How Big is Big and How Small is Small
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The International Astronomical Union (IAU), which is the scientific body that has jurisdiction over the naming of these bodies, had a long and difficult debate about what is a planet and whether Pluto was to be included. In the end they defined a planet as:
1. It orbits the Sun.
2. It has sufficient mass to force itself to be spherical.
3. It has “cleared the neighborhood” around its orbit of other material.
It is this last criteria that Pluto, Eris and even Ceres, a body found in the asteroid belt, have failed on. Clearing the neighborhood means that it is the dominant body of the region. It may accumulate material, acquire satellites or rings, or eject material. But it must be big enough and have resided in an orbit long enough to be the dominant object of the orbit.
Ceres, Pluto, Haumea, Makemake and Eris are now classified as dwarf planets, and there are certain to be others that will get added to this list and to Table 12.3. Pluto, Haumea and Makemake are part of the Kuiper belt, which consists of a myriad of small bodies. It is estimated that there are about 70,000 Kuiper belt objects that are greater than a kilometer across. Unlike rocky asteroids, these tend to be frozen chunks of ice: methane, ammonia and water. The Kuiper belt is also the home of Halley’s comet and other short-period (less than 200 years) comets. Beyond and around this region is an area called the scattered disk, which contains bodies (like Eris) presumably pushed there by the Jovian planets.
And beyond this? As of the time of this writing (2012) the two Voyager spacecraft are at about 120 and 100 AU from the Earth and Sun. They are starting to pass beyond the heliosphere, through a boundary called the heliopause. The heliopause is where the solar wind meets the interstellar or galactic wind.
Finally we arrive at the Oort cloud. This is a vast region of space from a few thousand AU to 50,000 or more AU. It is probably the origin of many comets. One of the things comet watchers have a hard time explaining is why we continue to see them. Comets are as old as the solar system (4–5 billion years) and most comets make only a few passes near the Sun before they collide with either the Sun or another planet. Shoemaker-Levy 9 was a comet that, in 1994, gave us a spectacular reminder of this when it broke up and collided with Jupiter. By now we should expect all comets to have collided with something. But new comets arrive every year.
Table 12.3 Some properties of the dwarf planets. We should expect more dwarf planets to be added.
The Oort cloud was postulated as a source of comets. The cloud is made of frozen chunks of ice out beyond the Kuiper belt and the scattered disk. The chunks of ice orbit slowly out there in darkness for eons until disturbed from their orbits by something, perhaps a passing star or a chance encounter with another Oort cloud object. The ice ball may then be sent into the inner regions of the solar system were we see them. In fact in the last few years astronomers have started directly seeing these distant objects.
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50,000 AU (7.5 × 1015 m) is only a quarter of the distance to the nearest star. However, on our logarithmic scale we have traveled a tremendous distance. Starting at the radius of the Earth (6.4 × 106 m) we have traversed over nine orders of magnitude. Most importantly, at this scale, we have seen gravity take over as the primary shaping force of nature. It makes planets spherical, it creates rings, it even divides ring with resonances. This weakest of forces happens to have a very long reach.
One way to think about 7.5 × 1015 m is to think about light traveling that distance. Light was too fast for Galileo to measure with his lanterns, but we have now measured its speed at 3 × 108 m/s. Light can travel around the Earth seven times in a second. It takes light just over a second to reach the Moon and about 16½ min to cross the Earth’s orbit. It takes light about 4 hours to travel from the Sun to Neptune. Radio signals from either of the Voyager spacecraft take over half a day to get to the Earth. Finally, it takes light almost a year to reach the outer limits of the Oort cloud, the edge of our solar system as we understand it.
13
From the Stars to the Edge of the Universe
In China they call it the Silver River, whereas in Japan they trade the description for its location and call it the River of Heaven. When you look into the night sky you can easily imagine that that streak of silver-white that arcs across the inky void is a river. It has coves and narrows, dark islands and an undulating shoreline. In Ukraine it is called the Way of Chumak. The Chumak were salt traders and one can imagine grains of salt spilled across the sky. In Sweden it is the Vintergatan, the winter street. Not only is it best viewed in the winter at northern latitudes, but it does look like moonlight on a road covered with new snow.
