Appendix: Redshift and Distance
Appendix: Redshift and Distance
For objects on extragalactic scales, we use something called the redshift to determine the object's distance. Redshift refers to the Doppler shift in the light of an object as it moves away from us.
Consider an approaching train. If the train is blowing its whistle as it approaches you, passes you, and speeds away from you, the pitch of the whistle will change. This is the Doppler shift of the sound waves as the train travels toward you and then away from you. Another way to describe this change in pitch is to indicate the alteration in wavelength, or frequency.
Similar shifts happen to light as an object travels toward or away from you. The wavelength or frequency of the light changes. The electromagnetic (EM) spectrum spans all light and runs from short wavelengths, where energetic gamma rays exist, to long wavelengths in the radio part of the spectrum [see “Electromagnetic Spectrum” for more information]. In general, the gamma rays are said to be on the blue end of the spectrum and the radio waves are toward the red end. These red and blue labels come from the visible spectrum, where red light within the visible spectrum is on the radio side of the EM spectrum and blue and violet are on the gamma-ray side of the spectrum.
If an object is moving away from us, we observe the wavelength of the light to increase and the light appears to decrease in energy. This is called redshifted light. Conversely, if an object is approaching us, its light is shifted to shorter wavelengths and appears more energetic. This is called blueshifted light.
From “Extragalactic Atlas Overview,” we know the Universe is expanding. In 1912, Vesto Slipher discovered that all the spiral galaxies he observed had a redshifted spectrum. In the 1920s, Edwin Hubble began plotting the redshift, or recessional velocity, of galaxies versus their distance and discovered that there was a linear correlation. We now know this relationship as Hubble's Law. It is simply stated
Mathematically, Hubble's constant is just the slope of the straight line relating the velocity and the distance. Physically, it is the rate of expansion of the Universe and is one of the most important quantities in astrophysics. It remains the source of occasionally heated debate among astronomers. The units of the constant are in speed over distance and are typically in km/sec/Mpc (kilometers per second for each megaparsec).
Using various methods, astronomers narrowed the value of this constant down to the range 45-90 km/sec/Mpc. Some believed it to be closer to 50, while others were in the 90 km/sec/Mpc camp. The latest results from the WMAP mission derives the Hubble constant from the fluctuations in the cosmic microwave background. Their results accurately determine the value to within 5% and place its value at 71 km/sec/Mpc.
Redshift is measured by the literal shift in an object's light toward the red end of the EM spectrum. Astronomers first observe the spectrum of a far-off galaxy. Then they compare the wavelengths of the spectral features (absorption lines) from where they would be for an object at rest. This shift determines the recessional velocity as a percentage of the speed of light. If the redshift of a galaxy is 0.2, then it is moving away from us at 20% the speed of light.
This presents a problem, since the highest redshifts observed are more than 6.0. Is the object speeding away at 6 times the speed of light? No, nothing can travel faster than the speed of light. Large redshifts are called cosmological redshifts, and they require us to factor in relativity.
The Doppler formula, which assumes the velocity is much less than the speed of light, is not correct for quasars that appear to be moving away from us at close to or more than the speed of light. For these objects, we must take into account the expansion of the Universe itself. This is why astronomers have introduced the look-back time, which is a measure of how long ago the light was emitted from the object. For nearby objects, the look-back time and the distance are equal. For more distant objects, the look-back time and the distance diverge because the Universe is expanding. Light from the edge of the observable Universe has a look-back time of about 13 billion years; however, the distance to the horizon is now 42 billion light-years, due to the expanding Universe. The simple equations for Doppler shift and Hubble's Law do not apply at these great redshifts, where astronomers must use relativistic versions of the equations to account for the expanding Universe.
© 2002-2005 American Museum of Natural History
Last Modified: 2007-12-19 by Brian Abbott