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Publications of the Astronomical Society of the Pacific, 119: 605­615, 2007 June 2007. The Astronomical Society of the Pacific. All rights reser ved. Printed in U.S.A.

Measuring the Balmer Jump and the Effective Gravity in FGK Stars
Michael S. Bessell
Research School of Astronomy and Astrophysics, Australian National University, Mount Stromlo, Weston, Australia; bessell@mso.anu.edu.au Received 2006 October 17; accepted 2007 May 18; published 2007 June 21

ABSTRACT. It is difficult to accurately measure the effective gravity (log g ) in late-type stars using broadband (e.g., UBV or SDSS) or intermediate-band (uvby) photometric systems, especially when the stars can cover a range of metallicities and reddenings. However, simple spectroscopic obser vational and data reduction techniques can yield accurate values for log g through comparison of the Balmer jumps of low-resolution spectra with recent grids of synthetic flux spectra. Online material: color figure 1. INTRODUCTION The abundance analyses of the oldest stars in the Galaxy are of great importance to our understanding of which elements were created during the life and death of the first generation of stars and how the fraction of heavy elements built up through the evolution of subsequent generations of stars. The effective temperature is the most important stellar atmosphere parameter to assign in the determination of abundances, but for those elements only represented by lines of the neutral species, it is necessar y to establish the electron pressure or the effective gravity of the star. This is because hotter than about 4500 K, most of the heavy elements are once ionized, and significant corrections are required to determine the total element abundances from the neutral species. Theoretical isochrones for a range of metallicities and ages are readily available (Pietrinferni et al. 2006; VandenBerg 2000; Salasnich et al. 2000), and the normal log (L /L , ) versus log Tef f relations can be readily transformed to log g versus Teff [log g p 4log Tef f log ( L /L , ) 10.608]. Figure 1 shows a typical halo isochrone for an age of 12 Gyr. For old stars (age 1 10 Gyr), the shape of the isochrone changes little as the main-sequence turnoff (TO) moves to cooler temperatures with older age. As can be seen from the figure, for a given temperature, there are normally only three different possible values for log g for a halo star, depending on whether the star is on the main sequence (MS), the subgiant/ giant branch (SGB), or on the horizontal branch (HB) or asymptotic giant branch (AGB). Cooler than about 5500 K, it is generally quite easy to choose between a MS (log g p 5), GB (log g p 3.5), and HB star (log g p 2.5), but near the MS turnoff, the differences in gravity are quite small and more difficult to discern. The Balmer discontinuity is an obvious feature to measure in the spectra of late-type halo stars in order to determine ° log g. Blueward of 3636 A, the continuous opacity is mainly H , whereas redward it is H plus H i. As log g (and log P) e 605 decreases, the H opacity decreases and the size of the Balmer discontinuity increases. But as the H i opacity decreases steeply with decreasing temperature, the Balmer jump becomes less sensitive to changes in log g. Although low-dispersion spectra are regularly taken of halo stars in order to measure the H and K lines of Ca ii and the Hd line for metallicity and temperature estimates, little or no effort is put into measuring the Balmer discontinuity. I think that there are three main reasons for this. First, as the Balmer discontinuity is near the confluence of the hydrogen lines, the continuum is changing rapidly and it seems impossible to uniquivocally extrapolate a cur ved line that fits the continuum ° from the 4100 to 4800 A region, where the continuum is well defined. Second, the sensitivity of most spectrographs and ° CCDs decreases rapidly below 3900 A, leading many people ° to think there is little point in obser ving below 3600 A. And finally, many think that it may be possible to overcome these difficulties only if a full relative-absolute spectrophotometric calibration is undertaken, and this seems like too much effort for an uncertain return. This paper aims to show how, with a minimal amount of extra effort at both the telescope and with the data reduction, the Balmer jump can be readily measured and compared with similar data from the detailed grid of synthetic spectra provided by Munari et al. (2005). 2. TECHNIQUES 2.1. Atmospheric Dispersion When doing ground-based spectroscopy in the UV/blue, it is highly desirable that the effect of atmospheric dispersion is minimized, either by using an atmospheric dispersion corrector (Filippenko 1982) or by rotating the spectrograph slit so that it is parallel to the atmospheric dispersion. Other wise, at large zenith distances, if the guider is centering the green or red image, a significant proportion of the UV/blue light will miss