In most of Europe it is called the Milky Way, a translation from the Greek word, γαλαξιαζ or galaxias, which also gave us our word galaxy. The name is traced to the mythology of ancient Greece. Zeus wanted the infant Hercules, his half mortal son, to be nursed by his divine wife Hera and so set the baby on the sleeping Hera. However, when Hera awoke and found a strange baby nursing she pushed Hercules away and milk was spilt across the sky.
Not all Greeks were storytellers and poets. Democritus (450–370 BC) was the philosopher who looked at solid matter and imagined that it could be build up of a myriad of atoms. He also looked at the night sky and proposed that the Milky Way is also a myriad, this time of distant stars.
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In this chapter we will look at the remaining scales of nature, out to the edge of the observable universe. We will talk about why things have the shapes and sizes they do, as well as how we know this. It is one thing to say that the Crab nebula is 11 light years (or 1017 m) across or the breadth of the Capricornus void is 230 Mly (2 × 1024 m). It is far harder to measure that distance. We cannot simply pace it off or send a probe.
In the last chapter we traveled a long way in our solar system; the Oort cloud is ~ 7 × 1015 m out there. But the universe is full of a lot of things we have not yet touched on: nebulae, black holes, galaxies, galactic groups and clusters, even cosmic walls and voids. When you step out at night and look up all those things are there. But what you primarily notice are the stars, including that collection that we call the Milky Way.
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In all of our discussion of the solar system in the last chapter we left out the largest object, the Sun. Stars come in a great range and variety. There are red giants, white and brown dwarfs, ancient stars and stars that burn bright. Our own star is in the middle of these ranges. It is very average, which is convenient since when astronomers describe stars they do it by comparing it to our own. When an astronomer measures the size of Altair they may report it as 1.8M, with a radius of 2R. The symbol for sun is part of the same system of symbols that uses ⊕ for Earth, for Venus and for Mars. So we could write the mass of our Sun as:m = 333, 000 M⊕=1.989 × 1030kg.
The Sun contains 99.96% of the mass of the solar system. This is so similar to the fact that a proton contains 99.5% of the mass of a hydrogen atom that it is worth looking into the parallels. The radius of the Sun is or 6.96 ×108 m. The radius of the orbits of the outermost planet Neptune is about 30 AU or 4.5 × 1012 m, so there is a bit less than four orders of magnitude between them. That is only a tenth of the ratio between the size of the proton and the orbit of the electron. However, Neptune is not really the end of the solar system; the Kupier belt and the heliopause are much farther out and closer to the hydrogen atom ratio, so perhaps the analogy is not so bad. Of course if we include the Oort cloud, which is six or seven orders of magnitude bigger than the Sun, the analogy also collapses.
How do we understand the size of the Sun? It has a diameter of 1.4 × 109 m, almost a million miles. It is about 100 times the diameter of the Earth and about twice the diameter of the Moon’s orbit. It takes between 4 and 5 s for light to travel this far. A truck or bus might drive this distance in their lifetime, but very few cars will make it. Airline jets will fly this distance in a little less than a year of service. Did that transatlantic flight of five hours seem long? It would take
about 60 days for a jet to fly 1.4 × 109 m, or six months to fly around the Sun.
The Sun is an average star, neither the smallest nor the largest, but instead someplace in the middle of the range of star sizes. That range is due to a balance between nuclear forces and gravitational forces. Briefly, a star is formed when a cloud of gas in space collapses in on itself because of the gravitational attraction of every atom and molecule in that cloud. As it becomes denser, the probability of the nuclei of those atoms colliding increases and with collisions comes nuclear fusion and the release of energy in the form of heat and light. If the amount of matter is too low it could form a planet instead, with the atoms keeping their separation distance as everyday matter does on Earth. The lower limit is called the hydrogen burning limit and is about 0.08M
At the upper limit, with too much matter a star would burn extremely hot and bright, and in that fury blow away excess material until it reached a more stable size. This balance between the outward radiation pressure and the inward gravitational pressure is called the Eddington luminosity or the Eddington limit and predicts that stars will not exceed about 0.08M.
