North Berwick High School Department of Physics Higher Physics Unit 1 Our Dynamic Universe Section 6 The Expanding Universe Section 6 The Expanding Universe Note Making Make a dictionary with the meanings of any new words. The Doppler Effect and Hubble 1. State what is meant by the Doppler effect and give examples. 2. Copy the Doppler equations for moving sources. 3. Describe briefly how Cepheid variables are used to measure the distances to galaxies. 4. Copy Hubble's formula (make sure that you understand the units). Evidence for the Expanding Universe Rotational velocity 1. Describe how the mass of galaxies can be calculated. 2. What problem did this produce? Seeing the light 1. Describe how light can be used to calculate the mass of a galaxy. 2. What problem did this produce? 3. How much of the universe is thought to be dark matter? Dark matter 1. Explain what is meant by MACHOs and WIMPs. MACHOs 1. Describe 2 examples of MACHOs. 2. Briefly describe how gravitational lensing can be used to indicate the presence of a MACHO. 3. Briefly describe how black holes can be detected. 4. State the evidence for and against MACHOs. WIMPs 1. State that WIMPs are non-baryonic and their prime candidates. 2. State the evidence for and against Wimps. Section 6 The Expanding Universe Contents Content Statements ..................................................................................... 1 The Doppler Effect ....................................................................................... 4 Evidence for the Expanding Universe.......................................................... 10 Measuring the mass of galaxies .................................................................. 10 Rotational velocity ..................................................................................... 10 Seeing the light .......................................................................................... 11 Dark matter ............................................................................................... 13 MACHOs vs. WIMPs .................................................................................... 13 MACHOs .................................................................................................... 14 Detecting MACHOs ..................................................................................... 15 Searching with Hubble ............................................................................... 15 Gravitational lensing .................................................................................. 15 Circling stars .............................................................................................. 16 WIMPs ....................................................................................................... 17 Debate the arguments ............................................................................... 20 The Expanding Universe Problems .............................................................. 21 Solutions .................................................................................................... 31 Content Statements Contents Notes Contexts a) The Doppler The Doppler Effect is Doppler Effect in terms Effect and observed in sound and of terrestrial sources redshift of light. For sound, the e.g. passing galaxies. apparent change in ambulances. frequency as a source Investigating the moves towards or apparent shift in away from a stationary frequency using a observer should be moving sound source investigated. and datalogger. Applications include measurement of speed (radar), echocardiogram and flow measurement. The Doppler Effect Measuring distances to causes similar shifts in distant objects. wavelengths of light. Parallax measurements The light from objects and data analysis of moving away from us is apparent brightness of shifted to longer standard candles. wavelengths – redshift. The unit ‘Particles and The redshift of a galaxy Waves’ includes an is the change in investigation of the wavelength divided by inverse square law for the emitted light. Centres may wavelength. For slowly wish to include this moving galaxies, activity in this topic. redshift is the ratio of the velocity of the In practice, the units galaxy to the velocity used by astronomers of light. include light-years and (Note that the Doppler parsecs rather than SI Effect equations used units. for sound cannot be Data analysis of used with light from measurements of 1 fast moving galaxies galactic velocity and because relativistic distance. effects need to be taken into account.) The revival of Einstein’s cosmological constant in the context of the accelerating universe. b) Hubble’s Law. Hubble’s Law shows the relationship between the recession velocity of a galaxy and its distance from us. Hubble’s Law leads to an estimate of the age of the Universe. c) Evidence for the Measurements of the expanding velocities of galaxies Universe. and their distance from us lead to the theory of the expanding Universe. Gravity is the force which slows down the expansion. The eventual fate of the Universe depends on its mass. The orbital speed of the Sun and other stars gives a way of determining the mass of our galaxy. The Sun’s orbital speed is determined almost entirely by the gravitational pull of matter inside its orbit. Measurements of the mass of our galaxy and others lead to the conclusion that there is significant mass which 2 cannot be detected – dark matter. Measurements of the expansion rate of the Universe lead to the conclusion that it is increasing, suggesting that there is something that overcomes the force of gravity – dark energy. 3 Section 6 The Expanding Universe The Doppler Effect The Doppler effect is the change in frequency observed when a source of sound waves is moving relative to an observer. When the source of sound waves moves towards the observer, more waves are received per second and the frequency heard is increased. Similarly as the source of sound waves moves away from the observer less waves are received each second and the frequency heard decreases. Examples of the Doppler effect are: a car horn sounding as it passes a stationary observer; a train whistling as it passes under a bridge. In ‘Doppler ultrasound’, blood flowing in the body is measured using ultrasound reflections from the arteries. There are two situations to be considered when deriving the apparent frequency associated with the relative movement of a source of sound waves and an observer. Either the source moves relative to the observer, or the source is stationary and the observer moves. Source moves relative to a stationary observer The source is moving at speed vs and its frequency is fs . At positions in front of the moving source the waves 'pile up'. Let v = speed of sound and the source produces waves of wavelength λ; λ = v fs An observer in front of the moving source will receive waves of a shorter wavelength, λobs. v vs 1 λobs = - = (v - vs) fs fs fs 4 The observed frequency, v v v fobs = = = fs λobs 1 (v - vs) (v - vs) f s v Thus fobs = f s for a source moving towards a (v - vs) stationary observer, v and fobs = fs for a source moving away from a (v + vs) stationary observer. The two formulae above can also be written as v f = fs (v ± vs) Note: the fractional change in wavelength z may be calculated using z = (λobs - λrest) / λrest Complete the exercise to find the velocity of the galaxy M31 at the http://imagine.gsfc.nasa.gov/YBA/yba-intro.html website. Einstein’s famous general theory of relativity implied that the universe should be either expanding or contracting. However, the accepted scientific wisdom at that time was that the universe was of fixed dimensions and had been so for all time. This would lead Einstein to include in his theory what he has described as ‘the biggest blunder of my life’, by including a cosmological constant that brought a balance to the universe and kept it stable. Working entirely independently from this, American Vesto Slipher had discovered that light from stars showed similar characteristics to the Doppler shift of sound waves. When light was travelling to an observer the wavelength 5 would appear to contract and create a blue shift in the wavelength. However, Slipher was to also discover that the stars were all moving away from the Earth and created a cosmic red shift. Slipher’s observations did not receive much notice, although they were essential to the pioneering work of Edwin Hubble. The name Hubble is most famous now for the telescope in orbit around the Earth. But where does the name come from? Edwin Hubble was one of the greats of 20th century astronomy. (See the science timeline section to find out more of his story.) At the end of World War I the number of known galaxies in the universe totalled one: our own Milky Way. Everything that was observable was believed to be part of the Milky Way or unimportant puffs of gas at the periphery of the universe. Hubble was to demonstrate that there are many more galaxies. Currently astronomers believe that there are possibly 140 billion galaxies in the universe. In other words, if a galaxy was a chocolate raisin, there are enough to fill the SECC. Hubble’s two driving pursuits in his work were to discover the age and the size of the universe. To do this he had to use stars known as ‘standard candles’, stars whose luminosity can be reliably calculated and used as a reference point to measure the luminosity and relative distance of other stars. However, it was not Hubble who found these reference stars. The term ‘standard