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Astron. Astrophys. 337, 757-771 (1998)

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7. Discussion

7.1. Prominence clouds

The observed evolution of transient A reminds that of the absorption features detected in the case of HK Aqr (Byrne, Eibe & Rolleston 1997). It agrees well with the expected behaviour of a prominence co-rotating cloud during its transit across the stellar disk. An estimate of the cloud location in the stellar atmosphere can be derived from the observed variation of its radial velocity. This has been done by following a specific formulation developed by VEB98. In that work it is shown how to estimate the possible heights and latitudes for a co-rotating cloud, on the basis of its radial velocity evolution with time and period of visibility in front of the stellar disk. A brief outline of the method is given below in order to introduce some parameters that are going to be discussed later. For more detailed description the reader is referred to VEB98.

VEB98 assume that the absorption transients are caused by ideal, point-like clouds in the stellar atmosphere and thus ignores possible effects due to their sizes. In addition, the motion of the clouds is restricted by the condition of co-rotation with the star at some fixed distance above its surface, i.e. the system is rotating as a rigid body. Constraints on the cloud height ([FORMULA]) and co-latitude ([FORMULA]) can then be derived from the variation of its measured radial velocity (v) with time. This should be linear when the cloud is seen near disk centre, verifying:


where [FORMULA] is the stellar angular velocity and [FORMULA] is the cloud's spheric coordinate, [FORMULA]. The origin of [FORMULA] is set at the stellar disk centre. K is defined as [FORMULA], which is a constant quantity for a given cloud. The K value may be, therefore, estimated from the observed radial velocity evolution and is used to derive some limits for [FORMULA] and [FORMULA].

In order to detect the cloud in absorption, its projected position must be within the stellar disk. For a given inclination of the star, this only occurs for certain combinations of [FORMULA] and [FORMULA], thus providing a second relation to estimate the location of the cloud.

Analytically, it is impossible to determine independently both values, [FORMULA] and [FORMULA]. VEB98 introduced a contour technique which allows to constrain them from the observations. Contours of K as a function of [FORMULA] and [FORMULA] will be used here in order to establish limits.

The other absorption transient events appear to show more complex behaviour and are re-examined to see whether they can also be associated to similar phenomena.

7.1.1. The cloud detected as transient A

Fig. 9 shows the radial velocity variations observed on each night. Linear least-squares fits to the data are presented in Fig. 12. Results for different nights are in generally good agreement. Peculiar to the June 26 observations is the systematic redshift that was found in the first five velocity measurements. This would affect significantly the results of the fit. From Figs. 3 and  9 it is seen that the absorption appears weaker at this time, being more difficult to detect. It is not possible to determine whether this is just an effect of the lower signal-to-noise of the observations at that night or it represents a real variation, perhaps due to a larger influence of the emission in progress (see Sect. 6.2). In any case those points were not included in the fit. The crucial values for the treatment that will follow are those close to zero velocity.

[FIGURE] Fig. 12. Observed variation of the cloud (transient A) radial velocity (RV) with phase for the nights 25 June (+), 26 June ([FORMULA]), 27 June (o). The straight lines are the linear fits: 25 June (-), 26 June (...), 27 June (- - -). See text for a definition of parameters

The results from these fits are listed in Table 3. It can be seen that the parameters derived from the different nights are consistent and agree extremely well within the calculated errors. Ingress and egress occur within a short fraction of the rotational period, suggesting the feature is at a considerable distance above the surface if in rigid rotation with the star. Clearly it must be over the bright transient that has been fully described in Sect. 6.2.1as the discrete propagating emission is completely obscured at these phases.


Table 3. The main parameters of the cloud identified as transient A.

Assuming an inclination of [FORMULA], constraints on the height and latitude of the cloud are set by applying the method developed by VEB98, which has been briefly outlined above. The average of the three K values in Table 3 is used to determine the K-contour corresponding to the cloud in the [FORMULA] diagram shown in Fig. 14. This diagram indicates the domain of possible heights ([FORMULA]) and co-latitudes ([FORMULA]) for the co-rotating cloud detected as transient A (thick solid line contour). Limits to the cloud coordinates, [FORMULA] and [FORMULA], can also be derived analytically for an inclination of [FORMULA] applying the formulae derived in VEB98. Results obtained in this way are [FORMULA] and [FORMULA] or, equivalently, [FORMULA]75-[FORMULA], for the northern latitude solution. In any case, the cloud is found to be well below the co-rotation radius, but at a very large distance compared to solar prominences.

The location of cloud A suggests interesting aspects related to the clouds formation and stability. First, the cloud latitude is reasonably constrained and not far away from the equatorial plane. This may constitute an important condition favouring prominence formation. VEB98 investigated the mechanical forces governing the equilibria of neutral material confined in the stellar magnetic field at some height above the chromosphere of rapidly-rotating stars. In their analysis it is assumed that at sufficiently large distances from the star, the effective component of the magnetic field is the dipole component. Under this assumption it is found that force equilibrium on a field line is possible only in the equatorial plane. Second, the fact that cloud A lies below the co-rotation radius is also consistent with the picture obtained in the case of the rapidly rotating late-type star, HK Aqr (Byrne et al. 1996, VEB98). Therefore, the prominence formation mechanism invoked in Collier-Cameron's model (1988) must be excluded in these cases.

