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HUBBLE’S LAW:

THE DISTANCE TO GALAXIES

Introduction:

          In the early part of the 20^th century, Edwin Hubble demonstrated that the Milky Way was not the only galaxy.  By using Cepheid variable stars he concluded that the Great Nebula in the constellation of Andromeda was actually an external galaxy of its own.  He saw, and measured, Cepheid variables within what was thought to be a gaseous nebula.  As a result of Hubble’s observations, astronomers had a new, much larger concept of the size of the Universe.  Hubble continued with his research on galaxies and in 1929 introduced another, quite amazing, conclusion about galaxies:  the more distant a galaxy, the greater its spectral lines are red shifted.   The implications were simple, obvious and unavoidable – the Universe was expanding.  Galaxies are moving farther apart.  And the farther out into the Universe we look, the greater their speed.

          This landmark observation resulted in the theory for the formation of the Universe.  If the galaxies in the Universe are moving away from all the other galaxies in the Universe, then yesterday they were closer together.  Last week they were even closer together… last month… last year… a million or a billion years ago, they were much closer together.  How far back in time can we imagine this scenario?  Were the galaxies ever all together in a single lump?  This is the concept of the theory of the formation of the Universe called the Big Bang.  It suggests that the Universe started from a much (very much) smaller size and has expanded to its present dimensions and, is still expanding.  Hubble was made famous by his recognition of this state of the Universe as well as determining the rate of expansion.

Purpose:

          The manner in which Hubble made his conclusions is an excellent example of how the gathering of information, organization and analysis of the findings leads to a greater understanding of the natural world.  In this lab you will follow along in the development of the ideas that led to the Big Bang theory of the Universe.

Materials:

          Calculator

          Plastic ruler

Procedure:

          As Hubble amassed information about galaxies he noticed a tremendous array of sizes and shapes.  Unfortunately, most galaxies were too distant for observations to be made of individual stars so he could not use Cepheid variables as he had done in the past.  To estimate distances to the galaxies he made an assumption.  He assumed that a certain type of elliptical galaxy was fairly constant in size.  If this were true, the smaller the image of this type of galaxy in a photograph, the greater the distance.  For example consider the following picture of a series of quarters along a ruler.  Obviously the quarters are all the same size but the more distant quarters appear smaller.  If you know the size of the quarter, you could determine its distance.

          Even though the limited depth of field of the camera lens does not allow all of the quarters to photographed in focus, measure the diameter of all of the quarters to the nearest millimeter and place the information on the following table. 

This is the way Hubble estimated the distance to certain elliptical galaxies.  Here are some examples of elliptical galaxy images Hubble used in his work.

          Of the the five images above, the first three are of actual galaxies.  Image A is of the giant elliptical galaxy M 87 in the Virgo cluster of galaxies.  Image B is of an elliptical galaxy in Ursa Major and Image C is an elliptical galaxy in Corona Borealis.  The last two images are just dots that represent galaxies.

          Because Hubble knew the distance to M 87 was 24 Mpc (mega parsecs) and assumed that the other ellipticals were about the same size, he was able to determine their distances.  Fill in the blanks of this table.

Measure the size of each galaxy as accurately as possible.  Try to estimate to a fraction of a millimeter.  Enter each measurement in the column labelled “Size in mm”.

          The distance is determined by making a comparison to galaxy A (M 87) which has a known distance of 24 Mpc.  (Think of the examples with the quarters.) For example if a galaxy you measured was 10.5 mm in diameter then it would 24/10.5 times farther away than M 87. 

24/10.5 = 2.3

The measured example would be 2.3 times farther than 24 Mpc or 55.2 Mpc.  Use this method to determine the distance to each galaxy.

          Hubble, as a result, had a rough estimate of the distances to these elliptical galaxies.  Next he matched the red shift of the galaxies from their spectrums.  Galaxies, of course, are collections of hundreds of millions to a trillion stars.  The spectrum we receive is a cumulative spectrum of all the light sources in the galaxy.  There are a couple of spectral lines that are useful in this type of study (because they are easily seen).  They are the H and K lines of calcium.  The wavelength of the “H” line is 396.8 nm. 

          Hubble and his colleagues (notibly Vesto Slipher at Lowell Observatory in Flagstaff, Arizona) had obtained spectral signatures for many galaxies and determined the postion of the calcium “H” lines.  This information is given in the following table:

To determine the velocity of the galaxy,  Hubble used this equation for the Doppler shift:

Velocity = ( Dl / original l) c

Explanation of equation:

          Dl is the change in the galaxy’s “H” spectral line wavelength and the                        laboratory wavelength of that line. 

          The original l is the laboratory wavelength of the calcium “H” line and            is (396.8 nm)

          c = the speed of light (300,000 km/s)

The following table show the results of these calculations.  Note that the galaxy with the highest redshift (E) has the greatest recessional velocity.