Observations back this up. The smallest star measured is GLE-TR-122b (with billions of stars to catalogue, some have less-than inspiring names). It has a mass of 0.09M just over the hydrogen burning limit. Actually there are smaller stars out there, but they are not burning purely hydrogen and so have smaller theoretical limits.
At the other end of the size scale, large stars burn fast and furious. A star with a mass of 150M will last only a few hundred million years, a lifetime that is perhaps only 5% of that of our Sun.
For a long time the biggest star we knew of was Eta Carinae, or η Carinae, which gives us a reason to look at the way the brighter stars are named. The name η Carinae tells us that this is the seventh brightest star in the constellation Carinae. In fact we should be able to go to Ptolemy’s star catalogue, the Almagest, and find it listed with that name. Except you don not. In the Almagest you will find it listed in the constellation Argo. This is because long after Ptolemy’s time it was decided that the constellation Argo was too big, and it was subdivided, leaving the unchanging sky… changed.
The more people have studied η Carinae the more curious it is. It is believed to have had a mass of about 150M, near the Eddington limit, but to have lost about 30M over time. It is embedded in a nebula, which makes it hard to observe, and it has a smaller companion star. But as we have been able to look out farther and farther we have found more stars near the Eddington limit. HD 269810 in the Large Magellanic Cloud, an area outside the Milky Way is about 150M.
But the word “biggest” implies a size a not a mass. For a long time VY Canis Majoris was the biggest star that had been measured, with a radius of about 1, 400R or 6.6 AU. A recent analysis has lowered the measurement by about 15% and there are new candidates vying for that title of biggest. Still VY Canis Majoris has a radius slightly bigger than the orbit of Jupiter. Despite its size, it falls well below the Eddington limit, with a mass of only 17 ± 8M.
But just when we think we understand stars we find an exception. R136a1 was characterized in 2010 and found to have a mass of about 265M which is well over the Eddington limit. In fact it is thought that it had substantially more mass, but has shed over 50M over the last million years, as it works its way down to a more stable mass. Because the theories of star formation are so well founded, and they say that stars cannot form over 150M, it is believed that stars like R136a1 were actually created out of the merger of multiple stars.
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One of the first attempts to measure the distance to a star was made by Christiaan Huygens (1629–1695). Huygens was a Dutch astronomer, a contemporary of Newton and Cassini, and an early supporter of Rømer’s measurements. He made a series of tiny holes in a screen and let sunlight shine through them. He then picked out the hole that he estimated let through the same amount of sunlight in the day as what he saw from Sirius, the Dog Star, at night. He then calculated that the angular size of his hole was 1/30,000 the size of the Sun and so Sirius was about 30,000 AU away. It was an ambitious attempt and Huygens underestimated the distance by a factor of about 20, which was due to the fact that Sirius is about 20 times more luminous than our Sun, but he had a rough estimate with which to start.
The best method to measure the distance to stars is stellar parallax. We have already encountered solar parallax when measuring the distance to the Sun. In that case an astronomer would measure the position in the sky of the Sun from two locations widely separated, ideally from opposite sides of the Earth, to get the longest baseline. In stellar parallax an astronomer is surveying the distance to the star by constructing a triangle. One measures the position of a star in the sky and then repeats that measurement about six months later when the Earth has moved halfway around its orbit (see Figure 13.1). One side of the triangle is 2 AU or 3 × 109 m, the diameter of the Earth’s orbit. But this is a small number, a short distance when compared to the distance to the stars. These triangles are incredibly long and thin. Using Huygen’s estimate, the height is 15,000 times the length of the base. In the end it is not really the angle that matters, but how that angle changes, and that change must be measured from our moving, spinning Earth.
Figure 13.1 Parallax of a near star. Note that the horizontal and vertical directions are not to scale so the angles drawn here are about a million times too large.
