Publications of the Astronomical Society of the Pacific 101: 787-810, September 1989

BOLOMETRIC LUMINOSITIES AND COLORS FOR Κ AND M DWARFS AND THE SUBLUMINOUS STARS OF THE HALO

JESSE L. GREENSTEIN Palomar Observatory and Department of Astronomy, California Institute of Technology Pasadena, California 91125 Received 198

ABSTRACT This review deals with the H-R diagrams of dM, sdK, and sdM proper-motion stars. It depends heavily on the rapid growth in precision of small parallaxes, combining them with various photometry to produce different types of H-R diagrams. Given my multichannel spectrophotometry and published mid-infrared filter photometry, a method for integrating energy distributions (including blanketing) by using discrete weights is developed. The bolometric corrections are evaluated at various wavelengths; an easy method is proposed for obtaining luminosities even if the star lacks infrared data. The various color-luminosity diagrams show that the high-velocity, low-metallicity stars of the halo are clearly subluminous. They are found to be bluer and brighter than low-mass OD m analogs; the apparent cutoff in the halo is close to Mbol = 12 . Well-known OD stars are far redder, reaching Mbol = 13?7. In both populations, the lowest luminosities observed are near those predicted with an energy-generation cutoff at low masses. A crucial test is proposed—examining the faintest stars in metal-poor globular clusters, where the predicted cutoff is accessible with the space telescope. Comparison of disk and halo stars with the theoretical model interiors for low-mass stars proves difficult, problems arising from a still poorly known effective temperature scale. The observed speed of halo stars, exceeding 425 km s1, confirms that the escape velocity from the Galaxy is high. Key words: stars: luminosities-stars: subdwarfs-stars: high velocity

1. Introduction reduced proper motion, H, were observed. Of 450 stars, Accumulation of data on the faint red stars makes it now 275 had usable parallaxes; 140 of these had published IR possible to study some of the physical properties of dK magnitudes, so 140 bolometric magnitudes could have and dM stars of various populations. I here analyze a been determined by integrating the full flux distribution. combination of my multichannel spectrophotometer A simplified method exists, discussed below; I here deter- (MCSP) observations, published mid-IR magnitudes, and mine Mbol for 71 stars with full data which then serve to parallaxes that lead to the relation between bolometric calibrate bolometric corrections to be applied. Many of these stars are close neighbors; for them other data will be magnitude Mbol and various colors. An MCSP observing program with the Hale 5-meter reflector, completed in found in the Gliese (1969) and Gliese and Jahreiss (1979) 1979, gave data on 450 proper-motion stars selected by catalogs. Sample MCSP energy distributions are in size of their reduced proper motions (H = m + 5 + Greenstein (1978); a preliminary review, in Greenstein 5 log μ). These are mostly from the Lowell Observatory (1989), outlines broadly a range of observational and theo- Proper Motion Survey (Giclas, Burnham, and Thomas retical problems of the lower main sequence as I now view 1971, 1978); those catalogs were complete to mpg = 16?5 them. A valuable, and much broader, general review with and motions of 0'/26 per annum but do not cover the entire extensive bibliography is Liebert and Probst (1987). sky. I observed all Lowell northern stars with μ > Γ.Ό The sample is not ideal for studies requiring statistical together with a random selection with 0'/5 < μ < Γ.Ό completeness but was not thought to be seriously biased selected by large H, some at negative declinations. The except by the magnitude limit of the Lowell catalogs. program was in part a search for new, faint yellow and red With one goal study of halo dwarfs special emphasis was degenerates and colors LC = 1,2 were preferentially placed on selection for high tangential motion {vt ^ 150 selected in the sample with motions less than 1". This km s1). Unfortunately, few such stars prove to have proved fortunate, supplying many subdwarfs. Some published IR data; at a given color, old-disk outnumber fainter LHS stars (Luyten 1979), of particularly large halo stars by ~ 1000, the latter will be 5m fainter (and,

787 © Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 788 JESSE L. GREENSTEIN therefore, missing from various source lists). It appears, working on these important problems. Perhaps the data in fact, that published IR data have been not only severely here presented will help stimulate their labor. brightness limited but particularly rare for high-velocity stars. In the direct determination of bolometric luminosi- 2. Sources of Data ties I have included almost every known high-velocity The MGSP provides an overabundance of data, 64 or northern star with complete data, some fainter LHS stars, 128 points; limiting measurements to seven representa- and a few candidate "brown dwarfs". To balance these a tive points proves adequate. These were selected as spots group of high-velocity stars was added, whose Mbol could with least possible blanketing in data taken at 80 A or be calibrated by a method based on those stars having IR 160 A resolution. Table 1 gives the nomenclature, origi- data. Early discussions of subluminous red stars are Eg- nally chosen for my work on the white dwarfs, but with gen (1968, 1969) and Greenstein (1969). some points shifted onto maxima between TiO bands. The work of Berriman and Reid (1987, hereafter BR) These points are identified either by names or by fre- marks an important step forward in the technique of using quency, the latter always given in square brackets [ ], mid-IR information to obtain Mbol. Their modest-resolu- with units inverse microns. The peaks were selected near tion IR spectroscopy demonstrated the existence of H2O central wavelengths of common broad-band systems. My bands with strengths like those predicted by Mould s R is at a narrow, only partly clear peak; is at the most (1976a,¿) model atmospheres. These bands affect Mbol nearly clear peak in the red, but possibly affected by Ha significantly; allowance for H2O is made by BR and in the emission; Β has been shifted to avoid 4227 A of Ga I. present study, thus improving the Greenstein, Neuge- Mould (1976a, 1978) used some of these same high bauer, and Becklin (1970) least-squares blackbody fit, a spots to compute "continuum" fluxes in his models to ν ^ method also used by Veeder (1974). We must look at this [1.712]. The data reductions were on the original Oke- in some detail since the temperature scale for the dM's Schild AB69 system, but corrections to AB79 are negligi- remains an elusive, most important problem. How signif- ble on the scale of colors of red stars. (A word of excuse icant is a least-squares blackbody fit for temperature, may be in order; over 100 tapes of my MGSP observations given the severely nonblackbody shape of the energy were lost during a building modernization, so rereduction distributions? In the use of L = L may be obtained was impossible. Digital and graphical outputs were, for- accurately by integration of the fluxes. But depressed tunately, preserved. All data had to be typed into the fluxes in bands and lines affect the shape strongly enough computer. Such are the hazards of electronic data re- that decisions must be made how to weight data points in trieval.) The AB system gives fluxes in meaningful energy determining reff. Specifically, BR determine Teíí, fitting units, millijanskies or cgs. But the IR magnitudes are Planck curves of equal area; I quote "normalized to the published on scales with Vega set at 0m; the Gal tech flux density at 2.2 μιη (assumed to measure the stellar calibration to place them on an energy scale, additive to continuum)". An approximately equivalent method of fix- filter magnitudes (see Table 1), give AB such that, like the ing the temperature is to compute with the Planck func- MGSP magnitudes, fluxes are derived from: tion, BV{T), a bandwidth Δν(Γ) such that, after assuming logio/v^ -0.4 XABV +6.56 . (1) that the observed flux FK = BK{T), the correct luminosity, 26 -1 2 -1 L = FKX Δν(Τ), is obtained. It proved difficult in practice Here fluxes are in mjy, i.e., HT ergs s cnT Hz . On to obtain a useful parameter Δν to describe adequately this physical scale, in which the mid-IR magnitudes are the mid-IR fluxes, from the limited observations made written in lower case, colors are {j — h) = {J — H) — 0?46; through filters at arbitrary fixed intervals. The blackbody energy distribution narrows at low temperatures, table 1 through the exp — (hv/kT) factor, and might be fitted if Nomenclature and Properties of Standard Wavelength Bands used in Multichannel Spectrophotooetry; Calibration enough spectrophotometric data (low resolution) were of the Mid-IR Filter Bands to the AB Scale available. An empirical Δ ν is also affected by the (largely IR AB Relation nU unknown) shape of infrared absorption bands. Formal (microns) (inverse errors of the BR fits are satisfactorily small, ± 110 K, but microns) the systematic errors in Te{[ may be appreciably larger, M m nFtt+3.42 4.8 0.208 L 1 1=1.+2.79 3.5 .286 given the restriction on the least-squares method im- Κ k ksR+l.87 2.2 .454 posed by the heavy weight ascribed the 2.2-μιη data. A H h h=H+1.36 1.65 .606 J j jeJ+0.90 1.25 .800 direct fit to theoretical model atmospheres including I* 1.00 1.000 H2O, TiO, MgH, and CaH bands and the myriads of I 0.8265 1.21 R 0.7102 1.408 atomic lines would be ideal; ample data exist to justify R* 0.6579 1.52 V 0.5405 1.85 such a program. Unfortunately, model atmospheres are G 0.4717 2.12 still incomplete, rare, and completely lacking below Β 0.4132 2.42 3000 K. Groups headed by Bessell and by Wehrse are

{h — k) = {H — K) — 0?51; an absolute magnitude, e.g., interpolate corrections as a function of a broad baseline m Mh = MK + l 87. The (/ - Η\(Η - Κ) color-color color. Further infrared spectroscopy may permit this. diagram is centered near zero on the {j — h),(h — k) scale. Available MC S Ρ photometry also permits blanketing at ν The basic IR data are from the useful Gezari, Schmitz, > 1 to be evaluated for each star. Therefore, the true and Mead (1987) compilation, neglecting differences be- luminosity can be derived from the summation Σιι^ X /v., tween the different observers' scales. Bessell and Brett where the u;, including blanketing will be modifiable as (1988) provide systematic corrections for careful use of the convenient. Table 2A provides sets of such weights; for variegated IR data, which I neglected. The parallaxes are the unblanketed case, columns labeled None; H2O blan- on an absolute system, by W. van Altena, in his ongoing keting alone, labeled Water; both H2O and metallic-line revision of the Yale Parallax Catalog (YPC); he kindly blanketing, labeled All. Since data at L,M are often un- provided a printout of data through 1987. Important small available, weights are given for use when Κ is the longest parallaxes used are mostly recent U.S. Naval Observatory wavelength observed. We include in the first weight, Wj, (USNO) values corrected to absolute; I have used a few an estimate for unobserved low frequencies, 0-2.2 mi- US NO unpublished CCD parallaxes (by Monet and crons. Assume a Rayleigh-Jeans shape below a lowest Dahn). I am grateful to them and to Gezari, van Altena, frequency Vq; its integral Vq X /(v0)/3 can be included in and Dahn for personal communications. w (v0). To fit the far-infrared more realistically, rather than With up to 12 data points in the flux, integration of total starting the Rayleigh-Jeans law at K, predict L,M statisti- energy may seem trivial, except for the systematic effect cally from K,L,M, using the six reddest stars in BR. Their = = produced by their choice at less than average blanketing. mean ratios of fluxes are: /0 286 0.565 X /0.454, /0.208 BR display the H2O bands as deep, wide absorptions 0.308 X /0.454. Add the Rayleigh-Jeans tail beginning at between peaks of infrared emergent flux. The IR filters this predicted/0 208 to determine the coefficient, given in were located at minima in the terrestrial H20 absorption, Table 2A, wk which multiplies the observed/^. and stellar radiation blanketed by H2O emerges at the How large is the optical region blanketing in a dM? We ]HK filter peaks. The confusing nature of the illustrate in Figure 1, and use the data for, the low-veloc- {J — H),{H — K) diagram may arise from subtle details of ity flare star Gliese 15B, G171-48, GQ Andromedae, type this reradiation as well as from the fact that the filters M6e, for which highest-resolution MCSP data were include spectrum with both stellar and terrestrial H20. If kindly made available by J. E. Gunn. It has Ml85= 13^2, we connect peaks by straight lines we overestimate the Mbol = 10^9, and Teñ ~ 3000 K. Connect peak fluxes at radiated flux; between J and the spectrum seems rela- [1.85] and [2.12] by lines and divide the interval into four tively undisturbed, while at higher frequencies the dips parts; residual intensities are 0.83, 0.68, 0.69, and 0.75 of below connecting straight lines reach 30%-60% in ab- those indicated by the lines drawn. Over that full interval, sorption. Detailed line and band blanketing were not the total light lost is 23%. The residual intensities fluctu- allowed for in the BR computation, based only on broad- ate even more at short wavelengths, but little flux re- band magnitudes. mains, so the integrated luminosity is less affected. The blanketing factors ^ 2), about 7%-30% for Gliese 15B, in 3. Blanketing Computations, Weight Functions Table 2B, permit computation of for ν > 1.00. A first attempt at evaluating Lboi was carried out by The absorption by H2O has more significance in the integrating flux distributions composed of straight lines, cool dM's of normal metallicity, where much of the lumi- numerically, or with a planimeter, over frequency limits nosity is found in regions where water absorbs. Unfortu- Vi, V2 set by data available, giving the sum Σ^, v2). (We nately, the BR data are given only sparsely; I supplant estimate the difference between blanketed and unblan- them with predictions from Mould s (1976&) 3250 Κ keted values of Σ later.) To define the Mbol scale, adopt as 33 _1 solar values, Mbol = 4?64, Lboi = 3.86 X 10 erg s , Tefi = TABLE 2Ά 5780 K. To include blanketing is difficult when sums are Weights for Integration of Fluxes Derived over irregularly spaced frequency intervals; integrating from AB Magnitudes In Ν Dwarfs under straight lines is equivalent to the results using the Freq Name BLANKETING None None All All Water trapezoidal rule. Each pair of data points contributes to Σ v v 0.208 M 0.108 0.108 a quantity 0.5(1^ + ^2)( i ~ 2)> nonuniform spacings .286 L .123 .108 make the computational improvement like the parabolic .454 Κ .166 0.262 .132 0.226 0.226 .606 Η .173 .173 .150 .150 .150 rule hard to apply. But the form of the trapezoidal rule .800 J .197 .197 .187 .187 .187 1.000 I* .205 .205 .198 .198 .205 itself suggests that we allow for blanketing by reducing 1.21 I .204 .204 .188 .188 .204 1.408 R .155 .155 .130 .130 .155 each frequency interval, (vj — ν2), by the fraction of flux 1.52 R* .220 .220 .155 .155 .220 1.85 V .300 .300 .220 .220 .300 lost between those peaks, replacing the frequency range 2.12 G .285 .285 .221 .221 .285 Ml -^) χ Κ - v2). If detailed H2O band profiles were 2.42 Β 0.250 0.250 0.187 0.187 0.250 available for enough stars we could evaluate all e s and

Frequency Frequency

Fig. 1-( A)—A multichannel spectrum of a late dM, Gliese 15B (G171-48), Mv ~ 13^2, Mhol ~ ΙΙΊΌ, plotted as absolute fluxes. The {Lv, v) data (unit erg s_i μηΓ1) small circles. Four large circles at left from mid-IR magnitudes; at ν > 1.0 MCSP magnitudes measured at least heavily blanketed points. Dashed lines connect these peak fluxes; broad depressions, ~ 30%, caused by H2O probably exist in the mid-IR. MCSP data near [1.00] seem consistent with the flux at [0.80], /, suggesting that the optical and IK calibrations roughly agree. (B) Note changes in both scales. The MCSP high points large circles) connected by dashed lines. The solid curve passes through data points measured at 40 A resolution. The fractional blanketing em n between frequencies m,n is the flux between the dashed and solid lines. (C) R,R*,V connected by dashed lines are bordered by strong TiO, e,,, „is large. Broad-band (V — /), (fí — /) are affected by this composition-dependent blanketing. (D) V, G, Β are near strong TiO; MgH at [1.9], [2.1], Mg ι [1.93]. The last "high point" at [2.42] (offscale to the right) must be affected by atomic lines; the [2.3] depression is in part Ca 1.

