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THE ASTROPHYSICAL JOURNAL, 475 : 399È413, 1997 February 1
( 1997. The American Astronomical Society. All rights reserved. Printed in U.S.A.
THE SBF SURVEY OF GALAXY DISTANCES. I. SAMPLE SELECTION, PHOTOMETRIC
CALIBRATION, AND THE HUBBLE CONSTANT1
JOHN L. TONRY2 AND JOHN P. BLAKESLEE2
Physics Department, Room 6-204, MIT, Cambridge, MA 02139 ; jt=antares.mit.edu, john=arneb.mit.edu
EDWARD A. AJHAR2
Kitt Peak National Observatory, National Optical Astronomy Observatories, P.O. Box 26732, Tucson, AZ 85726 ; ajhar=noao.edu
AND
ALAN DRESSLER
Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101 ; dressler=omega.ociw.edu
Received 1996 June 24 ; accepted 1996 August 26
ABSTRACT
We describe a program of surface brightness Ñuctuation (SBF) measurements for determining galaxy
distances. This paper presents the photometric calibration of our sample and of SBF in general. Basing
our zero point on observations of Cepheid variable stars, we Ðnd that the absolute SBF magnitude in
the Kron-Cousins I band correlates well with the mean (V [I) color of a galaxy according to
0
M1 \ ([1.74 ^ 0.07) ] (4.5 ^ 0.25)[(V [I) [ 1.15]
I
0
for 1.0 \ (V [I) \ 1.3. This agrees well with theoretical estimates from stellar population models.
Comparisons between SBF distances and a variety of other estimators, including Cepheid variable
stars, the planetary nebula luminosity function (PNLF), Tully-Fisher (TF), D -p, SN II, and SN Ia,
demonstrate that the calibration of SBF is universally valid and that SBF errorn estimates are accurate.
The zero point given by Cepheids, PNLF, TF (both calibrated using Cepheids), and SN II is in units of
megaparsecs ; the zero point given by TF (referenced to a distant frame), D -p, and SN Ia is in terms of a
n zero points yields a Hubble
Hubble expansion velocity expressed in km s~1. Tying together these two
constant of
H \ 81 ^ 6 km s~1 Mpc~1 .
0
As part of this analysis, we present SBF distances to 12 nearby groups of galaxies where Cepheids,
SN II, and SN Ia have been observed.
Subject headings : distance scale È galaxies : clusters : general È galaxies : distances and redshifts È
galaxies : photometry
1.
INTRODUCTION AND SAMPLE SELECTION
spread function in the power spectrum of a CCD image.
They applied this method to images of the galaxies M32
and NGC 3379. Subsequent work by Tonry, Luppino, &
Schneider (1988) and Tonry, Ajhar, & Luppino (1989, 1990)
revised and reÐned the analysis techniques and presented
further observations in V , R, and I of early-type galaxies in
Virgo, Leo, and the Local Group.
Tonry et al. (1990) found that the I band was most suitable for measuring distances and attempted to calibrate the
SBF method theoretically using the Revised Yale Isochrones (Green, Demarque, & King 1987). There were
obvious problems with this calibration, however, so a completely empirical calibration for M1 was presented by Tonry
(1991). The calibration was basedI on the variation of m6
with (V [I) color in the Fornax cluster and took its zeroI
point from 0the Cepheid distance to M31. Tonry used this
calibration to derive the Hubble constant. A detailed review
of the modern SBF technique can be found in Jacoby et al.
(1992), which also provides some historical context for the
method.
In recent years, the SBF technique has been used to
measure distances and study a variety of stellar populations
in several di†erent bands. K-band SBF observations have
been reported by Luppino & Tonry (1993), Pahre & Mould
(1994), and Jensen, Luppino, & Tonry (1996). These studies
Ðnd that m6 is also a very good distance estimator. Dressler
(1993) has Kmeasured I-band SBF in Centaurus ellipticals,
1.1. Background
The surface brightness Ñuctuation (SBF) method of distance determination works by measuring the ratio of the
second and Ðrst moments of the stellar luminosity function
in a galaxy. This ratio, called L1 , is then the luminosityweighted, average luminosity of a stellar population and is
roughly equal to the luminosity of a single giant star. In
terms of magnitudes, this quantity is represented as M1 , the
absolute ““ Ñuctuation magnitude.ÏÏ What we measure, of
course, is the apparent Ñuctuation magnitude in a particular
photometric band, in our case the I band, m6 . In order to be
I
useful as a distance estimator, m6 must be calibrated,
either
I
empirically, by tying the measurements to the Cepheid distance scale, or theoretically, according to stellar population
synthesis models.
Tonry & Schneider (1988) were the Ðrst to quantify the
SBF phenomenon. Their method was based on a measurement of the amount of power on the scale of the point
1 Observations in part from the Michigan-Dartmouth-MIT (MDM)
Observatory.
2 Guest observers at the Cerro Tololo Inter-American Observatory and
the Kitt Peak National Observatory, National Optical Astronomy
Observatories, which are operated by AURA, Inc., under cooperative
agreement with the National Science Foundation.
399
400
TONRY ET AL.
Ðnding evidence in support of the Great Attractor model.
Lorenz et al. (1993) have measured I-band SBF in Fornax,
and Simard & Pritchet (1994) have reported distances to
two Coma I galaxies using V -band SBF observations. Ajhar
& Tonry (1994) reported measurements of m6 and m6 for 19
I
V
Milky Way globular clusters and considered the implications for both the distance scale and stellar populations.
Tiede, Frogel, & Terndrup (1995) measured m6 and m6 for
I
V
the bulge of the Milky Way and derived the distance to the
Galactic center. Sodemann & Thomsen (1995, 1996) have
used Ñuctuation colors and radial gradients to investigate
stellar populations in galaxies. Finally, an enormous
amount of progress has been achieved on the theoretical
SBF front through the stellar population models of
Worthey (1993a, 1993b, 1994), Buzzoni (1993, 1995), and Yi
(1996).
1.2. Genesis of the SBF Survey
When it became apparent that I-band SBF observations
could indeed provide accurate and reliable distances to galaxies, we undertook a large survey of nearby galaxies. The
sample selection is not precisely deÐned because the measurement of SBF depends on a number of criteria which are
not ordinarily cataloged, such as dust content. In addition,
because the measurement of SBF is fairly expensive in terms
of telescope time and quality of seeing, it simply was not
possible to observe all early-type galaxies within some magnitude limit out to a redshift which is large enough to make
peculiar velocities negligible. Nevertheless, we have tried to
manage fairly complete coverage of early-type galaxies
within 2000 km s~1 and brighter than B \ 13.5, and we
have signiÐcant coverage beyond those limits.
Comparison with the Third Reference Catalog of Bright
Galaxies (de Vaucouleurs et al. 1991) reveals that of the
early-type galaxies (T \ 0) with B ¹ 13.5 in the RC3, we
have observed 76% with heliocentric velocity v \ 1000 km
s~1, 73% with 1000 \ v \ 1400 km s~1, 64% with
1400 \ v \ 2000 km s~1, 49% with 2000 \ v \ 2800 km
s~1, and we have data for more than 40 galaxies with
v [ 2800 km s~1. Virtually all of the galaxies closer than
v \ 2000 km s~1 where we lack data are S0s for which
measuring SBF is complicated by dust and/or disk/bulge
problems, and, since many of them are in the cores of clusters such as Virgo, we do not regard their distances as being
important enough to delay completion of our survey. The
survey is, however, an ongoing project, with some data still
to be reduced. About 50% of our sample is listed as E
galaxies (T ¹ [4), about 40% as S0s, and 10% as ““ spirals ÏÏ
(T º 0). Our sample of galaxies is drawn from the entire
sky, and the completeness was mainly driven by the vicissitudes of weather and telescope time, so the sampling is fairly
random. The survey includes a large number of galaxies in
the vicinity of the Virgo supercluster, and the next paper in
this series will present an analysis of their peculiar motions.
The following section describes the SBF survey in more
detail, including the observations, photometric reductions,
and consistency checks. In ° 3 we use our observations of
galaxies in groups to derive the dependence of M1 on
I
(V [I) . Seven of these groups also have Cepheid distances,
0
which we use to set the zero point of the M1 È(V [I) relaI theory and
tion. This new M1 calibration agrees well with
I
supersedes the old calibration of Tonry (1991). We then
compare our distances to those found using a number of
other methods. In ° 4 we discuss the tie to the large-scale
Vol. 475
Hubble Ñow and implications for the value of H . The Ðnal
0
section provides a summary of our main conclusions.
2.
OBSERVATIONS AND REDUCTIONS
All in all, the SBF survey extends over some 40 observing
runs at six telescopes. Table 1 lists these runs along with
some salient information. Note that the date of the run is
coded in the name as (Observatory)MMYY ; the remaining
columns are described below.
The normal observing procedure when the skies were
clear was to obtain sky Ñats each night and observe a
number of Landolt standard stars. We preferred observing
the faint standard star Ðelds of Landolt (1992) in which
there are several stars per CCD Ðeld and where the observations are long enough that shutter timing is not a problem.
Table 2 gives our usual Ðelds. During a typical night we
would observe about 10 Ðelds comprising perhaps 50 stars
over a range of air masses from 1.1 to 2.0. We also strived to
observe stars over a wide range of color ranging from
0 \ (V [I) \ 2. Because there is substantial fringing seen in
the I band with thin CCDs, at some point in a run we would
spend several hours looking at a blank Ðeld in order to
build up a ““ fringe frame.ÏÏ We have found the fringing
pattern for a given CCD and Ðlter (although not the
amplitude) to be remarkably stable from night to night
(even year to year). Hence, a single fringe frame was used to
correct an entire runÏs data, and we usually collected a new
one for each run.