606 BESSELL the slit. But, as the Balmer jump is measured at one wavelength, it is not absolutely essential to measure the same proportion of light at all wavelengths. However, although a reasonable discontinuity may be measured under these circumstances, any possibility of measuring a temperature-sensitive slope or color, such as B V, is lost. If an atmospheric dispersion corrector is unavailable, spectra should be taken with the slit tracking the parallactic angle, or the star should be acquired in that mode and then obser ved with the position angle fixed to use an offset guide star in an alt-az telescope. 2.2. Division by Blackbody Spectrum Bessell (1999) discusses the advantages of obser ving smooth-spectrum stars as part of any obser ving program. After the raw spectra have been extracted, the first step is to divide all spectra by the normalized spectrum of a star with a nearblackbody (BB) energy distribution. There are several near-continuous bright white dwarfs (WDs) that are well suited for such division. These are EG 131 and L745 46a, which are accessible in opposite seasons, together with vMa 2 and two carbon-rich white dwarfs, LHS 43 (Bessell 1999) and LHS 4043 (Dufour et al. 2005). It is necessar y to remove the weak C2 bands from the carbon WDs and the Ca ii H and K and Mg i lines from L745 46a and vMa 2, or fit a line through the continuum before division. Greenstein & Liebert (1990) and Bergeron et al. (2001) discuss the spectra of these stars, while Koester & Wolff (2000) and Dufour et al. (2005) discuss the theoretical fluxes of some of the stars. There are two main reasons for dividing by a normalized near-BB spectrum. First, in the red it removes most of the atmospheric (telluric) absorption lines, and second, for both blue and red spectra, it removes most of the instrumental response due to vignetting, grating blaze, filters, mirrors, and CCD response. The net effect of this division is to provide spectra in which the continuum level changes slowly and smoothly with wavelength, which in turn means the corrections (with wavelength) to place the fluxes on a relative absolute flux scale can be well fitted with a smooth low-order polynomial or spline. 2.3. Linearization of the Continuum An unanticipated dividend of the division by a warm nearBB spectrum was the fact that the continuum levels of FGK stars above and below the Balmer jump were transformed from cur ves into almost straight lines. This enables the continua to ° be extrapolated with confidence to 3636 A, and the Balmer jump to be measured accurately and consistently. Division by EG 131, with a blackbody temperature of about 11,800 K, straightens the continuum in stars with temperatures from 7500 to 5000 K. Division by the cooler L745 46a (8600 K) leaves some residual cur vature for spectra hotter than 6500 K, but is good for cooler stars. The two carbon-rich white dwarfs LHS 43 and LHS 4043 have intermediate blackbody temperatures between EG 131 and L745 46a; vMa 2 is cooler. Figure 2 shows examples of raw extracted blue spectra obtained with the Double Beam Spectrograph (DBS) on the Australian National University 2.3 m telescope. The data have not been flat fielded. From the top are the white dwarf LHS 43 and the halo stars G64 12 (sdF0; 6500 K, log g p 4.0, [Fe/H] p 3.4), HD 84937 (sdF5; 6200 K/4.0/ 2.3), G24 3 (sdF8; 5900 K/4.2/ 1.7), and CD 38 245 (4800 K/1.5/ 4.1). The bracketed quantities are the approximate stellar parameters of the stars. The spectra are offset by 0.2 divisions for clarity. Figure 3 shows the same raw spectra divided by the spectrum of EG 131. The weak carbon bands in LHS 43 and the Balmer jumps in the halo stars are much more obvious and easier to measure in the divided spectra. 3. THEORETICAL FLUXES: MODEL SYNTHETIC SPECTRA Line-blanketed fluxes are available for the ATLAS9 and MARCS grid of model atmospheres. The Munari et al. (2005) ° ATLAS9 synthetic spectra at 1 A resolution are particularly 1 useful. The MARCS sampled photospheric fluxes, available on their Web site, are provided with a warning that they are not likely to give a good representation of the integrated fluxes in a limited wavelength region. However, they look adequate for the lowest metallicities. Figure 4 shows Munari et al. synthetic fl spectra for an abundance of [Fe/H] p 2.5, a temperature of 5750 K, and three different effective gravities. The spectra have been smoothed to ° a resolution of 3 A, the same as the DBS data. The Balmer ° discontinuity at 3636 A can be seen, but the slope of the continuum redward of this limit makes it difficult to measure it. The synthetic spectra can also be divided by an 11,800 K blackbody to measure the theoretical Balmer jumps more reliably. Figure 5 gives the same 5750 K spectra divided by an 11,800 K blackbody. Figures 6 to 10 show similarly divided Munari et al. synthetic spectra for several more temperatures and sets of gravities appropriate for main-sequence, giantbranch, and horizontal or asymptotic giant branch stars. For each temperature plot, the divided spectra have been normal° ized at 5300 A and are plotted with equal offsets for better visibility. One can draw straight lines through the continua on the various figures to see how linear the continua of the divided obser ved and synthetic spectra are and how well defined the Balmer jumps are, even when they are small. 4. BALMER JUMP MEASUREMENTS 4.1. Theoretical Spectra The tabulated model spectra were interpolated to a uniformly spaced wavelength scale (using the task scrunch) and then
1

