Abstract
Establishing accurate extragalactic distances has provided an immense challenge to astronomers since the 1920s. The situation has improved dramatically as better 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. New instrumentation, the development of new techniques for measuring distances, and recent measurements with the Hubble Space telescope all have resulted in new distances to galaxies with precision at the ±5–20% level. The current statistical uncertainty in some methods for measuring H0 is now only a few percent; with systematic errors, the total uncertainty is approaching ±10%. Hence, the historical factor-of-two uncertainty in the value of the H0 is now behind us.
Though there has been remarkable progress in measuring the cosmological parameters, the accuracy of these quantities is determined by the available technology and measurement techniques and is still not sufficiently high to discriminate among the various existing world models (1). Because of the fundamental dependence on the cosmological parameters in all of the models, accurate determinations are critical to make reliable predictions based on the current models. For instance, a reliable value of the Hubble constant is required to constrain the density of baryons from nucleosynthesis at an early epoch of the universe. The Hubble constant sets the time and length scale at the epoch of equality of the energy density of matter and radiation. In the structure formation paradigm based on gravitational instability, the horizon scale at matter-radiation equality specifies the critical range of the density perturbation spectrum turnover, and an accurate knowledge of the Hubble constant allows a quantitative comparison of the anisotropies in the cosmic background radiation and theories of the large-scale structure of the universe. In addition, in the issue addressed in this session, that of the age of the universe, there is a direct confrontation between the expansion age inferred from the Hubble constant in the standard model and age dating of the oldest objects in the universe. The reason for testing the cosmological model by using the age of the universe is obvious: there should be no astronomical object in the universe older than the universe itself. Consequently, the oldest objects known provide the minimum age of the universe.
What is required to measure an accurate value of H0? According to the Hubble law, what is needed are measurements of both redshifts of galaxies (via spectral lines), and distances to galaxies (at sufficiently large distances where peculiar motions relative to the smooth Hubble flow are slow). The Hubble constant then follows immediately from the slope of correlation between the redshift and distance. However, the precise determination of galaxy distances remains a longstanding fundamental problem in astronomy. In principle, measuring the distance of a distant galaxy relies on the following property of propagation of light in space: the apparent brightness of a light source varies inversely with the square of distance. Accordingly, the distance to an object may be determined by knowing its intrinsic luminosity and then comparing that with its apparent brightness.
For reviews on recent progress in measuring distances, see, for example, the conference proceedings for the Space Telescope Science Institute meeting on the Extragalactic Distance Scale edited by Donahue and Livio (2).
The Hubble Space Telescope (HST) Key Project to Measure H0
The three Key Projects for the HST were selected by peer review to enable science to be undertaken that might require large amounts of telescope time. The HST H0 Key Project was designed to measure H0 to ±10% (3–5). Rather than concentrate on a single method (which might be affected by unknown, systematic effects), the goal of the Key Project is to undertake a comparison and a calibration of several different methods so that cross-checks on both the absolute zero point as well as relative distances, and therefore on H0, can be obtained.
The underlying basis of the Key Project is the discovery of a class of well-understood stars, known as Cepheid variables. These stars obey a tight correlation between their periods of oscillation and their luminosities (see the reviews, e.g., refs. 6 and 7). With a measurement of the period and observed brightness, and a calibration of the intrinsic brightness, the distance is obtained according to the inverse-square law of light. The period-luminosity (P-L) relation is calibrated with aid of a small sample of nearby Cepheids whose absolute distances are measured in an independent way. Given an absolute calibration, distances to galaxies obtained by using Cepheids can, in turn, be used to calibrate other methods for distance determination that can be used beyond the reach of the Cepheids; these methods often are referred to as secondary methods.
The H0 Key Project has been designed with three primary goals: (i) to discover Cepheids in galaxies located out to distances of about 20 Mpc (where 1 Mpc = 3.09 × 1022 m), and thereby measure accurate distances to spiral galaxies that are suitable for the calibration of several independent secondary methods, (ii) to provide a check on potential systematic errors both in the Cepheid distance scale and the secondary methods, and (iii) to make direct Cepheid measurements of distances to three spiral galaxies in each of the Virgo and Fornax clusters (located at approximately 16–18 Mpc).