The reductions of the photometry proceed by bias subtraction, Ñattening, and, following Landolt (1992), summing
the net Ñux from photometric standards within a 14A aperture. We also estimate a Ñux error from the sky brightness
and variability over the image and remove any stars the
expected error of which is greater than 0.02 mag. Once all
the photometric observations from a run have been
reduced, we Ðt the results according to
m \ m [ 2.5 log f[A sec z ] C(V [I) ,
(1)
1
where f is the Ñux from the star in terms of electrons per
second. We have found that m and C are constant during a
1 so we Ðt for a single value
run with a given CCD and Ðlter,
for these parameters and extinction coefficients A for each
night. The rms residual of the Ðt is typically about 0.01 mag,
which is satisfactory accuracy for our purposes. Table 1 lists
typical values for m , A, and C for each run in the two Ðlters
V and I. Note the1havoc in the extinction caused by the
eruption by Pinatubo in 1991.
Galaxy reductions proceed by Ðrst bias subtraction, division by a Ñat Ðeld, and subtraction of any fringing present in
I band data. We always take multiple images of a galaxy
with the telescope moved by several arcseconds between
images and determine these o†sets to the nearest pixel. Any
bad pixels or columns are masked out, and the images are
shifted into registration. We next run a program called
““ autoclean ÏÏ which identiÐes cosmic rays in the stack of
images and removes them by replacement with appropriately scaled data from the rest of the stack. Autoclean also
gives us an estimate of how photometric the sequence of
observations was by producing accurate Ñux ratios between
the exposures. Finally, we make a mask of the obvious stars
and companion galaxies in the cleaned image and determine the sky background by Ðtting the outer parts of the
galaxy image with an r1@4 proÐle plus sky level. This is
usually done simultaneously for V and I images, and when
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
401
TABLE 1
OBSERVING RUNS
Run
Telescope
CCD
A/p
K0389 . . . . . .
M1189 . . . . . .
C0990 . . . . . .
K0990 . . . . . .
H0291 . . . . . .
L0391 . . . . . .
C0491 . . . . . .
K0691 . . . . . .
C1091 . . . . . .
H1091 . . . . . .
L1191 . . . . . .
M1191 . . . . . .
C0492 . . . . . .
M0492 . . . . . .
H0592 . . . . . .
M0892 . . . . . .
L1092 . . . . . .
M1092 . . . . . .
L0493 . . . . . .
M0493 . . . . . .
M0493 . . . . . .
M0593 . . . . . .
M0593 . . . . . .
M0893 . . . . . .
M0294 . . . . . .
L0394 . . . . . .
L0994 . . . . . .
G0395 . . . . . .
G0495 . . . . . .
G0495 . . . . . .
G0695 . . . . . .
G0995 . . . . . .
G1095 . . . . . .
M0295 . . . . . .
M0395 . . . . . .
L0495 . . . . . .
L1095 . . . . . .
M1295 . . . . . .
M0196 . . . . . .
M0396 . . . . . .
KPNO 4 m
MDM 2.4 m
CTIO 4 m
KPNO 4 m
CFH 3.6 m
LCO 2.4 m
CTIO 4 m
KPNO 4 m
CTIO 4 m
CFH 3.6 m
LCO 2.4 m
MDM 2.4 m
CTIO 4 m
MDM 2.4 m
CFH 3.6 m
MDM 2.4 m
LCO 2.4 m
MDM 2.4 m
LCO 2.4 m
MDM 2.4 m
MDM 2.4 m
MDM 2.4 m
MDM 2.4 m
MDM 2.4 m
MDM 2.4 m
LCO 2.4 m
LCO 2.4 m
MDM 1.3 m
MDM 1.3 m
MDM 1.3 m
MDM 1.3 m
MDM 1.3 m
MDM 1.3 m
MDM 2.4 m
MDM 2.4 m
LCO 2.4 m
LCO 2.4 m
MDM 2.4 m
MDM 2.4 m
MDM 2.4 m
TI-2
ACIS
TI
TI-2
SAIC
Tek
Tek1
TI-2
Tek2
SAIC
Tek
ACIS
Tek2
Lorl
STIS
Lorl
Tek
Lorl
Tek
Lorl
Tek
Lorl
Tek
Lorl
Tek
Tek
Tek
Lorl
Lorl
STIS
Lorl
Lorl
STIS
Tek
Tek
Tek
Tek
Tek
Tek
Tek
0.299
0.465
0.299
0.299
0.131
0.229
0.472
0.300
0.472
0.131
0.229
0.257
0.472
0.343
0.152
0.343
0.229
0.343
0.229
0.343
0.275
0.343
0.275
0.343
0.275
0.229
0.229
0.637
0.637
0.445
0.637
0.637
0.445
0.275
0.275
0.229
0.229
0.275
0.275
0.275
m
1V
26.15
23.47
26.23
26.26
24.86
24.92
26.06
25.97
26.21
A
V
0.150
0.179
0.160
0.160
0.089
0.15
0.16
0.155
0.45
C
V
[0.070
0.013
0.0
0.0
0.0
0.0
0.0
0.0
[0.007
*V
m
24.92
25.11
26.05
24.69
25.91
24.64
24.92
24.68
24.92
24.67
25.32
24.70
25.32
24.82
25.11
24.92
24.92
23.22
23.15
23.11
23.13
22.97
22.98
25.11
25.11
24.92
24.92
25.11
25.11
25.11
0.15
0.205
0.220
0.33
0.210
0.254
0.15
0.32
0.15
0.21
0.24
0.22
0.198
0.19
0.150
0.15
0.15
0.15
0.15
0.15
0.15
0.14
0.15
0.150
0.150
0.15
0.15
0.150
0.150
0.150
0.0
0.0
0.005
0.000
0.0
0.000
0.0
0.000
0.0
0.022
0.005
0.022
0.025
0.012
[0.017
0.0
0.0
0.019
0.015
0.015
0.042
0.014
0.005
[0.014
[0.017
0.0
0.0
[0.017
[0.017
[0.017
0.014
0.000
[0.026
0.019
[0.016
0.024
0.069
[0.002
0.019
0.000
0.034
[0.025
0.014
0.010
[0.010
0.000
0.000
0.010
0.027
[0.004
[0.004
[0.033
[0.033
[0.021
[0.040
0.026
0.016
[0.029
[0.041
[0.041
[0.015
[0.009
[0.015
[0.040
[0.040
0.008
0.000
[0.040
[0.040
[0.040
1I
25.42
22.44
25.29
25.39
24.62
24.62
26.02
25.36
26.08
24.62
24.62
24.53
25.93
24.84
25.60
24.74
24.62
24.82
24.62
24.35
24.60
24.35
24.74
24.54
24.84
24.62
24.62
22.84
22.83
22.65
22.79
22.81
22.70
24.84
24.84
24.62
24.62
24.84
24.84
24.84
A
I
0.070
0.065
0.080
0.080
0.033
0.07
0.11
0.06
0.3
0.07
0.07
0.102
0.145
0.20
0.110
0.145
0.07
0.22
0.07
0.13
0.11
0.138
0.134
0.10
0.058
0.07
0.07
0.064
0.064
0.100
0.061
0.05
0.06
0.058
0.058
0.07
0.07
0.058
0.058
0.058
C
I
0.000
0.000
0.0
0.0
0.0
0.0
0.0
0.0
0.025
0.0
0.0
0.035
0.030
0.045
0.0
0.045
0.0
0.046
0.0
0.030
0.012
0.030
0.030
0.025
0.015
0.0
0.0
0.026
0.010
0.010
0.026
0.026
0.008
0.012
0.015
0.0
0.0
0.015
0.015
0.015
*I
0.012
0.000
[0.003
0.045
0.029
0.030
0.061
0.019
0.040
0.000
[0.014
0.007
[0.020
0.007
[0.038
0.000
0.000
0.029
[0.070
0.014
0.014
[0.009
[0.009
[0.006
[0.074
[0.030
0.022
[0.007
[0.012
[0.012
0.000
[0.015
[0.015
[0.074
[0.074
[0.027
0.000
[0.074
[0.074
[0.074
NOTE.ÈColumns give run name, telescope, detector, plate scale (A/pixel), photometric zero-point, extinction, color term, and run o†set for
the V band then I band.
the sky levels are determined, we also compute (V [I)
colors as a function of radius from the center of the galaxy. 0
In order to knit all of our observations into a consistent
photometric system, we attempted to make sure that there
were overlap observations between runs, and we developed
a pair of programs called ““ apphot ÏÏ and ““ apcomp ÏÏ to
compare observations. ““ Apphot ÏÏ converts a galaxy image
with its photometric calibration into a table of circular
aperture photometry. This only depends on plate scale
(which is well known) and therefore permits comparison of
di†erent images regardless of their angular orientation.
““ Apcomp ÏÏ then takes the aperture photometry from two
observations and Ðts the two proÐles to one another using a
photometry scale o†set and a relative sky level. These two
TABLE 2
LANDOLT FIELDS
Field
SA 92-250 . . . . . . . . . . .
SA 95-190 . . . . . . . . . . .
SA 95-275 . . . . . . . . . . .
SA 98-650 . . . . . . . . . . .
Rubin-149 . . . . . . . . . .
PG 0918]029 . . . . . .
PG 1323[085 . . . . . .
PG 1633]099 . . . . . .
SA 110-232 . . . . . . . . .
SA 110-503 . . . . . . . . .
Markarian A . . . . . . .
R.A.
00
03
03
06
07
09
13
16
18
18
20
54
53
54
52
24
21
25
35
40
43
43
41
16
40
11
13
36
44
29
50
05
59
decl.