See http://marcs.astro.uu.se.

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Fig. 1.--Isochrone from Pietrinferni et al. (2006) for 12 Gyr. [See the electronic edition of PASP for a color version of this figure.]

Fig. 2.--Raw extracted blue 2.3 m spectra. See text for details.

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Fig. 3.--Same stars as in Fig. 2, but divided by EG 131.

Fig. 4.--Synthetic fl spectra for [Fe/H] p

2.5, 5750 K, and log g p 4.5, 3.5, 2.5.

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Fig. 5.--Synthetic spectra divided by an 11,800 K BB for [Fe/H] p

2.5, 5750 K, and log g p 4.5, 3.5, 2.

Fig. 6.--Synthetic spectra divided by an 11,800 K BB for [Fe/H] p

2.5, 7500 K, and log g p 4.0, 3.0.

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Fig. 7.--Synthetic spectra divided by an 11,800 K BB for [Fe/H] p

2.5, 6500 K, and log g p 4.5, 4.0, 2.5.

Fig. 8.--Synthetic spectra divided by an 11,800 K BB for [Fe/H] p

2.5, 6000 K, and log g p 4.5, 4.0, 2.5.

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Fig. 9.--Synthetic spectra divided by an 11,800 K BB for [Fe/H ] p

2.5, 5500 K, and log g p 5.0, 3.5, 2.0.

Fig. 10.--Synthetic spectra divided by an 11,800 K BB for [Fe/H] p

2.5, 5250 K, and log g p 5.0, 2.5, 2.0.

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TABLE 1 Munari et al. Spectra [Fe/H] p Teff 6500 ...... log g 4.5 4.0 3.5 4.5 4.0 3.5 4.5 4.0 3.5 4.5 4.0 3.5 4.5 4.0 3.5 4.5 3.0 BJ 0.40 0.52 0.67 0.30 0.41 0.52 0.23 0.31 0.42 0.16 0.23 0.31 0.11 0.16 0.23 0.07 0.20 b y 1 V I BJ 0.36 0.48 0.63 0.28 0.39 0.51 0.18 0.28 0.39 0.13 0.20 0.28 0.09 0.13 0.18 0.07 0.16 [Fe/H] p b y 1.5 V I BJ 0.31 0.44 0.59 0.23 0.34 0.46 0.17 0.24 0.33 0.09 0.14 0.22 0.03 0.07 0.12 0.00 0.11 [Fe/H] p b y 2.5 V I

6250 ......

6000 ......

5750 ......

5500 ......

5250 ......

0.289 0.279 0.269 0.319 0.311 0.303 0.349 0.344 0.338 0.381 0.377 0.373 0.413 0.412 0.410 0.447 0.450

0.545 0.532 0.519 0.600 0.591 0.580 0.656 0.650 0.643 0.716 0.712 0.706 0.778 0.776 0.772 0.848 0.842

0.293 0.283 0.272 0.323 0.314 0.306 0.354 0.347 0.340 0.387 0.381 0.375 0.422 0.417 0.414 0.459 0.453

0.551 0.538 0.523 0.605 0.597 0.585 0.662 0.656 0.647 0.722 0.717 0.711 0.786 0.781 0.778 0.856 0.848

0.300 0.290 0.278 0.330 0.321 0.311 0.362 0.354 0.346 0.397 0.389 0.382 0.437 0.427 0.420 0.482 0.458

