The Hubble Redshift

Transcript

OFFICIAL USE ONLY Name_____________________ The Hubble Redshift-Distance Relation Student Manual to Accompany the CLEA computer exercise 1 Historical Background One of the most important discoveries in the 20th Century was that virtually all the galaxies in the universe (with the exception of a few nearby ones) are moving away from the Milky Way galaxy. This curious fact was first discovered in the early 20th Century by astronomer Vesto Slipher, who noted that absorption lines in the spectra of most spiral galaxies had longer wavelengths (were “redder”) than those observed from stationary objects. Assuming that the redshift was caused by the Doppler shift, Slipher concluded that the red-shifted galaxies were all moving away from us. In the 1920’s, Edwin Hubble measured the distances of the galaxies for the first time, and when he plotted these distances against the velocities for each galaxy he noted something even stranger: the further a galaxy was from the Milky Way, the faster it was moving away from the Milky Way (see Figure 1). 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. The distance between all galaxies in the universe was getting bigger with time, like the distance between dots painted on an expanding balloon. 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. The rate of expansion of the universe tells us how long it has been expanding. We determine the rate by plotting the velocities of galaxies against their distances, and determining the slope of the graph (see Figure 1), a number called the Hubble Parameter, Ho, which tells us how fast a galaxy at a given distance is receding from us. So Hubble’s discovery of the correlation between velocity and distance is fundamental in reckoning the Figure 1: A graph of Hubble’s measurements showing the velocity of a galaxy compared to its distance from the Milky Way. history of the universe. Using modern techniques of digital astronomy, we will repeat Hubble’s experiment. The technique we will use is fundamental to cosmological research these days. Even though Hubble’s first measurements were made three-quarters of a century ago, we have still only measured the velocities and distances of a small fraction of the galaxies we can see, and so we have only small amount of data on whether the rate of expansion is the same in all places and in all directions in the universe. The redshift distance relation thus continues to help us map the universe in space and time. 2 Summary of the Technique The software for the CLEA Hubble Redshift Distance Relation laboratory exercise will use the Virtual Educational Observatory (VIREO) that puts you in control of a large optical telescope equipped with an electronic spectrometer. Using this instrument, 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 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 (3970 and 3933 Ångstroms), because the galaxy is moving away. The spectrometer also measures the apparent magnitude of the galaxy from the rate at which it receives photons from the galaxy. So for each galaxy you will have recorded the wavelengths of the H and K lines and the apparent magnitude. From the data collected using the virtual telescope, 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 megaparsecs –or– Mpc) for each galaxy. The galaxy clusters you will observe have been chosen to be at different distances from the Milky Way, giving you a suitable range to see the straight line relationship Hubble first determined. The slope of the straight line 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 the age of the universe. The details of the measurements and calculations are described in the following sections. Using the Hubble Redshift Program Welcome to the observatory! We will simulate an evening’s observation during which we will collect data and draw conclusions on the rate of expansion of the universe. We will gain a proficiency in using the telescope to collect data by working together on the first object. Collecting data for the other 12 objects will be left to you to complete the evening’s observing session. Then you will analyze the data, draw your conclusions, and use the information to predict the age of the universe. Let’s get started! 3 Installing and Running the CLEA VIREO Software 1. Download the VIREO software package from the class website. 2. Double click on the install icon or file name and a self-extracting program will run. This program will install the software on your computer. Follow the instructions that are shown to you. 3. Once the program is finished installing, there will be an icon located on your desktop that looks like this: Starting the VIREO: Hubble Redshift-Distance Relation Program 1. Open the VIREO program by double-clicking on the VIREO icon (shown above) on your computer desktop. The first screen should look like this: 2. You must first select “File” from the menu before taking data. Choose the “Login” option. A pop-up window will appear that looks like this: DO NOT ENTER ANYTHING IN THIS WINDOW! 4 Click “OK” to continue. The program will show you a warning box that looks like this: Click “OK” and continue. 3. The next screen will look like this: 4. Click on “File”. Choose the “Run Exercise” option. Then select the “The Hubble Redshift-Distance Relation” option. 