Physics

Key unit Competence

By the end of the unit the learner should be able to explain the origin, the structure and the evolution of the Universe.

My goals

•Outline types of galaxies and cluster of galaxies.

•Explain the structure of Milky way galaxy and earth’s position

•Apply planetary motion knowledge to explain phenomena of planet motion.

•Explain Doppler shift due to cosmic expansion.

•State Hubble’s law.

•Explain the big bang theory and relate to the expansion of universe.

Introductory activity

1. a. Why are there different types of stars, such as red giants and white dwarfs, as well as main-sequence stars?

d. Were they all born this way, in the beginning? Or might each different type represent a different age in the life cycle of a star?

2. How can astronomers tell the galaxies are moving away? How the explosion at the beginning can explain such expansion?

14.1 GALAXIES AND CLUSTERS

Activity 14.1 Our place in the Universe

1. Our planet is the Earth and it orbits around the Sun, does the sun orbit anything?

2. How does the sun interact with other objects in the Universe?

14.1.1 The structure of the Milky Way Galaxy

The Milky Way is our own galaxy.It is a spiral galaxy, composed of three parts:

•The disk. Most of the stars in the Milky Way are located in a disk about 2 kpc thick, and about 40 kpc across. A parsec (pc) is a unit of distance commonly used in astronomy, 1pc=3.86x1016 m=3.26 ly. The disk is composed primarily of hot, young stars, and contains lots of dust and gas.

•The bulge. The bulge lies in the center of the galaxy. It is about 6 kpc across, and extends above and below the disk. There is very little gas or dust which arethe material required to form new stars. Therefore the bulge consists mainly of old stars.

•The halo. The halo is primarily made up of globular clusters, and is roughly spherical in shape. It is centered on the center of the galaxy, and is about 30 kpc to 40 kpc in radius. Again, there is very little dust and gas. The halo is primarily composed of old stars. Interestingly, most of these stars are low metallicity stars, which mean that they have even fewer metals than the Sun.

Our Galaxy has a diameter of almost 100 000 light-years and a thickness of roughly 2000 ly. It has a central bulge and spiral arms (Fig.14.1).

Our Sun, which is a star like many others, is located about halfway from the galactic centre to the edge, some 26 000 ly (8.5 kpc) from the centre. Our Galaxy contains roughly 400 billion stars 9(400 10 )×. The Sun orbits the galactic centre approximately once every 220 million years, so its speed is roughly 200km/s relative to the centre of the Galaxy. There is also strong evidence that our Galaxy is permeated and surrounded by a massive invisible “halo” of “dark matter”

In 1915, Shapley attempted to figure out the location of the center of the galaxy by mapping out the positions of globular clusters. A globular cluster is a group of hundreds of thousands of stars, all tightly bound together in a ball 20 pc to100 pc across. They have a very distinctive appearance, and so are easy to find (Halliday, Resneck, & Walker, 2007).

He discovered that 20% of the clusters lay in the direction of the constellation Sagittarius, and occupied only about 2% of the sky, and inferred that the bulk of the Galaxy must lie in that direction. He used RR Lyrae stars to estimate the distances to the globular clusters. He found that these globular clusters are centered on a point about 15 kpc from the Sun. Shapley reasoned that if the clusters were distributed evenly about the Galaxy (and there’s no reason to think they shouldn’t be), then the center of the Galaxy lies in the direction of Sagittarius, about 15 kpc away. Shapley didn’t know about dust and consequently he overestimated the distance to the center of the Galaxy by a factor of two. The center is actually about 8.5 kpc away (Douglass, PHYSICS, Principles with applications., 2014).

Example 14.1: Our Galaxy’s mass

Estimate the total mass of our Galaxy using the orbital data above for the Sun about the centre of the Galaxy. Assume the mass of the Galaxy is concentrated in the central bulge.

