Close binaries

If the two stars in a binary system are very close to each other, each has the effect of altering the structure of the other star. When this occurs we call the system a close binary system. The surface of a star can be distorted by the stronger gravitational force that the companion exerts on the near side than on the far side. Remember, we said that any effect that depends on variations in the gravitational force from one position to another is called a tidal effect. (A similar situation applies as the Sun and Moon distort the Earth's ocean surface, raising the tides.)

The distortion of stars results in internal dissipation of energy. As a star rotates, different material is incorporated in the bulge. Different layers of material rub against each other, in a fluid friction. This lost energy has to come from somewhere. It comes from both the orbital energy and the rotational energy of the star. As a result, eventually the orbits circularize and the two stars always keep the same sides towards each other. This is the lowest energy arrangement for the system (see Problem 12.1). We say that the spins are synchronized. (The Moon's spin and orbital motion around the Earth are synchronized, and the Moon keeps the same side towards the Earth.)

In certain situations, it is possible for material from one star to be pulled off the surface onto the other star.

Coordinate systems

When we want to locate a star, or any other astronomical object, we only need to specify its direction. We don't need its distance. We therefore need only two coordinates, two angles, to locate an astronomical object. Sometimes, it is convenient to think (as the ancients did) of the stars as being painted on the inside of a sphere, the celestial sphere. Just as we can locate any place on the surface of Earth with two coordinates, latitude and longitude, we need two coordinates to locate an object on the celestial sphere.

We choose coordinate systems for convenience in a particular application. In general, to set up a coordinate system we first identify an equator and then choose coordinates that correspond to latitude and longitude.

A convenient system for any particular observer is the horizon system. The horizon becomes the equivalent of the equator in that system. The angle around the horizon, measured from north, through east, south and west, is the azimuth. The angle above the horizon is called elevation. Instead of elevation, we can use the zenith distance, which is the angle from the zenith (overhead) to the object. From their definitions, we can see that the sum of the zenith distance and the elevation is always 90°. The azimuth ranges from 0° to 360°, and the elevation from −90° to 90° (with negative elevations being below the horizon).

We start our discussion of the planets with the one with which we are most familiar, the Earth. In understanding the processes that are important on the Earth, both now and in the past, we are setting a framework for our understanding of the other planets. Therefore, in this chapter we will develop many of the ideas that should apply to all planets, both in terms of what properties are important and how we measure them.

History of the Earth

Early history

The main steps in the history of the Earth are shown in Fig. 23.2. Somehow, the Earth accreted from the material in the original solar nebula. We will discuss more about the solar nebula in Chapter 27. Enough material collected together so that its own gravitational pull was able to keep most of the material from escaping. As particles fell towards a central core, they were moving closer together, so their gravitational potential energy decreased. This means that their kinetic energy increased. This kinetic energy was then available to heat the forming planet. In addition, heat was provided by the radioactive decay of potassium, thorium and uranium. Such decays led to heating, because the energetic particles – alpha, beta, gamma – were absorbed by the surrounding rock. The relatively massive alpha particles were particularly effective in this heating. The heating resulted in a liquid, or molten, interior.

General relativity is Einstein's theory of gravitation that builds on the geometric concepts of spacetime introduced by special relativity. Einstein was looking for a more fundamental explanation of gravity than the empirical laws of Newton. Besides coming up with a different way of thinking about gravity (in terms of geometry), general relativity makes a series of specific predictions of observable deviations from Newtonian gravitation, especially under strong gravitational fields. These predictions provide a stringent test of Einstein's theory (e.g. Fig. 8.1).

Curved space-time

A central tenet of general relativity is that the presence of a gravitational field alters the rules of geometry in space-time. The effect is to make it seem as if space-time is “curved”. To see what we mean by geometry in a curved space, we look at geometry on the surface of a sphere, as illustrated in Fig. 8.2. The surface is two-dimensional. We need only two coordinates (say latitude and longitude) to locate any point on the surface. However, it is curved into a three-dimensional world, and that curvature can be detected.

