Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/~tbrown/m32nuv/m32_stis.ps Äàòà èçìåíåíèÿ: Fri Sep 24 16:51:36 1999 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 07:29:46 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: galactic collision

TO APPEAR IN THE ASTROPHYSICAL JOURNAL
Preprint typeset using L A T E X style emulateapj v. 04/03/99
DETECTION AND PHOTOMETRY OF HOT HORIZONTAL BRANCH STARS IN THE CORE OF M32 1
THOMAS M. BROWN 2 , CHARLES W. BOWERS, RANDY A. KIMBLE, ALLEN V. SWEIGART
Laboratory for Astronomy & Solar Physics, Code 681, NASA/GSFC, Greenbelt, MD 20771. tbrown@pulsar.gsfc.nasa.gov,
bowers@band2.gsfc.nasa.gov, kimble@ccd.gsfc.nasa.gov, sweigart@bach.gsfc.nasa.gov.
HENRY C. FERGUSON
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. ferguson@stsci.edu.
To appear in The Astrophysical Journal
ABSTRACT
We present the deepest near­UV image of M32 to date, which for the first time resolves hot horizontal branch
(HB) stars in an elliptical galaxy. Given the near­solar metallicity of M32, much larger than that of globular
clusters, the existence of an extended horizontal branch is a striking example of the second parameter effect, and,
most importantly, provides direct evidence that hot HB stars and their progeny are the major contributors to the
UV upturn phenomenon observed in elliptical galaxies. Our image, obtained with the Space Telescope Imaging
Spectrograph (STIS), detects approximately 8000 stars in a 25 00 \Theta 25 00 field, centered 7:7 00 from the galaxy nucleus.
These stars span a range of 21--28 mag in the STMAG system, and in the deepest parts of the image, our catalog
is reasonably complete (? 25%) to a magnitude of 27. The hot HB spans a magnitude range of 25--27 mag at
effective temperatures hotter than 8500 K. We interpret this near­UV luminosity function with an extensive set of
HB and post­HB evolutionary tracks.
Although the UV­to­optical flux ratio in M32 is weak enough to be explained solely by the presence of post­
asymptotic giant branch (post­AGB) stars, our image conclusively demonstrates that it arises from a small fraction
( ¸ !5%) of the population passing through the hot HB phase. The production of these hot HB stars does not appear
to rely upon dynamical mechanisms -- mechanisms that may play a role in the HB morphology of globular clusters.
The majority of the population presumably evolves through the red HB and subsequent post­AGB phases; how­
ever, we see far fewer UV­bright stars than expected from the lifetimes of canonical hydrogen­burning low­mass
post­AGB tracks. There are several possible explanations: (1) the transition from AGB to T eff ? 60000 K could
be much more rapid than previously thought; (2) the vast majority of the post­AGB stars could be evolving along
helium­burning tracks; (3) the post­AGB stars could be surrounded by circumstellar dust during the transition
from the AGB to T eff ? 60000 K.
Subject headings: galaxies: evolution --- galaxies: abundances --- galaxies: stellar content --- ultraviolet:
galaxies --- ultraviolet: stars --- stars: evolution
1. INTRODUCTION
The nearest elliptical galaxy available for study is M32, a
companion to M31. Because M32 has a high surface brightness
that is centrally concentrated, a near­solar metallicity, and a pre­
dominantly old population, it is usually considered a ``compact
elliptical'' galaxy, as opposed to a ``dwarf elliptical'' or ``dwarf
spheroidal'' (see Da Costa 1997). Due to its proximity (770
kpc), space­based observations are able to resolve individual
cool stars near its center. Hot stars can also be detected in the
center itself, because they are relatively rare, so crowding is not
serious, and because the cooler, dominant populations are sup­
pressed in the solar­blind UV bandpasses. Because M32 can
be studied through colors, spectra, luminosity functions, and
color­magnitude diagrams, it represents a natural benchmark in
our understanding of elliptical galaxies.
Stellar population studies of M32 at optical and infrared
wavelengths have shown no evidence for an extended hori­
zontal branch (HB) (Grillmair et al. 1996), and population syn­
thesis work often assumes that the galaxy has a ``red clump'' HB
1 Based on observations with the NASA/ESA Hubble Space Tele­
scope obtained at the Space Telescope Science Institute, which is op­
erated by the Association of Universities for Research in Astronomy,
Incorporated, under NASA contract NAS 5­26555.
2 NOAO Research Associate.
morphology (e.g., Worthey 1994). In the ultraviolet, Brown
et al. (1998) found indirect evidence for an extended HB in
M32: the UV­bright post­HB stars apparently follow evolution­
ary tracks originating from the hot end of the HB. In spectral
synthesis studies, the assumption of a red clump HB morphol­
ogy contributes to the need for an intermediate­age component
to the stellar population, to provide the necessary ultraviolet
flux (see Grillmair et al. 1996 and references therein). Direct
proof of an extended HB would therefore relax the requirement
that M32 has a composite population, with a dominant old com­
ponent (of age 8 Gyr or more), and a minority younger compo­
nent (of age ¸5 Gyr).
Considered as an extreme case in the sequence of true el­
liptical galaxies, M32 has the weakest UV­to­optical flux ratio
measured to date (1550 \Gamma V = 4:5 mag; Burstein et al. 1988).
Known as the UV upturn, the sharp rise in the spectra of ellip­
tical galaxies at wavelengths shorter than 2500 å was discov­
ered with the OAO­2 satellite (Code 1969). Prior to this discov­
ery, researchers did not expect such a UV­bright component in
supposedly old, passively­evolving populations. Many candi­
dates were suggested to explain the upturn, including young
massive stars, hot white dwarfs, hot HB and post­HB stars,
and non­thermal activity (for a complete review, see Greggio
& Renzini 1990; O'Connell 1999). As the measurements of lo­
1

2
cal ellipticals were expanded, IUE observations demonstrated a
large variation in the strength of the UV upturn from galaxy to
galaxy, even though the spectra of ellipticals appear very simi­
lar at longer wavelengths. Characterized by the 1550 \Gamma V color,
the UV upturn becomes stronger and bluer as the metallicity
(optical Mg 2 index) of the galaxy increases, while visible col­
ors become redder (Burstein et al. 1988).
Today, it is widely believed that HB stars and their progeny
are responsible for the far­UV emission in elliptical galaxies.
There are three classes of post­HB evolution, each evolving
from a different range of effective temperature on the zero­age
HB (ZAHB; see Figure 1). Following core helium exhaustion,
stars on the red end of the HB will evolve up the asymptotic
giant branch (AGB), undergo thermal pulses, evolve as bright
post­AGB stars to hotter temperatures, possibly form planetary
nebulae, and eventually descend the white dwarf (WD) cool­
ing curve. At hotter temperatures (and lower envelope masses)
on the HB, stars will follow post­early AGB evolution: they
evolve up the AGB, but leave the AGB before the thermal puls­
ing phase, continue to high temperatures at high luminosity,
and descend the WD cooling curve. The bluest HB stars, with
very little envelope mass, will follow AGB­Manqu' e evolution,
evolving directly to hotter temperatures and brighter luminosi­
ties without ever ascending the AGB, and finally descending
the WD cooling curve. These three classes of post­HB be­
havior have very different lifetimes, in the sense that the post­
AGB stars are bright in the UV for a brief period (¸ 10 3 \Gamma 10 4
yr), the post­early AGB stars are UV­bright for a longer period
(¸ 10 4 \Gamma 10 5 yr), and the AGB­Manqu' e stars are UV­bright for
very long periods (¸ 10 6 \Gamma 10 7 yr). The HB phase itself lasts
¸ 10 8 yr, and so the presence of hot HB stars in a population,
combined with their long­lived UV­bright progeny, can produce
the strong UV upturn seen in the most massive, metal­rich el­
lipticals (see Dorman, O'Connell, & Rood 1995 and references
therein). In galaxies with a weak UV upturn, a significant frac­
tion of the far­UV flux can theoretically come from post­AGB
stars (see Brown et al. 1997), and in the weakest UV upturn
galaxies -- such as M32 -- the spectra alone do not require the
presence of a hot HB.
The ZAHB is not only a sequence in effective tempera­
ture: it is also a sequence in mass (see Dorman, Rood, &
O'Connell 1993). For T eff ¸ ? 6000 K, a small change in en­
velope mass ( ¸ ! 0:1 M fi ) corresponds to a large change in
T eff (\DeltaT eff ¸ ? 10;000 K), assuming solar abundances. Because
the main­sequence turnoff (MSTO) mass decreases as age in­
creases, the ZAHB will become bluer as a population ages,
assuming all other parameters (e.g., mass loss on the red gi­
ant branch, metallicity, helium abundance, etc.) remain fixed.
Note that this does not necessarily imply that age is the ``second
parameter'' of HB morphology (e.g., Fusi Pecci & Bellazzini
1997; VandenBerg 1999; Sweigart 1999). The assumed first pa­
rameter of the HB morphology debate is metallicity; the HB be­
comes bluer at lower metallicity, assuming all other parameters
(age, mass loss, etc.) remain fixed. This is due to two reasons.
First, the MSTO mass at a given age is lower at lower metal­
licity, because a metal­poor star is more luminous (and thus
shorter­lived) than a metal­rich star of the same mass. Second,
as the metallicity decreases, the envelope opacity decreases,
leading to a higher effective temperature on the HB. In short,
HB morphology tends to become bluer at lower metallicity and
higher ages, but other parameters may also play a role (rotation,
He abundance, deep mixing, etc.). Although HB morphology
in globular clusters (GCs) tends to become redder at increas­
ing metallicity, there are examples of relatively metal­rich GCs
with extended blue HBs (e.g., Rich et al. 1997), leading to the
``second parameter'' debate. Although elliptical galaxies should
not be considered as overgrown globular clusters, they are gen­
erally believed to be metal­rich, old populations, and thus the
presence of a hot HB in M32 can provide further insight into
the production of blue HBs.
M32 has been the subject of several UV imaging programs
with the Hubble Space Telescope (HST). The earliest of these
observations (King et al. 1992; Bertola et al. 1995) were taken
with the Faint Object Camera (FOC) before the correction of
the spherical aberration, and were subject to large photomet­
ric uncertainties due to the calibration and aperture correc­
tions. After the HST refurbishment with COSTAR, Brown et
al. (1998) also observed M32 with the FOC, and detected the
UV­bright post­HB phases of stars descended from the hot HB;
although the calibration was improved in these later observa­
tions, the FOC was still subject to considerable uncertainties,
such as an unexplained format dependence to the photomet­
ric zero points, and red leak. Here, we describe the deep UV
imaging of M32 performed with the Space Telescope Imaging
Spectrograph (STIS), a 2nd­generation HST instrument with
a vastly improved performance and calibration. Our image is
sufficiently deep to reach the HB at temperatures hotter than
8500 K, and in fact does reveal the presence of these stars, pro­
viding the first direct detection of hot HB stars in an elliptical
galaxy. We interpret our data with a new set of evolutionary
tracks, and compare our results to expectations from canonical
tracks in the literature.
3.5
4.0
4.5
5.0
log T eff (K)
0
1
2
3
log
L/L
Zero-age HB
Main Sequence
Turnoff
AGB-ManquÈ
Post-early AGB
Post-AGB
White Dwarf
RGB
AGB
3.5
4.0
4.5
5.0
log T eff (K)
0
1
2
3
FIG. 1-- The three classes of post­HB evolution arising from
different ranges of effective temperature and envelope mass
on the zero­age HB. The tracks shown assume solar metallic­
ity and helium abundance, and are from our own calculations
(see §6.3.1). For populations older than 1 Gyr, the HB phase
(light grey) is brighter than the main sequence turnoff, which
also contributes to the flux in the near­UV.

