E4. Cosmology

E6. Galaxies

IB Physics Power Points

Option E

Astrophysics

www.pedagogics.ca

Galaxies

A galaxy is basically a very large group of stars. Galaxies are not distributed randomly in space. They are usually found in groups called clusters. Galaxy clusters are grouped together on an even larger scale as superclusters.

There are three types of galaxies

1. spiral

2. elliptical

3. irregular

Spiral Galaxies

Characterized as disk shaped with a central bulge.

M31 M51

Our Galaxy – The Milky Way is a spiral galaxy

Elliptical Galaxies

Characterized by all bulge with no disk. Elliptical shaped and no gas (all stars)

M32 M87

Irregular Galaxies

Irregular shape

M82

Big Bang Theory and the Expanding Universe

The Big Bang theory is one explanation of the origin of space and time. • approximately 15 billion years ago, • the entire universe was concentrated into a single point. • rapid expansion from this origin.

Since the Big Bang, the density and temperature of the Universe has been decreasing as the Universe expands and the matter and energy become more spread out.

This rate of expansion has been decreasing due to gravitational attraction between all the masses in the Universe.

Big Bang Theory and the Expanding Universe

Support for the Big Bang Theory comes from 3 areas:

1. Olber’s Paradox

2. Galactic Red-shift

3. Microwave Background Radiation

Olbers’ Paradox - Why is it dark at night?

(see video on WIKI)

Newton’s view of the Universe

1. Extends infinitely

2. Contains an infinite number of stars

3. Static

4. Will exist forever

Heinrich Olber (early 1800’s) : if the above

statements are valid, no matter which

direction you look from Earth, you should

see a star. The light from billions of stars

should produce a bright night sky, not a dark one.

This argument can be extended quantitatively:

Assume that the stars in the universe are distributed evenly, in other words a uniform star density r.

For an observer on Earth, the Universe can be thought of as a series of ever expanding spherical shells.

The volume of a thin shell (thickness = x) can be determined by:

V = 4pr2x

r

x

The number of stars in a shell can then be determined by:

number of stars = (4pr2x)(r)Conclusion: the volume of each successive shell (and the number of contained stars) increases with r2.

For an observer on Earth, the amount of light received from these distant stars is less for stars that are further away. Recall that brightness is inversely proportional to r2.

Conclusion: the amount of light reaching Earth from a distant star decreases with r2.

Therefore the Universe should be equally bright in all directions! Every line of sight should end with a star.

Olbers’ Paradox - Solutions

We know it is dark at night so ……..

1. Perhaps the universe is not infinite

(not the current model)

2. Perhaps some star light gets absorbed

(but by what? No evidence for this)

3. The universe is expanding (support for Big Bang model)

Light from far away shells still has not reached us.

Implies the universe has a beginning.

The Expanding Universe?

Recall: Doppler effect. Assume there is motion between a light source and an observer such that they are moving away from each other. The Doppler effect states that the frequency perceived by the observer will be less than the frequency emitted by the source. In the case of light, this is called a red shift.

The current model of the expanding universe has all galaxies moving away from each other. The evidence for this is a red shift in emitted spectra.

Absorption lines appear at a certain place on the spectrum for an object at rest in relation to an observer.

Red-shift observed if the star is moving away from observer

Blue-shift observed if the star is moving toward observer

If the relative velocity between the star/galaxy and the observer is small (compared to that of the speed of light), a simplified equation can be used to relate the wavelength shift to the relative speed.

v

c

Where

Dl is the change in wavelength (positive if increasing)l is the wavelength emitted

v is the relative velocity between source and observer

Sample problem N02 F2 (c): A certain spectral line measured in the laboratory has a wavelength of 390.0 nm. When measured in the spectrum of a galaxy, the wavelength is found to be 395.8 nm. Determine the recession speed of the galaxy.

96 -1

9

(5.8 10 ) 4.5 10 ms

390 10

c cv

Background Microwave Radiation

In 1965, Arno Penzias and Robert Wilson used a radio antenna and found a previously undetected radiation that appeared to be the same regardless of the direction the antenna was pointing.

The spectrum of this radiation

models a Planck curve for a

black body with a temperature

of about 3 K.

What is the peak wavelength?

(use Wiens Law)

WMAP

The Wilkinson Microwave Anisotropy Probe project has created a full sky image of this microwave light. This is the oldest radiation in the universe and was emitted 380 000 years after the Big Bang (13 billion years ago) before stars even existed.

The colours represent temperature variations from 2.725 K average (and also variations in density)

Consider that light from the sun takes 8 minutes to reach Earth. When we observe the sun, we are in a sense looking 8 minutes back in time.

