DISTANCE INDICATORS, EXTRAGALACTIC R. BRENT TULLY There are two principal reasons for the great interest in the extragalactic distance scale. In the first place, the distances of objects must be known if we are to have a correct understanding of their properties, such as their masses or the energy that they produce. In the second place, the scale of the universe is linked with the age of the universe, and there is some difficulty in reconciling several different kinds of observations in the context of the standard world model. This review elaborates upon certain aspects of the entry Cosmology, Observational Tests. DISCOVERY OF AN EXPANDING UNIVERSE It was first firmly established that galaxies were independent selfgravitating islands of stars at large distances in 1925, when Edwin Hubble found that the Andromeda nebula (now called the Andromeda galaxy) and Messier 33 (M33) contained a certain kind of pulsating star ons of called a Cepheid variable. It had been known from observations of the same kind of objects in the Small Magellanic Cloud made by Henrietta Leavitt in 1912 that the pulsation periods are closely correlated with the luminosities of the stars. Those that brighten and dim over a hundred days are intrinsically brighter by a factor of 20 than those that perform similar oscillations over a few days. The critical perception by Hubble was to appreciate that the pulsating objects in the separate systems were basically the same, but dimmed in Andromeda and M33 because of the very much greater distances. Just a few years later, in 1929, Hubble made a second remarkable discovery that the spectra of almost all galaxies are displaced from our expectations based on laboratory experiments in the sense that the wavelengths of familiar spectral features are displaced toward longer values. Because observations at the time were only in the optical passband of the electromagnetic spectrum and the color red is at the long-wavelength limit of this band, the effect came to be called the redshift. The corollary of Hubble's discovery was that this redshift is larger for galaxies that are fainter and, hence, farther away. A description of the linear relationship between redshift and distance is given by the equation *********************, where ******* is the spectral displacement, d is the distance of the object, c is the velocity of light, and H* is the Hubble constant. The subscript O indicates that we are referring to the present epoch. The standard interpretation of this redshift posits that the universe is in expansion, so systems that are farther away from an observer are rushing away with higher velocity, whence cz is a relative velocity. The value of the Hubble constant is a measure of the scale of the universe, as it is the link between the observed relative velocities, or redshifts, of galaxies and their separations. Indeed, once the Hubble constant has been determined reliably, then the distance of a galaxy can be found by calculating the quotient of the galaxy's redshift divided by the Hubble constant. The smaller the value of the Hubble constant, the greater the distance between galaxies and, hence, the larger the observable universe. The inverse of the Hubble constant, *****, is a measure of the age of the universe, because taking the simplest case, if objects with known separation are moving apart at constant velocity, the time when they were at the same point is defined. HISTORICAL DEVELOPMENT OF THE MEASUREMENT OF Ho The generally accepted value of the Hubble constant was revised radically during the first two decades after World War II, from a value of around 500 kilometers per second per megaparsec (******************* where ************) to a value that, over the last two decades, has been argued to lie between 50 and 100 km *********. One of the reasons for the drastic downward revision was the determination that the Cepheids observed in Andromeda, M33, and the Small Magellanic Cloud are, in fact, not exactly the same as the stars with similar behavior that are close by and provided the distance calibration. Hubble's idea was right, but observers were fooled by a quirk that two kinds of stars have similar properties. Moreover, in more distant galaxies where the pulsating Cepheids could not be seen, astronomers had been confusing star clusters and emission nebulae individual stars, resulting in underestimated distances. ALTERNATIVE DISTANCE ESTIMATORS The example of the Cepheid variable was provided as a means of estimating distances. The correlation between the pulsation period and intrinsic luminosity emitted by such objects is so tight that the root-mean-square (rms) scatter corresponds to only a 10% uncertainty in distance and, if detailed information is available on a few dozen stars in a single galaxy, a distance with an internal error of only a few percent is possible. Systematic errors because of problems with intervening obscuration and scale calibration should be restricted to less than 10%. Unfortunately, Cepheid stars are not sufficiently bright to be easily detected in any but the nearest galaxies. There are other stars called RR Lyrae variables that also have well-delineated luminosities, hut they are even fainter and more difficult to