I’ve been led to understand that “Never Apologize!” is a sort of Glib motto, right up there with “FYTW” and “Is that a euphemism?”.  That said, I’m feeling a bit like Robert Jordan here.  This was supposed to be the final episode, but it got too long.  So this is Part 3… of 4. Hopefully the intermediate parts won’t be as boring as his intermediate books and, more importantly, I won’t suffer his fate before finally ending this.

In Part 1, the measurement of cosmological distances using standard candles was introduced. In Part 2 a couple of types of standard candles, Cepheids and SN Type 1a were described. Here, we’ll go over how the analysis of very distant Type 1a supernovae (Type 1a SNe) seems to indicate the not only is the Universe expanding, but that the expansion is accelerating, the later property implying the existence of “dark energy”. The exact nature of dark energy is not understood; it is simply a property of the Universe postulated to explain the observed apparent acceleration. There are post hoc physical mechanisms that have been put forth regarding what dark energy is, but those are beyond the scope of this article.  A lot of the time, if you read “beyond the scope” in a scientific paper, it means “I don’t know” or “I’m lazy”; I’ll leave you decide what the proper translation is here.

Simple Hubble diagram, velocity measured from spectra on the vertical axis, distance measured from Cepheids on the horizontal axis.

Back in Part 2, we saw that observations of the Cepheids implied that the Universe was expanding. Most people have heard of Edwin Hubble, if only through the fact that the Hubble Space Telescope (HST) carries his name. Hubble became famous, or as famous as an astronomer gets, by noting that the recession velocity of a galaxy was directly proportional to it’s distance; the further away a galaxy was, the faster it was moving away from us. The simplest explanation for that observation is that we live in an expanding Universe. The distance to an astronomical object is very difficult to measure.  But, given Hubble’s diagram, we know that, if we can measure the velocity of distant galaxy (more easily than the distance), we can immediately read off distance to that galaxy without even having to measure a standard candle in that galaxy!

So how does one go about measuring the velocity of a galaxy?

A siren – half of what most astronomer’s probably wish they studied instead of a bunch of squiggly lines on a plot.

In astronomy, velocity is almost always measured using the concept of the Doppler shift. We’re all familiar with the phenomena from our exposure to sirens. When a vehicle with a siren is approaching you, most likely to hassle you for your joint or to try and stop you from having ass-sex with an illegal Mexican, the pitch of the sound is shifted higher. When he passes you by (and you realize he’s actually after the un-vaccinated person without a mask trying to go grocery shopping), the pitch of the sound is shifted lower. This phenomena occurs because, as the siren approaches, each successive air compression (sound is perceived as a result in variation in density and pressure in the air setting up vibrations in your ear drum) is emitted slightly closer to you than the last due to the motion of the vehicle, so the peaks will be closer together. Conversely, as the siren recedes, the peaks will be further apart. The distance between the peaks in the air compression/density of the sound wave, its frequency, is what our brains perceive as pitch. So we perceive the pitch of an approaching siren to be of higher pitch and the receding siren to be of lower pitch. Since light is also a wave (thanks Maxwell!), the same phenomena occurs. Light emitted from an approaching source will shift to higher frequency, from a receding source, to a lower frequency. In contrast to sound though, rather than pitch, we perceive shifts in the frequency of light as color. In our evolutionary determined visual system, we see things in the optical and in the optical, blue light is “high” frequency and red light is “low” frequency. So, in common parlance, something moving away towards us is called blue-shifted and away from us, red shifted.

Examples of redshift; on the left, the concept. On the right, actual data. In both cases, atomic lines from a given element are shifted with respect to their rest (non-moving) wavelength by an amount proportional to the velocity. For example, on the right, the line labeled H-alpha is emitted at 6563 Angstrom at rest in a vacuum, rather than ~7200 Angstrom in this galaxy – that shift tells you how fast the galaxy is moving away from you and hence its distance.

Now we just need a way to measure the frequency of light of the light.  That’s most commonly done by looking at the spectra[:s/a/e within] of astronomical objects. Spectra are just plots of the brightness of an object versus frequency (wavelength). All elements have unique spectral signatures determined by electronic transitions between energy states in the atoms of that element and since the available energy states of each element are unique based on the structure of that elements atom, there are features that appear in the spectra of each element at unique frequencies. At rest, we can measure the nominal frequencies of all these electronic transitions and create a unique fingerprint of each element. When an object is in motion, the frequencies will be shifted to the blue (if approaching) or to the red (if receding), with the amount of shift being directly proportional to its velocity. So in very simple terms, measuring the velocity of an object is accomplished by taking a spectrum of an object and measuring how much lines of various elements are shifted with respect to the nominal, or “rest”, wavelength.

The expansion of the Universe is apparent on a large scale – for example, not all galaxies are moving away from each other – in fact our own Milky Way galaxy is on a collision course with our nearest (large) neighboring galaxy, Andromeda. If you look at a spectrum of Andromeda, you will see a blue shift. One has to map velocities on a large enough scale to be in the “Hubble flow”, where the local motions of galaxies are dominated by the cosmological expansion of the Universe.

Now back to the expansion [velocity] and acceleration. In the Hubble flow, we can measure the velocity (red-shift) of a galaxy and directly read off the distance if we assume a cosmological model, a model of how the Universe is expanding. So how do we infer an accelerating expansion? Briefly, one looks at very distant – in the Hubble flow – Type 1a SNe (Part 2) and measures the red-shift of the galaxy they occur in. As we saw above, for a given cosmological model, e.g. a uniformly expanding Universe with a given constant (on large scale) matter density, the red-shift (recession velocity) translates directly to a distance in that cosmological model. But as we saw in Part 2, owing to the standard candle nature of Type 1a SNe, we have an independent way of directly measuring their distance. We simply measure their apparent brightness and infer an intrinsic brightness from their light curve characteristics. So with the apparent and intrinsic brightness we have a direct measure of the distance, independent of the cosmological model.

The evidence for accelerating universe. Left – from the ‘discovery‘ paper. Right – a bit more clear. The ‘cloud’ of red points are the evidence for an accelerating universe; they fall systematically above the black line which represents a uniformly expanding universe.

Now we have all the elements we need to see where the postulate that the expansion of the Universe is accelerating comes from. We take the baseline as the distance inferred from the red-shift (measured velocity of a large sample of galaxies) with our best, non-accelerating, model of the Universe and compare that the distance we find directly from the Type 1a SNe for that same set of galaxies. The difference between these two measures is called the “Hubble Residual” or HR. If our model of the universe is correct, it should be 0 – the distances we determine from ‘independent’ means for the same sources should be the same, otherwise, one of our estimates is wrong. When we do that for these data, we see a positive HR. This means that the measured Type 1a SNe are more distant than the ‘null hypothesis’ of a uniformly expanding none-accelerating Universe would predict. That’s it. The only way (if you believe all the observations, assumptions, and models that precede figuring out the distance to Typs 1a SNe) for that to happen is that the Universe is accelerating. And if the expansion is accelerating, you need to put some energy into it. Since we don’t see or measure said energy in an independent way, it gets the moniker “Dark Energy”. Note that the effect is fairly large, roughly 20% in brightness, so it takes a fair amount of error to explain away, which is part of the reason people have some confidence in the result.

And with that, the stage is set for Part 4, the truly final episode. Hopefully it doesn’t become Parts 4 and 5 with  page after page of Rand al’Thor lamenting that he doesn’t understand women while some man who identifies as a woman smooths his skirts and tugs on his penis.