To discuss the geometry of a sphere, we must first extend our concept of a straight line. In a plane, the shortest distance between two points is a straight line. On the surface of the sphere it is a great circle. Examples of great circles on the Earth are the equator and the meridians. (A great circle is the intersection of the surface of the sphere with a plane passing through the center of the sphere.)

In this chapter we look at the steps that led up to life on Earth, starting with the formation of the Solar System. We then look at the possibilities of finding life on other planets, both within the Solar System, and around other stars.

Origin of the Solar System

One of our goals in studying the Solar System is understanding how it formed. As we studied the planets we saw that they provide many clues to the Solar System's history. In this section, we briefly outline some of the ideas that have been proposed. Any theory on the formation of the Solar System should be able to explain such things as the fact that the planets' orbits are approximately in the same plane, and the fact that the planets orbit in the same direction. In addition, it must be able to explain the distribution of angular momentum in the Solar System. Also, the different compositions and appearances of the planets must be explained.

Historically, two basic scenarios have been discussed. In one, the Solar System formed as a byproduct of the Sun's formation. The material left over from the Sun's formation is the material out of which the planets formed. The idea was first discussed by Rene Descartes in 1644, and was elaborated upon by Immanuel Kant, and farther by Pierre Simon de Laplace, who was the first to take the effects of angular momentum into account.

In Chapter 14, we discussed the contents of the interstellar medium, the material out of which new stars must be formed. In this chapter, we will identify those parts of the interstellar medium that are involved in star formation, and see what we know, and what we have to learn, about the star formation process.

Gravitational binding

In Chapter 13, we talked about gravitational binding for clusters of stars. The same concepts apply to interstellar clouds, with the stars in the cluster being replaced by the particles that make up the cloud (either H or H2). The gravitational potential energy is now due to the interaction among all of the particles in a cloud. For a uniform spherical cloud, the gravitational potential energy is−(3/5)GM2/R. The kinetic energy is still related to the rms velocity dispersion, but with a large number of particles, which can easily be related to the cloud temperature, so the kinetic energy is (3/2)(M/m)kT, where M is the total mass of the cloud and m is the mass per particle.

The clouds are kept together by the gravitational attraction amongst all of the particles in the cloud. If the gravitational forces that hold the cloud together are greater than the forces driving it apart, we say the cloud is gravitationally bound. We can think of the random thermal motions in the gas as resisting the collapse.

Einstein's theory of relativity caused us to rethink the meaning of both space and time, concepts that had been taken for granted for centuries. The foundation of this revolution is the special theory of relativity, which Einstein published in 1905. The general theory of relativity, published in 1916, is really a theory of gravitation set in the foundations of the special theory; it also allows us to analyze the properties of frames of reference that are accelerating.

In Chapter 2 we discussed the continuous spectra of stars and saw that they could be closely described by blackbody spectra. In this chapter, we will discuss the situations in which the spectrum shows an increase or decrease in intensity over a very narrow wavelength range.

Spectral lines

We know that if we pass white light through a prism, light of different colors (wavelengths) will emerge at different angles with respect to the initial beam of light. If we pass white light through a slit before it strikes the prism (Fig. 3.1), and then let the spread-out light fall on the screen, at each position on the screen we get the image of the slit at a particular wavelength.

Both William Hyde Wollaston (1804) and Josef von Fraunhofer (1811) used this method to examine sunlight. They found that the normal spectrum was crossed by dark lines. These lines represent wavelengths where there is less radiation than at nearby wavelengths. (The lines are only dark in comparison with the nearby bright regions.) The linelike appearance comes from the fact that, at each wavelength, we are seeing the image of the slit. It is this linelike appearance that leads us to call these features spectral lines. If we were to make a graph of intensity vs. wavelength, we would find narrow dips superimposed on the continuum. The solar spectrum with dark lines is sometimes referred to as the Fraunhofer spectrum. Fraunhofer gave the strongest lines letter designations that we still use today.

If we are to understand the workings of stars, it is important to know their masses. The best way to measure the mass of an object is to measure its gravitational influence on another object. (When you stand on a bathroom scale, you are measuring the Earth's gravitational effect on your mass.) For stars, we are fortunate to be able to measure the gravitational effects from pairs of stars, called binary stars.

