5 Discussion

The motivation of our search was to improve our knowledge of the distance distribution and of the extinction of the microlensing source stars used in Papers I and II. In the following we use the RR Lyræ which are well-known distance indicators and have been observed in all six directions that we investigated. The GSA fields having a high non-uniform absorption, we give only an average reddening towards our fields, based on EROS data alone.

For each selected RR Lyræ we estimate the extinction $A(V) = 2.4 \times E(V-I)$using the standard extinction coefficients (Schlegel et al. 1998; Stanek 1996). The colour excess E(V-I) is derived from the colour that we measured and their intrinsic colour: $\left( V - I \right)^{\rm RRab}_{0} = 0.4$ and $\left( V - I \right)^{\rm RRc}_{0} = 0.2$ (Alcock et al. 1998). The uncertainty on individual extinctions is estimated to be $0.5^{\rm mag}$. This error includes the $0.2^{\rm mag}$ uncertainty on the EROS colour measurement (see Eq. (1)) and a $0.1^{\rm mag}$ magnitude uncertainty on the intrinsic colour. The absolute magnitude of RR Lyræ is $M_{V}^{\rm RR} \sim 0.71$with a precision of $0.07^{\rm mag}$ (Gould & Popowski 1998). Finally, we estimate the distance to each star simply by using the relation $m - M = 5 \times \left( \log(d)-1 \right) + A$. The typical uncertainty on the distance is 20%. The left panels of Fig. 11 show the obtained extinction A(V) versus the calculated distance. The mean extinction of the RR Lyræ is $A(V) \sim 3.6 \pm 0.2$ mag towards $\theta$ Mus and $3.3 \pm 0.1$ towards $\gamma$ Nor, with a dispersion of 1 mag. The mean distance of the RR Lyræ is $\sim$ $4.7\pm 0.3$ kpc towards $\theta$ Mus and $5.3 \pm 0.2$ kpc towards $\gamma$ Nor. The dispersion of the values is 1.4 kpc which reflects the spread in distance of disc stars. The disc population contributes to the sources of the microlensing events that we observe in the Galactic plane. A model based on the distribution of matter in the disc and the luminosity function of neighbooring stars has been used in Derue (1999) to estimate the distance of the star population from the disc. The distance of RR Lyræ is in good agreement with the one obtained with this model.

Figure 11: Extinction A(V) versus the distance of RR Lyræ (in  kpc) towards $\theta$ Mus and $\gamma$ Nor. The right panels show the inferred distance distribution.