How Big is Big and How Small is Small

by Smith, Timothy Paul

  We cannot directly measure the distance to a star beyond a few hundred (and soon few thousand) parsecs. But this is similar to the limit optical microscopes have; they cannot see atoms directly. Likewise we could not see quarks directly. But we can use other techniques to push back the limits of what we can measure. To find a new technique we can also ask what it is besides distance we can measure in these nearby stars. Two things stand out: we can measure the brightness of a star and its color.

  How bright a star is is called its magnitude, as was mentioned in Chapter 4. What we directly measure is its apparent magnitude. But how bright a star appears depends upon how bright it really is, as well as how far away it is; that is, the amount of light we see drops with increasing distance because the photons from that star are spread over a larger and larger area the farther they radiate out. If we know the distance to a star we can calculate how bright it would be if viewed from a standard distance. This is the same thing that was done with the Richter scale. By convention, the standard distance is ten parsecs, and the brightness at that distance is called its absolute magnitude.

  In about 1910 Ejnar Hertzsprung (1873–1967) in Denmark and Henry Norris Russell (1877–1957) in America, independently recognized a trend in stars that would help measure stellar distances beyond the parallax limit. What they did was take the data of the well-measured stars and plot their color (temperature) versus their absolute magnitude (see Figure 13.2). About 90% of the stars fell on a line that reached from the hotter (blue) bright stars to the cooler (red) dim stars. The trend is striking and we refer to this band as the main sequence, and the whole diagram as the Hertzsprung–Russell diagram, or sometimes simply as the H–R diagram. This means that if an astronomer measures a star’s color, they know how big and bright it is. Astrophysicists also plot the evolution of stars on H–R diagrams, but for us what is most important is that it correlates color (temperature) to absolute magnitude. So this gives us a new technique for measuring stellar distances. We look at a star and measure its color and apparent magnitude. From its color, using the H–R diagram, we can figure out its absolute magnitude. Finally by comparing the absolute and apparent magnitudes we can figure out how far away it is.

  Figure 13.2 The H–R diagram of star color versus intensity. The color index is related to temperature. The luminosity is related to absolute magnitude. The streak of stars from the upper-left to lower-right contains about 90% of the stars and is called the main sequence.

  This technique is called spectral parallax, even though it does not really use parallax at all. It is sometimes also referred to as the third rung of the cosmic ladder. The first rung was determining the AU, now best done with radar bouncing off planets. The second rung was stellar parallax. Every step outward requires that the previous step be firmly established. It also means that uncertainties in measurements of galactic scales have uncertainties in the AU and the H–R diagram embedded in them.

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  Before pushing our horizon out beyond our galaxy there are two smaller objects to look at: black holes and nebulae. One of the most curious types of objects found by astronomers in the last half century are black holes. These objects have so much mass that light cannot escape from them. They are the ultimate “stealth” object, the astronomical counterpart to quarks. We cannot extract quarks from inside of other particles, but we still know a lot about them. The same is true about black holes. We cannot see them directly, but we can observe their effects upon the things around them, including in particular, and most curiously, light.

  Black holes have the ability to bend the path of light, an effect that is sometimes described as gravitational lensing. Actually, any body with mass will do this, but black holes do it well and it is an effect we can observe even if we cannot see the black hole itself. Some of the first observational evidence for black holes were double images of stars and galaxies. Light from a galaxy headed in two different directions would pass on either side of a black hole where both light-rays are bent to where we see it. We look in two different directions, on either side of the black hole, and see the same galaxy.

  The most common black holes are stellar black holes, formed from the gravitational collapse of a big star. After it has burned its fuel and there no longer is a strong radiation pressure pushing the surface out, or in fact keeping the atoms separate, the worn-out star can gravitationally collapse and form a black hole. Stellar black holes typically have masses of about ten solar masses (10M) and radiuses of about 30 km.

  There are also supermassive black holes, found at the center of most galaxies. We have now observed stars orbiting these black holes. They have masses of the order of 100, 000M, although their radius may only be about 0.001 AU, which is about half the distance to the moon. Even these supermassive black holes really are not very big.

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  The other type of object in our galaxy are nebulae. In some sense, nebulae might not even make our list of objects since they really do not have a structure that is determined by a force, in the way that gravity forms planets and the electromagnetic force forms atoms. But they are very big objects that play an important role in star formation and are also markers of the demise of a star. So we will briefly look at them.

  One of the most studied nebulae is the Crab nebula, having “historic significance.” This nebula is the remnant of a supernova, a star that died in a great explosion, spewing out its remaining gases and newly formed heavy elements. With an apparent magnitude today of about +8, we cannot see it with the naked eye; our eyes can see celestial objects with magnitudes down to about +6. But it does not take much of a telescope to see it; even a good pair of binoculars will resolve it. It was first seen as a nebula by John Bevis in 1731. In the early part of the twentieth century astronomers had taken several photographs of it and realized that over the years it was expanding. By measuring the expansion rate they could work back to when it had been just a point, and arrived at its birth year of about 1050.

