Astron. Astrophys. 358, 233-241 (2000)

5. The Herculis kinematic group

Stars tend to form in groups, but most of the clusters and associations that are the birthplace of stars end up dispersing. The most probable cause for this dispersion is an encounter of the young cluster with a massive object. As the cluster disintegrates, it must go through intermediate stages where the entire group cannot be identified anymore, yet within some region one can still find stars that are moving in nearly the same velocity, i.e. direction and speed (after the words of Soderblom & Mayor (1993)). These stars would constitute a stellar kinematic group (SKG). To be considered part of a SKG, stars need to have certain characteristics:

i) All stars should be approximately the same age. Since they were formed in the same Giant Molecular Cloud, which disperses on a typical time scale of 0.1 Gyr, their ages shouldn't differ by more than this value.

ii) They should have the same chemical composition, which they share with the cloud from which they originated.

iii) They should be moving at the same rate in the same direction, with only minimal velocity dispersion, which reflects their spatial cohesion. It's specially important that the members of a SKG have their V velocities with very low dispersion (U, V and W are the components of a star's velocity relative to the Sun, measured in a galactic frame and positive towards the galactic centre, in the direction of galactic rotation and towards the north galactic pole respectively). The galactic forces that dissolve clusters lead to diffusion in all three directions. But motions in U and W only lead to oscillations of the stars about the mean motion of the group, whereas diffusion in V takes a star away from the group forever (Binney & Tremaine, 1987).

In Table 6 we present all stars classified as members of the Her SKG according to Woolley (1970). The group presents an average velocity in the direction of galactic rotation V = 47.9 3.3 km s^-1. This value has a standard deviation that is sufficiently low so that the group could be considered cohesive in terms of velocity. The orbital parameters mean values are  = 0.8524  0.0134 and e  = 0.2008  0.0130, with i 0.04 for all stars (in brief, is the average distance to the galactic center, e is the orbit eccentricity and i is the orbit inclination). According to Woolley (1970) stars in a SKG must have a low orbit inclination, which all stars in Table 6 have. The low standard deviations of and e indicate a high spatial cohesion. All these stars are located less than 31 parsecs away from the Sun. We can see that, from the kinematical point of view, these stars do form a SKG. But we still have to examine if they satisfy the chemical composition and age criteria.

Table 6. Kinematic data for the stars that, according to Woolley (1970), belong to the Her group. Velocities in km s^-1.
References: Velocities have been kindly calculated by G. Quast (CNPq/LNA, Brazil), based on data from the Hipparcos catalogue (ESA, 1997), except for Gliese 456 (Woolley et al., 1970). The orbital parameters , e and i come from Woolley et al. (1970).

We searched the literature thoroughly for detailed spectroscopic analyses of the group stars. Then we selected for each star the paper which we considered to be the most trustworthy. The selected papers were: for  Hyi, Abia et al. (1988); for  Her, Chmielewski et al. (1995); for HD 158614, McWilliam (1990); and for  Pav, Edvardsson et al. (1993). The effective temperatures and metallicities of 1 Hya and HD 14680, which have not been subjected to any spectroscopic analysis, have been determined using photometric calibrations. To determine the effective temperatures from (B-V) and (b-y) we used Porto de Mello (1996) calibrations and to have the metallicities from m₁, that of Schuster & Nissen (1989). The regression of the metallicity calibrations has a 0.16 dex dispersion and the probable error can amount to 0.20 dex. We take (B-V) indices from Hoffliet & Jaschek (1982) for 1 Hya and from Nicolet (1978) for HD 14680. The (b-y) index for HD 14680 comes from Olsen (1994a). The (b-y) index for 1 Hya and m₁ for both stars were taken from Olsen (1994b). Some useful parameters of the stars of Table 6 can be found on Table 7.

Table 7. Useful parameters for the stars that, according to Woolley (1970), belong to the Her group.
References: Visual magnitudes come from Hoffleit & Jaschek (1982), except for GL 456 (van Altena et al., 1995) and HD 14680 (Olsen, 1994a). Spectral types are from the Michigan Catalogue of Spectral Types (Houk & Cowley, 1975; Houk, 1982; Houk & Swift, 1999), except for Her A and B (Hoffleit & Jaschek, 1982), and GL 456 (van Altena et al., 1995). Parallaxes are from van Altena et al. (1995), and from the Hipparcos catalogue (ESA, 1997). For bolometric magnitudes, effective temperatures and metallicities, see text.

