Planets, Stars, Galaxies, and the Universe

The Distance Ladder


Now that we have a reasonable understanding of the formation, evolution, and properties of galaxies, we can begin to use them as tracers of the properties of the entire Universe. If we consider again the historical context, scientists like Einstein, Hubble, and others were pursuing these types of questions during the early part of the 20th century. One of the breakthroughs that we will study in the next lesson is Hubble's Law. The foundation of that discovery was the accurate measurement of the distances to large numbers of galaxies. So, to transition from this lesson to the next one, we will consider in some detail the "distance ladder" for determining the distances to ever farther galaxies. Astronomers use the analogy to a ladder, because each type of distance measurement relies on the previous one to move you further and further from the Earth.

First, let's review the first few "rungs" of the distance ladder:

  1. Trigonometric parallax: By measuring the apparent motion of nearby stars against the background, we can directly calculate their distances. This technique has been used to measure the distances to many nearby stars and star clusters out to approximately 100 parsecs from the Earth.
  2. Spectroscopic parallax: Using the flux / luminosity / distance relationship, we can calculate the distance to any star with a known luminosity if we measure its flux on Earth.

By comparing just these first two steps, you can already see how the ladder analogy comes into play. In order to use step 2, you need to know the luminosity of a comparison object. How do we know the luminosities for comparison objects? Well, we can measure the distances to a sample of comparison objects (e.g., O stars) using trigonometric parallax, measure their fluxes, and then calculate their luminosities since we have 2 out of the 3 quantities in the flux / luminosity / distance relationship equation.

So far, we have talked about measuring distances to single stars because we can estimate their luminosities based on their positions in the HR diagram. Then, we considered variable stars. They are useful because the period of their variability is directly related to their luminosity. So, we can measure their luminosities very easily. Using observations of Cepheid variable stars from, for example, the Hubble Space Telescope, we can calculate the distances to galaxies approximately 20 million parsecs (20 Mpc) from Earth.

Cepheid variable stars are one of the most useful objects for measuring distances, and are called standard candles. Any object that is considered a standard candle has the following properties:

  • Easy to identify. That is, it is not easily confused with the many other objects in the sky.
  • Has a known luminosity that is almost constant from object to object to object.
  • Is very bright, so it is easily visible even at large distances.

In practice, the best standard candles have some easily measurable property that is directly related to their luminosity, just like in Cepheid variables where the period of the variability is directly proportional to the luminosity. Some other examples of standard candles are:

  • Type I Supernovae
  • Spiral Galaxies with measured rotation speeds (The Tully-Fisher Relation relates the rotation speed to the luminosity for these objects).

Let's consider the Tully-Fisher Relation briefly. Recall that the orbital speeds of objects are directly related to the sum of the masses of the orbiting objects by way of Newton's version of Kepler's third law. So, if you increase the mass of a galaxy, the rotation speeds of stars in that galaxy will increase, too. So, faster rotating galaxies must be more massive. More massive galaxies are also more luminous, because they contain more stars. So, if you can measure a galaxy's rotation curve (which you can do for some galaxies using the Doppler shifted lines in their spectra), you can estimate with some accuracy that galaxy's luminosity. Then, if you measure its flux, you can calculate its distance, just like we do for stars.

In order to determine the luminosity of a new potential standard candle (say, Type I supernovae), we have to measure the distance to a few of them first using some other technique. We calibrate new standard candles using distances measured to them with old standard candles. For example, if you have a single galaxy with a distance measured by the presence of Cepheid variables in it, and that galaxy has a Type Ia supernova go off, you can calibrate the luminosity of that Type Ia supernova by measuring its flux and using the Cepheid variable distance to its host galaxy. Type Ia supernovae and entire spiral galaxies are brighter than Cepheid variables, so they extend our capability to measure distances out to billions of parsecs.

Because there is always going to be some error associated with a distance measurement, the errors get larger and larger as we get higher and higher up the distance ladder. Given this set of techniques, though, we can measure distances to most galaxies.