Cepheid-Based Calibrations.

Prior to the 1950’s, there were only a few methods thought to be reasonably accurate to determine distances to the galaxies: resolvable Cepheid and RR Lyrae variable stars for the closest galaxies, then nova, supernova and brightest cluster galaxies to determine the further ones. Since that time, improvements in ground-based astronomy, HST and other satellite astronomical platforms have provided many alternative methods. The best of these methods have been agreed upon for the HST Key Project on the Extragalactic Distance Scale to evaluate the Hubble constant. Each of these methods is based on straightforward physics and has a solid empirical calibration. However, each of these distance, “standard candles” or “yardstick scales”, whatever we would call them, each have their own merits and drawbacks.

RED-SHIFT OF THE GALAXIES; the HUBBLE CONSTANT

After Edwin Hubble first resolved the brightest stars in M31 and found Cepheid variable stars there, he continued other important work on galaxies. He compiled pictures of different types of galaxies, trying to make sense of their structural forms, and he measured their movements towards or away from the Milky Way by determining the Doppler shifts in their spectral lines.
At that time, the prevalent thought was that a somewhat static Universe existed of galaxies as island continents of stars drifting in remote space. At first, nothing seemed unusual in interpreting the photographic plate spectral line shifts of the closer Local Group galaxies. Some like the M31 Andromeda Galaxy were approaching us, and others were receding. However, Hubble found that all other galaxies beyond the Local Group were receding from the earth, and he determined there was a linear proportion between the galaxy’s radial velocity and its distance surmised by other methods. Because the velocity uniformly indicated remote galaxy recession, it became known as the “red-shift,” since all of the spectral lines in remote galaxies moved from their usual positions to the red end of the spectrum.

In 1929, Hubble announced there is a basic linear relationship between a galaxy’s recessional velocity and its distance; the greater the distance, the greater the galaxy’s red-shift. In 1931, Hubble and Humason erroneously determined the proportionality as 559 kilometers per second per megaparsec (km/s/Mpc) with a stated very naively stated uncertainty factor "of the area of ten percent." This proportionality would later be known as the Hubble constant (H0). Then in 1952, the German-American Walter Baade doubled the inter-galactic distance scale when he recognized that galactic distances had to be revised based on his observations with the 200-inch reflector at Mt. Palomar.

Baade analyzed the Cepheids in M31 and other nearby galaxies comparing Population I star regions with Population II star regions and noted that Population I Cepheids were 1.5 magnitude brighter than the Population II Cepheids as noted above in our prior discussion of Cepheid variable stars. Unfortunately, the distance to M31 had been derived by comparing the brighter Population I Cepheids in M31 with Population II Cepheids in Milky Way clusters. This caused the distance to M31 to be underestimated by a factor of two. Therefore, the distance to M31 had to be revised, and this, in turn, caused the red-shift value for observed galaxies to be decreased to 250 km/s/Mpc.

Since then, there have been many additional estimates for the Hubble constant with the arguments raging between two main camps. In 1956, Alan Sandage of the Carnegie Institutions discovered that Hubble had been studying luminous clouds of hot gas, rather than individual stars. This resulted in Sandage and his colleagues estimating the Hubble constant as ~ 50 km/s/Mpc, while Gerard Vaucoulers of the University of Texas and his colleagues believed it is around 100 (Sky & Telescope, December 1983, pages 511-516). The true value of the Hubble constant is fundamental to our understanding not only the size and shape of the Universe but also its age, rate of expansion, and its future.

Galaxy red-shifts are assumed to be the result of the expansion of the Universe which started with the Universe’s formation at the time of the Big Bang approximately 12-14 billion years ago. By observing galaxies with red-shifts of billions of light years, we are looking back into the early days of the formation of the Universe. Until the Hubble Space Telescope was launched and became fully operational, astronomers were limited to reaching galaxies only about as faint as 24th magnitude with Earth based imaging. Now galaxies as faint as 30th magnitude can be reached by the HST.

The launching of the 94.5-inch diameter HST in 1989 and its updates by astronauts in later Shuttle flights coupled with recent major advances in satellite and ground-based astronomy, such as the coming online of large 8-10 meter telescopes with advanced adaptive optics, has accelerated the systematic search for extremely faint and distant galaxies and quasars. HST and the large Earth based telescopes have extended distance measurement of galaxies, galaxy clusters, and quasars out to more than 6 billion light years. We are literally looking at the “edge of the Universe” and young galaxies as they were forming.

There has always been great difficulty in determining with reasonable accuracy the distance to quasars like 3C283, one of the earliest quasars to be recognized as such. For that matter, there are an enormous number of galaxies whose distances have not been determined. Various attempts have been made over the years to fill this gap, particularly with galaxy optical brightness and quasar radio brightness measurements. By assuming red shift is a linear relationship, the distance can easily be calculated from a galaxy or quasar’s red shift. For example, the red shift of quasar 3C283 is 40,000 km/s, and the Hubble Constant was estimated to be 72 km/s/Mpc by the HST Key Project for Extragalactic Distances; therefore, the distance to 3C283 is: 40,000 km/s / 72 km/s/Mpc = 194.4 Mpc = 1.81 billion light years.

The Hubble Space Telescope’s Key Project to Measure the Hubble Constant was supposed to end the debate about the value of H0. The project’s goal was to locate Cepheid variable stars in 31 distant spiral galaxies to calibrate the distance to these galaxies and to determine a more accurate value for the Hubble constant. The most recent measurements from the HST indicate that H0 has an intermediate value of 74 + or – 7 km/s/Mpc (Sky & Telescope, November 2000, page 28; February 2002, pages 18-19).

However, Cepheid variable stars are only resolvable in other galaxies with the HST out to a distance of 100 million light years, too small a distance to be useful alone to measure the Hubble constant and separate differing theories about the origin and future of our Universe.

