1. 5A-3 Astrophysics Cosmology Astrophysics booklet pages 54 to 65 August 21st, 2010 CLASS NOTES HANDOUT VERSION

2. The Doppler Effect ABCDE ABCD As the ambulance travels forwards: The sound wave in front is compressed - decreasing its wavelength - increasing its frequency The sound wave behind is stretched out: - increasing its wavelength - decreasing its frequency

3. The Doppler Effect also occurs with light and radio waves. With light waves: In front of the moving object decreasing wavelength and increasing frequency makes the light BLUER Behind the moving object increasing wavelength and decreasing frequency makes the light REDER

4. v Radial and tangential velocity Consider a galaxy moving relative to the Sun at velocity v. This velocity can be split into two components: radial velocity, v r v r = v cos θ and tangential velocity, v t v t = v sin θ The Doppler Effect can be used to measure radial velocities. vrvr θ vtvt

5. Doppler effect equations When the radial speed of the object, v is MUCH LESS than the speed of light, c. change of frequency = object radial speed source frequency speed of light Δf = v fc

6. Also: change of wavelength = object radial speed source wavelength speed of light Δλ = - v λ c In either case, The Doppler Shift, z is given by: z = Δf = - Δλ = v f λ c Remember: v MUST BE << c

7. Question 1 Light of frequency 4.000 x 10 14 Hz is emitted from a galaxy that is moving away from us at 600 kms -1. Calculate: (a) the frequency shift caused and, (b) the observed frequency. c = 300 000 kms -1

8. Question 2 The Andromeda Galaxy has a Doppler Shift of 0.000 5. The observed wavelengths are also smaller than the source wavelengths. (a) Calculate radial velocity of the Andromeda Galaxy relative to the Earth. (b) What will be the observed wavelength of red light if the source was 700.00 nm? c = 300 000 kms -1

9. Question 3 A hydrogen radio source emits waves of frequency 1420 MHz. A radio telescope observes these waves to have a frequency of 1430 MHz. Calculate radial velocity of the source relative to the Earth. c = 300 000 kms -1

10. Doppler shift summary Doppler shift, z in frequency Δf f in wavelength Δλ λ Colour shift with light Source moves towards observer Source moves away from observer + v c + v c - v c - v c RED SHIFT BLUE SHIFT

11. 400 500 600 700 wavelength / nm Doppler shift in spectra Stationary source HαHα Receding source RED SHIFT HαHα Approaching source BLUE SHIFT HαHα

12. Question The hydrogen-alpha spectra line of a distant galaxy occurs at a wavelength of 680 nm. In the Sun this wavelength is 656 nm. Calculate the recessional radial velocity of the galaxy. c = 300 000 kms -1

13. The Doppler effect with binary stars A binary star system consists of two stars in mutual orbit about each other. The two stars are often too close together to be resolved by a telescope as separate stars. However, as they orbit each other they will be moving away and towards the Earth. The stars will produce both red and blue shifts which can be measured. This type of system is called a spectroscopic binary. From the Doppler shift measurements the orbital speeds of the stars can be found.

14. Question A spectral line of a certain spectroscopic binary merges once every 4 years and splits to a maximum displacement of 0.036 nm and 0.015 nm from its laboratory wavelength of 656 nm. Calculate: (a) the orbital speed of each star and (b) the radius of the larger orbit. c = 300 000 kms -1

15. Hubble’s Law In 1929 after plotting the redshift calculated speeds of about thirty galaxies against their distances Hubble noticed that a ‘rough’ straight line through the origin was obtained.

16. Hubble’s law states that the speed of recession of a galaxy is proportional to the distance to the galaxy. v α d inserting a constant of proportionality: v = Hd H = the Hubble constant = 65 km s -1 Mpc -1 Notes: (a) Mpc = megaparsec (= 3.26 million light years) (b) Hubble’s law does not work with some nearby galaxies (which are approaching us!)

17. Question 1 Calculate or state the speeds expected for galaxies at distances: (a) 1 Mpc; (b) 10 Mpc & (c) 1 billion light years. 1 Mpc = 3.26 million light years

18. Question 2 Calculate the distance, in light years, to a galaxy if its recessional velocity is 10% of the speed of light. c = 300 000 kms -1 & 1 pc = 3.26 lyr

19. The expansion of the Universe Hubble’s law tells us that distant galaxies are receding from us and that the further they are away the faster they are moving away from us. Hence the Universe is expanding. Balloon model of the expanding Universe The space between the galaxies expands and so the galaxies grow further apart

20. Estimating the age of the Universe Hubble’s constant tells us that the speed of a galaxy increases by 65 kms -1 for every Mpc or 3.26 million light years. For a galaxy to be receding at the speed of light its distance would be: (300 000 kms -1 ) / (65 kms -1 Mpc -1 ) = 4 615 Mpc = 4 615 x 3.26 million light years = 15 billion light years Galaxies cannot travel this fast. Therefore light cannot have been travelling for this length of time. Therefore the Universe must be less than 15 billion years old. The current greatest length of time observed is about 13.5 billion years.

21. As can be seen in the above calculation, the maximum size of the Universe, D is given by: D = c / H But distance = speed x time For a galaxy travelling at speed c for the age of the Universe T. D = c T Therefore: c / H = c T 1 / H = T Hence the maximum age of the Universe is given by: T = 1 H Note: All of the above assumes that the Hubble constant has not changed during the lifetime of the Universe.