TABLE 2Β model of normal composition, easier to use numerically than the BR graphical output. After connecting peak Observed Blanketing within Frequency Ranges fluxes at , J, Η, K, and L, I find the H20 absorptions, 6^2 IR Water Factor MCSP Metals Factor also in Table 2B. About 14% of the light between L and J is Freq Freq 1.00 - i.¿1 or- absorbed by water in the Mould model. In a later flare star 0.30 - 0.42 0.18 1.21 - 1.41 0.09 (Gliese 406, G45-20, Wolf 359), near 2600 K, one of the 1.41 - 1.52 0.28 0.46-0.58 0.17 1.52-1.85 0.30 reddest in BR, the band depths are 20%-30%, occupying 1.85-2.12 0.23 much of the space between filter peaks. But, at least, 0.63 - 0.77 0.10 2.12 - 2.42 0.22 2.42 - 2.80 0.30 there is a rough agreement with Mould; we use the factors in Table 2A, valid for the Mould 3250 Κ model, to com-

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System LOWER MAIN SEQUENCE IN DISK AND HALO 791 pu te the final blanketed For bluer stars of the halo How much are computed bolometric magnitudes af- both metal and HgO blanketing is small, and the latter is fected by the range of frequencies for which data exist, unknown. We evaluated Σ, and thence Mbol, using un- when we must use incomplete data? We evaluate the blanketed coefficients from Table 2B if (V — fc) < 2^0, and summed contributions Σ over partial ranges. In one of the fully blanketed coefficients for redder stars. A single blan- reddest stars with complete data, VB 10 (Gliese 752B), keting correction does not introduce a large error, since the results of test summations using various sets of rele- the sources of blanketing operate in different regimes. vant Wi are: fully blanketed, range M to Β, Mbol = 13? 14; The ratio/i 85//0 45 = 0.06 for Gliese 15B, and/2 ^//0.45 = range KtoB, Mbol = 13T20 but if only H20 blanketed, it is 0.02. In such red stars, whether we use a single value of 13? 19; with infrared data only, range M to/, 13?34, which metal blanketing or none hardly affects the answers. But without blanketing would be 13?03. For seven stars with in all cool dM s we must use H2O blanketing. Bluer (V — k) from 1^8 to 6^8, the difference between full and high-velocity stars should have H2O weakened, if low Ζ is no blanketing averages 0?14, half from the metals in the accompanied by low O/H. Infrared spectrophotometry is bluer stars, nearly all from H 0 in the redder. If one lacks badly needed to test this prediction. 2 We have emphasized the blanketing problem for cooler all information about metal blanketing, a safe estimate is stars; for bluer stars it is less important, since they emit to add 0T06 to the answer obtained by connecting high little energy at long wavelengths. Sum fluxes from a optical points; similarly, including H2O adds 0?10. For 3000 Κ blackbody; the sum, Σ^. Χ Β (vj gives a total 17.53 those suspected brown dwarfs that are as yet unobserved (arbitrary units), between frequencies [0.208]-[2.42], optically, integration of the infrared alone (v ^ 0.8) un- 11.41 in the mid-IR, between [0.208] and [0.800], and derestimates the brightness by at most ^0?15. 6.12 in the optical region, [1.00]-[2.42]. The Rayleigh- In review, we use the blanketing, as derived from Jeans extrapolation beginning at Κ involves less than 4% Gliese 15B (for metals) and the 3250 Κ model (for H2O), to of the energy; the optical region contributes 35%, the give a consistent, reliable scale of luminosities. Some visual band, [1.85], only 2.2%; Η and / together con- practical details involve the units; if we correct the star to tribute 37%. This should remind us, and emphasize, how 10 pc distance, the apparent mv(i) are absolute Mv(i) and poorly Mv indicates luminosity; its bcV (bolometric cor- from equation (1) give monochromatic Fv(¿) in millijan- rection) depends far too steeply on temperature. Ml or MR skies. The integration used weights on a scale wave num- will be preferable in studying the luminosity function or bers per micron; converting to cgs, and per Hz, and to a initial mass function. M^. or Mu are even better, because of distance of 10 pc, we have Lv(i): small bolometric corrections; if possible, statistical stud- 28 ies of, as well as searches for, low-mass stars should be L- 3.59 χ 10 Χ Σί^υ(ί) , (2) shifted to Ml or longer. 6 L/Lö = 9.30 χ 10~ Χ Σιν^ , (3) The final wi were evaluated twice with differences ~ 3%. The absolute calibration from the mid-IR magnitudes Mbol = 17.219 - 2.5 x log1(£u;¿Fv(¿). (4) to their AB values may be uncertain by ±5%, dwarfing The reader can derive the apparent magnitudes by using errors of integration (except for variations in blanketing). the Yale Parallax Catalog; however, I hope to publish raw The parallax error usually remains the largest uncertainty magnitudes separately, with a detailed spectroscopic in M . We compare our M with those of BR. They used bol bol measurement of the depth of bands. different IR data, calibration, and parallaxes; we adopted their data and parallaxes (their Appendix A) for the eight 4. The Bolometric Luminosities and Corrections stars in common. Using my fully blanketed wi the mean We present in Table 3 some data on 71 Κ and M stars. difference between Mbol(/LG) and BR is: Column 1 gives Gliese, Gliese, and Jahreiss or parallax m m (Mbol(/LG) - MUBR)) - +0 025 ± 0 010 , catalog (YPC) numbers; other names and 1950 positions with σ = ±0,!1026. Inclusion of Gliese 447 (FI Virginis) are in columns 7 and 8. All but two of these stars, and the raises the mean difference to 0?048 ± 0?026, with σ = two suspected brown dwarfs, are in the LHS catalog. ± 0m072; the BR analysis of that star may be numerically They represent a good sampling of objects with motions incorrect. Evaluating the difference between Mbol from greater than 075 including sdG, a few dK and sdK and my own data (as shown in Table 3) and eight from BR gives many dM and sdM. The color in column 2 is (V — A:), i.e., —0T023 ± 0T034, over the range 8?5 — 12T7, consistent [1.85] - [0.45], remembering that k = K + lm87. The V with expected photometric errors and different treatment magnitude measured at 5405 A, [1.85], is not identical of blanketing. Using the wi is simple, and my MCSP data with the broad-band V, whose wide filter bandpass con- are preferable to the broad-band magnitudes when evalu- tains deep TiO band depressions. Section 3 described ating energy at the higher frequencies. One result of a how MCSP and infrared magnitudes, converted to the AB fixed blanketing at (V — k) > 2T0 is a downward step in scale, were used to compute the Mbol in column 4. The m Mbol-0 10. absolute parallax system is that of the new YPC, in W. Van

TABLE 3 Colors, Luminosities,and Bolometric Corrections for 71 Main Sequence and Subdwarf Stars CAT V-k R*-I* Mbol bck QV NAME RA DEC bcV bvR bel be I* 1 2 3 4 5 6 7 8 9 10 11 12 15A 2.15 1.24 8.93 -0.71 6171047 0015+437A 1.44 0.35 -0.31 -0.70 15B 3.08 1.85 10.99 -0.87 6171048 0015+4373 2.21 0.88 -0.20 -0.72 48 2.49 1.66 8.39 -0.74 6242076 0058+714 1.75 0.65 -0.36 -0.70 1029 4.24 2.70 10.95 -1.02 6069047 0102+282 3.17 1.60 0.03 -0.65 65ABb 4.68 2.95 11.77 -1.06 6272061 0136-182 3.62 1.97 0.15 -0.63 83.1 3.52 2.15 11.20 -0.91 1 6003033 0157+128 2.61 1.23 -0.22 -0.64 87 2.00 1.22 8.18 -0.53 3 6073035 0209+033 1.47 0.31 -0.23 -0.57 105B 2.98 2.02 9.88-0.83 2 6073071 0233+066 2.15 0.90-0.33-0.77 123 1.57 0.83 7.12-0.57 2 6076058 0303+017 1.00 0.04-0.36-0.60 129 1.66 0.92 10.48 -0.47 5 6005022 0310+186 1.19 0.26 -0.24 -0.54 Y717 -0.10 0.35 6.39 0.30 8 6246038 0326+665 0.20 -0.06 -0.26 -0.36 Y749.01 1.84 0.61 9.14 -0.60 5p 6077061 0330+018 1.24 0.05 -0.14 -0.45 1062 2.27 1.28 10.30 -0.59 5 6160005 0335-116 1.69 0.62 -0.18 -0.53 1064 1.70 0.90 9.45 -0.42 7 6095059 0346+432 1.28 0.16 -0.23 -0.57 158 0.32 0.46 6.78 0.06 4 HD25329 0359+351 0.38 -0.04 -0.15 -0.42 169.1A 3.29 2.16 9.79 -0.91 6175034A 0426+588 2.38 1.03 -0.18 -0.73 184 1.76 1.06 7.69 -0.44 6191019 0459+530 1.32 0.31 -0.27 -0.58 5.24 3.78 12.42 -0.97 LHS0207 0529+795 4.27 2.11 0.13 -0.70 1083ABb 4.70 3.16 11.17 -1.05 6100028 0537+247 3.65 2.04 0.14 -0.65 211 0.11 0.31 5.53 0.19 Y001289 0537+534 0.30 -0.10 0.24 -0.36 212 2.05 1.12 7.91 -0.68 6191051 0537+534 1.37 0.27 -0.36 -0.68 213 2.98 2.07 10.15 -0.82 6102022 0539+124 2.16 0.93 -0.26 -0.72 226 2.45 1.42 8.68 -0.66 6222011 0559+821 1.79 0.61 -0.21 -0.61 1093 4.48 3.01 11.72 -1.04 6109035 0656+194 3.44 1.85 0.06 -0.68 268 3.68 2.35 9.76 -0.94 6087026 0706+386 2.74 1.31 -0.05 -0.70 273 2.91 1.95 9.68-0.79 2 6089019 0724+053 2.12 0.84-0.29-0.75 299 3.05 2.06 11.15 ^0.79 4 6050022 0809+089 2.26 0.91 -0.35 -0.79 1111 5.31 3.56 12.47 -1.11 1 6051015 0826+269 4.20 2.36 0.25 -0.61 310 1.81 1.01 7.07 -0.50 2 6243038 0831+674 1.31 0.35 -0.20 -0.49 328 1.58 0.94 7.82 -0.42 2 6046009 0852+017 1.16 0.23 -0.28 -0.55 366 2.02 1.27 8.18 -0.60 2 6252044 0941+762 1.42 0.39 -0.37 -0.65 369 1.98 1.15 8.36 -0.63 3 6161080 0948-120 1.35 0.27 -0.32 -0.67 373 1.81 0.97 7.52-0.46 1 6235049 0952+630 1.35 0.31-0.22-0.53 378 1.88 1.11 7.66 -0.45 3 6146006 0959+483 1.43 0.39 -0.20 -0.54 380 1.48 0.76 7.14 -0.40 1 6196009 1008+497 1.08 0.18 -0.23 -0.48 402 3.18 2.00 9.97 -0.87 6044040 1048+070 2.31 0.95 -0.19 -0.69 406 5.14 3.39 12.18 -1.12 6045020 1054+073 4.02 2.31 0.27 -0.57 411 2.05 1.23 8.74 -0.51 6119052 1100+362 1.54 0.44 -0.25 -0.62 412A 1.99 1.17 8.67 -0.66 6176011 1102+437A 1.34 0.22 -0.41 -0.79 412B 4.32 2.77 12.08 -0.93 6176012 1102+437B 3.36 1.82 -0.07 -0.69 424 1.81 1.05 8.15 -0.48 3 6236065 1117+661 1.33 0.32 -0.24 -0.58 436 2.48 1.59 8.71-0.74 2 6120068 1139+269 1.74 0.55-0.35-0.75 445 2.74 1.82 9.98 -0.74 3 6254029 1144+789 2.00 0.71 -0.31 -0.77 447 3.34 2.12 10.77-0.85 1 6010050 1145+010 2.49 1.06-0.06-0.61 451A 0.09 0.35 6.46 0.18 7 6122051 1150+380 0.27 -0.10 -0.25 -0.38

Altena s current revision and with the few CCD values (R^ — ZJ = [1.52] — [1.00], the least blanketed color already mentioned on the same system. Individual stars measurable with the MCSP. M [1.00] itself proves useful, without parallaxes (e.g., suspected brown-dwarf compan- giving Mbol when infrared measurements are absent; note ions of white dwarfs) or without optical data are included, how nearly constant hcl^ (column 12) is. Given a measure for which I had to "invent" (V — k), (R^ — /J to permit of M [1.00] uniform plotting of Table 3 data. Those are indicated by 350 in steps of 50 km s . Stars with Qv> 4 are derived from the composite magnitudes, corrected for likely to be members of the halo subdwarf group and may the visual Am given for the companion. In column 3 are be expected, statistically, to have lower metallicity, Z.

