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Astron. Astrophys. 353, 666-690 (2000)

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6. Chromospheric activity

6.1. Chromospheric emission in the Ca II [FORMULA] line

Linsky et al. (1979) demonstrated that the flux level in the central core of the Ca II [FORMULA] line is a sensitive function of the level of stellar chromospheric activity as deduced from other observational sources, e.g. the core emission reversals in the H and K resonance lines of Ca II. Shine & Linsky (1972, 1974) had already discussed this sensitivity in the solar case in quiet regions compared to regions of various activity levels. In their observations of the Ca II [FORMULA] line in a sample of 50 F8-K2 stars of all luminosity classes (at a resolution of 0.14 Å), Linsky et al. (1979) find no evidence for any central self-reversed emission feature (contrary to what is observed for bright plage regions in the Sun), but a clear filling-in of the central core in chromospherically active stars. They derive chromospheric radiative loss rates in this line which correlate well with rates in the Ca II H and K lines as well as with other activity indicators. However their non-LTE calculations of the Ca II [FORMULA] line, for a simplified 3 levels plus continuum model Ca II ion and for different empirical model chromospheres, predict profiles which are not in good agreement with observed data. This happens even in the line wings which should be formed in conditions close to LTE and are consistently well represented by LTE synthetic profiles. According to J.J. Drake (1999, private communication) this unsatisfactory agreement may result from a poor choice of stellar parameters and to inappropriate model photosphere temperature structures.

Cayrel et al. (1983) estimated the level of activity in two solar type Hyades dwarfs, VB 64 and VB 73, from observations of the Ca II IRT lines. They carried out non-LTE calculations using three VAL model solar chromospheres (Vernazza et al. 1981) and a 5 levels plus continuum model Ca II ion. They obtain line shapes in better qualitative agreement with the observations, which allow them to estimate the average activity of the Hyades dwarfs as equivalent to that of solar very bright network elements. Herbig (1985) used as a secondary activity indicator an index of chromospheric emission in the three IRT lines and showed this index to correlate very well with another index measuring the emission in the core of [FORMULA]. Similarly Soderblom et al. (1993b) used the emssion in the cores of [FORMULA] and Ca II [FORMULA] to investigate the activity of the solar-type stars of the Pleiades.

The relation between the flux in the core of the Ca II IRT lines and stellar chromospheric activity has also been studied empirically by Foing et al. (1989) on higher resolution observations of a sample of 16 F9-K4 dwarf and subgiant stars. Again the central depths of these lines are found to be very sensitive discriminators of stellar activity.

More data on the central depth of the [FORMULA] line in dwarf or subgiant stars are scattered in the literature in tabular or graphical form, mostly in papers by the groups headed by G. Cayrel de Strobel or by G. Smith. Among the profiles published for active stars, a few do show central emission reversals like [FORMULA] (Cayrel de Strobel et al. 1994) and HD 17925 (Cayrel de Strobel 1992); some others show conspicuous shoulders in their core, such as [FORMULA] (Drake & Smith 1993) or [FORMULA] (Ruck & Smith 1995). This is contrary to the findings of Linsky et al. (1979), owing probably to the lower spectral resolution and photometric accuracy of their observations. Published central depths of the [FORMULA] line are collected in Table 4. Data for two specially well studied giants (Arcturus, [FORMULA], and Pollux, [FORMULA]) have been added to the table. The stars in Table 4 are all bright stars which have been submitted to detailed spectroscopic analysis. The "spectroscopic" effective temperatures of the stars, most often given in the references quoted in the table, are listed in column 2, and the normalized central depths of the [FORMULA] line, D, are found in column 5. High chromospheric activity is often found in young stars; since high photospheric lithium abundance is also often associated with young stellar age, this abundance has been given in column 7 for comparison. Column 8 indicates whether the star is considered, on other grounds, as quiescent (a=0) or active (a=1).