CONCEPT CHECK:

What is the speed of the fastest galaxy moving away from us?   __________

All of these galaxies are moving away from us with a speed that is realted to their distance.  This relationship is called:

HUBBLE’S LAW

          If this relationship holds true, then Hubble could measure the red shift of any galaxy, determine its recessional velocity and then find its distance.   

          Many astromers have worked on this relationship.  Some were very conservative with the information and some very liberal.  This has produced a wide range of values for Hubble’s Constant.  Values range from H = 30 km/s per megaparsec to as high as H = 220 km/s per megaparsec.  These large differences imply different origins for the Universe. 

Which of these values would imply the youngest Universe and WHY?

          The consesus among astronomers is that the H = 75 km/s/mpc.

(This reads: Hubble’s constant is equal to seventy five kilometers per second per mega parsec.)  It means that the Universe is expanding and the rate of expansion for every megaparsed is 75 kilometers per second.

          In Hubble’s Universe the distance to a remote galaxy (or Quasar) can be found once the recessional velocity is determined from the spectral lines by this equation:

D = V/H

          Using 75 km/s/mpc, calculate the distance to a galaxy that has a recessional velocity of 45,000 km/sec.

          D = ___________________ (Be sure to inluce the appropriate units.)

Hubble also classified galaxies.  He became the leading expert on galaxies.  His famous “tuning fork” diagram is hown below.  It is simply a tool used to determine the type of galaxy.  It was not meant to imply the evolution of galaxies, just what kind it represents.

          The specifics of Hubble’s Tuning Fork Diagram can be found in your textbook or by doing an internet search.  But here are the basics:

Elliptical Galaxies have no spiral arms.  Their classification is based on their shape.  Nearly round ellipicals are E0.  As they become more elongate or flattened they pass though E1, E2, E3, E4, E5, E6, and E7.

 An E0 galaxy   An E6 galaxy

Spiral Galaxies are divided into two categories -  normal spirals and barred spirals.  Both types of spiral galaxies are characterized by spiral arms.  The barred spirals, as the name implies, have a bar or bridge across the nuclear bulge.  It has been determined that our galaxy, the Milky Way, is a barred spiral of typ SBbc.  (Obviously astronomers have a need for more than the basic classification scheme.)

Spirals are classified as either Sa, Sb, or Sc (and SBa, SBb, and SBc) by noting the size of the nuclear bulge and the appearance of the spiral arms.

 Sa galaxy   SBa galaxy

 Sb galaxy       SBb galaxy

 Sc galaxy       SBc galaxy

Sa or SBa galaxies have a large nuclear bulge and many arms.  The arms may be partially blended together and difficult to distinguish.

Sb or SBb galaxies have an intermediate sized nuclear bulge with distinct arms.

Sc or SBc galaxies have the smallest nuclear bulge with sparse arms that are easily distinguished.

Irregulars, as the name implies, are just everything else.  These are some of the most interesting types of galaxies.  Some represent the collisions of galaxies.

In this group of NASA and Hubble Space Telescope photos, classify the galaxies according to Hubble’s Tuning Fork Diagram.

 Rio Galaxy 1  Classification ____________

This one is an elliptical.

  Rio Galaxy 2     Classification __________

The bluish fringe indicates an area of active star formation.

  Rio Galaxy 3     Classification _________

  Rio Galaxy 4  Classification ________

This is most likely the result of a collison.  Use the large picture on the right.  (Blue ring with yellowish white center)

  Rio Galaxy 5     Classification  _____________

Here too the blue area represents active star formation.

  Rio Galaxy 6  Classification __________

The red is heated hydrogen gas.

  Rio Galaxy 7    Classification __________

This has been called the “Galactic Tunnel”.  The dark bands between the galaxies appear to be real.  It may be that the galaxies have some sort of gravitational exchange of matter going on. 

  Rio Galaxy 8  Classification  __________

Probably another collision.

  Rio Galaxy 9  Classification _________

Classify just the inner, yellowish part of the galaxy.

  Rio Galaxy 10  Classification _________

This is a nearby spiral seen nearly “face-on”.

  Rio Galaxy 11 Classification  _________

  Rio Galaxy 12  Classification __________

Both images are of the same galaxy.  Note the small nuclear bulge.

  Rio Galaxy 13  Classification  _________

This is the Sombrero Galaxy (M101).  One of my favorites.  Note the well defined dust lane across its middle.  This is a lane of dust associated with spiral arms.  Classify this galaxy by the size of the nuclear bulge.

  Rio Galaxy 14  Classification  __________

  Rio Galaxy 15  Classification  __________

  Rio Galaxy 16  Classification  __________

  Rio Galaxy 17  Classification  __________

  Rio Galaxy 18  Classification __________

  Rio Galaxy 19  Classification __________

Rio Galaxy 20 (negative image)  Classification ______