Astrophysics Part V: The End of the Universe

Andromeda Galaxy

So we have considered the evolution of stars, and evidence supporting the big bang, however, we have not yet covered the end of our universe.  This topic has, like many  phenomena of astrophysics been debated over for many years.  There are multiple theories, but all of them depend on the mass of the universe.  The universe could be either

• Closed
• Open
• Flat

Possible Fates of the Universe

A closed universe means that gravity will stop the universe from expanding, causing it to contract, this would result in a massive contraction of the universe in a big crunch, from which the universe could begin again.  The density of the universe would have to exceed the critical density, ρ > ρ_c.

An open universe means that gravity would be too weak to stop the expansion.  The universe would expand forever, the density of the universe would be less than the critical density thus ρ < ρ_c.  The universe will end in either a big rip or big freeze.  In the big rip, acceleration of the expansion of the universe caused by the presence of dark energy would become too large, and would supersede the strong nuclear force, the electromagnetic and gravitational forces, resulting in the reduction of all matter to elementary particles.  However, the possibility of a big freeze is also possible.  As the universe expands, the concentration of dust and gas clouds would decrease, and the fuel needed for star growth would decrease as well.  This would result in less stars from forming.  Furthermore, the extreme redshift of electromagnetic waves, would leave the waves with little energy.  Meanwhile, the distance between galaxies would be rapidly increasing.  The universe would be unable to sustain life, as Earth would become too cold.

Lastly, the universe may be flat.  The density is equal to the critical value, consequently the universe will only begin to contract after an infinite amount of time. This means that the universe’s density must equal critical density, ρ = ρ_c.  The fates of the universe would be the same as an open universe.

Astrophysics Part III: Stellar Evolution and the Different Types of Stars

In our previous two articles we have covered basic topics of astrophysics such as stellar clusters and apparent brightness. In this article we will exploring the more complicated, the evolution of a star, and exploring the different possible paths a star’s evolution can take. The sun is the nearest star to Earth, and without it, life would not be able to exist.  Our planet is held in orbit by this star, however, eventually the sun will expand and engulf our planet.  This article will look at the evolution of stars and the different names for different stages of a star’s life.

A Planetary Nebula

Stars, surprisingly, begin as nebulas, clouds of dust and gas in space.  Gravitation brings the particles together, which increases the temperature of the particles and also ionises them, and they produce light.  At this point it becomes a protostar, which is very large and can have a surface temperature of 3000K.  However, at this point it is much larger than a star with similar mass, and the gravitation continues, decreasing the volume of the star.  The contraction continues until the core has become completely ionised plasma. Nuclear fusion begins converting the hydrogen in the core to helium, the protostar is now a star, which can be found on the Hertzsprung-Russel diagram. As described in our earlier post, the Introduction to Astrophysics, the gravitational pressure and radiation pressure are equal.

A Hertzsprung-Russel Diagram

The larger the mass of the star the greater its luminosity and temperature, stars can be found in the main sequence. The size of the original mass of the star determines how long its time on the main sequence is.  Our sun, is actually a relatively small star, and will burn for approximately 10¹⁰ years, however, a star with a mass of 25 times our sun’s will have burn its hydrogen core for only 10⁶ years. After this is complete, the star leaves the main sequence, becoming a red giant. The fusion in the core has stopped and now with no opposing forces the gravitational contraction increases the temperature of the core, and the outer layers of the star. As the outer layers increase in temperature, the star expands, the luminosity increases, but surface temperature decreases.  Helium is created from the fusion of hydrogen, and this causes to core to further contract, until the temperature becomes so high that helium becomes to fuse, to produce Oxygen-16 and Carbon-12.  The process is repeated. Surprisingly, as the core decreases, the size of the star increases.

Once the fusion of helium in the core is complete, the core contracts again increasing the temperature of the outer layers, allowing helium fusion.  This is the second red giant phase,  and when the sun goes through this phase, it will likely engulf Earth. During this phase however, the outer layers of the star are expelled, exposing its hot core.  The 100000K core ionises the outer layers, causing them to emit visible radiation.  This stage is called a planetary nebula.  However, if the mass of the star is between 4-8 solar masses, it is possible to produce heavier elements through fusion, namely neon, sodium, oxygen and magnesium. The lack of fusion causes the core to cool, and the sun becomes a white dwarf cooling down and out of sight.