Background Radiation Supports Big Bang Theory

What was unique about the radiation is that it came from all directions and did not appear to have a source.

The background radiation source is the Universe itself (the light was emitted a very long time ago)

As the Universe expands, the light stretches (increases wavelength) and cools (from Wiens Law). This is like distributing the same amount of heat energy in an every expanding oven.

The Big Bang is not really an explosion but rather a beginning. The Big Bang model suggests a rapid expansion of space itself beginning with an initial very tiny very dense volume.

The evolution or development of the Universe since the Big Bang is described by the standard cosmological model.

It is thought that very early on, all four forces were unified.

Quarks were initially free but became confined with the formation of hadrons. Eventually atoms formed.

Until 380 000 yrs in, the Universe was opaque to photons. With the birth of atoms, this changed and photons were free to spread. This is the background microwave radiation we observe today.

Further development of the Universe

With the birth of atoms, the Universe became matter dominated. The Universe continued to expand (and cool) with the wavelengths of those first unhindered photons stretching with the space they travelled through.

Stars and galaxies began to form as the expansion continued. The gravitational attraction between the bodies in the Universe slows the expansion down.

One exception to this slowing was a period of accelerated expansion between 5-7 billion years ago. Explanations for this expansion have introduced the ideas of dark matter and dark energy.

Will the Universe continue to expand forever?

There are three ideas about the future of the Universe:

Open Universe

The Universe will continue to expand forever although the rate of expansion will decrease.

Flat Universe

The Universe expansion will eventually reach zero rate.

Closed Universe

The expansion will stop, followed by a contraction and possible collapse of the Universe (the Big Crunch)

Same point

Slight to show slowing rate of expansion

Different “ages” of Universe – how long ago was Big Bang

<

Critical Density

The theoretical value for the density of a flat Universe is called the critical density. This is estimated to be about 10-26 kg m-3.

An open universe would have a density > rcritical

A closed universe would have a density < rcritical

Current thought suggests that the Universe is very close to flat. The implications of this are the subject of much ongoing research – remember the video

A flat universe would have a density = rcritical

The problem is that the recent experiments put the total amount of “normal” matter in the Universe at only 4% of the total required to reach the critical density.

Of the other 96%, approximately 23% is thought to be dark matter (nonluminous invisible matter – nature unknown)

The other 73% - this is the big unknown. It has been called dark energy and has been linked to the acceleration of the expansion of the Universe roughly 5 billion years ago.

Perhaps we don’t really understand gravity, perhaps there is some other repulsive effect we don’t know about.

Ideas to account for dark matter/energy

MACHOs – Massive Astronomical Compact Halo Objects: low mass failed stars, high mass planets, or even black holes. Emit little if any light. Is this dark matter?

WIMPs – Weakly Interacting Massive Particles: new particles we do not know about.

Or maybe current gravitation theories are wrong?

Stay tuned for the rest of your life for more…..

HL Only : Topic E6 Hubble’s Law

The speed at which a galaxy moves away from our galaxy (the Milky Way) is proportional to how far from us the other galaxy is.

This means, galaxies farther away from us show more red-shift than galaxies closer to us.

Mathematically: v = Hd

Where H is called the Hubble parameter, the current value for which is about 5% uncertain.

LOOK for problems that combine Hubble’s Law with the simplified Doppler equation.

Sample Problem N02, F2

Note v = Hd : slope equals Hubble constant.

In this example H = 70 km s-1 Mpc-1 meaning that the recessional speed of distant galaxies increases by 70 km s-1 for each Mpc of distance away.

Hubble’s Law

Limitations: does not work well for nearby galaxies. Some nearby galaxies actually show blue-shifts due to random local motion (stars within the galaxies)

The value of the Hubble constant has a large uncertainty associated with it (it does not appear in the data booklet).

For problems in class use, H = 70 km s-1 Mpc-1

H = 22 km s-1 Mly-1

On tests, use the value provided and be prepared to make unit conversions.

Hubble’s Law

The Hubble parameter is one way to estimate the age of the Universe. The time required for a distant galaxy to reach its present position can be calculated by:

this assumes a constant rate of expansion

(what is wrong with this assumption)

distance apart

recessional velocity

dt

v

Hubble’s Law

We can substitute the Hubble expression for speed.

Given a value of 70 km s-1 Mpc-1 for the Hubble parameter

This requires some unit conversion magic

This corresponds to about 14 billion years

1 s Mpc

70 kmt

1d dt

v Hd H

6 15171 s Mpc 1 km 3.26 10 ly 9.46 10 m

4.4 10 s70 km 1000 m 1 Mpc 1 ly

t