Binary stars

Many stars we can observe appear to have companions, the two stars orbiting their common center of mass. It appears that approximately half of all stars in our galaxy are in binary systems. By studying the orbits of binary stars, we can measure the gravitational forces that the two stars exert on each other. This allows us to determine the masses of the stars.

We classify binaries according to how the companion star manifests its presence:

1. Optical double. This is not really a binary star. Two stars just happen to appear along almost the same line of sight. The two stars can be at very different distances.

2. Visual binary. These stars are in orbit about each other and we can see both stars directly.

3. Composite spectrum binary. When we take a spectrum of the star, we see the lines of two different spectral type stars. From this we infer the presence of two stars.

4. […]

To this point we have been studying the stellar life cycle and how stars and other material are arranged in the Milky Way Galaxy. We will now turn to studies on a much larger scale. We will first look at other galaxies, and see that some of them tell us more about our own galaxy, which is so hard to observe. When we talk about how the universe is put together, each galaxy has only as much importance as a single molecule of oxygen has in describing the gas in your room.

As we go to larger scales, we will look at how galaxies are distributed on the sky, and how they move relative to one another. We will also see how the problem of dark matter becomes more important as we go to larger and larger scales.

As we go to larger scales, increasing the number of galaxies that we observe, we also find a variety of interesting phenomena associated with galaxies. In Chapter 19 we will discuss aspects of galactic activity, particularly as evidenced by radio galaxies and quasars.

In Chapter 20 and 21 we will turn to cosmology, the study of the universe on the largest scales. This also includes the past and future evolution of the universe. It is in the study of the past that we encounter one of the most fascinating aspects of modern astrophysics research, the merging of physics on the smallest (elementary particles) and largest (structure of the universe) scales.

An understandable universe

Our curiosity about the world around us is most naturally manifested when we look up at the night sky. We don't need any special instruments to tell us something interesting is going on. However, only with the scrutiny afforded by a variety of instruments can these patches of light, and the dark regions between them, offer clues about their nature. We have to be clever to collect those clues, and just as clever to interpret them. It is the total of these studies that we call astronomy.

We are fortunate to live in an era of extraordinary astronomical discovery. Some have even called this the ‘Golden Era of Astronomy’. For centuries astronomers were restricted to making visual observations from the surface of the Earth. We can now detect virtually any type of radiation given off by an astronomical object, from radio waves to gamma rays. Where necessary, we can put observatories in space. For the Solar System, we can even visit the objects we are studying.

For all of these capabilities, there is a major drawback. We cannot do traditional experiments on remote astronomical objects. We cannot change their environment and see how they respond. We must passively study the radiation that they give off. For this reason, we refer to astronomy as an observational science rather than an experimental one. It is because of this difference that we must be clever in using the information that we do receive.

The Solar System naturally divides into two groups of planets, separated by the asteroid belt. The four inner planets have many things in common with the Earth, whereas the next four planets present worlds of an entirely different type. (Pluto is an additional enigma.) In this chapter, we look at Mercury, Venus and Mars, comparing their properties with each other, and with the Earth.

Basic features

Mercury

Mercury is the closest planet to the Sun, and is not much larger than our Moon. There is an interesting story concerning its rotation period. Since Mercury is so close to the Sun, we never have a really good view of it, and surface features are hard to recognize. By noting the positions of large surface features, it appeared that the rotation period was 88 days, the same as the planet's orbital period. This would have meant that Mercury always keeps the same face towards the Sun (just as the Moon keeps the same face towards the Earth). Since Mercury is so close to the Sun, it seemed plausible that some tidal effect could keep its rotation period synchronized with its orbital period.

However, the situation was corrected following radar observations. Radio waves were bounced off Mercury and then detected back on Earth. The planet's rotation causes a spread in the Doppler shifts of the reflected waves. From the amount of spread, we can tell how fast the planet is rotating.

When we look at the spatial distribution of stars in our galaxy, we find that most of the light is concentrated in a thin disk. We are inside this disk, so we see it as a band of light on the sky, called the Milky Way. We will discuss this farther in Part III, but we will see in this chapter that location of stars in the galaxy can tell us something about those stars. In particular, some stars are confined to the thin disk of the Milky Way, while others form a more spherical distribution. In this chapter, we will discuss groupings of stars, called clusters, and see how they vary in size, content and galactic distribution.

