W. L. Freedman
Carnegie Observatories, 813 Santa Barbara St., Pasadena, CA 91101
Keywords: distances, Cepheids, galaxies, cosmology
The expansion rate or Hubble constant, H
, determines both the
expansion time scale and the size scale of the Universe. The expansion
rate also constrains estimates of the amount of dark matter in the
Universe, the density of baryons produced in the Big Bang, and early
structure formation in the Universe. Hence, the present lack of an
accurately determined value of H
impacts many areas in astronomy,
physics, and cosmology, and the determination of an accurate value of
H
remains of very high priority. In the mid-1970's, providing a
solution to this problem was a prime consideration in determining the
final aperture size for the Hubble Space Telescope (HST). The
aperture size was set to allow the discovery of Cepheid variable stars
in galaxies as distant as the Virgo cluster. In the mid-1980's, the
Space Telescope Science Institute Working Group on galaxies specified
the measurement of the Hubble constant as one of the top priority,
`Key Projects', to be carried out by the HST. The goal of the Key
Project on the extragalactic distance scale is to provide a
measurement of the Hubble constant to an accuracy of 10
.
The underlying basis of the Key Project rests upon measuring accurate distances to galaxies using the period-luminosity (PL) relation for Cepheid variables. (For recent reviews of the Cepheid distance scale see Feast & Walker (1987), Madore & Freedman (1991), Jacoby et al. (1992), and Freedman & Madore (1996).) The goals of the Key Project are described in detail in Kennicutt, Freedman & Mould (1995). Briefly, the strategy adopted by our Key Project team has three primary objectives:
1) Discovery of Cepheids and measurement of distances to about two dozen nearby spiral galaxies with distances in the approximate range of 4 < d < 20 Mpc. The distances of these primary galaxies will be used to calibrate several secondary distance techniques which then extend out to distances in the range of 20 to 100 or more Mpc (for example, the Tully-Fisher relation, surface brightness fluctuations, the planetary nebula luminosity function, and supernovae of both types Ia and II).
2) Discovery of Cepheids and measurement of the distances to galaxies in the two nearby clusters of Virgo and Fornax.
3) To test for systematic effects in the measurement of extragalactic distances. For example, we are undertaking a) external checks on the zero point of the Cepheid period-luminosity relation, b) tests for a dependence of the Cepheid zero point on heavy element abundance, and c) a search for systematic errors in the various secondary indicators.
Results from this Key Project to date are briefly described below. In addition, new HST results using the tip of the red giant branch (TRGB) have been obtained for NGC 3379 in the Leo I group. These results are also briefly described. Other HST programs to measure distances to galaxies are covered elsewhere in this volume (the Cepheid calibration of type Ia supernovae by Gustav Tammann, and Cepheid distances to two spiral galaxies in the Leo I group by Nial Tanvir).
The first target in the Key Project sample was the nearby galaxy M81,
and a search for Cepheids in this galaxy was undertaken in Cycles 1
and 2, prior to the refurbishment mission. These observations were
undertaken to provide a test of the new discovery algorithms (Madore
& Freedman 1996, in preparation). These algorithms were designed to
detect Cepheids with a range of initially unknown periods, using a
minimum of spacecraft time, and further restricted by the small
(approximately 60-day) observing windows available only once in any
given year. Thirty Cepheids were discovered in two fields searched in
M81 and a reddening-corrected distance modulus of 27.80 
0.20 mag
was derived (Freedman et al. 1994b). Previous ground-based
attempts to discover variables in this galaxy yielded only two
confirmed Cepheids, one of which was intentionally targeted by the Key
Project as a test of the search procedure. This Cepheid was recovered
and confirmed to have a period in agreement with the more extensive
ground-based determination derived from decades worth of data.
Immediately following the December 1993 repair mission, BVR images of
the Virgo spiral galaxy M100 were obtained as part of a collaboration
between the WFPC2 IDT and the Distance Scale Key Project team.
ALLFRAME photometry was obtained for over 30,000 stars. By overlaying
the position of the mean Cepheid instability strip on the resulting
color-magnitude diagrams, it was possible to demonstrate that stars
were present with the magnitudes and colors expected for Cepheid
variables at the distance of the Virgo cluster. Given this success, a
sequence of 12 V and 4 I exposures was begun in April 1994. Twenty
high signal-to-noise Cepheid variables were found (Freedman et
al. 1994a). Allowing for the uncertainty in the position of M100
with respect to the Virgo cluster core, in addition to the uncertainty
in the Virgo cluster recession velocity, a preliminary value of the
Hubble constant of H
= 80 
17 
Mpc
was determined. A
discussion of the random and systematic errors in this estimate was
given by Freedman et al. (1994b). Recently, a new determination of the
distance to M100 has been made based on a larger sample of over 50
Cepheids and an improved calibration (Ferrarese et al. 1996). A
value of 15.8 
1.5 Mpc is obtained, in good agreement, to within
the measurement uncertainties, with the earlier value.