In their review of quasi-static coronal loop models, van den Oord & Zuccarello (1996) show that loops having a temperature inversion at their apices can also be generated by decreasing the heating at the summit or increasing their cross-sectional area. In this new scenario, however, temperature reversals are not restricted to heights above the co-rotation radius.

Finally, evidence for this cloud is not found in any of the other chromospheric lines, which prevents further investigation of the physical conditions of the plasma contained in the prominence. In particular, with the H[FORMULA] observations alone it is impossible to determine both the kinetic temperature and the turbulent velocity from the line-broadening.

7.1.2. Transient B

Transient B is very interesting because of its apparent variation from night to night. The fact that it is seen as a deep and blueshifted absorption on the first night could imply material is moving outward with significant mass loss for the star. Its behaviour on the second night is in better agreement with the symmetric track followed by a co-rotating source while on the last night it becomes more enhanced in the red, suggesting receding absorbing material in front of the stellar disk. If due to a circumstellar structure, it could not be very high in the atmosphere as inferred from the relatively long disk-crossing time. In addition, from Fig. 3 it is seen that B26 shows less contrast than A26 against the concurrent emission component in the red. This may be due to changes in plage brightness and/or differences between the absorbing power of both transients. However, care must be taken when speculating about these possibilities since the signal-to-noise ratio on the night of June 26 is lower.

The amplitude of the radial velocity of transient B is very hard to estimate due to simultaneous excess emission in the profiles. However, based on the striking symmetry of the velocity track exhibited on June 26 with an approximate amplitude of 50 km s-1, an estimation of its latitude was derived assuming a surface feature. In this case,


where [FORMULA] is the latitude of the feature and [FORMULA] is the amplitude of its radial velocity. Therefore, an amplitude of 50 km s-1 would imply a latitude, [FORMULA].

Fig. 13 shows the results obtained in an attempt to determine the radial velocities from gaussian fits to the H[FORMULA] ratio profiles. The crosses are for measurements on June 26 and the circles are for June 27. It can be seen that on June 27 the velocities are systematically redshifted and scatter increases towards the end of the event, presumably due to blending of more than one component as suggested above. Points for the other night correspond to the main component resolved in the profiles, which has been identified by comparison with Fig. 3 (B27). Also shown in Fig. 13 are the straight-line fits to the data. A considerable change of slope between the two nights is obvious. If the transient was interpreted in terms of one and the same feature, this would indicate either some variation in height or the development of velocity fields between the two nights.

[FIGURE] Fig. 13. Observed variation of the transient B radial velocity (RV) with phase for the nights 26 June (+) and 27 June (o). The straight lines are the linear fits: 26 June (-), 27 June (- -)

If the information from the linear fits and the observed phases of ingress and egress was used to estimate the location of such a feature according to the model of a co-rotating point source, one would find the following. The observations on June 26 are consistent with a cloud that co-rotates with the star at a relatively small height, [FORMULA]1.40-1.72R*. The data from the following night implies, however, a lower height, in the range 0.88-1.33R*. The domain of allowed heights and latitudes in both cases is represented graphically in Fig. 14.

[FIGURE] Fig. 14. Diagram showing the estimated position of the cloud associated to transient A (thick solid contour) and the ones that would correspond to transients B27 (left thin contour) and B26 (right thin contour). Note that if the interpretation in terms of a co-rotating point-like model for this feature is valid, a significant change of height between the two nights would have taken place. To construct this diagram an inclination of [FORMULA] was assumed (see Sect. 2). The thin vertical line marks the position of the co-rotation radius in the equatorial plane. See VEB98 for more details on the interpretation of this diagram

A possibility that comes to mind to explain the observed evolution of transient B is that it represents the development of a low-lying prominence-like structure. In this scenario the systematic blueshifts and redshifts observed on June 25 and June 27, respectively, may be indicative of the velocity fields involved in the formation of prominence clouds. For comparison, the escape velocity of the star at the surface is [FORMULA]600 km s-1.

7.1.3. Transient C

The behaviour of transient C appears to be more complex and is harder to interpret. On June 25 (C25 in Fig. 2) the initial concurrence of blueshifted and redshifted absorption components in the profile suggests the simultaneous occurrence of both upflows and downflows of material in the line-of-sight. In particular, the emission enhancement that is observed to precede the blueshifted absorption at [FORMULA]0.98 supports an interpretation based on mass-loss events. As described in Sect. 6.1.3, the specially strong absorption that is seen in the red at these phases may actually consist of two components merged into one. It is important to note that in this case the reliability of the velocities from gaussian fits is more doubtful due to possible effects caused by the superposition of bright emission and redshifted absorption in the profile.

