In the discussion following my article on symmetry (Elements of Symmetry) we had a brief diversion into dark matter and dark energy. In the course of those discussions, I began wondering if I could understand some of the ‘science’ behind dark energy well enough to convey it simply, especially since I think that sometimes the concepts of dark energy (and matter) are presented as a lot more settled than they actually are. Note that dark energy and dark matter are similar sounding names for two very different and unrelated phenomena. I’m going to focus on dark energy. The existence of dark energy was postulated based on an observation that implied that the universe was accelerating. Observations of very distant supernovae (see Part 2) seem to indicate that they were further away than we expected based on a universe that was simply expanding. In fact, for distant supernovae to be as far away as they appeared to be, the universe must be accelerating. Now something doesn’t expand without energy input, but we don’t see that energy anywhere. Hence, the existence of dark energy was postulated to explain the apparent acceleration inferred from the supernova distances. The 2011 Noble Prize in physics was awarded to the teams that made those observations, a little more than a decade after they were published.
As I was sketching it out, it was getting long, so I broke it into 3 parts:
Part 1 – Since distances determinations are central part of the argument that the universe is accelerating (and hence that something called dark energy exists), a brief review of how astronomical distances are determined. (This article)
Part 2 – An outline of using supernovae to determine distances and some of the complications they present that introduce uncertainty into the distance determination and hence the evidence used to support the hypothesis of dark energy.
Part 3 – Outline the story that lead to postulating the existence of dark energy using supernova distance.
With that, let’s get started.
While knowing distance is critical to determining whether the universe is static, expanding, or accelerating, actually measuring distance is difficult astronomically. The simplest, most error free method is to use parallax, using the apparent shift in position of an object against the fixed background (where fixed background means far enough away that you can’t measure position accurately enough to see shifts!) as the earth moves in its orbit. Then it’s a simple geometric calculation without a lot of room for error. Unfortunately, parallax is only good for pretty small distances, at least on the scale of the universe.
Once we measure the furthest things we can with parallax, we have to start relying on what are called “standard candles“. A standard candle is an object that you know the intrinsic brightness of. Then, since brightness falls off as the source gets further away in a well known fashion, comparing the apparent brightness of the object (what you actually measure) to its known intrinsic brightness, gives its distance directly. An everyday example that is often used is a light bulb. A 100 W light bulb has a known luminosity – it’s right there in the name, 100 Watts. If we move the light bulb across the room, it will appear dimmer. Down to the end of the driveway, even fainter. Across the street, across town, even fainter. The process can be continued as long as your instruments are sensitive enough to measure the apparent brightness of the light bulb. The ratio of what you know, the true brightness of the light bulb, to what you measure, the apparent brightness of the light bulb, gives you its distance. That’s exactly the rational used in measuring astronomical distances.
What are desirable properties of a standard candle? First of all you need something that is very bright intrinsically – you need to be able to measure it at great distances. Secondly, it needs to have a well defined intrinsic brightness that doesn’t vary across individual objects. Obviously, unlike the light bulb, we can’t take our astronomical standard candle and move it to different places, we have to rely on the objects that are already out there. So we’ll be looking at different individual objects and therefore the class of objects we use has to have a very small variation in the intrinsic brightness between members both in space and in time. It will turn out that this second requirement is the tough one and will be at the center of questions about the conclusion that the Universe is expanding.
As an example in practice, we’ll take a brief look at one of the most important standard candles used in determining cosmological distances, the Cepheid variables. Cepheid’s are a class of massive stars, usually about 8 times the mass of the sun (hence they are bright, satisfying one of our requirements). They also vary in brightness in a regular fashion, driven by pulsations of the atmosphere. That may seem to violate our requirement of a known intrinsic brightness – after all the brightness is changing all the time! However, it was determined empirically that the period of the brightness variation is directly correlated with the average intrinsic brightness of the star. What that means is that, if one measures the time between brightness peaks in the star, that gives the stars intrinsic brightness directly. This turns out to be ideal – measuring a change in brightness is easy and can be done as far away as you instrument can detect. Once you’ve measured the period of that brightness change in a Cepheid, you immediately know how intrinsically bright it is and therefore can derive the distance. This relationship has been critical in establishing the distance scale in the universe. In fact, the so called Cepheid period-luminosity relationship is what allowed Edwin Hubble to determine that the Universe is expanding in the early part of the 20th century.
While Cepheids have been foundational in determining distances, they are not bright enough. As a single star, there’s a limit to how bright they can get and so, even with very sensitive instruments, we are limited in how far away we can see them. For example, they are not bright enough that we can see them far enough away to measure acceleration of the universe. For that we need to turn to a new class of standard candle, the super novae. And that’s the topic for the next episode.