Teacher of the Week DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

TSOKOS LESSON E-2 STELLAR RADIATION

IB Assessment Statements Topic E-2, Stellar Radiation and Stellar Types Energy Source E.2.1. State that fusion is the main energy source of stars. E.2.2. Explain that, in a stable star (for example our Sun), there is an equilibrium between radiation pressure and gravitational pressure. Luminosity E.2.3. Define the luminosity of a star. E.2.4. Define apparent brightness and state how it is measured.

IB Assessment Statements Topic E-2, Stellar Radiation and Stellar Types Wien s Law and the Stefan-Boltzmann Law E.2.5. Apply the Stefan-Boltzmann Law to compare the luminosities of different stars. E.2.6. State Wien s (displacement) Law and apply it to explain the connection between the colour and temperature of stars. Stellar Spectra E.2.7. Explain how atomic spectra may be used to deduce chemical and physical data for stars. E.2.8. Describe the overall classification system of spectral classes.

IB Assessment Statements Topic E-2, Stellar Radiation and Stellar Types Types of Stars E.2.9. E.2.10. Describe the different types of stars. Discuss the characteristics of spectroscopic and eclipsing binary stars. The Hertzsprung-Russell Diagram E.2.11. Identify the general regions of star types on a Hertzsprung-Russell (HR) diagram.

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

Objectives Give the definition of luminosity as the power radiated into space by a star and apparent brightness as the power received per unit area on the earth 4 b 2 L AT L 4d

Objectives State the Wien displacement law and solve problems using it T 2.90 x10 0 3 K m Appreciate the kind of information a stellar spectrum can provide

Objectives State the main properties of main sequence stars, red giants, white dwarfs, and binary stars Describe the structure of an HR diagram and place the main types of stars on the diagram

Energy Source of Stars Stars are composed of a core and a dense atmosphere of extremely hot gasses The core is a dense mass that creates gravitational force that tries to draw the atmosphere into the core In the atmosphere, nuclear fusion reactions are taking place between hydrogen atoms that release energy that generates heat

Energy Source of Stars High temperatures overcome electrostatic repulsion between hydrogen protons High pressure allow atoms to come close enough to collide and fuse

Energy Source of Stars Each fusion cycle turns 4 hydrogen atoms into 1 helium atom with the release of 2 electrons, 2 photons, and 2 neutrinos H He He He He H H e H H H e 1 1 4 2 3 2 3 2 0 0 3 2 2 1 1 1 0 0 0 1 2 1 1 1 1 1 2

Energy Source of Stars The heat creates a radiation pressure that keeps the star from collapsing under the gravitational pressure To remain stable, the gravitation and radiation forces must be in equilibrium

Luminosity Luminosity is the amount of energy radiated by a star per second, which is the same as saying it is the amount of power radiated by the star L AT σ is the Stefan-Bolzmann constant, equal to 5.67x10-8 W/m 2 K 4 4

Luminosity Luminosity depends on 2 things: the surface temperature and the surface area of the star Think of the star as a sphere and consider that it radiates power in all directions from the surface of the sphere

Apparent Brightness Imagine that you could put a detector somewhere on the surface of the star The detector would measure the energy at that spot That spot represents a fraction of the total surface area and the energy it measures would be the same fraction of the total energy generated by the star

Apparent Brightness This is called the apparent brightness whose units are W/m 2 If we can measure the apparent brightness, which is the energy at a spot, we can then calculate the Luminosity L b 4d 2

Apparent Brightness Measured using a charge-coupled device or CCD It has a photosensitive silicon surface that releases an electron when hit by a photon The number of electrons released is proportional to the number of incident photons We then measure the charge released and that becomes a direct measure of the brightness of the object

Black Body Radiation Black-body Law - A body of surface area A and absolute temperature T, radiates energy in waves according to the Stefan-Bolzman law (Section 7-2, pages 434-435)

Black Body Radiation Therefore, luminosity is the amount of energy radiated per second by a star of surface area A and absolute surface temperature T, and is given by the equation, L AT 4

Black Body Radiation L AT 4 A is the surface area of a sphere T is absolute surface temperature in Kelvin And σ is the Stefan-Bolzman constant 5.67 x 10-8 W/m 2 K 4 So the units for luminosity will be watts

Black Body Radiation Using the previous equation for apparent brightness, we now find this equation, L AT 4 AT 4 b L 4d 2 b 4d 2

Wavelength The energy radiated by a star is in the form of electromagnetic radiation that covers an infinite range of wavelengths This figure gives the radiation profiles for different temperatures

Wavelength This is also called the spectrum of a black body and is the energy radiated per second per wavelength interval from a unit area of the body

Wavelength The horizontal axis represents the wavelength in micrometers The vertical scale is relative intensity in W/m 3

Wavelength Majority of emitted energy centers around the peak wavelength, λ 0 Colour of a star is determined by this wavelength Total power, L, is area under the curve L AT 4