  Historic records show that in July of 1054 a new “star” was seen in the sky in the constellation of Taurus, at the tip of the bull’s horn. That is the same location as the Crab nebula. It was so bright that it could be seen in daylight for the first three weeks and at night for the next two years. It was recorded in both Europe and China, where it was called a guest “star,” and upset a lot of ideas about the permanence of the celestial sphere.

  By looking at the stars in front and behind it, we have now measured the distance to Crab nebula at about 6,500 ly and its size as 11 ly across. It continues to expand at about 1500 km/s. Since we on Earth saw it explode in 1054, it really exploded in about 5,450 BC, because light takes a while to get here.

  Supernovae are the only source of heavy elements; that is, elements heavier then iron. They are created via nucleosynthesis in that moment of destruction. But nebulae have a more active role at the other end of the stellar lifetime. Nebulae, with an abundance of gasses, are sometimes called the nurseries or incubators of stars. This is where an embryo star can sweep up the raw materials to form itself and be born.

  Another famous nebula is the Orion nebula. With an apparent magnitude of +3, it is visible to the unaided eye, located in the dagger hanging from Orion’s belt. This cloud of gas glows because of the stars that reside within it. Presently astronomers have identified over 700 proto-stars and 150 proto-planets with in it. It is about 24 ly (2.3 × 1017 m) across and 1,340 ly (1.2 × 1019 m) away.

  Location, location, location: one of the largest nebulae in the sky is the Great Nebula of Cerina. It is an order of magnitude larger than the well-studied Orion nebula and even contains the star η Carinae, the massive star we talked about earlier in this chapter. But it is not well known or studied because it lies in the southern celestial hemisphere and is not visible from Europe, Asia, or North America, where most of the telescopes and astronomers are.

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  But we need to move on. We still have seven orders of magnitude before we reach the edge of the observable u
niverse.

  The next biggest objects are galaxies. Our galaxy, the Milky Way, is a pretty big one. For many years we assumed that the Milky Way looked very much like the Andromeda galaxy. If that were the case it would simplify the study of our home galaxy, since we have a good view of Andromeda. Our own galaxy is hard to see from the inside. It is like standing in the midst of the crowd in Times Square on New Year’s Eve and trying to figure out how many people there are and where the edge of the crowd is. With visible light we can only see about 3 kpc (kpc = kiloparsec) (10,000 ly = 1020 m) through the Milky Way because of all the dust and gasses. We expected, because of looking at Andromeda, that this was only about 10% of our galaxy. In fact, it was only with the development of radio astronomy that we were able to see farther and figure out in which direction was the galaxy center (see Figure 13.3).

  We now think the Milky Way is a barred spiral galaxy, which means that in the center is a bar, an elongated region thick with stars. Extending out from the ends of the bar are spirals, much like what we see in Andromeda. Our solar system is located in the Orion spur, a small finger that sticks out of the Perseus arm, one of the major spirals of the galaxy. When naming regions of space we see the same classic names again and again. What a name like the Perseus arm tells us is that this arm is in the same direction of the sky as the constellation Perseus. The same scheme named the Andromeda galaxy, the Sagittarius arm and so forth.

  The whole disk of the Milky Way, bar and arms, is about 100,000– 120,000 ly (1021 m) across and relatively thin, perhaps only 1,000 ly. The bar itself is a few times thicker. (This is one of those confusing cases where the size of the Milky Way is most often quoted in light-years, but most other things in parsecs. I think it is because the number 100,000 is easier to remember than 30,000 parsec, or 30 kpc.) This bar is an interesting feature, and we now know that about two-thirds of all spiral galaxies have them. Recent computer simulations of galactic evolution indicate that they are a normal part of a galaxy’s life cycle; they form, dissipate, and reform over time. They are a normal mode of the galaxy, much like atoms have wavefunctions with different shapes. Also, when a bar is present, that tends to sweep up gasses and helps in star formation.

  Figure 13.3 A map of the Milky Way. The Milky Way is about 100,000– 120,000 ly across, or 1021 m. Courtesy NASA/JPL-Caltech/R. Hurt (SSC).

  But there is more to our galaxy than just the disk. Surrounding the galaxy and gravitationally tied to it are globular clusters, collections of older stars. These clusters are not confined to the plane of the galactic disk and instead mark out a spherical region about 100,000 ly in radius; that is, as much as twice the radius of the disk.

  A disk of stars swirling in space, rotating every hundred million years or so: it is a simple picture of our galaxy, and most other galaxies, except it has a problem. It does not explain the structure we see. The rate of rotation should follow Kepler’s laws and the arms should get mixed together. In fact it is this problem that has led to the hypothesis of dark matter. There must be more mass out there beyond the galaxy’s halo to give it the structure we observe.

