Classification of Stars Flashcards
Describe the events for star formation
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
When during the formation of a star does the fusion of Hydrogen nuclei take place?
The ignition of the protostar is the point at which the temperature is high enough for nuclear fusion of Hydrogen to take place
Give the equation to calculate the energy released by a star on the main sequence
E = mc²
Give the 3 reactions for the fusion of Hydrogen nuclei to a helium nucleus
¹₁H + ¹₁H → ²₁H + ⁰₁e⁺ + ⁰₀ν
²₁H + ¹₁H → ³₂He + ⁰₀γ
³₂He + ³₂He → ⁴₂He + 2¹₁H
Name and descibe an alternative method for the production of Helium nuclei in a star
CNO Carbon-Nitrogen cycle where the carbon and nitrogen nuclei effectively act as catalysts for the 4 protons changing to a helium nucleus
Explain why a star will not react all of its Hydrogen
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
Define giant stars
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
State Stefan’s law
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
Using Stefan’s law, explain why the radius of giant stars are larger
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
Describe how a giant star is formed
- 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
What 2 common groups can giant stars often be characterised into? Give an example of each
Red Giants (what our sun will become) Super Giants (Betelgeuse)
Define the Chandrasekhar limit
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
What does the symbol Ms stand for?
The mass of the sun
Describe a white dwarf and state what prevents them from collapsing
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)
Describe and explain the position of white dwarf stars on the Hertzsprung-Russell diagram
Bottom left, because they have large values for absolute magnitude and have a high surface temperature
State and define what surround dwarf stars
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)
State the mass range for the formation of a Neutron star
Above the Chandrasekhar limit and below 3Ms
1.4Ms
Describe a neutron star and state what prevents them from collapsing
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
State the density and average diameter for the matter inside neutron stars
Same density as nuclear matter (10¹⁷ kgm⁻³)
Average diameter is a few tens of kilometers
Give the sequence of evolution for small/medium dust clouds
1) Small/Medium Dust Cloud
2) Yellow Star
3) Red Giant
4) White Dwarf & Planetary Nebular
Give the sequence of evolution for large dust clouds
1) Large Dust Cloud
2) Blue/White Star
3) Red Supergiant
4) Supernova Explosion
5) Neutron Star or Pulsar
Define fermion
A subatomic particle, such as a nucleon, which has half-integral spin and follows the statistical description given by Fermi and Dirac
Describe black holes and how they are formed
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
Define the Schwarzschild radius and give its symbol
The point a certain distance away from a black hole in which light can start to escape
Symbol: Rs
Give the equation for tan object of mass m to just escape the surface of another object of mass M₁
The total energy must be 0:
Eᵀ = Eᴷ + Eᴾ = ½mv² - (GM₁m / R₁) = 0
Give the equation for the Schwarzschild radius
Rs = 2GM / c²
M is the mass of the black hole
G is the gravitational constant
Define the event horizon
The effective boundary provided by the Schwarzschild radius, where objects any closer have an escape velocity greater than the speed of light
Give the sequence of evolution for large dust clouds into blackholes
1) Large Dust Cloud
2) Blue/White Star
3) Red Supergiant
4) Supernova Explosion
5) Black Hole
State 2 main types of supernovae
Type 1a supernovae
Type 2 supernovae
Describe type 1a supernovae and how they are formed
- 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
Describe type 2 supernovae and how they are formed
- 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
When and why are larger elements than iron formed?
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
Define standard candles and state 2 different examples
- 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
Define cepheid variables
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
Why are cepheids described as intrinsic variables?
Because the variation in luminosity is due to what happens in the star itself not down to it being eclipsed in something (extrinsic variables)
When are supernovae more useful as standard candles than cepheids?
When the cepheids are very distance, they become very dim, so supernovae become more useful (distances beyond 1000Mpc)
State the period-luminosity law
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.
Define absolute magnitude
The magnitude (brightness) of a celestial object as it would be seen at a standard distance of 10 parsecs.
Describe how cepheids are used as standard candles
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
Give the equation for the difference between the magnitude m and absolute magnitude M of a star
m - M = 5 log(d/10)
where d is distance in parsecs
State the 7 spectral classes of stars
O, B, A, F, G, K, M
For the spectral class of stars O, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) Blue
ii) 25000 - 50000
iii) He⁺, He, H
For the spectral class of stars B, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) Blue
ii) 11000 - 25000
iii) He, H
For the spectral class of stars A, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) Blue-white
ii) 75000 - 11000
iii) H (strongest), Ionised metals
For the spectral class of stars F, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) White
ii) 6000 - 7500
iii) Ionised metals
For the spectral class of stars G, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) Yellow-white
ii) 5000 - 6000
iii) Ionised & neutral metals
For the spectral class of stars K, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) Orange
ii) 3500 - 5000
iii) Neutral metals
For the spectral class of stars M, state:
i) The intrinsic colour
ii) Temperature range (K)
iii) Prominent absorbtion lines
i) Red
ii)
Define the Balmer series and explain the trend in prominence of balmer lines for the different spectral classes of star
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
State Wein’s law
λᵐᵃᵡT = constant = 2.9x10⁻³mK
