Classification of stars (3.9.2)

Luminosity is the total power output (in watts) of a star: the amount of light energy it emits per second.

Intensity is how much of that light reaches a specific area (in ). The intensity is a measure of the star’s effective brightness from Earth. Intensity follows the inverse square law, meaning it decreases rapidly as distance increases:

Where:

• is the intensity
• is the luminosity of the star (W)
• is the distance between the star and the observer.

As intensity is inversely related to the square of the distance to the star, doubling the distance makes the intensity four times smaller.

Luminosity is an objective property of the star; intensity (and by extension, apparent brightness) depends on both the star’s output and the observer’s distance from it.

Apparent magnitude measures how bright a star looks from Earth. It depends on both the star’s luminosity and its distance from us.

The Hipparcos scale ranks stars from (brightest) to (faintest visible to the naked eye).

It’s a logarithmic scale, where each increase of one in magnitude means the star appears 2.51 times dimmer.

Therefore, a star of magnitude 1 appears 100 times brighter than one of magnitude 6. This scale allows for consistent comparison of stellar brightness, accounting for our eye’s logarithmic response to light.

Parallax is the apparent shift in position of a nearby star against the background of distant stars, caused by Earth’s movement around the Sun.

The parallax angle is half the angle the star appears to move over six months. The larger the parallax angle, the closer the star.

To determine the parallax angle:

1. Observe the star from Earth 6 months apart (e.g. January and July).
2. Measure the angular shift in position against the background stars.
3. The parallax angle is half this total angular shift.

A parsec (pc) is defined using stellar parallax: it is the distance at which 1 AU subtends an angle of 1 arcsecond:

To derive the value of a parsec draw a right-triangle with:

• opposite side = (Earth–Sun radius)
• adjacent side = (distance to the star)
• angle

Because is tiny,

Convert 1 arcsecond to radians:

So:

A black body radiator is a theoretical object that absorbs and emits radiation at all wavelengths. While true black bodies are ideal and do not exist in reality, stars provide the closest real-world approximation.

The spectrum of radiation emitted by a black body is determined solely by its temperature.

The intensity–wavelength graph for black bodies shows the relationship between the temperature and the peak wavelength of emitted radiation for different objects. As the temperature in kelvin rises, the peak wavelength reduces, and the intensity increases.

Based on Wein’s displacement law:

• Hotter objects emit radiation with shorter peak wavelengths, meaning they appear white or blue.

• Cooler objects have longer peak wavelengths, giving them a red or yellow appearance.

• Hotter objects also emit greater intensity at each wavelength compared to cooler ones.

Recall how wavelength varies along the electromagnetic spectrum, so reducing wavelength means the radiation moves from the radio end of the spectrum towards the gamma end of the spectrum. Within the visible light region, a lower wavelength means light moves from red to violet.

Stars are grouped into spectral classes (O, B, A, F, G, K, M) based on their surface temperature and absorption lines.

To remember the spectral classes O, B, A, F, G, K, M, try:

“ O h B e A F ine G irl/G uy, K iss M e”

This classic mnemonic helps you recall the order from hottest to coolest stars.

Stars show absorption lines in their spectra, and these lines depend on the star’s surface temperature.

The Hydrogen Balmer lines are visible when electrons in hydrogen atoms are excited between energy level and higher levels. These lines are strongest in A-type stars, where the temperature is just right to partially excite hydrogen atoms.

• If the star is too hot (e.g. O-type), most hydrogen atoms are ionised, so fewer transitions occur from
• If the star is too cool, electrons rarely get excited to or from

This means Balmer line strength is temperature-dependent, peaking in stars around

Hertzsprung-Russell diagrams are graphs which plot the temperature of a star against its luminosity:

• X axis: surface temperature is measured in kelvin, with hotter stars on the left.

• Y axis: luminosity compared to our sun, with brighter stars towards the top.

When astronomers first plotted the stars, they had clustered them together in four groups:

• Main sequence
• White dwarfs
• Giants
• Supergiants

Most stars in the universe are on the main sequence. This is where stars spend most of their lives, in their stable core hydrogen-burning phase. When a star leaves the main sequence, it becomes either a white dwarf, a giant, or a supergiant, depending on its mass:

• Brighter stars have a proportionally higher surface temperature.

• The coolest stars are red, while the hottest stars are blue.

A star is considered low mass if it has between roughly 0.5 and 10 solar masses. Our Sun falls within this range.