3
TABLE 1: Near­UV Photometric Catalog (abridged)
x y STMAG error region RA a Dec a
(pix) (pix) (mag) (mag) (#) (J2000) (J2000)
38.6 112.9 25.64 0.11 1 0:42:40.4795 40:51:39.109
39.0 578.3 26.41 0.15 1 0:42:41.3862 40:51:34.325
39.2 199.4 27.33 0.40 1 0:42:40.6486 40:51:38.233
... ... ... ... ... ... ...
354.9 821.3 22.39 b 0.02 3 0:42:42.1502 40:51:38.900
355.8 620.1 26.44 0.24 3 0:42:41.7592 40:51:40.992
... ... ... ... ... ... ...
a Note that the relative astrometry is quite accurate (tenths of a 0.025 00 STIS pixel), but the absolute
astrometry is subject to a ¸1 00 --2 00 uncertainty (associated with the position of the guide stars).
b Stars associated with planetary nebulae in our field. Note that one of the four PNe in our field is at
the edge of the frame and is thus not included in the catalog.
2. OBSERVATIONS
STIS observed M32 on 19 October and 21 October 1998,
with four exposures on each day; the total exposure of the
summed images is 22962 sec. The combined image, shown
with a logarithmic stretch to enhance the faint stars, is shown
in Figure 2. The data were taken with the near­UV multi­anode
microchannel array (NUVMAMA), using the crystal quartz fil­
ter (F25QTZ); the filter blocks light shortward of 1450 å and
thus reduces the sky background from terrestrial airglow lines
of O I and Lyman ff. The long wavelength cutoff of the band­
pass is 3500 å, due to the sensitivity of the detector, and red
leak at longer wavelengths is minimal (Baum et al. 1998). The
STIS MAMAs are photon counters that register less than one
count per incident cosmic ray; thus, cosmic ray rejection is not
required, as it is with CCD imaging (where an incident cosmic
ray causes a massive many­count ``hit''). A full description of
the instrument and its capabilities can be found in Woodgate et
al. (1998) and Kimble et al. (1998).
The 25 00 \Theta 25 00 (1024 \Theta 1024 pixel) field was centered 7.7 00
south of the M32 center, in order to overlap with earlier FOC
UV imaging of M32 (Brown et al. 1998), to allow imaging in
regions of lower diffuse galaxy background while still includ­
ing the center of the galaxy, and to place the field farther from
M31. The images were dithered between three positions along
the X/Y diagonal of the detector: +0:23 00 =+0:23 00 , 0 00 =0 00 , and
\Gamma0:23 00 = \Gamma 0:23 00 . Given the plate scale of 24.465 mas pix \Gamma1 ,
these offsets were equivalent to shifts of ú9 pixels along each
axis of the detector, which is useful for smoothing out small­
scale variations in detector sensitivity. A small fraction of the
field near the detector edge is occulted by a scattered­light mask
very close to the focal plane: the lower right corner (ú9000 pix­
els), the upper right corner (ú2700 pixels), the bottom 20 rows,
the first 8 columns, the top row, and last 4 columns. Although
the mask slightly decreases the field of view, it does not vignette
stars in the remainder of the field, and it does allow an accurate
characterization of the dark counts in the data.
The STIS focal plane is tilted with respect to the detector
when in imaging mode (STIS is optimized for spectroscopy).
Thus, the PSF changes in shape and width as one moves from
left to right in the field, and it also changes in time due to tele­
scope breathing. Our final summed image averages over time
to produce a PSF that is very nearly circular in the left half of
the image, and noticeably elliptical in the right half of the im­
age. Our detection limits are driven by the combination of both
focus and galaxy background. In this image, the focus is best
where the diffuse background from the core of M32 is faintest.
This combination makes the limiting sensitivity significantly
non­uniform over the summed image, but provides the deepest
possible sensitivity in the well­focussed portions of the image.
An elliptical Gaussian fit to isolated bright stars in the field has
a FWHM range of 2.42--3.96 pix (0.06--0.1 00 ), and an axial ratio
range of 0.64--0.95.
We detect ¸8000 stars in the near­UV. Because the image
contains ú 2:4 \Theta 10 5 resolution elements (in the regions where
we are actually cataloging stars), this is obviously a crowded
field, with an average of one star per 30 resolution elements;
near the M32 center, the crowding is severe, with one star per
12 resolution elements, but farther from the center it drops to
one star per 63 resolution elements. The combination of this
crowding with the variable PSF and the variable galaxy back­
ground makes photometry difficult, but not impossible, as we
will discuss below.
Although the internal interstellar extinction within M32 is
unknown, it is presumably small in comparison to the Galac­
tic foreground extinction, thought to be anywhere in the range
0:035 Ÿ E(B \Gamma V ) Ÿ 0:11 mag (Tully 1988; McClure &
Racine 1969; Burstein et al. 1988; Ferguson & Davidsen 1993;
Burstein & Heiles 1984). For the purposes of this paper, we
assume E(B \Gamma V) = 0:11 mag when comparing the data to the
predictions of stellar evolutionary tracks, corresponding to 0.8
mag of extinction in the STIS bandpass.
Of the ¸ 8000 stars resolved in the STIS image, four of the
brightest roughly coincide with the positions of the only known
planetary nebulae (Ciardullo et al. 1989) in this field. Specifi­
cally, if one takes their positions in the SIMBAD database, there
is a very bright star in the STIS image approximately 1 00 west
of each position, implying that there is a global offset between
the astrometry of our image and that of the planetary nebulae.
These stars are flagged in our catalog (Table 1, available from
the CDS), and their positions are marked in Fig 3.
3. DATA REDUCTION
We reduced the raw images via the CALSTIS package in
IRAF, including an updated pixel­to­pixel flat field file. Two
steps in the reduction were done outside of CALSTIS: geomet­
ric correction was applied during the final combination via the
IRAF DRIZZLE package, and dark subtraction was performed
by subtracting a scaled and flat­fielded dark image from each
data frame, with the scaling determined from the occulted right­
hand corners of the detector. All frames were cross­correlated
to provide accurate relative shifts. The calibrated frames were
then drizzled to a 1060 \Theta 1060 pixel image that included the
data from all dither positions. The resulting image has a narrow
strip of underexposed pixels along the edges, due to the dither

4
FIG. 2.--- This false­color image of the M32 center uses a logarithmic scaling to enhance the faintest stars on the HB. The STIS field is 25 00 \Theta 25 00 , and the
combination of the dithered positions have been summed onto a 1060 \Theta 1060 pixel image (cropped to 1024 \Theta 1024 pixels here). The occulted portions of the image
are due to a scattered light mask, and vignetting is negligible.

5
TABLE 2: Photometry
x­position a FWHM b resolution detected fraction of near­UV resolved fraction
region (pix) (pix) elements stars flux resolved c – 25:5 mag d
1 37--141 2.68 30806 556 0.33 0.17
2 142--341 2.52 63677 1008 0.19 0.11
3 342--541 2.62 59818 1316 0.13 0.09
4 542--741 3.00 44864 2150 0.11 0.10
5 742--941 3.43 27366 2226 0.10 0.11
6 942--1037 3.62 13035 765 0.09 0.10
a Each region extends the full height of the image, excluding occulted detector areas and a 4 00 \Theta 2:7 00 ellipse
centered on M32. The galaxy center is at (x;y) = (842:7;392:7).
b This is the average FWHM of a Gaussian fit to the stars in each region, and is used for object detection.
c From all detected stars in the uncorrected catalog, and assuming a sky background of 9 \Theta 10 \Gamma4 cts sec \Gamma1 pix \Gamma1 .
d From the corrected luminosity function, assuming a sky background of 9 \Theta 10 \Gamma4 cts sec \Gamma1 pix \Gamma1 .
pattern. This strip is scaled correctly to account for the smaller
exposure time, but thus has higher noise than the fully exposed
area of the image. Stars in the underexposed strip are not in­
cluded in our catalog, and this strip was not included in the
Monte Carlo simulations discussed in §4.2 and §4.3.
The drizzle ``dropsize'' (also known as pixfrac) was 0.1, thus
improving the resolution over a dropsize of 1.0 (which would be
equivalent to simple shift­and­add). This small dropsize does
not cause problematic ``holes'' in the final image, because the
pixel scale was unchanged; it is thus equivalent to interlacing
the individual frames. In the final image, pixels outside of the
dither pattern or occulted are set to a count rate of zero. The
pixel mask used in the drizzle for each input frame included
the occulted regions of the detector, a small number of hot pix­
els, and pixels with relatively low response (those with values
Ÿ 0:75 in the pixel­to­pixel flat field).
4. PHOTOMETRY
4.1. PSF Fitting
Because the M32 image is fairly crowded, there are two ob­
vious options for performing photometry: PSF fitting or small­
aperture photometry. However, the PSF also varies strongly
with position in the image, and so the aperture correction for
small­aperture photometry would be a strong function of posi­
tion, possibly introducing systematic errors in our catalog. We
felt that PSF fitting offered the most accuracy for these data.
As an initial estimate of the PSF variation, we used the IRAF
routine FITPSF to fit an elliptical Gaussian to 180 of the bright­
est isolated stars in the image. The result defined a map of the
Gaussian semi­major axis width as a function of position in the
image. The map confirmed that the PSF varies as a function of
horizontal position.
For our PSF fitting, we used the January 1998 version of
the DAOPHOT­II package (Stetson 1987). The software al­
lows calculation of relative photometry with a variable PSF
defined by the user. Our iterative procedure was similar to that
described in the User's Manual, to which we refer interested
readers for details. However, because the PSF and the diffuse
background from unresolved stars both vary with position, we
chose to perform our photometry on six image regions (defined
in Table 2). Object detection and PSF fitting for each region
were done with the region boundaries extended 50 pixels into
the neighboring regions, to avoid edge effects with stars near
the region boundaries. Thus, at each region boundary, there is
a 100­pixel wide strip where stars are fit twice, and we use this
FIG. 3-- This schematic of the STIS image shows some of
the details of the reduction discussed in the text. The six la­
beled vertical strips are the regions used for PSF fitting and
photometry. Stars were rejected from the catalog within the
black ellipse in the center of the galaxy. White circles show
the positions of the bright stars that correspond to the posi­
tions of the four known planetary nebulae in our field; from
left to right, they are: Ford­NGC221­21, Ford­NGC221­23,
Ford­NGC221­27, and Ford­NGC221­24.
overlap to put the stars in each region on the same magnitude
system (see below). Each region spanned the entire height of
the image, with region 5 encompassing the center of the galaxy.
From our initial map of elliptical Gaussian fits, we determined
the ``average'' width of a star in each region (Table 2), and used
this width for object detection. DAOPHOT convolves an image
with a Gaussian as part of its object detection algorithm, but the
user must specify a constant width for each image under con­
sideration. Thus, our use of a different width for each region
allows optimization of the object detection.
To determine a variable PSF for each region, we first sub­
tracted a median­filtered image from the data to remove the
varying galaxy background. We found that this subtraction pre­
vented a spurious biasing of the PSF wings; fitting the PSF with