[TABLE]

Table 4. Observed central depressions of the Ca II [FORMULA] line found in the literature, in relation to the Mount Wilson [FORMULA] activity index.
References:
(1) Cayrel de Strobel et al. 1994; (2) Cayrel de Strobel 1992; (3) Cayrel de Strobel et al. 1989; (4) Cayrel de Strobel & Bentolila 1989; (5) Chmielewski 1999 (in preparation); (6) Chmielewski et al. 1995; (7) Chmielewski et al. 1992; (8) Chmielewski et al. 1991; (9) Cristaldi 1992; (10) Drake & Smith 1991; (11) Drake & Smith 1993; (12) Foing et al. 1989; (13) Friel et al. 1993; (14) Linsky et al. 1979; (15) Perrin et al. 1988; (16) Ruck & Smith 1995; (17) Smith et al. 1992; (18) Smith & Drake 1990; (19) Smith & Drake 1987; (20) Smith & Ruck 1997; (21) Cayrel et al. 1983.


Apart from the 0.14 Å resolution vidicon data of Linsky et al. (1979), all the other measurements of the central depths come from modern Reticon or CCD, high signal-to-noise (S/N) ratio spectra obtained with the Mc Donald 2.7 m, CFHT, ESO CAT-CES or OHP Aurélie coudé spectrographs in their higher resolution modes, which means that they are not very homogeneous. For some stars, several different measurements are available showing a significant dispersion, which can be noted already in the data of Linsky et al. (1979) or Foing et al. (1989). This dispersion may have a number of origins such as: scattered light in the spectrograph, resolution and S/N ratio effects, continuum location and stellar rotation rate. However, it is known that chromospheric emission varies with time in most of the stars, even the quietest. Repeated measurements on solar flux spectra show a typical dispersion of 0.015 which is similar to that of the other quiescent stars. The most active stars exhibit a much higher dispersion which cannot be explained in terms of instrumental effects only, and thus reflects real time variations in the level of activity of individual stars. Such variations, attributed to magnetic activity variations and stellar cycles, have been observed in the Ca II H and K central emission and have long been monitored and documented, especially at Mount Wilson (see references in next section). The value of the line depth given in Table 4 is an average of all measurements available; since there are only few measurements for each individual star, sometimes these averages may not be too well defined.

Fig. 14 shows the central depth as a function of effective temperature. There appears to be a clear dividing line between active and quiescent stars which shows some slope with effective temperature. A similar separation between active and quiescent stars was already observable in Fig. 4 of Foing et al. (1989).

[FIGURE] Fig. 14. Mean observed depressions at the center of the [FORMULA] line as a function of effective temperature. Filled squares represent active dwarf stars and open squares stand for quiescent dwarfs. The three Hyades dwarfs, VB 52, VB 64, VB 73, and 9 Cet (HD 1835, a member of the Hyades moving group) are represented by filled triangles. The Sun is represented by an open circle and the subdwarf Gmb 1830 by a cross. The "plus" signs correspond to evolved stars which, in this sample, are all reputed to be quiescent.

6.2. Relation with the HK emission fraction

For many years, astronomers at Mount Wilson used the Ca II H and K lines as indicators of chromospheric emission. Vaughan & Preston, 1980 (VP) started an extensive survey of HK emission among northern late type dwarfs within 25 pc. They measured a chromospheric emission index, S, which is the ratio of the flux in the cores of the H and K lines to the flux in two 20 Å continuum windows on opposite sides of H and K. A definite time variability of the S index is found for almost all the stars. For many of them a clear rotational modulation is detected, leading to precise rotation periods. Noyes et al. (1984) studied the relationship between the rotation period and the HK emission strength. They characterized the emission strength by calculating, from the value of S, the ratio [FORMULA] of the HK flux to the stellar bolometric flux, which is corrected for the photospheric contribution to the measured HK flux to yield [FORMULA], a pure measure of the chromospheric emission. They could derive a tight empirical relation between the [FORMULA] emission strength and the Rossby number, i.e. the ratio of the rotation period to the convective turnover time. This relation was used by Soderblom (1985) to investigate the distribution of chromospheric emission and of angular velocities [FORMULA] of 177 nearby solar type dwarfs of the VP survey (northern hemisphere).

