## From Frontier Fields: “Light Detectives: Using Color to Estimate Distance”

October 28, 2014
Dr. Brandon Lawton

Distances are notoriously difficult to measure in astronomy. Astronomers use many methods for estimating distances, but the farther away an object is, the more uncertain the results. Cosmological distances, distances on the largest scales of our universe, are the most difficult to estimate. To measure the distances to the farthest galaxies, those gravitationally lensed by massive foreground galaxy clusters, astronomers really have their work cut out for them.

If a massive stellar explosion, known as a supernova, happens to go off in a galaxy and we catch it, then we can use the “standard candle” method of computing the distance to the galaxy. Supernovae are expected to be discovered in the Frontier Fields, but not at the numbers that will help us find distances to most of the galaxies in the images. Without these standard candles, astronomers must use other means to estimate distances.

A Spectrum is Worth a Thousand Pictures

One of the more accurate methods for measuring the distance to a distant galaxy involves obtaining a spectrum of the galaxy. Getting a galaxy’s spectrum basically means taking the light from that galaxy and breaking it up into its component colors, much like a prism breaks up white light into the rainbow of visible colors. By comparing the brightness of light at each component color, a spectrum can give us a wealth of information. This can include detailed information about a galaxy’s composition, temperature, and how fast it is moving relative to us. Because the universe is expanding, we observe most galaxies, and all distant galaxies, to be moving away from us.

When looking at a distant galaxy’s spectrum, the expansion of the universe causes the component colors in the spectrum to be stretched to longer wavelengths. For visible light, red has the longest wavelengths, which leads to the term ‘redshift’. This cosmological redshift can be accurately measured from a spectrum. Astronomers then use mathematical models of the expansion rate of our universe to convert the measured redshift into an estimate of distance. Larger values of redshift correspond to larger distances.

This video, developed by the Office of Public Outreach at the Space Telescope Science Institute, gives a demonstration of how light is redshifted as it travels through the expanding universe. Here, the lightbulb stands in place of a galaxy. As the universe expands, it stretches the light traveling through the universe, increasing the light’s wavelength. As the wavelength increases, it becomes more red. Light traveling longer distances through the universe will be stretched/reddened more than light traveling short distances. This is why astronomers use instruments sensitive to redder light, including infrared light, when they attempt to observe the light from very distant galaxies. Watch this video on Youtube.

Larger redshifts not only correspond to larger distances, but they also correspond to earlier times in our universe’s history. This is because light takes time to travel to us from these distant galaxies. The more distant the galaxy, the longer the light has been traveling before we intercept it with sensitive telescopes, like Hubble.

Assuming typical contemporary mathematical models, the universe is about 13.8 billion years old. Galaxies at a redshift of 1 are seen as they existed when the universe was about 6 billion years old. Galaxies at a redshift of 3 are seen as they existed when the universe was about 2 billion years old. Galaxies at a redshift of 6 are seen as they existed when the universe was about 1 billion years old. Galaxies at a redshift of 10 are seen as they existed when the universe was only about 500 million years old.

It is notoriously difficult to obtain a spectrum of a very distant galaxy. They are very faint, and an accurate spectrum relies on obtaining a lot of light. One is, after all, taking what little light you get and breaking it up further into the component colors, meaning that you start with little light and get out even less light at each component color. Getting enough light to take an accurate spectrum of a distant galaxy requires very lengthy observations with sensitive telescopes. This is not always feasible.

Redshifts measured via spectra are called spectroscopic redshifts. Many of the nearer galaxies in Abell 2744 have measured spectroscopic redshifts. There will likely be many follow-up observations from ground- and space-based observatories to obtain spectra of many of the fainter and more distant galaxies in the Frontier Fields. So stay tuned!
I Can’t Obtain a Spectrum! What to do?

If you do not have a spectrum, are there other ways to estimate the redshift and distance to a galaxy? Yes! Just take a look at the galaxy’s colors.

All Hubble images are taken with filters. Blue filters allow Hubble’s instruments to capture only blue light, red filters allow Hubble’s instruments to capture only red light, and so on. By comparing a galaxy’s brightnesses in these different colors, astronomers can estimate the distance to the galaxy. The redder the color, the more likely the galaxy is to be redshifted, and thus, farther away.

This technique of using color to estimate redshift is called photometric redshift. The following two primary methods are used for estimating a photometric redshift:

compare the colors of your high-redshift galaxy candidate to a set of typical galaxy color templates at various redshifts, or
compare the colors of your high-redshift galaxy candidate to a set of galaxies with measured spectroscopic redshifts and, utilizing specialized software, compute the most likely redshift for your galaxy.

In the first case, the photometric redshift comes from the best match between the observed high-redshift candidate colors and the colors of the template galaxies. The template galaxy colors stem from observations of galaxies that tend to be relatively close but are then mathematically reddened over a range of redshift values.

In the second case, astronomers use a set of observed galaxies whose redshifts have been measured spectroscopically, as explained in the prior section. This set contains galaxies at various redshifts. They then use machine-learning algorithms to compare the colors of this set of galaxies with the colors of the target high-redshift galaxy candidate. The software selects the most likely redshift.

Whichever method is used, astronomers are careful to give confidence levels in their calculations. For the computation of photometric redshift, there is typically an uncertainty of around a few percent for high-quality data. In addition, there is the lingering issue of whether the high-redshift galaxy candidate is truly redshifted, or if it is a nearer galaxy that is intrinsically redder. It is not uncommon to read results where astronomers find a galaxy with a probable high photometric redshift and a less probable low photometric redshift, or vice versa.

Credit: Adapted from Adi Zitrin, et al., 2014. Shown is a high-redshift galaxy candidate in Hubble’s observations of Abel 2744, discovered using filters. Dark regions represent light in these images. Notice how the galaxy drops out of the image in the bluest filters. This is a hint that the galaxy may be significantly redshifted.

Many of the first results for the Frontier Fields utilize photometric redshifts. In the absence of spectra, photometric redshifts are the next best thing to obtaining estimates of distances for large samples of galaxies. They are readily computed from the current Frontier Fields data.