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The morphology and luminosity function of the Galactic bulge from TMGS star counts

The bulge of the Galaxy is analysed by inverting K-band star counts from the Two-Micron Galactic Survey in a number of off-plane regions. A total area of about 75 square degrees of sky is analysed. Assuming a non-variable luminosity function within the bulge, we derive the top end of the K-band luminosity function and the stellar density function, whose morphology is fitted to triaxial ellipsoids. The luminosity function shows a sharp decrease brighter than $M_K=-8.0$ when compared with the disc population. By fitting ellipsoids, we find that the bulge is triaxial with the major axis in the plane at an angle with line of sight to the Galactic centre of $12^\circ$ 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 best fit for the stellar density, assuming an ellipsoidal distribution, is $D(t)=1.17(t/2180)^{-1.8}\exp(- (t/2180)^{1.8}) stars pc^{-3}$, for $1300<t<3000$, where $t$ is the distance along the major axis of the ellipsoid in parsecs.