M dwarfs from Hubble Space Telescope star counts. IV.

We study a sample of about 1400 disk M dwarfs that are found in 148 fields observed with the Wide Field Camera 2 (WFC2) on the Hubble Space Telescope and 162 fields observed with pre-repair Planetary Camera 1 (PC1), of which 95 of the WFC2 fields are newly analyzed. The method of maximum likelihood is applied to derive the luminosity function and the Galactic disk paramete rs. At first, we use a local color-magnitude relation and a locally determi ned mass-luminosity relation in our analysis. The results are consistent wi th those of previous work but with considerably reduced statistical errors. These small statistical errors motivate us to investigate the systematic u ncertainties. Considering the metallicity gradient above the Galactic plane , we introduce a modified color-magnitude relation that is a function of Ga lactic height. The resultant M dwarf luminosity function has a shape simila r to that derived using the local color-magnitude relation but with a highe r peak value. The peak occurs at M(V)similar to 12 and the luminosity funct ion drops sharply toward M(V)similar to 14. We then apply a height-dependen t mass-luminosity function interpolated from theoretical models with differ ent metallicities to calculate the mass function. Unlike the mass function obtained using local relations, which has a power-law index alpha = 0.47, t he one derived from the height-dependent relations tends to be flat (alpha = -0.10). The resultant local surface density of disk M dwarfs (12.2 +/-1.6 M-circle dot pc(-2)) is somewhat smaller than the one obtained using local relations (14.3 +/-1.3 M-circle dot pc(-2)). Our measurement favors a shor t disk scale length, H = 2.75 +/-0.16 (statistical) +/-0.25 (systematic) kp c.