]00
]00
]00
[00
[00
]02
[08
]09
]00
]00
[10
41
16
27
19
31
47
49
46
01
29
47
11
25
24
23
58
03
16
54
51
10
42
V
min
14.09
12.63
12.17
11.93
11.48
12.27
12.08
12.97
12.52
11.31
13.26
V
max
15.35
14.34
14.12
13.75
13.87
14.49
14.00
15.27
14.28
14.20
14.82
(V [I)
min
0.67
0.42
1.40
0.17
[0.11
[0.29
[0.13
[0.21
0.89
0.65
[0.24
(V [I)
max
1.34
1.37
2.27
2.09
1.13
1.11
0.83
1.14
2.36
2.63
1.10
NOTE.ÈColumns give Ðeld name, J2000 coordinates, V magnitude of the brightest and faintest
star, and the (V [I) colors of the bluest and reddest star.
402
TONRY ET AL.
programs can give us accurate o†sets between the photometry of two images, good at the 0.005 mag level.
We learned, however, that good seeing is much more
common than photometric weather, and we realized that
many of our ““ photometric ÏÏ observations were not reliable
at the 0.01 mag level. As the survey progressed and the
number of overlaps increased, we also realized that
although we only need 0.05 mag photometry of m6 , M1 is
I
sensitive enough to (V [I) color that we neededI better
0
photometry. The existing photoelectric (PE) photometry,
although probably very good in the mean, is neither extensive enough nor accurate enough to serve to calibrate the
survey.
We also became aware that there are many peculiar CCD
and shutter e†ects which make good photometry difficult.
For example, we have found photometry with Tektronix
(SITe) CCDs particularly challenging for reasons we do not
fully understand. Because of their high quantum efficiency
and low noise they have been the detectors of choice, but
run to run comparisons with apphot and apcomp show
consistent zero-point o†sets at the 0.05 mag level. While not
a serious problem for m6 , we had to do much better in
I
measuring (V [I) .
0
Accordingly, we undertook an auxiliary survey in 1995 of
a substantial fraction of our SBF survey from the McGrawHill 1.3 m telescope at the MDM Observatory. We shared
the time with another program and used only nights which
were photometric, as judged by the observer at the time and
as revealed later from the quality of the photometric standard observations. We did not use Tek CCDs but primarily
used the front-illuminated, Loral 20482 CCD Wilbur
(Metzger, Tonry, & Luppino 1993), we used Ðlters which
match V and I as closely as possible, and the large Ðeld of
view permittedKC
us to make very good estimates of sky levels.
Over Ðve runs this comprised about 600 observations in V
and I. We made certain to have a generous overlap between
these observations and all our other observing runs, reaching well south to tie to the CTIO and LCO data.
We then performed a grand intercomparison of all the
photometric data in order to determine photometric o†sets
from run to run. Using apphot and apcomp, we determined
o†sets between observations, and we built up a large table
of comparison pairs. In addition, photoelectric (PE) photometry from de Vaucouleurs & Longo (1988), Poulain &
Nieto (1994), and Buta & Williams (1995) served as additional sources of comparison, and we computed di†erences
between PE and our photometry for every galaxy in
common. We have found that (V [I) colors often show
somewhat better agreement than the 0individual V and I
measurements, presumably because thin clouds are reasonably gray, so we also compared colors directly in addition
to photometric zero points.
The results are illustrated in Figure 1. In each of three
quantities V , I, and (V [I) , we Ðtted for zero-point o†sets
for each run (photoelectric0sources were considered to be a
““ run ÏÏ), minimizing the pairwise di†erences. We set the
overall zero point by insisting that the median run o†set be
zero. Upon completion, we found that the rms of the zeropoint o†sets to be 0.029 mag, and the rms scatter of individual comparisons between CCD data to be 0.030 mag in V ,
0.026 mag in I, and 0.024 mag in (V [I) . The scatter was
0
bigger for CCD-PE zero-point comparisons,
0.047 mag in
both V and I. The ““ zero-point o†sets ÏÏ for the photoelectric
photometry were 0.003 mag in V , 0.017 mag in I, and 0.004
Vol. 475
FIG. 1.ÈHistograms of photometric di†erences in surface photometry
between all pairs of observations (including published photoelectric data)
of the same galaxies, in V (top), I (middle), and (V [I) (bottom) The points
and wider Gaussian curves are the distribution of pairwise di†erences prior
to application of run o†sets, and the histograms and narrower Gaussians
reÑect the improvement from using these o†sets. This pair by pair comparison is used to deÐne zero-point o†sets between runs and bring all the
photometry onto the same scale as photoelectric photometry.
mag in (V [I) , which we take to be close enough to zero
0 choose to modify our overall median zero
that we did not
point to force them to zero.
Finally, we chose zero-point corrections for V and I for
each run according to these o†sets. The di†erence of the
corrections was set to the (V [I) o†set from the compari0 was the sum of the V
son, and the sum of the corrections
and I o†sets. We therefore believe that (a) our photometry is
very close to Landolt and photoelectric in zero point, (b) the
error in the V or I photometry for a given observation is
0.02 mag, and (c) the error in a given (V [I) color measure0 21@2 to get the
ment is 0.017 mag (where we have divided by
error for single measurements). We also add in quadrature
0.25 of the zero-point o†set which was applied. The o†sets
*V and *I for each run are listed in Table 1.
The reductions of m6 are described elsewhere (e.g., Jacoby
I Ðt a galaxy model to the summed,
et al. 1992). BrieÑy, we
cleaned, sky-subtracted galaxy image and subtract it. If
there is dust present (all too common in ellipticals and S0s
as well as the large bulge spiral galaxies we observe), we
mask it out as well. Experiments with masking di†erent
portions of M31 and M81 (where we used B band observations to show us clearly the location of the dust) indicate
that reasonable care in excising dust will produce a reliable
m6 , both because the extinction is less in the I band and also
I
because
the dust tends to cause structure at relatively large
scales which are avoided by our Ðt to the Fourier power
spectrum. We run DoPhot (Schechter, Mateo, & Saha 1993)
on the resulting image to Ðnd stars, globular clusters, and
background galaxies ; Ðt a luminosity function to the
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
results ; and derive a mask of objects brighter than a completeness limit and an estimate of residual variance from
sources fainter than the limit. Applying the mask to the
model-subtracted image, we calculate the variance from the
Ñuctuations in a number of di†erent regions. Finally, this
variance is converted to a value for m6 by dividing by the
I
mean galaxy Ñux and subtraction of the residual variance
estimate from unexcised point sources. Generally speaking,
the various estimates of m6 are quite consistent from region
I
to region, and a weighted average and error estimate are
tabulated for each observation. If the observation was
photometric, we also record the (V [I) color found in the
0
same region in which we measure m6 .
I
There are many galaxies for which (V [I) and m6 have
I
0
been measured more than once, and intercomparison
of the
di†erent observations can be used to evaluate whether our
error estimates are reasonable. If we consider all pairs and
divide their di†erence by the expected error, the distribution
should be a Gaussian of unity variance. Figure 2 illustrates
these distributions for m6 and (V [I) . Evidently, the error
I
0 discordant obserestimates are usually quite
good, with
vations occurring rarely. In most cases of discordances, it is
clear which of the observations is trustworthy, and we
simply remove the other observation from further consideration. These excised observations occur 1.5% of the time for
m6 and 0.3% of the time for (V [I) and are an indication of
I frequently bad observations occur.
0
how
After observations are averaged together, they are subjected to some Ðnal corrections. The mean (V [I) color of
the Ñuctuations is the mean of a galaxyÏs color (V [I) and
the ““ Ñuctuation color ÏÏ m6 Èm6 , or (V [I) B 1.85 (since the
V root
I of the Ñux from the galaxy
rms Ñuctuation is the square
and the Ñux from m6 ). The value of m6 is corrected according
I for the runÏs phototo this mean color Iand the color term
metry. The values of m6 and (V [I) are corrected for galactic
extinction according toI
(2)
A : A : E(B[V ) \ 3.04 : 1.88 : 1.00 ,
V IKC
where E(B[V ) comes from Burstein & Heiles (1984), who
give A \ 4.0E(B[V ), the relative extinction ratio
B
FIG. 2.ÈDi†erences for multiple observations of the same galaxy in
(V [I) (top) and m6 (bottom). Each histogram shows the distribution of the
0 between Imultiple observations divided by the estimated error. A
di†erence
Gaussian of unity variance and normalization equal to the number of pairs
is shown for comparison.
403
A /A \ 0.62 is taken from Cohen et al. (1981) for a star
IKC V
halfway between an A0 and an M star, and A /E(B[V ) is
V
an adjustment of a value of 3.1 for A0 stars common in the
literature (e.g., Cardelli, Clayton, & Mathis 1989) to a value
of 3.04 more appropriate for early-type galaxies, following
the ratios given in Cohen et al.
The Ðnal modiÐcation is the application of K-corrections
which brighten magnitudes in V and I by 1.9 and 1.0 ] z,
respectively (Schneider 1996), and brighten Ñuctuation magnitudes in I by 7.0 ] z (Worthey 1996). Note that the very
red color of SBF causes Ñux to be shifted rapidly out of the I
band with redshift, but the m6 K-correction amounts to
I
only 0.05 mag at a typical distance of 2000 km s~1.
3.
CALIBRATING M1
I
The next step we take in trying to establish how M1 varies
I
according to stellar population is to look at how m6 varies
I
from galaxy to galaxy within groups, where the distance to
the galaxies is essentially constant. We originally chose to
observe SBF in the I band because stellar population
models indicate that M1 is relatively constant from population to population andI that the e†ects of age, metallicity,
and IMF are almost degenerateÈin other words, M1 is
I
nearly a one-parameter family.
