Nature of the Universe

Chapter 13

Double Stars, Variable Stars, Clusters and Nebulae

Our Sun is a single star with approximately constant brightness. In fact, in the universe, many stars are not alone, they interact with each other to form binary or multiple star systems. Besides, many stars vary in their brightness, they are called variable stars. There are also clusters and nebulae. They are important objects in studying stellar evolutions.

Binary Stars

Many stars orbit around other stars under the mutual gravitational attractions. If two stars orbit around one another, they form a binary star system. If three or more stars interact with each other, they form a multiple star system. In fact, over 50% of the stars are members of binary or multiple star systems. As a remark, binary stars are also known as double stars.

There are basically five types of binary stars, according to how the binary systems are discovered. Thus, some systems could belong to more than one type.

Visual Binary: Binary systems in which both components can be seen are called visual binary stars. However, not all stars apparently close together are gravitationally connected, they could be actually at different distances from the observer. Such stars are called optical doubles, e.g. zeta Ursa Majoris, which consists of two physically unrelated stars, Mizar and Alcor. They do not have much physical significance.
Spectroscopic Binary: In a binary system that is too distant or in which the stars are too close together to be resolved, the two stars will appear as one. We can still confirm that it is a binary system by investigating its spectrum, because the Doppler effect (See Chapter 5.) induced by their orbital motion will affect the spectra. Such systems are called spectroscopic binaries.
Eclipsing Binary: Sometimes, in a binary star system, one star will pass in front of the other producing what we call eclipsing binary. It can be treated as a special kind of visual binary. Eclipsing binary systems are variable stars (see below). The following is a typical eclipsing binary, Algol.
Contact Binary: In these binary stars, components are too close together that they have material exchange. The mutual gravity may also deform the stars and glue them together.
Astrometic Binary: It could happen that one star of the binary is not observable for some reason, but we could detect if the other star moves across the sky. Since the stars are orbiting around the center of mass of the binary, the visible one will move in a wavy line. This was how we discovered the companion of Sirius.

By studying the periods of mutual rotations of the binary systems, we can find the masses and sizes of the component stars. Those parameters are very difficult to be measured for single stars.

Variable Stars

Some stars vary their brightness from time to time, they are called variable stars. There are several types of variable stars. The graph showing the variation of brightness with respect to time is called the light curve.

Eclipsing Variables: They are actually eclipsing binaries. When a star goes behind another, there will be a reduction of total luminosity. Since the motion of the stars is periodic, the light curve will also be periodic. However, not all binary systems are eclipsing, it depends on the inclination angles of the plane of orbit of the systems.
Pulsating Variables: Unlike the eclipsing variables that are related to geometry, some variable stars are variables because of their intrinsic structure. Pulsating variables are stars that are continuously expanding and contracting and therefore show variations in brightness.

The most famous class is the Cepheid variables with the light curves similar to the ones above. Their periods, in the range of a few days to a few months, have a definite relation with the luminosities. The longer the period, the brighter the star is. Thus, by measuring the period of a Cepheid variable, we know its absolute magnitude, hence, we can tell how far it is away by comparing with its apparent magnitude.
Well, you may ask: How can we determine the luminosity-period relation? We have to use some other methods to measure the luminosity or equivalently the absolute magnitude of the Cepheid variable. Since we can readily measure the apparent magnitude of a Cepheid variable, to measure the luminosity means measuring the distance. We use some distance measurement methods, for example, parallax, to determine the relation. This usually means that we find out the relation using stars near us, then apply the relation to greater distances. In general, we use accurately determined distance indicators for small distance to calibrate distance indicators for greater distances. We have to use quite a few distance indicators because there is no single one that can measure all the distances. This is the cosmic distance ladder. Cepheid variable is the foundation of this ladder.

Courtesy STScI.
Eruptive Variables: Pulsating variables vary periodically, but for some stars, there may be sudden changes in their brightness. Such kinds of stars are called eruptive variables. They include novae and supernovae. Novae are usually binary stars. Materials are transferred from one component to another. Explosions on or closed to the surface of the recipient star will happen after sufficient material is accumulated. We will talk about supernovae in Chapter 16.

Stellar Clusters

Stellar cluster or cluster of stars is a group of stars bounded by their mutual gravity. When compared with the multiple star systems, they consist of many more stars, from tens to millions. Stars in a cluster formed at the about the same time, hence have roughly the same age. They are also at approximately the same distance from the observer. This greatly simplifies the various analyses, for example, their relative apparent magnitudes are equal to their relative absolute magnitudes.

There are two types of clusters.

Open Cluster: An open cluster consists of about a few hundred stars, the stars are mainly younger stars. The typical diameter of an open cluster is less than 100 light years. They are called open because their stars are relatively far apart and their shapes are irregular. An example is M45 of Taurus.

Courtesy NASA.
Globular Cluster: A globular cluster consists of over ten thousand stars in a region of 100 light years. Comparing with the open cluster, their stars are older. Moreover, the stars are concentrated. An example is M80 in Scorpius.

Courtesy STScI.

Nebulae

In most region of space, the particle density is about 1 atom per cubic centimeter, however, in some region of space, the density is over 1000 atom/cm³. (The density of air is about 10¹⁹ atom/cm³, while the best vacuum made by human is about 10⁷ atom/cm³.) These regions are called nebulae. The typical size of a nebula is about hundred light years. Nebulae are made up of gases and dusts. An example is M42 in Orion.

Courtesy NASA.

Nebula by itself cannot produce any energy. However, some may scatter light from the other stars and so be seen. Also, in the cases where there are some bright stars nearby, the gases may be ionized and emit red light. Nebulae are the birth places of stars. (Don't confuse nebulae with planetary nebulae, which we will discuss in Chapter 15.)

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