TABLE 3 (continued) CAT V-k R*-I* Mbol bck QV NAME RA DEC bcV bvR be I be I* 1 2 3 4 5 6 7 8 9 10 11 12 488 1.56 0.86 6.90 -0.49 6014006 1248-004 1.07 0.12 -0.35 -0.65 4.16 2.73 11.65 -0.99 LHS0362 1345+238 3.17 1.64 -0.02 -0.73 7.7 5.0 14.99 -1.37 GD0165B 1422+195 7.23 4.24 13.65 -1.29 LHS2924 1426+334 5.94 3.65 1.31 -0.14 552 2.25 1.34 7.79 -0.71 6135056 1427+157 1.54 0.39 -0.36 -0.71 6.28 4.04 12.92 -1.21 1 LHS2930 1429+594 5.07 3.12 0.58 -0.48 569B 6.3 4.1 12.58 -1.25 1 6136028B 1452+163 570.2 1.44 0.84 9.07 -0.36 3 6166057 1455+316 1.08 0.16 -0.27 -0.54 579.2A 0.12 0.39 6.82 0.15 8 HD134439 1507-161 0.27 -0.15 -0.29 -0.41 579.2B 0.36 0.48 7.06 0.07 8 HD134440 1507-162 0.43 -0.05 -0.26 -0.42 589A 2.45 1.54 9.78-0.71 2 6137026 1533+178 1.74 0.61 -0.36 -0.76 630.lAb 2.98 2.01 10.32-0.78 4 6225067A 1633+572 2.24 0.91 -0.30 -0.81 643 2.86 1.84 10.34-0.78 1 WOLF629 1652-082 2.08 0.78 -0.29 -0.81 644C 5.85 4.03 12.71-1.10 1 VB008 1652-083 4.76 2.63 0.33 -0.68 687 2.54 1.61 8.83-0.75 1 6240063 1736+683 1.90 0.66 -0.33 -0.72 699 2.86 1.88 10.85 -0.75 6140024 1755+045 2.11 0.79 -0.37 -0.83 701 2.02 1.21 8.39 -0.61 6020022 1802-030 1.41 0.31 -0.41 -0.75 2.42 1.17 10.91 -0.70 LHS3382 1824+771 1.72 0.37 -0.27 -0.62 Y4308 1.59 0.93 8.45 -0.37 6021023 1839+008 1.22 0.21 -0.23 -0.57 752A 2.42 1.48 8.54 -0.74 6022022 1914+050A 1.68 0.49 -0.34 -0.75 752B 6.78 4.50 13.20 -1.27 1 VB010 1914+050B 5.51 3.32 0.81-0.37 781 1.97 1.07 9.35 -0.50 6230026 2003+542 1.47 0.41 -0.20 -0.56 Y791.2 3.58 2.20 10.41 -0.94 6024016 2027+095 2.64 1.25 -0.10 -0.68 812 A 2.72 1.77 8.74 -0.75 VB011 2054-050 1.97 0.77 -0.32 -0.74 Y5092 1.92 1.14 9.90 -0.45 6231027 2106+595 1.47 0.40 -0.29 -0.60 866b 4.57 2.96 11.56-1.04 2 6156031 2235-155 3.53 1.89 0.14-0.63

Columns 5, 9, 10, 11, and 12 give the negatives of bolo- culty. In the reddest known OD stars FeH absorption is metric corrections to the magnitudes at frequencies visible but not strong. We list these negative factors, but [0.45], [1.85], [1.408], [1.21], and [1.00] μηΓ1. In column prospects for a long-wavelength filter magnitude with 5, bck = Mk — Mbol is a slowly varying quantity measuring CCDs seem favorable. The TiO bands weaken at lower Δνκ (see Section 1); it estimates a blackbody temperature optical frequencies; the H2O becomes stronger at still quite similar to that derived by BR. lower frequencies. Somewhere in the 9000 A to 10000 A In spite of the higher resolution of the MCSP, com- range is the least-blanketed region of dM spectra, provid- pared to broad-band filters, all measurements at frequen- ing the nearest to an ideal measurement of absolute cies ν > 1.1 μηι-1 are in or near heavily blanketed re- "continuum" flux possible. Figure 2, discussed below, gions. All broad-band colors represent a combination of shows the relation between {R^ — 7J,(V — k). band strengths and continuum rather than pure contin- In Figure 3 we plot bolometric corrections, bcX, for uum fluxes. From my experience [1.52]-[1.00] involves individual stars, with the cubic polynomials fit to the data. less blanketing than does [1.85]-[0.45]. It should, there- In fitting, we omit those stars with incomplete data and fore, be less subject to effects of differential blanketing in G77-61 (Y749.01), the carbon-rich evolved dwarf star stars with various metallicities. The heavy blanketing in which deviates from the normal color-color relations by the yellow-green, e.g., near [1.85], apparently discour- about 0?5. The bcV = Mv — Mbol is near the (negative of) aged Mould (1976¾) from predicting higher-frequency the commonly used bolometric correction. As for bck, emergent fluxes; his theoretical colors are limited to although the measurement at 2.2 μιη is near the energy points longward of [1.712]. maximum in the infrared, late and early dM's are too hot Although {R^ — /J is a favored color, drawbacks exist to for the k magnitude to represent the total flux as well as photometry at photocathodes used for the infrared end the magnitude does. Figure 3 shows the expected clear of the multichannel were type S-l, low in sensitivity, high progression from lock, which decreases with increasing in noise, and possibly unstable. These longest wave- {V — k), to hcl^ with a shallow minimum, through be/, lengths in the MCSP had photon noise levels ±0,!1015 to bcR to bcV, which increase with (V — fc), with amplitudes ±0m019 for a star of 12m, but ±0m07 to ±0m09 at 15m. largest for observations at V. Visual absolute magnitudes, Thus, the magnitude becomes noisy in sdM s, which in fact, give an unfortunately overstated impression of are faint stars that are not very red. The strong atmo- spurious faintness, caused by the rapid increase of TiO spheric water-vapor extinction near is a technical diffi- blocking. V is both composition- and temperature-depen-

0 2 4 6

[1.85] - [0.45] Fig. 2-Comparison of the most useful colors, (R^ — 7J, (V — k), the latter incorporating an infrared Κ filter magnitude, transformed to the AB scale Ί (i.e., /: = Κ + 1" 87). Plotting symbols indicate tangential velocity: Qv = 1, plus; Qv = 2, X ;QV = 3, solid star; Qv = 4, 5, small circle; Qv = 6, 7, 8, large circles. Blue high-velocity stars deviate somewhat from the locus plotted, the cubic derived from 128 stars. The Qc = 3 stars are not distinguishable colorimetrically, Table 4 has the coefficients of this cubic polynomial fit. An (R^ - ZJ predicted from (V - k) has error about ± 0^08, a predicted (V — of about ± 0"115. Red high-velocity stars are rare. The difference in blanketings between metal-poor, high-velocity, and low-velocity OD stars causes systematic color differences ^ OTIS. All magnitudes are on the Oke-Schild AB69 scale.

dent. In my opinion, MR, Mj are to be preferred, with the quadratic are often negligible. On the Planck slope of concentration on M (/), at 8260 A practically feasible. The a blackbody, where most optical data are located, a con- brightnesses at V,R are measured at peaks difficult even tinuum color, (i — j), in magnitudes is larger in proportion with the MCSP, more so with broad-band filters. The to the frequency interval spanned, (v¿ — v^). Nonlinear faintest fully observed star, VB 10, is 13T2 bolometrically, terms then are measures of local distortions produced by 14?0 at 1.21 μιη-1, and 18?? visually. The reddest dM's bands. Assume that blanketing in magnitudes increases in are really not very faint; the lowest (stellar, still slightly proportion to frequency; then blanketing increases all uncertain) luminosity in Table 3, LHS 2924, is Mbol = such colors from their line-free "continuum" values pro- -4 13^65, i.e., 2.5 X 10 Lö, but its Mv = 19?6 corresponds portionally. A narrow color-color relation is thus pre- to only 10-6 of the solar visual luminosity. served. But the temperatures labeling the colors would In order to represent all data on the various correlations not be the same for all Z. Establishing a meaningful in a systematic fashion. Table 4 contains unweighted, temperature scale from colors remains the ultimately least-squares coefficients in the formula sticky point in understanding the dM's. But empirical relations are practically useful and should permit transfer = üq + öjX + CI2X2 + · (6) Ύ of data from one practical system to another; it should be Note that we use cubics only for consistency, the shape possible to express my colors in terms of broad-band VR1 having no physical significance; improvements in χ2 over for stars measured on such broad-band systems. A num-

2 4 2 4 [ 1.85 ] - [ 0.45 [ 1.85]-[0.45]

Fig. 3-The differences Mv — Mho\ = bcv, between absolute magnitudes at ν and the bolometric luminosity, negatives of the bolometric corrections. 68 stars from Table 3 are plotted with the cubic fit to the 38 low-velocity stars, Qv = 1, 2; symbols as in Figure 2. The circled cross for G77-61 deviates most strongly, with its flux distorted by strong C2. The amplitudes of the corrections vary systematically with ν and color index: (A) bcA: becomes more negative; (B) be/* has a shallow minimum, and small range, O'Î'S; (C) and (D) be/ and befí become more positive; (E) bcV becomes much more so, 111 attaining a range near 6 . The energy maxima are close enough to one micron that Ml 00 alone predicts the bolometric magnitude. ber of these stars, identified by Gliese numbers, are in OD and halo stars. Most stars in Table 3 have old-disk Leggett and Hawkins (1988); Dahn (private communica- composition; we use the 38 stars with complete data and tion) is measuring broad-band (V — Z) for faint parallax Qj. = 1, 2 in Table 3 to compute the coefficients of the candidates on a system quite close to the MCSP. cubic polynomials (eq. (6)) which define the OD locus The size of (χ2/Ν)1/2 for the fits in Table 4 gives an used for this paper. The smaller χ2 per data point reduces estimate of internal errors. The combined errors of com- the σ to 0m03 - 0m06. paring one color with another, or of the bolometric cor- The array of coefficients gathered in Table 4 might rections, have σ ~ 0?04 — 0?06 in a sample combining suggest that substantial differences exist between sam-

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System j 796 JESSE L. GREENSTEIN O\—I M TABLE 4 Ccu g Coefficients for Cubics Fitted to Color-Color Relations, 2 Bolometric Corrections, and HR Diagrams

Relation χ 1 X Clr-clr V-k R*-I* -0.85 3.189 -0.7897 0.10398 3.02 128 0.1399 -0.01209 0.91 128 Clr-cir R*-I* V-k. 0.29 0.2196 a Clr-clr V-I R*-I* -0.30 2.592 -0.8857 0.14444 0.42 57 Clr-clr V-I R*-I* -0.03 1.914 -0.4177 0.05287 1.05 110 Clr-clr R-I V-I 0.14 -0.1515 0.3441 -0.04430 0.30 57 a 0.3002 -0.03804 0.57 110 Clr-clr R-I V-I 0.11 -0.0809 a Clr-clr R-I R*-I* -0.05 0.5293 0.1231 0.03203 0.24 57 Clr-clr R-I R*-I* -0.08 0.6125 0.0365 -0.01022 0.55 110 -0.6041 0.0975 -0.00609 0.121 54b bck Mk-Mbol V-k 0.28 c V-k 0.25 -0.5954 0.0956 -0.00596 0.047 38 bck Mk-Mbol 54b bcV MV-Mbol V-k 0.27 0.4099 0.0921 -0.00557 0.128 bcV MV-Mbol V-k 0.25 0.4134 0.0930 -0.00575 0.057 38c bcV MV-Mbol R*-I* 0.20 I.0165 -0.0137 0.01442 1.25 54t> 0.0165 0.00983 0.97 38 c bcV MV-Mbol R*-I* 0.19 0.9840 c bcR MR-Mbol V-k -0.12 -0.0178 0.1461 -0.00994 0.147 38 bcR MR-Mb o 1 R*-I* -0.09 0.0540 0.2919 -0.02802 0.75 38c 0.0256 0.00215 0.28 54b bel MI-Mbol V-k -0.21 -0.1057 c bel MI-Mbol V-k -0.23 -0.1053 0.0296 0.00162 0.20 38 bel MI-Mbol R*-I* -0.12 -0.3070 0.1275 -0.00133 0.77 54b MI-Mbol R*-I* -0.11 -0.3662 0.1683 -0.00725 0.56 38 c bel 54b bel* MI*-Mbol V-k -0.29 -0.2470 0.0330 0.00004 0.26 bel* MI*-Mbol R*-I* -0.18 -0.5939 0.1853 -0.01245 0.23 54b -0.0034 -0.00953 16.7 54b Lum- clr Mbol V-k 5.09 1.669 c Lum- clr Mbol(OD) V-k 4.92 1.581 0.0448 -0.01420 8.39 38 -0.5542 -0.03996 17.4 54b Lum- •clr Mbol R*-I* 4.73 3.618 c Lum- ■clr Mbol(OD) R*-I* 4.20 4.112 -0.7259 0.05933 8.79 38 Lum- •clr Mbol V-I 4.20 2.368 0.0693 -0.03534 15.3 54b Lum- •clr MI V-I 3.63 2.949 -0.2427 0.01909 17.6 54b Lum- ■clr MV V-I 4.05 3.227 0.0736 -0.02000 17.0 54b Lum- •clr MI R*-I* 4.34 3.950 -0.7673 0.08644 19.5 54b Lum- ■clr MV R*-I* 4.85 4.790 -0.6430 0.06366 21.1 54b -2.542 0.3783 25.6 57 a Lum- -clr Mbol(HSD) V-I 3.57 6.824 a Lum- ■clr MI(HSD) V-I 3.28 7.033 -2.757 0.4334 26.4 57 Lum· -clr MV(HSD) V-I 3.28 8.019 -2.744 0.4307 26.5 57 a Lum- -clr Mbol(HSD) R*-I* 3.25 10.986 -5.826 1.0644 30.0 57 a Lum· -clr MI(HSD) R*-I* 3.01 II.000 -5.920 1.1071 30.2 57 a Lum· -clr MV(HSD) R*-I* 2.71 13.599 -6.808 1.2512 33.9 57 a

A cubic does not fit some clr-clr plots well, especially for the bluer stars; 128 stars of all velocity classes with IR and MCSP data define the mean relation. A partly independent sample of 110 (from Tables 3, 5) is about half high-velocity stars; the 57 from Table 5 all have high velocity. The HR diagrams for the 54 OD stars differ from those for the halo stars; formulae for the latter must not be extrapolated. Their cubics have strong inflections. MCSP (V-I)+0.2 mag place them near the broadband USNO system.

