Measuring the Universe

You are a child of the universe no less than the trees and the stars; you have a right to be here, and whether or not it is clear to you, no doubt the Universe is unfolding as it should."
--The Desiderada

Using spectroscopic techniques, it was now possible to determine distances to most objects within the Milky Way (and to those objects in orbit around the Milky Way). Now we could truly examine the size and shape of our galaxy:

Except for the two Magellanic Clouds (visible from the southern hemisphere), which turn out to be small, satellite galaxies of the Milky Way, we did not know the distances to any other galaxies: they were so far away that we could not obtain spectra of the individual stars. Only the most luminous stars were visible, and these stars are difficult to use for distance estimates due to their large intrinsic spread in luminosity. We needed some type of star that we could measure a distance to without having to obtain a spectrum (Note that you can image these faint stars quite easily, but to obtain a spectrum of a star, you have to break up the light by a factor of 1000 or more. Thus you could image stars that were 1000X fainter than the stars for which you could obtain a spectrum). The breakthrough came with the discovery of "Cepheid variables" (named after the first one discovered in the constellation Cepheus). Cepheid variables display a continually, and smoothly changing brightness with time. The "light curve", the plot of brightness versus time, of a Cepheid variable is shown below:

It was soon discovered that the absolute luminosity of a Cepheid variable was directly related to its period, the longer the period between two maxima (or minima), the more luminous the star. The relationship was soon calibrated, and the result is the "Period-Luminosity" diagram/relationship:

Thus, if you could find a Cepheid variable (or better yet, many such objects) in a distant nebula, all you had to do was measure its period, and you could then determine its distance! Another useful star of similar nature are the "RR Lyr" variables, a kind of star that all have the same luminosity, but are fainter, and pulsate much more quickly than Cepheids. The discovery of Cepheid varaibles in other galaxies now meant we could figure out their distances! This was done for the biggest, and brightest galaxies--those expected to be the nearest examples--and we soon found out how big the Universe was. For example, Messier 33 mentioned earlier was found to be 3 Million light years away! We could see other galaxies like Messier 33 in deep photographs, and these objects were small and dim--they must be 100's of millions of light years away! The Universe was truly enormous.

But this realization also lead to another conclusion: that the space between galaxies was mostly empty. We could determine the extent of the Milky Way, and the other nearby galaxies--our local Universe is mostly empty, with the galaxies filling less than1% of the volume! But this still did not resolve Olber's paradox, as even if the Universe is mostly empty, if it is infinite, your line of sight will eventually still encounter a distant galaxy. We will need to make more progress to understand why the night sky is dark.

Backtracking a bit, how did Newton's paradox get resolved? It was soon realized that spectroscopy could tell you how fast an object was moving towards you, or away from you. Just as an approaching ambulence siren increases in pitch, an approaching star has its spectrum change pitch: the light is "blue shifted". Receeding objects exhibit "red shifted" spectra. The wavelengths of the photons of light (or sound) are being scrunched (blueshifted) or stretched (redshifted). This is called the "Doppler effect":

Through careful observation of stars in our galaxy, it was soon shown that the Milky Way galaxy is rotating, and thus the stars have an orbital motion that counteracts the pull of gravity, thus they don't all collapse into a single, massive ball! This orbital motion allows us to estimate the mass of the Milky Way galaxy: 100 billion solar masses. It also means the Sun is whizzing through space at the enormous velocity of 220 km/s (1,320,000 mph)! Since the Sun is located about 27,000 light years from the center, the circumference of the Sun's orbit is 170,900 ly. Even at its tremendous speed, it still takes the Sun 240 million years to go around the Milky Way just one time. Since the Sun formed about 4.5 billion years ago, we see that the Sun has only made 19 trips around the galaxy. Some of these facts are summarized in Monty Python's Galaxy song (written by Eric Idle):

Just remember that you're standing on a planet that's evolving And revolving at nine thousand miles an hour. It's orbiting at nineteen miles a second, so it's reckoned, 'Round the sun that is the source of all our power. Now the sun, and you and me, and all the stars that we can see, Are moving at a million miles a day, In the outer spiral arm, at fourteen thousand miles an hour, Of a galaxy we call the Milky Way.