6
the galaxy background intact incorrectly tilts the PSF wings
along the slope of the galaxy background. Our PSF in each
region is a Moffat function with a lookup table of empirical cor­
rections. The PSF in each region was allowed to vary linearly
with position. Although DAOPHOT allows quadratic variations
in the PSF, our PSF subtraction was worsened when we at­
tempted to allow such higher order variation. The PSF determi­
nation was done though an interactive selection of the brightest
isolated stars, with iterations to subtract the PSFs of the neigh­
boring stars, as described in the manual for the software. The
PSF was defined with a radius of 10 pixels.
After determining a variable PSF for each image region, we
performed object detection and PSF fitting on the data, again
using the regions defined in Table 2 (but without the galaxy
background subtraction). To maintain positional consistency,
we did not actually extract the regions from the image; we
simply set those pixels outside of a given region to a ``bad''
pixel value, thus producing a mask for each region. In re­
gion 5, which contains the M32 center, we also masked off a
0:75 00 \Theta 0:5 00 ellipse aligned to the axis of M32 (45 o counter­
clockwise from the +y axis of the image), in order to prevent
an unnecessary biasing of the ``sky'' level, and because the very
center appeared hopelessly crowded. In the final catalog, we
actually rejected stars in a larger 4 00 \Theta 2:7 00 ellipse, after reeval­
uating the severity of the crowding. We set the detection thresh­
old to 5 oe; setting a lower threshold produces many false de­
tections, because the diffuse background varies with position,
even within the subsections we defined. The detection algo­
rithm convolves the image with a symmetrical Gaussian with a
width equal to the FWHM of the PSF, and then looks for devi­
ations above the local sky background (see Stetson 1987 for a
complete description). We set the ``roundness'' and ``sharpness''
criteria to twice their default values, because the STIS PSF is
not symmetrical and there is no need to reject cosmic rays in
STIS MAMA images. After a first pass of object detection and
PSF fitting, the star­subtracted image is used for a second pass
at object detection, and the final combined catalog is used for a
second pass of PSF fitting. The PSFs were fit to the stars using
a fitting radius of 3 pixels and a sky annulus spanning 8--15 pix­
els in radius. The DAOPHOT package is capable of iteratively
solving for the sky under the star itself (hence the inner radius
of the sky annulus falls within the PSF radius).
DAOPHOT calculates the relative magnitudes of stars in
each region. Putting all of the stars in each region on the same
system required several additional steps. The PSF in region 2 is
the most circular and has the smallest FWHM. We performed
aperture photometry on the 10 brightest stars in region 2, with
the aperture varying from 3--10 pixels in radius. Next, we
performed the same aperture photometry on the quasar in the
Hubble Deep Field South (HDF­S) near­UV image (Gardner et
al. 1999). The encircled­energy variation with aperture size in
our M32 image was nearly identical to that of the quasar. We
then used the quasar (with object masking for the other galaxies
in the HDF­S) to determine an aperture correction of 0.524 mag
for a 3­pixel radius aperture, and used this aperture correction
to calculate the corrected magnitudes of the 10 bright stars in
M32. This then determined the zero­point for the DAOPHOT
magnitudes in region 2. Next, we used the 100­pixel­wide over­
laps at region boundaries (see above) to place all of the stars on
the same magnitude system as region 2; the photometry in each
region was shifted by less than 0.1 mag as part of this correc­
tion. Our magnitudes are specified in the STMAG system:
m = \Gamma2:5 \Theta log 10 f – \Gamma 21:10
f – = counts \Theta PHOTFLAM=EXPTIME
where EXPTIME is the exposure time, and PHOTFLAM is
5:588 \Theta 10 \Gamma18 erg s \Gamma1 cm 2 å \Gamma1 / (cts s \Gamma1 ).
The entire photometric catalog (Table 1) is available from the
CDS. Table 3 shows the raw (uncorrected) luminosity functions
in each region.
TABLE 3: Uncorrected Luminosity Functions
No. of stars in region
mag 1 2 3 4 5 6
21.0 0 0 0 0 1 0
21.5 0 1 0 2 2 0
22.0 0 0 1 4 5 2
22.5 1 2 2 4 1 0
23.0 2 1 2 7 6 1
23.5 1 3 4 10 16 5
24.0 6 9 12 29 69 16
24.5 7 7 31 58 197 31
25.0 14 43 95 248 403 146
25.5 66 196 328 588 649 271
26.0 110 306 416 706 555 214
26.5 154 255 323 388 254 69
27.0 139 135 92 102 67 10
– 27.5 56 50 10 4 1 0
4.2. Completeness
In the deepest regions of the image, we are detecting stars
down to 28 mag. However, the catalog becomes seriously in­
complete well before this point is reached, and the complete­
ness varies from region to region. To determine the complete­
ness as a function of magnitude in each region, we ran thou­
sands of Monte Carlo simulations, using the DAOPHOT pack­
age and our own IDL­based programs. For each region, 10 stars
at a given magnitude were placed within the region at random
positions, using the variable PSF for that region, and including
Poisson noise in the artificial stars. The entire object detec­
tion and PSF fitting process was then performed, and the cat­
alog was checked to see if the stars were recovered. This pro­
cess was then repeated until the calculated completeness was
deemed well­determined, with the criteria that the calculated
completeness not change significantly (by ?1%) over many
runs. Because we only add 10 stars per simulation, we are not
significantly affecting the crowding in the data (which contains
hundreds of stars in each region). Table 4 lists the complete­
ness versus magnitude for each region. Note that the object de­
tection is done with a Gaussian convolution of constant width
(specified in Table 2), while the artificial stars are created us­
ing the empirically­corrected Moffat function that was deter­
mined from the STIS data (and significantly different from a
Gaussian); thus, the completeness determination is not a cir­
cular process, and it does accurately model the true detection
process. Because the strength of the galaxy background has a
strong influence on the completeness, the completeness is best
in region 1, even though the PSF is sharpest in region 2.
To ensure that inaccuracy in our variable PSF template does
not skew the determination of the completeness, we recalcu­
lated a set of completeness simulations using smoothed PSFs
for the artificial stars. Because these test PSFs were not as

