In the 1920s, Edwin Hubble, using the newly constructed 100" telescope at Mount Wilson Observatory, detected variable stars in several nebulae, diffuse objects whose nature was a topic of heated debate in the astronomical community. His discovery was revolutionary for these variable stars had a characteristic pattern resembling a class of stars called Cepheid variables. Earlier, Henrietta Levitt, part of a group of female astronomers working at Harvard College Observatory, had shown there was a tight correlation between these period of a Cepheid variable star and its luminosity. Thus, Hubble by measuring the period of these stars and their fluxes was able to show that these nebula were not clouds within our own Galaxy, but were external galaxies far beyond the edge of our own Galaxy.
Hubble's second revolutionary discovery was based on his plot of the Cepheid-based galaxy distance determinations and measurements of the relative velocities of these galaxies. He showed that more distant galaxies were moving away from us more rapidly: The universe was not static, but rather was expanding. This discovery marked the beginning of the modern age of cosmology. Today, Cepheid variables remain the best method for measuring distances to galaxies and are vital to determining the expansion rate and age of the universe.
The structure of all stars, including the Sun and Cepheid variable stars, is determined by the opacity of matter in the star. If the matter is very opaque, then it takes a long time for photons to diffuse out from the hot core of the star, and strong temperature and pressure gradients can develop in the star. If the matter is nearly transparent, then photons move easily through the star and erase any temperature gradient. Cepheid stars oscillate between two states: when the star is in its compact state, the helium in a layer of its atmosphere is singly ionized. Photons scatter off of the bound electron in the singly ionized helium atoms, thus, the layer is very opaque and large temperature and pressure gradients build up across the layer. These large pressures cause the layer (and the whole star) to expand. When the star is in its expanded state, the helium in the layer is doubly ionized, so that the layer is more transparent to radiation and there is much weaker pressure gradient across the layer. Without the pressure gradient to support the star against gravity, the layer (and the whole star) contracts and the star returns to its compressed state.
Cepheid variable stars have masses between five and twenty solar masses. The more massive stars are more luminous and have more extended envelopes. Because their envelopes are more extended and the density in their envelopes is lower, their variability period, which is proportional to the inverse square root of the density in the layer, is longer.
There have been a number of difficulties associated with using Cepheids as distance indicators. Until recently, astronomers used photographic plates to measure the fluxes from stars. The plates were highly non-linear and often produced faulty flux measurements. Since massive stars are short lived, they are always located near their dusty birthplaces. Dust absorbs light, particularly at blue wavelengths where most photographic images were taken, and if not properly corrected for, this dust absorption can lead to erroneous luminosity determinations. Finally, it has been very difficult to detect Cepheids in distant galaxies from the ground: Earth's fluctuating atmosphere makes it impossible to separate these stars from the diffuse light of their host galaxies.
Another historic difficulty with using Cepheids as distance indicators has been the problem of determining the distance to a sample of nearby Cepheids. In recent years, astronomers have developed several very reliable and independent methods of determining the distances to the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), two of the satellite galaxies of our own Milky Way Galaxy. Since the LMC and SMC contain large number of Cepheids, they can be used to calibrate the distance scale.
Recent technological advances have enabled astronomers to overcome a number of the other past difficulties. New detectors called CCDs (charge coupled devices) made possible accurate flux measurements. These new detectors are also sensitive in the infrared wavelengths. Dust is much more transparent at these wavelengths. By measuring fluxes at multiple wavelengths, astronomers were able to correct for the effects of dust and make much more accurate distance determinations.
These advances enabled accurate study of the nearby galaxies that comprise the "Local Group". Astronomers observed Cepheids in both the metal rich inner region of M31 (Andromeda) and its metal poor outer region. This work showed that the properties of Cepheids did not depend sensitively on chemical abundances. Despite these advances, astronomers, limited by the Earth's atmosphere, could only measure the distances to the nearest galaxies. In addition to the motion due to the expansion of the universe, galaxies have "relative motions" due to the gravitational pull of the neighbors. Because of these peculiar motions, astronomers need to measure the distances to distant galaxies so that they can determine the Hubble constant.
Trying to push deeper into the universe, astronomers have developed a number of new techniques for determining relative distances to galaxies: these independent relative distance scales now agree to better than 10 For example, there is a very tight relation, called the Tully-Fisher relation, between the rotational velocity of a spiral galaxy and its luminosity. Astronomers also found that Type Ia supernova, which are thought to be due to the explosive burning of a white dwarf, all had nearly the same peak luminosity. However, without accurate measurements of distance to large numbers of prototype galaxies, astronomers could not calibrate these relative distance measurements. Thus, they were unable to make accurate determinations of the Hubble constant.
Over the past few decades, leading astronomers, using different data sets, reported values for the Hubble constant that varied between 50 km/s/Mpc and 100 km/s/Mpc. Resolving this discrepancy, which corresponds to a factor 2 uncertainty, is one of the most important outstanding problems in observational cosmology.
One of the "key projects" of the Hubble Space Telescope is to complete Edwin Hubble's program of measuring distances to nearby galaxies. While the Hubble Space Telescope (HST) is comparable in diameter to Hubble's telescope on Mount Wilson, it has the advantage of being above the Earth's atmosphere, rather then being located on the outskirts of Los Angeles. Thus, HST can resolve Cepheids in more distant galaxies. The key projects aims to get distances to nearby 20 galaxies. With this large sample, the project can calibrate and cross check a number of the secondary distance indicators. The project will also be able to check if the properties of Cepheid variables are sensitive to stellar composition.
HST image of M100 before and after repair
NASA's repair of the Hubble Space Telescope restored its vision and enabled the key project program. The figure shows several images of M100, one of the nearby galaxies observed by the key project program. Note that with the refurbished HST, it is much easier to detect individual bright stars in M100, a necessary step in studying Cepheid variables. Because M100 is close enough to us that its proper motion is a significant fraction of its Hubble expansion velocity, the key project team used relative distance indicators to extrapolate from the Virgo cluster, a cluster containing M100, to the more distant Coma cluster and to obtain a measurement of the Hubble Constant: H0 = 80 km/s/Mpc. The statistical error on this measurement is 17 km/s/Mpc. The dominant source of error is the extrapolation from M100 to the more distant Coma cluster.
The key project determination of the Hubble constant is consistent with a number of independent efforts to estimate the Hubble constant: a recent statistical synthesis by G.F.R. Ellis and his collaborators of the published literature yields 66 < H0 < 82 km/s/Mpc However, there is still not complete consensus on the value of the Hubble constant: a recent analysis by Allan Sandage using Type Ia supernovae yields a value for the Hubble constant that is formally inconsistent with many of measurements: H0 = 47 km/s/Mpc.
In the past year, the key project has detected Cepheids in 8 other galaxies and the inferred distances are consistent with M100. These new observations make possible a number of important checks and calibrations: In M101, the key project has detected Cepheids in both metal poor and metal rich regions: this will enable a test to see if the Cepheid properties depend on abundances. A particularly important measurement is the determination of the distance to the Fornax cluster, a nearby group of galaxies used to calibrate the supernova distance scale. This measurement should hopefully resolve any remaining discrepancy. Ultimately, the key project should be able to make a reliable measurement of the Hubble constant that is accurate to better than 10%.
This page was adapted from an article by D.N. Spergel, M. Bolte (UC, Santa
Cruz) and W. Freedman (Carnegie Observatories).
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David N. Spergel / dns@astro.princeton.edu