Our galaxy itself contains a hundred million stars; It's a hundred thousand light-years side to side; It bulges in the middle sixteen thousand light-years thick, But out by us it's just three thousand light-years wide. We're thirty thousand light-years from Galactic Central Point, We go 'round every two hundred million years; And our galaxy itself is one of millions of billions In this amazing and expanding Universe.

Our Universe itself keeps on expanding and expanding, In all of the directions it can whiz; As fast as it can go, that's the speed of light, you know, Twelve million miles a minute and that's the fastest speed there is. So remember, when you're feeling very small and insecure, How amazingly unlikely is your birth; And pray that there's intelligent life somewhere out in space, 'Cause there's bugger all down here on Earth!

Leaving the Neighborhood

Now astronomers had some tools to allow them to map the Universe. But this was not as easy as it sounds. While Cepheid variables were an excellent way to measure distances within the Milky Way, they really were not bright enough to see at distances much beyond the very local neighborhood. Before we go much further, we first must use a more useful unit of distance, the Mega-parsec (Mpc). Astronomers devised the unit of parsecs from parallax. A star that had a parallax of one arc second (a "parallax second") was said to be "one parsec" away. An object at ten parsecs would have a parallax of 1/10th of an arcsecond, and so on. A parsec is 3.26 light years. Remember that a light year is the distance light travels in one year: (3 x 105 km/s) X (3.15 x 107 sec/yr) = 9.46 x 1012 km = 5.68 x 1012 miles, that is, almost 6 trillion miles. Thus, a parsec is about 18 trillion miles. A Mpc is one million times that. The nearest large galaxies Messier 31 (the "Andromeda Galaxy"), and Messier 33, are only about 1 Mpc away. It is quite easy to see Cepheids in both of these nearby galaxies using rather modest telescopes (those with mirrors with diameters of 1 meter). Even using the Hubble Space Telescope, the furthest we can see Cepheids is 17 Mpc. For example, here is what a Cepheid looks like in M100, a galaxy at 17 Mpc:

The Cepheid is barely detectable at the distance of M100 using the most powerful telescope there is! This is because the brightness of an object falls off as 1/R2, that is if you go double the distance, the object is only 1/4th as bright. As galaxies go, M100 is fairly close by, it can be seen with a telescope about the same size as that used by Galileo! Obviously, we are going to have to find something brighter if we are going to go much further and figure out how far away the fainter galaxies are.

A number of different types of the most luminous objects known were proposed to fulfill this need, but most were discarded as they lead to rather uncertain distances. Fortunately, there is a type of object that can be seen to great distances: a supernova. We have already mentioned both Tycho's and Kepler's discovery of "new stars", and how these were actual supernova explosions. What is a supernova? Before we can answer this question, we briefly need to discuss how stars shine. In the center of the Sun (or any star) the density and temperatures are very high. At the core, hydrogen nuclei (protons) are fused into helium nuclei. This releases energy, and the eventual leakage of this energy to the surface of the Sun/star causes it to shine. The energy generated in the core of the Sun balances the pressure of gravity--this balance, "hydrostatic equilibrium", keeps the Sun from contracting into a tiny ball of dense gas. Stars more massive than the Sun burn their fuel more quickly, while stars less massive than the Sun burn their fuel more slowly. For example, the Sun has enough fuel to burn for another four or five billion years. Thus, the lifetime of the Sun is about 8 to 10 billion years. A star with one half the mass of the Sun has a lifetime of about 60 billion years, while a star with twice the mass of the sun has a lifetime of about two billion years. A star with 15 times the mass of the Sun has a lifetime of only 10 million years! A massive star burns fuel more rapidly, and is therefore hotter. Thus, the hottest stars are the most massive ones, and the coolest stars are the lowest mass objects.

