Lecture Notes

Arny Chapter 16 & 17

About Lecture Notes
Return to Astronomy Homepage

Chapter 16 Galaxies
We will cover just sections 2, and 3 of chapter 16.
Skip sections 4, 5, and 6.

Chapter 17 Cosmology
We will cover sections 1, 2, 3, and 4 of chapter 17, not section 5.


Section 16.2 Measuring the Properties of Galaxies

Quickly define galaxy.
[A galaxy is a large collection of stars all orbiting a common central point. Like a giant solar system of stars. The galaxy we live in is called the Milky Way, it has a spiral shape. Our Sun orbits in one of the spiral arms.]

Distances to Galaxies
We've never been to another galaxy, not even close.
Nothing launched from Earth has ever even visited another star, we haven't explored anything other than our own solar system.
How can we determine the distance to another galaxy?
You need telescopes just to see them.

Most of our distance estimates involve the same idea.
If we know the luminosity of an object (how much light it emits), we can determine the distance.
Just combine that luminosity with the observed brightness and use the inverse-square law.
This is called the method of standard candles.

1. Cepheid Variables
Cepheid variables are a special type of giant star.
They are pulsating variable stars, their luminosity varies with time.
We learned about them back in section 13.5 (Yellow Giant stars).
Cepheid variables are regular, they get brighter than dimmer than brighter than dimmer with a constant period.
Cepheid variables have periods that range from days to months.

The important property of Cepheid variables is that their period is related to their maximum luminosity.
The bigger, more luminous Cepheids vary in brightness over a longer period of time.
This is called the period-luminosity relationship.

Cepheid variables are a wonderful tool.
They are bright stars, we can see them even in other galaxies.
They are also a very common type of star, there are many 'Cepheids' nearby to our Sun in our Galaxy.

Watch it, measure how long its period is (time from one max brightness to the next).
From the period, we can use the period-luminosity relationship to get the luminosity.
Knowing the luminosity, we can figure out the distance.

Cepheid variables are our most accurate tool for determining distances to other galaxies.
Unfortunately, we can only see Cepheids in nearby galaxies.
This is one of the main tasks the Hubble Space Telescope has been used for, it can pick out Cepheid variable stars even in fairly distant galaxies.
But not really distant galaxies, for them we use:


2. Supergiants, Planetary Nebulas, Novas, Globular Clusters, Supernovae
We have a rough idea how luminous each of these things are and they are all bright enough to be seen in very distant galaxies.
Observed brightness + guessed luminosity => distance.

These methods are not very accurate, because we don't really know how luminous the objects are.
Having multiple things to measure does improve the accuracy.

Best are Type I Supernovae (white dwarf pushed over the Chandrasekhar limit by a companion red giant).
Type I Supernovae all have the same luminosity (because they are explosions in every case of essentially identical objects).
But supernovas are extremely rare, and Type I's even more so.
We can only use this technique for galaxies in which we happen to see a supernova occur.

3. Galaxy Size
If we know (or can guess) the actual size of a galaxy, we can determine its actual distance from how big it appears.
On page 485 of the text, this process is done in reverse.
There they use the distance and apparent size to figure out the actual size but it can also be done in reverse.
[See figure 16.17 on page 486.]

 

 

 



4. Other methods
[Extending Our Reach section on page 485.]
[May skip this if not enough time.]

Graininess of Galaxy's Picture
The closer a galaxy is, the more detail we should be able to see in its picture.
Judging our ability to resolve stars can be used to estimate the distance.

Tully-Fisher Method
The luminosity of a galaxy depends on the number of stars.
The number of stars is related to the total mass of the galaxy.
The total mass is related to how fast the galaxy rotates.
The galaxy's rotation affects the light reaching us (Doppler shifts).
So from the arriving light we can estimate the actual mass and luminosity.
Then we can calculate the distance.



5. Hubble's Law
Hubble's Law is very important.
It will give us a new technique to estimate the distance to any object (not just galaxies).
It will also give us insight into where our universe came from and where it's going.

Edwin P. Hubble discovered, in 1930, that all distant galaxies have spectra that are red-shifted.
All galaxies are moving away from us!

Not only that, but galaxies
which are further from us
are moving away faster.
A plot shows a linear
relationship
[See figure 16.16 on page
484.]

The recession velocity
(the speed the galaxies are
moving away from us)
and the distance away from
us are linearly related.