Types of clusters

We distinguish between two types of star clusters – galactic clusters and globular clusters.

Galactic clusters are named for their confinement to the galactic disk. A selection of images of galactic clusters is in Fig. 13.1. A familiar galactic cluster, the Pleiades, is shown in Fig. 13.1(a). Note the open appearance in which individual stars can be seen. Because of this appearance, galactic clusters are also called open clusters. Galactic clusters typically contain <103 stars, and are less than ~10 pc across. Recent sensitive near IR surveys are showing more members than we had previously thought in many clusters. In the photograph, we see some starlight reflected from interstellar dust. Galactic clusters are sometimes associated with interstellar gas and dust.

Our study of the Milky Way has been aided greatly by studies of other galaxies. However, for a long time it wasn't clear that the spiral nebulae we see in the sky are really other galaxies. From their appearance, it might just be assumed that these nebulae are small nearby objects, just as HII regions are part of our galaxy.

The issues were crystallized in 1920 in a debate between Harlow Shapley and Heber D. Curtis. Curtis argued that spiral nebulae were really other galaxies. His argument was based on some erroneous assumptions. First, he confused novae in our galaxy with supernovae in other galaxies. Shapley thought the spiral nebulae were part of our own galaxy, partly based on an erroneous report of a measurable proper motion for some nebulae.

The issue was settled in 1924 by the observational astronomer Edwin Hubble (after whom the Space Telescope is named). Hubble studied Cepheids in three spiral nebulae (including the Andromeda Galaxy), and clearly established their distance as being large compared with the size of the Milky Way. There is some problem with Hubble's analysis, involving type I vs. type II Cepheids. However, even this factor of 2 error in the distance was not enough to alter the basic conclusion that spiral nebulae are not part of our own galaxy. Following this work, Hubble made a number of pioneering studies of other galaxies, essentially opening up the field of extragalactic astronomy.

In this chapter we look at galaxies with unusual activity within and around them. For many years astronomers thought of these various types of activity as being distinct. We now realize that many of them have similar origins, but differ in the specific conditions within the galaxy or its environment. We realize that all of this activity takes place in the nucleus of the galaxy, or is driven by activity in the nucleus. We say that these phenomena are associated with active galactic nuclei (AGN).

Starburst galaxies

Some galaxies appear to be giving out excessive amounts of radiation in the infrared. When we studied star formation in Chapter 15, we saw that regions with recent star formation give off a lot of infrared radiation. The energy comes from the newly formed stars, and heats the dust (from the parent cloud) surrounding the stars. The dust then glows in the infrared. The more energy the young stars put into the cloud, the more infrared radiation is released. The excess infrared radiation from some galaxies suggests that those galaxies have very high rates of star formation. The rate is so high that it cannot be sustained for very long, or it would use up all of the interstellar material. This leads to the idea that this excessive star formation is a short-lived phenomenon. We therefore call such galaxies starburst galaxies.

There are a vast number of smaller objects in our Solar System, not as substantial as our Moon, but which provide important clues on the history of the Solar System. These are asteroids, comets and meteoroids. We have also included the ninth planet, Pluto, in this chapter. As we will see below, recent determinations of Pluto's mass make it by far the least massive planet, and it has more properties in common with the other less massive objects in the Solar System.

Pluto

Pluto was discovered in 1930, following an extensive search, by Clyde Tombaugh. The search was initiated by Percival Lowell after it was thought that a planet beyond Neptune might be perturbing Neptune's orbit. Calculations narrowed the range of possible locations on the sky, and a search was carried out. As Fig. 26.1 shows, Pluto doesn't stand out very well against the background of stars. It is detectable as a planet only by its very slow motion with respect to the stars.

For Pluto to have a perturbing effect on other planets, its mass must be greater than that of the Earth. For this reason, since its discovery, Pluto's mass has been overestimated. We now know that its mass is much less than previously thought, and that it has no measurable effect on other planets. In a sense, Pluto's discovery was accidental. It was a result of an extensive search of a particular region in the sky.