Guided by theoretical models we seek to establish
whether three statements are a fair description of our data :
1. M1 is a one-parameter family, with a universal depenI (V [I) [i.e., M1 is a function of (V [I) with small
dence on
I
0
residual scatter].0
2. The zero point of the M1 È(V [I) relation is universal.
I is consistent
0
3. The M1 È(V [I) relation
with theoretical
I
0
models of stellar populations.
To this end we chose approximately 40 nearby groups in
which we currently have (or will have) observed more than
one galaxy. The groups are deÐned by position on the sky
and a redshift range and in most cases correspond to one of
the groups described by Faber et al. (1989). Table 3 lists our
groups. Note that we are not trying to include all groups,
nor do we have to be complete in including all galaxies
which are members. We are simply trying to create samples
of galaxies for which we are reasonably conÐdent that all
galaxies are at the same distance.
3.1. Universality of the m6 Dependence on (V [I)
I
0
Figure 3 illustrates the m6 È(V [I) relationship in six
I
groups where we have measured
SBF0 in a number of galaxies : NGC 1023, Leo, Ursa Major, Coma I & II, Virgo,
and Fornax. The lines are drawn with slope 4.5 and zero
point according to the Ðt to the data described below. We
see that galaxies which meet the group criteria of position
on the sky and redshift are consistent with the same m6 È
I
(V [I) relationship, where the scatter reÑects both the
0
measurement error and the group depth inferred from
spread across the sky. In Virgo we Ðnd NGC 4600 much
brighter than the rest of the galaxies, NGC 4365 signiÐcantly fainter, and NGC 4660 (the point at (V [I) \ 1.21
and m6 \ 28.9) also with an unusually bright m6 0 for its
color. IThese three galaxies, marked as smaller,I square
symbols, are discussed below.
Note that ellipticals and S0 galaxies are intermixed with
spirals (NGC 3368 in Leo, NGC 4548 in Virgo, NGC 891 in
the NGC 1023 group, and NGC 4565 and NGC 4725 in the
Coma I & II group). The two galaxies in Fornax marked as
404
TONRY ET AL.
Vol. 475
TABLE 3
NEARBY SBF GROUPS
Group
Example
R.A.
decl.
Rad
Local Group . . . . . .
Cetus . . . . . . . . . . . . . .
N1023 . . . . . . . . . . . . .
N1199 . . . . . . . . . . . . .
Eridanus . . . . . . . . . .
Fornax . . . . . . . . . . . .
Dorado . . . . . . . . . . . .
N1700 . . . . . . . . . . . . .
N2768 . . . . . . . . . . . . .
M81 . . . . . . . . . . . . . . .
N3115 . . . . . . . . . . . . .
Leo III . . . . . . . . . . . .
Leo I . . . . . . . . . . . . . .
Leo II . . . . . . . . . . . . .
N3640 . . . . . . . . . . . . .
UMa . . . . . . . . . . . . . .
N4125 . . . . . . . . . . . . .
VirgoW . . . . . . . . . . . .
Coma I . . . . . . . . . . . .
CVn . . . . . . . . . . . . . . .
N4386 . . . . . . . . . . . . .
N4373 . . . . . . . . . . . . .
Virgo . . . . . . . . . . . . . .
Coma II . . . . . . . . . . .
N4594 . . . . . . . . . . . . .
M51 . . . . . . . . . . . . . . .
Centaurus . . . . . . . . .
Cen A . . . . . . . . . . . . .
N5322 . . . . . . . . . . . . .
N5638 . . . . . . . . . . . . .
N5846 . . . . . . . . . . . . .
N5898 . . . . . . . . . . . . .
N6684 . . . . . . . . . . . . .
N7144 . . . . . . . . . . . . .
N7180 . . . . . . . . . . . . .
N7331 . . . . . . . . . . . . .
Grus . . . . . . . . . . . . . . .
N0224
N0636
N1023
N1199
N1407
N1399
N1549
N1700
N2768
N3031
N3115
N3193
N3379
N3607
N3640
N3928
N4125
N4261
N4278
N4258
N4386
N4373
N4486
N4494
N4594
N5194
N4696
N5128
N5322
N5638
N5846
N5898
N6684
N7144
N7180
N7457
I1459
10.0
24.2
37.0
45.3
53.0
54.1
63.7
72.2
136.9
147.9
150.7
153.9
161.3
168.6
169.6
180.0
181.4
184.2
184.4
185.0
185.6
185.7
187.1
187.2
189.4
200.0
191.5
200.0
212.5
216.0
226.0
228.8
281.0
327.4
329.9
338.7
343.6
41.0
[7.8
35.0
[15.8
[21.0
[35.6
[55.7
[3.5
60.2
69.3
[7.5
22.1
12.8
18.3
3.5
47.0
65.5
6.1
29.6
44.0
75.8
[39.5
12.7
26.1
[11.4
45.0
[41.0
[39.0
57.0
3.5
1.8
[23.9
[65.2
[48.5
[20.8
34.2
[36.7
5
10
9
2
6
6
5
3
4
8
8
3
2
3
2
8
3
2
3
7
5
2
10
5
5
4
3
15
6
3
2
2
10
6
10
9
5
v
ave
[300
1800
650
2700
1700
1400
1300
4230
1360
[40
700
1400
900
950
1300
900
1300
2200
1000
500
1650
3400
1150
1350
1100
480
3000
550
2000
1650
1700
2100
850
1900
1500
800
1600
v
min
[500
1500
500
2500
500
500
700
3600
1100
[200
100
1000
500
650
1200
700
1000
2000
200
400
1500
2500
[300
1200
900
380
2000
200
1600
1400
1200
2000
500
1500
1300
800
1400
v
max
[100
2000
1000
3000
2300
2100
1700
4500
1700
400
900
1700
1200
1500
1800
1100
1700
2800
1400
600
2100
3800
2000
1400
1200
580
5000
600
2400
1900
2200
2700
1200
2000
1900
1100
2300
7S
282
26
29
32
31
211
100
215
45
57
48
50
54
55
98
35
56
235
58
226
245
68
70
71
78
84
265
231
NOTE.ÈColumns : Group name, sample member, R.A. and decl. (B1950), group radius (deg), mean
heliocentric velocity, minimum and maximum velocities for inclusion in the group, and group number
from Faber et al. 1989.
““ spiral ÏÏ (NGC 1373 and NGC 1386) might better be classiÐed as S0 on our deep CCD images. For this admittedly
small sample we see no o†set between SBF measurements
in spiral bulges and early-type galaxies. We regard this as
conÐrmation of our assumption that SBF measurements
are equally valid in spiral bulges as in early-type galaxies.
In order to test the hypothesis that M1 has a universal
I
dependence on (V [I) in a more systematic
way than
0
Ðtting individual groups, we simultaneously Ðt all our galaxies which match the group criteria with
m6 \ Sm6 0T ] b[(V [I) [ 1.15] ,
(3)
I
I j
where we Ðt for values of Sm6 0T for each of j \ 1, N groups
I quantity
j
and a single value for b. The
Sm6 0T is the group
I j of (V [I) \
mean value for m6 at a Ðducial galaxy color
I
0
1.15. The measurements of (V [I) and m6 carry errors
0 the averaging
I
which the pairwise comparisons and
procedure of ° 2 indicate are accurate.
We also anticipate that there will be an irreducible
““ cosmic ÏÏ scatter in M1 . Accordingly, in Ðtting m6 as a funcI for this
I
tion of (V [I) , we include
an error allowance
0
cosmic scatter which is nominally 0.05 mag (i.e., for this Ðt
the error in m6 is enhanced by 0.05 mag in quadrature). In
I also see scatter because the galaxies within
addition, we will
groups are not truly at the same distance. We therefore
calculate the rms angular position of the galaxies making up
each group and divide this radius by 21@2 as an estimate of
the rms group depth. Converting this to a magnitude, we
add it in quadrature to the error in m6 . We then perform a
linear Ðt of N]1 parameters, whichI allows for errors in
both the ordinate and abscissa, according to the ““ least
distance ÏÏ method used by Tonry & Davis (1981). (This also
appears in a slightly di†erent guise in Press et al. 1992.)
We remove the three Virgo galaxies which we believe are
at signiÐcantly di†erent distances from the rest of the group
(NGC 4365, NGC 4660, and NGC 4600), mindful that what
is considered to be part of Virgo and what is not is somewhat arbitrary. We also choose to exclude NGC 205 and
NGC 5253 from the Ðt because recent starbursts make them
extremely blueÈwe do not believe our modeling extends to
such young populations.
With 149 galaxies we have 117 degrees of freedom, and
we Ðnd that s2 \ 129, s2/N \ 1.10, and the slope of the
M1 È(V [I) relation is 4.5 ^ 0.25. The galaxies contributing
0 a color range of 1.0 \ (V [I) \ 1.3. Because
to Ithe Ðt span
0
Virgo still contributes Ðve of the seven most
discrepant
points (the other two are in Cetus), the rms depth used for
Virgo (2¡.35 ] 0.08 mag) may be too small, making s2/N
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
405
FIG. 3.ÈThe distribution of m6 as a function of (V [I) for six groups : NGC 1023, Leo, UMa, Coma I and II (including both the NGC 4278 and NGC
I Spiral galaxies (i.e., RC3
0 T-type T [ 0) are indicated with Ðlled symbols, and the vertical error bar shows our estimate of
4494 subgroups), Virgo, and Fornax.
rms group depth (derived from the angular extent of the group across the sky) multiplied by 5 as an expectation for the peak-to-peak depth of the cluster.