If we regard the  Her SKG as a metal deficient group then we should disregard  Her A (a blow of destiny!) and HD 158614 as members, because these stars have solar iron abundances. Porto de Mello & da Silva (1991), who had already analysed the group in terms of element abundances and evolutive stages, disregarded these same stars based on the determination of the stellar ages.

We also compared the abundances of elements other than iron, for the stars which had these abundances determined (Table 8). The four stars present aluminum abundances that are compatible with each other within the probable errors ( Ret and  Hyi abundances are only marginally compatible).  Hyi and  Pav have barely compatible calcium abundances (within 2). We should keep in mind, however, that the calcium abundance of  Hyi has been determined based on the analysis of only 1 absorption line. The four stars have Si, Ti and Ni abundances that are perfectly compatible with one another. The agreement between the stars abundances reinforces the thesis that they have originated from the same interstellar cloud.

Table 8. Comparison between spectroscopically determined abundances for probable  Her SKG members. The number of lines used is given for each star.

Finally, we analysed if the stars have the same age. We did so using the Gen92/93 set of isochrones corrected for the metallicity of and  Ret (Fig. 5). It should be clear that the following is an imperfect analysis, because not all probable members have exactly the same metallicity and because of the interpolation made to construct the Z = 0.0113 set of isochrones (see Sect. 4).

Fig. 5. The same as Fig. 4, but using parallaxes form the Hipparcos catalogue (ESA, 1997) to compute the luminosities.

Pav, 1 Hya, and  Ret are all compatible with the log t = 9.7 (5.0 Gyr) isochrone. Hyi can be considered to have marginal, 2 compatibility with the same isochrone. Because these five stars meet the characteristics required of an SKG, the existence of a group is confirmed. However,  Herculis itself appears not to be a member, and so we suggest that the group's name be Reticuli. So, when we talk about  Ret SKG from now on, we will be refering to these five stars.

Another way to estimate stellar ages is through the analysis of the "chromospheric age". Young stars present generally very high levels of chromospheric activity, linked to high rotation, and these decay monotonically with time owing to magnetic braking that transfers angular momentum to the stellar wind. The traditional spectroscopic diagnostics of this activity is the core emission of very strong lines, the prototype being the CaII H and K lines (Pasquini, 1992). These core emission equivalent widths allow an estimate of the chromospheric flux and the age through a flux -age relation.  Ret presents an easily detectable emission at the CaII K line core (Fig. 6), much stronger than the solar one, indicating stellar youth.  Ret presents a much smaller emission. This is baffling for stars of equal age, very much alike, with similar luminosities and temperatures, and therefore similar masses. One conceivable explanation to this discrepancy is the possibility that  Ret is a close binary. This possibility was already examined by da Silva & Foy (1987), with the conclusion that this is highly improbable. This result could be recently confirmed on the basis of the radial velocity monitoring of and  Ret by Endl, Kürster and Els (2000). Their analysis was accomplished using a total of 14 CAT/CES spectra distributed in 185 days, for  Ret, and 58 spectra distributed in 1977 days, for  Ret. The r.m.s. dispersion of the radial velocities of these objects are 21.8 m s^-1 and 17.7 m s^-1 for and  Ret, respectively, showing no hint of stellar or substellar companions. Therefore, and  Ret seem to have followed different histories in their decreasing levels of chromospheric activity.

Fig. 6. CaII K profiles of and Reticuli.

We estimated chromospheric ages for and  Ret using the CaII H and K chromospheric fluxes from Pasquini (1992) and the following flux-age relation (Soderblom et al., 1991)

and obtained t( Ret) =  Gyr and t( Ret) = Gyr. This last estimate is in reasonable agreement with the general isochronal age of 5.0 Gyr for the group. We could not find CaII H and K published fluxes for the other group stars. Such flux-age relation analysis provides the marginal possibility of a common age (t 3.4 Gyr) for the  Ret stars, but only in view of the rather large errors involved.