Wien Displacement Law Relates the wavelength to surface temperature by, T const 2.90 x10 0 3 Km Implies that the higher the temperature, the lower the peak wavelength and vice versa

Stellar Spectra - Temperature Using Wien s Law, stellar temperature determined by peak wavelength T const 2.90 x10 0 3 Km

Stellar Spectra Chemical Composition Chemical composition obtained from emission spectra Typical composition is, 70% hydrogen 28% helium 2% other heavier elements

Stellar Spectra Chemical Composition Most stars have the same composition, but different spectra caused by temperature In hot stars the hydrogen is ionized. Atoms cannot absorb and re-emit photons thus lines will not show Cooler stars will have most hydrogen electrons in state n=2 and will show spectra for transitions to n=3 and n=4 Cold stars will have most of its electrons in the ground state and will only absorb and re-emit ultraviolet photons

Stellar Spectra Spectral Classes Stars are divided into spectral classes based on colour/temperature Oh Be A Fine Girl/Guy Kiss Me

Stellar Spectra Rotation As a star rotates, one side is moving toward the observer and one side is moving away from the observer Side moving toward the observer will be blueshifted (shorter wavelength, higher frequency) Side moving away from the observer will be redshifted (longer wavelength, lower frequency)

Stellar Spectra Magnetic Fields In a magnetic field, a spectral line may split into two or more lines (Zeeman effect) Measurement of the amount of splitting in the spectra provides information about the magnetic field of the star

Hertzsprung-Russell Diagram Correlations between luminosity and temperature Between temperature and size Between absolute magnitude and spectral class Result was the HR Diagram

Hertzsprung-Russell Diagram Important Notes: Luminosity along the left vertical axis is in terms of our sun s luminosity Surface temperature along lower horizontal axis goes from right-toleft Scales on the axes are not linear

Hertzsprung-Russell Diagram Features: Most stars fall along a diagonal from upper left to lower right main sequence stars Top right, large reddish cool (in temp) stars red giants Bottom left, small, bright, hot (in temp) stars white dwarfs

Hertzsprung-Russell Diagram Features: 90% of all stars are main sequence 9% are white dwarfs 1% are red giants

Hertzsprung-Russell Diagram Features: As you move from bottom right to top left on main sequence, luminosity and mass increase Bottom right = red dwarfs Top left = blue giants

Types of Stars Main Sequence Stars Our sun is a main sequence star Luminosity increases as mass increases Produce enough energy in the core to balance gravitational force

Types of Stars Red Giants Very large, cool, reddish appearance Luminosity much greater than main sequence stars of the same temperature up to a billion times greater Mass as much as 1000 times our sun but low density Hot core surrounded by envelope of gas

Types of Stars White Dwarfs Sirius A and B most well known Faint and hard to detect Mass similar to the sun but size similar to earth = density 10 6 times that of earth Formed when collapsing stars stabilize as a result of electron degeneracy pressure

Types of Stars White Dwarfs Electron degeneracy pressure occurs when forced into the same quantum state Pauli exclusion principle says they will acquire large kinetic energy which allows the star to resist gravitational pressure to collapse

Types of Stars Variable Stars Luminosity varies with time light curve Periodic or non-periodic Mainly due to changes in internal structure of the star As the core becomes more dense, outer gas envelope expands Mass ejected from outer layers as nebula or supernovas

Types of Stars Variable Stars When mass ejected, luminosity increases by a factor of a million Matter can also be transferred from one star to another which will heat up and radiate further increasing luminosity

Types of Stars Variable Stars Cepheids Most prominent of the periodic variables Periods of 1-50 days Relationship between period of light curve and peak luminosity Peak luminosity compared to apparent brightness yields distance to stars

Types of Stars Variable Stars Cepheids Study of variable stars provides information about internal structure of stars and testing ground for theories

Types of Stars Binary Stars Two stars that orbit a common center Important because they allow determination of stellar masses

Types of Stars Visual Binary Formula for common period of rotation given below Measurement of the separation distance and period gives the sum of the two masses making up the binary T 2 4 G M 1 2 d 3 M 2

Types of Stars Eclipsing Binary Orbit plane in relation to the earth such that the light of one is periodically blocked by the other

Types of Stars Spectroscopic Binary Detected by analyzing the Doppler shift of the light from each z 0 v 0 c

Summary Review Do you understand that a star is in equilibrium under the action of two opposing forces, gravitation and radiation pressure of the star? Do you appreciate that nuclear fusion provides the energy source of the star?

Summary Review Can you give the definition of luminosity as the power radiated into space by a star and apparent brightness as the power received per unit area on the earth? 4 b 2 L AT L 4d

Summary Review Can you state the Wien displacement law and solve problems using it T 2.90 x10 0 3 K m Do you appreciate the kind of information a stellar spectrum can provide

Summary Review Can you state the main properties of main sequence stars, red giants, white dwarfs, and binary stars Can you describe the structure of an HR diagram and place the main types of stars on the diagram

QUESTIONS?

Homework #1-26