The Hubble Redshift Distance Relation

Student Manual

Lab Partner:

The Hubble Redshift Distance Relation Student Manual

10/22/2013

Department of Physics Gettysburg College Gettysburg, PA

Telephone: (717) 337-6019 Email: [email protected] Introduction

In the 1920’s, Edwin Hubble measured the distances of the galaxies for the first time, and when he plotted these distances against the recessional velocities of these galaxies he noted something wild. The further a galaxy was from the Milky Way, the faster it was moving away. Was there something special about our place in the universe that made us a center of cosmic repulsion?

Astrophysicists readily interpreted Hubble’s relation as evidence of a universal expansion of the universe. The distance between every pair of galaxies in the universe was getting bigger with time, like the distance between raisins in a baking loaf of raisin bread. An observer on ANY galaxy, not just our own, would see all the other galaxies traveling away, with the furthest galaxies traveling the fastest.

This was a remarkable discovery. The expansion is believed today to be a result of a “Big Bang” which occurred between 10 and 20 billion years ago, a date which we can calculate by making measurements like those of Hubble, as we will do in this lab.

Figure 1: The Hubble Law

Technique

The software for the CLEA Hubble Redshift Distance Relation laboratory exercise puts you in control of a large optical telescope equipped with a TV camera and an electronic spectrometer. Using this equipment, you will determine the distance and velocity of several galaxies located in selected clusters around the sky. From these data you will plot a graph of velocity (the y-axis) versus distance (the x-axis).

How does the equipment work? The TV camera attached to the telescope allows you to see the galaxies, and “steer” the telescope so that light from a galaxy is focused into the slit of the spectrometer. You can then turn on the spectrometer, which will begin to collect photons from the galaxy. The screen will show the spectrum—a plot of the intensity of light collected versus wavelength. When a sufficient number of photons are collected, you will be able to see distinct spectral lines from the galaxy (the H and K lines of calcium), and you will measure their wavelength using the computer cursor. The wavelengths will be longer than the wavelengths of the H and K labs measured from a non-moving object (397.0 and 393.3 nanometers), because the galaxy is moving away and so its light is “redshifted.” The spectrometer also measures the apparent magnitude of the galaxy. So for each galaxy you will have recorded the redshift of the H and K lines and the apparent magnitude.

From the data collected above, you can calculate both the speed of the galaxy from the Doppler-shift formula, and the distance of the galaxy by comparing its known absolute magnitude (assumed to be (-21) for a typical galaxy) to its apparent magnitude. The result is a velocity (in km/sec) and a distance (in mega parsecs, Mpc) for each galaxy. The slope of the straight line relating velocity to distance will give you the value of Ho , the Hubble Parameter, which is a measure of the rate of expansion of the universe. Once you have Ho , you can take its reciprocal to find a rough estimate of the age of the universe.

Procedure:

1. Before getting any data, open Excel and start a table with the following column headers: “ Object Name”; “Abs. Mag. (M)”; “App. Mag. (m)”; “Dist. in pc”; “Dist. in Mpc”; “Redshift (z)”; “Speed of light (c)”; and “Vel. in km/s”. In the column for “Abs. Mag.” type , and in the column for “speed of light,” type 3E5.

2. Open the Hubble Redshift program by double clicking on the VIREO icon. Select File…Log in from the menu bar, and enter student names and the lab table number. Click OK when ready. The title screen appears.

3. Select File…Run Exercise...”The Hubble Redshift-Distance Relation” from the menu bar.

The Hubble Redshift Distance Relation program simulates the operation of a computer-controlled spectrometer attached to a telescope at a large mountain-top observatory. It is realistic in appearance, and is designed to give you a realistic feel of how astronomers collect and analyze data for research.

Notice that the dome is closed and tracking status is off. Select Telescopes...Optical...Access 4.0 Meter. Before you can access the telescope controls, a message appears notifying you that you have control of the telescope. Click OK to continue. The screen shows the view in the “warm room” at the observatory.

4. To begin our evening’s work, first open the dome by clicking on the dome switch. Then, click on Telescope Control Panel. The dome opens and we get a view through the finder scope. The finder scope is mounted on the side of the main telescope and points in the same direction. Because the field of view of the finder scope is much larger than the field of view of the main instrument, it is used to locate the objects we want to measure. The field of view is displayed on-screen by a CCD camera attached on the finder scope. Note that it is not necessary for astronomers to view objects through an eyepiece.

5. Also note that the stars are drifting in the view window. This is due to the rotation of the earth and is very noticeable under the magnification of the finder telescope. It is even more noticeable in the main instrument which has even a higher magnification. In order to have the telescope keep an object centered in the spectrometer opening (slit) to collect data, we need to turn on the drive control motors on the telescope. We do this by clicking on the tracking button. The telescope will now track in sync with the stars. Now, locate the View button on the control panel and note its status, i.e. finder.

