Hubble's Law and the Expanding Universe

In the early 1900s (1910s), an important discovery was made by V. M. Slipher, which was subsequently followed up by Edwin Hubble. Slipher (and then Hubble) found that all distant galaxies appeared to be receding from the Earth. Actually, what they found was that all distant galaxies showed redshifts, which they inferred to mean that the galaxies were streaming away from us. The origin of this streaming will be discussed later.

Question: How did Slipher and Hubble Accomplish Their Feat?

Spectroscopes and Rainbows

Slipher and Hubble acquired spectra of distant galaxies (see the image for the spiral galaxy M51, the Whirlpool Galaxy below) by passing their light through a dispersive device (a device which separates a blend of light into its constituent colors), a spectroscope. Here, the prism acts as the dispersive device separating the light into its constituent colors.

The bottom left picture of a rainbow shows a naturally occurring dispersive device, namely, droplets of water spread the white light from the Sun into its constituent colors.

Spectra and Absorption Lines

To the left are shown spectra of different types of stars. The dark absorption lines are the fingerprints of individual elements. Each pattern is unique to the element. absorption lines of hydrogen, helium, carbon, and other elements are shown. Because distant galaxies are made of stars, one expects that the light from a galaxy will appear as the combination of hundreds of billions of stars! Slipher and Hubble acquired spectra of many galaxies and noticed something quite interesting. They found that the light from distant galaxies was shifted to the red end of the spectrum, the light was redshifted.

Redshift, z

A redshift is a shift in the measured wavelength of some spectral feature to a value greater than its value as measured in a laboratory on the Earth. The redshift, z, is defined as

Here the Greek letter lambda represents the wavelength of the light. The redshift is then the relative change in the wavelength of the spectral line (feature). If the observer and the source are in relative motion, then z will be nonzero. If there is no relative motion then, z = 0.

Hubble's Law

Slipher and Hubble demonstrated that the larger the redshift, z, the greater the distance to the object. This can be easily seen in the above where the sources with the smaller redshifts present larger images on the sky. Since we know that angles (apparent sizes of objects on the sky) decrease as you move an object farther away roughly as angle ~ size/distance, smaller appearing objects must be farther away.

Slipher and Hubble found what is referred to as Hubble's Law. Algebraically, we have that

  • Hubble's Law ===> the redshift z is proportional to distance

Following Slipher and Hubble, if we interpret the redshift as due to motion, we can re-state Hubble's Law in its more familiar form. However, note that the redshift measured for distant galaxies is primarily due to the expansion of the Universe, and not to what are called peculiar velocities. An approximation to the redshift, z, driven by the expansion of the Universe is found to be v ~ cz when v is much smaller than cz. Here, c is the speed of light, 300,000 kilometers per second.

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