Classification of Stars

Question 1

Describe the events for star formation

Answer 1

1) Clouds of gas in interstellar space (nebulae) contract under their own gravitational forces
2) This forms a protostar, containing a fixed mass of gas which results in a rise in temperature when it contracts
3) When temperatures reach values in the order of 10⁶K, the protostars ignite, stabalise, and appear on the main sequence of the Hertzsprung-Russel diagram
4) The star stabilises because the gravitational attraction that causes the collapse is balanced out by the radiation pressure due to the nuclear fusion in the core of the star

Question 2

When during the formation of a star does the fusion of Hydrogen nuclei take place?

Answer 2

The ignition of the protostar is the point at which the temperature is high enough for nuclear fusion of Hydrogen to take place

Question 3

Give the equation to calculate the energy released by a star on the main sequence

Answer 3

E = mc²

Question 4

Give the 3 reactions for the fusion of Hydrogen nuclei to a helium nucleus

Answer 4

¹₁H + ¹₁H → ²₁H + ⁰₁e⁺ + ⁰₀ν
²₁H + ¹₁H → ³₂He + ⁰₀γ
³₂He + ³₂He → ⁴₂He + 2¹₁H

Question 5

Name and descibe an alternative method for the production of Helium nuclei in a star

Answer 5

CNO Carbon-Nitrogen cycle where the carbon and nitrogen nuclei effectively act as catalysts for the 4 protons changing to a helium nucleus

Question 6

Explain why a star will not react all of its Hydrogen

Answer 6

The fusion reactions will start to die away after only a small amount (approx. 0.0003) of the remaining Hydrogen has reacted.
This is because Hydrogen can only fuse in the core where temperatures are high enough

Question 7

Define giant stars

Answer 7

Giants are stars which have the same temperature and therefore appearance of colour as the main sequence stars below them on the HR diagram, but are many times brighter. They therefore have a significantly larger radius

Question 8

State Stefan’s law

Answer 8

The total energy emitted per unit time (power) per unit surface area of a blackbody is directly proportional to the forth power of the temperature in kelvin
P / A = σT⁴

Question 9

Using Stefan’s law, explain why the radius of giant stars are larger

Answer 9

P / A = σT⁴
Since A = 4πr²
Therefore P = 4πr²σT⁴
Thus if T remains constant, an increase in power P (luminosity/brightness) means an increase in r²

Question 10

Describe how a giant star is formed

Answer 10

• when enough of the star’s Hydrogen has been reacted, the rate of Hydrogen fusion decreases
• this results in less pressure from the radiation since the core is mainly Helium
• The core starts to collapse under the gravitational forces
• As a result, the temperature rises and helium begins to fuse together. The next layer out (mainly Hydrogen) will ignite causing the star to expand

Question 11

What 2 common groups can giant stars often be characterised into? Give an example of each

Answer 11

Red Giants (what our sun will become)
Super Giants (Betelgeuse)

Question 12

Define the Chandrasekhar limit

Answer 12

The Chandrasekhar limit (1.4Ms) is the maximum mass of a stable white dwarf star.
Below this limit, the star will become a white dwarf.
Above this limit, the star will become a supernova

Question 13

What does the symbol Ms stand for?

Answer 13

The mass of the sun

Question 14

Describe a white dwarf and state what prevents them from collapsing

Answer 14

White dwarf stars have no fusion occurring, so have low luminosity and will therefore gradually cool down and become black dwarf stars
They are prevented from further collapse due to the electron degeneracy pressure (due to the Pauli Exclusion Principle)

Question 15

Describe and explain the position of white dwarf stars on the Hertzsprung-Russell diagram

Answer 15

Bottom left, because they have large values for absolute magnitude and have a high surface temperature

Question 16

State and define what surround dwarf stars

Answer 16

Planetary Nebular are ring shaped clouds of gas and dust which are visible in the night sky, and surround an ageing star (e.g. dwarf stars)

Question 17

State the mass range for the formation of a Neutron star

Answer 17

Above the Chandrasekhar limit and below 3Ms

1.4Ms

Question 18

Describe a neutron star and state what prevents them from collapsing

Answer 18

When Red Supergiant stars (above the Chandrasekhar limit but below 3Ms) collapse, the gravitational force is strong enough that it forces the electrons and protons together to form neutrons.
Since the neutrons are fermions (like electrons), they are kept apart by the Pauli Exclusion Principle, which creates pressure know as the “neutron degeneracy pressure” and prevents further collapse

Question 19

State the density and average diameter for the matter inside neutron stars

Answer 19

Same density as nuclear matter (10¹⁷ kgm⁻³)

Average diameter is a few tens of kilometers

Question 20

Give the sequence of evolution for small/medium dust clouds

Answer 20

1) Small/Medium Dust Cloud
2) Yellow Star
3) Red Giant
4) White Dwarf & Planetary Nebular

Question 21

Give the sequence of evolution for large dust clouds

Answer 21

1) Large Dust Cloud
2) Blue/White Star
3) Red Supergiant
4) Supernova Explosion
5) Neutron Star or Pulsar

Question 22

Define fermion

Answer 22

A subatomic particle, such as a nucleon, which has half-integral spin and follows the statistical description given by Fermi and Dirac

Question 23

Describe black holes and how they are formed

Answer 23

Black holes are formed from stars above 3Ms, which collapse with such force that there is nothing in the known universe that can prevent collapse (inc. neutron degeneracy pressure).
They are treated as singularities since they have extremely large mass and effectively 0 volume. This distorts the whole of space-time, not even light can escape