When a low mass star exhausts the hydrogen in its core, hydrostatic equilibrium is disrupted. The core contracts while the outer layers expand and cool, forming a red giant. The star eventually sheds its outer layers as a planetary nebula (unrelated to planets, the name is historical), leaving behind a dense, hot remnant called a white dwarf.

Nebula – stage 1 of star formation

Stars are born in clouds of dust and gas known as stellar nebulae. These clouds are composed primarily of hydrogen and helium, along with heavier elements.

Nebulae are often material leftover from previous supernovae, the explosive deaths of massive stars. This means the atoms in our Sun and solar system were forged inside earlier generations of stars.

Over time, denser regions within the nebula begin to contract under the force of gravity; this process is called gravitational collapse. As the dust and gas are compressed, gravitational potential energy is converted into thermal energy, causing the temperature to rise.

Protostar – stage 2 of star formation

As gravitational collapse continues, the densest regions of the nebula form protostars. These continue to contract and heat up as gravitational potential energy is converted into thermal energy.

For nuclear fusion to begin, both temperature and pressure in the core must become high enough for hydrogen nuclei (protons) to overcome the electromagnetic repulsion between them. Since protons are all positively charged, they naturally repel each other. Only at extreme temperatures (~15 million °C) do they move fast enough to get close enough for the strong nuclear force to bind them together, fusing hydrogen into helium.

Main sequence phase – stage 3 of star formation

Once nuclear fusion is sustained, the outward radiation pressure produced by hydrogen fusion in the core balances the inward pull of gravity. This balance is called hydrostatic equilibrium.

The star has now entered the main sequence phase, where it will spend the majority of its life. This process of fusing hydrogen into helium in the core is known as core hydrogen burning (though no combustion is involved, the term ‘burning’ is used loosely in astrophysics).

More massive stars have hotter cores, which means they fuse hydrogen at a much faster rate. Counterintuitively, this means they exhaust their fuel supply and leave the main sequence sooner than less massive stars. Our Sun will spend roughly 10 billion years on the main sequence; a star ten times its mass may last only 20 million.

Red giant phase – stage 4 of star formation

Over time, the hydrogen in the core becomes depleted. The outward radiation pressure from fusion decreases, and hydrostatic equilibrium is lost. Gravity now dominates, causing the core to contract and heat up.

This rising core temperature heats the surrounding layers, causing them to expand dramatically. As the outer layers expand, the same amount of energy is spread over a much larger surface area. This reduces the surface temperature, shifting the star’s colour toward red (cooler stars emit longer wavelength light). The star has become a red giant.

Shell hydrogen burning phase – stage 5 of star formation

Although hydrogen in the core is depleted, significant hydrogen remains in the surrounding layers. Previously, these regions were not hot enough for fusion to occur.

As the core contracts and heats up, it transfers thermal energy to the layer (or shell) immediately surrounding it. Eventually, temperatures in this shell become sufficient for hydrogen fusion to begin. This process is called shell hydrogen burning. This is quite different from a main-sequence star, where fusion occurs only at the centre.

Core helium burning phase – stage 6 of star formation

As the core continues to contract, its temperature rises further. Eventually it becomes hot enough (approximately 100 million °C) for helium nuclei to fuse into carbon and oxygen. This process is called core helium burning.

Core helium burning restores outward radiation pressure in the core, temporarily re-establishing hydrostatic equilibrium. Meanwhile, shell hydrogen burning continues in the layer surrounding the core.

The combined energy output from both the core and the shell pushes the outer layers further outward, increasing the star’s size.

Shell helium burning phase – stage 7 of star formation

Eventually, the helium in the core is exhausted and fusion stops. Once again, hydrostatic equilibrium is lost. Gravity dominates, and the core contracts and heats up further.

This heat is transferred outward to the surrounding shell, which becomes hot enough for the helium within it to begin fusing into carbon and oxygen. This is called shell helium burning.

Beyond this, a further outer shell also becomes hot enough for hydrogen fusion to occur. The star now has a layered structure: a carbon-oxygen core, a helium-burning shell, and a hydrogen-burning shell.

For a low mass star, this is as far as fusion progresses. The core will never reach the temperatures needed to fuse carbon into heavier elements, so the star’s nuclear fuel is now effectively finite.

Core stops collapsing – stage 8 of star formation

In low mass stars, the carbon-oxygen core will never reach the temperatures required to fuse heavier elements. This is because heavier nuclei carry greater positive charge, meaning the electromagnetic repulsion between them is stronger, requiring more energy to overcome.

