1. OPTION E - ASTROPHYSICS E2 Stellar radiationand stellar types Energy source

2. E.2.1 State that fusion is the main energy source of stars.  Stars are formed by interstellar dust coming together through mutual gravitational attraction.  The loss of potential energy is responsible for the initial high temperature necessary for fusion.  The fusion process releases so much energy that the pressure created prevents the star from collapsing due to gravitational pressure.  Stars are formed by interstellar dust coming together through mutual gravitational attraction.  The loss of potential energy is responsible for the initial high temperature necessary for fusion.  The fusion process releases so much energy that the pressure created prevents the star from collapsing due to gravitational pressure. Very high temperatures are needed in order to begin the fusion process: usually 10 7 K.

3. E.2.2 Explain that, in a stable star (for example, our Sun), there is an equilibrium between radiation pressure and gravitational pressure.  As the nuclear fusion happens, it releases a huge amount of energy and creates an outwards pressure: the radiation pressure. This causes the star to expand.  The radiation pressure counteracts the gravitation that collapses the star.  When the two forces are in equilibrium, the star is stable.

4. A star is a big ball of gas, with fusion going on at its center, held together by gravity! There are variations between stars, but by and large they’re really pretty simple things. Massive Star Sun-like Star Low-mass Star

5. OPTION E - ASTROPHYSICS E2 Stellar radiationand stellar types Luminosity

6. The most important thing about a star: MASS! The mass of a normal star almost completely determines its LUMINOSITY and TEMPERATURE! Note: “normal” star means a star that’s fusing Hydrogen into Helium in its center (we say “hydrogen burning”). E.2.3 Define the luminosity of a star.

7. The LUMINOSITY of a star is the energy it gives off per second, that is, its power output. The energy the Sun emits is generated by the fusion in its core… This light bulb has a luminosity of 60 Watts E.2.3 Define the luminosity of a star.

8. What does luminosity have to do with mass? The mass of a star determines the pressure in its core: Pressure Gravity pulls outer layers in, Gas Pressure pushes them out. The core supports the weight of the whole star! The more mass the star has, the higher the central pressure!

9. The core pressure determines the rate of fusion… MASS PRESSURE & TEMPERATURE RATE OF FUSION …which in turn determines the star’s luminosity!

10. Luminosity is an intrinsic property… it doesn’t depend on distance! This light bulb has a luminosity of 60 Watts… …no matter where it is, or where we view it from, it will always be a 60 Watt light bulb.

11. Luminosity The Luminosity of a star is the energy that it releases per second. Sun has a luminosity of 3.90x10 26 W (often written as L  ): it emits 3.90x10 26 joules per second in all directions. The energy that arrives at the Earth is only a very small amount when compared will the total energy released by the Sun.

12.  When the light from the Sun reaches the Earth it will be spread out over a sphere of radius d.  The energy received per unit time per unit area is b, where:  When the light from the Sun reaches the Earth it will be spread out over a sphere of radius d.  The energy received per unit time per unit area is b, where: d b is called the apparent brightness of the star E.2.4 Define apparent brightness and state how it is measured.

13. Luminosity Exercise 13.1 The Sun is a distance d=1.5 x 10 11 m from the Earth. Estimate how much energy falls on a surface of 1m 2 in a year. d L  = 3.90x10 26 W

14. At a distance of d=1.5 x 10 11 m, the energy is “distributed” along the surface of a sphere of radius 1.5 x 10 11 m d The sphere’s surface area is given by: A = 4πd 2 = 4 π x (1.5 x 10 11 ) 2 = =2.83 x 10 23 m 2 The energy that falls on a surface area of 1m 2 on Earth per second will be equal to: b = L  /A = 3.90x10 26 / 2.83 x 10 23 = = 1378.1 W/m 2 or 1378.1 J/s m2 In a year there are: 365.25days x 24h/day x 60min/h x 60s/min = 3.16 x 10 7 s So, the energy that falls in 1 m 2 in 1 year will be: 1378.1 x 3.16 x 10 7 = 4.35 x 10 10 joules