0.556 0.543 0.528 0.611 0.602 0.590 0.668 0.661 0.652 0.729 0.722 0.716 0.796 0.788 0.783 0.872 0.853

smoothed to approximate the obser ved medium-resolution spectra. The Munari et al. spectra were smoothed to a resolution ° ° of 5 A, and the MARCS fluxes to 6 A. All model spectra were divided by an 11,800 K blackbody and then plotted, and the Balmer jumps were measured by hand as for the obser ved spectra. The size of the Balmer jump in magnitudes are given in Tables 1 and 2. The depth of the Hd line was also measured, as it is a good temperature indicator; but for comparison with obser vations, it is necessar y to carefully match the resolution, whereas the Balmer jump measurement is not as sensitive to the resolution. The theoretical b y , B V , V R, and V I colors were also computed for the synthetic spectra. Figure 11 is a plot of the measured Balmer jumps for the

Munari et al. spectra ([Fe/H] p 2.5 [plus sign] and 1.5 [square with plus sign]) and the MARCS spectra ([Fe/H] p 2.5 [filled circle] and 1.5 [open circle]). There is good general agreement for the two grids, except for the coolest and strongest line spectra, where as noted above, the MARCS sampled photospheric fluxes are not likely to give a good representation of the integrated flux in a limited wavelength region. Full-spectrum synthesis is needed for the MARCS models in order to properly compare them. However, both sets of theoretical spectra show that for temperatures above 5500 K, the Balmer jump can readily distinguish main-sequence and subgiant branch stars, while for temperatures at around 5000 and 5250 K, only gravities below log g p 3.0 can be distinquished

TABLE 2 MARCS Statistical Line Opacity Spectra [Fe/H] p Teff 6500 ...... log g 4.5 4.0 3.5 4.5 4.0 3.5 4.5 4.0 3.5 4.5 4.0 3.5 4.5 4.0 3.5 4.5 3.5 BJ 0.40 0.55 0.67 0.33 0.43 0.54 0.30 0.36 0.42 0.24 0.28 0.34 0.24 0.27 0.30 0.22 0.22 b y 1 V I BJ 0.39 0.50 0.64 0.30 0.40 0.51 0.22 0.30 0.39 0.19 0.23 0.30 0.15 0.15 0.20 0.11 0.09 [Fe/H] p b y 1.5 V I BJ 0.33 0.47 0.61 0.26 0.34 0.47 0.16 0.24 0.34 0.10 0.15 0.24 0.06 0.09 0.13 0.00 0.06 [Fe/H] p b y 2.5 V I

6250 ......

6000 ......

5750 ......

5500 ......

5250 ......

0.285 0.277 0.267 0.313 0.307 0.300 0.342 0.339 0.334 0.371 0.371 0.368 0.403 0.403 0.403 0.437 0.441

0.540 0.528 0.515 0.595 0.587 0.576 0.651 0.646 0.639 0.711 0.706 0.703 0.776 0.772 0.770 0.850 0.842

0.290 0.281 0.270 0.318 0.312 0.303 0.349 0.343 0.337 0.379 0.376 0.372 0.412 0.409 0.408 0.445 0.444

0.546 0.535 0.520 0.601 0.593 0.582 0.657 0.652 0.644 0.716 0.712 0.708 0.780 0.777 0.774 0.852 0.845

0.297 0.287 0.277 0.326 0.318 0.309 0.357 0.350 0.344 0.392 0.385 0.378 0.429 0.422 0.416 0.472 0.458

0.553 0.541 0.525 0.607 0.599 0.587 0.664 0.657 0.649 0.724 0.718 0.713 0.789 0.784 0.780 0.864 0.853

