Unit 6: Double Stars, Variable Stars and Clusters of Stars, and What Can Be Learned from Them
 
 

OVERVIEW

The types of double (binary) stars are discussed along with their importance for deducing the masses of stars. The trends with mass on the main sequence in the HR diagram is described, along with the mass-luminosity relationship. The implications for the lifetimes of stars are discussed. Some kinds of variable stars are described. The two kinds of star clusters are discussed along with the properties of Population I (disk) and Population II (halo) stars in the Galaxy.

LEARNING OBJECTIVES

At the end of this unit you should be able to:

1. Describe the various types of double (binary) stars, along with their importance for studying the masses of stars.

2. Explain the systematics of the masses of stars on the main sequence and how stellar mass on the main sequence is related to stellar surface temperature and luminosity.

3. Discuss the mass-luminosity relation for the main sequence and what this implies for the lifetime of a star of a given mass.

4. Describe some of the properties of variable stars.

5. Describe stellar populations in the Milky Way Galaxy, and the properties of population I and population II stars, including their chemical composition.

 6. Describe the disk and halo of the Milky Way Galaxy, and the location and properties of open (Galactic) and globular clusters.

7. Discuss the age of clusters, how age affects the appearance of a cluster's main sequence, and the implications for stellar evolution theory.

 KEY WORDS double star

binary star

visual binary

spectroscopic binary

eclipsing binary

astrometric binary

light curve

stellar mass

mass-luminosity relation on the main sequence

stellar lifetime

variable star

Mira variable

Cepheid variable

RR Lyrae variable

Milky Way Galaxy

stellar population

population I

population II

disk

halo

star cluster

open (Galactic) cluster

globular cluster

chemical composition of a star

short or long main sequence

cluster age

stellar evolution

 WRITTEN NOTES

Binary Stars

Astronomers call double stars which orbit each other binary stars.

Binary stars revolve around each other because of their mutual gravitational attraction.

There are various kinds or types of binary stars. The classification of a binary star system's type depends on its observed properties. It is possible for a binary to be of more than one type.

Four main types of binary stars are:

1. Visual Binary. This is a binary star system that is seen to be double through a telescope.

2. Spectroscopic Binary. This is a binary that is known to be double because the Doppler shifts in the spectral lines are observed to change with time. The Doppler shifts change because the stars alternatively come toward and go away from the Sun-Earth system while the stars orbit each other.

3. Eclipsing Binary. This is a binary in which one star periodically hides (occults or eclipses) the other. This causes periodic light variations.

4. Astrometric Binary. A star that is part of an astrometric binary star system `wiggles' as it moves across the sky (proper motion) because it is orbiting around another star. The other star may or may not be visible.

 By studying the different types of binaries we learn about the properties of stars. The best cases for learning about stars occur when we study binaries that are of more than one type.

Note that the shape of the light curve of an eclipsing binary star system depends on the diameters of the stars and the angle from which we view them. A light curve of a binary is a plot or graph of its apparent brightness (or apparent magnitude) at different times. Analyzing a light curve is a common way for astronomers to study any object that changes its brightness as a function of time.

 Stellar Masses If a star system is both a spectroscopic binary and an eclipsing binary, observations yield enough information to determine accurate orbits for the two stars. By using the theory of gravity, the masses of each individual star can be calculated.

From observations of binaries we find that there are many more low mass stars than high mass stars. Stars may have masses as low as 0.2 solar masses and as high as 100 solar masses.

From observations of binaries we also find that, for main sequence stars, there is a correlation between the luminosity (L) of a star and its mass (M). This is given by the mass-luminosity relation which indicates that the luminosity of a main sequence star increases rapidly as the mass of the star increases (roughly L ~ M3.5).

The most massive main sequence stars are the hot O types, while the least massive main sequence stars are the cool M types. In order of decreasing mass and decreasing temperature (and decreasing diameter), the types of main sequence stars are: O, B, A, F, G, K, M.

 Stellar Diameters We have already discussed how a star's diameter can be determined if we know it's luminosity (computed from its apparent brightness and its distance) and surface temperature. The Stefan-Boltzmann law helps us do this computation.

We have also noted how studying the shapes of light curves of eclipsing binary stars is another way to determine the diameters of individual stars.

[In addition to those traditional methods, there are several other ways to determine stellar diameters.]

Stellar diameters can be determined by observing how long it takes a star to disappear behind the edge of the Moon. This is the lunar occultation technique.

 Stellar diameters can be determined using interferometry, a technique which measures incoming radiation from two locations and then combines the two signals. This technique yields very high resolution images.

Stellar diameters can be determined using speckle interferometry, a technique which uses high speed imaging to overcome the blurring effect of the earth's atmosphere.