Henry et al. (1996) extended the VP survey to southern hemisphere solar type stars, providing [FORMULA] values for 746 targets. The histogram of the [FORMULA] values (Figs. 5 and 8 of Henry et al.) shows a clear bimodal distribution, which had already been noted in the northern hemisphere survey by Vaughan & Preston (1980) and allows a rather clear separation between chromospherically active stars and low activity stars. A majority of low activity stars are distributed in a narrow peak around [FORMULA]. A second group of stars, comprising about 30% of the sample, is distributed around a secondary mode at [FORMULA]. Between the two modes, Henry et al. confirm the existence of the "Vaughan-Preston gap" (rather, a transition region), where very few stars are found with intermediate chromospheric emission fractions in the range [FORMULA]. Henry et al. locate the dividing line between active and non-active stars at [FORMULA], although the minimum between the two modes is situated rather around a value of -4.67. The distribution of the chromospheric emission fractions must be interpreted bearing in mind the basic time variability of chromospheric emission. Typically, solar [FORMULA] monthly means vary between -4.78 and -5.00. At the peak of its activity cycle the Sun may have [FORMULA] and its lowest activity during the Maunder Minimum corresponded to [FORMULA]. Henry et al. (1996) argue that, in their time variation, stars very seldom slip from one mode into the other: the stars rather oscillate within the mode to which they belong. We might therefore consider that we are dealing with two groups showing distinct behaviours in their activity cycles. Henry et al. also identify a secondary transition zone at [FORMULA] separating very active stars (of which a significant fraction are close binary systems), as well as a distinct population of very quiescent solar type stars which, they suggest, may be currently in a Maunder Minimum type phase.

For most of the stars in our Table 4 measurements of the HK chromospheric emission fraction [FORMULA] are found in the papers of Henry et al. (1996), Soderblom (1985) or Noyes et al. (1984). For the three Hyades dwarfs [FORMULA] values are found in Duncan et al. (1984). For the visual double star [FORMULA] A+B, a value of [FORMULA] is found only for the integrated light of the two components A+B. As B is the very active component whereas A shows a rather low activity (Cayrel de Strobel et al. 1994), the [FORMULA] value has been attributed to component B in Table 4. The average values of [FORMULA] are given in column 6 of the table. Fig. 15 shows the Ca II [FORMULA] line central depth, D, versus [FORMULA], with vertical and horizontal bars joining extreme values of D, as well as of [FORMULA], found in the literature for each star (they should not be interpreted as error bars). To be really meaningful the average values and the variability bars should result from long time monitoring of the stars, which is not the case for most D and many [FORMULA] values. Despite this drawback, we find a good correlation between the average values of D and [FORMULA].

[FIGURE] Fig. 15. Central depression of the [FORMULA] line versus the HK emission fraction index. The horizontal and vertical bars connect the extreme values recorded for each parameter when several measurements can be found in the literature. An average relation between the activity indices is shown by the continuous curve. A few interesting stars are identified.

A few interesting stars are identified in Fig. 15. This figure illustrates, on our limited sample with unclear selection effects, the conclusions drawn by Henry et al. (1996), namely that the stars group into two distinct modes, with only very few stars showing an intermediate level of activity.

Considering the variability and inhomogeneity of the data, a mathematical description of the relation between D and [FORMULA] should be as simple as possible. Clearly a linear relation is not adequate and some curvature is required. A simple parabolic fit gives a good overall representation of the data but shows a minimum at [FORMULA] which is not physically meaningful (this is near the maximum of the distribution of the low activity stars). As the level of chromospheric activity decreases, the central depth of the [FORMULA] line should saturate to a value not reaching 100%, which may depend on the stellar atmospheric parameters; the distribution of [FORMULA] for low activity stars reaches zero at [FORMULA] and there are only very few stars with [FORMULA]. This is why the relation between D and [FORMULA] is expected to be rather flat at this limit. It seemed therefore reasonable to represent this relation by a parabola constrained to have its minimum at [FORMULA]. If [FORMULA] and [FORMULA], such a parabola is described by the formula:

[EQUATION]