Mathematically, V = H D

V = velocity moving away from us (in km/s)
D = distance away from us (in megaparsecs, Mpc)
A megaparsec = million parsecs = 3.26 x 10^6 light-years
H = Hubble's constant

Hubble's constant has a (recently measured accurately) value of 70 (km/s)/Mpc
That is, for every million parsecs of distance of galaxies (or anything) away from us, they move away from us with an additional 70 km/s (about 160,000 mph).

We can use Hubble's Law to calculate distances.
Look at a galaxy, measure the redshift of its spectrum, calculate the recessional velocity, use Hubble's Law to calculate the distance.


Example: Chapter 16 Problem 2
A galaxy has a recession velocity of 13,000 kilometers per second. What is its distance in megaparsecs?

Solution: H = 70 km/s/Mpc.
V = HD =>
D = V/H = (13,000 km/s)/(70 km/s/Mpc) = 186 Mpc = 186 million parsecs or about 600 million light-years.

We are assuming the expansion rate has been constant, if not the answer could be different.


Why is everything flying away from us?
And why with higher velocities at greater distances?
Does this mean that we are at the center of the universe?

Hubble answered all these questions.
We live in an expanding universe.
But this is a chapter 17 topic.

Section 16.3 Dark Matter
Here's a surprise: the Sun is orbiting the Galaxy (slightly) faster than it should be!
The Sun orbits because of all the mass in the galaxy inside its orbit (the mass outside of its orbit cancels out).
But the mass we see is not as much as the gravitational pull indicates.
There seems to be more mass than that we can see.
For stars further from the center of the galaxy, the speeds are far different than expected.

 

Astronomers work this out by
making a rotation curve.
See figure 16.18 on page 487.

The "expected" line is the orbiting
speed of stars we expect based on
the stars (and gas and dust) we see.
The "observed" is how the stars in
our Galaxy (and others) actually move.

This is telling us that there is more mass
in our Galaxy than that we see in stars.



Stars appear to make up only a small fraction of our Galaxy's mass!
What is the rest of our galaxy made of?

Brown dwarfs and white dwarfs?
Black holes?
Neutrino particles?
Something new and unexpected?

Astronomers have not yet figured it out.
This unseen component of the Galaxy is called dark matter.
There has to be ten times more dark matter in our galaxy than there is mass in stars!
It appears to exist in all other galaxies as well.
From the way stars move (from the rotation curve), astronomers can tell that much of this dark matter is in the "halo" of the Galaxy, a spherical region beyond most of the stars (see figure 15.8 on page 442).

Some recent searches indicate that some of the dark matter is dim stars, white dwarfs, red dwarfs, and the like, but at best this explains only a fraction of the dark matter.
We don't know what most (90%) of our Galaxy is made of!
This is currently one of the biggest unsolved problems in astronomy.


An alternate theory is that gravity varies with distance in a way different from that predicted by Newton (and Einstein).
If gravity is very slightly stronger at astronomical distances than expected, it might eliminate the need to invoke dark matter.
Astronomers pursuing this idea have not yet convinced the majority of astronomers but it is an interesting alternative.

 

Chapter 17 Cosmology
Cosmology = the study of structure and evolution of the universe.
Or, the answer to questions like:
How old is the universe or has it always been the same?
How big is the universe?
How did it form, where did it come from?
What will happen to our universe in the future?


Section 17.1 Observations of the Universe

We start with Hubble's discovery of the expanding universe.
What do we mean by an expanding universe?

Consider the following analogy.
The universe is a balloon (the
galaxies might be dots drawn
on the balloon's surface).
Expansion of the universe is
like blowing up the balloon.
The galaxies on the surface
will become further apart as
the balloon is inflated.
See figure 17.2 on page 507.

Each adjacent galaxy will move
further away from its neighbors.
No matter which galaxy you look
at, all the other galaxies will be
moving away from it.
Every galaxy is moving away from
the others.
And moving away faster when further apart.

This idea explains things beautifully.
It explains why everything in the universe is moving away from us.
It explains why we see faster motion away for objects more distant.
In fact, Hubble's law (V = HD) is required by this model. (?)
It does not mean we have to be at the center of the universe, expansion looks the same no matter which galaxy you're in.

Our universe is more complicated than a simple balloon.
But the same basic ideas hold.

Note that we are not saying that objects are flying through space away from each other.
Instead we are saying that it is the underlying space itself that is expanding, carrying the galaxies with it.
Like in our analogy, the dots on our balloon were not moving over the surface of the balloon, but were carried further apart by the expanding "fabric" of space.