Answer

We assume that the Sun (including our solar system) has total mass m and moves in a circular orbit about the centre of the Galaxy (total mass M), and that the mass M can be considered as being located at the centre of the Galaxy. We then apply Newton’s second law,Fmα= with αbeing the centripetal acceleration, α=and for F we use the universal law of gravitation

Our Sun and solar system orbit the center of the Galaxy, according to the best measurements as mentioned above, with a speed of about v at a distance r from the Galaxy center we use Newton’s second law:

In terms of numbers of stars, if they are like our Sun there would be about stars.

14.1.2 Types of galaxies

There are three main types of galaxies: Elliptical, Spiral, and Irregular. Two of these three types are further divided and classified into a system that is now known the tuningfork diagram Fig 14.2. When Hubble first created this diagram, he believed that this was an evolutionary sequence as well as a classification. He believed that all galaxies started out as E0 ellipticals and evolved into spirals, as the galaxy flattened out and developed arms. Astronomers have found today that instead, possibly it is the other way around. The spiral galaxies sometimes merge to form elliptical galaxies (Linda, 2004).

a. Spirals

Spiral galaxies have three main components: a bulge, disk, and halo. The bulge is a spherical structure found in the center of the galaxy. This feature mostly contains reddish, older stars. The disk is made up of dust, gas, and bluish, younger stars. The disk forms arm structures. Our Sun is located in one of the arms, called the Orion arm which is thought to be an offshoot of the Sagittarius arm in our galaxy, the Milky Way.The halo of a galaxy is a loose, spherical structure located around the bulge and some of the disk. The halo contains reddish, old clusters of stars, known as globular clusters.

Spiral galaxies are classified into two groups, ordinary and barred. The ordinary group is designated by S, and the barred group by SB. In normal spirals (as seen Fig.14.5) the arms originate directly from the nucleus, or bulge, where in the barred spirals (see Fig.14.5) there is a bar of material that runs through the nucleus that the arms emerge from. Both of these types are given a classification according to how tightly their arms are wound.

The classifications are a, b, c, d ... with “a” having the tightest arms. In type “a”, the arms are usually not well defined and form almost a circular pattern. Sometimes you will see the classification of a galaxy with two lower case letters. This means that the tightness of the spiral structure is halfway between those two letters.

Elliptical galaxies are classified according to the elongation from a perfect circle (also known as the ellipticity). The larger the number, the more elliptical the galaxy is. So, for example a galaxy of classification of E0 appears to be perfectly circular, while a classification of E7 is very flattened (the most elliptical).

The elliptical scale varies from 0 to 7. Elliptical galaxies have no particular axis of rotation.Ellipticals galaxies can also be sorted by size:

•Giant ellipticals are a few trillion parsecs across. They contain trillions of stars.

•Dwarf ellipticals, on the other hand, are only about a thousand parsecs across, and contain millions of stars.

There are many dwarf elliptical galaxies than the giants, but the giants are so large that they actually contain most of the mass that is found in elliptical galaxies. Ellipticals contain very little gas and dust. Fig. 14.8 shows a few elliptical galaxies.

c. Irregulars

Irregular galaxies are all the galaxies that don’t fit in the other two categories. In general, they are thought to be the result of collisions between galaxies. They contain a lot of dust and gas, and consequently are full of young stars. They have no regular or symmetrical structure and the fraction of such galaxies is very small.They are divided into two groups, Irr I and IrrII.

Irr I type galaxies have HII regions, which are regions of elemental hydrogen gas, and many Population I stars, which are young hot stars. Irr II galaxies simply seem to have large amounts of dust that block most of the light from the stars. All this dust makes almost impossible to see distinctly stars in this kind of galaxies.

14.1.3 Clusters of galaxies

In addition to stars both within and outside the Milky Way, we can see by telescope many faint cloudy patches in the sky which were all referred to once as “nebulae” (Latin for “clouds”). A few of these, such as those in the constellations Andromeda and Orion, can actually be distinguished with unaided eye on a clear night.

