Cosmic Distance Ladder | Part 4 of 4

On March 15,1929, Edwin Hubble presented a paper to the National Academy of Sciences. A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae stated that the 24 objects he studied were receding from Earth in a specific pattern. The farther ones were receding faster. In fact, the distance vs recessional velocity was a linear direct proportion. This finding has had profound consequences on our understanding of the nature of the universe, when it originated, how large it is, and what future course it will take.

This is the final part of the series Cosmic Distance Ladder. Here are links to part 1, part 2, and part 3. As promised, the arguments and information will be presented as conceptually as possible without emphasis on the mathematical details. The goal of this series has been to assist the non-technically trained reader to understand more about how we know the distances to objects in the universe. It is hoped we can all appreciate more the remarkable things we are learning about our place in the cosmos.

Previous Work by Vesto Slipher Laid the Foundation

Vesto M. Slipher was born on November 11, 1875 in Mulberry, Indiana. He was educated first at a high school in Frankfort, Indiana and later at the University of Indiana at Bloomington. Here, he received a bachelors degree in mechanics and astronomy in 1901, a masters degree in 1903, and a Ph.D in 1909. He began work at Lowell Observatory in August of 1901. His best known work at this institution concerns his discovery of the radial velocities of spiral nebulae, starting in 1912. Through this research, he determined that spiral nebulae were moving at approximately three times the speed of any other known object, a discovery which was later utilized by astronomer Edwin Hubble. In addition, Slipher discovered that these spiral nebulae are rotating.

Vesto Slipher laid the foundation for Edwin Hubble’s work. Slipher found that a number of spiral nebulae, or galaxies, were not stationary in space. Instead they were moving at rapid velocities. His 1913 paper reported the speed of Andromeda to be 300 km/s toward Earth. His method for determining those velocities involved observing the spectra of colors of the light from them. The method used a principle called the Doppler Effect.

What is the Doppler Effect?

Objects can be the source of different kinds of waves. Think of a vibrating guitar string, a vocalist singing a specific note, a car horn blaring, a water bug, a light bulb, a radio tower, a star, or a whole galaxy. For this example, consider a shallow pool of water.
At the center of the pool, touch the water surface to make a steady source of waves. Don’t move horizontally while you make the waves. The waves will radiate from the source in a concentric circle pattern as they travel the same speed in all directions. This image was made with a shallow, glass bottomed tank, water about 1 cm deep, and a light shining through. The crests of the waves act like curved lens surfaces and concentrate the light into bright rings. The troughs act like diverging lenses to spread the light into darker rings.

Click on the applet link at the right if you want to play with a simulation making waves. Give it a few moments to download and open the window. There are controls for features such as wave frequency, speed of waves, 3-D view, and many more. I hope your browser is set up for this type of applet. The 3-D view is good for seeing the crests and troughs of the waves. And for those who know about interference of waves, this applet can handle 2 wave sources. Interference is not part of this diary. But, this is fun to play with. And, I am all for having fun with science.

If the source of the waves is moving to the right across the water while the waves are made, the pattern becomes different. The waves ahead of the source don’t get as far away from the source. They are crowded a little closer together. In other words, they have a shorter wave length. Similarly, the waves behind the moving source get farther away from the source. They have a longer wavelength. This shift to a shorter or longer wavelength is called the Doppler Effect. It is named after Christian Doppler. Doppler postulated his principle (later coined the Doppler effect) that the observed frequency of a wave depends on the relative speed of the source and the observer, and he tried to use this concept for explaining the colour of binary stars. Buys Ballot tested the Doppler effect for sound waves in 1845 by using a group of musicians playing a calibrated note on a train in the Utrecht-Amsterdam line.

It is likely you have heard this effect with sound waves if you heard a train rush past with the horn blaring. The sounds you hear with the train approaching are from waves that are shortened, and hence heard as a higher frequency. The sounds you hear with the train receding are from waves that are lengthened, and hence heard as a lower frequency. You can also hear it with sirens, race cars, etc. The amount of frequency shift is an indication of how fast the train is moving. Of course, it is possible with sound sources for them to travel faster than the sound waves. This ‘breaking of the sound barrier’ produces a sonic boom.