15. OPTION E - ASTROPHYSICS E2 Stellar radiationand stellar types Wien’s Law and the Stefan-Boltzmann Law

16. E.2.5 Apply the Stefan–Boltzmann law to compare the luminosities of different stars.  A radiation spectrum can give information about luminosity.  The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body.  Stefan showed that this area was proportional to the fourth power of the absolute temperature of the body.  The total power emitted by a black body is its luminosity.  According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by:  A radiation spectrum can give information about luminosity.  The area under a black body radiation curve is equal to the total energy emitted per second per unit of area of the black body.  Stefan showed that this area was proportional to the fourth power of the absolute temperature of the body.  The total power emitted by a black body is its luminosity.  According to the Stefan-Boltzmann law, a body of surface area A and absolute temperature T has a luminosity given by: where, σ = 5.67x10 8 W m -2 K -4

17. Black body radiation  A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum.  There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum.  That relationship is known as Wien’s law: Black body radiation  A black body is a perfect emitter. A good model for a black body is a filament light bulb: the light bulb emits in a very large region of the electromagnetic spectrum.  There is a clear relationship between the temperature of an object and the wavelength for which the emission is maximum.  That relationship is known as Wien’s law: E.2.6 State Wien’s (displacement) law and apply it to explain the connection between the colour and temperature of stars

18. By analysing a star’s spectrum, we can know in what wavelength the star emits more energy. The Sun emits more energy at λ=500 nm. According to Wien’s law, the temperature at the Sun’s surface is inversely proportional to the maximum wavelength. So: By analysing a star’s spectrum, we can know in what wavelength the star emits more energy. The Sun emits more energy at λ=500 nm. According to Wien’s law, the temperature at the Sun’s surface is inversely proportional to the maximum wavelength. So: E.2.6 State Wien’s (displacement) law and apply it to explain the connection between the colour and temperature of stars

19. Black body radiation and Wien’s Law

20. Star’s Colour and Temperature

21. Why is this important?  The spectrum of stars is similar to the spectrum emitted by a black body.  We can therefore use Wien’s Law to find the temperature of a star from its spectrum.  If we know its temperature and its luminosity then its radius can be found from Stephan- Boltzmann’s law.  The spectrum of stars is similar to the spectrum emitted by a black body.  We can therefore use Wien’s Law to find the temperature of a star from its spectrum.  If we know its temperature and its luminosity then its radius can be found from Stephan- Boltzmann’s law.

22. Real spectra are more complicated than this (remember emission and absorption lines?) Blackbody Spectrum Emission and Absorption Lines

23. OPTION E - ASTROPHYSICS E2 Stellar radiationand stellar types Stellar spectra

24. Stars can be arranged into categories based on the features in their spectra… This is called “Spectral Classification” 1.by the “strength” (depth) of the absorption lines in their spectra 2.by their color as determined by their blackbody curve 3.by their temperature and luminosity How do we categorize stars? A few options: E.2.7 Explain how atomic spectra may be used to deduce chemical and physical data for stars.

25. First attempts to classify stars used the strength of their absorption lines… Williamina Fleming They also used the strength of the Harvard “computers”! Stars were labeled “A, B, C…” in order of increasing strength of Hydrogen lines.

26. OBAFGKM(LT)! Later, these categories were reordered according to temperature/color… Annie Jump Cannon

27. OBAFGKM - Mnemonics Only Boring Astronomers Find Gratification in Knowing Mnemonics! O Be A Fine Girl/Guy Kiss Me

28. Eventually, the connection was made between the observables and the theory. Observable: Strength of Hydrogen Absorption Lines Blackbody Curve (Color) Theoretical: Using observables to determine things we can’t measure: Temperature and Luminosity Cecilia Payne

29. E.2.8 Describe the overall classification system of spectral classes. ClassSpectrumColorTemperature O ionized and neutral helium, weakened hydrogen bluish 31,000-49,000 K B neutral helium, stronger hydrogen blue-white 10,000-31,000 K A strong hydrogen, ionized metals white 7400-10,000 K F weaker hydrogen, ionized metals yellowish white 6000-7400 K G still weaker hydrogen, ionized and neutral metals yellowish 5300-6000 K K weak hydrogen, neutral metals orange 3900-5300 K M little or no hydrogen, neutral metals, molecules reddish 2200-3900 K L no hydrogen, metallic hydrides, alkalai metals red-infrared 1200-2200 K T methane bands infrared under 1200 K

30. “If a picture is worth a 1000 words, a spectrum is worth 1000 pictures.”  Spectra tell us about the physics of the star and how those physics affect the atoms in it

31. OPTION E - ASTROPHYSICS E2 Stellar radiationand stellar types Types of stars

32. E.2.9 Describe the different types of star – single and binary stars, Cepheids, red giants, red supergiants and white dwarfs. Red Giants Very large, cool stars with a reddish appearance. All main sequence stars evolve into a red giant. In red giants there are nuclear reactions involving the fusion of helium into heavier elements. Red Giants Very large, cool stars with a reddish appearance. All main sequence stars evolve into a red giant. In red giants there are nuclear reactions involving the fusion of helium into heavier elements.

