Stars

• • Nebulae are formed over millions of years as the tiny gravitational attraction between particles of dust & gas pulls the particles towards each other, eventually forming the vast cloud
  • As dust & gas get closer together this gravitational collapse accelerates
  • Due to tiny variations in the nebula, denser regions begin to form
  • These regions pull in more dust & gas gaining mass & getting denser & also getting hotter as gravitational energy is eventually transferred to thermal energy
  • A protostar forms
• • For a protostar to become a star, nuclear fusion needs to start in its core
  • Extremely high pressures & temperatures inside the core are needed in order to overcome the electrostatic repulsion between hydrogen nuclei in order to fuse them together to form helium nuclei
• • Once a star is formed, it remains in a stable equilibrium with almost a constant size
  • Gravitational forces act to compress the star, but the radiation pressure from the photons emitted during fusion & the gas pressure from the nuclei in the core push outwards
  • The force from this radiation & gas pressure balances the force from the gravitational attraction & maintains equilibrium
• Planets --> An object in orbit around a star

  • It has a mass large enough for its own gravity to give it a round shape
  • It has no fusion reactions
  • It has cleared its orbit of most other objects
• Dwarf planet --> Dwarf planets have not cleared their orbit of other objects
• Asteroids --> Asteroids are objects too small & uneven to be planets, usually in near - circular orbits round the Sun
• Planetary satellites --> A planetary satellite is a body in orbit around a planet. This includes moons & man-made satellites
• Comets --> Range from a few hundred metres to tens of kilometres across. They are small irregular bodies made up of ice, dust & small pieces of rock. All comets orbit the Sun, many in highly eccentric elliptical orbits
• Galaxies --> A galaxy is a collection of stars, & interstellar dust & gas. On average a galaxy will contain 100 billion stars
• What happens at the start of the red giant phase?

  The core begins to collapse
• Why does the core of a star collapse during the red giant phase?

  Gravitational force exceeds radiation and gas pressure
• What occurs as the core of the star shrinks?

  Pressure increases enough to start fusion in a shell
• What type of cores do red giant stars have?

  Inert cores
• Why does fusion no longer take place in the core of a red giant star?

  Very little hydrogen remains and temperature is insufficient
• What continues to happen in the shell around the core of a red giant star?

  Fusion of hydrogen into helium
• How does the fusion process change from the core to the shell in a red giant star?

  Fusion stops in the core but continues in the shell
• Electron degeneracy pressure:

  • 2 electrons can't exist in the same energy state
  • When the core of a star begins to collapse under the force of gravity, the electrons are squeezed together, and this creates a pressure that prevents the core from further gravitational collapse
• Chandrasekhar limit:

  • The electron degeneracy pressure is only sufficient to prevent gravitational collapse if the core has a mass less than 1.44 M
  • This limit is the maximum mass of a stable white dwarf star
• Neutron star --> If the mass of the core is greater than Chandrasekhar limit the gravitational collapse continues, forming a neutron star
• Black hole --> If the core has a mass greater than about 3M, the gravitational collapse continues to compress the core

  • The result is a gravitational field so strong that in order to escape it an object would need an escape velocity greater than the speed of light
• Hertzsprung - Russell diagram:

  • A graph of stars in our galaxy showing the relationship between their luminosity on the y-axis & their average surface temperature on the x-axis
  • The temperature increases from right to left on the x-axis
• Luminosity:

  • The luminosity of any star is the total radiant power output of the star
  • The luminosity of a star is related to its brightness
• Energy levels in gas atoms:

  • An electron can't have a quantity of energy between 2 levels
  • The energy levels are negative because external energy is required to remove an electron from the atom. The negative values also indicate that the electrons are trapped within the atom or bound to the positive nuclei
  • An electron with zero energy is free from the atom
  • The energy level with the most negative value is known as the ground level or ground state
• • When an electron moves from a lower to a higher energy level within an atom in a gas, the atom is said to be excited
  • Raising an electron into higher energy levels requires external energy
• • When an electron moves from a higher energy level to a lower one, it loses energy
  • Energy is conserved, so as the electron makes a transition between the levels, a photon is emitted from the atom
  • This transition between energy levels is sometimes called de-excitation
• • The energy of any particular photon emitted in an electron transition from a higher to a lower energy level is given by
  • delta E = hf
  • delta E = hc / lambda
• Emission line spectra --> each element produces a unique emission line spectrum because of its unique set of energy levels
• Continuous spectra --> all visible frequencies or wavelengths are present. The atoms of a heated solid metal (e.g: lamp filament) will produce this type of spectrum
• Absorption line spectra --> this type of spectrum has series of dark spectral lines against the background of a continuous spectrum. The dark lines have exactly the same wavelengths as the bright emission spectral lines for the same gas atoms
• • If the atoms in a gas are excited, then when the electrons drop back into lower energy levels they emit photons with a set of discrete frequencies specific to that element
  • This produces a characteristic emission line spectrum
  • Each spectral line corresponds to photons with a specific wavelength
• • An absorption line spectrum is formed when light from a source that produces a continuous spectrum passes through a cooler gas
  • As the photons pass through the gas, some are absorbed by the gas atoms, raising electrons up into higher energy levels & so exciting the atoms
  • Only photons with energy exactly equal to the difference between the different energy levels are absorbed
• Diffraction grating --> an optical component with regularly spaced slits or lines that diffract & split light into beams of different colour travelling in different directions
• Black body radiation:

  • At any given temperature above absolute zero, an object emits electromagnetic radiation of different wavelengths & different intensities
  • A black body is an idealised object that absorbs all the electromagnetic radiation that shines onto it
  • When in thermal equilibrium, emits a characteristic distribution of wavelengths at a specific temperature
• Wien's displacement law:

  • Wien's displacement law relates the absolute temperature T of a black body to the peak wavelength lambda max at which the intensity is a maximum
  • Wien's displacement law states that lambda max is inversely proportional to T
  • For any black body emitter lambda max x T = constant
  • Wien's constant = 2.90 x 10^-3 mK
• • As the temperature of an object changes, so does the distribution of the emitted wavelengths
  • The peak wavelength reduces as the temperature increases, and the peak of the intensity - wavelengths graph becomes sharper
• Stefan's law:

  • the total power radiated per unit surface area of a black body is directly proportional to the 4th power of the absolute temperature of the black body
  • The total power radiated by a star is called luminosity
  • L = 4pi x r^2 x Stefan's constant x T^4
  • Stefan's constant = 5.67 x 10^-8 Wm^-2K^-4
• Stefan's law shows that the luminosity of a star is directly proportional:

  • to its radius
  • to its surface area
  • to its surface absolute temperature