M subdwarfs and the population II luminosity function

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We present a spectroscopic classification system for M-dwarfs and M-subdwarfs based on quantitative measures of TiO and CaH features in the region λλ06200-7400[...]. Our sample of cool stars covers the range from solar metallicity stars to the most extreme subdwarfs known. Using synthetic spectra computed by Allard and Hauschildt (1995), we derive metallicities for the stars. Stars are classified as dwarfs (M V), subdwarfs (sdM), or extreme subdwarfs (esdM). These classifications correspond to [m/H] ≈ 0.0, -1.2, and -2.0 respectively. Our metallicity scale agrees with theoretical HR diagrams and HST globular cluster measurements. We discuss some nearby subdwarfs of particular interest in light of our metallicity scale. We present spectra of three M subdwarfs which are common proper motion companions to F or G subdwarfs of known metallicity. The assumption that the companions have the same composition allows us to test the Gizis (1997, AJ, 113, 806) M subdwarf classification system and its correspondence to metallicity. The results are in excellent agreement with the Gizis (1997) scale, thereby showing that the Allard Hauschildt (1995, ApJ, 445, 433) Extended model atmospheres agree well in the 6200 - 7400[...] region for cool metal-poor stars. We also show that the results are consistent with the main sequences of globular clusters using the Reid (1997, AJ, in press) distance scale. We use optical spectra as well as optical and infrared broadband photometry to constrain the effective temperatures of M subdwarfs. We show that the coolest subdwarfs known have T[subscript eff] ≈ 3000 K. We present spectroscopic observations of two halo M subdwarfs which have Hα emission lines. We show that in both cases close companions are the likely cause of the chromospheric activity in these old, metal-poor stars. We argue that GI 781 A's unseen companion is most likely a cool helium white dwarf. GI 455 is a near-equalmass M subdwarf system. G1 781 A is rapidly rotating with v sin i ≈ 30 km s[superscript -1]. The properties of the chromosphere and X-ray coronae of these systems are compared to M dwarfs with emission (dMe). Although the relative strength of the X-ray coronae to the Hα emission are similar to that seen in field and young cluster dMe, G1 781 A's activity level is weaker than the young cluster dMe. This suggests that different ages and/or metallicities can make two otherwise equally rapidly rotating, equal-mass stars have different activity levels. Using a proper motion survey based upon the two Palomar Sky Surveys, We measure the luminosity function of the low-mass end of the field Population II. We combine this with earlier measurements of higher mass stars to show that the luminosity function increases down to M[subscript I] ≈ 9.5, but may be flattening at the lowest luminosities M[subscript I] > 9.5. We discuss the constraints this puts on the mass function of metal-poor stars. The mass function is consistent with a power-law of slope α ≈ -1.35