See the guide for this topic.
D.4 – Stellar processes
The Jeans criterion
Stars form when a portion of interstellar cloud collapses gravitationally.
The Jeans mass criterion is determined by asking when the magnitude of the gravitational potential energy exceeds the magnitude of the gas’s kinetic energy.
The collapse of an interstellar cloud may begin if M>Mj where Mj is the Jeans criterion.
Nucleosynthesis is the process of combining light elements into heavier elements, also known as fusion. Nucleosynthesis requires high speed collisions and high temperatures. Temperatures in the core are much higher than on the surface of a star. The main process for energy production in a star is nuclear fusion of hydrogen to helium. This is the process that occurs during most of a star’s lifetime. After the hydrogen in the star’s core is exhausted, the star can burn helium to form progressively heavier elements, carbon and oxygen and so on, until iron and nickel are formed. Up to this point the process releases energy. The formation of elements heavier than iron and nickel requires the input of energy. Supernova explosions result when the cores of massive stars have exhausted their fuel supplies and burned everything into iron and nickel. The nuclei with mass heavier than nickel are thought to be formed during these explosions.
All stars follow a simple proton-proton cycle in order to maintain equilibrium between gravity and pressure. When the star is expanding, it rises in temperature and therefore rises in pressure. This is required in order to keep a balance between the force of gravity that is trying to compress the star. At the beginning of a star’s life cycle the star consists mainly of hydrogen; in fact they are 98% made of hydrogen. There are three basic stages of the proton-proton cycle:
- Two hydrogens fuse to form deuterium plus a positron and a neutrino. Each positron is annihilated to create 2 gamma particles which are in turn absorbed and re-emitted as 200,000 photons of light per gamma particle.
- A deuterium and a hydrogen fuse to create helium and a gamma particle. Another deuterium and a hydrogen fuse to create helium and a gamma particle. Thus far, there have been 4 gamma particles created with 800,000 photons of light. That’s one bright star!
- Two helium atoms fuse to create a heavy helium atom. Once the hydrogen in the star runs out, it begins to consume the created helium from hydrogen reactions. Based on the star’s color, you can find out what type of fuel it’s consuming. This is where the Hertzsprung-Russell diagrams were derived from (see later section).
Nucleosynthesis off the main sequence
Clouds of hydrogen and helium form into main sequence stars, where nuclear fusion takes place, fusing hydrogen to form helium. Further fusion only takes place in heavier stars, otherwise the pull of gravity forces the star to contract and cool to a red dwarf. If further fusion takes place, the star becomes a red giant.
Red giants are formed when the hydrogen in the core of the star has fused into heavier helium and helium fusions occur to create beryllium. Gravity causes the star to contract and heat up. The hydrogen around the core burns more fiercely and causes the outer part of the star to expand and cool down. Small red giants (1.4 solar masses – Chandrasekhar limit) cannot withstand the pull of gravity, so it shrinks, becomes extremely hot, until it finally cools into a white dwarf. Larger red giants fuses until iron is formed, however, further fusion cannot take place without energy input. Therefore, the star contracts and heat up because of the large kinetic energy in the particles and explode as a supernova, spilling its rich elements into space to form future stars and planets
Type Ia and II supernovae
Type Ia supernova
Type Ia supernovae occur in a binary system — two stars orbiting one another. One of the stars in the system must be a white dwarf star, the dense, carbon remains of a star that was about the size of our Sun. The other can be a giant star or even a smaller white dwarf.
White dwarf stars are one of the densest forms of matter, second only to neutron stars and black holes. Just a teaspoon of matter from a white dwarf would weigh five tons. Because white dwarf stars are so dense, their gravity is particularly intense. The white dwarf will begin to pull material off its companion star, adding that matter to itself.
When the white dwarf reaches 1.4 solar masses, or about 40 percent more massive than our Sun, a nuclear chain reaction occurs, causing the white dwarf to explode. The resulting light is 5 billion times brighter than the Sun.
Because the chain reaction always happens in the same way, and at the same mass, the brightness of these Type Ia supernovae are also always the same. To find the distance to the galaxy that contains the supernova, scientists just have to compare how bright they know the explosion should be with how bright the explosion appears. Using the inverse square law, they can compute the distance to the supernova and thus to the supernova’s home galaxy. Thus, Type Ia supernovae are also known as “standard candles”.
Type II supernova
Most stars that are eight or more times the mass of our sun die as a Type II Supernova. A Type II Supernova is a supernova that is classified as having hydrogen lines in its spectra that are made by the explosion of a very large star. The hydrogen lines come from the hydrogen-rich outer layers of the star as the star explodes.
The top shows the evolution of a Type Ia supernova while the bottom shows the evolution of a Type II supernova.
D.5 – Further cosmology
The cosmological principle
The idea of a uniform universe is called the cosmological principle. There are two aspects of the cosmological principle:
- The universe is homogeneous. This means there is no preferred observing position in the universe (everywhere looks the same). However, homogenous does not mean that all regions of space should appear identical or be smoothly filled with particles. It only means that the same types of structures — stars, galaxies, clusters, and superclusters — are seen everywhere.
- The universe is also isotropic. This means you see no difference in the structure of the universe as you look in different directions. In other words, no observation can be made that will identify an edge or a center. The concept of isotropy is supported by the fact that galaxies do not bunch up in any direction in the sky and by the fact that we observe the same Hubble relation in different directions in the sky. Large telescopes have been used to count faint and distant galaxies in different direction and the numbers are always statistically the same.