Only in Fornax and in Leo are the SBF measurement errors as big as the putative depth of the group. The three small squares in the Virgo panel are for NGC
4600, NGC 4365, and NGC 4660, galaxies which we believe to be foreground or background even though they meet the Virgo group criteria. The lines show
the SBF relation for each of these groups from our overall Ðt to all the data.
slightly bigger than one. If we replace the three Virgo galaxies we omitted earlier, we Ðnd that s2/N rises to 1.75 for
120 degrees of freedom and the slope changes to 4.7 ^ 0.25,
showing that even though these galaxies are signiÐcantly
outside of Virgo, the slope is robust. When we experiment
with adding and removing di†erent groups we Ðnd that the
slope changes slightly, but is always consistent with the
error above.
These values for s2 include an allowance for cosmic
scatter of 0.05 mag and the nominal, rms group depth.
These two, ill-constrained sources of error can play o†
against each other : if we double the group depth error
allowance, we get s2/N \ 1.0 for zero cosmic scatter ; if we
increase the cosmic scatter to 0.10 mag, we need to decrease
the group depth to zero in order to make s2/N \ 1.0.
Therefore, even though we cannot unambiguously determine how much cosmic scatter there is in the M1 È(V [I)
I
0
relation, it appears to be D0.05 mag.
The referee pointed out that even if we make no allowance for group depth, the cosmic scatter of 0.10 mag makes
SBF the most precise tertiary distance estimator by far and
wanted to know how sensitive this is to our estimates of
observational error. There is not much latitude for the
cosmic scatter to be larger than 0.10 mag. The distribution
of measurement error in m6 and (V [I) (which also enter
s2) starts at 0.06 mag and Ihas quartiles0 at 0.11, 0.16, and
0.20 mag. If we wanted to increase the cosmic scatter by 21@2
to 0.14 mag, we would have to have overestimated the
observational errors by 0.10 mag in quadrature, and apart
from the fact that a quarter of the measurements would
then have imaginary errors, our pairwise comparison of
multiple observations from the previous section would not
allow such a gross reduction in observational error.
Figure 4 illustrates how m6 depends on (V [I) when all
0
the group data have been slidI together by subtraction
of the
group mean at (V [I) \ 1.15. Note again that spiral galaxies, in this case four 0galaxies with both Cepheid and SBF
distances, show no o†set relative to the other early-type
galaxies making up the groups in which they appear, other
than the usual trend with (V [I) . The overall rms scatter,
0
0.18 mag, arising from all the e†ects
discussed above, is a
testament to the quality of SBF as a distance estimator.
The Local Group galaxies NGC 205, NGC 147, and
NGC 185 have also been plotted in Figure 4 (although they
were not used in the Ðt), under the assumption that they are
at the same distance as M31 and M32. This may or may not
406
TONRY ET AL.
FIG. 4.ÈThe distribution of m6 [ Sm6 0T as a function of (V [I) for all
I
I
0
galaxies belonging to our groups. A line through (1.15, 0.0) with the mean
slope of the SBF-color relation is drawn. The four spiral galaxies for which
we have both Cepheid and SBF distances, NGC 224, NGC 3031, NGC
3368, and NGC 7331, are plotted as large, solid hexagons and demonstrate
that SBF is the same for spiral bulges as for elliptical and S0 galaxies. The
round, solid points above the line are various locations in NGC 205, and
the round, solid points below the line are NGC 147 and NGC 185 (not
used in the Ðt). The inset shows NGC 205 again, along with NGC 5253 and
IC 4182, which are placed according to their Cepheid distances.
be a valid assumption for NGC 147 and NGC 185, but they
agree reasonably well with the mean relation. In contrast to
these two galaxies, which are blue because of extremely low
metallicity, NGC 205 has undergone a recent burst of star
formation and has a strong A star spectral signature.
Because our models do not extend to such young populations, the systematic deviation from the mean relation is
not unexpected.
The inset in Figure 4 extends the color range to show that
this deviation continues for two other galaxies where there
has been recent star formation : NGC 5253 and IC 4182.
NGC 5253 is 0.5 mag fainter than one would expect using a
naive extrapolation of the relation to its color of (V [I) \
0
0.84, and IC 4182 has an SBF magnitude which is 0.75 mag
fainter than one would judge from its Cepheid distance and
its color of (V [I) \ 0.71. Qualitatively this makes sense
0
because the very young
stars change the overall color of the
galaxy quite a bit but are not very luminous in the I band
compared to the stars at the top of the RGB which are the
main contributors to the SBF m6 . It may be that these very
I
young populations can be understood
well enough that one
can safely predict the SBF absolute magnitude from the
mean color, but this is beyond the scope of this paper.
Tammann (1992) expressed concern that there are
residual stellar population e†ects in SBF even after the correction for (V [I) color. However, his critique was based
0 to correlate m6 as a function of (V [I)
on an early attempt
(Tonry et al. 1990). Unfortunately, Ithat work had the wrong0
sign for the slope (appropriate for the JHK bandpasses but
not I), because it was based on the Revised Yale Isochrones
(Green et al. 1987), which did not properly model the line
blanketing in metal-rich, high-luminosity stars. The e†ect
noted by Tammann was a residual correlation of the corrected m6 0 with the Mg index among galaxies within a
I
cluster. Figure
5 shows 2these trends do not exist for the
Vol. 475
present data and the new m6 È(V [I) relation : in both
I
0
Fornax and Virgo there is no residual correlation with
either Mg or galaxy magnitude.
2
We conclude that a one-parameter, linear relation
between M1 and (V [I) suffices to describe our data for
I
0
1.0 \ (V [I) \ 1.3 ; the slope of the M1 È(V [I) relation is
0
I detecting
0
universally 4.5 ^ 0.25, and we are indeed
cosmic
scatter in M1 of order 0.05 mag. Very few galaxies fail to
I
follow the relation, and for every such galaxy at least one of
the following statements is true : (1) the measurement of m6
I
or (V [I) is doubtful ; (2) the galaxy may not be a member
0
of the group we assigned it to ; (3) the stellar population is
bluer than (V [I) \ 1.05 as a result of to recent star forma0
tion.
Note that this slope is steeper than the value of 3 tendered by Tonry (1991) and used by Ciardullo, Jacoby, &
Tonry (1993), who suggested that it might be as steep as 4.
Basically, the reason for this is that the older data were
noisier and were Ðtted only to errors in the ordinate,
whereas in fact the errors in (V [I) are quite signiÐcant,
particularly for the better measured m06 , which count heavily
I
in any weighted Ðt.
3.2. Universality of the M1 Zero Point
I
We have e†ectively tested the hypothesis that the zero
point of SBF is universal within groups, but in order to
extend the test from group to group we need independent
distance estimates. Since the groups are all nearby, the
groupÏs redshift is not an accurate distance estimateÈthere
are likely to be substantial non-Hubble velocities included
in the groupÏs recession velocity. We therefore turn to other
distance estimators : Cepheids, planetary nebula luminosity
function (PNLF), Tully-Fisher (TF), D -p, Type II supernovae (SN II), and Type I supernovaen (SN Ia). Some of
these estimators have zero points in terms of megaparsecs
(such as Cepheids and SN II), others have zero points in
terms of kilometers per second based on the Hubble Ñow
(such as D -p), and a few have both (such as TF). For our
n
initial discussion
we seek only to establish whether the relative distances agree with SBF ; for now we do not care about
the zero point, although it will soon be addressed.
Figures 6 and 7 show the comparison between the values
of the SBF parameters Sm6 0T derived previously for each of
I
our groups and the distances
to the groups according to
these six methods. The results of Ðtting lines of unity slope
(allowing for errors in both coordinates) to the data in each
panel are given in Table 4. We use the published error
estimates for all of these other indicators so s2/N should be
viewed with some caution : outliers and non-Gaussian
errors or overoptimistic error estimates can inÑate s2/N
even though the mean o†set is still valuable. Since each
comparison is very important, we brieÑy discuss them
individually.
3.2.1. Cepheids
There is now a growing number of Cepheid distances
with which we compare, but we are faced with the complication that Cepheids occur in young stellar populations,
while SBF is best measured where such populations are not
present.
There are Ðve galaxies which have both Cepheid and SBF
distances : NGC 224 (Freedman & Madore 1990), NGC
3031 (Freedman et al 1994), NGC 3368 (Tanvir et al. 1995),
NGC 5253 (Saha et al. 1995), and NGC 7331 (Hughes 1996).
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
407
FIG. 5.ÈThe (V [I) corrected m6 quantity, m6 0, as a function of Mg and B magnitude (from the RC3) in the Virgo and Fornax clusters. The lack of
0 m6 is a one-parameter
I
I
2
T (V [I) adequately delineates the variations of stellar population over this
correlation indicates that
function
of stellar population,
and
I
0
color range.
NGC 5253 is especially problematic for SBF because its
recent starburst has produced a much younger and bluer
stellar population than we have calibrated. We can, of
course, also compare distances according to group membership. There are seven groups where this is currently possible : Local Group, M81, Cen A, NGC 1023 (NGC 925
from Silbermann et al. 1996a, 1996b), NGC 3379 (also
including NGC 3351 from Graham et al. 1996), NGC 7331,
and Virgo (including NGC 4321 from Ferrarese et al. 1996,
NGC 4536 from Saha et al. 1996a, and NGC 4496A from
Saha et al. 1996b ; we exclude NGC 4639 from Sandage et
al. 1996 because we are also excluding NGC 4365 and the
W cloud from the SBF mean). In the former case we Ðnd
that Ðtting a line to Sm6 0T as a function of (m[M) yields a
I
TABLE 4
DISTANCE COMPARISONS
Estimator
Grp/gxy
Distance
N
Cepheid . . . . . . . . . . . .
Cepheid . . . . . . . . . . . .
Cepheid . . . . . . . . . . . .
PNLF . . . . . . . . . . . . .
PNLF . . . . . . . . . . . . .
SN II . . . . . . . . . . . . . .
SN II . . . . . . . . . . . . . .