5. The next screen will look like this: 6. Click on “Telescopes”. Choose “Optical”, then choose “Access 4.0 Meter” The next screen will look like this: Click “OK” to continue. 5 Open the Observatory Dome Click on the Open/Close button: The telescope dome will open (there will be an audible sound while it opens). Then click on the “Telescope Control Panel” button: The next pop-up window will look like this: This is the VIREO Optical Telescope Control Panel. 6 VIREO Optical Telescope Control Panel Options: TRACKING Turns on/off the telescope drive. Turning tracking ON causes the telescope to counteract the effect of the Earth’s rotation and is necessary in order to take measurements. Turning tracking OFF allows the star field to drift through the field of view as the Earth turns. SLEW RATE Controls the rate of telescope movement when the N, S, E, W direction controls are pressed. The slew rate can be set to 1, 2, 4, 8, or 16. The larger the number, the faster the movement rate. Slow speeds are useful for centering a galaxy on the slit. Faster rates are useful for quickly moving around the field of view. N, S, E, W Directional controls. Click one of these buttons to cause the telescope to move north, south, east, or west. When the telescope is moving, a red light next to the direction button glows. Movement in the selected direction continues until the same button is clicked again, or a different direction button is similarly selected. RIGHT ASCENSION Displays the celestial coordinates of the center of the field of view. Right Ascension is displayed in hours, minutes and seconds. DECLINATION Displays the celestial coordinates of the center of the field of view. Declination is displayed in degrees, minutes and seconds. VIEW Select FINDER to see a wide angle view of the stars. The red square identifies the field of view when in the TELESCOPE mode. The TELESCOPE mode shows a close-up of the star field. INSTRUMENT This setting allows you to choose the instrument that you will be using with the telescope. In this exercise we will be using the spectrometer. To prepare to take the required measurements, you will need to have the Control Panel adjusted to the following settings: SLEW RATE = “4” VIEW = “FINDER” INSTRUMENT = “SPECTROMETER” The Spectrometer: The Hubble Redshift-Distance Relation program simulates the operation of a computer-controlled spectrometer attached to a telescope at a large mountain-top observatory in Arizona. A spectrometer is the instrument that takes starlight and breaks it down into its component colors (a.k.a. its “rainbow”). This allows astronomers to see and measure the absorption or emission lines that come from the object. These lines contain many different pieces of information about the object. The spectrometer used in this virtual observatory is realistic in appearance, and is designed to give you a good feeling for how astronomers collect and analyze data for research. 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 on7 screen by a CCD camera attached on the finder scope (it is not necessary for astronomers to view objects through an eyepiece anymore.) Notice that the stars are drifting in the view window. This is due to the rotation of the Earth and is very noticeable under high 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 over the spectrometer opening (slit) to collect data, we need to turn on the drive control motors on the telescope. Procedure In this section, you will be walked through the procedure of how to move the telescope, take readings and record your data for each galaxy. You will then repeat these steps for all of the remaining galaxies on the observing list. 1. Turn on the Tracking Telescopes are equipped with a motor drive which moves the telescope in a direction opposite to the rotation of the Earth and at the same rate. The motor (often called the telescope’s clock drive) cancels the effect of the Earth’s rotation and the galaxies seem to stand still permitting extended study. Click on “Tracking” and note how the stars cease to drift. You must have the telescope tracking on before you can operate the spectrometer. Once the tracking is turned on, the directional controls can be clicked to move the telescope around in the sky (see the figure to the right). The red square in the center of view is the field of view seen by the spectrometer when you switch to the TELESCOPE mode. The directional controls, N, E, S, W, move the telescope with respect to the sky. Moving the telescope to the west appears to make the stars move to the east. Try it. The SLEW RATE control adjusts in steps and changes how much the telescope is moved when the directional controls have been activated. Try various settings of the SLEW RATE and move the telescope around in all directions. 