astronomy homeworks ( Astronomy of the Universe AST 101)

Homework 1 notes

1st part

Electromagnetic Spectrum

Components:

Light behaves as both a particle and a wave. At this moment we are only going to focus on the wave properties.

There are two major divisions for waves:

1) Transverse: A distortion that is perpendicular to the direction of travel. Be comfortable with understanding that waves at the beach coming toward the shore are transverse waves.

2) Longitudinal: A distortion that is parallel to the direction of travel.

Shorter wavelength corresponds to higher energy.

Also know the colors of visible light in order of decreasing wavelength

1) Red

2) Orange

3) Yellow

4) Green

5) Blue

6) Indigo

7) Violet

There are three different types of spectra:

1) Continuous

2) Emission

3) Absorption

Is the speed of light constant? NO

The correct way to think of this is “All observers measure the speed of light in a vacuum to have the same value.”

A prism changes the medium through which the light is traveling. This causes the light to slow down and change direction. When the light leaves the prism it speeds up again. The change in angle due to the change in speed is dependent on the wavelength (color) of the light.

A continuous spectrum occurs when light at all wavelengths (within the visible light portion of the spectrum) is present.

Consider hydrogen as the simplest example for all elements (and molecules, etc.).

Hydrogen has a proton for the nucleus and an electron that orbits around the nucleus at various distances. These are referred to as the orbital shells.

1) The laws of physics are the same everywhere in the Universe. This cannot be proven (with current technology and understanding of physics). However, we have observational data that supports this. A consequence of this is that all protons (in reality all particles) in the Universe must have exactly the same properties. This verifies that all interactions between protons will have the same results. Expanding on this idea requires that all electrons in any given hydrogen molecule orbit at the same distance.

2) The Universe is lazy. This means that the Universe tries to do everything using as little energy as possible, and entities (molecules, systems of particles, etc.) try to remain in their lowest energy state. For our hydrogen molecule, this means that the electron wants to be in the first orbital shell (closest to the nucleus).

Any interaction between charged particles that results in the release of energy will release that energy in the form of photons.

When electrons move toward a nucleus, energy is released and photons are observed. These are called “transitions” and are categorized by where the electron lands.

These transitions are defined by the electron landing on shell

1) First shell Lyman transition UV photons given off

2) Second shell Balmer transition Visible light photons

3) Third shell Paschen transition IR photons

4) Fourth shell Brackett transition IR photons

This gives me the information needed to create “fingerprints” for emission spectra to use for comparison with observation.

The Doppler effect applies to waves and changes the apparent wavelength based on motion.

Applying this to light, if a light source is moving toward an observer then the light’s wavelength appears shorter than it really is and this is referred to as a blue shift. Conversely, if the light source is moving away from an observer then the light’s wavelength appears longer than it really is and this is referred to as a red shift.

Overall the effect is the same whether the light source and/or the observer are moving. If the distance between them is decreasing then there is a blue shift. If the distance between them is increasing then there is a red shift.

If a light wave is blue shifted that does not mean that it is blue in color. Similarly, if a light wave is red shifted that does not mean that it is red in color.

2nd part

When a galaxy forms, gravity pulls all of the material toward the center of the mass distribution.

Conservation of angular momentum – one consequence of this is that if a rotating object’s volume is decreased the object will rotate faster.

Remember the discussion about randomness. While the material that will make up the galaxy is collapsing, the individual molecules still have some random motion. The way to think about this is that there is a bulk motion (gravitational collapse) and a random motion (particles moving individually) and the combination of this determines the outcome.

In this random motion, it is expected that roughly (but not exactly) half of the material is rotating clockwise and half of the material is rotating counterclockwise. Combining these thoughts means that as the bulk motion causes the material to collapse, an overall rotation will become significant.

Now consider our solar system. The planets that are further from the Sun are in a weaker gravitational field. This means that they orbit around the Sun more slowly.

As the material collapses to form a galaxy, much of it will gain an orbital speed that is high enough to keep it from moving inward further. In other words, the gravity pulling the material together is not strong enough to pull in material with significant rotation. The result of this is that the majority of the material forms a supermassive black hole at the center and the remainder creates a debris field around it.

Initially, this debris field will have a spherical distribution. Eventually, it will flatten out into a disk. This forms our spiral galaxy. The debris in the disk eventually forms the stars, planets, etc.

Stars form basically the same way as a galaxy. Gravity pulls together material to form the star. There is a debris field around the star which becomes planets, asteroids, comets, etc.

Solar vs Stellar … Solar refers to our Sun while stellar refers to stars in general. The name of our sun is Sol.

Stars form from molecular clouds. Are the molecules within the molecular clouds moving or at rest? They must be moving fast enough to keep the cloud from collapsing due to gravity. They must also be moving slow enough to keep the cloud from dispersing.

What is an arbitrary volume? It is a defined region of space that does not have any physical boundaries and is used to describe the behavior in that region.