TF . . . . . . . . . . . . . . . . .
TF (Mrk II) . . . . . . .
Dn-sigma . . . . . . . . . .
SN Ia (M ) . . . . . .
SN Ia (*mmax ) . . . . . .
SN Ia (M 15) . . . . . .
SN Ia (*mmax ) . . . . . .
SN Ia (M 15) . . . . . .
SN Ia (*mmax ) . . . . . .
Theory . . . .15
.........
Grp
gxy
gxy
Grp
Grp
Grp
Grp
Grp
Grp
Grp
Grp
Grp
gxy
gxy
gxy
gxy
(m[M)
(m[M)
(m[M)
(m[M)
(m[M)
(m[M)
(m[M)
(m[M)
5 log d
5 log d
5 log d
5 log d
5 log d
5 log d
5 log d
5 log d
7
5
4
12
10
5
4
26
29
28
6
6
5
5
4
4
Sm6 0T[d
I
[1.74
[1.75
[1.82
[1.63
[1.69
[1.80
[1.76
[1.69
13.55
13.64
13.92
14.01
13.86
14.01
13.64
13.87
[1.81
^
rms
s2/N
0.05
0.06
0.07
0.02
0.03
0.12
0.12
0.03
0.08
0.05
0.08
0.08
0.12
0.12
0.13
0.13
0.16
0.33
0.12
0.33
0.20
0.36
0.22
0.41
0.59
0.44
0.38
0.40
0.54
0.43
0.22
0.30
0.11
0.6
3.4
0.3
7.5
2.2
1.4
1.1
2.1
2.1
1.9
3.6
3.6
4.9
3.2
1.0
1.8
Comments
Less N5253
Less Coma I/II
Less N7331
Less N5253
Less N5253
NOTE.ÈColumns give name of the estimator, comparison by group or by galaxy, estimatorÏs zero point based on
Mpc (m[M) or Hubble Ñow (5 log d km s~1), number of comparison points, mean di†erence between SBF and the
estimator, expected error in this mean based on error estimates, rms scatter in the comparison, s2/N, and comments.
408
TONRY ET AL.
Vol. 475
FIG. 6.ÈThe mean Sm6 0T derived for our groups compared to other distance estimators : Cepheids, SN II, SN Ia (treated as standard candles), and SN Ia
I
(correcting the peak magnitude
for the rate of decline *m ). The other estimatorsÏ distances are either in terms of Mpc, expressed as a distance modulus
15
(m[M), or in terms of km s~1, plotted as 5 times the logarithm.
The lines are drawn according to a weighted Ðt of unity slope between each set of distances.
The ““ fast decline ÏÏ SN Ia are plotted as solid points but are not used in any of the Ðts. NGC 7331 is drawn as a solid point in the SN II comparison because
the SN II distance is discordant with both SBF and Cepheids. Above each distance comparison is a histogram of the di†erences Sm6 0T [ (m[M) or
I
Sm6 0T [ 5 log d.
I
mean o†set of [1.75 ^ 0.05 mag with s2/N of 3.4 for 4
degrees of freedom, and [1.82 ^ 0.06 mag with s2/N of 0.3
for 3 degrees of freedom when NGC 5253 is excluded. In the
latter case we get a mean o†set of [1.74 ^ 0.05 mag with
s2/N of 0.6 for 6 degrees of freedom. When NGC 5253 is
excluded, the rms scatter is remarkably small, only 0.12 mag
for the galaxy comparison and 0.16 mag for the group comparison.
3.2.2. PNL F
Ciardullo et al. (1993) reported virtually perfect agreement between SBF and PNLF, but recent publications
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
409
FIG. 7.ÈSame as Fig. 6, but comparing SBF and the tertiary estimators PNLF, TF (Mpc zero point), TF (from Mark II catalog), and D -p. The recent
n
PNLF distances for the Coma I and II galaxies are plotted as solid symbols.
(Jacoby, Ciardullo, & Harris 1996) have raised some discrepancies. Examination of Figure 7 reveals that our Ðt has
two outliers : Coma I (i.e., NGC 4278) and Coma II (i.e.,
NGC 4494). Because we do not know how to resolve this
issue at present, Table 4 gives the result for Sm6 0T [
I
(m[M)
for the entire sample and in the case in which
PNLF
these two outliers are removed. Since PNLF is fundamentally calibrated on Cepheids, this is not independent of the
previous number, but it does conÐrm that PNLF and SBF
are measuring the same relative distances.
3.2.3. SN II
The expanding photospheres method (EPM) described
most recently by Eastman, Schmidt, & Kirshner (1996)
o†ers distance estimates which are largely independent of
the Cepheid distance scale. There is only one galaxy with
410
TONRY ET AL.
both an EPM and an SBF distance (NGC 7331), but there
have also been two SN II in Dorado (NGC 1559 and NGC
2082), two in Virgo (NGC 4321 and NGC 4579), and one in
the NGC 1023 group (NGC 1058). The agreement between
EPM and SBF (Fig. 6) is good. The farthest outlier is NGC
7331, for which SBF and Cepheid distances are discordant
with the SN II distance. Table 4 lists separately the zeropoint, scatter, and s2/N for the cases in which NGC 7331 is
included and is excluded.
3.2.4. T F (Megaparsec Calibration)
Tully (1996) was kind enough to provide us with TF
distances to the SBF groups in advance of publication. The
Ðt between TF and SBF gives Sm6 0T [ (m[M) \ [1.69
I
^ 0.03 mag. This is again not independent of the Cepheid
number, since the TF zero point comes from the same
Cepheid distances. Figure 7 demonstrates that the agreement is generally good, despite the high s2/N that comes
from a few non-Gaussian outliers. We cannot tell whether
these outliers reÑect non-Gaussian errors in the methods or
simply the difficulties of choosing spirals and early-type galaxies in the same groups.
3.2.5. T F (Kilometers per Second Calibration)
We applied the SBF group criteria to the ““ Mark II ÏÏ
catalog of galaxy distances distributed by D. Burstein. We
selected all galaxies with ““ good ÏÏ TF distances (mostly from
Aaronson et al. 1982) and computed an average distance to
the groups, applying the usual Malmquist bias correction
according to the precepts of Lynden-Bell et al. (1988) and
the error estimates from Burstein. Because these distances
have a zero point based on the distant Hubble Ñow, we
derive an average o†set of Sm6 0T [ 5 log d \ 13.55 ^ 0.08
I
mag.
3.2.6. D -p
n
Most of the SBF groups are the same as those deÐned by
Faber et al. (1989). We compare their Malmquist bias corrected distances to these groups (which are based on a zero
point from the distant Hubble Ñow) with SBF and Ðnd the
same result as Jacoby et al. (1992) : the distribution of errors
has a larger tail than Gaussian, but the error estimates
accurately describe the central core of the distribution. The
ratio s2/N is distinctly larger than 1, but the di†erence histogram in Figure 7 reveals that this is because of the tails
of the distribution. The Ðt between D -p and SBF gives
n
Sm6 0T [ 5 log d \ 13.64 ^ 0.05 mag.
I
3.2.7. SN Ia
Extraordinary claims have been made recently about the
quality of SN Ia as distance estimators. Some authors (e.g.,
Sandage & Tammann 1993) claim that suitably selected
(““ Branch normal ÏÏ) SN Ia are standard candles with a dispersion as little as 0.2 mag. Others (e.g., Phillips 1993)
believe that they see a correlation between SN Ia luminosity
and their rate of decline, parametrized by the amount of
dimming 15 days after maximum, *m . Still others (e.g.,
Riess, Press, & Kirschner 1995) agree 15
with Phillips (1993)
but believe that they can categorize SN Ia better by using
more information about the light curve shape than just this
rate of decline. Finally, there is the ““ nebular SN Ia
method ÏÏ of Ruiz-Lapuente (1996) that tries to determine
the mass of the exploding white dwarf by consideration of
the emission lines from the expanding ejecta. We therefore
choose to compare SBF distances with SN Ia under two
assumptions : that SN Ia are standard candles, and that
Vol. 475
m [ a *m is a better indicator of distance. In both
max
15
cases we restrict our Ðts to 0.8 \ *m \ 1.5, as suggested
15
by Hamuy et al. (1995), and use a distance error of 0.225
mag for each SN Ia.
SN Ia have been carefully tied to a zero point according
to the distant Hubble Ñow (one of the main advantages of
SN Ia) by Hamuy et al. (1995), under both assumptions.
There have also been vigorous attempts to tie the SN Ia to
the Cepheid distance scale which we have chosen not to use
because of the circularity with our direct comparison
between SBF and Cepheids.
The results are both encouraging and discouraging. We
Ðnd that there is indeed a good correlation between SN Ia
distance and SBF, with average values of Sm6 0T [ 5 log
d \ 13.92 ^ 0.08 mag and 14.01 ^ 0.08 mag for Ithe group
comparison under the two assumptions. As illustrated in
Figure 6, m [ a *m does correlate better with distance
max as long 15
than m , but
as ““ fast declining ÏÏ SN Ia are left out
max
there is scant di†erence between the zero point according to
the two methods.
The panels of Figure 6 showing SBF and SN Ia hint at a
systematic change between the nearest three and the farthest three groups, in the sense that there appears to be a
change in zero point by about 0.7 mag. One might worry
that this is evidence that SBF is ““ bottoming out,ÏÏ but there
is no hint of this in the comparisons with TF and D -p in
Figure 7 which extend to much fainter m6 . One mightn also
worry about whether there are systematicIdi†erences in SN
Ia in spirals and ellipticals, and biases from the lack of
nearby ellipticals or S0 galaxies. However, it is probably
premature to examine these points in too much detail. For
example, the point at Sm6 0T B 28 uses the SBF distance to
I
Leo I, but the SN Ia occurred
in NGC 3627 which lies 8¡
away from the Leo I group. This is a fundamental difficulty
in the SBFÈSN Ia comparison, which will improve as SBF
extends to greater distances and more nearby SN Ia are
observed.