find at large distances. (Objects with such well-defined properties can be called "standard candles.") About 10 galaxies within 4 Mpc have accurately known distances through the pulsating star methods. However, this limited domain is not relevant for the determination of the Hubble constant, because the nearest galaxies have relative motions that are dominated by local gravitational influences rather than the overall expansion of the universe. It is usually considered necessary to study objects beyond 10 Mpc to have a hope of measuring H*. Until recently, there were no well-calibrated standard candles that were useful at these distances. All that were available were less-precise distance estimators, such as upper limits on the luminosities of the brightest stars in a single galaxy, or morphological characteristics of galaxies related to their intrinsic brightness, or a tendency for clusters of old stars to have integrated luminosities that might be the same from galaxy to galaxy. Supernovae provide interesting possibilities as distance estimators, because they are so bright and can be seen at great distances. There is a particular kind, called Type Ib, that are especially promising as distance estimators because they appear to be restricted to a narrow range in luminosity at maximum light. The progenitors of the explosive event are taken to be white dwarf stars that are accreting mass from a close companion in a binary star system. If the white dwarf gathers enough mass from the companion to exceed the Chandrasekhar limit of 1.4 solar masses, then the inward pull of gravity overcomes the outward pressure provided by the lattice of degenerate matter that has supported the white dwarf. The subsequent free-fall collapse of the core to the state of a neutron star releases energy that is transferred to shocks that blow off the outer envelope. The precise mass of the progenitor at the time of the explosion might explain the limited range of observed luminosity maxima. Though there is growing evidence that Type Ib supernovae are good standard candles, the problem remains that they must he calibrated. If a strictly empirical approach is taken, then good distances to a few nearby galaxies with Type Ib events must be known by alternative techniques. However, the situation in this regard is not satisfactory because supernovae are so rare. Alternatively, the luminosity of the supernova event can be reckoned from theoretical calculations. Such considerations lead to low values for **, implying a relatively large and old universe. However, these results are contradicted somewhat by results that will be discussed next. This contradiction means that either there is a problem with the theoretical supernova calculations or with the train of the ensuing discussion. TULLY-FISHER, FABER-JACKSON, AND PLANETARY NEBULA METHODS It can be argued that a value for ** at the level of 20% uncertainty is at hand. There appear to be several precision distance estimators that are giving consistent results and suggest that ** is on the high side of the range of modern values. The technique with the longest history as a precision distance tool is based on the Tully-Fisher relation. This method draws upon an empirically observed correlation between a measure of the internal motion of galaxies and their luminosities (see Fig.1). The physical basis for the correlation is related to the fact that both motions and luminosities are tied to the mass of a system: More-massive galaxies are more luminous and rotate faster than less-massive galaxies. A simple measure of the internal motion of a spiral galaxy is given by the width of the neutral-hydrogen spectral line at wavelength 21 cm. This line is emitted by cold interstellar gas moving in near-circular orbits. The global width of this line is an observable directly related to the mass of the system and is unaffected by distance. The luminosity measured at optical or near-infrared bands depends on the number of ordinary stars and fades as the square of the distance. Depending on the authority, the luminosity-line width correlation has a dispersion that might be as low as to correspond to an rms uncertainty of only 15% or as high as to correspond to an uncertainty of 60%. If errors are anything like the optimistic expectation, then the true dispersion cannot be calibrated by other methods, which are inferior, and can only be ascertained by drawing samples from a few nearby clusters, where there are many galaxies at essentially the same distance. The optimistic expectation is sustained by studies of several well-defined samples. However, the dispersion has been found to be substantial in the direction of the Virgo cluster. This cluster has historically played a key role in the study of the distance scale because it is nearby and contains hundreds of members. At present, there is an ongoing debate. One viewpoint holds that we can measure distances accurately and that many of the objects in the line of sight toward the Virgo cluster are actually in the background. Hence, the observed scatter is large because of our inability to discriminate in favor of true members when the sample is chosen. The other viewpoint holds that the luminosity-line width distance