A group of stars within a galaxy which are close to each other and held together by gravitational attraction is called stellar cluster. Some are star clusters (Fig. 14.10a), groups of stars that are so numerous they appear to be a cloud. Others are glowing clouds of gas or dust (Fig. 14.10b), and it is for these that we now mainly reserve the word nebula.

Most fascinating are those that belong to a third category: they often have fairlyregularelliptical shapes. Immanuel Kant (about 1755) guessed they are faint because they are a great distance beyond our Galaxy. At first it was not universally accepted that these objects were extragalactic—that is, outside our Galaxy. But the very large telescopes constructed in the twentieth century revealed that individual stars could be resolved within these extragalactic objects and that many contain spiral arms.

Edwin Hubble (1889–1953) did much of this observational work in the 1920s using the 2.5 m telescope on Mt. Wilson near Los Angeles, California, and then the world’s largest. Hubble demonstrated that these objects were indeed extragalactic because of their great distances.

The distance to our nearest large galaxy, Andromeda, is over 2 million light-years, a distance 20 times greater than the diameter of our Galaxy. It seemed logical that these nebulae must be galaxies similar to ours. (Note that it is usual to capitalize the word “galaxy” only when it refers to our own.) Today it is thought there are roughly 1110galaxies in the observable universe—that is, roughly as many galaxies as there are stars in a galaxy. (See Fig. 14.11.)

Many galaxies tend to be grouped in galaxy clusters held together by their mutual gravitational attraction. Our own, called localgroup, contains at least 28 galaxies. Of these, three are spirals, eleven are irregulars and fourteen are ellipticals. There may be anywhere from a few dozen to many thousands of galaxies in each cluster. Furthermore, clusters themselves seem to be organized into even larger aggregates: clusters of clusters of galaxies, or superclusters.

Some astronomical measurements indicate that there is “something else” among the stars and interstellar materials. This is called dark matter, because it cannot be seen, but it apparently has mass and does affect other matter and gravitational fields. Although the so-called dark matter appears to account for around 90% of the mass of most galaxies, the nature of this material is not well understood. At the center of some galaxies, there may be super massive black holes. Again, they cannot be seen but they are indicated on how they affect the nearby stars.

14.1.4 Checking my progress

1. List the three major classifications of Galaxies. What do they all have in common?2. What is the name of the Galaxy that you live in?

14.2 COSMOLOGY

Activity 14.2: How stars are formed

What does it mean that distant galaxies are all moving away from us, and with ever greater speed the farther they are from us? Explain how the Hubble constant may be used to estimate the age of the universe

1. How do stars form? What factors determine the masses, luminosities, and distribution of stars in our Galaxy?

Cosmology aims to explain the origin and evolution of the Universe, the underlying physical processes, and thereby to obtain a deeper understanding of the laws of Physics assumed to hold throughout the Universe. Cosmology is the study of the history of the Universe as a whole, both its structure and evolution.

The study assumes that over large distances the Universe looks essentially the same from any location (the Universe is homogeneous) and that the Universe looks essentially the same in all directions (the Universe is isotropic). The two assumptions are known as the cosmologicalprinciple. In addition, it is assumed that the same laws of Physics hold everywhere in the Universe.

To study the evolution of the Universe, astronomers rely on observations of distant objects. For example, the Andromeda Galaxy (M31) is about 2 million light years away. This means that our photographs of M31 show the galaxy as it was 2 million years ago. The Virgo cluster of galaxies is about 50 million light years away, and the information presently received by our telescopes describe the state of the cluster as it was 50 million years ago. Information received from galaxies that are billions of light years away pertains to the state of these objects as they were billions of years ago, when they were much younger, possibly just forming. Receiving information from distant objects is equivalent to receiving information from the past. This information is vital in reconstructing the evolutionary stages of the galaxies, and the Universe as a whole.

14.2.1 Doppler shift due to cosmic expansion

Activity14.3: Doppler Effect

How Doppler Effect is used in communication with satellites?

1. How is the Doppler Effect used in Astronomy?

Movement toward or away from a source of radiation does indeed change the way we perceive the radiation.