The universe is expanding, getting bigger.
In the past, the universe must have been smaller!
We can extrapolate backwards, the universe in the past must of been smaller and smaller until at some distant time long ago the whole universe was microscopic.

This is the basis for postulating the Big Bang model for the origin of the universe.
The Big Bang is believed to be some event in which our universe was created, all the universe starting as some microscopic dot.
It expanded from that start until the state we're at today.
We'll say much more about this Big Bang model shortly.

Age of the universe.
Given the rate at which the universe is expanding today, we can back-track to determine how long ago it began.
The result is (math details worked out in the text on page 509. )
Age of universe t = 1/H = 14 billion years
Different answers can result from different assumptions about changes in the rate of the universe's expansion in the past.
Some more accurate recent calculations have given ages of 13.7 billion years or 13.5 billion years and I may sometimes use those values instead of 14 billion years.]

Size of the universe.
This too gets complicated because of expansion and "inflation" and other concepts.
We'll just give the "obvious" (although probably incorrect) answer to this question.
If the universe has existed for 14 billion years, then light from as far away as 14 billion light-years could reach us.
So the radius of the (visible) universe is 14 billion light-years.
The latest results support the idea that the universe is infinitely large - whether galaxies and stars extend forever as well is not known.

Where did the universe come from?
The universe is expanding because of the Big Bang.
An explosion(?) of energy which marked the creation of the universe.
The Big Bang model does not tell us where this energy came from!

Out of nowhere? That doesn't make any sense.
Did God create the universe with a Big Bang? Where did God come from?
Why does anything exist?
Are there other - separate from ours or preceeding ours - universes created from other Big Bangs?

I don't have answers to these questions.
For now at least, that is a question more for a philosophy class than a science class.
It doesn't make sense to just say things have always existed.
But it makes even less sense to have a beginning with nothing before it.

Just because the universe is expanding, does that really mean there was a Big Bang?
No, there are other theories that can explain an expanding universe without a Big Bang.
But there is other evidence for the Big Bang.
We need to look at the Big Bang model in more detail.

The Big Bang Model
Again, the Big Bang was an explosion of energy.
Enough energy to produce the entire universe we know today.
E = mc^2, that's a lot of energy!
And all this energy in a microscopic volume.
We have good reason to call this the "Big Bang".

Unmeasurably hot to start with.
The universe starts to expand.
Microscopic > grain of sand size > fist size > star size > etc.
The energy cools as it expands.

Our Sun heats itself by converting matter into energy (through the nuclear fusion process).
In the early universe, the opposite process occurred, energy into matter.


The early moments of our universe:
[See figure 17.16 on page 522.]
photons => protons, neutrons, electrons, photons
. . . protons, neutrons, electrons => hydrogen (76%) & helium (24%) => which go on to form stars, galaxies, and planets
. . . photons => ??

 


 

The universe started with just energy (photons).
Some energy became matter, protons, neutrons, and electrons.
As the temperature drops, soon (like 3 minutes after the Big Bang started) there is not enough energy in the photons to form any more matter (particles).
Over the next few minutes, hydrogen nuclei (protons) will undergo fusion reactions (just like occur today in the core of the Sun) to produce helium nuclei.

In many ways, the universe was very simple to understand in these earliest moments.
We've done experiments with colliding photons and electrons and so on, and we know how they should interact.
The Big Bang model makes a very clear prediction, we should have 76% of the mass coming out of the Big Bang as hydrogen, 24% as helium.
The universe expanded and cooled too quickly to form any heavier elements.

Everything in the universe does seem to have started as 3/4 H, 1/4 He.
The Big Bang explains this, more support for the Big Bang.

Since then, the H and He clouds condensed to forms stars and galaxies.
What has happened to the leftover energy (photons)?


The Cosmic Background Radiation
The leftover radiation has continued to cool as the universe continued to expand.
The radiation is still around today.
But nowadays the radiation has cooled to 3K [2.7K], almost absolute zero.

The Big Bang predicts there should be such leftover radiation.
This radiation has been found, discovered in 1965.
[Penzias and Wilson trying to explain noise in microwave antenna.]

This leftover radiation is called the Cosmic Microwave Background Radiation (microwaves are a part of the electromagnetic spectrum, a subset of the radio part of the spectrum, near infrared).
This radiation fills the universe, a substantial part of the white noise static on an untuned TV is due to the Cosmic Microwave Background.