^he 57 halo subdwarfs having velocities exceeding 150 km/s, from Table 5, with G 77-61 omitted. They may have intrinsically different HR diagrams and do have small parallaxes; the Mbol is from MI*, using bel* (except for those with infrared data, whose Mbol is taken from Table 3). bA Table 3 sample of 54 stars with complete data and Qv=l,2,3. csame; the 38 stars with Qv=l,2 defining the OD loci in HR diagrams.

2 pies. The apparently large changes of the an and χ , Similarly, the blanketing at R^ needs to be less by 0^61. however, arise from instability in polynomial fitting. Es- Subluminous stars are extensively discussed by Eggen pecially for color-color relations or bcX, computed differ- (1969, 1971, and later) using broad-band (R — Z). Among ences between samples of 54 and 38 stars average only stars he mentions there is a near twin of Barnard's star, 0?02 within the range of star colors defining the relations; G124-23 (Yale 1352 = LHS 368), with (R, - ZJ = lm12, one should not extrapolate the formulae beyond the well- which Eggen (1971) viewed as very subluminous. The m m mapped regions, (fí, - /J < 3 , {V - k) < 5 In the H-R improved parallax leaves it subluminous, at Mbol = 10T11,

diagram relations, i.e., between Mx and color, however, but it has apparently normal TiO. An extremely metal- the difference is physical and significant. Descriptions of poor sdK in Eggen (1971) is G266-1 (LHS 4037), which the samples used are in notes to Table 4. More data than still lacks both infrared magnitudes and parallax. We will Table 3 provides are needed for an adequate (V — fc), assume that stars may be subluminous in the astrophysi- (R^ — IJ relation; a larger sample of 128 stars for which cally meaningful log L, log diagram, if they appear both MC S Ρ and mid-IR data existed was created to be grossly subluminous in a Mbol, color diagram. We should not forget such concerns but with demands on the differ- more uniformly distributed in color and Qv. Figure 2 shows the results, with cubic fits in Table 4; residuals still ential blanketing extreme (in the light of the model atmo- persist for the halo sdG subdwarfs at the left. The χ2 is spheres) we will, at least temporarily, assume that ap- reduced by using only the low-velocity OD stars to estab- pearance and reality conform. lish the fiducial curve; cubics hardly differ whether stars 5. Color-Luminosity Diagrams of Stars with Qv = 1,2 or Qv = 1,2,3 are used; the σ ~ 0?08. While with Infrared Data no clear dependence on velocity (and we hope on Ζ ) is apparent in the data, small systematic deviations appear Figures 4 and 5 are two primary color-luminosity dia- over parts of the curve. For only approximate use, linear grams, the first using the commonly available, very wide relations were fitted omitting the blue stars; valid for baseline {V — k); the other uses (R^ — ZJ, which is as (V - fc) > 1?4 or (R, - IJ > 0m7 are insensitive to differences in metallicity as possible with the MCSP. In these, 38 Qv = 1,2 stars have a cubic fitted (R, - 7J = -0m19 + 0.692 Χ (V - k) , (7) to define the OD main sequence. Open symbols are the 14 high-velocity stars, clearly subluminous for their colors {V-k)= +0T29 + 1.436 X (R, - 7J . (8) m by about 2 . The sample with Qv^4 contains no very red Note that ratio of frequency intervals for these two colors stars; a safe generalization is that among the halo stars is 0.52/1.40 ^ 0.37, far different from the ratio of 0.69 in with Qv > 4, with my apparent-magnitude limit and equation (7). These colors are not on the exponential tail selection criteria (including existing parallax and infrared of a blackbody. The columns of Table 3 listing the various magnitudes), the colors found are (V — A:) < 3m, and m bolometric corrections permit computation, from bcX — (R+ - ZJ < 2 . The scatter in these halo sdK, sdM sug- bcY, of any color (X — Y) of individual stars. In principle, gests that they do not fit a narrow, single color-luminosity were model atmospheres available, these could provide a relation; it is intrinsic. A (quite poor) linear fit for = 1,2 full Teff calibration as function of metallicity. is, only for orientation, Consider the color-luminosity relations: Barnard's star m Mbol = 5 85 + 1.209 X (V - k) , (9) (Gliese 699, G140-24) has a radial velocity which results in 1 m a total space motion 141 km s placing it in the = 3 Mbol = 6 ll ± 1.768 X (R, - ZJ . (10) class. Observed colors are (V — k), (R^ — IJ = 2T86, 1?88; The χ2 deviations from the cubic for the OD stars, how- the cubic predicts (R^ — ZJ = 1?78, only a modest devia- ever, suggest a moderately large but acceptable σ ~ 0?48; tion. But using either observed or predicted colors, it is this cannot arise from errors of parallax and color only. subluminous by about 1?2. Perhaps this is large enough Note that only two out of 38 OD stars were corrected for that we need not overemphasize astrophysical concerns duplicity, from cataloged observed differences between about detailed color-color relations which block the goal two components; a fraction of the other OD stars may well of finding the unique, reliable Tefrco\or relation. From be doubles. No search of the literature was made for the cubics for luminosity in Table 4, {V — k) predicts Mbol duplicity. But equal doubles are 0T75 overluminous. = 9?48, (R^ — IJ predicts 9?76. The observed value is Some of the supposedly OD stars are known flare stars, 10?85 and the parallax error (0''547 ± Ο'.ΌΟΙ) has negligi- others are dMe's and must show chromospheric activity, ble effect. The colors predicted from Mbol = 10T85 are and some may be young enough not to have fully evolved {V-k) = 3m84, (R, - 7J = 2m49. Thus, to place Barnard's to their MS position. We neglect the effects of youth on star on the low-velocity sequence requires that blanket- the spread in what we called OD on the basis of velocity ing in (V — A:) (which is largely the depression in V criteria alone. Some of the OD (and probably many Qv = magnitude) be 0?98 less than it is in the low-velocity stars. 3 stars) are old enough to have modest deficiency in metal

[1.85] - [0.45] [1.52] - [1.00]

Fig. 4-The bolometric luminosity, Mbo], versus (V — k). The H-R Fig. 5-The Mboi are plotted against (f^ — ZJ color; symbols as in Figure diagram for 71 stars shows that stars of high Q deviate from the locus 4. The highest-velocity stars are again about 2ni underluminous for this v m representing the OD. Plotting symbols, by space motion Qv, are as in color; some of intermediate velocity Qv = 3 are about l subluminous. Figures 2 and 3. The solid curve is a cubic fitted to the 38 stars of Qv = Relatively bluer sdM's, near (fí+ - Ij = ITO, are among the faintest 1,2, presumably OD composition. Some (^ = 3 stars are below the high-velocity stars. Blanketing by TiO and metals is far less at plotted OD locus, e.g., Barnard's star at 2^86, 1(05. Two suspected (6579 A) than at V (5405 A). Models of different Ζ (Mould 1976¾) predict brown dwarfs are at the lower right, color only estimated. The highest- differential blanketing, i.e., changes in (fí+ — IJ at a given reff too small velocity stars are about 2m subluminous for their color but have not been to shift the high-velocity, metal-poor sdM's as far to the left of the OD as found fainter than llm. Stars of lower metallicity have less blanketing at observations indicate. V than do OD stars, but lack of atmospheric models prevents evaluation of the effect of differential blanketing on (V — k). perature; energy so absorbed, if radiated in the mid-infrared, is included in the bolometric luminosity deter- abundance Z; the MS location is sensitive both to helium mined. Very low-temperature dust is possible, but these content Y and to Z. stars are mostly too faint for the IRAS survey. At the upper left, the H-R diagrams rise steeply; the After this work was completed, spectra of LHD 2924 (fí^ - ZJ of G2 V stars places the Sun just off these and LHS 2930 taken for me by Gunn, Schmidt, and diagrams, at (R^ — /J ~ 0^15, Mbol = 4^64. In that region Schneider with the four-shooter CCD instrument at the the lines are weak, and blanketing has only moderate 200-inch (5-m) telescope became available. These pro- effect on colors. The shape of the lower end, however, vided slit spectra at 25 A resolution, usable for at least depends on the extreme red color produced by strong rough spectrophotometry, but had excellent, high signal- TiO bands, which stretch the {V — k) scale; measured to-noise ratio. These confirm completely the puzzling colors, also, for the faintest stars need improvement. The weakness of all features in LHS 2924 (Probst and Liebert red stars with complete data have luminosity decreasing 1983; Liebert et al. 1984). We hope to analyze these soon; slowly, while both (V — — O increase rapidly, we have improved entries for these stars in the present presumably because their band absorption is so strong. Table 3. Their location in the various graphs, however, We mention again the strange case of LHS 2924, the did not change much from that with "invented data", reddest and faintest, which has much weaker TiO bands which proved correct to within ± 0?2. Why the cooler, and atomic lines than does the slightly brighter LHS 2930 fainter LHS 2924 has weaker lines and TiO bands than its (Probst and Liebert 1983; Liebert, Boroson, and Gi- near rival LHS 2930, O1!1? brighter, remains unknown. ampapa 1984). Their suggestion is that veiling begins in The cubic (or quadratic) fitted to the data has an appar- these coolest objects, affecting the run of color with tem- ent, not physically plausible minimum. This could be

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System LOWER MAIN SEQUENCE IN DISK AND HALO 799 caused partly by the "Malmquist" selection effect in impression that the bluer sdM's are extremely metal which only the brighter stars of a broad Gaussian have yet deficient. The spectroscopically peculiar LHS 3382 is been found in a magnitude-limited sample, in spite of the slightly redder and fainter, with comparable Mbol = m m m m vigorous search made for the faintest possible main-se- 10 91, Mv = 12 63, {V - k) = 2 42, (Z^ - ZJ = l 17; its quence stars. The two faintest M^/s are: VB 10 at 13^2, luminosity is based on a new small CCD parallax by LHS 2924 at 13?7; note the resolved companion, Monet and Dahn (unpublished), for which I am very GD 165B, at 14T99, which may be either the faintest grateful. Comparison with the OD prediction makes it established star or a brown dwarf (Becklin and Zuckerman 2^47 ± 0^44 subluminous. Its SIT spectrum at 7 A reso- 1989). The suggested brown dwarf, Gliese 569B (Forrest, lution (illustrated in Fig. 5 of AK, where it is called Skrutskie, and Shore 1988), for which no MCSP data LP 24-219) has strong MgH and CaH, weak TiO, very 1 exist, is not plotted. It has Mbol ~ 12 ¾ in Table 3, i.e., is strong Ca 1, and normal Na I, which are features of other not as faint as the LHS stars. Skrutskie (private communi- sdM's seen by Dawson and DeRobertis. cation) reports observation by a colleague of remarkably In a very different situation is the faintest halo suspect strong infrared H2O bands in Gliese 569B, suggesting a in Table 3, which has Qv > 4. It is Gliese 299, G50-22, a blanketing larger than used in my weighting factors but much redder star at Mboi = 11?15, Mv = 13T41, {V — k) = reasonable for a cool star (approximately 2200 K). 3^05, {R^ — ZJ = 2?06, which is not obviously spectro- We may correlate very high space motion with low Z, scopically peculiar at the MCSP resolution and shows expecting from theory that low-metallicity stars will be quite strong TiO bands. Almost certainly it has higher subluminous (see Section 7) for their temperature; the metallicity and is only 1^22 ± 0T17 subluminous. This colors at a given Τ may be somewhat bluer, for different Z, seems near the limit of redness at which the spectroscopic because of differential blanketing. Many stars in Table 3 peculiarities of halo stars remain obvious. The four halo have such high tangential velocities that we expect them stars studied by AK and DR suggest the importance, and to show, statistically, the metal deficiency similar to well- probably the relative simplicity, of model-atmosphere studied sdG's, i.e., Ζ ~ 0.0001. (See Laird ^0/. 1989.) It analysis of the extreme sdM's. Analysis of G50-22 will be will require a separate spectroscopic investigation to more difficult. Low temperature may affect our certainty demonstrate how small Ζ can be in these stars. A few have in calling a halo star metal deficient, when clearly sublu- already been described by Ake and Greenstein (1980, minous in a color-luminosity plane. Whether it is also hereafter AG) and in an important paper by Dawson and subluminous in the Mbol, log Teff plane will take a major DeRobertis (1988, hereafter DR). DR obtained radial study. We confine ourselves to luminosity, color dia- velocities, found a mean total space motion of 340 km s-1 grams. for the four AK objects, and demonstrated their extreme For the intermediate velocity group, Qv = 3 (100 < Vt spectroscopic peculiarity. Even at the low resolution of ^ 149) km s"1, ten of 14 stars lie below in Figure 4. the MCSP, these stars are startlingly different from OD Comparing with the OD polynomial, Mboi, (V — k) in dM's; some have the MgH bands the only strong remain- Table 4, the average displacements are: +0^4 ± 0?2 at Çv m m m m ing feature. Consider the interesting halo star, G5-22 = 3; +0 8 ± 0 4 at ρ, = 4; + l 8 ± 0 2 for Qv > 5. Only m m (Gliese 129); it has Qv = 5, Mbol - 10 48, Mv = ll 67, for the last group of ten highest-velocity stars does (V — k) = 1?66, (R^ — ZJ = 0T92. It is far from red (with a "subluminous" seem a genuinely significant term. The Lowell color estimate of only +2), but bolometrically it is systematic corrections arising from selection and parallax among the faintest high-velocity stars known. An MCSP errors (Malmquist or Lutz-Kelker) do not seem to be spectrum shows it to be nearly devoid of TiO; MgH bands responsible. We find a rare type of stars too faint; in a are its strongest feature. Its parallax, 0'.Ό311 ± 0'.Ό038 is magnitude-limited sample, statistical corrections make well determined; with the nominal parallax error, using them brighter. The parallaxes are smaller for sdM's. The both (V — k) and (R^ — ZJ it lies 2?97 ± 0T27 below the five smallest parallaxes used in Table 3 have a median OD sequences of Figures 4 and 5 and the cubics of Table value of 0'Ό22 and the next five have median 0'.Ό42. If we 4. The {R^ — ZJ needed to move G5-22 to the right onto ascribe errors of ± 0'.Ό04 (typical of modern USNO data), the OD sequence is 2?27. The 1T35 differential blanket- the derived M are in error by — 0T43, +0?36 for the ing required seems again to be unacceptably large. Gunn, smallest parallaxes, producing a systematic asymmetry of Schmidt, and Schneider kindly provided four-shooter only 0T04 (negligible for higher parallaxes). One more CCD slit spectra of this star at 25 A resolution. There are serious effect is that stars are excluded if the parallax is too no surprises: The MgH bands are the strongest feature in small compared to its error. Further, parallax observers the spectrum, no TiO is seen, and CaH is moderately often drop a star from their program if preliminary mea- strong as is Na I. However, the higher resolution and sures suggest an unfavorable ratio of parallax to error. signal-to-noise ratio suggest that some weak atomic lines Near the limiting size of parallax we include stars for exist, including the Ca II triplet and blends of Fe 1 listed which parallax may have been measured too large, a bias in Turnshek et al. (1985). The new spectrum justifies the making stars too faint absolutely. A parallax measured too