Without fusion to provide outward pressure, gravity continues to compress the core until it is roughly the size of Earth, incredibly dense, with a teaspoon of material weighing several tonnes.

At this point, electrons within the core resist being compressed any further. This outward force is called electron degeneracy pressure, and it is sufficient to halt gravitational collapse, establishing a new and final equilibrium.

White dwarf and planetary nebula formation – stage 9 of star formation

As the core contracts, the helium-burning shell becomes increasingly unstable. The star begins to pulsate, and these pulsations eject the outer layers of the star into space, forming an expanding cloud of gas and dust called a planetary nebula (the name is historical; it has nothing to do with planets).

This material enriches the surrounding interstellar medium with heavier elements such as carbon and oxygen, which may eventually form part of new stellar nebulae, beginning the cycle again.

The exposed remnant left behind is a white dwarf: an extremely hot, dense core in which no nuclear fusion occurs.

A white dwarf is the stellar remnant of a low mass star. Once the outer layers have been expelled as a planetary nebula, what remains is the exposed core, composed primarily of carbon and oxygen, supported against gravity by electron degeneracy pressure. No nuclear fusion takes place.

Key properties:

• Approximately the size of Earth (diameter of a few thousand kilometres)
• Extremely dense. A teaspoon of white dwarf material would weigh several tonnes
• Very hot initially, but with no energy source it slowly radiates away its thermal energy

It is useful to note that over trillions of years, a white dwarf is theorised to cool into a black dwarf. A cold, dark remnant. None yet exists, as the universe is not old enough.

When a high-mass star (greater than approximately 1.4 solar masses) dies, it will supernova:

1. Star runs out of nuclear fuel, so fusion ceases.
2. The core collapses rapidly under gravity.
3. The outer layers fall inward and rebound off the now dense rigid core, generating a powerful shockwave.
4. The shockwave ejects stellar material violently into space, creating a supernova.
5. As the shockwave moves outward, it causes the fusion of elements heavier than iron and ejects them into space.

A defining feature of supernovas is a sudden rise in absolute magnitude, making the star briefly outshine entire galaxies. A supernova can release around 1044 joules, equivalent to the Sun’s total output over its entire lifetime.

The final remnant depends on the star’s mass, creating either a neutron star or a black hole.

If the remaining core of a star after a supernova is between 1.4 and 3 solar masses, it collapses into a neutron star.

• Under immense gravity, protons and electrons are forced to combine via reverse beta decay, forming neutrons.

• These stars are incredibly dense. A teaspoon of neutron star material weighs about 100 million tonnes. With a radius of ~10 km, they rival atomic nuclei in density ().

• Some neutron stars spin rapidly, emitting beams of electromagnetic radiation from their poles. These are known as pulsars, and can rotate hundreds of times per second.

If the core of a collapsing star exceeds about three solar masses, the core continues collapsing until it forms a black hole: an object so dense that its escape velocity exceeds the speed of light.

• The boundary where the escape velocity equals the speed of light, is known as the event horizon or Schwarzschild radius.
  • Outside the event horizon the escape velocity is less than so light can escape and anything outside this boundary can be observed.
  • Inside the event horizon the escape velocity is greater than Light cannot escape and anything inside this boundary cannot be observed and is unknown: this is what causes the ‘black hole’.
• At this point, classical physics breaks down and general relativity must be used to describe its behaviour.
• At the centre of a black hole is a singularity: an infinitely dense point where the laws of physics completely break down.
• Black holes are invisible, but their presence is inferred from gravitational effects on nearby stars or emissions from surrounding accretion discs.

It is useful to note that the black hole shadow is actually a magnified image of the black hole’s event horizon, appearing roughly twice its size due to gravitational lensing.

A type 1a supernova has a distinctive light curve, which makes it useful as a standard candle.

After the initial explosion, the luminosity increases rapidly over a few days to a sharp peak, corresponding to an absolute magnitude of about –19.3. This rise is due to the sudden onset of thermonuclear fusion in the white dwarf.

• After peaking, the brightness declines in two stages: a rapid drop over a few weeks followed by a slower exponential decay lasting months.
• The decline is driven by the radioactive decay of nickel-56 to cobalt-56, which then decays to iron-56.
• The predictable shape and brightness of the curve allow astronomers to identify type 1a events and use them to determine vast cosmic distances.