7
strongly peaked, they could possibly reduce the detectability.
We first smoothed the true PSF with a kernel that redistributed
10% of the flux in each pixel to its 8 neighbors, and then with
a kernel that redistributed 20% of the flux in each pixel to its
8 neighbors. The artificial stars were then added to the data
with Poisson noise, as before. Although we used these altered
PSFs to generate the artificial stars in the Monte Carlo simu­
lations, we used the true PSF for the PSF fitting, thus simu­
lating a mismatch between the object PSF and the fitted PSF.
Fortunately, the recalculated completeness versus magnitude
remained virtually unchanged when these altered PSFs were
used, thus demonstrating that small errors in the assumed PSF
do not significantly affect the completeness determination.
TABLE 4: Completeness in Near­UV Number Counts
region
mag 1 2 3 4 5 6
21.5 1.00 1.00 1.00 1.00 0.91 0.98
22.0 1.00 1.00 1.00 1.00 0.90 0.97
22.5 0.99 0.99 1.00 0.98 0.88 0.96
23.0 1.00 0.99 0.99 0.98 0.89 0.96
23.5 0.99 0.99 0.98 0.96 0.85 0.94
24.0 0.99 0.98 0.98 0.95 0.83 0.92
24.5 0.97 0.97 0.96 0.93 0.81 0.89
25.0 0.97 0.96 0.95 0.87 0.73 0.77
25.5 0.96 0.96 0.92 0.79 0.55 0.60
26.0 0.92 0.87 0.71 0.48 0.29 0.22
26.5 0.68 0.46 0.25 0.14 0.08 0.04
27.0 0.24 0.11 0.05 0.04 0.02 0.01
27.5 0.06 0.02 0.01 0.00 0.01 0.00
4.3. Spurious Sources
Because we set the DAOPHOT detection threshold a bit
higher than the nominal value of 4 oe, we do not expect many
spurious sources to be detected in the data, except perhaps in
region 5, where the galaxy background varies strongly with po­
sition. However, to quantify exactly how many spurious detec­
tions we have in our catalog, we ran another series of Monte
Carlo simulations.
Each simulation starts with a model of the diffuse light, de­
rived by taking the median of the true image, and assuming
elliptical isophotes to handle edge effects and occulted regions.
This galaxy model was then used to create a starless simulation
of each of the eight STIS exposures, by dithering the model,
scaling by the exposure time, applying detector occultation in
the corners and along the edges, adding dark counts, and adding
Poisson noise. The eight simulated exposures were then driz­
zled into one image, in the same manner as the true data. This
image matched the noise characteristics of the actual data in the
areas free of point sources. Finally, two passes of object detec­
tion and PSF fitting were then applied, again following the ac­
tual data reduction described above. The process was repeated
100 times for each region, to determine the average number of
spurious sources one would expect as a function of magnitude
in each region. The results are tabulated in Table 5.
As expected, spurious sources do not significantly contami­
nate our catalogs where the completeness is larger than 10%.
The number of spurious sources also begins to drop at the
faintest magnitudes, because such stars fluctuate below the 5 oe
detection limits.
TABLE 5: Spurious Source Contamination
region
mag 1 2 3 4 5 6
23.5 0 0 0 0 0 0
24.0 0 0 0 0 1 0
24.5 0 0 0 0 3 0
25.0 0 0 0 0 14 0
25.5 0 0 0 1 42 1
26.0 0 0 0 9 88 15
26.5 0 0 1 62 120 41
27.0 3 6 20 55 36 9
27.5 17 21 12 1 0 0
4.4. Systematic Errors
4.4.1. Comparison with FOC
UV imaging of the evolved stellar populations in M31 and
M32 has been subject to considerable calibration problems, and
the story of these problems underscores the need for faint UV
standards appropriate for direct imaging with today's sensitive
instruments. King et al. (1992) imaged M31 and M32 with the
pre­COSTAR FOC and assumed that the FOC sensitivity was
degraded to 80% of nominal. Bertola et al. (1995) imaged the
same galaxies, and their adoption of a degraded FOC sensitiv­
ity (at 30--40% of nominal in the UV) implied even brighter
UV luminosities for these stars. Both sets of pre­COSTAR data
required large aperture corrections (? 2 mag) because of the
spherical aberration present in the first­generation instruments.
Subsequent recalibration of the FOC showed that the UV sen­
sitivity of the King et al. (1992) data was supposedly at 144%
of nominal, due to the format dependence of the FOC zero­
points (Greenfield 1994). After refurbishment of HST, Brown
et al. (1998) used the FOC to image M31 and M32, and found
that its nominal calibration implied that the stars common to
both the Brown et al. (1998) data and the King et al. (1992)
data were 1.9 mag fainter than previously thought by King et
al. (1992); this discrepancy dropped to 1.2 mag once the format
dependence of the FOC zero­points was included in the King
et al. (1992) magnitudes. Brown et al. (1998) attempted several
cross­checks of the refurbished FOC calibration, and found in­
conclusive evidence for 0.25 mag systematic shifts to the zero
points, in the sense that these UV­bright stars could be 0.25 mag
brighter than implied by the nominal calibration of the refur­
bished FOC. However, these checks were done via comparison
to spectra and galaxy photometry -- no images of globular clus­
ters or isolated stars were available in the appropriate imaging
modes.
Our new STIS observations of M32 include the entire field
observed by Brown et al. (1998) with the FOC. Given the
STIS magnitudes (m NUV ) and the FOC magnitudes (m F175W and
m F275W ) for these stars, color­color diagrams of m NUV \Gamma m F175W
versus m F175W \Gamma m F275W and m NUV \Gamma m F275W versus m F175W \Gamma
m F275W demonstrate that the FOC magnitudes in Brown et al.
(1998) should be revised 0.5 mag brighter than listed in the
Brown et al. (1998) catalog, assuming that the observed stars
span a range of effective temperature from 8000--30000 K.
This revision would further reduce the discrepancy between the
Brown et al. (1998) data and the King et al. data (1992) to 0.7
mag, and so this remaining discrepancy might be due to the
large aperture corrections in the pre­COSTAR data. However,
we note that this means the UV­bright stars in the King et al.
(1992) data are 1.4 mag fainter than originally thought by King
et al. (1992); thus, these stars are not bright enough to be post­

8
AGB stars (the interpretation of King et al. 1992 and Bertola et
al. 1995), and are consistent with post­HB evolution from the
hot end of the HB, as described in Brown et al. (1998). Shifting
the stars in the Brown et al. (1998) color­magnitude diagrams
by 0.5 mag in both filters does not move the bulk of the stars
onto post­AGB tracks.
4.4.2. Comparison with WFPC2
The STIS photometric calibration is reliable at the 0.15
mag level, according to the STScI documentation (Baum et al.
1998); this is considerably more secure than that of the earlier
generation instruments on the HST. At the time of this writ­
ing, new calibration efforts at STScI will revise the photomet­
ric zero­points slightly, and adaptation of these new zero points
would make our stars up to 0.07 mag brighter. Our analysis is
not sensitive to such a small shift in sensitivity, and so we do
not adopt the revision.
Our own consistency check, using STIS & WFPC2 UV im­
ages of the globular cluster NGC6681, confirms the photomet­
ric accuracy of STIS. In the UV, this GC is not crowded and
does not have an underlying galactic background; it gives a
much better sensitivity check than the data available for checks
of the FOC calibration. STIS imaged NGC6681 with the near­
UV crystal quartz filter and the far­UV SrF 2 filter (m FUV ); 22
bright isolated stars are available in the field for accurate pho­
tometry. The same field was also observed by WFPC2 using
the F160BW filter (m F160BW ). The F160BW filter has very low
throughput, but very little red leak. These bright stars have
¸ ! 0:05 mag statistical errors in the WFPC2 frame, and ¸ ! 0:01
mag statistical errors in the STIS frames. Color­color diagrams
of m FUV \Gamma m F160BW versus m FUV \Gamma m NUV and m NUV \Gamma m F160BW
versus m FUV \Gamma m NUV are consistent at the 0.1 mag level when
compared to expectations for stars spanning a range of effective
temperature 8000--30000 K. The expected colors were calcu­
lated by folding the synthetic spectra of Kurucz (1993) through
the bandpasses of the IRAF SYNPHOT package.
4.4.3. Comparison with IUE
The center of M32 was observed by IUE at low signal­to­
noise (S/N) in the wavelength range 1150--3200 å, thus cover­
ing most of the STIS bandpass. We compare the STIS image to
a composite UV+optical aperture­matched spectrum (Calzetti,
private communication); because the red leak in STIS is so low,
the optical portion of the spectrum has little affect on the anal­
ysis, but is included for completeness. We show our bandpass
and this spectrum in Figure 4.
The IUE aperture was a 10 00 \Theta 20 00 oval. Because M32 is not
centered in the STIS image, we must define two regions in the
STIS field that can be used for comparison to IUE: a 10 00 \Theta 10 00
square centered on the M32 nucleus, and an adjacent semicircle
with a radius of 5 00 . The addition of the flux in the square with
twice that of the semicircle is equivalent to the IUE aperture.
Within this artificial aperture, STIS measures a dark­
subtracted count rate of 3228 cts sec \Gamma1 . A template of the ``av­
erage'' sky background, available from the STScI web page,
shows that ¸275 cts sec \Gamma1 of this could be from the sky back­
ground, and so the sky­subtracted count rate measured by STIS
in an IUE­equivalent aperture is ¸2950 cts sec \Gamma1 . Folding
the composite IUE+optical spectrum of IUE through the STIS
bandpass (via the IRAF package SYNPHOT) predicts 2738 cts
sec \Gamma1 , within 10% of the actual value measured by STIS. Given
the uncertainty in the true sky level, the IUE and STIS observa­
tions are in acceptable agreement.
1000 1500 2000 2500 3000 3500 4000
Wavelength (å)
0
200
400
600
800
1000
1200
Effective
Area
(cm
2
)
STIS
bandpass
M32 nuclear
spectrum
0
0.5
1
Flux
(10
-13
erg
s
-1
cm
-2
å
-1
)
1000 1500 2000 2500 3000 3500 4000
Wavelength (å)
0
200
400
600
800
1000
1200
Effective
Area
(cm
2
)
FIG. 4-- The nuclear (10 00 \Theta 20 00 ) spectrum (solid; Calzetti,
private communication), an aperture­matched splice of IUE
and ground­based data, demonstrates that the STIS band­
pass (grey shaded) incorporates flux from both the short­
wavelength UV upturn population and the cooler stars in ear­
lier evolutionary phases. Given that these cooler populations
are several magnitudes fainter than our detection limit in this
bandpass, they contribute to the diffuse background in our
data.
5. RESOLVED FRACTION OF NEAR­UV LIGHT
Because the STIS image is the deepest near­UV image of
M32 to date, we compare the resolved flux with the total flux
in the STIS bandpass. The fraction of resolved flux varies with
position in the image: a much larger fraction of the near­UV
light is resolved into stars as one moves away from the M32
center. In Table 2, we show the fraction of M32 flux within the
STIS bandpass resolved into stars, for each of the 6 regions de­
fined in the table. In each region, we subtract a sky background
of 9 \Theta 10 \Gamma4 cts sec \Gamma1 pix \Gamma1 , which comes from the ``average''
sky template available on the STScI web page, folded through
the SYNPHOT package bandpass. We then calculated the re­
solved fraction via two different methods. In the first method,
we simply took the catalog of stars for that region, summed
the flux from those stars, and divided by the total flux in that
region. This did not assume any completeness correction, nor
did it reach a uniform depth as a function of position in the im­
age. In the second method, we summed the flux in the corrected
luminosity function for those magnitude bins – 25.5 mag (i.e.,
better than 50% completeness everywhere), and then divided by
the total flux in that region. Thus, this second method reaches
a uniform limiting magnitude across the image. We resolve
¸10% of the near­UV flux in most of the image, and about a
third of the near­UV flux in the deepest section. We do not ex­
pect to resolve all of the flux, because a considerable fraction
of the light in our bandpass comes from the cooler populations
that are below our detection limits in the near­UV (see Figure
4). It would take much deeper imaging in this bandpass, at
much higher resolution, to resolve significantly more flux, be­