2. Move the Telescope to a Galaxy You must now move the telescope to one of the galaxies on our list. To do this in the Optical Telescope Control Panel click on the “Slew” button along the top menu. Then choose “Observation Hot List” then “View/Select from List”. The pop-up menu will list all of the galaxies in order. The items you see are the fields that contain the galaxies we have selected to study tonight. An 8 astronomer would have selected these galaxies in advance of going to the telescope. Select the first galaxy from the list by double-clicking the choice. A pop-up screen (shown to the right) will appear. No changes are necessary, click “OK”. A confirmation screen will appear: Click “Yes” and the coordinates will be automatically entered into the Optical Telescope Control Panel and the telescope will move to the coordinates (you will hear a sound). On the Optical Telescope Control Panel, move the “View” switch to “Telescope” and you will see the faint galaxy inside of two red lines (this is the spectrometer slit that allows light into the spectrometer): The more light you get into your spectrometer, the stronger the signal it will detect, and the shorter will be the time required to get a usable spectrum. Be sure that the spectrometer slit is on the brightest portion of the galaxy. If the slit is positioned on the fainter parts of the galaxy, you are still able to obtain a good spectrum but the time required will be much longer. If the slit is completely off the galaxy, you will just get a spectrum of the sky, which will be mostly random noise. If necessary you can move the telescope (and hence move the slit) by using the N, S, E, W control buttons. You are now ready to take your first observational measurement (described in the next section). 9 3. Switch the telescope to Spectrometer Mode When you are in the Spectrometer mode, the two red lines represent the slit on the spectrometer. This slit allows a narrow beam of light from the galaxy to enter the instrument (see the figure above). The computer program you will use is a realistic simulation of a spectrometer attached to a moderate sized research telescope. The telescope is controlled by a computer that allows you to move from galaxy to galaxy and make measurements. To access the spectrometer, in the Optical Telescope Control Panel make sure that the Instrument setting is on “Spectrometer” and press the “Access” button. The pop-up screen will look like this and is the Reticon Spectrometer Reading: If the galaxy is positioned accurately over the slit, click on the “Go” button on the Reticon Spectrometer Reading window. The screen will then begin to fill with data and will look like this: The yellow dots are the data that the spectrometer is gathering and represents a graphical version of an absorption-line spectrum of the galaxy. Be sure to let the process run until the Signal to Noise Ratio is at least 100 or more. This can sometimes take several minutes to get above 100. Click “Stop” once the S/N ratio is above 100. 10 4. Recording the Data On the data sheet (located at the end of this manual) record the following information from the measurement: Object (Name) Photon Count App. Mag (V) 5. Saving the Data Once you have recorded the data for this galaxy, click on “File→Data→Save Spectrum”. A window will appear that will allow you to save your data. Leave the file name as the default object name. Click “Save”. You can now click on the “X” in the upper right corner to continue to the next galaxy (a warning pop-up will remind you to save your data if you did not save it in the last step). REPEAT STEPS 2 - 5 UNTIL YOU HAVE GATHERED DATA FROM ALL OF THE GALAXIES ON THE TARGET LIST. Analyzing the Data We are about to analyze the data from each galaxy. We will be looking at the spectrum from the galaxy measured by the spectrometer. The spectrum of the galaxy will exhibit the characteristic H & K lines of the element calcium which would normally appear at wavelengths 3968.85 Å and 3933.67 Å, respectively, if the galaxies were not moving. However the galaxies are rushing away from us and so the H & K lines will be redshifted to longer wavelengths depending on how fast the galaxy is receding (based on the Doppler Effect). From the menu on the Observatory window choose “Tools→Spectrum Measuring”. The VIREO Spectrum Measuring Engine window will appear (shown to the right). 11 To open a saved spectrum, choose “File→Data→Load Saved Spectrum”. Choose the first object listed on your data sheet and click “Open”. The spectrum of the galaxy will now appear in the window of the VIREO Spectrum Measuring Engine. 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 in the upper left area of the window. 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. Hold the left mouse button and move the mouse so that the crosshair is located on the very bottom tip of the left absorption line of calcium (see the figure to the right). Once you are at the bottom you can let the mouse button go and a set of lines will appear to show you how well you made your measurement. The wavelength of the center of that line will be displayed as “Wavelength” in a box below and left of the spectrum. Record this number on the data sheet in the column titled “λK measured K line” Repeat this for the absorption line on the right. Record this number on the data sheet in the column titled “λH measured H line” IMPORTANT!! • It is important to be as accurate as possible with your measurements. • The calcium K-line is the always the line that is on the left, the calcium H-line is the line that is on the right. Repeat this process for each galaxy until you have gathered the wavelengths of both the K-line and H-line for each of the galaxies listed on your table. Working with the Data Once the data has been collected and recorded for all 13 galaxies, you are ready to make the required calculations. You can exit all of the windows and exit the VIREO program. You will need a pencil, a ruler, and a scientific calculator for the following steps. 