finally, from $\varphi=1.16$ until $\varphi=1.30$,the profile slowly moves to the red and becomes more and more sharper. This is well illustrated on Fig.a: from $\varphi=0.15$ to 0.64, the velocity curve is smooth. Then, the asymmetric profile can be fitted with two gaussians, providing for both components an increasing velocity, the red component being in the continuity of the velocity curve, while the blue component decelerates.

When the two components are visible, the blue curve undergoes the first discontinuity which shifts the velocity to zero by 70km.s^-1, while the red curve vanishes at $\varphi=0.96$, inducing a gap of about 180km.s^-1. Moreover, it appears that the stillstand is not really constant, the velocity, after a very short expansion, being slightly positive. Then the second doubling induces the second velocity discontinuity, affecting first the blue component, with a gap around 80km.s^-1. After this violent expansion, the velocity seems to follow a ballistic motion.

This behaviour is nearly, but not exactly, the same in the upper atmosphere where H$\alpha$ is formed. Indeed, because the Siiii line has a larger ionization and excitation potential compared to that of H$\alpha$, it is thought to be formed lower in the stellar atmosphere (see Sect.4). Hence, the physical conditions may be different between the two line formation regions. Figure represents, for the same phases as Fig., the H$\alpha$ spectra.

  

Figure: Same as Fig.1, but for the H$\alpha$ line. Note that the velocity scale ($\Delta \lambda/\lambda_{0}$, where $\lambda_{0}$is the laboratory wavelength) is the same as in Fig.1. The constant small absorptions present through the profile are caused by telluric H₂O lines

Of course, the H$\alpha$ profile being very broad, it is not as easy as in the case of the Siiii line to appreciate at which phase the profile becomes asymmetric, and even to distinguish the line doubling components. Only spectra at $\varphi=0.90$ and 0.93 show such an evidence. Furthermore, the second doubling phase can only be suspected at $\varphi=1.10$.However, it seems that the amplitude of the doubling phase is comparable for both Siiii and H$\alpha$ lines. The only difference between them is that the doubling discussed above for the Siiii line happens slightly later for the H$\alpha$ one ($\Delta\varphi \simeq 0.03$).

  

Figure: Same as Fig.1, but for the night August 8$^{\rm th}$

We have compared these spectra with those obtained on night August 8$^{\rm th}$ which are represented, for the Siiii line, on Fig.. The most striking difference between the two nights is that the line doubling is poorly seen during the second night. This is particularly true on phase $\varphi=0.89$.Also, during the first discontinuity, the spectra obtained on August 8$^{\rm th}$ are much more symmetric (until $\varphi=0.74$). The same velocity curves as in Fig. are displayed in Fig..

  

Figure: Same as Fig.2, but for the night August 8$^{\rm th}$.Note that axis scales are the same as in Fig.2

One can see that the red curve is not a straight line as in Fig. but decelerates at nearly the same amount as the blue one. During the first velocity discontinuity, the velocity jump associated to the red curve is about 130km.s^-1, and that associated to the blue curve is around 70km.s^-1. As for the second velocity discontinuity, the gap is larger for the red component, being around 100km.s^-1.