9
cause the main sequence turnoff is several magnitudes below
the HB (see Figure 1).
6. COMPARISON WITH EVOLUTIONARY TRACKS
6.1. The Stellar Evolutionary Flux
Before comparing our luminosity functions to the expecta­
tions from stellar evolutionary tracks, it is important to place
constraints on the population under consideration. We cannot
have an arbitrary number of stars leaving the MSTO and even­
tually passing through the HB phase; the bolometric luminosity
of the population and the stellar lifetimes constrain the num­
ber of stars in a given evolutionary phase (Greggio & Renzini
1990; Renzini 1998). The stellar death rate, or stellar evolution­
ary flux (SEF), is given by the relation SEF =B(t)L T , where L T
is the total bolometric luminosity of the population, and B(t) is
the specific evolutionary flux. The specific evolutionary flux is
a weak function of age, and for a population of age ¸ 10 Gyr,
B(t) ¸ = 2:2 \Theta 10 \Gamma11 stars yr \Gamma1 L \Gamma1
fi (Renzini 1998).
The section of the STIS image most appropriate for an anal­
ysis of the HB is the sum of regions 1, 2, and 3 (see Table 2).
Restricting our comparison to this deep portion of the STIS im­
age avoids the complications of crowding, systematic errors due
to a steeply varying background, and seriously incomplete pho­
tometry at the magnitudes of interest (¸ 27 mag). We will refer
to this section as R 123 ; the left and right edges of this section are
20 00 and 8 00 from the center of M32, respectively. Later analy­
ses, especially if color information becomes available on these
stars, may include the full catalog, with some appropriately
bright magnitude cutoff in the regions that are very crowded.
The luminosity function (LF) in R 123 is shown in Figure 5. Two
key features of this LF, which will be addressed later, are the
lack of stars brighter than 22 mag and the large number of stars
near 26 mag.
We determined the bolometric luminosity in R 123 in the
following manner. First, we registered the archival WFPC2
F555W image (HST Guest Observer ID No. 5236) to our STIS
field and summed the count rate in R 123 to obtain 2.62\Theta10 4
cts sec \Gamma1 . The corresponding M F555W is 11.44 mag on the
STMAG system. Conversion to Johnson V involved a small,
color­dependent correction; we used the M32 nuclear spectrum
to derive an offset of \Gamma0:03 mag, giving m V = 11:41 mag.
Assuming a foreground extinction of E(B \Gamma V ) = 0:11 mag
with R V = 3:1 (see §2) and a distance modulus of 24.43 mag
gives M V = \Gamma13:36 mag. Worthey (1994) gives bolometric
corrections for passively evolving populations as a function
of age and metallicity; for these purposes, we assume an age
of 8 Gyr and solar metallicity (see Grillmair et al. 1996; Da
Costa 1997 and references therein), giving BC V = \Gamma0:875 mag.
Note that this parameter is sensitive to the assumed age and
metallicity. At [Fe/H] = 0.0 and an age of 5 Gyr or 12 Gyr,
BC V is \Gamma0:768 or \Gamma0:963 mag, respectively; at 8 Gyr and
[Fe/H] = \Gamma0:25 or +0.25, BC V is \Gamma0:679 or \Gamma1:130, respec­
tively. Using our assumed metallicity and age, the bolometric
luminosity is 3.92\Theta10 7 L fi in R 123 , and thus the associated SEF
is 8:62 \Theta 10 \Gamma4 star yr \Gamma1 . This is the upper limit we will place
upon the number of stars entering the evolutionary tracks in the
following discussion. Note that the SEF in the entire STIS im­
age, which includes significantly more luminosity than that in
R 123 , is 4:18 \Theta 10 \Gamma3 star yr \Gamma1 , using the same calculations and
assumptions.
In the subsequent discussion, we will translate tracks from
the literature and from our own calculations into magnitudes in
the STIS bandpass. These translations will be obtained from the
solar­metallicity Kurucz (1993) synthetic spectra, interpolating
in effective temperature from the grid points with the closest
match in surface gravity and metallicity. We then assume a
foreground reddening of E(B \Gamma V) = 0:11 mag, following the
Cardelli, Clayton, & Mathis (1989) parameterization, and a dis­
tance of 770 kpc. Because we are comparing to the STIS data
in 0.5 mag bins, our analysis is not very sensitive to these as­
sumptions.
20 22 24 26
1
10
100
1000
Model population
Post-early AGB + HB predecessors
AGB-ManquÈ + HB predecessors
Magnitude (STMAG)
Number
of
Stars
20 22 24 26
1
10
100
1000
1
10
100
1000
STIS image (R 123 )
Raw LF
Corrected LF
1
10
100
1000
FIG. 5-- The STIS luminosity function in the deepest half
of the image (R 123 ) is shown with and without corrections
for incompleteness in the number counts (top panel). A mi­
nority population of hot HB stars and their progeny (bottom
panel; see §6.3) can easily explain the STIS luminosity func­
tion. This model population is comprised of the tracks listed
in Table 8. Note the logarithmic scaling.
6.2. Post­AGB Evolution
At an age of 8 Gyr, the main sequence turnoff mass is
¸ 1:1 M fi at solar metallicity (Bertelli et al. 1994), and the core
mass of post­AGB stars is expected to be low ( ¸ ! 0:6 M fi ; Vas­
siliadis &Wood 1993). Assuming that the dominant population
in M32 is at an age of at least 8 Gyr, most of the stars that leave
the red end of the HB should pass through the post­AGB tracks
of lowest mass in the compilations of Sch¨ onberner (1987) and
Vassiliadis & Wood (1994). The luminosities of these stars as
they cross the HR diagram from the AGB to the white dwarf
cooling curve are listed in Table 6. We are comparing the STIS
data to these tracks from the literature because they have been
widely used; our own set of evolutionary models includes post­
AGB behavior that produces very similar luminosity functions.
Note that our post­AGB track shown in Figure 1 crosses the HR
diagram at a very low­mass (0.538 M fi ), and is thus somewhat
dimmer in luminosity than the tracks taken from the literature.
A post­AGB star should cross the HR diagram at a luminos­
ity near that of the AGB tip luminosity. Several recent investi­
gations of the AGB tip luminosity in M32 show there is a sig­
nificant population of stars on the AGB at luminosities brighter
than the tip of the red giant branch (RGB) (see Grillmair et

10
al. 1996 and references therein). However, earlier studies that
found very bright AGB stars, like those associated with young
populations, were apparently affected by crowding; instead, it
appears that the bright AGB stars in M32 belong to a population
of long period variables (LPVs) and blue­straggler progeny,
like those found in the old metal­rich globular clusters 47 Tuc
and NGC6553 (Guarnieri, Renzini, & Ortolani 1997; Renzini
1998; Grillmair et al. 1996). Note that in a solar­metallicity
population of age 8 Gyr, the RGB tip lies at log(L=L fi ) = 3:2
(Bertelli et al. 1994). The lack of bright AGB stars associated
with young populations supports the premise that the majority
of the post­AGB stars in M32 should be evolving along low­
mass tracks (near this luminosity).
TABLE 6: Post­AGB Crossing Luminosities
Mass log(L=L fi )
H­burning 0.546 M a
fi 3.2
H­burning 0.569 M b
fi 3.5
H­burning 0.597 M b
fi 3.7
H­burning 0.633 M b
fi 3.9
He­burning 0.567 M b
fi 3.5
He­burning 0.600 M b
fi 3.6
a Sch¨ onberner (1987). A post­early AGB track just below
the mass required for post­AGB behavior.
b Vassiliadis & Wood (1994).
Until the middle of this decade, post­AGB stars were thought
to be predominantly H­burning (see Vassiliadis & Wood 1994
and references therein). H­burning post­AGB stars leave the
AGB between He­shell flashes, while He­burning post­AGB
stars leave the AGB near or during a flash, and the ratio of
He­burning to H­burning lifetimes over the He­shell flash cycle
was thought to be on the order of 20%. However, Vassiliadis
& Wood (1994) suggested that at lower masses, the chance of
producing a He­burning post­AGB star increased (see also Ren­
zini & Fusi Pecci 1988; Renzini 1989). Post­AGB evolution
remains as one of the least­understood phases of normal stellar
evolution; more observational evidence is needed to determine
the relative frequency of H­burning and He­burning tracks (see
Dopita, Jacoby, & Vassiliadis 1992).
TABLE 7: Comparison with Post­AGB Tracks
Data Theoretical Maximum Number of Post­AGB Stars
Raw LF Corrected LF 0.546 M a
fi 0.569 M b
fi 0.597 M b
fi 0.567 M b
fi 0.600 M b
fi
mag regions 1+2+3 regions 1+2+3 H burning H burning H burning He burning He burning
20.0 0 0 0 0 1 0 0
20.5 0 0 0 6 2 1 0
21.0 0 0 0 4 0 1 2
21.5 1 1 54 3 1 1 1
22.0 1 1 40 2 1 1 4
22.5 5 5 30 2 1 2 14
23.0 5 5 23 2 0 2 2
23.5 8 8 24 2 1 29 2
24.0 27 27 29 2 1 4 1
24.5 45 47 26 2 1 4 1
25.0 152 159 26 2 0 3 1
25.5 590 631 16 1 1 3 1
26.0 832 1055 15 2 0 3 1
26.5 732 2079 22 7 1 11 4
27.0 366 3045 32 33 3 22 10
a Sch¨ onberner (1987). A post­early AGB track just below the mass required for post­AGB behavior.
b Vassiliadis & Wood (1994).
M32 has a very weak UV upturn, and thus, prior to our ob­
servations, the UV flux could theoretically be explained by low­
mass post­AGB stars alone; no hot HB stars were required. We
know that hot HB stars, if present, can only comprise a minority
of the population, else the UV upturn in M32 would be consid­
erably stronger; the elliptical galaxies with the strongest UV
upturns only require ¸ 10% of the SEF to pass through the hot
HB and its descendants (Brown et al. 1997). We expect most of
the stars in M32 to pass through the red end of the HB and the
subsequent low­mass post­AGB tracks. While post­AGB stars
evolve very rapidly through their UV­bright phases compared
to the hot HB stars and their progeny (see §1), the low­mass
post­AGB tracks nevertheless evolve slowly enough to produce
dozens of stars at very bright magnitudes in the STIS bandpass.
This is shown in Table 7, which shows the luminosity functions
obtained by placing the entire SEF (determined for R 123 in §6.1)
into selected low­mass tracks from the literature. For compar­
ison, we show the raw and corrected luminosity functions ob­
tained in the deepest half of the STIS image, R 123 (see §6.1). It
is obvious from Table 7 that low­mass H­burning tracks suffer
from two problems when trying to explain the STIS luminosity
function: the models predict far too many stars at bright mag­
nitudes ( ¸ ! 23 mag) and far too few stars at faint magnitudes
( ¸ ? 24 mag), even when the faint magnitudes are not corrected
for completeness. Low­mass He­burning post­AGB tracks fair
somewhat better with the bright end of the STIS luminosity
function, as they do not predict nearly as many bright stars, but
these tracks still produce far too few stars at faint magnitudes.
These He­burning tracks also produce a fairly bright local max­
imum in their luminosity functions (see Table 7) that is not seen
in the STIS data, but the luminosity of this phase depends upon
the mass and the details of the evolution. Thus this spike in
the LF could be easily hidden in the STIS data if there was
a small dispersion in post­AGB mass, centered at a low mass
( ¸ ! 0:567 M fi ).
The lack of UV­bright stars in the STIS data requires that the
transition from the AGB to T eff ? 60000 K occurs on a much
more rapid timescale than predicted by the low­mass H­burning
tracks, or, alternatively, that this transition be hidden by circum­
stellar dust produced during the preceding AGB mass­loss (see