6. We now need to find galaxies to study. And, to make a good Hubble Law plot we want many galaxies in different directions. Thirteen different fields for tonight’s observing session are stored in the observatory’s computer. To see these fields, select Slew...Observation Hot List…View/Select from List from the menu bar at the top of the control panel. You will need to select a galaxy from each of 12 fields and collect data with the spectrometer. Double click on the 4th field in the list (which is Coma Berenices at RA 12 hr 59 min and Dec. 27 deg 41 min). Press OK to move the telescope to the correct position. Notice that the telescope “slews” (moves rapidly) to the RA and DEC coordinates of the field selected. The view window will show a portion of the sky that was electronically captured by the charge coupled device (CCD) camera attached to the telescope.

The view window has two magnifications (see Figure 2): Finder View is the view through the finder scope that gives a wide field of view and has a red square which outlines the instrument field of view. Telescope View is the view from the main telescope with red vertical lines that show the position of the slit of the spectrometer. 7. Select telescope view and look for a galaxy, which should look different from the dot-like images of stars. Use the directional buttons (N, S, E or W) to “slew”, or move, the telescope to carefully position, in the slit, the galaxy you intend to use to collect data—any of the galaxies are suitable. Note that you can adjust the speed or “slew rate” of the telescope. (1 is the slowest and 16 is the fastest).

Figure 2: Field of View from the Finder Scope

8. When you have positioned the galaxy accurately in the slit, click on the Access button (to open a window for the spectrometer) and then click Go. You will see a spectrum developing. Click Stop and the spectrum freezes. The spectrum of the galaxy will exhibit the characteristic G, H, and K calcium lines. We must collect a sufficient number of photons to allow a reliable identification of the wavelength and so we need to “integrate” for some time before we can accurately measure the spectrum. The more photons collected, the less “noise” in the spectrum, making the absorption lines easier to pick out. To collect more data, press Go again (and then Stop).

9. Note that below the spectrum in the Spectrometer Reading window the “Object” and “App. Mag. (V). are listed.” Read and record these data in the appropriate column of the Excel data table.

10. When you’re happy with the spectrum select File...Data...Save Spectrum and then return to the main telescope window and select Tools...Spectrum Measuring, which opens a new window. In the Spectrum Measuring window, select File...Data...Load Saved Spectrum. Using the mouse, place the arrow anywhere on the spectrum, press and hold the left mouse button. Notice the arrow changes to a cross hair and the wavelength data appears at the top of the display. As you hold the left mouse button, move the mouse along the spectrum. You are able to measure the wavelength and intensity at the position of the mouse pointer.

11. Select Comparison Spectrum...Select...Absorption lines in a normal galaxies (H,K, & G band). Vertical lines corresponding to the rest wavelengths of three common absorption lines will appear in the spectrum. Identify the absorption features in your observed spectrum that displays the same pattern but are shifted to larger wavelengths. At the bottom of the window is a slider for adjusting the redshift (i.e. z). Click and hold the right arrow of the slider and watch as the vertical lines shift to the right. Stop when the comparison spectral lines line up perfectly with the observed absorption lines. Read and record the redshift.

12. Return to the Telescope Control Panel, select Slew...Observation Hot List, choose another field, and find another galaxy, and repeat steps 7 - 11. Record data on the Excel table for a total of 12 galaxies. NOTE: At higher radial velocities the spectral features at longer wavelengths may be redshifted out of the recorded spectral range. Measure only those lines for which you can accurately determine the line center. When this happens, in the Spectrometer Reading window you can select File...Preferences...Spectral Range and select larger wavelength to allow observations of all the lines. You may also find that the redshift slider doesn’t seem to go far enough. Click the recenter button just to the right and below the slider and then you’ll be able to move it further.

Calculating the Hubble Parameter

You will accomplish the following calculations using Excel, as explained by your instructor. For your report, though, you should understand the process of this analysis.

The distance of each galaxy is calculated using the “distance modulus” equation, i.e. m - M = 5 * log D(in pc) - 5 where m is the apparent magnitude, which describes how bright an object appears to us, which includes the apparent dimming due to distance, and M is the absolute magnitude, which describes how much light the object gives off intrinsically and is independent of its distance, and D is the distance of the object. The equation to yield distance is D (in pc) = 10(m – M + 5)/5

The recessional velocity of a galaxy is related to its redshift by v = c * z where c = 3x105 km/s.