1. Calculate the distances to the galaxies: Use the equation to the right to determine the distance to each galaxy on your data sheet. “M” is the absolute magnitude of the galaxy (use -21 for all calculations), and “m” is the apparent magnitude (found in column 5 of your data sheet). 12 Here is an example: log D = 15.6 − (−21) + 5 = 8.32 5 NOTE: Your answer will be the log of D. To get D, you must raise 10 to your answer (see below) Here is an example: 10(8.32 ) = 208,929,613 Your answer will be in units of distance called “parsecs”. Record your answer in column 6 of the data sheet. Repeat this for all 13 galaxies. 1. Converting the Distances Convert the distances from parsecs to Megaparsecs (1Mpc = 1 million parsecs) by dividing all of your answers in column 6 by one million (1,000,000). Record your answers in column 7 of the data sheet. Here is an example: 208,929,613 = 208.9 1,000,000 or 209 Mpc. 2. Determine the Velocities Determine the change in wavelength (∆λ) for each of your measured calcium H & K lines using the formulae below. ∆λ for calcium H and K lines are given to you on the bottom of your data sheet: ∆λ H = λ H Here is an example: measured − λH ∆λ K = λ K measured − λK ∆λ H = 4165.00 − 3968.85 = 196.15 Calculate the velocity that each galaxy is rushing away from the Milky Way using the formulae below. “c” is the speed of light and the value is found on the bottom of your data sheet. You will measure a speed according to each of calcium absorption lines: VH = c × Here is an example: VH = c × ∆λH λH VK = c × ∆λK λK 196.15 = (299,000)(0.04942) = 14,777 km sec 3968.85 Finally, average the velocity for the H-line and the velocity for the K-line for each galaxy and record your answer in column 14 of the data sheet. Repeat this for all galaxies listed on your data sheet. 13 Creating Your Graph Using the graph paper provided at the end of this exercise, create a graph that plots the average velocity of each galaxy (column 14) versus distance to each galaxy in Megaparsecs (column 7). Determine the Hubble Constant The Hubble Constant is a measure of how quickly the universe is expanding. It is found from the graph by determining the slope of the dots on your graph. a) Using a ruler, draw a straight line that goes from the origin (0,0) through all of the dots on your page. Don’t worry if the line does not go through each point, just draw a straight line that goes down the middle of all of the dots. b) Pick anywhere on the line and determine (1) the velocity at that point and (2) the distance at that point. c) Calculate the value for the Hubble Constant from the following equation: H= v D where H is the Hubble Constant in km/sec/Mpc v is the velocity measured from your line D is the distance measured from your line d) Record your value for the Hubble Constant on your data table in the space provided. e) Mark the point you used on your graph 14 Determining the Age of the Universe The Hubble Law equation can be used to determine the age of the universe. Using your value for H (from your data sheet), calculate the recessional velocity (v) of a galaxy that is at a distance (D) of 800 Mpc away: v = H ×D Velocity of a galaxy 800 Mpc away: ______________________km/sec You now have two important pieces of information: 1. 2. How far away the galaxy is. 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 = Rate (or velocity ) x Time which we can write as: or solving for T: as an example: T= D v 2 hours = D = v ×T (Equation 1) 120 miles 60 miles hour Now let’s determine when the universe started its “trip” (when it started to expand). The distance to the galaxy in the previous step is 800 Mpc. First convert Megaparsecs into kilometers because the rate, or velocity, is in km/sec. (The conversion from Mpc to km is on the data sheet). 800 Mpc = _____________________km Use equation 1 (above) and the velocity of this galaxy (at the top of this page) to determine how many seconds ago the universe started to expand: T = _____________________seconds 7 There are about 3.15 x 10 seconds in one year. Divide the age of the universe in seconds (above) by this number to convert your answer into years: T =_____________________ years This is the age of the universe in years. Congratulations, you are finished! Turn in the cover sheet with your name on it, this page, the graph, and the data table. 15 16 Object Name Abs. Mag. Photon Count M 1 -21 2 -21 3 -21 4 -21 5 -21 6 -21 7 -21 8 -21 9 -21 10 -21 11 -21 12 -21 13 -21 App. Mag.(V) Distance (in parsecs) (in Megaparsecs) m pc Mpc Distance Using your graph, and your measured slope to the line, the value of H is: λK measured λH measured K line H line ∆λH ∆λK Velocity H Velocity K Velocity Average km/sec km/sec km/sec H = ___________________ km/sec/Mpc Useful Equations and Numbers: log D = m−M +5 5 D = 10 log D vH = c × ∆λ H λH ∆λ vK = c × K λK ∆λ H = λ H measured − λH λH = 3968.85 ∆λ K = λ K measured − λK λK = 3933.67 1 Mpc = 3.09 x 1019 km C = 299,000 km/sec 1 Mpc = 1,000,000 pc 17