How Does Doppler Effect Apply to Galaxies in Space?

Galaxies are also emitters of waves. They are emitters of electromagnetic waves. Light waves travel at a specific finite speed of 299,792,458 m/s. The source of these light waves is largely the abundant quantities of Hydrogen and Helium making up most of the mass of the stars in the galaxies. But, there are also many other elements contributing to the colors emitted. The mix of many colors blends together for an overall white. By passing the light through a prism, the colors can be separated into a broad spectrum. Interpreting these stellar spectra is much like looking for fingerprints to identify a person. Notice in the different rows of spectra from a variety of stars how there are faint dark vertical lines scattered across each one. These are called absorption lines.

The atmosphere of each star contains atoms formed by the fusion process within the star. Light photons of a specific energy and wavelength passing through the atmosphere of the star can be absorbed and stopped. Photons of other energy and wavelength don’t get absorbed and can reach our detectors. The result is a dark vertical line in the spectrum for each color absorbed.

Each element in the stellar atmosphere has a unique set of photon energies and wavelengths it can absorb, hence, a unique set of dark lines will appear in the spectrum for each element. These unique lines are comparable to the unique fingerprint lines for people. So, the chemical composition of the star can be inferred.

Here is the important point to make. The stars of the distant galaxy might be moving away from us while the light is emitted. That will cause the absorption lines to appear at longer wavelengths than if the stars were stationary. The lines will be shifted toward the red end of the spectrum. Red light is of a longer wavelength than blue light. The enlarged portion of this image shows such a redshift. And, just as with sound waves, the amount of shift (∆λ) is an indication of the recession speed of the source of waves, the stars in this case.

Calculation of Speed from Doppler Shift

When speed of a moving wave source is slow relative to the speed of light, c , the equation at the right will allow calculation of the speed of the source, v . The top left term is the amount of wavelength shift. The lower left term is the wavelength if the source was not moving. It is a simple equivalence of two ratios.

Re-arrangement of terms gives the calculation of the velocity, v , of the source of waves. There is an adjustment to this formula for sources which are moving nearer the speed of light. For Hubble’s work, that was not an issue. Stars in the galaxies he observed were not moving nearly as fast as the speed of light.

What Did Edwin Hubble Observe?

Hubble had to spend many bitterly cold nights sitting at the powerful 100″ Hooker telescope on Mt. Wilson. In October 1923, he spotted what he first thought was a nova star flaring up dramatically in the M31 “nebula” in the constellation of Andromeda. After careful examination of photographic plates of the same area taken previously by other astronomers, he realized that it was a Cepheid star. Hubble measured the distance to the new Cepheid. He could then place M31 a million light-years away – far outside the Milky Way and thus itself a galaxy containing millions of stars. The known Universe had expanded dramatically that day and – in a sense – the Cosmos itself had been discovered! Even The New York Times of the day realised the importance of the discovery: “Finds spiral nebulae are stellar systems. Doctor Hubbel [sic] confirms view that they are ‘island universes’ similar to our own.”

This discovery was of great importance to the astronomical world, but Hubble’s greatest moment was yet to come. He began to classify all the known nebulae and to measure their velocities from the spectra of their emitted light. In 1929 he made another startling find – all galaxies seemed to be receding from us with velocities that increased in proportion to their distance from us – a relationship now known as Hubble’s Law.

Below are spectra for five nebulae at increasing distance from Earth. A pair of absorption lines, H + K from ionized Calcium, are indicated in each spectrum redshifted to the right. Resulting calculations of the recessional velocity of each are shown below each spectrum.

Hubble’s 1929 paper produced the following graph of distance versus speed of recession for the small number of nebulae he was able to measure. It suggested a linear direct proportion between distance and speed. Speed is on the vertical axis. Farther objects are moving faster away from us.