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 800 JESSE L. GREENSTEIN small can move a star to a higher-velocity bin, Qv, where it 1"Ό0. Of 58 stars in HCM, 19 are called "halo" , two with would appear too bright. Although accidental errors are (R - /)K > 1?00. In my Table 3 there are 68 stars with proportionately larger for sdM's than for the brighter, complete data; at Qv = 1, 2 there are 21 redder than nearer OD stars, we do not suspect their apparently (R — / ) > 1?00; at = 3 there are six; at (¾ 4 there are subluminous nature to result from statistical bias. The two. The 16 stars with (¾ > 4 have a median {R — I) = questionable parallaxes and colors used in Table 3 have no 0^46, are uniformly distributed in color, and reach 1^26 significant effect; upper limits to the brightness of the for Gliese 299, a star not apparently very metal deficient. brown-dwarf suspects in Table 3 with "invented" data My stars are somewhat bluer than the HCM sample. But would be important to define the shape of the H-R dia- note that the extreme metal-deficient and highest-veloc- grams for the faintest, reddest objects. ity stars do stand out here and in HCM, most vividly at This important result is neither completely surprising (V — fc) ~ 2m, {R^ - /J ~ 1?3. They apparently form a nor new; Eggen (1968, 1969, 1971) noted this using the continuous subluminous band from 0?5 to 3?0 fainter broad-band (R - I) scale. Eggen (1968) used brighter than the basic OD sample; this is brighter than Eggen s stars and larger parallaxes only, therefore emphasizing (1971) suggestion, but at nearly the same colors. the intrinsically brighter of this group. In fact, only three 6. A Larger Sample of Halo Stars Is Subluminous such stars meet the criterion used here that for the extreme halo Qv > 3. Greenstein (1969) called the red, most Fortunately, we can provide better statistics and ex- subluminous stars RSL or "Eggenites". Dahn and Har- tend the sample in Table 3. There are 250 stars with rington (1978) gave an early contrary view based on the known parallaxes measured in my MCSP program for few small modern parallaxes then available, but the situa- which (at 1 micron) gives good bolometric brightnesses. tion has much improved. VandenBerg et al. (1983) used Isolating all with Qv>: 4 not in Table 3 supplies 45 new measures of Teff from Veeder (1974), Mould (1978), Ake M (IJ, for which Mbol can be derived without IR data by and Greenstein (1980), and Upgren and Weis (1975) to using the dependence of bc/^ on color from Table 4 (see suggest that stars with low Ζ could be 2m-3m bolometri- Fig. 3B). The high-velocity stars from Table 3 are added, cally subluminous in the astrophysical diagram relating giving the group in Table 5; more detail is now included, luminosity and Teñ- In Hartwick, Cowley, and Mould i.e., three colors, three absolute magnitudes, Mbol, M185, (1984, HCM) new data are combined with theory; from Mj 21 and, in column 10, the reduced proper motion, broad-band (R - I)k colors of faint LHS fast-moving stars, H[1.21]. Comparison with commonly used broad-band they find late-type red Population II stars down to Μυ = systems (R - I)c, (R - Ι)κ, {V - I)0 can be made with 14m. They also obtained spectra showing weak TiO ac- these data. Selection for large H was largely from the companied by strong CaH, which together with the large Lowell catalog to mvg = 16?5, complete for parallax stars reduced proper motion HI (see eq. (15)) establishes that with > 1" in the northern sector of Giclas et al. (1971). The subluminous, low-Z stars do exist. Their colors lie in the restriction placed by the availability of IR data is obviated. range O'M < (fí — Z)K < 1?2; their important, faintest Data for the first 36 stars come from Table 3, which gives m group has reduced proper motions 18 < HI < 21?5. their positions, other names, etc. Entries in column 6 of Since Η and M correlate statistically through the mean Table 5 are a first large set of halo bolometric luminosities. space motion (for which they assume 320 km s-1), they Eggen (1987) gives references to his measures of broad- give M (/ ) corresponding to an assumed mean space mo- band (R — Z)o for most southern proper-motion stars, tion. HCM compare the VandenBerg et al. (1983) theo- which he is completing for the north. He shows the retical H-R diagram for low Ζ = 0.0001 with their various luminosity sequences resulting; his broad-band Π1 {R — J)K? HI diagram, with reasonable success. Redder M{1), (R — 1) diagram, however, reaches M{I) = +8 , stars with smaller Hj and with less-extreme metallicity ours to -11^5. (say Ζ = 0.001) are found to be consistent with interior Figure 6A-F shows the various color-luminosity dia- theory by adjusting their mean space motion to lower grams for the halo sdK and sdM's together with the data values. Are their most subluminous stars like LHS 3382, for 35 individual OD stars with Qv= 1,2 taken from Table G5-22, and others in my Figures 4 and 5? I believe so. Is 3. We omit G77-61 from numerical solutions but plot it in my lack of analogs to their faintest stars caused by my limit figures. We also omit the 16 stars of Table 3 with ζ)υ = 3 to to brighter apparent magnitudes? I attempt to answer this emphasize the gap between the OD and halo stars. Of the in detail in Section 6, concluding that the reddest HCM present sample of 58 halo stars, 24 have Mbol ^ 10^0; the m m halo stars might reach at most to lm fainter. While bright faintest are at ll 79 (LHS 17) and ll 34 (G260-1); the enough to appear in the Giclas Catalog, they lack infrared latter appears quite metal deficient. Table 5 also contains observations. [1.408] — [1.21] colors for the halo stars. These (R — Z) With only seven in common, comparison between my when converted to the HCM scale predict broad-band list and HCM data is difficult. Their reddest halo stars colors of 1^80, ΓΜ2, approaching colors of their reddest have (R — I)K= ITl; these correspond to MCSP (fí — /) < LHS stars. The median of my (R^ — ZJ color distribution is

Fig. 6-H-R diagrams for 57 halo stars (from Table 5), velocities > 150 km s_1. The Sun lies near the upper left corner. Symbols: Qv = 4, asterisk; small parallax X; Qv = 5, 6, ηo filled square, small parallax open square; Qv 2 = 6, 7, 8 filled five-pointed star, small parallax open star. The most subluminous halo star, LHS 453, with a very small CCD parallax, is at (V — Ζ ) = 2^12. The OD stars from Table 3 (small open circles) run offscale to the lower right, bolometrically fainter than any known halo star. Their cubic fits are those plotted in Figures 4 and 5. Cubics fitted to the halo stars (omitting G77-61) always have [1.85] - [1.21] [1.408] - [1.21] an inflection point, different from the OD. The bluer halo stars are nearly as subluminous as the redder. Interpretation depends on how complete the sample is. Theory predicts that stars with lowest Ζ exist only to (V — / ) < 2m; intermediate Ζ stars can be redder and fainter. Given a halo with a variety of low metallicities, we predict an inflection as observed. But in a magnitude-limited sample the intrinsically faintest are lost, also flattening the luminosity-color relation. To my observing limit, the high-velocity locus merges into that for the OD near = UTO. In (A) and (B) note the changed location of G77-61, the carbon star (circled cross). None of the 450 proper-motion stars inspected with the MCSP shared its peculiar spectrum. (B) The Mboi, {R — I) diagram is steeply inflected at 1 1 2 1 2 Mbo| ~ ΙΟ". In spite of its small amplitude [1.52] - [1.00] [1.85] - [1.21] with the MCSP, the H-R diagram for (R — I) resembles others in this figure. (C) The Μ^ι, {R^ — diagram retains the steeply inflected locus with most high-velocity stars well sepa- rated from the OD. A group at Μ^ι « 10™5 stretches over a wide range of color, 0^8 ^ (fí, - /J < 2m0. (D) The M[1.21], (V - I) relation shown is less inflected. (E) The M [1.21], (fí+ — /J diagram for halo stars retains a relatively clean separation from the OD stars until the loci merge. (F) The M [1.85], (fí, - IJ diagram has the least sharply inflected locus, with the least clear separation of the populations, probably because of the large bolometric corrections bcV. Here, the faintest OD stars are offscale m near Mv = 19 .

1 2 3 [1.52] - [1.00] [1.52] - [1.00] lm10, the reddest are LHS 17 (2m90) and G260-1 (2m22). are only labels for identification. Possibly they are inter- But these Qv = 4 stars are not spectroscopically very mediate in metallicity, like G50-22, which we will call Ζ = peculiar and are subluminous only by ΔΜ < ΓΓΟ. Note 0.001. But the effect of nearly quadrupling the size of the that in the absence of any quantitative analysis of any high-velocity sample has been to add red stars of this Ζ = metal-poor red sdM, the numerical values of Ζ used here 0.001 group; the most subluminous (with (ΔΜ ~ 2m))

TABLE 5

Colors, Luminositiesr and Reduced Proper Motions for,v High-Velocity Stars, with OD s £rom Table 3. (Parallax below 0. 015f Qv has !) 1 2 3 4 5 6 7 8 9 10 Star Name R*-I* V-I R-I Mbol MV MI Qv H(I) 15λ 1.24 1.75 0.66 8.93 10.37 8.62 13.60 15B 1.85 2.41 1.08 10.99 13.20 10.79 15.78 48 1.66 2.11 1.01 8.39 10.14 8.03 13.98 65ABb 2.95 3.47 1.82 11.77 15.39 10.92 16.80 83.1 2.15 2.83 1.45 11.20 13.81 10.98 15.81 105B 2.02 2.48 1.23 9.88 12.03 9.55 15.78 123 0.83 1.36 0.40 7.12 8.12 6.76 12.76 169.1A - 2.16 2.56 1.21 9.79 12.17 9.61 15.19 IGBSABb - 3.16 3.51 1.90 11.17 14.82 11.31 14.29 211 0.31 0.54 0.14 5.53 5.83 5.29 9.30 212 1.12 1.73 0.63 7.91 9.28 7.55 11.56 226 1.42 2.00 0.82 8.68 10.47 8.47 14.07 1093 3.01 3.38 1.79 11.72 15.16 11.78 16.80 268 2.35 2.79 1.36 9.76 12.50 9.71 13.75 273 1.95 2.41 1.13 9.68 11.80 9.39 15.16 1111 3.56 3.95 2.11 12.47 16.67 12.72 16.01 310 1.01 1.51 0.55 7.07 8.38 6.87 12.84 328 0.94 1.44 0.51 7.82 8.98 7.54 13.48 366 1.27 1.79 0.76 8.18 9.60 7.81 13.76 373 0.97 1.57 0.53 7.52 8.87 7.30 11.48 380 0.76 1.31 0.41 7.14 8.22 6.91 11.01 402 2.00 2.50 1.14 9.97 12.28 9.78 14.36 436 1.59 2.09 0.90 8.71 10.45 8.36 13.74 447 2.12 2.55 1.12 10.77 13.26 10.71 13.95 488 0.86 1.42 0.47 6.90 7.97 6.55 9.92 LHS362 - 2.73 3.19 1.66 11.65 14.82 11.63 17.83 LHS2924 - 4.24 4.63 2.34 13.65 19.59 14.96 19.60 LHS2930 - 4.10 4.57 2.50 12.89 18.06 13.49 17.96 58 9A 1.54 2.10 0.97 9.78 11.52 9.42 15.62 643 1.84 2.37 1.07 10.34 12.42 10.05 14.53 644C 4.03 4.43 2.30 12.71 17.47 13.04 17.52 687 1.61 2.23 0.99 8.83 10.73 8.50 12.47 752A 1.48 2.02 0.83 8.54 10.22 8.20 12.82 752B 4.50 4.70 2.51 13.20 18.71 14.01 19.88 Υ791.2 - 2.20 2.74 1.35 10.41 13.05 10.31 14.18 812 A 1.77 2.29 1.09 8.74 10.71 8.42 2 14.06 866b 2.96 3.39 1.75 11.56 15.09 11.70 2 16.91 G130043 0004+28 1.77 2.27 1.10 10.62 12.66 10.39 4 18.07 G030048 0006+08 0.86 1.32 0.42 9.34 10.42 9.10 5! 17.68 6217055 0028+52 1.76 2.21 1.04 9.51 11.45 9.24 17.67 G132057 0104+33 1.56 2.01 0.90 9.73 11.49 9.48 4 17.03 G034015 0113+24 2.03 2.48 1.21 10.98 13.27 10.79 4 18.73 G003029 0154+12 0.93 1.41 0.43 9.66 10.86 9.45 5 17.68 G003036 0200+05 1.01 1.51 0.52 8.77 10.02 8.51 7 17.62 G004029 0231+17 1.38 2.05 0.90 10.44 12.18 10.03 4 18.23