Rotation curves and the mass of galaxies
How do we measure the amount of mass in the universe? We measure gravity, indirectly by measuring motion and applying Newton’s law of gravity.
The orbital period of the Sun around the galaxy gives us a mean mass for the amount of material inside the Sun’s orbit. A detailed plot of the orbital speed of the galaxy as a function of radius reveals the distribution of mass within the galaxy. The simplest type of rotation is wheel rotation shown below.
Rotation following Kepler’s 3rd law is shown above as planet-like or differential rotation. Notice that the orbital speeds falls off as you go to greater radii within the galaxy. This is called a Keplerian rotation curve.
However, plotting the curves of observed data points, the rotation curve of the galaxy stays flat out to large distances, instead of falling off as predicted in the figure above (planet-like rotation). This means that the mass of the galaxy increases with increasing distance from the center (radius).
The surprising thing as there is very little visible matter far beyond the center of the galaxy. The rotation curve of the galaxy indicates a great deal of mass but these masses cannot be observed. In other words, the halo of our galaxy is filled with a mysterious matter of unknown composition and type known as dark matter.
Roughly 80 percent of the mass of the universe is made up of material that scientists cannot directly observe. Known as dark matter, this bizarre ingredient does not emit light or energy. Most scientists think that dark matter is composed of non-baryonic matter. The lead candidate, WIMPS (weakly interacting massive particles), have ten to a hundred times the mass of a proton, but their weak interactions with “normal” matter make them difficult to detect.
Fluctuations in the CMB
Although the temperature of the CMB is almost completely uniform at 2.7K, there are very tiny variations, or anisotropies, in the temperature on the order of 10^-5K. The anisotropies appear on the map as cooler blue and warmer red patches. But what do these minute fluctuations mean?
These anisotropies in the temperature map correspond to areas of varying density fluctuations in the early universe. Eventually, gravity would draw the high-density fluctuations into even denser and more pronounced ones. After billions of years, these little ripples in the early universe evolved, through gravitational attraction, into the planets, stars, galaxies, and clusters of galaxies that we see today.
The cosmological origin of redshift
During the first 380000 years after the Big Bang, the universe was so hot that all matter existed as plasma. During this time, photons could not travel undisturbed through the plasma because they interacted constantly with the charged electrons and baryons, in a phenomenon known as Thompson Scattering. As a result, the universe was opaque.
As the universe expanded and cooled, electrons began to bind to nuclei, forming atoms. The introduction of neutral matter allowed light to pass freely without scattering. This separation of light and matter is known as decoupling. The light first radiated from this process is what we now see as the Cosmic Microwave Background.
The CMB is a perfect example of redshift. Originally, CMB photons had much shorter wavelengths with high associated energy, corresponding to a temperature of about 3000K. As the universe expanded, the light was stretched into longer and less energetic wavelengths. By the time the light reaches us, 14 billion years later, we observe it as low-energy microwaves at a frigid 2.7K. This is why CMB is so cold now.
The more mass there is, the more gravity there is to slow down the expansion. Is there enough gravity to halt the expansion and recollapse the universe or not? If there is enough matter (gravity) to recollapse the universe, the universe is “closed'”. A closed universe would be shaped like a four-dimensional sphere (finite, but unbounded). Space curves back on itself and time has a beginning and an end. If there is not enough matter, the universe will keep expanding forever. Such a universe is “open”‘. An open universe would be shaped like a four-dimensional saddle (infinite and unbounded). Space curves away from itself and time has no end.
Instead of trying to add up all of the mass in the universe, a more reasonable thing to do is to find the density of a representative region of the universe where density=(mass in the region)/(volume of the region). If the region is truly representative, then the total mass of the universe=(the density)*(the total volume of the universe). If the density is great enough, then the universe is closed. If the density is low enough, then the universe is open. In the popular astronomy magazines, you will probably see the mass density of the universe specified by the symbol “W”, also known as the ratio of the current density to the “critical density” described in the next paragraph. If W < 1, the universe is open; if W > 1, the universe is closed.
The boundary density between the case where the universe has enough mass/volume to close universe and too little mass/volume to stop the expansion is called the critical density, which may be represented as
where H is the Hubble constant for a given cosmological time (such as the present). The current critical density is approximately 1.06*10^-29g/cm^3. This amounts to six hydrogen atoms per cubic meter on average overall.
A critical density universe has “flat” curvature. The W density parameter equals to exactly 1 in a flat universe. It is to be noted that the Hubble “constant'” is not really a constant – it is different at different cosmological times. The greater the value of the Hubble constant at a given cosmological time, the faster the universe is expanding at that time.
Although dark matter makes up most of the matter of the universe, it only makes up about a quarter of the composition of the universe. The universe is dominated by dark energy.
After the Big Bang, the universe began expanding outwards. Scientists once thought that it would eventually run out of the energy, slowing down as gravity pulled the objects inside it together (Big Crunch). But studies of distant supernovae revealed that the universe today is expanding faster than it was in the past, not slower, indicating that the expansion is accelerating (Big Rip). This would only be possible if the universe contained enough energy to overcome gravity – dark energy.
To understand the Big Crunch and the Big Rip as possible hypotheses of the end of the universe, see the link below.