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  A lot of what we know about galaxies actually comes from seeing other galaxies. After all, we live in just one of the several billion examples we can see. But for many years we did not even recognize that galaxies were out there, because they just appeared as distant, fuzzy, nebula-like objects. They were too far away to measure with stellar parallax and too fuzzy for us to pick out main sequence stars. It is true that some people viewed them as separate objects in space. As far back as 1755, Immanuel Kant introduced the term “island universe,” but without any real support. What was needed was a measurement of the distance to these nebulas, or island universes. We needed the next rung of the cosmic ladder.

  Back in Chapter 4 we described the star magnitude scale introduced in ancient times and then precisely defined by Pogson in 1853. With the introduction of astrophotography, the method of comparing star brightness became even more objective. You could now compare images of stars side by side on photographic plates. You could even compare images of the same star taken at various times, which led to the surprising discovery that some stars had changing magnitudes. Their brightness waxed and waned like the tides.

  Henrietta Swan Leavitt (1868–1921) worked at the Harvard College Observatory, where she measured and recorded the brightness of stars from photographic plates. People before her had understood that some stars vary in brightness, in particular a type of star called a Cepheid variable. Cepheid variables are named after the star Delta Cephei found in the constellation Cepheus and are notable because their brightness rises and falls with great regularity. What Leavitt realized was that the period of change was related to the absolute brightness of these stars.

  Leavitt was looking at stars in the Magellanic Cloud, a cluster of stars all at about the same distance from the Earth. She could determine the absolute brightness and therefore their distance from Earth. Her discovery gives us our next rung. With Cepheid variables we can measure stars as far away as tens of millions of parsecs. The most distant object measured by this method is a star in the NGC 3370 galaxy in Leo. Its distance from Earth has been measured at 29 Mpc (1024 m).

  In fact it was Cepheid variables that resolved one of the great scientific debates of the early twentieth century. Were things like the Andromeda galaxy a “nebula” or separate “island universe”? Edwin Powell Hubble (1889–1953) used Cepheid variables in the early 1920s to measure the distance to neighboring galaxies and concluded that these were indeed distant objects, island universes, separate and distinct from our own galaxy. Andromeda is about 2.54 Mly (2.4 × 1022 m) away and the Triangulum galaxy just a bit beyond that. That means they are about 25 times farther away than the width of our own galaxy. Andromeda subtends a wider angle than the moon; it is just very faint (see Figure 13.4).

  Figure 13.4 The Andromeda galaxy. Andromeda is about 2.5 Mly (2.4 × 1022 m). The well-illuminated part is about 100,000 ly wide, although it may in fact be a few times wider. Courtesy of NASA.

  Cepheid variables will help us measure distances out to twenty or thirty times farther than Triangulum galaxy, but first let us look at the world within a few million lightyears of Earth. This region of space is called the local group and consists of three major galaxies (Andromeda, Triangulum and the Milky Way galaxies) as well as about four dozen dwarf galaxies. All of the galaxies in the local group exhibit gravitational cohesion, with many of the dwarf galaxies identified as satellites of one of the major galaxies. This local collection gives astronomers about 700 billion or more stars to look at. With stars living tens of billions of years, there should be several stars being born and dying every year.

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  To continue to look deeper in space, and know how far we are looking, we need new techniques. Techniques such as using the main sequence or Cepheid variables are collectively referred to as candles. A candle is some feature of a star or galaxy that will tell us its absolute brightness or magnitude. Then, by comparing this figure to the object’s apparent magnitude we can figure out how far away it is from us. There are a number of candle techniques, but we will only add two more: the Tully–Fisher relationship and supernovae.

  The Tully–Fisher relationship is a correlation between the brightness of a galaxy and its rotation rate. The trick here is to measure the rotation rate. We cannot just take a photograph, wait a few years and take a second one and see how things have changed. Our own galaxy takes about 200,000,000 years to rotate, so we would have to wait a very long time to see a noticeable change. But the stars are actually moving quickly; our solar system moves at 230 km/s around the disk. So instead of looking at the rotation directly we will look for the Doppler effect of motion.

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  The Doppler effect is what happens when a train blasts its horn as it passes by. It sounds as if the horn has changed from a high pitch as it approaches to a low pitch after it passes. The motion of the source of sound affects the way we hea
r it, be it a siren, a race car, or a jet plane. If the source of light is moving fast, it will affect the way we see it. The effect is caused by the source either chasing after the waves it made, or running away from them. If a fishing bobber is bobbing up and down in the middle of a pond the water waves will spread out evenly in all directions around it (see Figure 13.5). However, if the bobber is moving to the east, because the angler is reeling it in or a fish is dragging it, the bobber will chase the eastern waves and leave behind the western ones. An observer on the eastern shore will see short, frequent waves, whereas the western observer will see longer wavelengths.

  If instead of a bobber on a pond, the source was a yellow light, as it moved towards us the waves would bunch up, the frequency would be higher and the wavelength shorter. The yellow light would appear to shift towards the blue end of the spectrum. If, however, the source was moving away from us it would red-shift. For most things the effect is very small because the waves are moving so much faster than the sources. Our solar system, traveling at 230 km/s around the center of the galaxy, is moving at 0.07% of the speed of light, a small but measurable effect.