Astrophysics (Stars)

Question 1

Describe the luminosity of a star.

Answer 1

The total amount of energy a star radiates per second (W).

Question 2

Describe the intensity of a star.

Answer 2

The energy received by an observer from a star (Wm^-2).
I = L / 4πr²

Question 3

Define apparent magnitude.

Answer 3

The brightness of an object as it appears in the sky from Earth.

Question 4

Define absolute magnitude.

Answer 4

The brightness of an object from a distance of 10 parsecs away.
m - M = 5 log₁₀(d / 10)

Question 5

What type of scale is used for brightness magnitudes?

Answer 5

Hipparchus scale, a reverse scaling system.
More positive values means a fainter star.
More negative values means a brighter star.

Question 6

If a star is one magnitude brighter than another star, how many times brighter is it?

Answer 6

A difference in magnitude of one corresponds to a star that is 2.51 times brighter.

Question 7

State two reasons why a star may appear brighter in the sky.

Answer 7

The star outputs more power at visible wavelengths.
The star is closer to the Earth.

Question 8

Which equation relates the intensity and apparent magnitude of stars?

Answer 8

(I₂ and m₂ are typically the values for the brighter star)
I₂ / I₁ = 2.5^{m₁ - m₂}

Question 9

State the three most used units for astronomical distances.

Answer 9

Astronomical units (AU)
Light years (ly)
Parsecs (pc)

Question 10

Define a light year and describe how it is calculated.

Answer 10

The distance travelled by light in a vacuum in one year.
Multiply the number of seconds in a year by the speed of light in vacuum

Question 11

Define a parsec.

Answer 11

• The distance to a star when 1 AU subtends an angle of 1 arc second.

Question 12

Describe the behaviour of a black body.

Answer 12

An object that absorbs all electromagnetic radiation of all wavelengths.
Can emit electromagnetic radiation of all wavelengths.
Stars can be approximated to behave as black bodies.

Question 13

State the law that links a stars surface temperature and peak wavelength emission.

Answer 13

Wien’s Displacement Law: The shorter the peak wavelength, the higher the surface temperature.
λ_maxT = 2.9 x 10^-3 mK

Question 14

State the law that links a stars luminosity with its surface temperature and surface area.

Answer 14

Stefan’s Law: Luminosity of a star is directly proportional to surface area, and proportional to the temperature raised to the power of four.
L = σAT⁴

Question 15

Explain how line absorption spectra of stars are produced.

Answer 15

Cooler gas in a stars atmosphere will absorb photons of light of certain energies depending on the molecules present.
These photons will have specific wavelengths related to the energy of the photons.
When photons of these wavelengths are absorbed, they are absent from the continuous spectrum received from the star (and appear in the spectrum as dark lines).

Question 16

Explain the importance of hydrogen Balmer lines.

Answer 16

Dark lines from wavelengths corresponding to electrons moving between hydrogen’s first excitation level (n = 2) and higher energy levels.
The intensity of these Balmer lines depends on the temperature of the star.

Question 17

List the seven stellar classes.

Answer 17

O, B, A, F, G, K and M.
Spectral classification depends on the spectra of stars (strength of certain absorption lines), not distance or brightness magnitude.
Each class has a specific colour, temperature range and absorptions.

Question 18

Describe an O class star.

Answer 18

Blue
Temperatures: 25,000 K – 50,000K
Strong helium (He) and helium-plus (He+) lines due to high temperatures.
Weak hydrogen (H) Balmer lines.

Question 19

Describe a B class star.

Answer 19

Blue
Temperatures: 11,000 K – 25,000K
Strong helium (He) and hydrogen (H) lines.

Question 20

Describe an A class star.

Answer 20

Blue-white
Temperatures: 7,500 K – 11,000K
Strongest hydrogen (H) Balmer lines, but some metal ion absorptions too.

Question 21

Describe an F class star.

Answer 21

White
Temperatures: 6,000 K – 7,500K
Strong metal ion absorptions.

Question 22

Describe a G class star.

Answer 22

Yellow-white
Temperatures: 5,000 K – 6,000K
Both metal ion and metal atom absorptions.

Question 23

Describe a K class star.

Answer 23

Orange
Temperatures: 3,500 K – 5,000K
Spectral lines mostly from neutral metal atoms.

Question 24

Describe an M class star.

Answer 24

Red
Temperatures: < 3500 K
Lines from neutral atoms, and molecular absorptions from compounds such as titanium oxide (TiO) since these stars are cool enough for molecules to form.

Question 25

State the characteristics of stars that are plotted on an H-R diagram and the values of the axes.