A least-squares fit to the data, eliminating stars discrepant by more than [FORMULA], yields a = -0.496 and c = -12.12, with a scatter [FORMULA] = 0.022, and the resulting curve is drawn in Fig. 15. Attempts to fit the data by a branch of hyperbola appeared less convincing. Inspection of Fig. 15 confirms that D is a good discriminator between low and high activity stars. Fig. 14 suggests that, in the variable D, the location of the boundary between low and high activity stars changes with the stellar effective temperature and the dividing line thus seems to have a significant slope in the diagram. In Fig. 15 the symbols representing the stars are coded according to their effective temperature (see insert). Unfortunately, given the limited size of the sample and limited accuracy of the data, we cannot see any obvious temperature effect on the mean relation between the two variables.

6.3. Discussion

The star [FORMULA] belongs to the rare population of extremely low activity stars suggested by Henry et al. to be in a Maunder Minimum type phase: the [FORMULA] line in this star is also the deepest ever reported in the literature (except for the cool giant Arcturus). A fit by a parabola constrained to have a minimum at [FORMULA], instead of -5.10, does not produce a significantly different representation.

The location and variability of the high velocity subdwarf Gmb 1830 in Figs. 14 and 15 is not among the least active stars, which might suggest that this very old, slowly rotating Population II star has kept some degree of chromospheric activity. This, however, raises the question of the sensitivity of our activity indicators to the stellar parameters (Drake 1999). Clearly, changes in gravity or abundance will affect the opacity and depth of formation of the lines. Figs. 12 and 13 show that, if the line core of [FORMULA] were formed in LTE, the central depth of the line would be shallower for decreasing metallicities and deeper for lower gravities. The line might be shallower in Gmb 1830 just on account of the lower calcium abundance. A realistic treatment of the problem would require non-LTE computations that go beyond the scope of this paper.

Two stars on the diagram, [FORMULA] and HD 131977, stand out as discrepant with the overall representation, lying at more than [FORMULA] under the mean relation: they belong to the high activity group according to their [FORMULA] whereas the depth of their [FORMULA] line is comparable with that of lower activity stars. This discrepancy may have to do with the fact that, as seen in Fig. 14, they are at the low effective temperature end of our sample; on the other hand, [FORMULA], which has a similar temperature, is not discrepant in Fig. 15. Yet, Erdelyi-Mendes and Barbuy (1991) have shown the growing pollution of the Ca II IRT spectral region by lines of the molecules CN and TiO at temperatures lower than about 4500 K; it may seriously affect the localization of the continuum (see, in particular, their Fig. 1c). Unfortunately, raising the continuum would go in the "wrong" direction, making the [FORMULA] line still deeper!

The above representation describes only first order effects. The treatment of the effective temperature effects would require more homogeneous data with averages based on long time baselines, and would represent a heavy observational load. The chromospheric HK emission fraction, [FORMULA], is derived by subtracting an estimated photospheric contribution from the total emission fraction [FORMULA]. This correction is carried out on the basis of the [FORMULA] colour index, assuming a unique relation between [FORMULA] and [FORMULA]. This photospheric correction could thus be somewhat improved. For a direct comparison between [FORMULA] and the depth D of the Ca II [FORMULA] line, this last parameter ought to be transformed into another chromospheric emission fraction, also corrected for the effects of the basic atmospheric parameters. Such a transformation is not easy to devise. A purely theoretical approach is beyond reach at the present time. It would require realistic non-LTE computations based on adequate model photospheres (remember also the upper depth-scale truncation problem mentioned above in Sect. 4). An empirical approach is also difficult since it is established that there are no really steady, chromospherically inactive stars. Practically, the Maunder-Minimum stars in the sample of Henry et al. could be used as references if they turned out to provide a dense enough network. Most of the stars in this group are subgiants of luminosity class IV. The [FORMULA] colours of all the very quiescent stars ([FORMULA]) in the sample of Henry et al. fall in the range [FORMULA], roughly corresponding to temperatures [FORMULA] [FORMULA] [FORMULA]. There is thus unfortunately no star in this sample which could be used as a convenient zero-activity standard in the lower temperature range, [FORMULA] [FORMULA]. Note that [FORMULA] is not defined either for [FORMULA].