Measurement of Cepheid Distances/Calibration of Secondary Methods
The extragalactic distance scale at present is still faced with the undesirable situation that there exists no single distance indicator for which local, geometric parallax measurements can be made and for which distances can be measured sufficiently far that the smooth, cosmic Hubble expansion is being probed. Locally, the gravitational interaction between galaxies and their neighbors, in addition to larger-scale, bulk motions introduce noise or “peculiar motions” into the measured velocities of galaxies.
Determination of H0 to an accuracy of 10% requires that measurements be acquired at great enough distances and in a variety of directions so that the average contribution from motions induced by the gravitational interaction of galaxies (peculiar motions) is significantly less than 10% of the overall expansion velocity. The current limit for detection of Cepheids with HST is a distance of about 30 Mpc (or about 0.01% of the visible universe. At these distances peculiar motions still can contribute 10–20% of the observed velocity. Hence, the main thrust of the Key Project is the calibration of secondary distance indicators that can be applied out to distances significantly greater than can be measured with Cepheids alone.
With the database of Cepheid distances assembled as part of the H0 Key Project, a number of secondary indicators can be directly calibrated and tested. Several of these methods can be applied to velocity distances of 10,000 km/sec or greater. These include, for example, type Ia supernovae, type II supernovae, and the Tully-Fisher relation. Type Ia supernovae can be observed at velocity distances of beyond 30,000 km/sec, or ≈10% of the visible universe. For details on other recent results from the Key Project, see refs. 8 and 9. This preliminary calibration yields a value of H0 = 73 ± 6 (random) ± 8 (systematic) km/sec per Mpc.
One of the most promising methods for measuring relative distances to distant galaxies is based on the measurement of type Ia supernovae luminosities. These supernovae are believed to result from the explosion of a carbon-oxygen white dwarf in a binary system. (However, the details of the role of the companion star are still not well understood.) Cepheid calibrators recently have become available for this method as a result of the availability of HST (e.g., ref. 10 and references therein). Several independent studies now suggest that type Ia supernovae all do not have the same intrinsic luminosities that they were earlier suggested to have, but they appear to obey a fairly well-defined relation between the absolute magnitude or brightness at maximum light and the shape or decline rate of the supernova light curve (11–13). The H0 Key Project also is undertaking a calibration of type Ia supernovae, independently of the Sandage et al. group (see ref. 8 for a discussion of the preliminary results of this calibration).
The calibration of Cepheid extragalactic distances currently is undertaken relative to the nearby companion galaxy, the Large Magellanic Cloud, located at a distance of 50 ± 5 kpc. The new Hipparcos results are consistent at a level of 4 ± 7% with this distance, which is based on a wide range of different methods. Currently, the distance to the Large Magellanic Cloud represents one of the largest outstanding sources of systematic error in the extragalactic distance scale and determination of H0. Parallax measurements from the upcoming Space Interferometry Mission (SIM) will be critical for improving this remaining uncertainty in the calibration.
Before leaving this section, we note that for a value of the Hubble constant of 73 km/sec per Mpc, the expansion age of the universe is 9 billion years for an Einstein de-Sitter universe (where Ω0 = 1, ΩΛ = 0). In an open universe, with Ω0 = 0.3 and ΩΛ = 0, the age is calculated to be 11 billion years. Finally, for Ω0 = 0.3, ΩΛ = 0.7, an older age can be accommodated, that is, 13 billion years.
Summary
Improved new methods for measuring relative distances to remote galaxies developed over the past decade, in parallel with improvements to the calibrating Cepheid distance scale, and large new numbers of Cepheid distances now available from HST, have led to an enormous increase in the accuracy and precision with which the expansion rate, or Hubble constant, H0, can be measured.
