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Astronomy (Types of Stars (White Dwarfs :full_moon:: (LOW luminosity …

- - - - \(L\propto M^{3.5}\)
  - - - Average luminosity dependent on period
        
        Use of apparent brightness
        to determine distance
    - - Outward radiation ionises helium ions in the atmosphere
        
        Results in…
        
        Increase in temperature :thermometer:
        
        Outer layers of the star EXPAND
        
        Radiation leaves stars when all helium is ionised
        
        Results in…
        
        Drop in temperature :snow_capped_mountain:
        
        Outer layers of the star CONTRACT
        
        Helium nuclei recombines with electrons
- - - - Distance at which 1 AU subtends a parallax angle of 1 arcsecond
      - \(3.26 \textrm{ light years}\)
    - - \(\frac{1}{3600}\ \textrm{degrees}\)
- - - - Approximating small angle
        \(\tan\theta \approx \theta\)
        
        \(d=\frac{1}{p}\)
        \(d\) is distance in parsecs
        \(p\) is angle in arcseconds
    - - measure difference in angle subtended by planet now and 6mths later
        
        Difference in angle is twice parallax angle
  - - - Surface Temperature :thermometer:
        (decreasing rightwards)
      - Spectral Class (O B A F G K M)
        
        Oh Be A Fine Girl Kiss Me
    - - Luminosity:bulb:
        (in terms of solar luminosity :sunny:)
    - - Radii
  - - - \(\lambda_0 T=2.9\times10^3\)
      - Peak wavelength decreases as temperature increases
- - - - Nuclear fusion produces outward radiation pressure
        
        Provides the energy that the star is radiating into space.
        
        High enough to balance inward gravitational pressure
    - - :two:
        \(\textrm{H}^+ +n\textrm{H}^+ \rightarrow -n\textrm{He}^{2+} + \gamma\)
        
        :three:
        \(-n\textrm{He}^{2+} + -n\textrm{He}^{2+} \rightarrow \textrm{He}^{2+} +2\textrm{H}^+\)
- - - - Planetary Nebula :bomb:
        
        At Chandrasekhar limit
        \(m_\textrm{core}<1.4\textrm{M}_\odot\)
        
        White Dwarf
        
        Pauli exclusion principle, electrons cannot occupy same mechanical place
        
        Black Dwarf
        
        Collapse of star due to inward gravitational pressure until
        
        Inward gravitational pressure balanced by outward electron degeneracy pressure
        
        Uniform electron degeneracy pressure ensures uniform radius
      - Nuclear fusion: Carbon core
      - Triple Alpha Process
        
        :one:
        \(\textrm{He}^{2+}+\textrm{He}^{2+}\rightarrow \textrm{Be}^{8+}\)
        
        :two:
        \(\textrm{He}^{2+}+\textrm{Be}^{8+}\rightarrow C^{12+}\)
        
        For stars with
        \(M≤8M_\odot\)
      - Conditions
        
        Fusion of hydrogen stops
        
        Fusion of helium begins
        
        Star expands and cools
    - - Nuclear fusion up to iron in large stars
        
        When fusion stops, radiation pressure insufficient to oppose gravitational pressure
        
        Since \(m<1.4\textrm{M}_\odot\)
        electron degeneracy pressure cannot oppose gravitational pressure so star implodes
        
        Neutron degeneracy pressure opposes further collapse of star, causing violent explosions
        
        Type II Supernova :bomb:
        
        \(m_{core}>3M_\odot\)
        
        1 more item...
        
        At Oppenheimer-Volkoff limit
        \(2\ \textrm{M}_\odot < m_{\textrm{core}} < 3\ \textrm{M}_\odot\)
        
        1 more item...
      - Iron Core
      - Electrons are forced into protons to form neutrons and neutrinos
      - Neutrons are compressed until neutron degeneracy pressure
    - - :one:
        
        :two:
        
        :three:
      - Only occurs if
        \(mass≥4M_\odot\)
      - Produces Helium