Motion along any particular line of sight is known as radial motion. It should be distinguished from transverse motion, which is perpendicular to the line of sight. Radial motion but- not transverse motion- brings about changes in the observed properties of radiation.

In visible light, red light has the longest wavelength, and violet light the shortest. The light of an object moving away from an observer is shifted toward longer wavelengths (red color). The light from an object moving at a high speed toward an observer is shifted toward the color violet.

This change in the observed wavelength of a wave be it an electromagnetic (light) wave or an acoustical (sound) wave is known as the Doppler Effect, in honor of Christian Doppler, the nineteenth century Austrian physicist who first explained it.

Astronomers most often use the Doppler Effect to measure the velocity of galaxies, which are moving away from Earth the (red-shift effect, a shift to lower frequencies) or toward the Earth (blue-shift, toward shorter wavelength).

•Blue-shift

The equation for the observed frequency of a light wave when the source is traveling toward you (blue-shift) is:

The blue-shift equation for wavelength is:

where

•fb is the observed blue-shift frequency

•vb is the velocity of the source moving toward you

•c is the speed of light. c >> vb (c is much greater than vs)

•λb is the observed blue-shift wavelength

•λ is the emitted wavelength (Greek symbol lambda)

•Red-shift

The equation for the observed frequency of a light wave when the source is traveling away from you (red-shift) is:

The red-shift equation for wavelength is:

Where

•rf is the observed red-shift frequency,

•rv is the velocity of the source moving away from you,

•rλ is the observed red-shift wavelength,

•λ is the emitted wavelength (Greek symbol lambda

Note that “−” and “+” are reversed as compared to the standard Doppler Effect equations of sound waves. In general, when an object is approaching or moving away, the wavelength of the light it emits (or reflects) is changed. The shift of the wavelength,, is directly related to the velocity, v, of the object:

This value is known as the cosmological redshift of a star, denoted

•If z is positive, the star is moving away from us (receding object)- the wavelength is shifted up towards the red end of the electromagnetic spectrum.

•If z is negative, the star is moving towards us. This is known as blue shift and the emitted wavelength appears shorter

Example 14.2

If a distant galaxy is moving away from us at approximately 50 000 km/s and we approximate the speed of light (λ= 434 nm, which is in the violet region of the visible spectrum) as c = 300 000 km/s, calculate the resulting wavelength

Answer

the resulting wavelength will be

Substitute values into equation:

The line has shifted from violet to green.

Quick check 14.1:

a. M31 (the Andromeda galaxy) is approaching us at about 120 km s^-1. What is its red/blue-shift?

b. Some light from M31 reaches us with a wavelength of 590 nm. What is its wavelength, relative to M31?

Velocity

Typically, an astronomer would study the spectrum of a distant star or galaxy and measure the new observed spectral lines of the various elements on the object. Then the direction and velocity of the star or galaxy would be determined.The blue-shift equation for velocity is:

The red-shift equation for velocity is: 

Where λ is the wavelength emitted if the object is at rest and v is the component of the velocity along the ‘‘line of sight’’ or the ‘‘radial velocity.’’

Example 14.3

Suppose that molecules at rest emit with a wavelength of 18 cm. You observe them at a wavelength of 18.001 cm. How fast is the object moving and in which direction, towards or away from you?

Answer

To find out how quickly, use the Doppler equation:This problem calls for the Doppler equation.

The molecules are travelling with a radial speed of 16.7 km/s. Since the wavelength is longer, the light has been red-shifted, or stretched out, and so the object is moving away from you.

Quick check 14.2.

A radio spectrum of an interstellar cloud shows the 21 cm line shifted to 21.007 cm. Is the cloud approaching, receding, or remaining at the same distance from us? If it is travelling, what is its speed?

14.2.2 The Hubble’s law

Activity 14.4: Hubble’s law

Discuss the limitations of Hubble’s law. Explain how the Hubble constant may be determined.