remain the yellower objects with Ζ = 0.0001. blanketing at [1.85]; faint stars now being observed at the The other columns of Table 5 permit us to plot the U.S. Naval Observatory by C. C. Dahn seem to be nearly color-luminosity diagrams of a more familiar nature for on my baseline, but with a 0^2 offset originating in the high-velocity stars, including M185, (V — Z) and M^i, definition of the zero point of broad-band color systems by (V — I), approximately like those obtainable from broad- AO stars. Figure 6 is a first display of properties of a band photometry. While previously I have criticized good-sized halo sample; with Table 5 these should pro- {R — I) because of sensitivity to TiO blanketing, its dia- vide observing lists for further detailed studies. gram has the same appearance as the others. It is difficult Figure 7 is the energy distribution of a metal-deficient to measure accurately at MCSP bandwidth, R located on a yellow halo star, G18-51 (2226+05, Y 5434.00, Wolf sharp peak between bands; in those with weaker TiO it 1037). It is one of the most subluminous stars in Eggen appears well behaved. My (V — /) is affected by the (1971). Its old parallax 0'.Ό54 has become 0'.Ό274 ± 0'Ό025

(continued) 6 7 1 Γΰ— Mbol MV MI Qv R(I) LHS0017 0243-05 2.90 3.28 1.80 11.79 15.12 11.84 4 19.90 6075047 0250+01 1.07 1.71 0.64 10.14 11.57 9.86 6! 18.83 6005007 0254+10 1.72 2.24 1.05 9.03 10.97 8.73 5! 17.00 6005022 0310+18 0.92 1.43 0.50 10.48 11.67 10.24 5 18.70 6078026 0313+37 0.69 1.08 0.33 7.84 8.68 7.60 4 15.08 6246038 0326+66 0.35 0.46 0.20 6.39 6.59 6.13 8 15.37 6077061 0330+01 0.61 1.38 0.19 9.14 10.38 9.00 5 17.25 6160005 0335-11 1.28 1.87 0.80 10.30 11.99 10.12 5 18.49 6079059 0339+12 1.20 1.79 0.81 9.73 11.27 9.48 4 17.19 6095059 0346+43 0.90 1.51 0.39 9.45 10.73 9.22 7 18.26 6007017 0358+18 1.06 1.63 0.59 10.08 11.43 9.80 8 19.20 HD25329 0359+35 0.46 0.53 0.11 6.78 7.16 6.63 4 14.61 6099033 0545+08 1.09 1.65 0.61 9.27 10.60 8.95 7 18.07 6105023 0611+15 1.26 1.84 0.74 10.44 12.01 10.17 5 18.56 6249046 0616+66 0.97 1.62 0.52 10.56 11.87 10.25 5 18.80 6103046 0634+34 1.71 2.16 0.97 10.90 12.81 10.65 4! 18.08 6112028 0733+03 0.69 0.99 0.29 8.79 9.54 8.55 7! 17.69 6251044 0737+72 0.71 1.34 0.44 8.53 9.52 8.18 7 17.30 6090025 0750+30 0.25 0.39 0.14 6.34 6.51 6.12 5 14.29 6050022 0809+08 2.06 2.61 1.26 11.15 13.41 10.80 4 18.54 6117061 0957+32 1.18 1.67 0.66 8.17 9.52 7.85 4 15.53 6010017 1119+06 1.75 2.31 1.07 10.22 12.27 9.96 4 17.52 6176040 1130+44 1.10 1.74 0.81 10.59 12.04 10.30 6 19.79 6122051 1150+38 0.35 0.52 0.15 6.46 6.73 6.21 7 15.10 6011035 1200+08 1.31 1.87 0.76 9.47 11.07 9.20 4 17.31 6061021 1253+15 0.85 1.28 0.38 9.28 10.32 9.04 7 18.29 H134439 1507-16 0.39 0.56 0.14 6.82 7.09 6.53 8 16.32 H134440 1507-16 0.48 0.69 0.21 7.06 7.49 6.80 8 16.59 6137008 1525+16 0.93 1.39 0.44 8.24 9.40 8.01 7! 17.22 6015026 1532+02 1.03 1.56 0.70 8.31 9.62 8.06 5 16.59 LHS0414 1612+02 1.77 2.28 1.18 10.50 12.44 10.16 5 18.76 LHS0055 1612+19 1.79 2.32 1.13 9.58 11.62 9.30 4 17.05 6138025 1622+15 0.87 1.48 0.53 8.87 9.61 8.13 6 17.51 6169007 1623+27 1.12 1.64 0.64 8.31 9.68 8.04 4 15.64 6017021 1628+04 0.20 0.28 0.09 4.81 4.86 4.58 5 12.94 6138059 1639+10 1.35 1.96 0.84 10.58 12.19 10.23 5 18.58 LHS0453 1738+51 1.24 2.12 0.71 11.45 13.22 11.10 8! 21.15 6260001 1817+08 2.22 2.80 1.42 11.35 13.96 11.16 4 18.77 LHS3382 1824+77 1.17 1.99 0.64 10.91 12.63 10.64 7! 19.96 6021023 1839+00 0.93 1.45 0.44 8.45 9.67 8.22 6 17.22 6142052 1944+11 1.17 1.76 0.72 9.42 10.95 9.19 7 18.35 LHS0489 2016+12 0.94 1.42 0.61 10.47 11.68 10.24 7 19.30 6210019 2025+35 1.21 1.81 0.81 9.73 11.28 9.47 7 18.49 LHS0061 2102-17 1.21 1.76 0.71 8.72 10.18 8.42 4 16.40 6231027 2106+59 1.14 1.76 0.69 9.90 11.37 9.61 5 18.12 6067030 2250+17 0.71 1.09 0.31 8.08 8.94 7.85 5! 16.14 6128034 2305+31 1.04 1.57 0.79 10.08 11.41 9.84 7 18.95 6028043 2307+00 0.36 0.52 0.20 6.07 6.33 5.81 7 14.95 6190026 2326+42 1.13 1.66 0.73 9.32 10.76 9.10 4 16.94

in the YPC, still subluminous at M = 10T3. This MCSP bol magnitude diagrams, the result would have been vt = 600 scan, at 40/80 A resolution, has little noise in most of the km s 1, far beyond the escape velocity. G18-51 is com- spectrum. Extremely weak TiO, barely detectable CaH, pared with the OD star Wolf 629 (Gliese 643), of nearly and strong MgH mark it as very metal poor; given the identical luminosity, but much redder, with strong TiO. weakness of TiO, note the strength of Ca I, Ca π. The For this comparison, in Figure 7A, the AB69 were shifted simplicity of the spectrum makes it an attractive candi- to make the stars coincide at 1 micron, i.e., close to Mbol = date for spectral synthesis. With the new, small parallax it 10?3. We also locate these stars on the theoretical H-R 1 has vt = 283 km s . If we had its color only, and had diagram (Fig. 8). We cannot fit Wolf 629 with available neglected the difference between the OD and halo color- models, since it is so cool, but G18-51 falls in the range of

Fig. 7-Multichannel spectra contrast the extremely weak-lined halo subdwarf (top, solid line) G18-51 with the OD, Wolf 629 (bottom, dashed line). The bolometric luminosities are nearly the same, 10?3, but all colors of Wolf 629 in the optical region are redder. The flux deficiency of Wolf 629 must be balanced by its infrared brightness; no infrared data exist for G18-51. The apparent magnitudes, Aß, are shifted to give 10^3 using: AB - 2m2 for G18-51, Aß + 1^ for Wolf 629. The MCSP resolution drops from 80 A to 40 A at [1.75]. Tangential motions (neglecting radial velocity) are 283 and 37 km s-1. (B) The spectra of G18-51 (bottom trace) and model atmospheres have been rotated in the (Mv, v) Frequency plane by plotting DEL Mv = Mv — 2.0 X v. This flattens the continua to make absorption features more visible. The 3750 Κ models shown are from Mould (1976¿?), with [Fe/H] = 1 the OD composition (top, solid curve); = 0.1 (plus, dot-dash) and = 0.01 (X, dashed curve); vertical shifts separate the curves. Note the fading of the TiO bands with decreasing [Fe/H]; they are nearly absent at 0.01, and in G18-51. Stellar CaH at [1.46] is even weaker than the 0.01 model. MgH at [1.90], [2.10], beyond the frequency spanned by models, are strong in sdK and sdM. The fit to the atmospheres is consistent also with the 250 Κ higher temperature and higher [Fe/H]. The colors of the apparent continua outside the bands hardly change with [Fe/H], i.e., differential blanketing has small effect.

the Mould (1976¿) models. Calibrating {R^ — colors as body. The Mould 3750 Κ outputs, for ΖΟΌ, 0.1 Χ ΖΟΌ, /(log Teff, Z, g) by the models, we estimate Teff = 3750 K. 0.01 X Zoo are shown in Figure 7B together with the To improve the visibility of features on a steep back- G18-51 data. Figure 7B displays how few features exist in ground, compute a linear combination of the data, equiv- G18-51 at resolution 80 A, how well the continuum is alent to a rotation, flattening the energy distribution. The defined, and how TiO bands seen in the top model spec- useful quantity, DEL, is trum have completely vanished. The strong CaH band in the model weakens only slightly with decreasing Ζ but is DEL AB = AB - . (11) v V Γ Χ ν weaker still in G18-51. We should not overemphasize this The rotation is proportional to Γ, which measures first attempt to fit; the models do not reach high-enough /i//cTcolor, the steepness of the exponential tail of a black- frequency to predict the observed very strong MgH band

with parallax is hard to quantify. Nine of the stars in Table 5 have parallaxes < 0'.Ό15; we have penetrated to consid- erable distances but to less than the scale height of high- velocity stars. The observed counts should have risen; their fall suggests that φ(Μ/), <$){Mhol) are flat or decreasing. All our stars are known proper-motion objects. The requirement that proper motion exceeds the value required for the Giclas or Luyten surveys limits the distance (40 pc) to which OD stars enter the proper-motion survey, while halo stars reach 120 pc. We modeled the observed counts by constructing classical (m, log r) tables and assuming φ(Μί). The actual flat counted numbers, increasing much more slowly than 10° 6mi prove consistent with a wide range of luminosity functions and cutoff luminosities. Extensive searches have been made for intrinsically faint stars by mapping all objects at the galactic pole to faint apparent magnitudes. Proper-motion selection em- phasizes proximity; such unguided surveys do not auto- matically guarantee intrinsically fainter stars, mainly pro- Log Effective Temperature viding more distant ones of the same luminosity until they Fig. 8-The H-R diagram relating luminosities and temperatures for reach beyond a scale height of the disk (whether thin or theoretical models with masses 0.10 < m/trio ^ 0.75 at various metallic- thick). To review a sample briefly, Reid and Gilmore ities. The halo sdM G18-51 is shown (large circle) at a temperature from (1982) used deep photographic exposures to Ζ = 17m at the the model of Figure 7(B). Wolf 629 (circled cross) is shown at log south galactic pole to find and count red dwarfs, finding a 3.498 given by Berriman and Reid. The two solidly drawn curves are m D'Antona (1987), open circles Ζ = 10~4; filled, Ζ = 10~3. The square φ(Μν) flat to Mv = 19 . Hawkins (1986) made a deeper boxes indicate mcrit whence brown dwarfs could have evolved downward search at the south galactic pole using filtered IIIa-F to the right. The dashed curves are the VandenBerg et al. (1983) emulsion for an R passband and IV-N for an I. He de- 4 3 computations (from left, plus Ζ = 10~ ; asterisk 10 ; circle 0.02; dots duced that his reddest, faintest object had Mj ~ 13?2; on 0.01). The agreement between the two computations is only fair. The his RF system a broad luminosity function ${M ) was upper nearly horizontal line connects models with 0.30 mo, the lower RF with 0.15 m©. The luminosity for given mass is only a slow function of ; roughly flat, decreased from a maximum, and then possi- Ζ m both mcrit and Lcrit increase at small Ζ. The location of G18-51 is consis- bly turned up at MRF = 16 . The faint turnup proves to be tent with a spectroscopically estimated low Z. Wolf 629 appears normal a controversial point. Leggett and Hawkins (1988) give a and lies near the Vandenberg et al. locus for Ζ = 0.01. The dotted lines 2 luminosity function φ(Μ/) for faint stars at the south galac- of0.50, 0.25, 0.10 R/Rq, from L = R X T^, run approximately parallel tic pole, selected without regard to motion. After a peak to lines of constant mass. m near Mj = 9 , a plateau at 10% of the peak reaches MI = at [1.93] nor the Ca I seen in Figure 7A. The theoretical 13m. Their separate list of subdwarfs is small, containing a (fí* — /J colors of the models are hardly affected by Z, subluminous OD star, Gliese 15B, Barnard's star, others since is as nearly band free as possible even in the high of Q, = 3 in my Table 3, but only Gliese 299 (G50-22) at Qv Ζ model in Figure 7B. In conclusion, a temperature of = 4. Unfortunately, such "intermediates" provide little 3750 Κ and very low Z, or somewhat higher values of new information on the faint end of φ(Μί) for low Z. both, are acceptable. Searches in the red, and much interesting statistical work, have been done; penetration to faint absolute mag- 7. Is There a Luminosity Cutoff in the Halo? nitudes is still modest. Examine the uncorrected frequency function of these Can we venture any conclusions on the basis of the halo stars without correcting for the volume of space present selection by proper motion? What is the incom- surveyed. The counts are flat, 8, 11, 15, 10 stars in bins pleteness in my list of subdwarfs in Table 5? The apparent m m m ΔΜν = r wide, from Mv = 9 5 to 12 5, four at 13 5 and m/s show that of 59 stars, only nine have ml > 13?0. This one at 15?5. The counts by Mz are different, since bcV is reflects the limit of the Lowell proper-motion survey, mpg m large and be/ small. In counts by either AMbol = l or ΔΜΙ = 16?5, and of older parallax programs; only few paral- m = l some red stars move out into brighter bins, leaving laxes exist for the fainter LHS stars. The Lowell mpg are an 18, 16, and 4 at 9?5, 10^5, and 11?5. Thus, an apparent undefined "photographic" measure with a refractor. In a m cutoff exists, brighter than Mbol = 12 . My observed random test group of 70, the 21 faintest m^i had mpg from sample became incomplete only near apparent magni- 15^0 to 16^7 and Lowell color groups LC = 2,3,4. Of tude I = 13?6 (see below). Incompleteness in the sample these, the brightest was J = 10?01; the median J = 11?50,

