Astrophysics 13.2.1 - 13.2.5 (stars)

Factors of how bright a star appears in the night sky

• Power output (Luminosity

• How far away it is from us

Power output (Luminosity)

• This means the total amount of energy emitted (in the form of EM radiation) - measured in watts

Intensity and how star emits radiation

• A star doesn’t emit radiation in one direction but in all in an expanding sphere -Inner sphere will have a higher intensity per m² than the outer sphere

• They produce every type of radiation but not in equal quantities

• I = Power/Area -Area = 4πr²

Apparent magnitude

• The brightness as viewed from earth

• The more negative/Lower the value of apparent magnitude. the bright the object.

Hipparcos Scale

• An apparent magnitude and logarithmic scale from 1 to 6 with 1 being brightest and 6 dimmest

• As you go from 6 to 1 the brightness increases by 2.51 times each step

Equation to compare the brightness of two stars

Absolute magnitude

• Based on how bright a star appears from 10 parsecs away (Nothing to do with distance with earth)

• The more negative absolute magnitude is, the brighter the star

The equation that links absolute + apparent magnitude and distance

Type 1a supernovae

• These supernovae are unique as when they explode and rapidly increase in brightness, they all have the same peak in absolute magnitude

• This means combined with apparent magnitude from earth we can work out the distance to them

• We call these' ‘standard candles’

• Because supernovae are so bright it means we can see them from a very long way away

• Allowing us to measure the distance to distant galaxies

Blackbody

• An object which absorbs all types of electromagnetic radiation

• Stars are therefore considered to be black bodies

Blackbody radiation + It’s curve

• Every type of radiation (visible, radio, microwave etc)

• Hotter stars produce more radiation than a cool star

• They ‘peak’ at a shorter wavelength, meaning they appear bluer

• Cooler stars ‘peak’ at longer wavelengths and they appear redder

Wein’s displacement law

Wein’s displacement law represented on a graph with radiation types

Factors of the power output of a star

• Temperate of the star

• Surface area of a star

Stefan’s power law

• Area = 4πr²

What factors determine how stars are grouped into 7 main classes?

• Surface temperature (Which affects their colour) - Wein’s displacement law

• Absorption spectra (Which is determined by what they are made of)

Classifying stars by absorption lines

• Electrons in a gas will be able to absorb very specific energies (wavelengths) of photons) which are unique to a specific element

• Stars are blackbodies which mean they produce all types of radiation - including a continuous spectrum in the visible section

• But stars have an ‘atmosphere’ of cooler gases around them - these gasses in this absorb some of the photons produced

• Absorption spectra is affected by temperature (hotter = more energy in electrons) - meaning they sit in higher and higher levels

• Therefore there will be less photons that can be absorbed meaning there will be less absorption lines in a hotter star compared to a cooler star

• Hydrogen balmer lines at n = 2 -There are no electrons in the ground state as the star is too hot

Balmer lines

• The absorption lines created by electrons in hydrogen at level 2 only

• There are no electrons in the ground state as the star is too hot

How different elements are visible depending on the temperature of the star

• Hotter stars have very intense helium lines

• Cooler stars will form heavy elements like metals

• Coolest stars will even form molecules

Spectral classes Table

Hertzsprung-Russell diagram

• A graph of absolute magnitude vs temperature

• Main sequence stars are in their long-lived stable phases when they are fusing hydrogen into helium -Ie. the sun (G class around 5700K, absolute magnitude of +5)

• Red giants have large surface areas, large negative absolute magnitudes, very high power output but also very low surface temperature -Fusion reactions other than hydrogen to helium are occurring

• White dwarfs have a tiny surface area, large positive absolute magnitude, low power output but also very high surface temperature -No fusion is occurring anymore -About the size of earth

How fusion defines if a star is ‘alive’

• A star is ‘alive’ when fusion is taking place

• This depends on: -Do you have fuel for fusion (eg. hydrogen and helium) -Is it got enough anywhere in that star for that fuel to fuse

• If conditions aren’t met fusion stops and star ‘dies’

Stellar evoluton steps

1. Stellar Nebula

2. Protostar

3. Main sequence star (core hydrogen burning)

4. Becoming a red giant

5. Shell hydrogen burning

6. Core helium burning

7. Shell helium burning

8. How electrons prevent further contraction

9. Planetary nebula and white dwarf

Stellar Nebula (Step 1)

• Stars are born in clouds of dust + gas known as stellar nebula

• Usually left from previous supernovae

• Denser clumps contract (very slowly due to gravity)

Protostar (Step 2)

• When these clumps get dense enough they form protostars

• These continue to contract and heat up

• When it reaches a few million degres hydrogen can fuse into helium

Main sequence star (core hydrogen burning - step 3)

• Where the star spends most of it’s life

• Pressure produced by the hydrogen fusion in the core balances out the gravitational collapse

• Called Core hydrogen burning

Becoming a red giant (step 4)

• When the hydrogen runs out nuclear fusion stops and so does pressure

• The core contracts and heats up

• Outer layers expand and cool

• Star becomes a red giant

Shell hydrogen burning (step 5)

• The material around the core still contains plenty of hydrogen (it just wasn’t hot enough before to fuse)

• As the core contracts this heats a layer (shell) around the core, the shell gets hot enough to fuse hydrogen into hlium

• Called Shell hydrogen burning

Core Helium burning (step 6)

• The core continues to contract until it gets hot and dense enough to fuse helium into carbon and oxygen, known as Core helium buring

• This releases a huge amount of energy which pushes the outer layers outwards

Shell helium burning (step 7)

• Eventually the helium in the core runs and fusion stops

• Once again the forces in the core are unbalanced causing it to contract again

• This heats a layer (shell) around the core

• This shell is now hot enough for the helium in it to fuse, called Shell helium burning

How electrons prevent further contraction (step 8)

• In low mass stars the carbon-oxygen core won’t get hot enough for any further fusion

• It contracts until it is about Earth size

• At this point electrons exert enough pressure to stop it collapsing further

Planetary nebula and white dwarf (step 9)

• As the core contracts the helium shell gets more and more unstable

• The star pulsates and throws off outer layers into a planetary layer

• Leaving behind a very hot, dense core (a white dwarf)

• No more fusion is occuring

A flowchart that explains the location and type of fusion occuring

How a star like star will move around an HR diagram over its life