Stellar parallax is actually an old idea. Tycho Brahe (1546–1601) did not accept Copernicus’s thesis based on the lack of observed stellar parallax and long before him Archimedes, in The Sand Reckoner, based his size of the universe upon the unobserved parallax. Edmond Halley, about the year 1700, looked for the effect by carefully measuring star positions. What he found was that his measurements did not match ancient catalogs because stars move over time. We now call this proper motion. Stars are not rigidly fixed on the spiral arms of the galaxy, they chart their own paths across space. James Bradley (1693–1762), the third Astronomer Royal again tried to measure parallax by raising the standards of precision angular measurements and discovered an effect called the aberration of light. As we orbit the Sun, sometimes we are moving towards a star and so along the path of the light ray, and sometimes we are moving across the path. Our motion and the finite speed of light will combine to make stars appear at different angles. Bradley did not see stellar parallax, but he did measure the speed of light.
By the 1830s measuring parallax and the distance to another star had become an obsession, a holy quest, for the international astronomical community. Finally, in 1838 three astronomers published successful measurements. First, Friedrich Bessel (1784–1846) measured the parallax of 61 Cygni at 0.314 arc-seconds. Then Friedrich Georg Wilhelm von Struve (1793–1864) reported the parallax of Vega. Finally Thomas Henderson (1798–1844) reported just under an arc-second for the parallax of Alpha Centauri. There are 60 arc-minutes in a degree and 60 arc-seconds in a arc-minute. So 0.314 arc-seconds is one ten thousandth of a degree. That is like a 2-mm shift as viewed from a kilometer, or a 2 hair-width shift as viewed from 100 m. A good telescope can easily see a hair at 100 m, but it is harder to look at it six months later and see the shift. Also one has to measure the proper motion and the aberration of light and remove those effects.
Measuring parallax was a laborious task. So the first trick was to pick a few stars that were promising candidates, stars that you thought might be near. Astronomers reasoned that nearer stars would most likely have greater proper motion, much like a person walking close by you will change their angular position faster than a distant walker. They would then chart these stars over time compared to the more distant stars behind them. Over a few years the candidates would march across the star field, two steps forward and one step back, much like the retrograde motion of the planets that inspired the complex epicycle theory of Ptolomy as well as Copernicus’s heliocentric model. The step back was an annual effect caused by the Earth’s motion around the sun, or parallax
.
The distance unit of choice when measuring parallax is the parsec. The term parsec comes from the words parallax and arc-second, and it is defined as the distance away an object is if it shifts by an arc-second when the observer has moved 1 AU. So Bessel’s measurement of 0.314 arc-seconds translates to 1/0.314 or about 3 parsecs (about 1017 m). Henderson picked out as his candidate the star that is the nearest one you can see without a telescope: Alpha Centauri. Modern measurements put this at 0.747 arc-seconds, which is 1.3 parsecs, 4.3 light years or 4 × 1016 m (see Table 13.1). If a Voyager probe was headed in that direction it would take about 75,000 years for it to reach the star.
There is one other unit of measurement that is used especially in popular literature: the lightyear. It is a unit whose very name invokes vast distances, the deep dark void of space, and the lonely stellar beacons of light. A lightyear (ly) is the distance light travels in one year. A year contains 31 million seconds, so a light year is about 1016 m. Whereas a lightyear is descriptive and has caught the popular imagination, professional astronomers tend to favor the parsec, a unit that is directly tied to the measurement technique.
Table 13.1 List of nearby stars.
From the surface of the Earth stars tend to shimmer and twinkle due to the atmosphere, which may be a pretty effect, but does not help when trying to make precision measurements of their positions. Ground-based measurements are limited to about 20 to 50 parsecs. With stars in our region of the galaxy spaced about every parsec, that means we can measure the distance to tens of thousands of stars, which is a drop in the bucket compared to the whole galaxy. So for four years, from 1989–93, the Hipparcos space telescope orbited above the atmosphere and measured stellar parallax out to 100 to 200 parsecs, which means the distance to about a million stars. Finally, over the next few years the GAIA mission should extend that measurement out to as much as 8,000 parsecs. With these types of measurements there is not a firm cut-off beyond which you cannot measure. It is just that at long distances the results have great uncertainty. For example, GAIA plans to look at stars near the galactic center, which is about 10,000 parsecs away, but at that distance it will expect an accuracy of only 20%. That is 1017 m, which means we have a long way to go to measure the distance to the edge of the observable universe.