## 2. ResultsAs explained above we consider K2-K5 III stars. The luminosity function is defined as usual, i. e. gives the number of stars per with an absolute K magnitude in the interval . It is here approximated by a Dirac's delta function, i.e. centred at . Its true dispersion is only 0.6 mag. The effect of a non-vanishing dispersion on absolute magnitude could be important, as the resulting value for the scale length could be affected by some sort of Malmquist bias. We have performed several numerical calculations using a gaussian distribution for the luminosity function, obtaining similar results. The final value of the estimated error is not affected either, as it mainly arises from the fitting process. Even though these kind of effects are difficult to evaluate, the approximation of the luminosity function by a was found to be a satisfactory assumption. In the fundamental equation of star counts (e. g. Mihalas and Binney, 1981; Gilmore and Reid, 1983; Calbet et al., 1995) the density function is also taken into account. It was assumed that: where is the density function, i. e. the
number density of stars taking its local value as unit, Defining as usual , as the number of stars per squared degree with magnitude between 9 and 10, the fundamental equation of star counts becomes where is the solid angle, As
© European Southern Observatory (ESO) 1998 Online publication: January 8, 1998 |