Jose Wudka - Space-Time, Relativity and Cosmology - Ch8 - The universe.. size, origins, contents.pdf - Astrofizyka i kosmologia - joe77joe77

Chapter 8

The universe: size, origins,

contents

8.1 Introduction

The general and special theories of relativity discussed in the previous chap-

ters are the tools currently used in the investigation and description of the

universe. Most of the objects in the universe are somewhat mundane: stars,

planets, rocks and gas clouds. Yet in many respects the universe is far from

being a placid and peaceful place. There are stars which explode with the

energy of a billion suns, black holes with millions of times the mass of our

sun which devour whole planetary systems, generating in one day as much

energy as our galaxy puts out in two years. There are enormous dust cluds

where shock waves trigger the birth of new stars. There are intense bursts

of gamma rays whose origin is still uncertain.

These phenomena are not infrequent, but appear to be so due to the

immense distances which separate stars and galaxies; for one of the most

impressive properties of the universe is its size. The universe is so large that

just measuring it is very dicult, and nding out the distance to various

objects we observe can be a very complicated proposition.

In order to extract information about the universe a toolbox of methods

has been devised through the years. I will rst discuss the most important of

these methods, and with these I will describe how measure the universe and

discuss its evolution. We need to determine sizes and distances because, as

we will see, they provide basic information about the history of the universe.

Most of the data we get from the universe comes in the form of light

(by which I mean all sorts of electromagnetic radiation: from radio waves

to gamma rays). It is quite remarkable that using only the light we can

determine many properties of the objects we observe, such as, for example,

their chemical composition and their velocity (with respect to us). In the

rst two sections below we consider the manner in which we can extract

information from the light we receive.

But detecting light is not the only way to obtain information from the

universe, we also detect high-energy protons and neutrons (forming the ma-

jority of cosmic rays). The information carried by these particles concerns

either our local neighborhood, or else is less directly connected with the

sources: isolated neutrons are not stable (they live about 10 minutes), so

those arriving on Earth come from a relatively close neighborhood (this de-

spite time dilation - Sect. ??). Protons, on the other hand are very stable

(the limit on their lifetime is more than 10 32 years!), but they are charged;

this means that they are aected by the magnetic elds of the planets and

the galaxy, and so we cannot tell where they came from. Nonetheless the

more energetic of these particles provide some information about the most

violent processes in the universe.

In the future we will use yet other sources of information. Both gravi-

tational wave detectors and neutrino telescopes will be operational within

the next few years. Neutrinos are subatomic particles which are copiously

produced in many nuclear reactions, hence most stars (including our Sun)

are sources of neutrinos. These particles interact very very weakly, and be-

cause of this they are very hard to detect. On the other hand, the very

fact that they interact so weakly means that they can travel through very

hostile regions undisturbed. Neutrinos generated in the vicinity of a black

hole horizon can leave their native land unaected and carry back to Earth

information about the environment in which they were born.

8.2 Light revisited

In this section I will describe two properties of the light we receive and the

manner in which it can be used to extract information about its sources.

8.2.1 The inverse-square law

A source of light will look dimmer the farther it is. Similarly the farther

away a star is the fainter it will look; using geometry we can determine just

how a star dims with distance

Imagine constructing two spheres around a given star, one ten times

farther from the star than the other (if the radius of the inner sphere is R,

the radius of the outer sphere is 10R). Now let us subdivide each sphere into

little squares, 1 square foot in area, and assume than on the inner sphere

I could t one million such squares. Since the area of a sphere increases

as the square of the radius, the second sphere will accommodate 100 times

the number of squares on the rst sphere, that is, 100 million squares (all

1 square foot in area). Now, since all the light from the star goes through

both spheres, the amount of light going through one little square in the inner

sphere must be spread out among 100 similar squares on the outer sphere.

This implies that the brightness of the star drops by a factor of 100, when

we go from the distance R to the distance 10R (see Fig. 8.1).

