5.4 The Cepheid-Calibrated Extragalactic Distance Scale

Establishing accurate extragalactic distances has provided an immense challenge to astronomers since the 1920's. The situation has improved dramatically as better (linear) detectors have become available, and as several new, promising techniques have been developed. For the first time in the history of this difficult field, relative distances to galaxies are being compared on a case-by-case basis, and their quantitative agreement is being established. Several, detailed reviews on this progress have been written (see, for example, the conference proceedings for the Space Telescope Science Institute meeting on the Extragalactic Distance Scale edited by Donahue and Livio 1997).

The Hubble Space Telescope (HST) Key Project on H₀ has been designed to undertake the calibration of a number of secondary distance methods using Cepheid variables (Freedman et al. 1994; Kennicutt, Freedman & Mould 1995; Mould et al. 1995). Briefly, there are three primary goals: (1) To discover Cepheids, and thereby measure accurate distances to spiral galaxies suitable for the calibration of several independent secondary methods. (2) To make direct Cepheid measurements of distances to three spiral galaxies in each of the Virgo and Fornax clusters. (3) To provide a check on potential systematic errors both in the Cepheid distance scale and the secondary methods. The final goal is to derive a value for the the Hubble constant, to an accuracy of 10%. Cepheids are also being employed in several other HST distance scale programs (e.g., Sandage et al. 1996; Saha et al. 1994, 1995, 1996; and Tanvir et al. 1995).

In Freedman, Madore & Kennicutt (1997), a comparison of Cepheid distances is made with a number of other methods including surface-brightness fluctuations, the planetary nebula luminosity function, tip of the red giant branch, and type II supernovae. (Extensive recent reviews of all of these methods can be found in Livio and Donahue (1997); by Tonry; Jacoby; Madore, Freedman & Sakai; Kirshner). In general, there is excellent agreement amongst these methods; the relative distances agree to within ±10% (1-). The use of both type Ia and type II supernovae for the purposes of determining H₀ are described in this volume by Filippenko.

The results of the H₀ Key Project have been summarized recently by Freedman, Madore & Kennicutt (1997); Mould et al. (1997); and Freedman (1997). For somewhat different views, see Sandage & Tammann (1997). The remarks in the rest of this section follow Freedman (1997). At this mid-term point in the HST Key Project, our results yield a value of H₀ = 73 ± 6 (statistical) ± 8 (systematic) km/sec/Mpc. This result is based on a variety of methods, including a Cepheid calibration of the Tully-Fisher relation, type Ia supernovae, a calibration of distant clusters tied to Fornax, and direct Cepheid distances out to ~ 20 Mpc. In Table 2 the values of H₀ based on these various methods are summarized.

Table 2. SUMMARY OF KEY PROJECT RESULTS ON H₀

Method	H0
Virgo	80 ± 17
Coma via Virgo	77 ± 16
Fornax	72 ± 18
Local	75 ± 8
JT clusters	72 ± 8
SNIa	67 ± 8
TF	73 ± 7
SNII	73 ± 7
DN -	73 ± 6
Mean	73 ± 4
Systematic Errors	± 4	± 4	± 5	± 2
	(LMC)	([Fe/H])	(global)	(photomteric)
Current values of H0 for various methods. For each method, the formal statistical uncertainties are given. The systematic errors (common to all of these Cepheid-based calibrations) are listed at the end of the table. The dominant uncertainties are in the distance to the LMC and the potential effect of metallicity on the Cepheid period-luminosity relations, plus an allowance is made for the possibility that the locally measured value of H0 may differ from the global value. Also allowance is made for a systematic scale error in the photometry which might be affecting all software packages now commonly in use. Our best current weighted mean value is H0 = 73 ± 6 (statistical) ± 8 (systematic) km/sec/Mpc.

These recent results on the extragalactic distance scale are very encouraging. A large number of independent secondary methods (including the most recent type Ia supernova calibration by Sandage et al. 1996) appear to be converging on a value of H₀ in the range of 60 to 80 km/sec/Mpc. The long-standing factor-of-two discrepancy in H₀ appears to be behind us. However, these results underscore the importance of reducing remaining errors in the Cepheid distances (e.g., those due to reddening and metallicity corrections), since at present the majority of distance estimators are tied in zero point to the Cepheid distance scale. A 1- error of ±10% on H₀ (the aim of the Key Project) currently amounts to approximately ± 7 km/sec/Mpc, and translates into a 95% confidence interval on H₀ of roughly 55 to 85 km/sec/Mpc.

While this is an enormous improvement over the factor-of-two disagreement of the previous decades, it is not sufficiently precise, for example, to discriminate between current models of large scale structure formation, to resolve definitively the fundamental age problem, or to settle the question of a non-zero value of . Before compelling constraints can be made on cosmological models, it is imperative to rule out remaining sources of systematic error in order to severely limit the alternative interpretations that can be made of the data. The spectacular success of HST, and the fact that a value of H₀ accurate to 10% (1-) now appears quite feasible, also brings into sharper focus smaller (10-15%) effects which were buried in the noise during the era of factor-of-two discrepancies. Fortunately, a significant improvement will be possible with the new infrared capability afforded by the recently augmented near-infrared capabilities of HST (the NICMOS instrument). Planned NICMOS observations will reduce the remaining uncertainties due to both reddening and metallicity by a factor of 3.