22. Question 1 The unit of 1 / H must be one of time. Calculate the value of 1 / H in seconds. 1 Mpc = 3.1 x 10 22 m

23. Question 2 In 2009 measurements from the Hubble Space Telescope yielded a Hubble constant of 74.2 ± 3.6 km s -1 Mpc -1. What is the maximum age of the Universe, in years, based on this measurement? 1 Mpc = 3.1 x 10 19 km

24. The Big Bang theory Hubble’s law supports the idea that the Universe started in some form of massive explosion. This idea is called the ‘Big Bang theory’. This theory was not generally accepted until 1965 before which an alternative explanation for the expansion of the Universe called the ‘Steady State theory’ was dominant.

25. Evidence for the Big Bang theory 1. Cosmic Microwave Background (CMB) radiation All of space emits thermal radiation with a maximum intensity wavelength corresponding to a temperature of 2.7K. It is radiation created in the Big Bang that has been travelling ever since the Universe became transparent (about 377 000 years after the Big Bang). The expansion of the Universe has gradually increased the wavelengths of this radiation so that it now occurs in the microwave region of the electromagnetic spectrum. This radiation was first detected by Penzias and Wilson in 1965.

26. The microwave detector used by Penzias and Wilson Cosmic Microwave Background radiation. CMB map of the whole Universe obtained by the COBE satellite in 1989

27. 2. Relative abundance of hydrogen to helium Using the Big Bang model it is possible to calculate the ratio of concentration of hydrogen to helium-4 by mass. This depends on the ratio of photons to baryons, which itself can be calculated independently from the detailed structure of Cosmic Microwave Background fluctuations. The ratio by mass predicted is about 4:1. The measured ratio of abundance is 3:1 which is roughly in agreement. Other ratios such as hydrogen to Lithium-7 or Helium-3 also give roughly similar results.

28. Revision Question Calculate the wavelength and frequency associated with a thermal temperature of 2.7K.

29. Revision of supernovae as standard candles Type 1a supernovae have a known peak luminosity allowing them to be used as ‘standard candles’. At their peak all of these supernovae have an absolute magnitude, M of -19.3 ± 0.03. By noting their apparent peak magnitude, m such supernovae can be used to determine this distances to galaxies using the equation: m – M = 5 log (d / 10)

30. Question In a distant galaxy a Type 1a supernova is observed to have an apparent magnitude of + 21 and a recessional speed (from red-shift measurement) of 60 000 kms -1. Calculate the distance to this galaxy (a) from the magnitude measurement (b) using Hubble’s law. Assume Type 1a supernovae have an absolute magnitude of – 19. Comment on your answers

31. Dark energy In 1998 astronomers discovered that very distant type 1a supernovae were further away than expected. Measurement of their red shifts (used to measure their velocities) and the use of Hubble’s Law to obtain their distances shows that these supernovae are fainter than expected. These mesurements indicate that the Universe is expanding faster now than when the supernovae exploded as the light has had to travel further to reach us than expected by a constant rate of expansion (assummed to be the case with Hubble’s Law). These and further measurements have led astronomers to conclude that the expansion of the Universe has been accelerating for about the past 5000 million years. Before this discovery, the expansion of the Universe was expected to be decelerating due to the attractive gravitational forces of galaxies on each other. Therefore there appears to be some unknown repulsive force acting which is releasing some hidden ‘potential’ energy which is currently known as dark energy.

32. The nature of dark energy is unclear. It is thought to be a form of background energy present throughout space and time. It is more prominent than gravity at large distances as gravity becomes weaker with distance (inverse square law) whereas the force associated with dark energy is thought to remain constant. Current theories suggest that it makes up 70% of the total energy of the Universe. The idea of dark energy leads to the speculation that in the future the force associated with dark energy will ultimately tear apart all gravitationally bound structures, including galaxies and solar systems, and eventually overcome the electrical and nuclear forces to tear apart atoms themselves, ending the universe in a "Big Rip".

33. Dark energy controversy It has been noted that if Newton’s law of gravitation: F = GMm/r 2 became: F = GMm/r at large, intergalactic distances, then the acceleration of the expansion of the universe no longer requires the existence of Dark Energy. Other alternative ideas for dark energy have come from string theory, brane cosmology and the holographic principle.

34. Quasars ‘Quasar’ stand for ‘quasi-stellar radio source’. A quasar is a compact region in the centre of a massive galaxy surrounding a central supermassive black hole. Its size is 10-10,000 times the Schwarzschild radius of the black hole. The quasar is powered by an accretion disc around the black hole. Quasars were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than extended sources similar to galaxies. Infra-red image of a quasar. Artist’s impression of a quasar

35. Quasars are among the oldest and most distant objects in the Universe. A quasar is characterised by: –its very powerful light output, much greater than the most massive of stars –its relatively small size, not much larger than a star –a large red shift indicating its distance is between 5 and 10 billion light years away. The first quasar discovered, 3C 273 produced strong radio emissions. However, not all quasars produce such emissions.

36. Question Light from a certain quasar was found to contain a spectral line that had been red-shifted by 80 nm from its normal wavelength of 486 nm. Calculate the recessional speed of this quasar. c = 300 000 kms -1