Figure 8.1: Illustration of the inverse-square law: all the light trough the 1

square-foot rst area goes through the second one, which is 100 times larger,

hence the light intensity per square foot is 100 times smaller in the second

area. The intensity drops as 1=R 2 .

If we go to a distance of 20R the brightness would drop by a factor of

400, which is the square of 20, for 30R there would be a decrease by a factor

of 900 = (30) 2 , etc. Thus we conclude that

The brightness drops as 1= (distance) 2 :

Light intensity drops as

1= ( distance ) 2 :

This fact will be used repeatedly below.

8.2.2 The Doppler eect

If one observes a redder

color (longer wavelength

than the one you know is

being emitted) then the

source is moving away from

you, if bluer (shorter

wavelength that the one you

know is being emitted) the

source is moving toward you

We have seen that light always travels at the same speed of about 300; 000km/s;

in particular light emitted by a sources in relative motion to an observer

travels at this speed. Yet there is one eect on light which shows that its

source is moving with respect to the observer: its color changes.

Imagine standing by the train tracks and listening to the train's horn.

As the train approaches the pitch of the blast is higher and it becomes lower

as the train recedes from you. This implies that the frequency of the sound

waves changes depending on the velocity of the source with respect to you,

as the train approaches the pitch is higher indicating a higher frequency and

smaller wavelength, as the train recedes from you the pitch is lower corre-

sponding to a smaller frequency and a correspondingly larger wavelength.

This fact, called the Doppler eect, is common to all waves, including

light waves. Imagine a light bulb giving o pure yellow light; when it moves

towards you the light that reaches you eye will be bluer, when the bulb

moves away form you the light reaching your eye will be redder. If you have

a source of light of a known (and pure) color, you can determine its velocity

with respect to you by measuring the color you observe. Qualitatively, if

one observes a redder color (longer wavelength than the one you know is

being emitted) then the source is moving away from you, if bluer (shorter

wavelength that the one you know is being emitted) the source is moving

toward you (see Fig. 8.2).

The important point here is that knowing the frequency at the source

and measuring the observed frequency one can deduce the velocity of the

source 1 If the source is moving suciently fast towards you the yellow light

will be received as, for example, X-rays; in this case, however, the source

must move at 99.99995% of the speed of light. For most sources the shift in

frequency is small.

8.2.3 Emission and absorption lines

When heated every element gives o light. When this light is decomposed

using a prism it is found to be made up of a series of \lines", that is, the

output from the prism is not a smooth spectrum of colors, but only a few of

them show up. This set of colors is unique to each element and provides a

unique ngerprint: if you know the color lines which make up a beam of light

(and you nd this out using a prism), you can determine which elements

were heated up in order to produce this light.

1 More precisely this is the velocity along the line of sight,

Figure 8.2: Diagram illustrating the Doppler eect. The source is moving

to the left hence a receiver on the right will see a red-shifted light while a

receiver on the left will see a blue-shifted one. .

Similarly, when you shine white light through a cold gas of a given el-

ement, the gas blocks some colors; when the \ltered" light is decomposed

using a prism the spectrum is not full but shows a series of black lines (corre-

sponding to the colors blocked by the gas); see Fig. 8.3. For a given element

the colors blocked when cold are exactly the same as the ones emitted when

hot.

The picture in Fig. 8.3 corresponds to a single element. For a realis-

tic situation the decomposed light can be very complex indeed, containing

emission and absorption lines of very many elements. An example is given

in Fig. 8.4.

After the discovery of emission and absorption lines scientist came to rely

heavily on the fact that each element presents a unique set of lines: it is its Each element presents a

unique set of lines

inimitable signature. In fact, when observing the lines from the solar light,

it was found that some, which are very noticeable, did not correspond to

any known element. Using this observation it was then predicted that a new

element existed whose absorption lines corresponded to the ones observed

in sunlight. This element was later isolated on Earth, it is called Helium

(from helios: sun).

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