1 Introduction

The context of this study as well as implications of the results for the solar circle kinematics understanding are in Chereul et al. (1998) (hereafter Paper II). This third paper aims at providing to the reader of Paper II the details of the phase space inhomogeneities brought to the fore by means of wavelet analysis and technical details on several features of the analysis.

Wavelet analysis is extensively used to extract deviations from smooth homogeneity, both in density (clustering) and velocity distribution (streaming). A 3-D wavelet analysis tool is first developed and calibrated to recognize physical inhomogeneities among random fluctuations. It is applied separately in the position space (Sect. 4) and in the velocity space (Sect. 5). Once significant features are identified (whether in density or in velocity), feature members can be identified and their behaviour can be traced in the complementary space (velocity or density). Thus, a real picture of the phase space is produced. Not only are some clusters and streams detected, but the fraction of stars involved in clumpiness can be measured. Then, estimated stellar ages help connecting streams and clusters to the state of the ISM at star formation time and providing a quantitative view of cluster melting and stream mixing at work.

Only once this picture has been established on a prior-less basis we come back to previously known observational facts such as clusters and associations, moving groups or so-called superclusters. A sine qua non condition for this analysis to make sense is the completeness of data within well defined limits. In so far as positions, proper motions, distances, magnitudes and colours are concerned, the Hipparcos mission did care. Things are unfortunately not so simple concerning radial velocities and ages. More than half radial velocities are missing and the situation regarding Strömgren photometry data for age estimation is not much better. So we developed palliative methods which are calibrated and tested on available true data to circumvent the completeness failure. The palliative for radial velocities is based on an original combination of the classical convergent point method (Sect. 5.1) with the wavelet analysis. The palliative for ages (Sect. 3) is an empirical relationship between age and an absolute-magnitude/colour index. It has only statistical significance in a very limited range of the HR diagram.

The sample was pre-selected inside the Hipparcos Input Catalogue (ESA, 1992) among the "Survey stars''. The limiting magnitude is $m_{v}\leq 7.9 + 1.1~\cdot ~\sin\mid b\mid$ for spectral types earlier than G5 (Turon et al. 1992). Spectral types from A0 to G0 with luminosity classes V and VI were kept. Within this pre-selection the final choice was based on Hipparcos (ESA, 1997) magnitude ($m_{v} \leq 8.0$), colours ($-0.1\leq B-V \leq 0.6$), and parallaxes ($\pi \geq 8$ mas). The sample studied (see sample named h125 in Paper I, Crézé et al. 1998) is a slice in absolute magnitude of this selection containing 2977 A-F type dwarf stars with absolute magnitudes brighter than 2.5. It is complete within 125 pc from the Sun.

Details concerning the wavelet analysis implementation through the "à trou'' algorithm and the thresholding procedure are given in Sect. 2. The palliative age determination method is fully described in Sect. 3. The results of the density analysis in position space (clustering) are given in Sect. 4. The convergent point method is explained in Sect. 5.1 and the procedures estimating spurious members and field stars among detected streams are given in Sects. 5.2.1 and 5.2.2 respectively. The results of the velocity space analysis (streaming) are in Sect. 5.3 including a detailed review of observational facts and a comparison with evidences collected by previous investigators. Conclusion in Sect. 6 summarizes the different results.