Additional work by Hubble with Milton Humason was published in 1931 and resulted in this next graph of data greatly expanding the range of distance. The 1929 data noted above fits into the small box at the lower left of this graph for comparison.

Finally, this more modern Hubble plot shows distances to nearly 700 Mega-parsecs using measurements of Supernovae brightness. They are intrinsically much brighter than Cepheids and can be seen at greater distances. Supernovae were the subject of the third post in this series. Notice the tiny red rectangle in the lower left of this graph. That red rectangle shows the range of distances and velocities measured by Hubble and Humason. It is very clear what the work by Hubble shows. Farther objects are moving faster away from us and in a mathematically predictable way.

The slope of the graph is known as the Hubble Constant of proportionality H_o and expresses the ratio between the velocity and the distance.

By observing the amount of redshift (∆λ), the velocity can be calculated.
By knowing the velocity, the distance to the object can be calculated.

The universe is huge. The universe is expanding.

What Can the Hubble Constant Tell Us About the Past?

Let’s make some bread. Raisin bread works well for cosmic recipes. We have established that the universe is huge and expanding. The frequently used analogy is that of rising raisin bread dough. Galaxies are like the raisins in the dough. Imagine you live on a raisin. Pick your home on any raisin and measure the distances to the other raisins. All the while the loaf is expanding. The farther raisins are moving away from your raisin faster than the nearer raisins.

Let’s run the clock in reverse. Think of the loaf contracting with time. The space it takes up will get less. Eventually, the whole mass will be contracted to a small point. How much time that would take depends upon the rate of expansion you had observed. The universe behaves the same way. Run the clock backward and space contracts to a point. We know the rate of expansion of the universe. It is expressed with the Hubble Constant in the previous graph.

Here we need a bit of mathematics. The slope is the Hubble Constant H_o. It is the rise divided by the run of this graph. If you consider the units used for the velocity v and distance d, this slope should have units of 1/time. In other words, suppose the velocity was meters/second and distance was meters. The meters unit will cancel in the numerator and denominator. That leaves per second as the unit.

If you invert the value for the slope, you will have a unit of time.

Using sample values for velocity and distance for this calculation, where velocity in km/s and distance in Megaparsec are converted, the time is about 13.8 billion years to a small margin of error. This is interpreted as the age of the universe since the Big Bang. What an incredible accomplishment.

What Can the Hubble Constant Tell Us About the Future?

NASA

Robert Frost imagined two possible fates for the Earth. Cosmologists see two possible fates for the universe of endless expansion or contraction into the “Big Crunch”.

There is a struggle between the momentum of expansion and gravity. The current rate of expansion is measured by the Hubble Constant. The strength of gravity depends on the density of the matter and energy in the universe.

If the density of the universe is less than the critical density, then the universe will expand forever. See the green or blue lines. Gravity might slow the expansion down over time. There isn’t enough to completely stop it. The universe will slowly cool as it expands.

If the density of the universe is greater than the critical density, gravity wins. The universe slows, stops, and fall back in on itself in the “Big Crunch”. See the orange line.

Today’s research into dark matter and dark energy investigates the roles they play in the fate of the universe. Supernova observations say the expansion of the universe is actually increasing. See the red line. That suggests a form of matter that exerts an outward force. This form of matter is called “dark energy”. Gravity slows the expansion down. Dark energy speeds expansion up. Current and future experiments may tell us there is enough dark energy to cause the universe to expand forever. It is still an unknown.

✩ ✩ ✩ ✩ ✩ ✩ ✩ ✩ ✩ ✩

I have attempted to explain the main features we have historically used to define the rungs of the Cosmic Distance Ladder. There are other new rungs of the ladder being defined and used to expand our knowledge of the size of the universe. Those I will leave untouched by this post. I hope you have enjoyed this climb as much as I have enjoyed writing about it. If the series has helped you in some small ways, then I feel good about that.

Thank you for joining me…Jim

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