Inversion of stellar statistics equation for the Galactic bulge

A method based on Lucy's iterative algorithm is developed to invert the equation of stellar statistics for the Galactic bulge and is then applied to the K-band star counts from the Two-Micron Galactic Survey in a number of off-plane regions (10 degrees > \b\ > 2 degrees, \l\ < 15 degrees). The top end of the K-band luminosity function is derived and the morphology of the stellar density function is fitted to triaxial ellipsoids, assuming a non-variable luminosity function within the bulge. The results, which have already been outlined by Lopez-Corredoira et al., are shown in this paper with a full explanation of the steps of the inversion: the luminosity function shows a sharp decrease brighter than M-K = -8.0 mag when compared with the disc population; the bulge fits triaxial ellipsoids with the major axis in the Galactic plane at an angle with the line of sight to the Galactic centre of 12 degrees in the first quadrant; the axial ratios are 1:0.54:0.33, and the distance of the Sun from the centre of the triaxial ellipsoid is 7860 pc. The major-minor axial ratio of the ellipsoids is found not to be constant, the best fit to the gradient being K-z = (8.4 +/- 1.7) x exp(-t/(2000 +/- 920) pc), where t is the distance along the major axis of the ellipsoid in parsecs. However, the interpretation of this is controversial. An eccentricity of the true density-ellipsoid gradient and a population gradient are two possible explanations. The best fit for the stellar density, for 1300 pc < t < 3000 pc, is calculated for both cases, assuming an ellipsoidal distribution with constant axial ratios, and when K-z is allowed to vary. From these, the total number of bulge stars is similar to 3 x 10(10) or similar to 4 x 10(10), respectively.