A-level Physics/Cosmology/Stars and Galaxies

The universe consists of millions of stars, which are grouped together as galaxies.

Stars
Stars, like our Sun, are giant hydrogen fusion reactors, producing huge amounts of energy for millions of years.

The birth of a star
Stars begin their life in interstellar gas clouds, where the particles attract each other by gravitational forces. These gas clouds consist mainly of hydrogen and helium, though more recent stars will contain heavier elements produced from older, and now dead, stars.

The gravitational attraction increases as the mass becomes heavier. A protostar is now formed, which is a local concentration of atoms that are large enough to form a star, and begins to increase in temperature, since the lost gravitational potential energy is converted to thermal kinetic energy.

Once the temperature reaches about $$10^{6} K$$, the core is hot enough for hydrogen fusion to occur. The star, over time, stabilizes its temperature, where the rate of energy released at its surface matches the rate of energy produced in its core, and stabilizes its size, where the outward pressure from the thermal reactions matches the gravitational attraction inwards.

The star is now a main sequence star, and will produce energy from hydrogen for many millions of years. Note that since more massive stars "burn" hydrogen at a much faster rate, they have much shorter life spans than less massive stars.

Nuclear Fusion within stars
Stars consist mainly of hydrogen, which is used for the fusion reactions that produce almost all of their energy. In this process four hydrogen nuclei fuse to form a helium nucleus. However, this does not happen directly, and actually happens in stages:


 * Two protons fuse to form a deuterium nucleus, and releases a neutrino and a positron.
 * $$\ ^1 _1H + \ ^1 _1H \rightarrow \ ^2 _1H + v + \ ^0 _{1}e$$


 * The deuterium nucleus fuses with another proton, and produces a helium-3 nucleus.
 * $$\ ^1 _1H + \ ^2 _1H \rightarrow \ ^3 _2He$$


 * Two helium-3 nuclei fuse to produce the helium-4 nucleus. Two protons are released.
 * $$\ ^3 _2He + \ ^3 _2He \rightarrow \ ^4 _2He + 2^1 _1H$$

Energy released
The energy released can be calculated by $$E = mc^2$$, where $$m$$ is the mass deficit i.e. the difference in mass between the daughter nuclei and parent nuclei. In the case of fusion, the total mass of parent nuclei is always larger than that of the daughter nuclides.

Red giants
Once most of the hydrogen in the star has run out, the star will be unable to maintain equilibrium. The core of helium will contract and hydrogen burning will continue in a shell surrounding the core. Since gravitational potential energy is lost when the core contracts, the thermal kinetic energy will increase. This increase causes the star itself to expand. The star is no longer a main sequence star, but is a red giant.

Helium burning within a red giant
Since the temperature of the core of the red giant increases, "helium burning" will occur when the temperature reaches about 100 million K. Like "hydrogen burning", "helium burning" happens in stages:


 * Two helium nuclei fuse to form a beryllium nucleus
 * $$2He \rightarrow Be$$


 * Another helium nucleus fuses with the beryllium nucleus to produce a carbon nucleus and a gamma photon.
 * $$Be + He \rightarrow C + \gamma$$


 * Yet another helium nucleus fuses with the carbon nucleus to form an oxygen nucleus and another gamma photon.
 * $$C +He \rightarrow O + \gamma$$

Further fusion reaction in red giants
More massive red giants that are more than 3 times the mass of the Sun can reach higher temperatures and fusion of heavier elements can occur:


 * At 600 million K, "carbon burning" occurs, producing neon and magnesium nuclei.
 * At 1 billion K, "neon burning" occurs, producing oxygen and magnesium nuclei.
 * At 1.5 billion K, "oxygen burning" occurs, producing silicon nuclei.
 * At 3 billion K, "silicon burning" occurs, with the production of iron nuclei.

After iron, nuclear fusion does not produce any energy, so the thermonuclear reactions cease. Elements heavier than iron are created in supernovae because the require a net input of energy from the surroundings, unlike the fusion of the smaller elements.

The death of a star
Once the temperature in the core is too low for the next thermonuclear reaction to begin, the star will become unstable. What happens next in the life cycle of a star depends on the Chandrasekhar limit, which is equal to 1.4 times the solar mass.

Stars with masses less than the Chandrasekhar limit
When the star is unstable, it will shed the outer layers of gas, which results in a planetary nebula (only called that because they were once thought to resemble planets, but they have nothing to do with planets). The core itself will shrink and become more dense, and reach a density so great, that one teaspoonful will have a mass of many tonnes. The core will stop shrinking once the fermi pressure of electrons that are packed very closely prevents any further collapse. The dense, but dim, star is now a white dwarf. There is no further energy in the core, and the white dwarf will gradually radiate it all away and cool down eventually reaching the same temperature as the surrounding space. At this point it is called a 'Black Dwarf'. It is thought that the Universe is just old enough for White Dwarfs to have formed and cooled down to Black Dwarfs, although none have yet been detected.