11
Figure 6). If the transition is only accelerated up to a some­
what cooler temperature (e.g., 30000 K or 50000 K), there
will still be too many stars in the LF bins brighter than 23.5
mag. The pace of this transition is naturally increased by as­
suming post­AGB tracks of higher mass ( ¸ ? 0:6 M fi ), but, as
we stated above, the observational and theoretical evidence on
the maximum AGB stellar luminosity seems to preclude this
option. Furthermore, the AGB precursors of a population of
stars this massive would produce an enormous amount of en­
ergy, leading to optical­infrared colors in disagreement with
observations (Greggio & Renzini 1999). Circumstellar extinc­
tion, while having a strong effect in the UV, would also ap­
pear to be an unlikely candidate, considering the rapid thinning
times for material surrounding post­AGB stars (K¨ aufl, Renzini,
& Stanghellini 1993; Brown et al. 1998), although we cannot
rule out this alternative.
5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6
log T eff (K)
1.5
2.0
2.5
3.0
log
L/L
20 22 24 26 28
Magnitude (STMAG)
0
50
100
150
Stars
20 22 24 26 28
Magnitude (STMAG)
0
50
100
150
Stars
FIG. 6-- The 0.546 M fi H­burning track of Sch¨ onberner
(1987), and the corresponding luminosity function from Ta­
ble 7. The track and model luminosity function have been
color­coded to demonstrate that the evolution up to T eff =
60000 K causes the discrepancy with the STIS luminosity
function (i.e., the dark segment of the track produces the
dark portion of the luminosity function bins). If this evo­
lution were more rapid or hidden, the lack of UV­bright stars
in the STIS image would be explained.
The most likely explanation for the lack of bright stars is that
most of the population evolves more rapidly from the AGB to
high effective temperature than predicted by the tracks in Tables
6 and 7. This might occur if the final mass ejection on the AGB
was triggered by a helium­shell flash which left the star out of
thermal equilibrium. The post­AGB evolution would then take
place on the more rapid thermal timescale, as argued by K¨ aufl
et al. (1993) and Greggio & Renzini (1999). Indeed, Table 7
already demonstrates that the discrepancy with the STIS data
is greatly reduced if the stars evolve as He­burners. Note that
the number of known planetary nebulae in the STIS field (four),
combined with the stellar evolutionary flux for the entire STIS
field (4:18 \Theta 10 \Gamma3 star yr \Gamma1 ), implies that the planetary nebula
phase only lasts for ¸ 1000 yr. Although we might have an ex­
planation for the lack of bright stars, there is no post­AGB track
that can produce the thousands of stars on the faint end of the
STIS luminosity function, and so we next explore the expecta­
tions from hot horizontal branch stars and their progeny.
6.3. Hot HB stars
As explained in §1, the HB phase (shown as a light grey re­
gion in Figures 1 and 7) lasts for ¸ 10 8 yr, and the UV­bright
post­HB lifetime for stars leaving the hot end of the HB is on
the order of 10 7 yr. These long lifetimes in the UV suggest that
hot HB stars and their progeny are much more likely to explain
the STIS luminosity function, compared to the brighter short­
lived post­AGB stars. We explore this possibility here, using
our own calculations of HB and post­HB evolution.
6.3.1. Models
We have calculated a detailed grid of HB and post­HB se­
quences with solar metallicity and helium abundance, over a
wide range in the HB mass, and for various rates of mass loss
along the AGB. A fine spacing in the HB mass was used, in
order to clearly define the changes in the HB morphology with
mass, as well as the transition between the AGB­Manqu' e, post­
early­AGB, and post­AGB evolution. Evolution was followed
from the ZAHB until the luminosity fell below 0.1 L fi along the
white dwarf cooling curve. In a few cases, the models under­
went a final helium­shell flash while descending the WD cool­
ing curve, and such sequences were stopped if the flash convec­
tion reached into the hydrogen envelope.
In order to obtain a ZAHB model at the red end of the HB,
we first evolved a 1 M fi stellar model from the zero­age main
sequence up the RGB, and then through the helium­core flash.
The parameters of the initial main­sequence model were de­
termined by calibrating the model on the sun; i.e., the main
sequence helium abundance YMS , heavy­element abundance
Z, and mixing­length ratio ff were adjusted until the model
matched the observed solar luminosity, radius, and Z=X ratio
at a solar age of 4.6 Gyr. The parameters derived in this fashion
are: YMS = 0:2798, Z = 0:01716, and ff = 1:8452. The he­
lium abundance increased to 0.3003 during the first dredge­up
along the lower RGB. Consequently, all of the HB and AGB se­
quences we have computed have the following envelope abun­
dances: Y = 0:3003 and Z = 0:01716.
Mass loss was included during the RGB phase using the
Reimers (1975) mass­loss formulation, with a mass­loss param­
eter j R of 0.4. As a result, the mass decreased to 0.8269 M fi by
the time the model reached the ZAHB. The age at that time was
12.2 Gyr. The use of a somewhat different initial mass (corre­
sponding to a somewhat different age) would have only a negli­
gible effect on the core mass and envelope helium abundance of
this ZAHB model. Thus our results do not depend significantly
on the choice for the zero­age main sequence model.
Lower mass ZAHB models were then computed by remov­
ing mass from the envelope of the red ZAHB model described
above. The lowest ZAHB mass considered here was 0.473 M fi ,
corresponding to an envelope mass of only 0.00162 M fi .
The ZAHB models computed in this manner were then
evolved through the HB phase using standard algorithms for
convective overshooting and semiconvection. The last model
from each HB sequence was then used as the starting model
for the subsequent AGB evolution. Mass loss was included in
the AGB sequences, using the Reimers (1975) formulation for
three values of j R : 0.0 (no mass loss), 0.4, and 1.0. Note that
these assumptions for AGB mass loss have no consequence for
the AGB­Manqu' e evolution, because such stars do not ascend

12
the AGB (see §1). For this reason, and because we lack color
information for these stars (given the one bandpass of our obser­
vations), we will only explore the models that assume j R = 0:4
in our discussion below. The variation in mass loss may be ex­
plored in future work if color information becomes available
for these stars.
The set of tracks with j R = 0:4 consisted of 35 ZAHB masses
(M ZAHB ), ranging from 0.473 to 0.700 M fi and covering a tem­
perature range from logT eff = 4.42 -- 3.67. Due to mass loss
on the AGB, the final masses on the white dwarf cooling curve
(MWD ) for these tracks is somewhat less. AGB­Manqu' e be­
havior was found for stars with M ZAHB Ÿ 0:505 M fi ; post­
early AGB behavior for stars with 0:505 !M ZAHB ! 0:610 M fi
(0:505 !MWD ! 0:542 M fi ), and post­AGB behavior for stars
with M ZAHB – 0:610 M fi (MWD – 0:542 M fi ).
These tracks permit the transition between the different
classes of post­HB evolution to be much better defined than
previously possible. Figure 7 shows examples of these evolu­
tionary tracks as they appear in the STIS bandpass (see also
Figure 1).
3.5
4.0
4.5
5.0
log T eff (K)
30
28
26
24
22
Magnitude
(STMAG)
Zero-age HB
AGB-ManquÈ
Post-early AGB
Post-AGB
White Dwarf
3.5
4.0
4.5
5.0
log T eff (K)
30
28
26
24
22
Magnitude
(STMAG)
FIG. 7-- The same tracks shown in Figure 1, but with lu­
minosity replaced by magnitude in the STIS bandpass, un­
der the STMAG system, assuming a distance of 770 kpc and
E(B \Gamma V ) = 0:11 mag. Note that assuming a lower reddening
of E(B \Gamma V) = 0:08 mag would make the tracks ¸ 0:25 mag
brighter. The HB phase (again shown by light grey shading,
as determined from our entire set of tracks), spans a range of
25--27 mag at T eff ? 8500 K.
6.3.2. Hot HB Luminosity Functions
We have constructed the luminosity functions for each of the
above HB and post­HB tracks in the STIS bandpass for compar­
ison with the corrected STIS luminosity function given in Table
7. Because we only have one bandpass and no color informa­
tion, it is difficult to constrain the mass distribution of stars on
the hot HB. This difficulty is further compounded by the fact
that post­AGB stars certainly contribute some small but non­
negligible component to the STIS luminosity function, because
we know the majority of the evolved population passes through
some sort of post­AGB phase, given the weak UV upturn in
M32. Color information would also help to separate these post­
AGB stars from the rest of the STIS data, because they spend
most of their time at much higher effective temperature.
The luminosity functions for four of our tracks can be added
to create a composite luminosity function that agrees quite well
with the STIS data (Figure 5). Two of these tracks follow AGB­
Manqu' e evolution and two follow post­early AGB evolution
upon leaving the HB. These tracks have been normalized to
maximize agreement with the STIS data from 23--27 mag, and
we show in Table 8 the relative contributions of these tracks to
this composite LF. We stress that this LF serves as an example,
to show that hot HB stars can reproduce the STIS luminosity
function; color information is required to properly constrain the
true distribution of mass on the hot HB. The STIS data confirm
that stars passing through the hot HB at T eff ? 8500 K comprise
only a small fraction (approximately 7%) of the total HB pop­
ulation in M32. This fraction of hot HB stars would be some­
what lower if the contribution of the post­AGB stars could be
subtracted from the STIS luminosity function.
Given the small fraction of the population entering the hot
HB, we must conclude that the vast majority of the population
passes through the red HB phase and the subsequent post­AGB
evolution. Although a small population of hot HB stars can ex­
plain the numerous faint stars present in the STIS image, we
still must explain the lack of bright stars. The likely explana­
tion, as discussed in §6.2, is that the transition time from the
AGB to the hotter post­AGB phases must be more rapid than
that expected from the canonical low­mass H­burning tracks.
The contribution of post­AGB stars to the STIS luminosity
function would then be small, even though most of the popu­
lation channels through post­AGB tracks.
TABLE 8: Hot HB Components of Composite LF
M ZAHB ZAHB SEF Fraction of
(M fi ) T eff (K) (stars yr \Gamma1 ) total SEF
0.475 24578 1:95 \Theta 10 \Gamma5 0.023
0.500 16372 3:03 \Theta 10 \Gamma6 0.004
0.520 12034 6:20 \Theta 10 \Gamma6 0.007
0.545 6057 3:20 \Theta 10 \Gamma5 0.037
7. DISCUSSION
7.1. Dynamical Creation Mechanism for Hot HB Stars?
In the Galactic field, hot HB and post­HB stars are often
found in binaries, and it has been suggested that a dynamical
mechanism may play a role in the production of hot HB stars in
old, metal­rich populations such as elliptical galaxies (Green
et al. 1997; Green & Chaboyer 1998). In globular clusters,
the role of dynamics remains a matter of debate. Horizontal
branch morphology tends to become redder as metallicity in­
creases, but examples of metal­rich GCs with blue HB mor­
phology demonstrate that other parameters are at work (e.g.,
Rich et al. 1997). One of these parameters may be a dynam­
ical mechanism, through binary or tidal interaction while on
the RGB. There is some evidence that dynamics plays a role in
HB morphology; e.g., Fusi Pecci et al. (1993) and Buonanno
et al. (1997) demonstrated that more concentrated clusters have
bluer HB morphologies with extended blue tails. Rich et al.
(1997) found two metal­rich GCs with extended HB morphol­
ogy (NGC6388 and NGC6441), although the evidence for a dy­
namical origin in that work appears inconclusive. These clus­
ters have some of the highest values of central surface bright­
ness, velocity dispersion, and stellar collision rates for Galactic
GCs, which may partially explain their blue HBs, but Rich et al.
(1997) find no evidence for a difference in the radial distribution
of blue and red HB stars, as expected if tidal or binary interac­
tion plays a role. Later work by Layden et al. (1999) did find
that the blue HB stars in NGC6441 were more centrally concen­
trated than the red HB stars, but the difference in these gradients
does not conform with theoretical expectations for a dynamical