There are seven galaxies bearing SN Ia where SBF distances have been measured : NGC 5253 (SN 1972E), NGC
5128 (SN 1986G), NGC 4526 (SN 1994D), NCG 2962 (SN
1995D), NGC 1380 (SN 1992A), NGC 4374 (SN 1991bg),
NGC 1316 (SN 1980N). Inasmuch as two of these are slow
decliners (SN 1986G, SN 1991bg), we Ðt the remaining Ðve
using the SBF distance to the galaxy instead of the group.
We derive Sm6 0T [ 5 log d \ 13.86 ^ 0.12 mag and
I the two methods.
14.01 ^ 0.12 mag for
We regard the SBF distance to NGC 5253 as uncertain
because we have not calibrated M1 for such a young stellar
I SBF and SN Ia again
population. We thus also compare
with NGC 5253 removed from consideration. The ratio
s2/N becomes dramatically smaller in both cases, and
Sm6 0T [ 5 log d becomes smaller by about 0.2 mag to
I ^ 0.13 mag and 13.87 ^ 0.13 mag.
13.64
3.2.8. Zero-Point Summary
These comparisons demonstrate that the second hypothesis is correct : the zero point of the M1 È(V [I) relationship
I Ðt to derive
0
is universal. We use the SBFÈCepheid
a Ðnal,
empirical relationship between m6 and (V [I) :
I
0
M1 \ ([1.74 ^ 0.07) ] (4.5 ^ 0.25)[(V [I) [ 1.15] . (4)
I
0
This zero point di†ers from that of Tonry (1991) by about
0.35 mag. The reason is simply that the 1991 zero point was
based entirely on M31 and M32, and the observational
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
FIG. 8.ÈComparison of the theoretical model predictions of M1 from
I
Worthey with our empirical calibration from Cepheids, M1 \ [1.74
I
] 4.5[(V [I) [ 1.15], drawn as a dashed line. The solid line shows a Ðt to
0 models using the empirical slope : the two di†er by 0.07 mag
the theoretical
in zero point or 0.015 mag in color. The models have ages of 5, 8, 12, and 17
Gyr (older are redder and fainter), and their metallicity relative to solar is
indicated by point type.
error in both m6 and (V [I) worked in the same direction,
I
0
as did the photometric
zero-point
errors (see Table 1 for
K0990). The SBF distances which have been published
therefore increase by about 15% (for example, Fornax
moves from 15 Mpc to 17 Mpc), except for Virgo, where the
earlier result included NGC 4365 which we now exclude in
calculating the average distance to the core of the cluster.
This new calibration is based on 10 Cepheid distances in
seven groups and 44 SBF distances. As seen in Figure 6 and
Table 4, these are highly consistent with one another with a
scatter of about 0.15 mag. Along with the extensive photometric recalibration, this zero point should be accurate to
^0.07 mag. This error estimate makes an allowance of 0.05
mag for the uncertainty in the Cepheid zero point in addition to the statistical error of 0.05 mag, and the comparisons with theory and SN II give us conÐdence that this truly
is correct.
3.3. Comparison with T heory
Finally, we test our third hypothesis by comparing our
M1 È(V [I) relationship with theoretical models of stellar
I
0 Figure 8 shows the model predictions of
populations.
Worthey (1993a, 1993b) along with the empirical line. When
the theoretical models are Ðtted with the empirically determined slope of 4.5, they yield a theoretical zero point of
[1.81 mag with an rms scatter of 0.11 mag for the SBF
relation. We enter this value in Table 4, with the scatter
o†ered as an ““ error estimate,ÏÏ but it must be remembered
that this is fundamentally di†erent from the other entries in
the table. There is good agreement here, although the theoretical result for M1 may be slightly brighter (0.07 mag) or
I mag) than the empirical result. Given
slightly redder (0.015
the difficulties that the theoretical models have in simultaneously Ðtting the color and Mg indices of real galaxies, we
2
regard this agreement as excellent
conÐrmation of the
empirical calibration.
4.
THE HUBBLE CONSTANT
The scope of this paper does not extend to comparing
411
SBF distances with velocity ; this will be the subject of the
next paper in the series. However, the comparison with
other distance estimators does provide us with a measurement of the Hubble constant.
The comparison with other estimators for which the zero
point is deÐned in terms of megaparsecs tells us the absolute
magnitude of SBF. At our Ðducial color of (V [I) \ 1.15,
0
we Ðnd that Cepheids give us an absolute magnitude M1 \
I
[1.74 ^ 0.05. We prefer the group-based Cepheid comparison because of the very few SBF measurements possible
in spirals which have Cepheids. The other megaparsecbased distance estimators are all consistent with this zero
point, as we would hope since they are calibrated with the
same Cepheid data. The results from theoretical models of
stellar populations and SN II are also consistent with this
zero point and provide independent conÐrmation of the
validity of the Cepheid distance scale.
The comparison of SBF with estimators for which the
zero point is based on the large-scale Hubble Ñow is less
consistent. The estimators based on galaxy properties, TF
and D -p, are consistent with one another and consistent
n
with SBF
in terms of relative distances. They give a zero
point for SBF at the Ðducial color of (V [I) \ 1.15 of
Sm6 0T \ 5 log d(km s~1) ] 13.59 ^ 0.07, where0 the error
I from the rms divided by (N [ 1)1@2.
comes
Supernovae and SBF are more interesting. The group
membership of the Cepheid galaxies was not difficult since
they were speciÐcally chosen to be group members. In contrast, the SN Ia are not easy to assign to groups in many
cases. Depending on (1) whether we Ðt galaxies individually
or groups, (2) whether we use the ““ standard candle ÏÏ model
for SN Ia or the ““ light curve decline ÏÏ relation, and (3)
whether we include or exclude NGC 5253 for which we
regard our stellar population calibration as unknown, we
get values for the SBF zero point as low as 13.64 and as high
as 14.01 (Table 4). Averaging the two methods and again
estimating uncertainties from rms divided by (N [ 1)1@2, we
Ðnd 13.96 ^ 0.17 for groups and 13.75 ^ 0.14 for galaxies.
Because these di†er from the TF and D -p by 2.0 p and
n be statistically
1.0 p, respectively, the discrepancy may not
signiÐcant.
It is possible that there are systematic errors in the tie to
the distant Hubble Ñow for TF and D -p, whereas the SN Ia
appear to be wonderfully consistentn with the large-scale
Hubble Ñow. On the other hand, the nearby SN Ia do not
agree with SBF or Cepheids as well as one might hope from
the scatter against the Hubble Ñow, which makes one worry
about the systematics with SN Ia. For example, the SN Ia
distances predicted for the Fornax clusters are signiÐcantly
larger than the very recent Cepheid measurement of the
distance to the Fornax cluster (Silbermann et al. 1996b). SN
II appear to agree pretty well with SBF and Cepheids, and
there should eventually be enough of them to tie very well
to the large-scale Hubble Ñow. In subsequent papers we will
present the direct tie between SBF and the Hubble Ñow,
both from ground-based observations as well as HST
observations beyond 5000 km s~1, but at present we
depend on these other estimators to tie to the Hubble Ñow.
It is therefore with some trepidation that we o†er a value for
H .
0We have a calibration for M1 ; we have several caliI
brations for m6 in terms of 5 log d(km
s~1), and, of course ,
I
(m[M) \ 5 log d(km s~1) ] 25 [ 5 log H . If we use the
TF and D -p calibration of SBF we get H0 \ 86 km s~1
n
0
412
TONRY ET AL.
Vol. 475
TABLE 5
SBF DISTANCES TO GROUPS
Group
Example
R.A.
decl.
Local Grp . . . . . .
M81 . . . . . . . . . . . .
Cen A . . . . . . . . . .
N1023 . . . . . . . . . .
Leo I . . . . . . . . . . .
N7331 . . . . . . . . . .
UMa . . . . . . . . . . . .
Coma I . . . . . . . . .
Coma II . . . . . . . .
Virgo . . . . . . . . . . .
Dorado . . . . . . . . .
Fornax . . . . . . . . .
N0224
N3031
N5128
N1023
N3379
N7331
N3928
N4278
N4494
N4486
N1549
N1399
10.0
147.9
200.0
37.0
161.3
338.7
180.0
184.4
187.2
187.1
63.7
54.1
41.0
69.3
[39.0
35.0
12.8
34.2
47.0
29.6
26.1
12.7
[55.7
[35.6
v
ave
[300
[40
550
650
900
800
900
1000
1350
1150
1300
1400
N
(m[M)
^
d
^
2
2
3
4
5
2
5
3
3
27
6
26
24.43
27.78
28.03
29.91
30.14
30.39
30.76
30.95
31.01
31.03
31.04
31.23
0.08
0.08
0.10
0.09
0.06
0.10
0.09
0.08
0.08
0.05
0.06
0.06
0.77
3.6
4.0
9.6
10.7
12.0
14.2
15.5
15.9
16.1
16.1
17.6
0.03
0.2
0.2
0.4
0.3
0.6
0.6
0.6
0.6
0.4
0.5
0.5
NOTE.ÈColumns give group name, sample member, R.A. and decl. (B1950), mean heliocentric velocity,
number of SBF distances, SBF distance modulus and error, and SBF distance (Mpc) and error.
Mpc~1. Examining groups and averaging the ““ standard
candle ÏÏ and the ““ *m ÏÏ assumptions about SN Ia gives us
15
H \ 72 km s~1 Mpc~1.