Consider an arbitrary volume in the molecular cloud. The motion of the individual molecules leads to density fluctuations within this volume.

How do the density fluctuations affect the gravitational field within the arbitrary volume? Remember that gravity is determined by mass and separation. This means that at low density the gravitational field is weaker. This is because there are fewer molecules (less mass) and on average the molecules are further apart. Conversely, at high density the gravitational field is stronger.

In order for a star to form, an arbitrary volume with enough mass (an amount of mass equal to the mass of a star) must reach a high enough density that the gravitational field is strong enough to collapse just the arbitrary volume in question.

After the first star forms, the outward flow of energy through the cavity left behind triggers more star formation. The majority of the material in the molecular cloud eventually becomes either part of a star or the stellar system around it.

As the material is collapsing the density, temperature, and pressure are all increasing. The increasing temperature leads to the formation of a plasma core. This plasma core will eventually sustain nuclear fusion and at this point you have a newly formed star.

At low enough temperature, water is a solid. The molecules are held together in a lattice structure and there is minimal motion. When enough energy is added that the water melts, it is now in liquid form and the molecules clump together due to surface tension.

Continuing to add energy will lead to the liquid evaporating to form a gas. Now the molecules are completely dissociated from one another.

What happens when the gas continues to be heated (more energy is continually added to the gas)? At significant temperature the molecular bonds begin to break and now there are isolated hydrogen and oxygen molecules instead of water molecules.

The final stage in the generation of the plasma is collisions that can strip the electrons away from their respective nuclei. The end result is protons (hydrogen nuclei), oxygen nuclei, and individual electrons. This means that the constituents are now ionized (electrons are negative and the nuclei are positive).

Assuming that the Big Bang Theory is correct, the universe began as roughly 75 percent hydrogen and 25 percent helium with trace amounts of other material. Observations today suggest that the universe is 70 percent hydrogen, 25 percent helium, and 5 percent other stuff.

A consequence of this is that molecular clouds will be roughly 70 percent hydrogen. This means that when a star forms inside a molecular cloud its plasma core will be roughly 70 percent protons (hydrogen nuclei). This means that once a star forms, it and all other stars will evolve through the same process.

What is nuclear fusion?

1) Nuclear – pertaining to the nucleus (mostly to the protons).

2) Fusion – to combine

3) Nuclear fusion is the combining of protons to form heavier elements.

Individual protons will repel one another. In order to have them fuse they need to be traveling at very high speeds (they need to be in a high temperature environment). After two protons fuse together they will be highly unstable due to the repulsive force between them.

One of two things is going to happen. Either the protons are going to rip back apart or something must happen to remove the repulsion. The answer is that one of the protons becomes a neutron and the repulsive force disappears.

The model for this is that protons and neutrons are made up of quarks. For now, the agitation in the protons after they fuse causes one of the quarks to change its properties. This causes the proton containing that quark to change from being a proton to being a neutron.

In physics we assume that the total amount of energy in the universe is constant. This means that energy can’t be created from nothing and it won’t just magically disappear.

In physics the work-energy theorem says that the change in energy is equal to the amount of work done.

The initial fusion process in any star (regardless of mass) is going to be hydrogen fusion. Specifically this is the proton-proton chain.

The first of three parts for the proton-proton chain is the fusion of two individual protons to form deuterium. Remember that deuterium is one of the isotopes of hydrogen. A deuterium nucleus has one proton and one neutron.

The second part is where a third proton is added and a helium-3 nucleus is made. Now this is an isotope of helium

The third part is where two helium-3 nuclei fuse together and form a helium-4 nucleus. This is the most stable isotope of helium.

The overall result is that after a star forms and develops a significant plasma core, hydrogen fusion begins and produces both helium-4 and excess energy (in the form of photons). The star holds on to the helium that was made and releases the excess energy into the environment.

Does the star have an infinite amount of hydrogen (fuel)? No

This means that eventually the core will no longer be able to sustain hydrogen fusion in this way. This means that one of three things must happen:

1) More hydrogen is added to the core

2) The fusion relocates to where there is more hydrogen

3) The fusion ceases

For the purposes of this class (and most astrophysics) a star is considered to be a sphere that is spherically symmetric.

An object that is spherically symmetric can be considered as a collection of infinitely thin spherical shells that are concentric.

A consequence of this is that the only variation in the star’s parameters are based on changes in distance from the center (radius).

Given this, once the core can no longer support hydrogen fusion, the fusion relocates to where there is more hydrogen. It moves outward because that is where the hydrogen fusion can take place efficiently.

Why does our sun stay the same size?

Gravity is always trying to make everything smaller. The energy being released by fusion is counteracting this and trying to make the star bigger. Think about this as a continuous outward flow of energy. The reason the star stays the same size is because these two effects are balanced and the star is in equilibrium.