This however, can only occur if the mass of the core is less than 1.44 solar masses.  At 1.44 solar masses, the gravitational contraction force is at equilibrium with electron degeneracy. This is the force of electrons repelling each other, when they are tightly packed together.  it exists because of the Pauli exclusion principle, which states that no two electrons can be in the same state. But if the core of the star is greater than 1.44 solar masses, the gravitational contraction force is greater than the electron degeneracy pressure, and the star becomes either a black hole or a neutron star. This is called the Chandrashekar limit. Whether it becomes a black hole, or stays a neutron star, will be discussed later in this article.

However if the mass of the star is above 8 solar masses, the process of fusion continues, once helium has been fused, carbon is created. Once all the carbon in the core is fused, the temperature rises to 10⁹ K, here neon is fused.  After this, the process repeats and oxygen is fused, producing silicon. Finally the temperature is large enough for the fusing of silicon, which produces iron, the most stable of all elements.  This is called a super red giant. 

Once the whole core is iron, it contracts rapidly, reaching a temperature of 6 x 10⁹ K.  High energy gamma photons, collide with the iron nuclei, breaking them into alpha particles.  Then the negative electrons and positive protons combine, producing neutrons and large quantities of neutrinos.  These carry energy away from the star, causing it to contract once more.  However, this rapid contraction creates produce a wave of pressure that moves outwards away from the centre of the star.  At the same time, because the core is contracting, matter is falling into the centre of the star, however, this is repelled by the outwards pressure wave. The wave accelerates, but soon reaches the speed of sound, becoming a colossal shock wave that rips the outer layers of the star apart.  This exposes the hot inner cores, and large amounts of radiation enter space.  The process is called a supernova.  Through this process 96% of the star’s mass is lost, and the material flung out into space forms nebulae, where new protostars can be created.

However, the stellar evolution is not yet finished. The remnant from the supernova has formed into neutrons, and these combine to form an extremely dense star called a neutron star.  The collapse is prevented by neutron degeneracy pressure.  If the mass is greater than between 2-3 solar masses however, a black hole is formed.  The figure is not precise, as the equations regarding extremely dense matter are not yet known. This marks the enter of the stellar evolution as we know it.

A neutron star is an extremely dense star, equal to the density of the whole human population packed into the size of a sugar cube. Neutron stars are typically small, and thus to conserve angular momentum must rotate.  This pheneomena is known as a pulsar. The rotating magnetic field of the pulsar produces radio waves, which are detectable from Earth. In fact, it was through these that pulsars were detected originally.

Now we will briefly look at black holes.  The earth has a gravitational constant of 9.81ms^-2, we can temporarily leave the surface if we jump, but gravity brings us back down.  However, if an object was so dense that this acceleration equalled to the speed of light, then nothing would be able to leave the surface of the Earth, not even light.  This is what we find in a black hole, and that is the reason why they are black, because nothing can escape then.  To picture this we must consider the fabric of space time. Large masses bend spacetime, however, if an object is so large, then space time will be bend around completely, preventing the escape of anything.  Even more interesting is the theory of General Relativity, which describes how in a gravitational field, time will slow down.  At points where the escape velocity equals to the speed of light, time ceases.  This is known as the event horizon.  Furthermore, when the entire mass of the star contracts into the event horizon, the density will be infinite. This is known as the singularity, where density is infinite.  A black hole consists of both a singularity and an event horizon.

The detection of black holes however, is difficult, as the phenomena does not emit radiation, and thus we cannot see them.  We have to look at the nearby stars, that may be having matter pulled off their surface, and radiation emitted by these types of processes.  Physicists believe their may be a black hole in the centre of our galaxy.

Astrophysics Part II: Stars as Black Bodies and Wien’s Law

In the earlier post, I described the solar system, and introduced concepts such as luminosity and brightness. These two qualities, denoted as L and b, are also used in other equations, which describe the characteristics of stars. But first the concept of black body radiators must be introduced.

