M Dwarfs fromHubble Space TelescopeStar Counts. IV.

We study a sample of about 1400 disk M dwarfs that are found in 148 fieldsobserved with the Wide Field Camera 2 (WFC2) on the Hubble Space Telescope and162 fields observed with pre-repair Planetary Camera 1 (PC1), of which 95 ofthe WFC2 fields are newly analyzed. The method of maximum likelihood is appliedto derive the luminosity function and the Galactic disk parameters. At first,we use a local color-magnitude relation and a locally determinedmass-luminosity relation in our analysis. The results are consistent with thoseof previous work but with considerably reduced statistical errors. These smallstatistical errors motivate us to investigate the systematic uncertainties.Considering the metallicity gradient above the Galactic plane, we introduce amodified color-magnitude relation that is a function of Galactic height. Theresultant M dwarf luminosity function has a shape similar to that derived usingthe local color-magnitude relation but with a higher peak value. The peakoccurs at $M_V \sim 12$ and the luminosity function drops sharply toward $M_V\sim 14$. We then apply a height-dependent mass-luminosity functioninterpolated from theoretical models with different metallicities to calculatethe mass function. Unlike the mass function obtained using local relations,which has a power-law index $\alpha = 0.47$, the one derived from theheight-dependent relations tends to be flat ($\alpha = -0.10$). The resultantlocal surface density of disk M dwarfs (12.2 +/- 1.6 M_sun pc^{-2}) is somewhatsmaller than the one obtained using local relations (14.3 +/- 1.3 M_sunpc^{-2}). Our measurement favors a short disk scale length, H = 2.75 +/- 0.16(statistical) +/- 0.25 (systematic) kpc.Comment: 20 pages, 10 ps figures, accepted for publication in Ap