In the near future, the satellite experiments MAP, to be launched by the National Aeronautics and Space Administration in 2000 (http://map.gsfc.nasa.gov), and Planck (http://astro.estec.esa.nl/SA-general/Projects/Planck), to be launched by the European Space Agency in 2007, will be able to measure the anisotropies of cosmic background radiation (CBR) with unprecedented accuracy. If the physics underlying the formation of CBR anisotropies is confirmed by the detection of the first acoustic peak in the angular power spectrum of CBR anisotropies (14), along with ongoing galaxy and supernova Ia searches, these complementary experiments will enable independent measurements of cosmological parameters. Though the final accuracy will depend on how well various systematic errors can be controlled or eliminated, these upcoming, promising experiments are likely to resolve definitively the essential issues in the cosmological paradigm.
Acknowledgments
Work on the H0 Key Project has been done in collaboration with the Key Project team on the Extragalactic Distance Scale. W.L.F. would like to acknowledge the contributions of R. Kennicutt, J. R. Mould (co-principal investigators), F. Bresolin, S. Faber, L. Ferrarese, H. Ford, B. Gibson, J. Graham, J. Gunn, M. Han, P. Harding, J. Hoessel, J. Huchra, S. Hughes, G. Illingworth, D. Kelson, L. Macri, B. F. Madore, R. Phelps, C. Prosser, D. Rawson, A. Saha, S. Sakai, N. Silbermann, P. Stetson, and A. Turner. This work is based on observations with the National Aeronautics and Space Administration (NASA)/European Space Agency Hubble Space Telescope, obtained by the Space Telescope Science Institute, which is operated by AURA, Inc. under NASA Contract No. 5-26555. Support for this work was provided by NASA through Grant GO-2227-87A from Space Telescope Science Institute. We would like to thank the National Academy of Sciences for a very stimulating meeting.
References
- 1.Freedman W L. In: Critical Dialogs in Cosmology. Turok N, editor. Teaneck, NJ: World Scientific; 1997. pp. 92–129. [Google Scholar]
- 2.Donahue M, Livio M, editors. The Extragalactic Distance Scale. Cambridge: Cambridge Univ. Press; 1997. [Google Scholar]
- 3.Freedman W L, Madore B F, Mould J R, Hill R, Ferrarese L, Kennicutt R C, Jr, Saha A, Stetson P B, Graham J A, Ford H, et al. Nature (London) 1994;371:757–762. [Google Scholar]
- 4.Kennicutt R C, Freedman W L, Mould J R. Astron J. 1995;110:1476–1491. [Google Scholar]
- 5.Mould J, Huchra J P, Bresolin F, Ferrarese L, Ford H C, Freedman W L, Graham J, Harding P, Hill R, Hoessel J G, et al. Astrophys J. 1995;449:413–421. [Google Scholar]
- 6.Madore B F, Freedman W L. Pub Astron Soc Pacif. 1991;103:933–957. [Google Scholar]
- 7.Jacoby G H, Branch D, Clardullo R, Davies R L, Harris W E, Pierce M J, Pritchet C J, Tonry J L, Welch D L. Pub Astron Soc Pacif. 1992;104:599–662. [Google Scholar]
- 8.Madore B F, Freedman W L, Silbermann N, Harding P, Huchra J, Mould J R, Graham J A, Ferrarese L, Gibson B K, Han M, et al. Astrophys J. 1999;515:29–41. [Google Scholar]
- 9.Freedman W L, Mould J, Kennicutt R C, Madore B F. In: Cosmological Parameters and the Evolution of the Universe, International Astronomical Union Symposium 183. Sato K, editor. Tokyo: Universal Academy Press; 1998. pp. 79–86. [Google Scholar]
- 10.Sandage A, Saha A, Tammann G A, Labhardt L, Panagia N, Macchetto F D. Astrophys J Lett. 1996;460:L15–L18. [Google Scholar]
- 11.Phillips M. Astrophys J. 1993;413:L105–L108. [Google Scholar]
- 12.Hamuy M, Phillips M M, Maza J, Suntzeff N B, Schommer R A, Aviles R. Astron J. 1995;109:1–13. [Google Scholar]
- 13.Riess A, Press W, Kirshner R. Astrophys J. 1995;438:L17–L20. [Google Scholar]
- 14.Hu W, Sugiyama N, Silk J. Nature (London) 1997;386:37–45. [Google Scholar]