A black body is a hypothetical object which absorbs all incident electromagnetic radiation

The emission spectra of black bodies are related to the temperature of the body. As the temperature of the body is increased:

• the intensity of each wavelength increases
• the total energy emitted is higher
• the increase in intensity of shorter wavelengths is greater than the increase in intensity of longer wavelengths

A black body is hypothetically black at room temperature, however, at higher temperatures, the object would begin to emit thermal radiation and glow. Mathematically, this can be expressed as:

E∝T⁴

This equation shows the proportionality and is referred to as Stefan’s Law. A commonly referred to example of a black body is that of a box which has had its insides painted completely black. The box is completely sealed, but for a small hole made in one of the sides. When placed in a bright room, light would be able to enter the box. However when inside, the black walls would absorb the majority of the light when the light ray bounced off the walls. Only a small portion of the light would be reflected each instance, so there would only be a small chance of any of the light ever being reflected back out of the small hole. A diagram aids the explanation:

When written completely, the equation is:

L=4πR²σT⁴

Here, R refers to the radius of the concerned star, sigma σ refers to the Stefan-Boltzmann constant, which has the value 5.67×10^-8 W m^-2 K^-4. The units cancel when multiplied together, so the luminosity has the units of watts, denoted as W. Using the equation, we can determine the luminosity of a star.

Again using the concept of a black body, another equation called ‘Wien’s law‘ shows a relationship between the wavelength which is emitted with maximum intensity from the star, and the temperature of the star. This equation is used for all black bodies, and as stars are considered to be black bodies, the Wien’s Displacement Law can be used for stars as well.

Here, the intensity peaks when the wavelength denoted by the symbol lambda is at just over 2μm. This value of wavelength is used as the λ_max. Whenever we see such a graph, by observing the wavelength with peak intensity, this value is the λ_max. The relationship between λ_max and temperature T is inversely proportional.

T∝k/λ_max

here ‘k’ refers to a constant.

The actual value of this constant is 2.9×10^-3 m K, thus the equation can be written as an expression of T in terms of λ_max. The value for λ_max must be expressed in m. 

Using this equation, by observing a star’s spectrum, the temperature of it can be predicted.

Introduction to Astrophysics

This blog post seeks to explore the basics of the Astrophysics option for HL Physics.

Galaxies are vast collections of stars. The solar system is a name for the collection of eight planets which orbit our sun, excluding Pluto, which has has its star status removed. Some of these planets have moons, satellites which orbit the planet. For Earth, the only moon is The Moon. But for other planets, specifically the gas giants, Saturn, Jupiter, Uranus and Neptune they may have many moons, for example, Saturn has 18 moons and Jupiter has 16. Of all the planets, Jupiter has the greatest equatorial diameter, at 143000km, and the largest mass – 19000 × 10²³ kg.

A stellar cluster differs from a constellation.

A stellar cluster is a group of stars held together by the forces of gravitational attraction, whereas a constellation is a collection of stars that form a recognizable group from earth, that may not actually be close together in the sky.

An example of a constellation is the ‘big dipper’, and I have included a photo of this below.

As the distances involved in this topic are great, a measure of distance called the light year is used.

The light year is the distance light travels in a year, a distance of 9.46 × 10¹⁵m.

The main source of energy in stars is nuclear fusion. Inside the star, hydrogen is converted in helium, with high temperatures of 10⁷K and high pressure present. The atoms must overcome coulomb repulsion in order to get close enough to fuse. This may occur from the repulsion between the like negative charged electrons in the electron rings.

Stars keep their shape as there is a balance of radiation pressure and gravitational pressure. As the star is massive, the centre acts to attract the contents of the star inwards. However, this is balanced by the radiation pressure, which is an outward pushing force, acting from inside the star. Radiation pressure results from the continuos fusion reactions which take place. An image showing this is included below.

Now some important equations describing the characteristics of stars can be considered. Stars have nuclear reactions which produce energy. Stars can be classified by the amount of energy they produce per unit time.

The luminosity of a star is defined as the total energy emitted by the star per unit time, and is denoted as L. It has the unit of Watts (W).

The sun has a luminosity of 3.90 × 10²⁶ W.

The luminosity of a star can be used to calculate the apparent brightness, a measure of the power which takes distance from the star into account. As the distance between the star and the Earth increases, the intensity of the power received falls. Apparent brightness is a measure of the energy received per unit time per unit area at the surface of Earth, and is given by the equation:

The luminosity of a star is spread over the total surface area of a sphere of radius ‘d’. This is explained in the image below:

As the distance from the source of light increases, the power of A is spread over a larger and larger area. As the distance increases by a factor of 2, the brightness decreases by a factor of 4. When the distance is increased by a factor of 3, the brightness decreases by a factor of 9. This shows the inverse square law.  The apparent brightness can be measured using a device called a bolometer. If the distance d can be measured, then the luminosity L of the star can be determined.