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This last section is a short essay that summarizes the ways we find distances to various objects in the universe.
Why do we care so much about finding distances in astronomy? If we know the distance to a star, we can determine its luminosity and mass. We can then discover a correlation between luminosity, mass, and temperature for main sequence stars that our physical theories must account for. Finding distances to stellar explosions like planetary nebulae and supernovae enables us to find the power needed to make the gaseous shells visible and how much was needed to eject them at the measured speeds. Stellar distances and distances to other gaseous nebulae are necessary for determining the mass distribution of our galaxy. We then have been able to discover that most of the mass in our Galaxy is not producing light of any kind and is in a dark halo around the visible parts of the Galaxy.
Finding distances to other galaxies enables us to find their mass, luminosity, and star formation history among other things. We're better able to hone in on what is going on in some very active galactic cores and also how much dark matter is distributed among and between galaxy cluster members. From galaxy distances, we're also able to answer some cosmological questions like the large-scale geometry of space, the density of the universe needed to stop the expansion (called W [``Omega'']), age of the universe, and whether or not the universe will be expanding. The cosmological questions will be discussed fully in the next chapter on cosmology. This is only a quick overview of the reasons for distance measurements and is by no means an exhaustive list of reasons why we care about distance measurements.
Now let's take a look at the distance scale ladder. The bottom foundational rung of the ladder is the most accurate and the most certain of all the distance determination methods. As we climb upward, each rung depends on the previous rung and is less certain than the previous one.
The entire main sequence of a cluster is used in the same way to find the distance to the cluster. We first plot the cluster's main-sequence on a color-magnitude diagram with apparent magnitudes, not absolute magnitude. We find how far the unknown main sequence needs to be shifted vertically along the magnitude axis to match the calibrated main sequence.
The age of the cluster affects the main sequence. An older cluster has only fainter stars left on the main sequence. Also, stars on the main sequence brighten slightly at a constant temperature as they age so they move slightly vertically on the main sequence. We must model the main sequence evolution to get back to the Zero-Age Main Sequence. This method assumes that all Zero-Age main sequence stars of a given temperature (and, hence, mass) start at the same luminosity. These methods can be used to find distances out to 50 kiloparsecs.
RR-Lyrae have the same time-averaged luminosity (about 49 solar luminosities or an absolute magnitude MV = +0.6). They pulsate with periods < 1 day. Cepheids pulsate with periods > 1 day. The longer the pulsation, the more luminous they are. There are two types of Cepheids: classical (brighter, type I) and W Virginis (fainter, type II). They have different light curve shapes. The period-luminosity relation enables us to find distances out to 4 megaparsecs (40 megaparsecs with the Hubble Space Telescope).
The Hubble law relates a galaxy's recession (expansion) speed with its distance: speed = Ho × distance. the redshift is easy, but measuring the distance is not. We can calibrate the Hubble law using galaxies out to 500 megaparsecs.
Rung 4 is the critical one now for the distance scale ladder. With the fixed Hubble Space Telescope, we are able to use the Cepheid P-L relation out to distances ten times further than what we can do now on the ground. The ground measurements of the Hubble constant are 50--100 km/sec/Mpc (a factor of two in range!). With Cepheid observations at farther away distances, we're able to constrain its value to 75 - 85 km/sec/Mpc. The value of 1/Ho is a rough upper limit on the age of the universe (assuming constant recession speeds!). The new Hubble constant measurements are implying an universe age of only 12 - 13 billion years. This is in conflict with the ages derived for the oldest stars (found in globular clusters) of about 15 - 16 billion years. Right now, there is a lot more confidence in the age determinations for the oldest stars than for the age of the universe. This is because we are still quite uncertain as to the history of the expansion speeds and what all can affect the expansion speed. So the recent Hubble Space Telescope distance measurements have forced astronomers to attack the deficiencies in the theory of the universe expansion.
Recent very accurate parallax measurements from the Hipparcos satellite call for revisions in the calibration of the Cepheid period-luminosity relation and the distances to globular clusters that may slightly lower the derived ages for the globular clusters and slightly increase the derived age of the universe enough so the globular cluster ages may just fit under the universe age boundary. Stay tuned for more late-breaking announcements!
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last update: 03 December 1997