13
mechanism, because it occurs too far from the cluster center.
In NGC6752, Landsman et al. (1996) found that the hot HB
is a continuous extension of the intermediate­temperature HB
population, suggesting that a common single­star mechanism
is responsible for both. In ! Cen, which has the largest known
fraction of hot HB stars, D'Cruz et al. (1999) find no evidence
for a radial gradient in the hot HB to red HB number ratio.
M32 is much smaller than other well­studied true ellipticals,
and it has the lowest Mg 2 optical metallicity index of all the
quiescent UV upturn galaxies in the Burstein et al. (1988) sam­
ple; in this sense, it is the elliptical galaxy that lies closest to the
realm of globular clusters. However, elliptical galaxies should
not be considered as overgrown globular clusters -- they clearly
inhabit a different regime of parameter space, especially when
considering the evolved population of stars that produces the
UV upturn. This is apparent in the modified version of the
Burstein et al. (1988) 1550 \Gamma V vs. Mg 2 relation shown by Dor­
man et al. (1995), which shows the GCs lying in a completely
distinct clump removed from the tight E galaxy sequence. It
is thus worth noting that the existence of hot HB stars in M32
cannot be easily explained by dynamical mechanisms, because
the stellar densities in elliptical galaxies are so much lower
than those in globular clusters (except for the very center of
ellipticals, which often harbor a black hole). The central lu­
minosity densities of NGC6388 and NGC6441 are respectively
1:86 \Theta 10 5 L fi pc \Gamma3 and 2:00 \Theta 10 5 L fi pc \Gamma3 (Djorgovski 1993).
M32 has a luminosity density of 4:9 \Theta 10 5 L fi pc \Gamma3 at a radius
of 0:1 00 , but this density drops rapidly by more than three orders
of magnitude at radii greater than 8 00 (Tonry 1988; Gebhardt et
al. 1996; private communication Gebhardt 1999). Furthermore,
the far­UV to B­band flux ratio increases with radius in M32
(Ohl et al. 1998). Because our STIS data firmly demonstrate
that the weak far­UV flux is due to hot HB stars, the increase
in the far­UV to B­band flux ratio indicates that hot HB stars
comprise a larger fraction of the population at increasing dis­
tance from the galactic center -- again, opposite to the behavior
expected from a dynamical creation mechanism such as tidal
interaction or binarism.
7.2. The Age of M32
In recent years, much of the effort on dating M32 has shown
a need for an intermediate­age (¸ 5 Gyr) component to its pop­
ulation. When this fact is considered in tandem with its small
size and proximity to M31, its utility as a template for other
ellipticals is somewhat diminished. However, even though it
may be unusual, M32 represents the only elliptical near enough
for intense study by all of the standard stellar population anal­
ysis methods (spectroscopy, line indices, color­magnitude di­
agrams, etc.), at least until we have a successor to HST with
UV­optical capability. With this in mind, are we certain that
M32 has a younger component to its older, dominant popula­
tion? We feel that this remains an open question.
Early color­magnitude diagrams reported evidence for a
younger population by finding very bright AGB stars, but later
interpretations of these data showed that both crowding (Ren­
zini 1998) and long­period variables (Guarnieri et al. 1997)
confused the earlier analysis; later observations (Grillmair et
al. 1996) also find no evidence for optically bright AGB stars,
but these stars were difficult to detect in the V band. Instead,
it appears that the brightest AGB stars in M32 are consistent
with those found in other old globular clusters (Guarnieri et al.
1997; Renzini 1998). We note that our own data show a lack of
the very bright post­AGB stars that should be present if they are
leaving the tip of the AGB at luminosities much brighter than
the RGB tip.
Spectral synthesis analyses using isochrones like those of
Worthey (1994) assume a pure red clump HB morphology, and
the STIS data show that this assumption is not entirely accu­
rate; note, however, that the Worthey models were not intended
to address UV flux. Depending upon how much of the popu­
lation extends beyond the red clump, an analysis that assumes
a pure red clump may be seriously incorrect. Our data demon­
strate that the hot horizontal branch is populated in M32, but
the lack of color information prevents us from constraining the
HB morphology further. The tracks that reproduce the STIS lu­
minosity function come from a wide range of T eff on the HB
(see Table 8), and so they are consistent with both a bimodal
HB distribution and with an extended, more uniform distribu­
tion. However, the integrated spectrum of M32 does not show
the strong 2500 å dip seen in UV­bright quiescent giant ellipti­
cals (compare Figure 4 with the spectra of Burstein et al. 1988
and Brown et al. 1997). Given the presence of hot HB stars
and the missing 2500 å dip, the distribution of effective tem­
perature on the HB might be more uniform in M32 than the
strongly bimodal distributions assumed in giant ellipticals. The
zero­age HB becomes more bimodal at increasing metallicity
and helium abundance (see Dorman et al. 1993); because M32
has an abundance much closer to solar than the giant ellipticals
(see Burstein et al. 1988), evolution theory favors a more uni­
form HB. Our hot HB model population (Table 8), if correct,
would be responsible for practically all of the flux at 2500 å,
and contribute to approximately 10% of the flux from 3000--
4000 å, even though it only comprises a small fraction of the
HB population (¸5%). Thus, this hot HB component should
not be ignored for population fitting in the mid­UV.
The H fi (– 4861 å) line index is often quoted as another
piece of evidence in favor of a young component in M32. It
is significantly stronger in M32 than in the higher metallicity
giant ellipticals (Bressan, Chiosi, & Tantalo 1996; Burstein et
al. 1984), with an equivalent width (EW) of 2.2 å compared
to an average value of 1.7 å. Metal­poor globular clusters have
even stronger H fi absorption than M32 (as high as 3 å EW),
but the index decreases in strength at increasing metallicity, and
high metallicity globular clusters show a weaker index than in
M32 (Burstein et al. 1984). Note, however, that these earlier
studies did not include metal­rich GCs with blue HB morphol­
ogy, such as those studied by Rich et al. (1997). Burstein et al.
(1984) claim that the addition of early A stars to the old stellar
population in M32 can increase the H fi appropriately, but the
resulting UV continuum would be too bright, and instead favor
later main­sequence F stars. Note that there is a radial gradient
to the H fi absorption in M32, in the sense that it is significantly
weaker in the deepest parts of the STIS image, compared to the
galactic center (Gonz' alez 1993; Hardy et al. 1994); this sug­
gests that the younger population, if present, is most prevalant
in the nucleus (see Grillmair et al. 1996).
It is possible instead that intermediate­temperature HB stars
could account for some of the extra H fi absorption (assuming
that M32 has a less bimodal HB mass distribution than seen in
giant ellipticals), but it is unlikely, given our data and models,
that the HB could account for all of this extra absorption. Ap­
proximately 20% of the light at H fi comes from the horizontal
branch (see, e.g., Yi, Demarque, & Oemler 1997). Thus, if a
large fraction of the ZAHB population was at F­star tempera­
tures (near 7000 K), the H fi
absorption would increase signifi­