The Big Bang model predicted this radiation should exist before the radiation had been discovered!
Very impressive.
More support for the Big Bang.


The early universe was filled with an even, dense fog of radiation.
As the radiation cooled, it became a dense fog of particles.
This was about 1 million years after the Big Bang.

But today the universe is far from uniform.
It is filled with groups of galaxies and giant voids (empty spaces).
How could the uniform early universe have turned into our current lumpy universe?

The theory is that the early universe was not uniformly dense.
There must have been slight density variations.
Where it was slightly more dense, there was more gravity which attracted still more gas.
These small density variations were the seeds around which galaxies and galaxy clusters formed.

The early density variations of matter should correspond to density variations of radiation.
And these variations in the radiation should be preserved today as variations in the cosmic background radiation.

But early studies of the Cosmic Background Radiation failed to reveal any density (temperature) variations.
Is there something wrong with the Big Bang Model?
It was decided that the necessary density variations might be just beyond the resolution of the current detectors.

A new satellite was sent into space, COBE ("coby"), the COsmic Background Explorer.
This satellite would detect the density variations in the background radiation if they exist.
The experiment was far more difficult than it sounds.
The results were announced in early 1992.
[See Figure 17.12 on page 519.]
[Many of the "latest" results I've been mentioning in this lecture come from COBE's successor, the WMAP spacecraft.]

This map shows minute temperature variations in the background radiation.
[Higher temperatures => lower density.]
This was a major triumph for the Big Bang Model.
Such density variations had to be found and they were.
This picture is basically a map of the very earliest universe.


Summary of Evidence for the Big Bang:
1. Expansion of the Universe
2. Element Abundances
(3/4 H, 1/4 He; even despite the work of stars for billions of years, the universe is still 99% H and He).
3. Cosmic Background Radiation

All three of these things are explained by the Big Bang model.
No other model can say the same thing.

The universe was created in a Big Bang 13.7 billion years ago.
Energy condensed into matter which went on to form galaxies.
Today the universe is still expanding.
What is the fate (future) for our universe?


Section 17.2 Evolution of the Universe: Open or Closed
There are two possible futures for our universe, the Open Universe and the Closed Universe.
Our universe is expanding, but the rate of expansion should be slowing due to gravity.
Will the universe expand forever?
Or will it slow down, stop, and then start contracting?

Open Universe = one that expands forever
(A special case of the open universe is called the Flat Universe).
Closed Universe = one that stops expanding and then contracts
Two very different possible fates.

Open Universe
Objects will continue moving further apart.
Stars will die, becoming white dwarfs, neutron stars, and black holes.
New star formation will become rare (after about 150 billion years).
Eventually there will be no more new stars formed.

The universe will become colder and darker.
The universe will live forever, but it will become a cold, dark, barren place.

Closed Universe
The universe will expand and cool like the Open Universe.
Stars will die; cold and dark.
But gravity will eventually stop the expansion.
The universe will start to contract, shrink.

Eventually things will start to get crowded.
Galaxies and black holes will slam into each other.
Fierce, hot, violent events.
Everything in the universe will crush down towards a single point.
This event is called the Big Crunch.

What will happen after the Big Crunch?
Will the universe rebound into another Big Bang?
Maybe we are part of a long or infinite series of Big Bangs and Crunches?
This is called the Oscillating Universe theory.

Keep in mind that a Big Crunch would involve colliding black holes.
Our understanding of black holes is incomplete so we can't say for certain what happens in the Big Crunch.
But the Big Crunch would definitely be an extremely unpleasant place, essentially our whole universe being crushed out of existence.

Do we live in an Open or a Closed Universe?
Even though we're talking about something that will have no effect on our universe until tens of billions of years in the future (long after the Earth will have been swallowed up by the Sun and after our Sun has died), this is a question many people are quite anxious to answer.
Most people seem to hope we are in a Closed Universe.
I think an Open Universe is actually a much nicer place.
I guess it comes down to whether you would prefer to live for a very long time, or die young in a blaze of glory.

But what we might prefer is irrelevant.
The answer depends simply on physics.
The speed with which the universe is expanding versus the strength of the gravitational pull trying to stop the expansion.
It's like escape velocity, with enough speed you can escape gravity, not enough and the masses are pulled back together.

How fast the universe is expanding is given by the Hubble Constant.
The strength of gravity depends on the mass and size of the universe (or just the density).