When a star like the Sun runs out of hydrogen to burn, the core contracts, and this added pressure allows the Sun to burn helium. Helium burning produces more energy than hydrogen burning, and the core of the Sun is now pumping out more energy than before. Since the mass has not changed, the Sun must expand to stay in hydrostatic equilibrium. The Sun becomes a red giant. When this occurs, life on Earth will be extinguished, for the Earth will now be orbiting inside the outer atmosphere of the Sun, where the temperature will be more than 3,000 degrees! The change is shown here:

Eventually the helium burning stops, the extended atmosphere is shed, and a hot, dense core is all that is left. These hot remnant stellar cores are called "white dwarfs". This evolutionary path can be traced in an HR diagram (the "main sequence" is where the Sun spends most of its life):

Soon after shedding the outer atmosphere, the remnant core is very hot (about 100,000 degrees), and very dense--60% of the Sun's mass is now in an object that is a few thousand miles in diameter! This hot core ionizes the ejected gaseous shell, creating a planetary nebula:

What keeps the white dwarf from collapsing is a phenomenon known as electron degeneracy pressure. Basically, electrons with a negative charge do not want to merge with postively charged protons, so a white dwarf reaches an equilibrium. A supernova generally results from the death of a massive star. Stars more massive than the Sun burn-up the hydrogen in their cores much more quickly, and once they run out, a chain of events follows that leads to a massive explosion. After running out of hydrogen, these stars quickly start burning all of the other elements in a complicated sequence (three helium nuclei become a carbon nucleus, etc.). Eventually, no more nuclear reactions are available to keep the force of gravity balanced. The core begins a rapid collapse, and this collapse creates a shock wave that blows most of the star apart (leaving a "collapsed core"--either a neutron star, or a black hole). The explosion of a supernova is very violent, and the energy generated produces a sudden, and enormous brightening. Here is a before (right hand side) and after (left hand image) of supernova 1987A in the Large Magellanic Cloud:

Supernovae are the most luminous stellar events in the Universe, with a luminosity that is MILLIONS of times that of the Sun! Some supernovae produce as much light as all of the other stars in the host galaxy. Thus, we finally have a probe that can be seen to very great distances--if we could calibrate their distances. To make a long story short, one family of supernova does seem to be pretty uniform in the maximum brightness they attain, and we can therefore calibrate the distances to other galaxies using these objects. (The bad thing about supernovae is they occur at random, so not all galaxies of interest will have one in a typical person's lifetime!)

The Expanding Universe

"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."
--From Hamlet, Prince of Denmark by William Shakespeare

Soon after the deployment of spectrographs (spectroscopes with a photographic capability) on large telescopes, astronomers began taking spectra of galaxies. The spectra of galaxies, as one might expect, looked like an assemblage of the spectra of lots of normal stars, except for one fact---the spectral lines were all redshifted! It appeared that just about all of the galaxies in the Universe were moving away ("receding") from Earth! This was a totally unexpected discovery. Since astronomers believed in the cosmological principle, the notion that "the same laws of physics apply everywhere in the Universe", they could not explain the motions of galaxies by invoking a change in the laws of physics. Thus, these motions had to be real. Because astronomers now had some tools to measure distances to galaxies, it was soon realized that the further away a galaxy was, the faster it was moving away from us. Edwin Hubble (1889 - 1953) soon realized that if he plotted the recession velocity (speed) of a galaxy versus its distance, you ended up with a linear relation between the two quantities:

This relationship, in equation form, is V = Ho x D, where V is the recession velocity, D is the distance, and the slope, Ho, is called the Hubble constant. The units on the Hubble constant are km/s/Mpc. But note that km and Mpc are actually both units of distance, and in reality, Ho has the units of 1/s (s-1), that is, inverse time. The current value of Ho = 72 km/s/Mpc. The implications of the Hubble law are striking. If we run the clock backwards, then all of the galaxies were twice as close to each other 6.8 billion years ago. If we continue this process to its logical conclusion, we find that all of the galaxies must have been in a single spot about 13.8 billion years ago!

1The Cepheid variable diagrams are from

2HR Diagram with evolution tracks from