The general photometric, spectroscopic, and kinematic properties of the late type halo stars are investigated from a sample of known true halo stars. Halo stars are distributed in a lower left region of infrared (J-H) vs (H-K) color-color diagram, which is recomfirmed to be useful for selection of halo stars. They move with average velocity components of 9 km/sec, -14 km/sec, and 5 km/sec in U, V, and W directions respectively. They are distributed seperately from disk stars in a diagram of metallicity index, CaH1/TiO5 vs (R-I).

The bright part of the halo luminosity function is derived from a sample of the 233 NLTT propermotion stars, which are selected by the 220 km/ see of cutoff velocity in transverse to rid the contamination by the disk stars and corrected for the stars omitted in the sample by the selection criterion. It is limited to the absolute magnitude range of Mv=4-8, but is based on the largest sample of halo stars up to now. This luminosity function provides a number density of 2.3 · 10-5pc-3 and a mass density of 2.3 · 10-5pc-3 for 4 < Mv < 8 in the solar neighborhood. These are not sufficient for disk stability. The kinematics of the sample stars are < U > = - 7 km/sec, < V > = - 228 km/sec, and < W > = -8 km/sec with (σu,σv,σw) = (192, 84, 94) km/sec. The average metallicity of them is [Fe/H] = - 1.7±0.8. These are typical values for halo stars which are selected by the high cutoff velocity. We reanalyze the luminosity function for a sample of 57 LHS proper-motion stars. The newly derived luminosity function is consistent with the one derived from the NLTT halo stars, but gives a somewhat smaller number density for the absolute magnitude range covered by the LF from NLTT stars. The luminosity function based on the LHS stars seems to have a dip in the magnitude range corresponding to the Wielen Dip, but it also seems to have some fluctuations due to a small number of sample stars.

The sample of sub dwarfs are selected from LHS catalogue on the bases of the reduced proper motion diagram utilizing Chui criteria, and confirmed with the available photometric and/or kinematic data. Among them, 20 sub dwarfs have trigonometric parallaxes with accuracy better than 20 % . The color­absolute magnitude relation is derived with them. By adopting this color-magnitude relation and V / V m method, we have derived the sub dwarf luminosity function over the absolute magnitude range of M v = 4.5 and 9.5. This halo luminosity function is consistent with that of Eggen(1987). By adopting the available mass-luminosity relations for halo stars, we have found that the halo IMF is steeper than disk IMFs of Scalo(1986) and Salpter(1955) in this small mass region.

From the kinematically unbiased sample of halo stars, the local mass density of halo dwarfs is estimated as 6.0 ∼ 6.3 × 10 − 4 m ⊙ / p c 3 by adopting a color-magnitude relation and a mass-luminosity relation. The derived halo mass density is not much different from the results of previous studies, which were derived from the kinematically biased sample of halo stars. Therefore it is confirmed that the local mass density of halo stars is far less than that required by Ostriker-Peebles to stabilize the galactic disk against barlike instabilities.