By measuring the density of stars in galaxies, and the density of galaxies in the universe, the density of the universe has been calculated.
(Roughly, because we are unsure of distances.)
It has also been calculated what the density of the universe must be in order for gravity to stop expansion and give us a Closed Universe.
This is called the critical density.
If the density of the universe is

= critical density means Flat universe (open)
> critical density means Closed universe
< critical density means Open universe

The result:
Counting the numbers of galaxies and using the number of stars per galaxy and the mass per star, astronomers calculate the density of the universe is only 1% (1/100) of the critical density needed to stop expansion.
So we have an Open Universe!

No! Wait!
That was only counting the mass we see in stars.
We must count all the mass in the universe.

Recall that the Milky Way has a strange rotation curve.
It implies that our galaxy has ten times more mass (the Dark Matter) than we can see in stars.
And all the other galaxies we look at seem to have the same.

So, taking this into account, the total mass in the universe, and hence the overall density, has just jumped by a factor of 10.
But this is still just 10% the total mass needed to stop expansion.
Discovery of thin gas (and dark matter?) between galaxies has boosted the known mass in the universe to about 30% of the critical amount.
Astronomers don't think there is any more hidden masses.
So we are still looking at an Open Universe.

The amount of mass in the universe is not enough for a Closed Universe.
The majority of astronomers now favor the Open Universe idea.

Einstein's Cosmological Constant
When Albert Einstein created his theory of General Relativity, he realized it predicted an unstable universe.
The universe should either be expanding or contracting, and gravity should slowly change the rate of expansion or contraction.
At the time the universe was believed to be a static place, things moved around but on average stayed the same distance apart.
Einstein added an extra term into his equations - the "cosmological constant" - which added an inherent expanding to the universe that could be exactly canceled by gravity and give a static universe.

A few years later, Hubble discovered the universe was expanding, not static.
Einstein quickly retracted his cosmological constant and called it his "greatest blunder".
You see, he could have trusted his theory and predicted that the universe must be expanding or contracting; instead he "fudged" the theory to make it conform to the prevailing opinions.

The latest results
In 1998, astronomers studying distant Type I supernovae announced a surprising result.
By studying these far away (and long ago) events, they could determine how fast the universe was expanding, compare to how fast the universe is expanding today, and figure out how the universe will end (an alternate approach from the mass density discussed above).
Their conclusion: the universe's rate of expansion is accelerating!
Getting faster and faster with time!

This is just the opposite effect expected, gravity should be slowing the expansion.
What could overwhelm gravity and cause this?
The simplest answer - the cosmological constant!
Maybe Einstein was right after all, or maybe wrong twice.

The generic name given to the force causing the accelerating expansion is Dark Energy.
Possible forms of dark energy include the cosmological constant, vacuum energy, quintessence, and others.
Depending on what the dark energy is, different futures are predicted for the universe, some of these even allow for the universe to be closed and eventually collapse.

It is quite possible that some unknown effect has thrown off these measurements and the universe's expansion is not really accelerating.
Maybe the ancient white dwarfs (which are what explode in the Type I supernova) are different from what we expect.
But for now, it seems that every measurement astronomers make point towards an Open Universe.

Section 17.3 The Shape of the Universe
If you set out in your airplane and keep flying east, after a while you run out of gas and crash.
If you remember to refuel, you return to Bakersfield.
You didn't turn around, the Earth is curved, it's a sphere.

If you get in your spaceship and keep flying in the same direction could it be that you will return to Earth after "circumnavigating" the whole universe?
Is the universe curved?
I know, this is hard to imagine because we are talking about a 3-D space curved, you'd have to look at it from 4-D space to "see" it.

A "Closed Universe" is spherical, you could go out and will return back to the starting spot from the opposite direction.
An "Open Universe" could also be curved, but curved oppositely ("negative curvature") so that a straight line never returns to its starting point.

The latest results
The combination of gravity and dark energy appear to give an infinite flat universe, not curved at all. (Just the way you've always imagined the universe.)
If the universe was "flat" and contained only normal matter, it would expand forever but only just barely - the expansion would slow but never quite stop.
Because about 70% of the mass/energy needed to make the universe flat comes from the dark energy, we appear to be in a flat universe with an expansion rate that will forever accelerate.

But I wouldn't be greatly surprised if astronmers someday change their mind about all this!

We are done!



Return to Astronomy Homepage