Other galaxies currently being analyzed as part of the HST Key Project include NGC 925 in the NGC 1023 Group (Silbermann et al. 1996, in preparation); NGC 3351 in the Leo I group (Graham et al. 1996, in preparation); two fields in M101, discussed above in the context of extending the metallicity test (Kelson et al. 1996, Stetson et al. 1996, in preparation, Kennicutt et al. 1996, in preparation); NGC 7331 (Hughes et al. 1996, in preparation), a Tully-Fisher calibrator in the field; NGC 4414 (Turner et al. 1996, in preparation), a distant and fairly inclined early-type spiral useful for calibrating a number of secondary methods including type Ia supernovae; and most recently, NGC 1365, a galaxy in the Fornax cluster (Madore et al. 1996, Silbermann et al. 1996 in preparation).
Instrumental light curves for two Cepheids, newly discovered in NGC 1365 are presented in Figure 1. These are the first Cepheids ever detected in the Fornax cluster. Analysis of these data is currently underway.
Figure: Instrumental F555W
light curves for 2 Cepheids in the barred spiral galaxy NGC 1365 in Fornax.
An I-band Tully-Fisher relation is presented in Figure 2. The
ground-based distances presented in Freedman (1990) (for M33, M31, NGC
300, and NGC 2403) have been supplemented with those for M81 Freedman
et al. (1994b), NGC 247 (Catanzarite et al. 1996), M100 (Ferrarese
et al. 1996), NGC 4536 (Saha et al. 1996, in preparation), NGC 4539
(Sandage et al. 1996, in preparation). The dispersion in this
relation amounts to only 
0.25 mag rms. This small measured dispersion
is encouraging; it does not appear to support the claims of Sandage (1988),
for example, who argued that the dispersion in the Tully-Fisher relation
was as high as 1.0 mag, and thus of limited value for the determination
of accurate distances.
Figure: Absolute I-band
Tully-Fisher relation for galaxies with Cepheid distances. Plotted
are absolute I-band magnitudes versus the logarithm of the HI-line
width.
One of the goals of the H
Key Project is to provide external
checks of the zero point of the Cepheid distance scale. A completely
independent (Population II) method for measuring the distances to
nearby resolved galaxies is that of measuring the position of the tip
of the red giant branch (TRGB). A recent application of the TRGB
method was undertaken by Lee, Freedman & Madore (1993). In this
study, published Cepheid and RR Lyrae distances to 10 nearby galaxies
were compared to the distances obtained using the TRGB. A remarkable
agreement between the two methods was found, at a level of 
0.1
mag. New TRGB distances have been obtained for two additional dwarf
irregular galaxies, Sextans A and Sextans B (Sakai, Madore & Freedman
1995a,b). The TRGB distances to these galaxies again are in excellent
agreement with the Cepheid distances. Recently Lee (1995a,b) has
measured TRGB distances to the dwarf galaxies LGS3 and Leo II. More
details of this method and its application are given in the above
references. Simulations aimed at understanding the limits to this
method were undertaken and published by Madore & Freedman (1995).
The most distant application of this method to date is based on deep
HST WFPC2 V and I imaging of the giant elliptical galaxy NGC 3379 in
the Leo I group (Sakai et al. 1996, in preparation). The TRGB
distance of 11.2 
0.8 Mpc agrees well with a recent Cepheid-based
distance of 11.6 
0.08 mag to NGC 3368, which is also apparently
a member of the Leo I group (Tanvir et al. 1995).
The relative accuracy of the TRGB method has now been established to
be comparable to that of the other most accurate primary indicators,
the Cepheids and RR Lyraes. While the TRGB stars are not as bright as
the brightest Cepheids, they are 4 magnitudes brighter than RR Lyrae
stars. A significant advantage, however, is that unlike Population I
Cepheids which are found only in spiral galaxies, the TRGB can be
observed in galaxies of all morphological types, including elliptical
galaxies (as well as spirals and irregulars). Hence, the TRGB
provides a direct means of calibrating secondary methods such as
surface brightness fluctuations, the planetary nebula luminosity
function, or the D
relation, and is likely to play an
important role in future applications to the extragalactic distance
scale.