14
cantly. Specifically, a small set of synthetic spectra calculated
for this purpose, using SYNSPEC (Hubeny, Lanz, & Jeffery
1994) and Kurucz (1993) model atmospheres, shows that the
H fi EW increases from 1.2 å at T eff = 5000 K to 8 å at 7500 K
(measuring EW as in Faber et al. 1985), eventually peaking to
9.5 å at 9000 K. ZAHB stars near 7000 K would lie at the
very faint (and incomplete) end of the STIS luminosity func­
tion (see Figure 7), and thus could be present in large numbers.
However, these stars become post­early AGB stars in their later
and brighter phases, and if such tracks are populated at signifi­
cant levels (¸ 50%), the STIS luminosity function would have
many more UV­bright stars than we actually see. Note that the
hot­HB model population shown in Table 8 comprising ¸ 5%
of the HB population, would only contribute to ¸ 5% of the
flux at H fi . One could place a large fraction of the ZAHB near
7000 K (thus accounting for all of the H fi absorption) only if
the later, UV­bright post­early­AGB phases were more rapid
than predicted from the models, as seen for the post­AGB stars.
Thus, even with a hot HB component in M32, the H fi absorp­
tion might be the one piece of evidence that is difficult to ex­
plain without some trace of younger stars or blue stragglers.
7.3. Summary
The STIS data presented here are the first to directly image
stars on the hot horizontal branch in any elliptical galaxy. In
previous work, the spectral energy distribution and the magni­
tude of the far­UV flux in giant ellipticals required the presence
of hot HB stars, unless UV­bright post­AGB stars were much
more efficient UV emitters than thought previously. Until these
STIS observations, M32 was the one example of an elliptical
where the weak UV flux could have been explained by canon­
ical low­mass post­AGB tracks. Our data show that the hot
HB is populated in M32, and that the UV­bright phases of post­
AGB evolution are less populated than expected from canonical
tracks; thus these data represent a direct confirmation that the
UV upturn in ellipticals originates in hot HB stars. Our find­
ings demonstrate that M32 does not have a pure ``red clump''
HB morphology, as assumed by many of the stellar population
analyses of this galaxy. If the HB effective temperature dis­
tribution is not extremely bimodal, our findings may weaken
the evidence for an intermediate age population in M32. Color
information would best constrain the HB morphology further,
and we will propose to carry out far­UV imaging of this same
field in the coming HST cycle; the far­UV data would provide
an excellent discriminator between stars hotter and cooler than
12000 K, which would constrain the bimodality of the HB in
M32. Furthermore, color information will allow us to discern
how many of the faint stars in our luminosity function are on the
white dwarf cooling curve, and this may shed light on the evo­
lution of post­AGB stars, which appear to be evolving rapidly
in the STIS field.
Support for this work was provided by NASA through the
STIS GTO team funding. TMB acknowledges support at God­
dard Space Flight Center by NAS 5­6499D. We wish to thank
K. Gebhardt for kindly providing the luminosity density profile
of M32. We also wish to thank P. Stetson, who provided the
DAOPHOT­II package and gave us assistance with its use. This
research has made use of the SIMBAD database, operated at
CDS, Strasbourg, France.
REFERENCES
Baum, S., et al. 1998, Space Telescope Imaging Spectrograph Instrument
Handbook, (Baltimore: STScI), 315
Bertelli, G., Bressan, A., Chiosi, C., Fagotto, F., & Nasi, E. 1994, A&AS, 106,
275
Bertola, F.,Bressan, A., Burstein, D., Buson, L. M., Chiosi, C., & Alighieri, S.
D. S. 1995, ApJ, 438, 680
Bressan, A., Chiosi, C., & Tantalo, R. 1996, A&A, 311, 425
Brown, T.M., Ferguson, H.C., Davidsen, A.F., & Dorman, B. 1997, ApJ, 482,
685
Brown, T. M., Ferguson, H. C., Stanford, S. A., & Deharveng, J.­M. 1998, ApJ,
504, 113
Buonanno, R., Corsi, C., Bellazzini, M., Ferraro, F. R., & Fusi Pecci, F. 1997,
AJ, 113, 706
Burstein, D., Bertola, F., Buson, L. M., Faber, S. M., & Lauer, T. R. 1988, ApJ,
328, 440
Burstein, D., Faber, S. M., Gaskell, C. M., & Krumm, N. 1984, ApJ, 287, 586
Burstein, D., & Heiles, C. 1984, ApJS, 54, 33
Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, 345, 245
Ciardullo, R., Jacoby, G. H., Ford, H. C., & Neill, J.D. 1989, ApJ, 339, 53
Code, A.D. 1969, PASP, 81, 475
Da Costa, G.S. 1997, in Proc. Eigth Canary Islands Winter School, Stellar
Astrophysics for the Local Group, ed. A. Aparicio & A. Herrero
(Cambridge: Cambridge Univ. Press), 351.
D'Cruz, N. L., O'Connell, R. W., Rood, R. T., Whitney, J. H., Dorman, B.,
Landsman, W. B., Hill, R. S., Stecher, T. P., & Bohlin, R. C. 1999, ApJ,
submitted
Djorgovski, S. 1993, in ASP Conf. Proc. 50, Structure and Dynamics of
Globular Clusters, ed. S. G. Djorgovski & G. Meylan (San Francisco: ASP),
373
Dopita, M. A., Jacoby, G. H., & Vassiliadis, E. 1992, ApJ, 389, 27
Dorman, B., O'Connell, R.W., & Rood, R.T. 1995, ApJ, 442, 105
Dorman, B., Rood, R.T., & O'Connell, R.W. 1993, ApJ, 419, 596
Faber, S. M., Friel, E., Burstein, D., & Gaskell, C. M. 1985, ApJS, 57, 711
Ferguson, H. C., & Davidsen, A. F. 1993, ApJ, 408, 92
Fusi Pecci, F., & Bellazzini, M. 1997, in Third Conference on Faint Blue Stars,
ed. A. G. Davis Philip, J. W. Liebert, & R. A. Saffer (Schenectady: L. Davis
Press), 255
Fusi Pecci, F., Ferraro, F. R., Bellazzini, M., Djorgovski, S., Piotto, G., &
Buonanno, R. 1993, AJ, 105, 1145
Gardner, J. P., et al. 1999, AJ, submitted
Gebhardt, K., Richstone, D., Ajhar, E. A., Lauer, T. R., Byun, Y.­I., Kormendy,
J., Dressler, A., Faber, S. M., Grillmair, C., & Tremaine, S. 1996, AJ, 112,
105
Gonz' alez, J. 1993, Ph.D. thesis, University of California, Santa Cruz
Green, E. M., & Chaboyer, B. C. 1998, BAAS, 30, 1404
Green, E. M., Liebert, J. W., Peterson, R. C., & Saffer, R. A. 1997, in Third
Conference on Faint Blue Stars, ed. A. G. Davis Philip, J. W. Liebert, & R.
A. Saffer (Schenectady: L. Davis Press), 271
Greenfield, P. 1994, in Instrument Science Report FOC­075, Format­Dependent
Sensitivity Effects,
http://www.stsci.edu/ftp/instrument_news/FOC/Foc_isr/foc_isr075.ps
Greggio, L., & Renzini, A. 1990, ApJ, 364, 35
Greggio, L., & Renzini, A. 1999, in UV Astronomy in Italy, ed. L. M. Buson &
Domitilla De Martino, in press.
Grillmair, C. J., et al. 1996, AJ, 112, 1975
Guarnieri, M. D., Renzini, A., & Ortolani, S. 1997, ApJ, 477, L21
Hardy, E., Couture, J., Couture, C., & Joncas, G. 1994, AJ, 107, 195
Hubeny, I., Lanz, T., & Jeffery, C. S. 1994, in Newsletter on Analysis of
Astronomical Spectra No. 20, ed. C. S. Jeffery (CCP7; St. Andrews: St.
Andrews Univ.), 30
K¨ aufl, H. U., Renzini, A., & Stanghellini, L. 1993, ApJ, 410, 251
Kimble, R. A., et al. 1998, ApJ, 492, 83
King, I. R., et al. 1992, ApJ, 397, L35
Kurucz, R. L. 1993, CD­ROM 13, ATLAS9 Stellar Atmosphere Programs and
2 km/s Grid (Cambridge: Smithsonian Astrophys. Obs.)
Landsman, W. B., Sweigart, A. V., Bohlin, R. C., Neff, S. G., O'Connell, R. W.,
Roberts, M. S., Smith, A. M., & Stecher, T. P. 1996, ApJ, 472, L93
Layden, A. C., Ritter, L. A., Welch, D. L., & Webb, T. M. A. 1999, AJ, 117,
1313
McClure, R. D., & Racine, R. 1969, AJ, 74, 1000
O'Connell, R. W. 1999, in Annual Reviews of Astronomy & Astrophysics, in
press
Ohl, R. G., O'Connell, R. W., Bohlin, R. C., Collins, N. R., Dorman, B., Fanelli,
M. N., Neff, S. G., Roberts, M. S., Smith, A. M., & Stecher, T. P. 1998, ApJ,
505, L110
Reimers, D. 1975, M' em. Roy. Soc. Li` ege, 8, 369
Renzini, A. 1989, in Planetary Nebulae, ed. S. Torres­Peimbert (Dordrecht:
Kluwer), 391
Renzini, A. 1998, AJ, 115, 2459
Renzini, A., & Fusi Pecci, F. 1988, ARA&A, 26, 199

15
Rich, R. M., et al. 1997, ApJ, 484, L25
Sch¨ onberner, D. 1987, in IAU Symposium 131, Planetary Nebulae, ed. S.
Torres­Peimbert (Dordrecht: Kluwer Academic Publishers), 463
Stetson, P. B. 1987, PASP, 99, 191
Sweigart, A. V. 1999, in Spectrophotometric Dating of Stars and Galaxies, ed.
I. Hubeny, S. Heap, & R. Cornett, (San Francisco: ASP), in press
Tonry, J. L. 1988, in Dynamics of Dense Stellar Systems, ed. D. Merritt,
(Cambridge: Cambridge University Press), 35
Tully, R. B. 1988, Nearby Galaxies Catalogue (Cambridge: University Press)
VandenBerg, D. A., 1999, in The Third Stromlo Symposium: The Galactic
Halo, ed. B. K. Gibson, T. S. Axelrod, & M. E. Putman (San Francisco:
ASP), 46
Vassiliadis, E., & Wood, P. R. 1993, ApJ, 413, 641
Vassiliadis, E., & Wood, P. R. 1994, ApJS, 92, 125
Woodgate, B. E., et al. 1998, PASP, 110, 1183
Worthey, G. 1994, ApJS, 95, 107
Yi, S., Demarque, P., & Oemler, A., Jr. 1997, ApJ, 486, 201