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Astron. Astrophys. 358, 869-885 (2000)

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7. The shape of the chromospheric activity-age relation

Soderblom et al. (1991) argued that the interpretation of the chromospheric activity distribution as evidence for a non-constant SFH is premature. Particularly, the authors have shown that the observations do not rule out a non-monotonic chromospheric activity-age relation, even considering that the simplest fit to the data is a power-law, like the one we used.

Presently, there is good indication that the chromospheric activity of a star is linked with its rotation, and that the rotation rate decreases slowly with time. However, it is unknown how exactly the chromospheric activity is set and how it develops during the stellar lifetime. The data show that there is a chromospheric activity-age relation, but the scatter is such that it is not presently possible to know whether the chromospheric activity decreases steadily with time, or there are plateaux around some `preferred' activity levels. There is a possibility that the clumps we are seeing in the chromospheric age distribution (which are further identified as bursts) are artifacts produced by a monotonic chromospheric activity-age relation.

To keep the constancy of the SFH, Soderblom et al. (1991) proposed an alternative chromospheric activity-age relation that is highly non-monotonic. We have checked this constant-sfr calibration with our sample, but the result is not a constant sfr. This is expected, since there are many differences in the chromospheric samples used by Soderblom (1985) and Soderblom et al. (1991) and the one we have used (see our Fig. 11 in Paper I). We have calculated a new constant-sfr calibration, in the way outlined by Soderblom et al. (1991). We have used 328 stars from our sample (just the stars with solar metallicity, to avoid the metallicity dependence of [FORMULA]), with weights given by the volume correction (to account for the completeness of the sample) and using the scale height correction factors to take into account the disk heating.

Fig. 22 compares the chromospheric activity-age relation we have used (solid line) with the constant-sfr calibration proposed by Soderblom et al. (dotted line) and the constant-sfr calibration from our sample (dashed line). The data and symbols are the same from Soderblom et al. (1991). Both constant sfr calibrations agree reasonably well for the active stars, but deviate somewhat for the inactive stars. This is caused by the fact that to be consistent with a constant sfr, the calibration must account for the increase in the relative proportions of inactive to active stars, especially around [FORMULA], after the survey of HSDB. Note that, our constant-sfr chromospheric activity-age relation is still barely consistent with the data and cannot be ruled out. There are few data for stars older than the Sun in the plot, and it is not possible to know whether the plateau for [FORMULA] in this calibration is real or not.

[FIGURE] Fig. 22. Comparison between the chromospheric activity-age relation we have used throughout this paper (solid line), the constant-sfr calibration proposed by Soderblom et al. (dotted line) and the constant-sfr calibration from our sample (dashed line). The data and symbols are the same from Soderblom et al. (1991): [FORMULA], the sun; H, Hyades; U, Ursa Major Group; open diamonds, field F dwarfs; filled diamonds, binaries.

We acknowledge that, given no other information , it is a subjective matter whether to prefer a complex star formation history or a complex activity-age relation. Nevertheless, there are numerous independent lines of evidence that also point to a bursty star formation history; the most recent and convincing is the paper by Hernandez, Valls-Gabaud & Gilmore (2000). They use a totally different technique (colour-magnitude diagram inversion) and find clear signs of irregularity in the star formation. In Sect. 6, we listed several other works that indicate a non-constant star formation history, and the majority of them use different assumptions and samples. Strongly discontinuous star formation histories are also found for some galaxies in the Local Group (see O'Connell 1997), in spite of the initial expectations during the early studies of galactic evolution that these galaxies should have had smooth star formation histories.

For all these methods to give the same sort of result, all the different kinds of calibrations would have to contain complex structure. It is simpler to infer that the star formation history is the one that actually has a complex structure. We think that when several independent methods all give a similarly bursty star formation history (although with different age calibrations, so they do not match exactly), our conclusion is supported over the irregular activity-age but constant star formation rate solution.

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© European Southern Observatory (ESO) 2000

Online publication: June 20, 2000