The Doppler Effect and Cosmic Red Shift

Christian Doppler (1803 – 1853) was an Austrian mathematician and physicist who is known for his principle, known as the Doppler Effect, that the observed wavelength and frequency of a wave depends on the relative speed of the source and the observer. This was first illustrated in 1845 by a Dutch scientist named Christophe Ballot who stationed two sets of trumpet players, one on a train platform and another on a railroad flatcar moving past the station, both playing the same note on their trumpets. Observers noticed a clear difference between the two notes as the train went by. We have all noticed that effect as any police car, ambulance or fire truck goes by. First we hear a higher pitch as the vehicle approaches and then a lower pitch as it recedes. The explanation is quite simple. As a wave producing object approaches an observer, the waves are compressed and the distance between waves decreases. This causes the frequency (pitch) of the sound to increase and the wavelength to decrease. The opposite occurs when the source of sound goes away from the observer. In this case the distance between waves stretches which causes the frequency to decrease as the wavelength increases.

This phenomenon works for all waves, not just sound waves, including the entire electromagnetic spectrum including radio waves, microwaves, infra-red light, visible light, ultra-violet light and gamma rays. There are many practical applications of this effect, such as police radar to detect the speed of cars, ultrasound to detect the speed of blood flow in the body, and Doppler radar to detect the motion of rain storms. The military also used the Doppler effect to establish the first satellite navigation system in the late 1960s, called Transit Navigation. They orbited multiple satellites in polar earth orbit which constantly broadcast their positions at a fixed radio frequency of 400 megahertz (MHz). Navy ships would receive the satellite signal, noticing that the received frequency went from above 400 MHz then through exactly 400 MHz and then below 400 MHz as the satellite passed over the ship. When the frequency was exactly 400 MHz, the operator would know that the satellite was directly overhead, as it was neither approaching or departing from the observer at that time. Since it was also telling the operator its own position, the navy ship would then know precisely where it was.

For astronomers the Doppler effect is a critical observational tool. If a source of light such as a star or galaxy is moving away from the earth, its light waves will be stretched toward a higher wavelength. This will move the light color toward the red end of the spectrum. Blue will become green, green will become yellow, etc. This is called the “red shift.” If a star or galaxy is moving toward the earth, the light waves will be compressed and will shift toward the blue end of the spectrum. This is called the “blue shift.” Almost all starlight that we observe is red shifted which leads us to understand that the universe is expanding. Furthermore, the farther away a source of light is located, the greater the red shift. In the 1920s, Edwin Hubble made a diagram plotting the recessional velocity of distant galaxies against their distance from us. These diagrams produced a straight line whose constant slope is now called the Hubble Constant, and the relationship between velocity and distance is called Hubble’s Law.

In order to explain how these velocities could be measured so accurately, we need to understand the spectrum of light produced by hydrogen, the main light emitting element in stars. When the light produced by excited atoms of hydrogen gas are observed with a fancy prism (spectroscope), one sees four lines of color rather than a continuous band of light. Niels Bohr (1885-1962) was a Nobel Prize winning physicist living in Denmark who made sense of these peculiar lines by a mathematical formula called the Bohr Model of the Hydrogen Atom. He correctly deduced that when a hydrogen atom is excited, the orbiting electron moves outwardly to a specific outer orbit, corresponding to the energy absorbed. When the electron cascaded back to the “ground state” it would give off a single photon of light of a specific energy (and wavelength). These energies are quantized and correspond to specific moves from one energy level to another. We now know that the four lines visible in the hydrogen spectrum come from energy level jumps between specific orbiting locations called excited states. There are also lines produced by higher energy level jumps which are in the ultra-violet region of the spectrum which we cannot see.

When astronomers observe light from distant galaxies through a spectroscope, they often see either the hydrogen spectral lines or absorption regions where these energies are absorbed by passing through a cloud of hydrogen. By carefully measuring the shift of these lines toward the red end of the light spectra, the speed of the receding galaxy can be determined. As the speed of recession increases the red shift becomes more pronounced until the visible lines of hydrogen are no longer visible, having been shifted into the infra-red or even into the microwave region of the spectrum. This is where the term “Cosmic Microwave Background Radiation” comes from. It is light that is so far from us and so heavily red shifted that it forms the outer reaches of our observable universe.

If you visit the Hall of the Universe in the American Museum of Natural History, upon leaving the Big Bang Theater you will be directed to a spiral ramp called the “Cosmic Pathway.” This ramp illustrates the passage of time from the Big Bang, 13.8 billion years ago until the present time. The photographs you see along the ramp are of extremely distant objects, whose light has taken billions of years to reach us. This light is extremely red shifted at first and less so as we move down the ramp to the present time at the end. It is the red shift itself which is quantized along this ramp with the symbol “Z.” Z represents the quotient of observed wavelength divided by actual wavelength -1. For example, if an ultraviolet wavelength of hydrogen emission is observed at a wavelength of 732 nanometers (nm) and its actual wavelength is 122 nm, then Z = (732 / 122) -1 = 6-1 = 5. This is called the cosmological red shift and is caused by the motion of galaxies away from us combined with the expansion of the universe itself during the time it takes the light to reach us.

Finally, we find that the Doppler effect and cosmic red shift provide us with an extremely useful tool in determining the structure of the universe. With it we can measure any motion within the universe, such as binary stars moving around each other and even the discovery of exoplanets, as their motion perturbs the motion of their own sun which can be detected by the subtle changes in red shift as it wobbles.

References:

Astronomy Today, Eric Chaisson and Steve McMillan, Addison-Wesley, 2011