Stars with masses greater than the Chandrasekhar limit
For stars that are greater than 1.4 solar masses, the Fermi pressure of electrons is too weak to prevent the gravitational collapse. In the space of a few seconds, the electrons are crushed against the protons to form neutrons, and the core now has a very immense pressure, and therefore, a very high temperature. Elements with atomic numbers higher than iron are produced during this collapse. When the collapse of the core suddenly halts, it causes an explosion due to the immense outward pressure. This explosion is called a supernova. The remaining cloud of dust may eventually form a group of new stars.

Neutron stars
The core within the supernova remains, and is composed entirely of neutrons, since electrons have been forced into the nucleus. Their density is so great, that the Earth at the same density would be only a few hundred meters in diameter. This leftover core is called a neutron star, because of the fact it is made of nothing other than neutrons.

Pulsars
Most stars have their own angular velocity, or rate of spin. When a star decreases in size rapidly, it will spin faster, because angular momentum is conserved. This is similar to the way an ice-skater can spin faster if she holds her arms closer to her body. Often, this is what happens when the core of a supernova shrinks to form a neutron star. The rate of rotation increases massively, and this results in a pulsar. We call it this because on Earth we detect them as regular radio pulses, with periods sometimes in the millisecond range. The regularity and short periods of these pulses led scientists to believe that aliens were trying to communicate with us, although the pulses are now known to come from the magnetic field of a spinning neutron star.

Like all stars, pulsars have their own magnetic field. As the rate of rotation of a star increases, the magnetic field strength around it also increases. The moving magnetic field creates an intense electric field. This intense electric field accelerates electrons and creates an intense beam of radiation at both magnetic poles. Because magnetic north and the axis of rotation aren't perfectly lined up, just like on Earth, it's possible for the beam of radiation to pass through the Earth and reach us, producing the observed pulses of radiation.

Black holes
If a neutron star is greater than approximately 3 solar masses, it will collapse further to an infinitely small point, called a singularity, and will become infinitely dense. The gravitational field strength at a few kilometres from the singularity is so intense that even light cannot escape, and the star is now a black hole (light is affected by gravity despite the fact that photons have no mass, this is explained by Einstein's general theory of relativity). Since nothing can travel faster than the speed of light (also explained by relativity), anything that falls into a black hole is lost forever.

Quasars
A quasar is a source of radiation which is very luminous, brighter than many galaxies. They vary in brightness with periods of a few days or months and because an object cannot change luminosity faster than the time it takes light to travel from one end to the other, they are thought to be relatively small objects, only a few light-days or light-months in diameter. Quasars have been calculated from their red shift to be very distant, as far away as 18 billion light-years, and the only explanation for them is that they are radiation emitted by matter as it falls into a black hole, as the gravitational potential energy of the matter is lost.

Measuring the distance to stars
To measure the distance of stars from Earth, several methods have been devised.

Parallax
We can measure the angle of parallax a star makes as it appears to move across the background of distant stars when the Earth moves from two extreme points in its orbit. We assume that the distant stars are stationary. The diagram shows what is meant by the parallax of a star:

From this angle, we can find the distance in parsecs by:

$$\text{distance} = \frac{1}{\text{parallax}}$$.

Therefore, the smaller the angle of parallax, the further away the star is from Earth, and when a star has a parallax of 1 arc second ($$\frac{1}{3600}th$$ of a degree) we say that it is one parsec away. One parsec is approximately equal to $$3 \times 10^{16}$$ m, or 3.26 light-years.

Intensity of light
Once, it was thought that all stars were exactly the same brightness, but some appeared dimmer than others because they were further away. We now know that stars can individually vary in brightness, but the magnitude system is still used.

Apparent magnitude
The visible stars were separated into 6 classes depending on their perceived brightness. The brightest stars were classed as magnitude 1, and the dimmest stars visible with the naked eye were classed magnitude 6. It was then found that a difference in magnitude actually represented a ratio of 2.5 in intensity, since the human eye works on a logarithmic scale. That means that a magnitude 1 star was $$2.5^{5} = 100$$ times more intense than a magnitude 6 star. The ratio of intensities of two stars can be found from their apparent magnitude by:


 * $$\frac{I_1}{I_2} = 2.5^{m_2 - m_1}$$

Today, with telescopes, we can measure stars with apparent magnitudes ranging from approximately +25 to -25, where smaller is brighter. We calculate it from the measured value of intensity, using the formula:


 * $$m = - 2.5 \log \ I + constant$$

where m is the apparent magnitude and I is the intensity.

Absolute magnitude
The apparent magnitude of a star gives us no information of its true intensity, only the intensity of light that reaches us. That means a very distant star could be more intense than a nearer one, but it would appear dimmer from Earth. The absolute magnitude of a star is the apparent magnitude it would have if it was at a distance of 10 parsecs. The absolute magnitude is given by the equation:


 * $$M = m - 5 \log ( \frac{d}{10} )$$

Where d is the distance of the star in parsecs.

The Milky Way
The galaxy we are in is called the Milky Way. It is a spiral galaxy and is thin, but lens like, in thickness. It has a radius of 100 000 light-years, and is about 2000 light-years thick giving it a profile somewhat like a CD. At its centre is a large ball of older stars called the Galactic Bulge at the centre of which is a super massive black hole. The Milky way contains between 200 and 400 billion stars and an estimated 2 trillion planets. The Milky Way has a number of spiral arms (between 2 and 6, the exact number is not yet known) which are regions of star formation.