Answer 25

A plot of absolute magnitude against absolute temperature (or spectral class. Absolute magnitudes from 15 to -10 - Temperatures from 50 000 K to 2 500 K (or OBAFGKM)

Question 26

State the name and location of the three main groups of stars plotted on an H-R diagram.

Answer 26

Main sequence stars: long diagonal band from top-left to bottom right. Red giants: Top-right White dwarfs: Bottom-left

Question 27

Describe the evolutionary path of a Sun-like star on an H-R diagram.

Answer 27

Starts off towards the centre of the long diagonal main sequence band. Hydrogen fusion stops, the star becomes a red giant and moves to the top-right of the diagram. Helium fusion stops, the star ejects it’s outer layers and becomes a white dwarf, moving left along the top of the H-R diagram and then down to the bottom-left of the diagram.

Question 28

Describe how a star is initially formed and how it becomes a protostar.

Answer 28

Stars are born in a cloud of dust and gas leftover from supernovae. These clouds contain denser clumps which slowly contract due to the force of gravity. When these clumps are dense enough, they fragment and heat up to form protostars.

Question 29

Describe how the protostar forms a stable main-sequence star.

Answer 29

Protostars eventually contract and heat up enough for hydrogen fusion to take place in the core. An outwards force is generated from nuclear fusion (radiation pressure) which balances the inwards force of gravity. The star reaches a stable equilibrium and remains like for as long as hydrogen is being fused (typically billions of years).

Question 30

What is core hydrogen burning?

Answer 30

The stage of a star where the inwards force of gravity is balanced by the outwards radiation pressure produced by the nuclear fusion of hydrogen in the core of a star.

Question 31

What is shell hydrogen burning?

Answer 31

When all the hydrogen in the core has fused into helium, the radiation pressure is lost and the helium core begins to contract. As the core contracts, it heats up and becomes hot enough to cause fusion of the hydrogen surrounding the core.

Question 32

What is core helium burning?

Answer 32

As the helium core continues to contract and heat up, it becomes hot enough to cause helium to fuse into carbon and oxygen

Question 33

What is shell helium burning?

Answer 33

When the helium in the core runs out, the carbon-oxygen core begins to contract and heat up as well. As the core heats up, it becomes hot enough to cause fusion of the helium layer surrounding the core.

Question 34

Describe a white dwarf and how they are formed.

Answer 34

In low mass stars, the carbon-oxygen core doesn’t get hot enough to fuse further. Once the core has shrunk to approximately the size of the Sun, electron degeneracy pressure prevents the core from collapsing. The star ejects it’s outer layers, leaving behind a very hot and dense core (white dwarf).

Question 35

Describe how a red supergiant is formed.

Answer 35

For high-mass stars, the force of gravity is great enough for fusion beyond the carbon-oxygen core. Layers of elements are built up around the core (like an onion) forming a red supergiant. For the most massive stars this continues all the way up to iron (beyond which fusion is energetically unfavourable).

Question 36

Describe a supernova

Answer 36

For stars with core greater than 1.4 times the mass of the Sun, electron degeneracy pressure is insufficient to stop the core from contracting. The core contracts and the outer layers of the star fall in and rebound off the core, causing huge shockwaves causing the star to explode.

Question 37

State the defining features of a Type 1a supernova.

Answer 37

A Type 1a supernova can be plotted on a light curve – a plot of absolute magnitude over time. These supernova always have a sharp initial park at -19.4, followed by a gradually decreasing curve (they are used as standard candles).

Question 38

Describe a neutron star and how they form.

Answer 38

If a star’s core is between 1.4 and 3 solar masses, the electrons in the core material become compressed and form neutrons and neutrinos. After supernova occurs, a dense star made mostly of neutrons is left behind.

Question 39

State the key features of a neutron star.

Answer 39

Incredibly dense Very small (approximately 20 km diameter) Can rotate very quickly (some also emit two beams of radio waves, called pulsars).

Question 40

Describe a black hole and how they form.

Answer 40

If a star’s core is greater than 3 solar masses, the force due to gravity is too great for neutrons to withstand. The core collapses to an infinitely dense point – this is a black hole.

Question 41

State the key feature of a black hole.

Answer 41

A gravitational field that is so strong that the escape velocity is greater than the speed of light – nothing can escape, not even light.

Question 42

Describe what is meant by an event horizon and how this can be calculated.

Answer 42

The boundary of the region around the black hole at which the escape velocity is equal to the speed of light. The radius of the event horizon is called the Schwarzschild radius and is calculated using: R_s = 2GM / c²