Hubble's Law and the Expanding Universe




Spectroscopes and Rainbows

Hubble and Slipher acquired spectra of distant galaxies (see the image below of MAssive Cluster Survey item 416 [MACS 0416], a cluster of galaxies located a distance 4.3 billion light years from the Earth).

Hubble and Slipher passed the light from each galaxy through a dispersive device (a device which separates blends of light into their constituent colors), a spectroscope. In the picture to the left, the prism is the dispersive device that separates the light into its constituent colors.

The bottom left picture of a rainbow shows a naturally occurring dispersive device, namely, droplets of water which spread the blended light from the Sun into its constituent colors. Using a telescope we find

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! Hubble and Slipher acquired spectra of many galaxies and noticed something quite interesting. They found that the lines for all of the elements present in the spectrum were shifted toward 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 the relative change in the wavelength of the spectral line (feature).

A redshift may arise if the source of the waves and the observer are in relative motion, If there is no relative motion then there is no shift and z = 0. This type of redshift is the Doppler effect. The Doppler effect is shown by waves of all kinds, for example, it is shown by sound waves (train whistle), and light waves. The frequency of a wave (for example, the pitch of a sound wave) is higher when the source of the waves is approaching; the frequency of a wave is lower when the source of the wave is running away from the observer.


Hubble's Law

Hubble demonstrated that the larger the redshift, z, the greater the distance to the object. This can be easily seen in the left image 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,

Hubble found what is referred to as Hubble's Law.

  • Hubble's Law → redshift z is proportional to distance. In their plot, they actually used cz, where c is the speed of light, 300,000 km per second. In this way, they expressed redshifts as speeds.

  • We have cz = speed = HoD


    Hubble Law and Hubble Constant

    The Hubble diagram produced by the Hubble Space Telescope is shown to the left. For this particular version of Hubble's Law, speeds are measured in kilometers per second and distances from Earth in millions of parsecs. The expansion rate of the Universe is measured by the slope of Hubble's Law as determined by galaxies near the Earth (distances close to 0, see lower left). The slope is called Hubble's Constant, Ho. The best current estimate for Ho determined using the method of Hubble is Ho = 73 km per second per million parsecs.

    The slope of the Hubble diagram changes at large distances, What might this be telling us?



Interpretation of Hubble Law


Hubble Law and Expansion of Universe I

Imagine a universe where the galaxies are initially confined to one region. At some point in the past an enormous explosion takes place that throws out galaxies in all directions at all speeds but leaves us stationary at the center.

What do we observe?

After say 1 billion years, the slower moving galaxies will have traveled less far and so will be closer to us. Galaxies that were traveling twice as fast as the slow ones will be twice as far away. Galaxies that were traveling three times as fast would be three times as far away

    → we would find Hubble's Law

This scenario reproduces Hubble's Law, but is it reasonable?


Hubble Law and Expansion of Universe II

Imagine a very large universe in the form of an uncooked loaf of raisin bread. Here, the universe could be very large but fixed in shape with the raisins embedded in the loaf. Now cook the raisin bread so that it doubles in size from 20 cm to 40 cm. As the raisin bread doubles in size, the distance between every raisin also doubles in size. That is, the raisin that was initially 5 cm away is now 10 cm away and the raisin that was 10 cm away is now 20 cm away. This means that if a wave stretched between each of these raisins, the wavelength of each will have doubled because of the expansion. Alternatively, it also means that it would appear that the more distant the raisin initially, the faster it would appear to move away from us!

    → This again is Hubble's Law

Note that if the universe is sufficiently large and we change our reference raisin, this same result would also hold, that is, the new raisin would also observe Hubble's Law. In fact, any arbitrary raisin in the raisin bread universe would see every other galaxy running away from them as well thus making each look as if they were at the center of an expanding universe, as long as the universe was sufficiently large.


Homework 1


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