Analysis of redshifts from many distant galaxies led Edwin Hubble to a remarkable conclusion. The speed of recession of a galaxy is proportional to its distance from us (Fig. 14.10). This relationship is now called the Hubble law; expressed as an equation,

Where

The is then commonly expressed in the mixed units (kilometers per second per megaparsec) where

To appreciate the immensity of this distance, consider that our farthest-ranging unmanned spacecraft have traveled only about 0.001 ly from our planet.

Another aspect of Hubble’s observations was that, in all directions, distant galaxies appeared to be receding from us. There is no particular reason to think that our Galaxy is at the very center of the Universe; if we lived in some other galaxy, every distant galaxy would still seem to be moving away. That is, at any given time, the universe looks more or less the same, no matter where in the universe we are. This important idea is called the cosmological principle.

There are local fluctuations in density, but on average, the universe looks the same from all locations. Thus the Hubble constant is constant in space although not necessarily constant in time, and the laws of Physics are the same everywhere.

Example 14.4 Recession speed of a galaxy

1. The spectral lines of various elements are detected in light from a galaxy in the constellation Ursa Major. An ultraviolet line from singly ionized calcium λ= 393nmis observed at wavelength λ=414rnm red-shifted into the visible portion of the spectrum.

a. At what speed is this galaxy receding from us?

b. Use the Hubble law to find the distance from earth to the galaxy

Answer

a. This example uses the relationship between redshift and recession speed for a distant galaxy. We can use the wavelengths λ at which the light is emitted and rλ that we detect on earth in Eq. (14.05) to determine the galaxy’s recession speed v if the fractional wavelength shift is not too great. The redshift is

For high redshift the speed is obtained by the following formula:

b. Use the Hubble law to find the distance from Earth to the galaxy Answer The Hubble law relates the redshift of a distant galaxy to its distance r from earth. We solve Eq.for r and substitute the recession speed v from Eq

14.2.4 The Big Bang theory and expansion of Universe

Activity 14.5: Stellar expansion

1. How does the curvature of the universe affect its future destiny?

2. Describe some of the evidence that the universe started with a “Big Bang.”

3. How does dark energy affect the possible future of the universe?

4. Explain how the big bang theory explains the observed Doppler Shifts of Galaxies.

The major theory of how the Universe started is the “Big Bang” theory. This states that about 13.7 billion years ago (13 700 000 000 years) all matter was compressed to what some estimate was the size of a golf ball. It then expanded in a “big bang” and spread out until it has reached the enormous size of the present-day Universe. While the matter was spreading out, it started to clump together into larger and larger masses. The turbulence of the expansion resulted in the spinning of the galaxies.

The whole idea of the Big Bang theory came when astronomers noticed that distant nebulas (or more correctly, nebulae) and galaxies were all moving away from us. It was also seen that they were moving away at speeds proportional to their distance from us. Since it is assumed that our galaxy is also moving in some direction, it was calculated that all of the galaxies in the universe were moving away from some given point in space.

The way astronomers were able to estimate the speed of the galaxies is by what is called the “red-shift” of their light. The red-shift is a form of Doppler Effect with light, such that when an object is moving away from you at high speeds, the light shifts towards lower frequencies.

Measurements show that the Universe is still expanding. By interpolating the directions and velocities backward, astronomers have estimated the beginning time of the explosion. Of course, such measurements are highly inaccurate. There is debate on this theory and whether the Universe will continue to expand or will start to contract.

The Hubble law suggests that at some time in the past, all the matter in the universe was far more concentrated than it is today. It was then blown apart in an immense explosion called the Big Bang, giving all observable matter more or less the velocities that we observe today.

When did this happen? According to the Hubble law, matter at a distance away from us is traveling with speed dv. the time needed to travel a distance is:

By this hypothesis the Big Bang occurred about 14 billion years ago. It assumes that all speeds are constant after the Big Bang; that is, it neglects any change in the expansion rate due to gravitational attraction or other effects. We’ll return to this point later. For now, however, notice that the age of the earth determined from radioactive dating is 4.54 billion years. It’s encouraging that our hypothesis tells us that the universe is older than the earth!