Another common diagnostic of chromospheric flux is (Pasquini & Pallavicini, 1991). It is a less sensitive diagnostic in the sense that the photospheric contribution is higher, but to its advantage is the fact that it is easily observable in cool stars. Our observations of and  Ret were discussed in Sect. 2. During the same runs we have also secured spectra of the Sun (moon) and of the Ret SKG members  Hyi and  Pav. These four stars are the ones, along with 1 Hya, presenting a high kinematical and chemical identity, and it should be very interesting to determine if their chromospheric flux levels are compatible with a common age. During 1994 and 1995 the Sun was between the 1991 maximum and the 1997 minimum, and our solar spectra can be regarded as that of an average activity Sun. The subtraction of the solar spectra from the stellar spectra, for these very solar-like stars, should leave essentially the chromospheric component of the line core flux, which defines a small peak of excess or missing flux with respect to the Sun. All four objects present some slight additional filling with respect to the Sun, and therefore could be regarded as slightly younger. There is however some spread in their fluxes,  Pav being in fact the one with the strongest chromospheric component, and  Ret presenting more filling than  Ret. It is not entirely clear if such differences are significant as they are not too far above the estimated error level. Such spread in their chromospheric fluxes could be partly explained by out of phase stellar cycles, although it remains difficult to explain the appreciably more intense emission in  Ret and  Pav by intercycle variation alone. These stars have about the solar age and the peak-to-peak amplitude of their central depth variation should not much exceed the solar one, 0.5% (Livingston et al., 1998). The peak-to-peak total difference in their central depths reaches 25%, mostly due to the higher filling of  Ret, the estimated uncertainty being about 5%. We are probably witnessing a true spread in chromospheric flux owing to different histories of decreasing activity levels. Such SKGs might be interesting laboratories in which to test theories of angular momentum transfer due to magnetic braking in the early stellar evolutionary stages.

Another possible test of a common age for the  Ret SKG stars is the abundance of Li. While the chemical evolution of Li in the Galaxy and its connection to stellar evolution remains a highly controversial subject, it is well known that young stars present a high ("cosmic") initial abundance of Li, which can be depleted with varying degrees of efficiency during stellar evolution. In this issue the  Ret SKG is also interesting:  Pav and  Hyi are both subgiants with high Li content, respectively log N(Li) = 2.5 (Soderblom, 1985) and log N(Li) = 2.4 (Dravins et al., 1993), about 10 times solar (in the usual scale log N(H) = 12.00). On the other hand, both  Ret and  Ret have depleted their original Li to a higher degree than the Sun, their abundances being estimated at log N(Li) 0.90 (Pasquini et al., 1994). One possible explanation put forward for such Li rich subgiants is the "ressurgence" scenario (Dravins et al., 1993), in which the subgiant star dredges up to the surface Li that has been preserved below the convectively unstable surface layers, or else by the fact that these stars have maintained their Li abundance owing to low levels of depletion while on the main sequence (Randich et al., 1999). Two groups might be distinguished in the case of the  Ret SKG: the  Ret pair of near solar mass stars with highly depleted Li, and  Pav and  Hyi, with 1.10 solar masses, already subgiants with enhanced lithium. Our current understanding does not preclude a common age for these four stars as judged by their Li abundances alone.

It would clearly be very interesting to perform a complete detailed analysis of these four objects plus the probable  Reticuli SKG member 1 Hya. Their similar Fe abundances were used as a criterion in favor of the existence of the  Ret SKG, but a comprehensive determination of the abundance distribution of other elements, with different nucleosynthetic origins, with respect to Fe have not yet been determined with sufficient accuracy to allow their putative chemical identity to be verified. Also, a comprehensive analysis of their CaII H and K chromospheric fluxes, tied to other indicators such as the infrared CaII triplet lines, would be useful in constraining their chromospheric activity level, allowing a further check of the group age. The dispersion of the chromospheric fluxes suggests that the  Reticuli SKG, and other similar groups, may serve as interesting laboratories to test how stars with similar ages experience different histories of chromospheric activity decay with time.

© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000
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