If we compare galaxies directly
0
without resorting to group membership, but leave out NGC
5253, we get an average H \ 80 km s~1 Mpc~1.
We suspect that there is0 more to the SN Ia story than is
currently understood, so we therefore prefer not to use it to
the exclusion of all other distance estimators. The range we
Ðnd for H is
0
H \ 72È86 km s~1 Mpc ,
0
and our best guess at this point is derived by averaging the
ties to the Hubble Ñow from TF, D -p, SN Ia (both
n
methods) in groups, and SN Ia (both methods)
galaxy by
galaxy. This weights the SN Ia slightly more heavily than
TF and D -p and gives a zero point of 13.72 which translates to n
H \ 81 ^ 6 km s~1 Mpc~1 .
0
The Ðnal error term includes a contribution of 0.07 mag
from the disagreement between the Cepheid and theory
zero points (which we hope is indicative of the true accuracy
of our calibrations), and an allowance of 0.13 mag for the
uncertainty in the tie to the distant Hubble Ñow (judged
from the scatter among the various methods).
In order to facilitate comparisons with SBF distances, we
o†er the SBF distance to 12 nearby groups in Table 5. The
relative distances are completely independent of any other
distance estimator, and the zero point uses our Cepheidbased calibration. As we Ðnish our reductions and analysis,
the remainder of the group and individual galaxy distances
will be published.
5.
SUMMARY AND CONCLUSIONS
We have described the observational sample which comprises the SBF survey of galaxy distances. The survey was
conducted over numerous observing runs spanning a
period of nearly 7 years. The photometry of the sample has
been brought into internal consistency by applying small
systematic corrections to the photometric zero points of the
individual runs. Based on comparisons between overlapping galaxy observations, we Ðnd that our error estimates
for (V [I) and m6 are reliable, after correction for the photometry o†sets. I
From our measurements of m6 within galaxy groups, we
I by a linear function of
conclude that M1 is well described
I
(V [I) . Comparison of our relative distances with Cepheid
0 to these groups indicates that this linear relationdistances
ship is universal and yields the zero-point calibration for the
SBF method. This calibration is applicable to galaxies that
are in the color range 1.0 \ (V [I) \ 1.3 and which have
not experienced recent bursts of star0 formation. Any intrinsic, or ““ cosmic, ÏÏ scatter about this relation is small, of
order 0.05 mag. Owing to many more data and improved
photometry, this new calibration di†ers in its zero point by
0.35 mag from the earlier one of Tonry (1991), but is much
closer to WortheyÏs (1993a) theoretical zero point, di†ering
by just 0.07 mag. We take this close agreement to be an
independent conÐrmation of the Cepheid distance scale.
An extensive set of comparisons between our SBF distances and those estimated using other methods provides
still further evidence for the universality of the M1 È(V [I)
relation. We Ðnd that the various methods are all Igenerally0
quite reliable, apart from occasional outliers which serve to
inÑate the s2 values for the comparisons. Coupled with our
distance zero point, our comparisons with methods tied to
the distant Hubble Ñow yield values of H in the range
72È86 km s~1 Mpc~1. The comparison with 0SN Ia suggests
values between 72 and 80, and D -p and TF call for values
n over H continues, but
around 86. Thus, the controversy
0
the famous ““ factor of 2 ÏÏ is now a factor of 20%.
Although the SBF survey is still a work in progress, it is
near enough to completion that the calibration presented in
this paper should not change in any signiÐcant way. Future
papers in this series will use the SBF survey distances to
address such issues as the velocity Ðeld of the Local Supercluster and a direct determination of H , bulk Ñows, the
Great Attractor, and the speciÐc details of0our SBF analysis
method, including comprehensive listings of our (V [I)
0
and distance measurements for individual galaxies.
We would like to thank many people for collecting SBF
and photometry observations for us : Bob Barr, Andre Fletcher, Xiaohui Hui, Gerry Luppino, Mark Metzger, Chris
Moore, and Paul Schechter. This research was supported
by NSF grant AST 94-01519, and A. D. acknowledges the
support of the National Science Foundation through grant
AST 92-20052.
No. 2, 1997
SBF SURVEY OF GALAXY DISTANCES. I.
413
REFERENCES
Aaronson, M., Huchra, J., Mould, J., Schechter, P., & Tully, R. B. 1982,
Pahre, M. A., & Mould, J. R. 1994, ApJ, 433, 567
ApJ, 258, 64
Phillips, M. M. 1993, ApJ, 413, L105
Ajhar, E. A., & Tonry, J. L. 1994, ApJ, 429, 557
Poulain, P., & Nieto, J-L. 1994, A&AS, 103, 573
Burstein, D., & Heiles, C. 1984, ApJS, 54, 33
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992,
Buta, R., & Williams, K. L. 1995, AJ, 109, 543
Numerical Recipes (2d ed. ; New York : Cambridge Univ. Press)
Buzzoni, A. 1993, A&A, 275, 433
Riess, A. G., Press, W. H., & Kirshner, R. P. 1995, ApJ, 438, L17
ÈÈÈ. 1995, ApJS, 98, 69
Ruiz-Lapuente, P. 1996, ApJ, 465, L83
Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245
Saha, A., et al. 1995, ApJ, 438, 8
Ciardullo, R., Jacoby, G. H., & Tonry, J. L. 1993, ApJ, 419, 479
Saha, A., Sandage, A., Labhardt, L., Tammann, G. A., Macchetto, F. D., &
Cohen, J. G., Frogel, J. A., Persson, S. E., & Elias, J. H. 1981, ApJ, 249, 481
Panagia, N. 1996a, ApJ, 438, 8
de Vaucouleurs, A., & Longo, G. 1988, Univ. Texas Monog. 5
Saha, A., et al. 1996b, ApJ, 466, 55
de Vaucouleurs, G., de Vaucouleurs, A., Corwin, H. G., Jr., Buta, R. J.,
Sandage, A., & Tammann, G. A. 1993, ApJ, 415, 1
Paturel, G., & Fouque, P. 1991, Third Reference Catalog of Bright
Sandage, A., Saha, A., Tammann, G. A., Labhardt, L., Panagia, N., &
Galaxies (New York : Springer)
Macchetto, F. D. 1996, ApJ, 460, L15
Dressler, A. 1993, in Proc. 9th Astrophys. Meeting, ed. F. R. Bouchet &
Schechter, P. L., Mateo, M., & Saha, A. 1993, PASP, 105, 1342
Marc Lachieze-Rey (Gif-sur-Yvette Cedex : Editions Frontie`res), 9
Schneider, D. 1996, private communication
Eastman, R. G, Schmidt, B. P., & Kirshner, R. P. 1996, ApJ, 466, 911
Silbermann, N. A., et al. 1996a, preprint
Faber, S. M., Wegner, G., Burstein, D., Davies, R. L., Dressler, A., LyndenSilbermann, N. A., et al. 1996b, poster presented at the STScI meeting on
Bell, D., & Terlevich, R. J. 1989, ApJS, 69, 763
the Extragalactic Distance Scale, 1996 May
Ferrarese, L., et al. 1996, ApJ, 464, 568
Simard, L., & Pritchet, C. J. 1994, ApJ, 107, 503
Freedman, W. L. 1989, AJ, 98, 1285
Sodemann, M., & Thomsen, B. 1995, AJ, 110, 179
Freedman, W. L., & Madore, B. F. 1990, ApJ, 365, 186
ÈÈÈ. 1996, AJ, 111, 208
Freedman, W. L., et al. 1994, ApJ, 427, 628
Tammann, G. A. 1992, Phys. Scr., T43, 31
Graham, J. A., et al. 1996, in preparation
Tanvir, N., et al. 1995, Nature, 377, 27
Green, E. M., Demarque, P., & King, C. R. 1987, The Revised Yale
Tiede, G. P., Frogel, J. A., & Terndrup, D. M. 1995, AJ, 110, 2788
Isochrones and Luminosity Functions (Yale : New Haven)
Tonry, J. L. 1991, ApJ, 373, L1
Hamuy, M., Phillips, M. M., Maza, J., Suntze†, N. B., Schommer, R. A., &
Tonry, J. L., Ajhar, E. A., & Luppino, G. A. 1989, ApJ, 346, L57
Aviles, R. 1995, AJ, 109, 1
ÈÈÈ. 1990, AJ, 100, 1416
Hughes, S. M. 1996, private communication
Tonry, J. L., & Davis, M. 1981, ApJ, 246, 680
Jacoby, G. H., et al. 1992, PASP, 104, 599
Tonry, J. L., Luppino, G. A., & Schneider, D. P. 1988, in Proc. ASP
Jacoby, G. H., Ciardullo, R., & Harris, W. E. 1996, ApJ, 462, 1
Meeting on The Extragalactic Distance Scale, ed. S. van den Bergh &
Jensen, J. B., Luppino, G. A., & Tonry, J. L. 1996, ApJ, 468, 519
C. Pritchet (New York : AIP), 1
Landolt, A.U. 1992, AJ, 104, 340
Tonry, J. L., & Schneider, D. P. 1988, AJ, 96, 807
Lorenz, H., Bohm, P., Capaccioli, M., Richter, G. M., & Longo, G. 1993,
Tully, R. B. 1996, private communication
A&A, 277, L15
Worthey, G. 1993a, ApJ, 409, 530
Luppino, G. A., & Tonry, J. L. 1993, ApJ, 410, 81
ÈÈÈ. 1993b, ApJ, 418, 947
Lynden-Bell, D., et al. 1988, ApJ, 326, 19
ÈÈÈ. 1994, ApJS, 95, 107
Metzger, M. R., Tonry, J. L., & Luppino, G. A. 1993, ASP. Conf. Ser., 52,
ÈÈÈ. 1996, private communication
300
Yi, S. 1996, private communication