The expansion of the universe suggests that typical objects in the universe were once much closer together than they are now. This is the basis for the idea that the universe began about 14 billion years ago as an expansion from a state of very high density and temperature known affectionately as the Big Bang.

The birth of the universe was not an explosion, because an explosion blows pieces out into the surrounding space. Instead, the Big Bang was the start of an expansion of space itself. However, after the expansion of the universe, matter exploded into stars and galaxies. The observable universe was relatively very small at the start and has been expanding, getting ever larger, ever since. The initial tiny universe of extremely dense matter is not to be thought of as a concentrated mass in the midst of a much larger space around it.

The initial tiny but dense universe was the entire universe. There wouldn’t have been anything else. When we say that the universe was once smaller than it is now, we mean that the average separation between objects (such as electrons or galaxies) was less. The universe may have been infinite in extent even then, and it may still be now (only bigger). The observable universe (that which we have the possibility of observing because light has had time to reach us) is, however, finite.

14.2.4 Stellar evolution

Activity14.6: How are stars born

1. Explain why giants are not in the main sequence on theH-R diagram.

2. How do their temperatures and absolute magnitudes compare with those of main sequence stars?

It is believed that stars are born, when gaseousclouds (mostly hydrogen) and dust called a nebula contract due to the pull of gravity. Gravitational forces cause instability within the nebula. A huge gas cloud might fragment into numerous contracting masses, each mass centered in an area where the density is only slightly greater than that at nearby points. Once such “globules” form, gravity causes each to contract in toward its center of mass see Fig.14.13.

As the particles of such a protostar accelerate inward, their kinetic energy increases. Eventually, when the kinetic energy is sufficiently high, the Coulomb repulsion between the positive charges is not strong enough to keep all the hydrogen nuclei apart, and nuclear fusion can take place. When the particles in the smaller clouds move closer together, the temperatures in each nebula increase. As temperatures inside each nebula reach 10 000 000 K, fusion begins. The energy released radiates outward through the condensing ball of gas. As the energy radiates into space, stars are born.

In a star like our Sun, the fusion of hydrogen (sometimes referred to as “burning”) occurs via the proton–proton chain, in which four protons fuse to form a 4/2Henucleus with the release of γrays, positrons, and neutrinos:

These reactions require a temperature of about 107 K , corresponding to an average kinetic energy of about 1 keV.

The tremendous release of energy in this fusion reaction produces an outward pressure sufficient to halt the inward gravitational contraction. Our protostar, now really a young star, stabilizes on the mainsequence. Exactly where the star falls along the main sequence depends on its mass. The more massive the star, the farther up (and to the left) it falls on the H–R diagram of Fig. 14.14.

Our Sun required perhaps 30 million years to reach the main sequence, and is expected to remain there about 10 billion years but a star ten times more massive may reside there for only More massive stars have shorter lives, because they are hotter and the Coulomb repulsion is more easily overcome, so they use up their fuel faster. As it moves upward, it enters the redgiant stage. Thus, theory explains the origin of red giants as a natural step in a star’s evolution.

As hydrogen fuses to form helium, the helium that is formed is denser and tends to accumulate in the central core where it was formed. As the core of helium grows, hydrogen continues to fuse in a shell around it.

When much of the hydrogen within the core has been consumed, the production of energy decreases at the center and is no longer sufficient to prevent the huge gravitational forces from once again causing the core to contract and heat up.

The hydrogen in the shell around the core then fuses even more aggressively because of this rise in temperature, allowing the outer envelope of the star to expand and to cool. The surface temperature, thus reduced, produces a spectrum of light that peaks at longer wavelength (reddish). This process marks a new step in the evolution of a star. The star has become redder, it has grown in size, and it has become more luminous, which means it has left the main sequence. It will have moved to the right and upward on the on the H–R diagram, as it moves upward, it enters the red giant stageas shown in Fig. 14.15