33. E.2.9 Describe the different types of star – single and binary stars, Cepheids, red giants, red supergiants and white dwarfs. Red Supergiants Larger than red giants but cooler, more luminous and bigger. Main sequence stars with greater mass evolve into a red supergiant. Red Supergiants Larger than red giants but cooler, more luminous and bigger. Main sequence stars with greater mass evolve into a red supergiant. Click on image for hyperlink to YouTube video The biggest stars in the Universe

34. White dwarfs A red giant at the end stage of its evolution will throw off mass and leave behind a very small size (the size of the Earth), very dense star in which no nuclear reactions take place. It is very hot but its small size gives it a very small luminosity. As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense. White dwarfs A red giant at the end stage of its evolution will throw off mass and leave behind a very small size (the size of the Earth), very dense star in which no nuclear reactions take place. It is very hot but its small size gives it a very small luminosity. As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense. A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K. E.2.9 Describe the different types of star – single and binary stars, Cepheids, red giants, red supergiants and white dwarfs.

35. Cepheid variables Cepheid variables are stars of variable luminosity. The luminosity increases sharply and falls of gently with a well-defined period. The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star. A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of Cepheid stars range from 10 3 to 10 4 times that of the Sun. Cepheid variables Cepheid variables are stars of variable luminosity. The luminosity increases sharply and falls of gently with a well-defined period. The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star. A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity. The luminosity of Cepheid stars range from 10 3 to 10 4 times that of the Sun. E.2.9 Describe the different types of star – single and binary stars, Cepheids, red giants, red supergiants and white dwarfs.

36. Cepheid variables

37. Types of Stars Neutron stars A neutron star is formed from the collapsed remnant of a massive star (usually supergiant stars – very big red stars). Models predict that neutron stars consist mostly of neutrons, hence the name. Such stars are very hot. A neutron star is one of the few possible conclusions of stellar evolution. Neutron stars A neutron star is formed from the collapsed remnant of a massive star (usually supergiant stars – very big red stars). Models predict that neutron stars consist mostly of neutrons, hence the name. Such stars are very hot. A neutron star is one of the few possible conclusions of stellar evolution. The first direct observation of a neutron star in visible light. The neutron star being RX J185635-3754.

38. Types of Stars Pulsars Pulsars are highly magnetized rotating neutron stars which emit a beam of detectable electromagnetic radiation in the form of radio waves. Periods of rotation vary from a few milliseconds to seconds. Pulsars Pulsars are highly magnetized rotating neutron stars which emit a beam of detectable electromagnetic radiation in the form of radio waves. Periods of rotation vary from a few milliseconds to seconds. Schematic view of a pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines and the protruding cones represent the emission beams.

39. Types of Stars Supernovae A supernova is a stellar explosion that creates an extremely luminous object. The explosion expels much or all of a star's material at a velocity of up to a tenth the speed of light, driving a shock wave into the surrounding interstellar medium. This shock wave sweeps up an expanding shell of gas and dust called a supernova remnant. Supernovae A supernova is a stellar explosion that creates an extremely luminous object. The explosion expels much or all of a star's material at a velocity of up to a tenth the speed of light, driving a shock wave into the surrounding interstellar medium. This shock wave sweeps up an expanding shell of gas and dust called a supernova remnant. Crab Nebula

40. Types of Stars Supernovae A supernova causes a burst of radiation that may briefly outshine its entire host galaxy before fading from view over several weeks or months. During this short interval, a supernova can radiate as much energy as the Sun would emit over 10 billion years. Supernovae A supernova causes a burst of radiation that may briefly outshine its entire host galaxy before fading from view over several weeks or months. During this short interval, a supernova can radiate as much energy as the Sun would emit over 10 billion years. Supernova remnant N 63A lies within a clumpy region of gas and dust in the Large Magellanic Cloud. NASA image.

41. Types of Stars Black Holes A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon. The name comes from the fact that even electromagnetic radiation is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process. Black Holes A black hole is a region of space in which the gravitational field is so powerful that nothing can escape after having fallen past the event horizon. The name comes from the fact that even electromagnetic radiation is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process.