Five secondary methods for determining the Hubble constant were also selected by the Hubble Space Telescope Key Project matching these secondary methods against calibrated Large Magellanic Cloud Cepheid variables:

1. Currently the Tully-Fisher (TF) relation is the most commonly applied secondary distance indicator. It is limited to spiral galaxies, either alone or in clusters. The data scatter is approximately ±0.3 magnitudes or ±15% in distance for a single galaxy. The TF calibration was based on data fitting of 31 clusters with accepted Cepheid distance measurements.

2. The Fundamental Plane (FP) method for elliptical galaxies is analogous to TF relation between spiral galaxy rotation velocity and luminosity. FP is estimated to be within 10-20% in estimating the distance of a sampling of elliptical galaxies in a cluster. The method can be appropriately used out to twelve billion light years.

3. The Surface Brightness Fluctuation (SBF) technique was found to be capable of making distance estimates for elliptical or spiral galaxies with prominent bulges, since the ability to resolve stars within galaxies is distance dependent.

4. Type Ia supernovae (SN Ia) can be observed in galaxies as far away as twelve billion light years (~ 400 Mpc), and the internal precision of using them to estimate galaxy distances is very high, an estimated + or – 20%. However, finding these supernovae is difficult. They are not only rare objects but recognizing them in distant faint galaxies is not easy since they tend to blend in with the background light of their parent galaxy. Only a few supernovae discovered in any year may be suitable for an accurate distance evaluation of a very far away galaxy.

5. Type II supernovae are much less useful for distance estimation. They are not common, and it is uncertain if they have similar enough luminosities for use as standard candles.

It should also be noted the Hubble constant determination requires not just accurate distances but correct radial velocities as well. The large-scale distribution of matter in clusters and other assemblages of galaxies is poorly understood and hypothesized dark matter can perturb the “local flow field”, causing additional motions. These perturbations can amount to a significant fraction of the directly measured red shift radial velocity particularly for closer galaxies. A number of astronomers such as Tonry, Giovanelli and others have extensively modeled corrections that need to be applied to the flow field. Although these corrective motions are usually around 200-300 km/sec, the flow field is additionally complicated locally by the presence of massive, nearby galactic structural systems, particularly the Virgo Cluster. The peculiar motion for an individual object can amount to 3,000 km/sec, a 7-10% perturbation, whereas for Type Ia supernovae (which reach out to 30,000 km/sec), these effects drop to less than 1%, on average. Similarly, the effects of other large scale structures like the so-called “Great Attractor” must somehow be accounted for if accurate distance estimates are to be ultimately derived.

At very large distances, the speed of recession becomes so great that relativistic factors have to be considered, and there is no longer a linear relationship between the distance of a galaxy and its red shift. Up to this point, SBF measurements have favored a higher value for H0, and supernovae a lower value. These two methods agree with each other in a relative sense. If one method, for example, the supernova technique, finds galaxy A twice as close as galaxy B, the SBF will find the same relative result. What needs to be done is to accurately link these two methods with Cepheid variable star determinations in a fashion agreed to by all sides. Alan Sandage who currently favors a Hubble constant of 58 + or – 6 advocates a different way of looking at Cepheid variable stars than Wendy L. Freedman who led the HST Key Project. In the future, Cepheid-free studies of eclipsing binary stars may help to standardize the supernova and SBF techniques more accurately.

The calibration and use of Cepheid variables as primary distance indicators is done in the context of the extragalactic distance scale. Comparison is made with the independently calibrated Population II distance scale and found to be consistent at the 10% level. The combined use of ground-based facilities and the Hubble Space Telescope now allow for the application of the Cepheid Period-Luminosity relation out to distances in excess of 20 Mpc. Calibration of secondary distance indicators and the direct determination of distances to isolated galaxies in the field as well as in the Virgo and Fornax clusters allows for multiple paths to the determination of the absolute rate of the expansion of the Universe parameterized by the Hubble constant.

Special celestial object survey projects like the Two-Degree-Field (2dF) Galaxy Redshift Survey, the Sloan Digital Sky Survey (SDSS), and the Two Micron All Sky Survey (2MASS), as well as the Hubble Space Telescope, have greatly improved our three dimensional view of the Universe. These more recent surveys to determine the large scale structure of the Universe have been preceded by other but not as comprehensive galaxy distribution surveys, such as by the Harvard-Smithsonian Center for Astrophysics, the UK-Australian effort by George Efstathiou and his team, Tod Lauer’s study at NOAO and Marc Postman’s survey at the Space Telescope Science Institute (Sky &Telescope, October 1994, page 28).

Collectively, these survey efforts have found that galaxies, already known to exist in clusters and superclusters, are distributed on an even larger scale loosely into sheets and strings with vast voids, as if in a fibrous mat or as a network of soap bubbles, out to 500 million or more light years away. Further out to fourteen billion light years quasars, thought to be the active nuclei of early-formed highly excited galaxies, seem to be the prevalent structure but in a more uniform distribution.

The most distant galaxies and quasars are receding so fast that a linear curve may not apply to the velocity distance relationship. Although the Universe began with a Big Bang, there is current evidence the expansion of the Universe is accelerating, and it will continue to expand forever. Dark matter and dark energy seem to pervade the Universe in as yet an unseen manner. No doubt there will continue to adjustments to the distance scales currently used for finding our place in a Universe, which surrounds us in 14-16 billion light years of space and 14-16 billion years of time.

first posted Wednesday December 1, 2004

minor revision and posting Tuesday February 4, 2014.

minor revision and posting Tuesday December 1, 2015

Please note the essay and references are ten or more years old. More current data is available, though the basic themes presented for finding our place in the Universe are still applicable.

tbh.

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