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TABLE 3 Balmer Jumps Measured from STIS Spectra Star BD 09 2860 ......... BD 17 4708 ......... BD 29 2091 ......... BD 37 1458 ......... BD 41 3931 ......... BD 42 3607 ......... BD 51 1696 ......... BD 59 2723 ......... BD 72 0094 ......... BD 12 2669 ....... CD 30 18140 ...... G115 58 ............ G029 023 ........... G88 27 ............. HD 002665 .......... HD 002857 .......... HD 006755 .......... HD 016031 .......... HD 019445 .......... HD 044007 .......... HD 045282 .......... HD 063791 .......... HD 087140 .......... HD 094028 .......... HD 111721 .......... HD 128279 .......... HD 132475 .......... HD 134439 .......... HD 134440 .......... HD 163346 .......... HD 163810 .......... HD 165195 .......... HD 184266 .......... HD 284248 .......... HD 345957 .......... [Fe/H] 1.7 2.1 1.6 1.8 2.0 1.4 1.7 1.6 1.5 2.2 1.4 2.0 1.9 2.0 1.6 1.6 1.8 2.0 1.7 1.5 1.7 1.6 1.3 1.1 2.1 1.3 1.5 1.5 1.4 2.2 1.8 1.4 1.3 MV 4.31 4.09 5.38 2.73 6.05 5.51 5.58 5.22 3.99 4.04 4.26 3.62 2.78 0.82 4.34 1.24 2.16 4.46 5.10 1.62 2.33 0.89 2.18 4.63 0.56 1.90 3.73 6.74 7.08 0.30 5.00 4.02 0.17 4.77 3.75 BJ 0.39 0.39 0.16 0.20 0.08 0.19 0.19 0.33 0.40 0.65 0.42 0.37 0.39 0.36 0.11 1.38 0.15 0.37 0.27 0.09 0.17 0.00 0.21 0.30 0.13 0.18 0.28 0.04 0.02 0.99 0.20 0.55 0.36 0.33 b y V I V R HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD HD TABLE 4 Balmer Jumps Measured from MILES Spectra Star 002665 002796 019445 045282 046703 064090 074000 084937 085773 088609 094028 103095 122563 140283 165195 187111 188510 218502 218857 219617 221170 237846 251611 284248 ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... [Fe/H] 2.0 2.3 2.1 1.4 1.6 1.8 2.0 2.2 2.2 2.6 1.5 1.4 2.6 2.5 2.2 1.8 1.6 1.8 1.9 1.4 2.1 2.6 1.7 1.6 Teff 5013 4950 5920 5350 6000 5450 6170 6230 4460 4513 5950 5030 4570 5690 4470 4260 5490 6030 5080 5880 4470 4960 5350 6025 log g 2.35 1.36 4.40 3.20 0.40 4.45 4.20 4.00 1.00 1.30 4.20 4.60 1.12 3.60 1.10 0.60 4.70 3.80 2.40 4.00 1.00 1.80 3.80 4.20 BJ 0.22 0.28 0.26 0.22 1.20 0.08 0.37 0.45 0.00 0.31 0.09 0.09 0.30 b y B V

0.413 0.316 0.372 0.409 0.415 0.344 0.394 0.337 0.303 0.227 0.298 0.325 0.338 0.316 0.537 0.085 0.489 0.305 0.329 0.548 0.448 0.588 0.461 0.327 0.507 0.449 0.363 0.424 0.516 0.380 0.384 0.894 0.418 0.321 0.345

0.798 0.629 0.731 0.774 0.809 0.639 0.778 0.708 0.671 0.500 0.570 0.696 0.684 0.654 1.005 0.216 0.957 0.629 0.681 1.045 0.861 1.127 0.946 0.685 0.981 0.908 0.778 0.857 1.059 0.839 0.745 1.533 0.817 0.659 0.742

0.393 0.306 0.352 0.373 0.401 0.308 0.380 0.340 0.315 0.236 0.270 0.335 0.334 0.312 0.494 0.089 0.467 0.298 0.319 0.511 0.422 0.549 0.452 0.324 0.480 0.432 0.365 0.429 0.538 0.403 0.368 0.774 0.400 0.316 0.347

0.23 0.43 0.18 0.26 0.20 0.15 0.39

0.509 0.520 0.345 0.458 0.302 0.424 0.322 0.301 0.737 0.676 0.347 0.487 0.653 0.361 0.830 0.809 0.403 0.309 0.492 0.348 0.712 0.489 0.474 0.328

0.720 0.724 0.445 0.658 0.421 0.608 0.407 0.374 1.046 0.941 0.462 0.754 0.903 0.474 1.219 1.215 0.591 0.414 0.705 0.478 1.049 0.668 0.664 0.422

from log g p 4.5 main-sequence stars. Cooler than 5000 K, the Balmer jump is virtually impossible to measure, except in the most extreme metal-poor stars. The model spectra show that the measured Balmer jump increases as the metallicity increases, probably due to the greater strength of metal line­blanketing in the UV than in the blue. 4.2. Observations There are several excellent spectral libraries that can be used for Balmer jump measurements and comparison with the models. The best librar y is probably the Next Generation Spectral Librar y2 of STIS data, by Gregg (2006). Preliminar y versions of the spectra have kindly been provided by M. Gregg and J. M. Appelaniz. The Sanchez-Blanquez et al. (2006) librar y3 is of similar quality and resolution, but has shorter wavelength ° coverage (3500­7500 A).
2 3