42. Binary stars A binary star is a stellar system consisting of two stars orbiting around their centre of mass. For each star, the other is its companion star. A large percentage of stars are part of systems with at least two stars. Binary star systems are very important in astrophysics, because observing their mutual orbits allows their mass to be determined. The masses of many single stars can then be determined by extrapolations made from the observation of binaries. Binary stars A binary star is a stellar system consisting of two stars orbiting around their centre of mass. For each star, the other is its companion star. A large percentage of stars are part of systems with at least two stars. Binary star systems are very important in astrophysics, because observing their mutual orbits allows their mass to be determined. The masses of many single stars can then be determined by extrapolations made from the observation of binaries. Hubble image of the Sirius binary system, in which Sirius B can be clearly distinguished (lower left). E.2.9 Describe the different types of star – single and binary stars, Cepheids, red giants, red supergiants and white dwarfs.

43. There are three types of binary stars  Visual binaries – these appear as two separate stars when viewed through a telescope and consist of two stars orbiting about common centre. The common rotation period is given by the formula: There are three types of binary stars  Visual binaries – these appear as two separate stars when viewed through a telescope and consist of two stars orbiting about common centre. The common rotation period is given by the formula: where d is the distance between the stars. Because the rotation period can be measured directly, the sum of the masses can be determined as well as the individual masses. This is useful as it allows us to determine the mass of singles stars just by knowing their luminosities. where d is the distance between the stars. Because the rotation period can be measured directly, the sum of the masses can be determined as well as the individual masses. This is useful as it allows us to determine the mass of singles stars just by knowing their luminosities. E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars.

44.  Eclipsing binaries – some binaries are two far to be resolved visually as two separate stars (at big distances two stars may seem to be one). But if the plane of the orbit of the two stars is suitably oriented relative to that of the Earth, the light of one of the stars in the binary may be blocked by the other, resulting in an eclipse of the star, which may be total or partial E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars.

48.  Spectroscopic binaries – this system is detected by analysing the light from one or both of its members and observing that there is a periodic Doppler shifting of the lines in the spectrum. E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars.

49. A blue shift is expected as the star approaches the Earth and a red shift as it moves away from the Earth in its orbit around its companion. If λ 0 is the wavelength of a spectral line and λ the wavelength received on earth, the shift, z, is defined as: A blue shift is expected as the star approaches the Earth and a red shift as it moves away from the Earth in its orbit around its companion. If λ 0 is the wavelength of a spectral line and λ the wavelength received on earth, the shift, z, is defined as: If the speed of the source is small compared with the speed of light, it can be shown that: The speed is proportional to the shift E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars.

51. OPTION E - ASTROPHYSICS E2 Stellar radiationand stellar types The Hertzsprung-Russell diagram

52. E.2.11 Identify the general regions of star types on a Hertzsprung–Russell (HR) diagram You are here This diagram shows a correlation between the luminosity of a star and its temperature. The scale on the axes is not linear as the temperature varies from 3000 to 25000 K whereas the luminosity varies from 10 -4 to 10 6, 10 orders of magnitude.

53.  The stars are not randomly distributed on the diagram.  There are 3 features that emerge from the H-R diagram:  Most stars fall on a strip extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.  Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).  The bottom left is a region of small stars known as white dwarfs (small and hot)  The stars are not randomly distributed on the diagram.  There are 3 features that emerge from the H-R diagram:  Most stars fall on a strip extending diagonally across the diagram from top left to bottom right. This is called the MAIN SEQUENCE.  Some large stars, reddish in colour occupy the top right – these are red giants (large, cool stars).  The bottom left is a region of small stars known as white dwarfs (small and hot) E.2.11 Identify the general regions of star types on a Hertzsprung–Russell (HR) diagram

55. 22 000 stars are plotted from the Hipparcos catalog and 1000 from the Gliese catalog of nearby stars. An examination of the diagram shows that stars tend to fall only into certain regions on the diagram. The most predominant is the diagonal, going from the upper-left (hot and bright) to the lower-right (cooler and less bright), called the main sequence. In the lower-left is where white dwarfs are found, and above the main sequence are the subgiants, giants and supergiants. The Sun is found on the main sequence at luminosity 1 and temperature 5780K (spectral type G2). H-R diagram (by Richard Powell)