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 806 JESSE L. GREENSTEIN which has mpg — I = 3?60, the faintest I = 13^73 for which (which they call intermediate and assume vt = 130 km 1 m m mpg — 1 = 2?47. The limiting I depends on the LC, s" ), with //(/) - 19 5, corresponds to M(/) - 12 3. The reddest stars being most severely affected. Searches for HCM redder stars are barely fainter than their yellow halo stars among the Lowell objects should concentrate stars. It would indeed be exciting if they, and we, have on the LC = 2 group, for which the effective limiting probed near the limiting Mbol a metal-poor star can have, magnitude is I = 13?6. at the critical mass mcrit below which nuclear energy does What do Lowell magnitudes and colors (given as in- not turn on. tegers) mean? Using my unpublished (G — I) the LC = 2 The H-R loci in the astrophysically significant Mbol, m m group has ((G -1)) = 2 58; LC = 3, ((G -1)) = 3 08; LC log reff diagram for low Ζ are given by D'Antona (1987) = 4, {(G — 1)) = 4^21, with large scatter arising in part and by VandenBerg et al. (1983), plotted in Figure 8. from the integer nature of LC. As a very rough approxima- Although theoretically computed L,Teñ differ consider- tion, the relation based on the MCSP m{l), ably, a shift to high /^appears to be a reliable prediction. Predictions are: Low m and low Ζ stars are bluer and m[1.21] == m — LC - 1 , (12) pg subluminous and lie to the left of the OD sequence; the proves useful. Lowell halo stars at LC = 2 would be critical mass for nuclear-energy generation, mcrit, is larger complete to 1 = 13T5. Inspection shows mpg to lie be- at low Z, and the luminosity higher. While uncertainty in tween m212 and m2A2, my G and Β magnitudes, not yet opacity and mixing-length theory are important, still used in this study. In the roughest approximation, we other difficulties exist. Burroughs, Hubbard, and Lunine relate mpg and by (1989, hereafter BHL) give recent computations for the solar Ζ at the lowest masses, together with a review of m [2.12] ~ m . (13) pg discrepancies with temperature scales suggested by vari- The ((G — 1)) = 3^27 for seven red sdM's with (R^ — /J > ous observers. BHL models differ by their assumed 1?5. For those, the cutoff (13^0 + 3T27 = 16^27) is nearly physics; plausible assumptions for models Ε and G give at the limit claimed by the Lowell survey. An intrinsically temperatures at the lowest end of the hydrogen-burning m m faint halo star, G260-1, has G = 16 37, Β = 18 03; the main sequence, log reff, from 3.46 to 3.32. If the tempera- Lowell mpg = 16T7. For a yellower sample, 0^5 < (R^ — /J ture scale of Berriman and Reid (1987) is correct, faint m < 1T0, ((G — 1)) = l 87; their cutoff should be at mpg = stars with presumably normal Z, like LHS 2924, 13m0 + lm87 - 14m87, lm6 too bright to cause the Mil) LHS 2930, VB 8, and VB 10, are near these limits; BR cutoff found. Among these ten yellow halo stars, the five place the coolest, VB 8, at log .39. Largely nega- faintest have (G) = 14?98, much brighter than the Lowell tive results have marked the search for cooler, fainter OD limit of 16?5. Thus, either halo subdwarfs of this color and stars, e.g., by Probst (1983). Becklin and Zuckerman Ζ do not exist fainter than the five at {Mbol) = 9?77 or a (1989 and private communication) have searched for red different selection factor removes them from my list. companions to white dwarfs (a dominantly OD group) and Possibly it is lack of interest as parallax candidates, undis- find intrinsically faint objects. The reff of LHS 2924, ap- tinguished color, and modest proper motion. While their parently the coolest OD so far (except for a suspected reduced proper motion (Η[1.21]) = 18?1 is large, the brown dwarf), will present a problem until its spectrum is actual mean observed parallax, O'.'OIQ, is small. Many understood. The BHL models for normal Ζ predict more candidates can now be found with parallaxes that faintest Mbol's ranging from 14^36-15^19. The Nelson, would be too small except for CCD measurements such as Rappaport, and Joss (1986) computations stop at a higher are now being carried out by Monet and Dahn at US NO. merit ~ 0.10 trio, with lowest log Teñ —3.48. The Vanden- Reasonable and practical selection criteria used in defin- Berg et al. (1983) high Ζ main sequence in Figure 8 ing the US NO photographic observing program may have terminates at log .42. This range of Teff for the excluded the faintest sdM's. well-studied OD leaves concern about the reliability of The only source of apparently fainter objects is the predictions for the far less-explored low-Z models. But in Hartwick et al. (1984) LHS sample, with its four faintest Figure 8, their displacement is gross, to log Teff = 3.54 — m 4 but not very red stars near H{1) = 21?1 (using broad-band 3.58; the faintest have Mbol = 12 for Ζ = 10~ . These are 1, which is not far from my m [1.21]). HCM did not use sufficiently different from the OD to suggest that what we parallaxes nor specifically compute M (/). From equation have observed is theoretically at least suggestive. Much 1 (15), with vt = 320 km s" , their faintest H (/) corresponds work remains on models for the interiors of low-Z, low- to M (/ ) = 12^0, close enough to my value to suggest that mass stars. In Figure 8 note that lines of computed con- our faintest stars are similar. Most importantly, while stant radius and of constant mass are parallel, in spite of their faintest halo stars were near apparent magnitude / = the large changes in Z, as expected for a complete convec- 16m, fainter than mine, HCM did not find them to be tive model. Opacity (dependent on Z) determines lumi- absolutely fainter than I did, if their assumed tangential nosity and, therefore, reff. Whether the theoretical and motion is correct. Their redder group of moderate (//) observational loci agree is still unknown, depending on

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System LOWER MAIN SEQUENCE IN DISK AND HALO 807 the observational temperature scale; see BHL (1989) and brown dwarfs just at or below mcrit will blur such cutoffs. Berriman and Reid. D'Antona has pointed out (personal Equipartition may segregate low-mass stars toward the communication) that it may not be impossible to decouple less-crowded outer fringes of a cluster, if it does not expel radius and mass, which would permit shifts within this them. Analogs of the faintest known halo stars might thus theoretical diagram. have a luminosity function determined, with less danger Near mcrit, stars do not turn off instantaneously, as of selection effects. The search for brown dwarfs near the discussed in BHL. For objects of concern here, D'An tona Sun has been treacherously difficult. It may not become (1987) gives long lifetimes for low-Z brown dwarfs near easier at the limit of the Η ST and is not to my knowledge mcrit. Her predicted lowest end of the main sequences: an approved Η ST program. But a straightforward look at m mcrit = 0.110, Mbol - 12 0, Teñ = 3467 Κ for Y = 0.23, Ζ = red or near-infrared images of the faintest stars in globu- 4 3 m ΙΟ" . For Y - 0.25, Ζ = 10 , mcrit = 0.09o, Mbol = 15 0, lar clusters of various metallicities promises to elucidate reff = 1928 K. At Ζ = 0.02, the assumed solar value, mcrit problems raised by nearby halo stars. Of course, if we = O.OSq; the bolometric cutoff is now not only somewhat may speculate, this could cast light on the question of fainter Mboi = 15?6, but the temperature, Teff = 1567 Κ is whether low-mass halo stars contribute to "missing mass", so much lower that such stars appear inaccessible opti- if the latter exists. cally, faint even in the infrared. Note that no definitely Success of the test depends on the existence of field and stellar temperature on the MS is below 2000 K. Enough cluster low-mass halo stars with the extreme metal defi- theoretical uncertainty exists to make prediction of the ciencies, Ζ ^ ΙΟ-4, required by the D'Antona models. cutoff risky at present, yet tantalizingly near the limit of Only a few extreme cases were singled out in Ake and observational check. Greenstein (1980) and confirmed by Dawson and De- An interesting and plausible future test does exist. Robertis (1988). These same few stand out when the Consider first a typical globular cluster with low Ζ and parallax is known in H-R diagrams of this study (e.g., in typical modulus 15^0, if a cutoff exists near to or just Fig. 6). Such extreme objects can also be detected in a beyond Mj ~ 12^0. The prediction from HCM and my purely color-color diagram of [2.42] — [1.85], [1.85] — present results is that a decrease of star frequency occurs [1.21], where the AK stars prove to be the only ones near I = 27T0 which (we trust) will be above the limit of apparently very faint in the ultraviolet. The effect might the Hubble Space Telescope. It would be a severe test of appear in a broadband {B — V),(V — I) plot, where V is CCD photometry at the large Northern Hemisphere tele- even more sensitive to TiO bands than is my m . The scopes. In a private communication, Liebert lists several 185 faintness is a secondary result of the large depression of southern globular clusters, of a variety of [Fe/H], that are m by TiO bands in OD stars, a depression which is closer, having moduli near 12?5. Let us explore the pre- 185 absent in the AK stars. The subjective impression from dictions, in at least a tentative fashion from Figure 8. The my ongoing study of such distortions of the energy distri- theoretical predictions are somewhat uncertain; accord- bution as seen with the MC S F is that extremely low Ζ ing to D'Antona (1987), a high-Z star near turnoff to the stars like the AK objects are very rare. brown-dwarf stage has M (m ) = 15?56, but a similarly bol crit Returning to our discussion of individual stars, we plot placed, lowest Ζ star has M i(m ) = llm97, which is 3?59 bo crit the location of G18-51, together with theoretical predic- brighter. In VandenBerg et al. (1983), who did not ex- tions in Figure 8. The T is from the fit to a model plore so close to m , the cutoff at low Ζ is even brighter, eff crit atmosphere discussed at the end of Section 6; expected at 10T30. The most recent work at solar Ζ by BHL gives a uncertainties can move the star slightly to the left, with range from M from 14?36-15?19 for the cutoff, on a bol higher Z, but a composition Ζ = 10-4 is reasonable. It variety of plausible physical assumptions. This is enough cannot be moved far to the right, there requiring OD fainter than the D'Antona (1987) low-Z cutoff to produce abundances, implausible given the spectrum shown in the difference, 6M , in bolometric cutoff between low-Z bol Figure 7. Lack of models prevents us from fitting to the and high-Z clusters of 2^4 < δΜ < 3^2. Inspection of 1χ)1 temperature of Wolf 629; fortunately, it is in Berriman Figure 3C shows bel with a range from — 0?3 to +0?6. and Reid (1987), called Gliese 643, with T = 3150 Κ, Near the observed cutoffs, the low-Z stars in this study are eñ close to the 3250 Κ given by Reid and Gilmore (1984). bluer and hotter than the faintest high-Z objects. From Plotted as a circled cross in Figure 8, Wolf629 lies close to be/ we predict M, = 11^67, at the D'An tona cutoff in the the Ζ = 0.01 theoretical locus of VandenBerg et al. (1983). lowest Ζ cluster. From BHL, at high Ζ the cutoff is at Mj The clear separation of G18-51 and Wolf 629 in Figure 8 = 14^96-15^79, giving a 3 < bM < 4 magnitudes. In a l reduces the doubt introduced by the problem of differen- nearer cluster with modulus ~ 13?5, the cutoff in the tial blanketing. The stars have the same luminosity and low-Z case can be as bright as 25^2 (where it is accessible they definitely appear to have different temperatures. to ground-based search, using a filtered CCD in two Radii are derived from colors). It would be as faint as 28^0-28^8 for high Ζ (stressing even the Η ST). The slow fading of the old -log R/Rg = 0.2 X Mbol + 2 X log reff - 8.452 . (14)

