Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
Cepheids, like RR Lyrae stars, are a class of variable stars which may be used as "standard candles". They are both better and worse than RR Lyrae stars:
Hey! How can we use Cepheids as standard candles if they don't all have the same luminosity? Well, take a look at this diagram; it shows the apparent magnitude of stars in a distance cluster called the LMC, plotted as a function of their period.
Thanks to the MACHO group
Notice two things:
However, there is a saving grace: the absolute magnitude of a Cepheid variable star is correlated with its period. Longer periods mean more powerful stars. This is especially clear if one plots the magnitude of stars against the logarithm of their periods:
It is possible to make a simple equation which will predict the absolute magnitude of a Cepheid star, given its period. One analysis suggests
Cepheids: (average) absolute V mag M = -1.0 - 2.8 * log(Period)
The colors of Cepheids cover quite a range, due to their wide range of masses and their variations as they pulse; to a rough approximation, they span (B-V) = +0.5 to +1.0.
Q: Where do Cepheid stars of period P = 10 days fall on the HR diagram?
Q: Where do Cepheid stars of period P = 100 days fall on the HR diagram?
Q: Recall that RR Lyrae stars have (B-V) colors between +0.20 and +0.50,
and mean absolute magnitudes MV = +0.6. Where do RR Lyrae
stars lie on the HR diagram?
So, all you have to do is
It's a bit more work than for RR Lyrae stars, but since Cepheids are brighter, you can use them to measure greater distances.
Give it a try: below are some measurements of one Cepheid star (delta Cephei, the prototype of its class). Can you figure out its distance away from the Earth?
In the early twentieth century, the construction of big telescopes at Mount Wilson (the 60-inch and 100-inch) allowed astronomers to determine the motions of galaxies for the first time.
Mt. Wilson 60-inch telescope (thanks to
MWOA Photo Gallery )
Adjusting the tertiary mirror of the Mt. Wilson 100-inch telescope (thanks to
MWOA Photo Gallery )
Measuring these radial velocities wasn't easy. Even nearby galaxies are relatively faint, and, unlike stars, their light is spread out over an extended area. Milton Humason used the 100-inch telescope on Mt. Wilson to obtain a spectrum of NGC 7619 in 1929, which yielded the largest radial velocity ever seen (up to that time): 3779 km/sec away from us. His paper describes the difficulties in an understated manner:
During the past year two spectrograms of N. G. C. 7619 were obtained with Cassegrain spectrograph VI attached to the 100-inch telescope. This spectrograph has a 24-inch collimating lens, two prisms, and a 3-inch camera, and gives a dispersion of 183 Angstroms per millimeter at 4500. The exposure times for the spectrograms were 33[h] and 45[h], respectively.At six hours per night, each exposure took at least five nights!
Even after the spectrum was obtained successfully, measuring its properties was no easy task:
Edwin Hubble used the Mount Wilson telescopes to studie galaxies. He photographed nearby galaxies and tried to find ways to determine their distances. In the nineteen-twenties, his best method (and it wasn't a great one) was based on the brightest stars in a galaxy. He assumed that the brightest stars were all of the same absolute luminosity, or standard candles; by comparing the apparent brightness of the brightest stars in different galaxies, he could calculate the distances.
It turns out that Hubble made several errors in his distance measurements; one of the most serious was mistaking compact clouds of glowing gas -- HII regions -- in some galaxies for the brightest stars in them. Although his relative distances weren't bad, his absolute distances were all much too small.
When Hubble plotted the velocities of nearby galaxies against their distances, he found a strong correlation:
Hubble used the slope of the line in this diagram to determine what has become known as the Hubble constant:
radial velocity (km/sec)
H0 = --------------------------
distance (Mpc)
Q: What is the value of the Hubble constant
based on Hubble's distance estimates?
Over seventy years have passed since Hubble and Humason first compared the recession velocities of galaxies to their distances. Astronomers no longer use the brightest stars or HII regions in a galaxy to estimate its distance (unless they have no other information at all). Modern equipment unavailable to Hubble (telescopes in space, and CCD detectors) allows us to use Cepheid variables to determine the distances to relatively nearby galaxies. We believe that our modern measurements are more accurate than the early ones.
Q: What is the value of the Hubble constant
based on these recent measurements?
As we shall see tomorrow, these nearby galaxies are a little TOO close to serve as accurate markers of the expansion of the universe. Nonetheless, it is clear that the modern value of the Hubble constant is much smaller than the original version.
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.