Table 3 lists the measured Balmer jumps of the STIS spectra, together with the Hipparcos MV and colors computed from the spectra. Table 4 lists the measured Balmer jumps of the MILES (Medium-resolution INT Library of Empirical Spectra) spectra, together with the atmospheric parameters from Cenarro et al. (2007) and the b y and B V colors computed from the spectra. In Figure 12, the MV versus b y diagram for the STIS spectra is shown, together with a halo isochrone. Some of the MV values are poorly determined because of large uncertainties in the parallax, and there are at least four stars whose absolute magnitudes are in disagreement with their Balmer jump measurements shown in Figure 13. Figure 13 is a plot of the obser ved Balmer jumps for the STIS sample versus b y. Lines have been drawn through the mainsequence, subgiant, and giant branch stars, as indicated from Figure 12. The stars whose MV values differ significantly from their Balmer jumps are marked in Figure 12. The theoretical values for the Munari et al. [Fe/H] p 1.5 and 2.5 spectra are also shown for log g p 3.5, 4.0, and 4.5, and temperatures Tef f p 6500, 6250, 6000, 5750, 5500, and 5250 K. The Balmer jumps from the synthetic spectra are in good agreement with the obser ved loci of metal-poor stars. Precise derivation of the gravities of individual stars involves knowledge of the metallicity and temperature (and the reddening, if fluxes are used), which is beyond the scope of this paper. 5. SUMMARY

See http://lifshitz.ucdavis.edu/mgregg/gregg/ngsl/download.html. See the MILES librar y, http://www.ucm.es/info/Astrof/miles/miles.html.

Dividing extracted raw spectra by the spectrum of a warm near-blackbody object such as EG 131, L745 46a, LHS 43,

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Fig. 11.--Measured Balmer jumps vs. V gravity for the [Fe/H] p 2.5 spectra.

I color for model spectra for [Fe/H] p

1.5 and

2.5. Connecting lines are drawn through points for the same

Fig. 12.--Absolute magnitude MV vs. b y diagram for the selection of STIS spectra of low-metallicity stars listed in Table 3. A halo isochrone is shown for orientation. The lines with arrows indicate the appropriate shifts for those stars whose MV values are inconsistent with their measured Balmer jumps.

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Fig. 13.--Measured Balmer jumps vs. b y color for the STIS stars (filled circles) and MILES spectra (open circles). Lines have been drawn to connect the stars on the main sequence and the subgiant and giant branch as identified in Fig. 12. The same relation for the Munari et al. spectra for [Fe/H] p 1.5 plotted in Fig. 11 is also shown.

or LHS 4043 results in spectra whose continua above and below the Balmer discontinuity are close to straight lines, thus making it easy to measure the size of the Balmer jump accurately. The recommendation is to obser ve a warm near-blackbody star at least once per run for each grating setting used, then divide all extracted raw spectra by a template made from the normalized extracted blackbody spectrum by removing any obvious lines or bands it may have, or by fitting the continuum. In order to accurately measure the theoretical Balmer jumps from synthetic spectra such as those of Munari et al. (2005), it is also important to divide the synthetic spectra by the normalized theoretical blackbody spectrum of a blackbody temperature similar to the template star used. Having followed these recommendations and measured the Balmer jump, the effective gravity can be derived from the model spectra. If the effective temperature of the FGK star is known to within 100 K, the Balmer jump will yield an effective gravity to about 0.2 dex for the hotter stars and 0.5 dex for

the cooler stars, sufficient precision to determine whether the star is a main-sequence, giant branch, or horizontal/asymptotic giant branch star. Best spectrophotometric results are achieved if an atmospheric dispersion corrector is used or if the spectrograph is rotated to put the parallactic angle along the slit. This is not essential to measure the monochromatic Balmer jump, but it does ensure that the spectra can be accurately calibrated onto a relative absolute flux scale, and that other temperature-sensitive colors can be derived.

I am grateful to Dr. Lajos Balazs, Director of Konkoly Obser vator y, and Dr. Katalin Olah for their hospitality during the writing of this paper. I am also grateful to Dr. Fiorella Castelli for providing the synthetic spectra, to Dr. Santi Cassisi for computing additional isochrones, and to Drs. Michael Gregg and Jesus Maiz Appelaniz for the preliminar y NGSL STIS spectra.

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