Other stars stand abnormally high above the mean curve in Fig. 15. The star [FORMULA] lies at 3.6[FORMULA] above the mean relation. Its lines are significantly rotationally broadened ([FORMULA]). It has been observed only once in each of the coordinates. More observations are required before definite conclusions can be drawn from its location on the diagram. Another star, [FORMULA], is found high (5.6[FORMULA]) above the mean curve. It belongs to the exotic visual binary system [FORMULA] (actually a quadruple system) discussed in detail by Cayrel de Strobel et al., 1994 (see also Pallavicini et al. 1987).

As a general scheme, high chromospheric activity, high rotation velocity and high surface lithium abundance are associated with young stellar age. At constant age, in main sequence stars cooler than [FORMULA] [FORMULA], the surface lithium abundance decreases dramatically with decreasing effective temperature (or decreasing mass). There are, however, notorious exceptions to these general rules. The old evolved star [FORMULA] (solar mass, but twice the solar age) is one of them: it has low activity, slow rotation, but a very high photospheric lithium content. Pasquini et al. (1994) show that the case of [FORMULA] is not truly exceptional: they confirm the existence of an important group of field G dwarfs with high Li content but apparently old age and conclude that a high Li abundance is a necessary but not sufficient condition for a star to be young. In young open clusters Soderblom et al. (1993a,1993b) and Soderblom (1995) show that, at a given color, there is a large scatter in activity and rotation as well as in the Li content, with the most rapidly rotating stars having the most Li. Yet, in the somewhat older Hyades cluster, a tight relation between Li content and stellar mass is established. The complicated picture that emerges may find an explanation in theories by Pinsonneault et al. (1989,1990) based on the transport of angular momentum from the stellar core outwards, implying that the abundance of Li depends more on the rotational history of the star rather than on rotation per se . The above mentioned [FORMULA] system also appears to be contradictory with the general picture. Each of the two components is itself a spectroscopic binary, and the system is better described as Aa + Bb. The study of Cayrel de Strobel et al. (1994) establishes that the spectrum of Aa shows a rather weak chromospheric activity and strong lithium abundance, whilst the spectrum of Bb indicates a temperature cooler than Aa by about 300 K (from [FORMULA]), a high chromospheric activity (from [FORMULA] as well as from the Ca II IRT) and undetectable lithium. The age of the system is bound between 2 and 8 Gyr, and the masses of the main components A and B are very similar, being [FORMULA]. The Bb system has quite a small orbital period of 3.98d, which suggests that the rotation period of this tight system is tidally locked to the orbital period. Cayrel de Strobel et al. explain that the high activity of [FORMULA] is due to its high rotation rate, and the abnormally low surface lithium abundance owes to the unusual mass loss rate caused by high activity maintained during several Gyr. A similar situation is found in RS Cvn binaries (Randich & Palavicini, 1991). This is all consistent with the now widely accepted idea that the real basic link is between high activity and high rotation rate. The question of the surface lithium content is somewhat more complicated.

Two of the stars listed in Table 4 fall into the Vaughan-Preston gap of intermediate activity stars according to their HK emission fraction. As seen in Fig. 14, the depth of the [FORMULA] line of HD 76151 falls on the upper edge of the area populated by low activity stars. The case of [FORMULA] is less clear. Here again more measurements are needed before reaching conclusions. It is interesting to note that the two stars have a high lithium abundance. I could not find any individual measurement of [FORMULA] for [FORMULA] (the separation between [FORMULA] and B is only 2.5 arc sec). Given its high surface lithium content and its location in Fig. 14, we expect [FORMULA] to be in the group of intermediate activity stars. Should this make us favour the lower bound of the age bracket of the system? It would in any case be interesting to monitor the activity in this visual double system in order to find the extent of variability of the two components and find eventual rotational modulations allowing to find the true rotation periods (the lines in their spectra are not obviously rotationally broadened and the system is probably seen pole-on).

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Online publication: December 17, 1999
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