estimator breaks down in the cluster environment, presumably because galaxy properties are altered, so our distance estimates are unreliable. There appears to be a way to choose between these possibilities. Overwhelmingly, the background contaminants should be gas-rich spiral systems, as these kinds of galaxies are the dominant population outside the environment of rich clusters. Gas-poor ellipticals in the region should lie in the cluster, and distance estimates to these objects should not suffer from the contamination problem. In recent developments, methods have been found to establish good distances to elliptical galaxies. The Faber-Jackson relation for gas-poor systems has the same physical basis as the Tully-Fisher relation for gas-rich systems. However, in lieu of measuring the motions of gas in near-circular orbits, one observes the spectral dispersion caused by the random motions of stars in a system with little global angular momentum (e.g., an elliptical galaxy). This measure related to the mass of the system is again correlated with the global luminosity, though the dispersion about the mean relation is greater and provides a less accurate distance estimate. However, it was subsequently found that the Faber-Jackson relation could be modified by incorporation of a third observable, a measure of the dimension of the system, and the improved relationship can provide distance estimates with rms uncertainties of 15%. There is a dearth of nearby ellipticals, but it appears possible to calibrate the zero point of the relationship using a reasonably reliable distance to a small group of galaxies in Leo that contains two ellipticals. In this manner, a distance is found for the Virgo cluster of 15 Mpc, which is a value in good agreement with the distance derived from gas-rich systems if the background contamination hypothesis is accepted. Finally, a promising new procedure is based on properties of a phase of stellar death that produces planetary nebulae. The stars eject matter that is subsequently illuminated by the star. Observations of this envelope are made in a spectral emission line of oxygen. There appears to be an abrupt high-luminosity cutoff in the nebular emission corresponding to a central star with about two-thirds of a solar mass. The limit is presumably due to the combined statistics of the evolution time scale for the planetary nebula phase, which decreases sharply for more massive stars, and the number of stars at a given mass which, again, decreases toward high mass. This cutoff can be established in galaxies at moderate distances and the displacement in luminosity with respect to the calibration gives a distance. To date, distances have been established to about a dozen galaxies with this method, and the agreement with the other precision estimates is excellent. Most recently, this method has been used to derive a distance to the Virgo cluster of 15 Mpc. SUMMARY There has been an ongoing dispute over the value of the Hubble constant, which provides a measure of the distances between galaxies. Modern estimates range between 50 and 100 km ****Mpc**. Now there are consistent measurements that place the Virgo cluster at a distance of 15 Mpc***10%. Some of the earlier dispute must be attributed to the background contamination problem. If the presently postulated distance for the cluster is sustained, then a value for the Hubble constant can be determined, since the Virgo cluster has a velocity (corrected for flow motions) of 1300 ********10%. Hence, ******** km s**Mpc**14%. Perhaps the greatest additional uncertainty is in the corrections necessary to account for flow patterns and random motions. However, if techniques compatible with those that lead to the Virgo cluster distance are used for other samples, consistent results are found. The corresponding characteristic age for the universe is *********** billion years (estimated 95% probability). In the standard model with ****, if the density is equal to the critical value for closure (preferred by some theories), the age of the universe would be **** billion years, and if the density is equal to 10% of the critical value (comparable with observations), the universe would be ***** billion years old. This estimate is in only marginal agreement with values of 13-18 billion years for the oldest star clusters in the Galaxy, which cannot be older than the universe. We are not compelled to consider more elaborate models of the universe, given the uncertainties, but the situation is not satisfactory. If the proposed distance scale is correct, then Type Ib supernovae are less bright than anticipated by theory by almost a factor of 2. Additional Reading Madore, B.F. and Tully, R.B., eds.(1986). Galaxy Distances and Deviations from Universal Expansion. Reidel, Dordrecht. Rowan-Robinson, M.(1985). The Cosmological Distance ladder. W.H. Freeman, New York. Van Den Bergh, S.(1975). The extragalactic distance scale. In Galaxies and the Universe, A. Sandage, M. Sandage, and J. Kristian, eds. University of Chicago Press, Chicago, p.509. Van Den Bergh, S. and Pritchet C.J.(1988). The Extragalactic Distance Scale (Astronomical Society of the Pacific Conference Series No.4). Brigham Young University Press, Provo, UT.