 A Note on Stellar Lifetimes on the Main Sequence The mass-luminosity relation for main sequence stars (L ~ M3.5) tells us that the luminosity of a main sequence star increases rapidly as the mass increases. The implication of this is that more massive stars use up their hydrogen fuel through nuclear energy generation much more quickly than lower mass stars.

The most massive stars (O types) will use up their fuel in less than 1 million years (106 years), while the least massive stars (M types) will take longer than 10 billion years (1010 years) to use up their fuel.

 Variable Stars A variable star is a star which changes its brightness with time. Single stars may vary because their diameter and/or surface temperature change with time. Stellar flares and other phenomena may also cause stars to change their brightness. As noted earlier, binary stars also vary in brightness if they eclipse each other periodically.

As noted earlier, a plot of the brightness of a star versus time is called a light curve. Many stars vary in a periodic way, and so the most important property of a light curve is its period.

Three notable types of single variable stars are:

1. Mira Variables. This is the most numerous type of variable in the sky. They are giant stars of type M which are many 100 times the diameter of the Sun. Their periods are long (years) and they may change in brightness by factors of 100 over their period. Their periods are not exactly regular. 2. Cepheid Variables. Cepheids are also very bright giant stars several 100 to 10,000 times brighter than the Sun, but they are relatively rare. Their periods are very regular, ranging from 1 to 100 or more days. If the period of a Cepheid is known, its luminosity can be determined (this follows from the period-luminosity relation for Cepheids which was determined from years of careful analysis of much Cepheid data). Since the luminosity of a Cepheid is known, these are the most important type of variable star. From the luminosity (absolute magnitude) and apparent brightness (apparent magnitude) of the Cepheid, the inverse square law can be used to calculate the distance to the Cepheid.

3. RR Lyrae Variables. This is another type of giant variable star, but periods are less than one day. On average, they have the same luminosity (absolute magnitude) and so they can also be used as distance indicators. Many of them are found in globular clusters.

 The Milky Way Galaxy The galaxy of 1011 stars that we live in is called the Milky Way Galaxy. It mostly looks like a flattened (disk-shaped) distribution of stars arranged in a spiral pattern, but it is also surrounded by a tenuous spherical halo of stars. Stellar Populations Astronomers broadly group stars found in the Milky Way Galaxy into Population I type or Population II type. This grouping is primarily based on the chemical composition of the star, but there are correlations with other properties of stars as well. Chemical composition refers to the degree to which heavy elements are present relative to hydrogen and helium. (Astronomers call elements which have more than two protons in their nucleus heavy elements.) 1. Population I stars have chemical compositions similar to that of the Sun. For reasons discussed later, they tend to be younger and lie in the plane of the Galaxy.

2. Population II stars have chemical compositions with fewer heavy elements than found in the Sun. For reasons discussed later, they tend to be older and lie in the halo of the Galaxy.

 Clusters of Stars A star cluster refers to a volume in space in which there is a large concentration of stars.

There are two types of cluster:

1. Open Clusters (sometimes called Galactic Clusters).

2. Globular Clusters.

 Clusters are important for two reasons: 1. All stars in a cluster are approximately the same distance from us. This means that an HR diagram can be plotted for a cluster more easily, without making corrections for variations in distance.

2. All stars in a cluster formed at approximately the same time.

 Open Clusters (also called Galactic Clusters) Open or Galactic Clusters tend to have the following properties: 1. They have no regular shape.

2. They contain hundreds of stars.

3. They are found in the Galactic disk.

4. Spectral analysis shows that they have chemical compositions like the Sun (Population I type stars).

5. They have long main sequences on the HR diagram which indicate that they are young (e.g., they contain young hot O and B type Population I stars). The stars must be young (i.e., less than 106 to 107 years old) because, if they were not, the O and B type stars would have used up their hydrogen fuel and evolved off the main sequence.

 Globular Clusters Globular Clusters tend to have the following properties: 1. They have a regular spherical shape (round) with the stars more closely packed toward the center.

2. They contain 104 to 106 stars per cluster.

3. They are found in the Galactic halo.

4. Spectral analysis shows that they have chemical compositions which are not as enriched with heavy elements as the Sun.

5. They have short main sequences on the HR diagram which indicate that they are old (i.e., they do not contain O, B, A, F, and G Population II stars). The stars must be old (greater than 1010 years old) because, if they were not, hot stars which had hydrogen fuel would still be present on the globular cluster main sequences.

 Checking the Theory of Stellar Evolution Observations of clusters are consistent with theoretical predictions of stellar evolution models. READING ASSIGNMENT

Text: Chapter 15

HOMEWORK

Text: Chapter 15, Problem 8. 
(Also pay attention to Review Question 19. Understand it, but you don't need to do it for homework.)