Question 24

Define the Schwarzschild radius and give its symbol

Answer 24

The point a certain distance away from a black hole in which light can start to escape
Symbol: Rs

Question 25

Give the equation for tan object of mass m to just escape the surface of another object of mass M₁

Answer 25

The total energy must be 0:

Eᵀ = Eᴷ + Eᴾ = ½mv² - (GM₁m / R₁) = 0

Question 26

Give the equation for the Schwarzschild radius

Answer 26

Rs = 2GM / c²
M is the mass of the black hole
G is the gravitational constant

Question 27

Define the event horizon

Answer 27

The effective boundary provided by the Schwarzschild radius, where objects any closer have an escape velocity greater than the speed of light

Question 28

Give the sequence of evolution for large dust clouds into blackholes

Answer 28

1) Large Dust Cloud
2) Blue/White Star
3) Red Supergiant
4) Supernova Explosion
5) Black Hole

Question 29

State 2 main types of supernovae

Answer 29

Type 1a supernovae

Type 2 supernovae

Question 30

Describe type 1a supernovae and how they are formed

Answer 30

• Type 1a supernovae are formed as part of a binary system and occur when a white dwarf close to the Chandrasekhar limit draws enough matter from its binary partner to make it equal to the limit of 1.4Ms. This re-ignites the star and causes its cataclysmic end
• The brightness increases and the magnitude decreases to -19.3
• Each reach the same peak value of magnitude and produce a very constant light curve

Question 31

Describe type 2 supernovae and how they are formed

Answer 31

• Type 1 supernovae are formed from a single very large star (10-100Ms)
• Are less bright by a couple of orders of magnitude and after a sharp fall in brightness there is a plateau on the light curve
• The explosion blows off the outer layers in a spectacular way, forming planetary nebula

Question 32

When and why are larger elements than iron formed?

Answer 32

During a supernovae explosion because there is a net energy input from the star due to it being unable to withstand the forces of gravity as it undergoes rapid collapse, thus large amounts of gravitational potential energy is released for endothermic fusion

Question 33

Define standard candles and state 2 different examples

Answer 33

• Objects whose brightness can be measured very accurately and therefore are used to give the most accurate determination of astronomical distance
• Supernovae and Cepheid variables are examples of standard candles

Question 34

Define cepheid variables

Answer 34

Stars which have a very regular period of varying luminosity caused by the star appearing to pulsate. This is because the star expands and contracts due to an imbalance in the pressures, increasing in brightness as the star contracts because the temperature increases from the decrease in radius

Question 35

Why are cepheids described as intrinsic variables?

Answer 35

Because the variation in luminosity is due to what happens in the star itself not down to it being eclipsed in something (extrinsic variables)

Question 36

When are supernovae more useful as standard candles than cepheids?

Answer 36

When the cepheids are very distance, they become very dim, so supernovae become more useful (distances beyond 1000Mpc)

Question 37

State the period-luminosity law

Answer 37

The period of light variation of a Cepheid variable is in direct relation with its absolute magnitude whereby intrinsically fainter stars have the shorter periods.

Question 38

Define absolute magnitude

Answer 38

The magnitude (brightness) of a celestial object as it would be seen at a standard distance of 10 parsecs.

Question 39

Describe how cepheids are used as standard candles

Answer 39

Due to the period-luminosity law, the period of the cepheid can be measured accurately from the Earth and the magnitude calculated. The distance of those that are close to Earth are then accurately determined and a graph of Magnitude vs. log(Period/d) is plotted. This can be used to calculate the distance once the magnitude has been measured

Question 40

Give the equation for the difference between the magnitude m and absolute magnitude M of a star

Answer 40

m - M = 5 log(d/10)

where d is distance in parsecs

Question 41

State the 7 spectral classes of stars

Answer 41

O, B, A, F, G, K, M

Question 42

For the spectral class of stars O, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 42

i) Blue
ii) 25000 - 50000
iii) He⁺, He, H

Question 43

For the spectral class of stars B, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 43

i) Blue
ii) 11000 - 25000
iii) He, H

Question 44

For the spectral class of stars A, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 44

i) Blue-white
ii) 75000 - 11000
iii) H (strongest), Ionised metals

Question 45

For the spectral class of stars F, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 45

i) White
ii) 6000 - 7500
iii) Ionised metals

Question 46

For the spectral class of stars G, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 46

i) Yellow-white
ii) 5000 - 6000
iii) Ionised & neutral metals

Question 47

For the spectral class of stars K, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 47

i) Orange
ii) 3500 - 5000
iii) Neutral metals

Question 48

For the spectral class of stars M, state:

i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines

Answer 48

i) Red

ii)

Question 49

Define the Balmer series and explain the trend in prominence of balmer lines for the different spectral classes of star

Answer 49

Balmer series is the transition of electrons to the energy level n=2. The electrons start in the n=2 state. To achieve this with a significant proportion of the
hydrogen, the atmosphere of the star must be fairly hot. Any hotter than about 10000K,
however, and the hydrogen starts to be ionised
Because of this, the Balmer lines are most prominent for A class stars, weaker for O, B and F, and are very weak for G, K and M class stars

Question 50

State Wein’s law

Answer 50

λᵐᵃᵡT = constant = 2.9x10⁻³mK