{ Week 22 Physics

 Understand that a star is in equilibrium under the action of two opposing forces, gravitation and the radiation pressure of the star  Appreciate that nuclear fusion provides the energy source of a star Stellar Radiation

 A star like the sun radiates about J/s  1,000,000,000,000,000,000,000,00 0,000  The source of this energy is nuclear fusion in the interior of the star. The energy source of stars

 Deuterium – “Heavy Water” formed by two joining protons, releasing a positron and a neutrino.  Positron – antiparticle of an electron, positive charge  Neutrino – little or no mass no charge moves at the speed of light.  Helium-3 – formed when a proton bombards a deuterium nucleus, releasing a photon in the form of a gamma ray.  photon – a quantum of light (unit of light emission or absorption)  Helium-4 – regular helium atom formed by a helium-3 nucleus bombarding another helium-3 nucleus, releasing two protons  These two protons are free to continue the whole process again.  The energy source of stars

 High temperature in the star allows two protons to fuse.  High pressure ensures a high probability of collision.  Energy is released in each of the three steps but most comes out of the third step.  Photons and neutrinos move the energy outward and collide with protons and electrons.  This outward motion stabilizes the star against gravitational collapse. The energy source of stars

 Each time the proton-proton cycle occurs 3.98 x J is released  J  All of the helium created as a by product collects at the core of the star and due to the immense pressure, the helium is compacted into heavier elements like nickel and iron. The energy source of stars

 Give the definitions of luminosity, L = σAT 4 as the power radiated into space by a star and apparent brightness, b =L/(4πd 2 ), as the power received per unit area on earth. Luminosity - objective

 Luminosity is the amount of energy radiated by the star per second; that is, it is the power radiated by the star.  Luminosity depends on the surface temperature and surface area of the star.  Luminosity of a star = L  Imagine a sphere of radius d centered at the location of the star.  If the star is assumed to radiate in all directions, then the energy radiated in 1 s can be thought to be distributed around this sphere. Luminosity

 A detector of area-a placed somewhere on the sphere will detect a small fraction of the total energy.  Apparent brightness is the perceived energy per second per unit area of detector and is given by…  b = L/(4πd 2 )  Measured in W/m 2 Apparent Brightness

 The stars energy distributed over an imaginary sphere of radius equal to the distance between the star that the observer. The observer only receives a fraction of the total energy.

 The amount of energy per second radiated by a star of surface area A and absolute surface temperature T (i.e. the luminosity) is given by L = σAT 4  σ is sigma and it represents the Stefan- Boltzmann constant  σ = 5.67 x W/m 2 K 4 Luminosity

 The radius of star A is three times that of star B and its temperature is double that of B. Find the ratio of the luminosity of A to that of B.  Start with the ratio  L A /L B  144 times more luminous than B Try this

 The stars from the last problem have the same apparent brightness when viewed from the earth. Calculate the ratios of their distances.  Start with the ratio  b A /b B = 1  12 times the distance to Star B And this

 The apparent brightness of a star is 6.4 x W/m 2. If the distance is 15 ly, what is the luminosity?  1.62 x W Try This

 A star half the sun’s surface temperature and 400 times its luminosity. How many times bigger is it?  Start with this ratio 400 = L/L sun  80 times larger Try This Too

 A body radiates energy away in the form of electromagnetic waves according to the Stefan- Boltzmann law  This Electromagnetic radiation is distributed over an infinite range of wavelengths Black-body Radiation

 The spectrum of a black-body is the energy radiated per second per wavelength interval from a unit area of the body.  “Relative intensity” shows apparent brightness (W/m 2 )  Overall intensity is represented as the area under the graph. Black-Body Radiation Profiles

 Peak wavelength (λ 0 ) emits the most energy  The color of the star is mainly determined by the color corresponding to λ 0.  Area under the curve is the total power radiated from a unit area irrespective of wavelength and is given by σT 4 Black-Body Radiation

 The Wien displacement law relates wavelength to temperature.  λ 0 T = constant = 2.90 x K m  The higher the temperature, the lower the wavelength at which most of the energy is radiated. Wien Displacement Law

 The sun has approximate black-body spectrum with most of the energy radiated at a wavelength of 5.0 x m. Find the surface temperature of the sun.  T = 5800 K Try This

 The sun (radius R = 7.0 x 10 8 m) radiates a total power of 3.9 x W. Find its surface temperature.  T ≈ 5800 K And This

 A great wealth of information can be gathered about a star from the studies of its spectrum.  Temperature  Chemical composition  Radial velocity  Rotation  Magnetic fields Stellar Spectra