Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Estimating Distances to Nearby Galaxies

Using Cepheids to measure distances to nearby galaxies

One of the main reasons for constructing the Hubble Space Telescope was to measure light curves of Cepheid variables in other galaxies. It is especially important to use Cepheids to measure distances to the galaxies in two nearby clusters: the Virgo Cluster (the nearest rich cluster), and the Fornax Cluster (a somewhat sparser collection of galaxies).

HST can zoom in on a small portion of a galaxy to find and measure Cepheids:

Even the HST has a hard time measuring the light of Cepheids at such great distances:

The light curves measured by HST for Cepheids in these galaxies are rather ratty:

Here are closeups of a long period (50 days) and shorter period (28 day) Cepheid. Note that the star with a shorter period has a significantly larger (fainter) magnitude.

Details of the Cepheid method

  1. Acquire HST images of the galaxy, through two filters: V (greenish-yellow) and I (very red). Take pictures at intervals of several days to a week over a span of several months.

  2. Reduce the HST images to remove flaws in the detector, cosmic-ray hits, etc. This is a (worse than usual) raw HST image of the galaxy NGC 2841:

    Here's a combination of two HST images, taken back-to-back, which allows one to remove most of the cosmic ray hits (and most of the satellite trail):

    And here (just for fun) is a combination of many epochs of HST images of NGC 2841. I've combined V and I images to make a pseudo-color image:

  3. Detect stars in the images taken at each epoch.

  4. Measure position and brightness of stars in each image.

  5. Use positions to match up stars from one epoch with stars all others. This creates a "master list" of stars detected at all epochs, and allows one to see variation in brightness as a function of time.

  6. Identify Cepheids by searching for periodic variations in brightness with their particular light curve shape. Here, for example, is the raw data for a star in the galaxy M81:

  7. Measure the period and average brightness of all Cepheids. Here's the same raw data (plus a little more) for the star in M81, after it has been "phased" by its period: 20.5 days, for this star.

  8. Make a figure showing brightness (in magnitudes) as a function of logarithm of period. Here's such a figure for Cepheids in the galaxy M81, as measured by HST (data taken from Freedman et al., ApJ 427, 628, 1994):

  9. Compare the magnitude vs. log(period) figure for this galaxy against the same figure for LMC, which is shown below (data taken by reading values from a plot shown in Madore and Freedman, PASP 103, 933, 1991).
    Shift the figures vertically until they match.

  10. Use the vertical shift (in magnitudes) to calculate the relative distances of the LMC and the galaxy.

  11. Calculate the distance to the galaxy, based on the known distance to the LMC.

The last two steps involve calculations in wierd units. Astronomers measure brightness in "magnitudes", which decrease with increasing brightness (I told you they were wierd). The simplest way to compare Cepheids in two different galaxies involves finding the shift in magnitudes which brings the "magnitude vs. log(period)" relationships together. If you measure this shift in magnitudes, then the ratio of distances between Galaxy 1 and Galaxy 2 is

        (dist 2)       0.2 * (mag 2 - mag 1)
        -------   =  10
        (dist 1)

The usual method is to compare Cepheids in some distant galaxy (Galaxy 2) against those in the nearby LMC (Galaxy 1). Since we know the distance to the LMC, we can calculate the distance to the distant Galaxy 2:

                                        0.2 * (mag 2 - mag 1)
        distance  =   (dist to LMC) * 10

                                        0.2 * (mag 2 - mag 1)
                  =      50 kpc     * 10

Cepheids aren't perfect

Cepheids aren't perfect distance indicators. For one thing, their brightness and periods of pulsation can vary with their chemical composition. There's also the problem of crowding and confusion: what if our view of a distant galaxy appears to show a single, varying Cepheid star .... but is really a combination of light from the Cepheid and several nearby stars, all mixed together?

Let's see how this could cause a systematic error in the distance measured via Cepheids:

  1. If we measure the light from 5 stars, all mixed together, and we think that the light is coming from a single Cepheid, then we will overestimate the apparent brightness of the Cepheid: we'll think it's brighter than it truly is ...
  2. .... so that when we use the inverse square law, comparing its apparent brightness to its luminosity (which we determine from its period), we underestimate the distance to the star: we think it's closer than it truly is.

That's the basic idea. A discussion has been going on in the astronomical literature for the past several years on the size and importance of this effect.

Results of the Key Project

After nine years of hard work, the Key Project team has measured distances to 18 different galaxies using Cepheid variables. Other groups of astronomers have used HST to look at Cepheids in another 10 or so galaxies. The most distant of these galaxies are about 25 Megaparsecs away. That sounds like quite a distance -- in fact, it's barely far enough to include galaxies in the Virgo Cluster, the nearest cluster of galaxies to our own Milky Way.

On the other hand, it's still only a tiny fraction of the distance to most of the galaxies we can see. The figure below shows a map of the local universe: each little blue dot represents a galaxy (there are many more galaxies in this volume than blue dots, by the way). The tiny red circle near the center represents the distance out to which we can measure distances with Cepheids. Obviously, Cepheids won't allow us to measure distances to most of the galaxies we can see.

So how did we make this plot, you might ask? Good question -- and a topic for next week. See the lecture on the distance-velocity connection.

For more information, see

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.