Being hotter, G18-51 has a small radius, 1.22 X 105 km, Table 5 having Carney and Latham (1987) radial veloc- 2 2 0.18 Rö; Wolf 629 has 0.24 Rö. Lines of constant radius ities, p. Computing total motion from T = (p + vf), we 2 drawn in Figure 8 come from L = R Γβ^. Burrows et al. recompute the velocity class, now properly called QT; (1989) show the OD radii decreasing with m toward a among the eight in common only one sdG (with ρ = —235 4 -1 minimum for brown dwarfs near 6 X 10 km. The faintest km s ) is changed from my Qt, = 5 to its true Qr = 7. A halo stars are somewhat larger than the hydrogen-degen- similar change had already been made for G225-67A erate brown dwarfs and much larger than helium-degen- (Gliese 630.1A), a spectroscopic binary with known large erate white dwarfs at 8 X 103 km. 7-velocity, which moved from = 3 to = 4. If changes in velocity class are this small and infrequent, we 8. Kinematics of Cool Stars in the Halo can rely on Qv as discriminant in studying the distribution The halo stars with MC S Ρ colors recognized spectro- of vt, color, and luminosity. The relation between the scopically, with parallaxes and therefore luminosities, reduced proper motion, H [1.21], and the luminosity is represent one of the larger samples of late-type stars M[1.21] = H[1.21] + 3.38 - 5 x logü, . (15) available. Recently, their precise radial velocities of halo stars permitted Carney, Latham, and Laird (1988) to give We neglect the angular distance of the star from the solar full space motions for halo stars, nearly all of earlier types, apex, since the solar motion with respect to the LSR is sdG and early sdK, recognized as metal deficient from small compared to the space motion of these fast-moving UV-excess in broad-band {R — V),{U — R) photometry. stars. We use what would more properly be called a The reddest stars in Laird, Carney, and Latham (1988) are T-component, which needs a statistical correction to yield HD 25329 (Gliese 158), HD 134439/40 (Gliese 579.2A/B), total T. Omitting only incomplete data and freak stars, we the bluest and brightest in my Table 3. The highest-veloc- present the results in Figure 9. From equation (15) we ity sdM's of low Ζ are low-mass analogs of the classical plot straight lines representing constant T. The Qv are sdG s and sdK s studied by Latham and collaborators, but "quantized" with plotting symbols arranged in arrays be- with less well-studied kinematics. tween the lines. Since vt is linear in distance, parallax While we lacked radial velocities, in general, the new errors significantly displace a star in M [1.21] and aifect I 1 data are practically useful. There are eight stars in my Qv. For an error Δρ/ρ = 0.25, ΔΜ[1.21] = ±0 ! 55 and

H[1.21 ] = m[1.21] + 5 + 5 log mu

Fig. 9-Absolute magnitude, MI, and reduced proper motion, Η (7 ), are related by tangential velocity; symbols as in Figures 4-6. Lines representing constant tangential velocity are coded from left; dash-dot, 20 km s l; dashes, 100 km s l; dots, 200 km s l; dash-dot-dot-dot 300 km s l; solid, 450 km _1 m s . Intermediate velocities, i.e., Qv = 3, are omitted. Some Qv = 1,2 stars run offscale to the lower right, reaching M[1.21] = 15 . The present limit for the halo is near llm (see Table 5). An upper limit to observed tangential velocities lies between 400 and 450 km s"1, confirming a high escape velocity from the Galaxy, with vesc at least 2 X t;circ. This diagram can be understood, if we assume that space motion and metallicity Ζ are correlated and if the stars of lowest mass with lowest Ζ have Mbol < 11^5, reasonable with present models for the interior.

~ 1; this large uncertainty should be understood for is very broad, spanning the entire range of known [Fe/H], stars with smaller parallaxes (the open plotting symbols). and might not be the same as that in globular clusters. The One most extreme object at the lower right (plotted as an sdM's, presumably of similarly low Z, would help define open star) transgresses the line for 450 km s_1; this is the low-mass end when observed in clusters. LHS 453, for which the tentative CCD parallax kindly supplied by C. C. Dahn is only Ο'.ΌΙΟΟ ± 0'Ό015. From 9. Final Remarks that alone, the tangential motion is 479 ± 73 km s-1; the To outline our review, we start with the attempt to Dawson and DeRobertis (1988) ρ = —1 km s1 leaves that provide numerous good bolometric luminosities for late- unchanged. Counting velocities of stars with good paral- type proper-motion stars having full data of MCSP spec- laxes, there are 19 with 300 450 km s1). The counts trophotometry, parallax, and mid-IR photometry. The in successive velocity groups, spaced 50 km s_1, from a luminosities can be obtained using my weights for the -1 table of 94 objects are: one at vt ^ 450 km s ; two from discrete set of fluxes given by filter and MCSP photome- 400-449; three from 350-399; and 14 from 300-349 km try. Infrared spectrophotometry of the H2O region, like s_1. Geometric relations give the contribution expected that of Berriman and Reid (1987), will be needed for from the radial velocity; they suggest a conservative maxi- further substantial improvement. A most urgent need is mum of Γ about 425 km s-1. The parallax errors should not both filter photometry and infrared spectrophotometry of reduce this by much, statistically. A systematic error is halo stars, like those in Table 5, to study the H2O bands introduced by the reduction from relative to absolute and evaluate their effect. The limitation on accuracy im- parallaxes; it should be less than 10%, even for the posed by parallaxes seems not to be a serious problem for smallest parallax used. The plausible local escape velocity OD stars, given the gains provided by years of published -1 derived, vesc ~ 425 km s or more, requires a ratio of total US NO measures. The large intrinsic spread found in the mass in the outer parts of the Galaxy to that in the interior main sequence is ~ ± 0?48 (in part, possibly, from unrec- parts of the disk larger than two, requiring substantial ognized duplicity) and reduces the need for more precise dark matter. bolometry. For astrophysical theory, the radius is impor- Carney et al. (1988) give the largest values of the total tant and predicts the mass of a convective model. What space motion near 500 km s-1; of their 32 stars with are the sources of error? In the graphical fitting of various extreme motion with respect to the local rest frame, H-R diagrams, a few approximations appeared to be suffi- four have 450 < < 500 km s1. I have only one such ciently linear to have practical usefulness. We can look among 94 stars, and it has very small parallax. But their forward to a time when similar formulae will be written distance scale is based on the photometric luminosities of connecting/(Teff) with a color. To a good approximation, sdG's derived from broad-band UBV colors and estimates for example, the sample of 54 OD stars ( as used for the of metallicity; their deduced distances are less directly cubics in Table 4) can be represented by: connected to measured quantities. Few new parallaxes m MI = 5 74 + 1.968 x (R, - 7J , (16a) have been measured for sdG s, since their luminosity is m relatively high and their frequency in space low. Their Ml = 4 49 + 2.081 x (V - Z) . (16b) tangential motions may consequently be less accurate; m Mv = 6 23 + 2.959 x (R* - ZJ , (16c) still, many of their radial velocities are large enough that m -1 Mv = 4 37 -f 3.124 x (V - Ζ ) . (16d) their estimated escape velocity, near vesc = 500 km s , appears significantly larger than my estimate of T. From The χ2 associated with these, about 0.34 per object, corre- the high ratio of veJT and therefore veJvrot, Latham et al. sponds to σ(Μ) ~ ±0?58. Thus, were the temperature derive a large ratio of spheroid to disk mass, near 4.9. known without error, equation (14) gives a spread in Kinematics of the cool stars with a distance scale based on log R/Rö ~ 0.11. i.e., 30%. Using the cubic representa- parallaxes resemble those of the extremely metal-poor tion of Mbol — /(V — A:) cuts the dispersion only to σ(Μ) ~ sdG, sdK stars, ten times more distant, studied by ±0?47, i.e., errors of log R/Rq ~ 0.09, or 24%. Whatever Latham and collaborators. The two groups have resem- its origin, the intrinsic scatter requires that a large num- blances and differences. While late subdwarfs are only ber of good temperature determinations need to be made beginning their evolutionary life, the hundred-fold to yield the mean stellar radius even to 10%. brighter sdG's are turning off the low-metal main se- When we studied fainter halo stars, infrared data are quence up toward the subgiants. Thus, Bell and Oke mostly lacking, and simple integration, or use of my (1986) find that four often-used spectrophotometric stan- weighting factors, permits evaluation of the total received dard sdG's are on a nearly vertical metal-poor isochrone, flux, but the inverse-square law now provides the obsta- 9 age 18 X 10 yr. They display a range of 1?5 in Mv at nearly cle. Parallax errors are still 20% since we deal with a rare constant color. The metallicity distribution function group whose closest example may be 50 pc distant. For -1 found for sdG s with vt ^ 220 km s by Laird et al. (1989) these, the improved CCD parallaxes are needed. After

© Astronomical Society of the Pacific · Provided by the NASA Astrophysics Data System 810 JESSE L. GREENSTEIN the precision attainable in the H-R diagrams of OD stars, Bessell, M. S., and Brett, J. M. 1988, M.N.R.A.S., 100, 1134. complexities of the halo stars seem numerous. From the- Burrows, Α., Hubbard, W. B., and Lunine, J. I. 1989, preprint (BHL). Carney, B. W., and Latham, D. W. 1987, A./., 93, 116. ory, given the variety of compositions in the halo, their Carney, B. W., Latham, D. W., and Laird, J. B. 1988, A./., 96, 560. H-R diagram is not a narrow sequence. The observed D'Antona, F. 1987, Ap. /., 320, 653. range of luminosities at a given color in the halo is at least Dahn, C. C., and Harrington, R. S. 1978, IAU Symposium 80, The HR double that in the OD, if observational errors have been Diagram, ed. A. G. D. Philip and D. S. Hayes (Dordrecht: Reidel), correctly estimated. They have a range of luminosities p. 129. and metallicities. Dawson, P. C., and DeRobertis, M. M. 1988, A./., 95, 1251 (DR). Eggen, O. J. 1968, Αρ. J. Suppl., 16, 49. To determine radii the first-order problem is the rela- 1969, in Low Luminosity Stars, ed. S. S. Kumar (New York: tion between color and Teff in the OD and in the halo. Gordon and Breach), p. 3. From the lowest temperatures and luminosities attained 1971, in IAU Symposium 42, White Dwarfs, ed. W. J. Luyten by common and nearby stars, after the all-important stel- (Dordrecht: Reidel), p. 8. lar atmospheres for late stars are computed, the proper- 1987, A.J., 92, 398. Forrest, W. J., Skrutskie, M. F., and Shore, M. 1988, Ap. J. (Letters), ties near mcrit will then be found. Involved is the critical 330, L119. question for the theory of low-mass stellar interiors, Gezari, D. Y., Schmitz, M., and Mead, J. M. 1987, Catalogue of whether the cessation of thermonuclear burning occurs in Infrared Observations, Part I, NASA Reference Pub. 1196. the proper regions of their H-R diagrams. We need to Giclas, H. L., Burnham, R. J., Jr., and Thomas, N. G. 1971, Lowell determine simultaneously temperature, luminosity, and Proper Motion Survey. The G-Numhered Stars (Flagstaff, AZ: Low- ell Observatory). composition of stars near the lower end of the main se- 1978, Southern Hemisphere Catalogue, Lowell Obs. Bull., No. quences for their Z. The numerous halo objects plotted in 164. the figures (with data from Tables 3 and 5) have colors and Gliese, W. 1969, Catalogue of Nearby Stars Veroff Asir. Rechen Inst. m Mbol ~ 10 near a critical region to test the dependence on Heidelberg, No. 22. Ζ of the theoretical luminosity and temperature. Those Gliese, W., and Jahreiss, H. 1979, Asir. Αρ. Suppl., 38, 423. Greenstein, J. L. 1969, in Low Luminosity Stars, ed. S. S. Kumar (New with small parallaxes need improvement; all still need York: Gordon and Breach), p. 281. careful spectroscopic analysis. No one has yet even dis- Greenstein, J. L. 1978, in IAU Symposium 80, The HR Diagram, ed. played the spectra of these on an adequate scale except A. G. D. Philip and D. S. Hayes (Dordrecht: Reidel), p. 101. Dawson and DeRobertis (1988), who showed that faint Greenstein, J. L. 1989, Comments on Αρ., 13, 303. LHS stars were accessible targets. Their spectra are satis- Greenstein, J. L., Neugebauer, G., and Becklin, Ε. E. 1970, Ap. /., 161, 519. fy ingly simple and more subject to quantitative analysis Hartwick, F. D. Α., Cowley, A. P., and Mould, J. R. 1984, Ap. /., 286, than brighter, crowded OD spectra. The subluminous 269 (HCM). stars have relatively simple continua, as a guide to tem- Hawkins, M. R. S. 1986, M.N.R.A.S., 223, 845. perature; abundances always depend most critically on Laird, J. B., Carney, B. W., and Latham, D. W. 1988, A./., 95, 1843. effective temperatures. Although there exist as yet no Laird, J. B., Rupen, M. P., Carney, B. W., and Latham, D. W. 1989, in The Abundance Spread within Globular Clusters, ed. G. G. de computed model atmospheres, they should prove sim- Strobel, M. Spite, and T. Lloyd Evans (Observatoire de Paris), p. pler to converge then heavily blanketed stars. Much re- 37. mains unknown in this area of stellar astronomy, but Leggett, S. K., and Hawkins, M. R. S. 1988, M.N.R.A.S., 234, 1065. seems within reach. Liebert, J., and Probst, R. 1987, Ann. Rev. Asir. Αρ., 25, 473. Liebert, J., Boroson, Τ. Α., andGiampapa, M. S. 1984, Ap./., 282, 758. I am indebted to Jim Liebert for extensive discussions on Luyten , W. J. 1979, LHS Catalogue (2d ed; Minneapolis, MI: Univer- M-dwarf problems and to Olin J. Eggen for his copious sity of Minnesota). knowledge of individual stars and their photometry. I am Mould, J. R. 1976a, Ph.D. dissertation, Australian National University. 1976b, Asir. 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