Moving the hydrogen fusion outward means that it is taking place on a larger surface. The fusion process is the same, but there is more of the process occurring. This means that the outward pressure goes up. Gravity has not changed. The end result is that the star gets bigger because it is no longer in equilibrium and the outward pressure is greater than gravity’s ability to try and make the star smaller.

Now that the fusion is making energy and helium, but this fusion is no longer taking place at the core, where does the helium go? The helium is heavier than its surroundings so it migrates toward the core and begins to stockpile

3rd part

Observation

First Observation:

All observed galaxies are red shifted (except for one). The exception is the Andromeda galaxy (M31) which is close enough to us that the mutual gravitational attraction overpowers the expansion.

Having already assumed that there is no preferred spot in the Universe, there is no reason to believe that our galaxy is at the center of the Universe. This means that we need to find a model that will allow for all of the galaxies to be moving randomly and yet their overall motion will be away from us.

The uniform expansion model can be thought of as placing a grid over the Universe and allowing the grid to expand. This results in every point in the Universe being further away from every other point.

This leads to two separate types of redshift. The physics principle involved is a Doppler shift for a wave. If the observed wavelength is shorter than it should be (shorter than the emitted wavelength) then the light is blue shifted. If the observed wavelength is longer than it should be then the light is red shifted.

The two classifications for redshift are derived from

1) Classical motion – motion through the environment

2) Cosmological motion – motion with the environment

If the motion of galaxies in the Universe were purely classical we would expect to see roughly half red shifted and half blue shifted. We would also expect the same degree of shift regardless of distance.

If the motion of galaxies in the Universe were purely cosmological we would expect to see all the galaxies redshifted. We would also expect galaxies that are further away to have larger red shifts.

What we actually observe is galaxy motion that is cosmologically dominated. This means that all of the galaxies (except Andromeda) are moving away from us and the further galaxies have a larger red shift.

Second Observation:

Several decades ago the US military was experimenting with microwaves. This led to a very interesting discovery with large astrophysical implications.

** In class number line example ** Develop the idea of an extremely small set that still has an infinite number of members.

This can be expanded to a thought exercise where I have a large sphere filled with photons. There are enough photons that they behave like an infinite set. This sphere is moved far enough away that it occupies an infinitely small portion of the sky. The result is that I have a system that behaves like an infinite number of photons residing in an infinitely small part of the sky.

The universe today is transparent and assuming the BBT is correct it should have started out being opaque. This requires that at some point in the past the universe changed from being opaque to being transparent.

What is the difference between intensity and energy as far as light is concerned? Energy is associated with wavelength and intensity is associated with photon count.

Low intensity microwaves are observed coming toward us from all directions. This is associated with the universe changing from being opaque to being transparent.

If the Big Bang Theory is correct then this would be expected.

Specifically, when the universe changed from being opaque to being transparent photons were released from all points in space and in all directions. The result of this is that regardless of where you are in the universe you will see background radiation coming toward you in the form of microwaves.

Third Observation:

What is a visible light map? Basically this is a star chart – it is a diagram that shows you where on the sky the visible light is coming from. This is something that allows you to determine which particular star, galaxy, etc. you are observing.

What then is a radio light map? As expected this would be a diagram that shows you where on the sky the radio waves are coming from.

Several decades ago (part II) astronomers began a project where they overlaid visible and radio light maps. The purpose of this is to determine what objects in the sky give off both types of radiation.

Several objects that were originally considered to be “small blue stars” were also demonstrated to be giving off radio waves. This was unexpected because stars were not thought to give off radio waves.

Now these objects are going to be studied in more detail. One of the first steps is to pass the visible light through a prism to gain information from the spectrum.

Doing this led to a very surprising result. Each of these “little blue stars” have a very large red shift. The next step becomes trying to determine if the red shift is classical or cosmological in nature.

If the red shift is classical, then it very well could be a nearby star but determining how it was accelerated to such a high rate of speed becomes an issue.

If the red shift is cosmological, the fact that it is very far away but still appears similar to stars in our galaxy means that it must be extremely large and intense.

The answer is that the red shift is cosmological in nature and the object is a forming galaxy. The formation process consists of gravity pulling the material together and the material coalescing to form the stars and everything else.

While gravity is pulling the material together, three measurable parameters are increasing:

1) Density

2) Temperature

3) Pressure

The outer regions of the forming galaxy will be at a lower energy. This means that the radiation given off there will show up as radio waves. The visible light being given off will come from locations nearer the center where the forming galaxy is more energetic.

This object is called a Quasar (often abbreviated QSR). This stands for Quasi-stellar radio source.

As the forming galaxy evolves, the outer regions will settle down first. This means that the outer regions will quit giving off light before the interior. Another way to think about this is as the galaxy formation process continues, the outer regions settle down and stop emitting radio waves while the interior continues to emit visible light.

This is the same object type, just more evolved. These are called QSO instead of QSR.

This is an abbreviation for Quasi-stellar object.