U is the velocity component (positive) towards the Galactic anti-centre, V is (positive) in the direction of the Galactic rotation and W (positive) toward the north Galactic pole.

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Equivalent width of the H $_\alpha$ emission line can be used in this case as an indicator of the chromospheric activity and, consequently, as age information.

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... computation

In the original catalogue, ages are rounded up to the nearest 0.1 ${\rm ~Gyr}$ but in this study, ages (and upper and lower 1 $\sigma$ confidence limits) rounded up to 0.01 ${\rm ~Gyr}$ are used (Jørgensen 2006).

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... diagram

For instance, Pont & Eyer (2004) demonstrate that the isochrone dating method is subject to significant biases that arise inevitably in regions of the HR diagram where the effects of age on the atmospheric parameters become small. Haywood (2006) recently studied this in depth and showed how biases, similar to those expected in real samples, greatly influence the physical interpretation of the Galactic age-metallicitydistribution.

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... values

They were not available when the present work was completed.

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... ages

Nordström et al. (2004) provides upper and lower limits for error estimates. Here we consider that a star has $\epsilon _{\rm age}\leq 30\%$ if this is true for both limits.

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... considered

For a discussion of the dependence of the degree of completeness of their sample on the cut-off by error in ages see Nordström et al. (2004).

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... software

http://thames.cs.rhul.ac.uk/~multires/

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... direction

Note that isotropy is not defined in non-metric spaces, such as some of the ones used here.

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... cost

The computing times are 4 s for the grid construction process with the whole sample (24 190 stars) and 1 s for the WT in a typical grid of $400\times400$ pixels and J=5 with an Intel(R) Xeon(TM) processor at 3.0 GHz.

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... scales

Note that the parameter n in the MR software is n=J+1.

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... scales

The computing time for a typical grid of $400\times400$ pixels and J=5 is 4 s with an Intel(R) Xeon(TM) processor at 3.0 GHz.

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... plane

We deal only with these two components of the velocity because classic moving groups are less visible in the W distribution due to the more thorough phase-mixing of the movement perpendicular to the Galactic plane (Seabroke & Gilmore 2007; Dehnen 1998).

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...tex2html_cite_multiple_mark

The list could be far more extensive; only the most significant groups have been chosen. Similar values for their components have been reported by other authors (see e.g. Montes 2001; López-Santiago et al. 2006).

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... Sun

Note that due to its source of radial velocities, this subsample is restricted to the northern equatorial hemisphere (see Famaey et al. 2005) and therefore, stars in these shells are not isotropically distributed around the Sun.

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... anti-centre

Note also that the observational spatial restriction affects the distribution of the subsamples in the direction perpendicular to the Galactic plane.

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...)

In Sect. 2 we mention that the H $\alpha$ equivalent width could be used as information on age for the M dwarfs. We have checked, however, that the number of stars per sample when active and non-active stars are analysed separately is too low to derive significant results from the distributions: too smoothed distributions are obtained by WD with $J_{\rm plateau}$ . This study has been postponed until the use of recent new data, i.e. Bochanski et al. (2007).

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...4-8 ${\rm ~Gyr}$

Asiain et al. (1999b), working only with the sample of B and A main sequence stars, found a significant variation of the Pleiades moving group with age. However, as ages in their sample are <0.5 ${\rm ~Gyr}$ , their interpretations cannot be applied here.

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... significant

Notice that the periodicity is statistically significant in the sense of the discussion in Sect. 3 ( $J=J_{\rm plateau}$ ).

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... metallicity

Notice that this correlation was not as clearly observed in Nordström et al. (2004, see their Fig. 32), despite using the same sample, which demonstrates the capabilities of the WD method and the rotation.

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