On the other hand the propagating feature partially observed on June 27 near the same phases (C27 in Fig. 4) argues for the possible presence of a more stable co-rotating structure. As it occurred near the end of the series only six spectra could be obtained. Velocities measured by fitting gaussians to the absorption fit well in a linear curve going from [FORMULA]-85 to [FORMULA]-27 km s-1. If this was interpreted as a co-rotating cloud it would be at a height close to 4R*. More observations are required to confirm the nature of this transient.

7.2. Plage activity

Some of the observational facts summarised in Sect. 6.2.1for transient a can be explained in terms of discrete bright regions close to the surface of RE 1816+541, which are ascribed to solar-like plages.

First, the small velocity width of the emission suggests it may arise in a localised centre of activity on the stellar surface. The duration of the transient and the observed radial velocities are consistent with this view. Detection of the feature on three successive nights indicates also that the phenomenon seen is not associated to an ephemeral brightening but to longer-lived structures. Finally, the interruption of the emission event by the prominence cloud provides additional support for the idea that the emission feature is located on or near the stellar surface, whereas the cloud is at a greater height and is seen in projection onto it.

The velocity variations of the plage can be used to determine its location, following a similar method to that derived for the study of prominence clouds (VEB98). The major difference in this case is that a bright structure does not have to be in projection on the disk to be detected. If the emission region is at some height above the surface, its associated feature should still be visible outside the stellar disk and at velocities exceeding [FORMULA]sini.

The linear least-squares fits to the radial velocity variations are shown in Fig. 15. Cloud parameters derived from these fits are shown in Table 4. Note that the plage was not visible at zero velocities,when it is supposed to cross the centre of the disk, due to occultation by a prominence cloud at larger heights. Measurements done near those phases are more uncertain and were not included in the fits. Although a linear approximation of the RV as a function of time is less reliable near ingress or egress, those are unfortunately the only data available.

[FIGURE] Fig. 15. Observed variation of the plage radial velocity (RV) with phase for the nights 25 June (+), 26 June ([FORMULA]), 27 June ([FORMULA]). The straight lines are the linear fits for the nights on which reasonable coverage of the transient was achieved: 25 June (-) and 26 June (- -). For comparison, predicted radial velocity curves of an absorbing point-like source in co-rotation with the star at distances close to the surface are overplotted. Note that radial velocities are always relative to the stellar centre of mass. Three different cases were considered, varying the height (R) and the co-latitude ([FORMULA]) of the feature: R = 1.0R*, [FORMULA] (curve 1); R = 1.0R*, [FORMULA] = [FORMULA] (curve 2); R = 1.3R*, [FORMULA] = [FORMULA] (curve 3)


Table 4. The main parameters of the plage (transient a)

The diagram in Fig. 16 shows the range of possible heights and latitudes for the plage, as determined by using the K-contours on each of the two nights' data providing a good coverage of its transit across the disk. In this plot, heights are shown in units of the stellar radius. It is seen that results for the two nights are in good agreement.

[FIGURE] Fig. 16. Same as Fig. 14 but for the plage-like region observed on RE 1816+541. The two thin contours show the possible solutions for the height and latitude of the feature in the stellar atmosphere, using data for the nights of June 25 and June 26 (see Table 4)

In Fig. 15 the linear fits and the data points are compared with the radial velocity curves predicted for plages located within the limits derived above and centred at [FORMULA]0.25. These were computed on the assumption that the plage can be described by a point source of emission in co-rotation with the stellar surface, at height R and co-latitude [FORMULA]. In this case its radial velocity (RV) is given by (see Sect. 7.1):


Three cases are considered varying R and [FORMULA] within the limits derived above:

  1. R=1.0R*, [FORMULA]=[FORMULA] (curve 1)

  2. R=1.0R*, [FORMULA]=[FORMULA] (curve 2)

  3. R=1.3R*, [FORMULA]=[FORMULA] (curve 3)

These fits cannot reproduce the observed asymmetry in the extreme radial velocities. An asymmetry effect could derive from intrinsic motion of the emission source. It could also result from temporary activation of the plage region at some phases (see below). On the other hand, the fit corresponding to the first night's data suggests a phase shift with respect to the data for the following night although it gives a similar slope and, therefore, similar results in Table 4. This effect is presumably due to the extreme blueshifts measured near [FORMULA]0.0 on June 25 and the change of slope near the end of the event on the same night, which coincides with a transient chromospheric brightening. The fact that H[FORMULA] emission is also enhanced at the closing phases on June 27 (a27 in Fig. 4) suggests a possible activation of the plage region at the end of its disk transit. Evidence of sudden brightening at these phases is also seen in the Ca II and He I D3 lines. Because the same effect has been detected on different nights and has a short duration, it cannot be attributed to a flare. An alternative explanation could be in terms of an active longitude at which the emission feature a is enhanced. It would be very interesting to investigate spot activity on this star and study the distribution of its spots in order to support this idea. Observational evidence for preferential longitudes favouring spot and chromospheric activity has been reported in Fernández & Miranda (1998).

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© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998