The Hubble redshift-distance relation is a simple equation relating the recessional velocity of a galaxy to its distance, expressed as v (in km/s) = H * D (in Mpc), where H is the Hubble Parameter (in units of km/s per Mpc). This is the same equation as that of a straight line going through the origin (i.e. y=mx), where D is on the x-axis, v on the y-axis, and H is the slope. By plotting your data of v on the y-axis and D on the x-axis, then, the Hubble parameter is inferred by measuring the slope of the straight-line. Note, though, that D must be in units of Mpc (1 million pc).

13. In your Excel table, Click on the first cell in the column for “Dist in pc,” and then click in the horizontal space near the top (next to the fx) and insert the equation for calculating distance as explained by your instructor. Similarly, insert the equations for “Dist. in Mpc,” and “Vel.” as instructed.

As demonstrated by the instructor, click on the first cell for “Abs. Mag,” grab the lower right corner with the mouse and drag down for 12 rows. Do the same for “speed of light”, “Distance in pc,” “Distance in Mpc,” and “Vel.”

Select the columns for “Dist. in Mpc” and “Vel”, and Insert a Scatter Plot. Make sure that Vel. appears on the y-axis and Dist on the x-axis. You should get a graph showing a straight line slanted upward. Fit a straight line and determine the slope by doing the following. i. Right-click on a data point, ii. Click on Add Trendline, Select Linear, iii. Check Select Intercept at Zero, and check Display Equation on Chart, Click close, iv. The Hubble Parameter H is the slope, shown in the equation as the coefficient of x.

Print a copy of the graph for each person. Data Sheet (if desired, instead of Excel) Speed of Abs Mag App Mag Distance in Distance in Redshift Object Name light in Velocity M m pc Mpc (z) km/s in km/s -21 3E5

-22 3E5

-21 3E5

-21 3E5 Name:______Worksheet for Determining the Age of the Universe

Show all your work! 1. Record your value for the Hubble Parameter on the line below.

Using the Graph: Average Value of H = ______km/sec per Mpc.

2. The Hubble Law, equation, can be used to estimate the age of the universe (ignoring any change of velocities in the history of the universe). Using your inferred value of H determined from your graph, calculate the recessional velocity of a galaxy which is 100 Mpc away.

V = ______km/sec Verify this velocity on your Hubble diagram by reading the y-axis value for a distance of 100 Mpc.

3. You now have two important pieces of information: 1. How far away the galaxy is. 2. How fast it is moving away from us.

You can visualize the process if you think about a trip in your car. If you tell a friend that you are 120 miles away from your starting point and that you traveled 60 miles per hour, your friend would know you had been traveling TWO hours. That is, your trip started two hours ago. You know this from the relationship:

Distance equals Velocity * Time, which we can write as

D = V * T or T = D / V

In this case, 2 hrs = 120 mi / 60 mi per hr

Now let’s determine when the universe “started its trip”. We have a distance of 100 Mpc. But, first convert Mpc into km (because the velocity is in km/sec).

D = ______Mpc * (3.09x1019 km/Mpc) = ______km

4. Using the speed-time-distance equation, i.e. T=D/V, determine how many seconds ago the universe started:

T = ______km / ______km/s = ______secs

5. There are about 3.16 x 107 seconds in one year. Convert your answer into years:

T = ______secs / (3.16x107 secs/year) = ______years

6. Therefore, the age of the universe is approximately ______billion years old. Useful Equations and Quantities

M = m + 5 – 5 * log D vK = c *  measured - 

c = 3 x 105 km/sec D = 10 (m – M + 5) / 5

1 pc = 3.09 x 1013 km 1 Mpc = 1 x 106 pc 1 Mpc = 3.09 x 1019 km

For your lab report:

Turn in the Calculating-the-Age-of-the-Universe worksheet, your Excel table, graph, and answers to the following the questions on a separate sheet of paper.

1) a) What is the Hubble Diagram? b) What is the vertical axis? c) What is the horizontal axis? d) What does the graph look like, when data points for distant galaxies are included?

2) What is Hubble's law? Give your answer as an equation, but also explain it in words. Make sure to identify the name of each symbol in the equation.

3) What remarkable fact does Hubble's law tell us? Explain.

4) Does Hubble's law mean we are at the center of the universe? Why or why not?

5) a)What is Hubble's constant? (In words, not numbers). b) What are the usual units given for Hubble's constant? c) What value did you get in this laboratory exercise? (should include units) d) What is the "accepted value" according to recent studies (it’s ok to check textbook or the web, but cite your source; is it a recent and reliable source?)

6) a) What key assumption did we make when estimating the age of the universe? b) How is our estimate for the age of the Universe related to Hubble's constant? (This is a formula). c) How does your inferred age compare to what we believe the correct age is? (13.6 billion years) Why might these values differ?