Figure: A comparison of
true distance moduli using Cepheid variables and the TRGB method. The
unit-slope line is plotted for reference; it is not a fit to the data.
A distance to the Leo I group is important for the calibration of
several secondary indicators including the Tully-Fisher relation,
surface brightness fluctuations, the planetary nebula luminosity
function, and the D
-
relation. A calibration of all of
these methods has been undertaken by Sakai et al. (1996). The
methods all yield good relative agreement with a value of H
70 
9
Mpc
.
Our results to date stand in contrast to those of the group led by
Allan Sandage based on a Cepheid calibration of type Ia supernovae.
Currently this group estimates a value of the Hubble constant of about
55--60 kilometers/second/Megaparsec (see the contribution by Gustav
Tammann, this volume, p. 
).
Understanding the source of this discrepancy is critical. In this regard, Fornax is a particularly important cluster for a number of reasons. Being a very compact cluster, Fornax will provide a calibration of several secondary methods. In particular, it contains two very well-observed recent type Ia supernovae which will allow a direct comparison between type Ia distance scale and other well-studied secondary indicators with small measured dispersions (like the Tully-Fisher relation, surface brightness fluctuations, and planetary nebula luminosity function).
Over the next two years, a considerable amount of important work
remains for the Key Project. The project has been designed to
confront outstanding discrepancies, to test for potential systematic
errors, and to measure and compare values of the Hubble constant based
on a variety of independent and different methods. Cepheid
calibration of type Ia supernovae and several other additional
secondary methods are all part of the core of the Key Project.
Our most recent results show that measurement of Cepheid distances in
the Virgo and Fornax clusters are feasible, and that the entire Key
Project is viable. The recent progress in measuring extragalactic
distances, both from the ground and from space, has been enormous.
These new results from the Hubble Space Telescope provide solid
reasons to be optimistic that within the next few years, we will have
measured a value of H
to within 
10
and thereby solved
one of the outstanding cosmological problems of this century.
This work has been partially supported by NSF grants AST 87-13889 and 91-16496, and by NASA through grant number GO-2227 from the Space Telescope Science Institute, which is operated by the AURA, Inc., under NASA contract NAS5-26555. I sincerely acknowledge the enormous contribution of my collaborators on the HST Key Project team: R. Kennicutt, J. Mould, F. Bresolin, L. Ferrarese, H. Ford, J. Graham, M. Han, P. Harding, J. Hoessel, R. Hill, J. Huchra, S. Hughes, G. Illingworth, D. Kelson, B.F. Madore, R. Phelps, A. Saha, N. Silbermann, P. Stetson, and A. Turner. We also acknowledge the substantial contributions and participation of the late Marc Aaronson who led the team when it was formed.
Catanzarite, J., Freedman, W. L., Madore, B. F., & Horowitz, I. 1996, in preparation
Feast, M. & Walker, A.R. 1987, ARA&A, 25, 345
Ferrarese, L. et al. 1996, ApJ, in press
Freedman, W. L. 1990, ApJ, 355, L35
Freedman, W.L. et al. 1994a, ApJ, 427, 628
Freedman, W.L. et al. 1994b, Nature, 371, 757
Freedman, W.L. et al. 1994c, ApJ, 435, L31
Freedman, W. L. & Madore, B. F. 1996, in Clusters, Lensing, and the Future of the Universe, ed. V. Trimble, Publs. Astron. Soc. Pacif. Conf. Series. in press
Graham, J. et al. 1996, in preparation
Hughes, S. M. et al. 1996, in preparation
Kelson, D. et al. 1996, in press
Lee, M. G. 1995a, AJ, 110, 1129
Lee, M. G. 1995b, AJ, 110, 1155
Madore, B. F. & Freedman, W. L. 1995, AJ, 90, 1104
Madore, B. F. et al. 1996, in preparation
Sakai, S., Madore, B. F., & Freedman, W. L. 1995a, AJ, in press
Sakai, S., Madore, B. F., & Freedman, W. L. 1995b, AJ, in preparation
Sakai, S., Madore, B. F., Freedman, W. L., Lauer, T. & Baum, W. 1996, in preparation
Sandage, A. 1988, Ap.J. 331 605
Silbermann, N. et al. 1996, in preparation
Stetson, P. B. et al. 1996, in preparation
Tanvir, N.R. et al. 1995, Nature, 377, 27
Turner, A. et al. 1996, in preparation