The following ALTERNATE DATA file “Expansion_Hubble Data PDF to answer questions.

Expansion Lab Question Hints PDF can be used to answer any questions.

The following resources are available if questions should arise.

YouTube: Live Lab Help Session Recording – Expansion Lab (Data Table & Hubble Plot)

YouTube: Live Lab Help Session Recording – Expansion Lab

Introduction

• Before Hubble, Vesto Slipher gathered observational evidence that except for the local group all galaxies have spectra with very large redshifts. This indicated that these objects moved away faster from us than anything else inside our Milky Way Galaxy. In 1929, Edwin Hubble independently determined the redshift and the distance of various galaxies. From the redshift he calculated the velocities with which the galaxies were moving away from us. He was the first to propose that these galaxies were each systems of hundreds of billions of stars and interstellar matter similar to the Milky Way Galaxy. Before Hubble, people believed that they were small nebulous objects which were part of the Milky Way Galaxy. Hubble plotted the recessional velocities versus the distances of the galaxies and fit a straight line to his data. The slope of this line is known ans the “Hubble Constant”.

◦ The Hubble Law: v = Hd, where v is the recessional velocity in units of km/s, H is the Hubble constant, and d is the distance in units of Mega parsecs or Mpc. This equation can be solved for the Hubble Constant by dividing both sides by the distance: H = v/d, its units will be km/s/Mpc.

• This lab will simulate observations of galactic spectra that you will analyze for the redshift of the H and K lines of calcium and for apparent magnitude. The redshift will yield the galaxy’s velocity and the apparent magnitude will allow you to calculate the distance. You will then plot your data and find the Hubble constant from the slope of your best fit line.

• Implications of the Hubble Law: All galaxies (except for members of the local group) are moving away from us. In fact, the greater the distance to a galaxy the faster it is moving away from us. This result implies that the universe is getting bigger! If we run the motion of galaxies in reverse (going back in time) we come to the conclusion that the universe had a beginning! We can estimate the age of the universe by taking the inverse of the Hubble constant. The units of the Hubble contant are in km/s/Mpc. You can convert the Mpc to km and then cancel out the km entirely. You are left with a number in units of 1/s. The inverse of this number is the age of the universe in seconds. This, in turn can be converted to billion years.

Procedures

• Start Up: Run the file “Clea_hub.exe”. The title page of the CLEA Hubble Redshift lab should come up. Click on “File”, then “Log in”. A window opens that prompts you for student names and a table number. It is enough to enter an arbitrary character in the field of the first student name and click ok. A window will ask you whether you are finished logging in, you can answer yes. Then you see the opening screen of the “Hubble Redshift Distance Relation” lab. Click on “File” and “Run”. The telescope control screen will open. Once you have control of the telescope, click “ok”, then click on “Dome”. The setting of the dome will change from closed to open. A field of stars and galaxies will come into view that slowly shifts due to the Earth’s rotation. Click on “Tracking”, so that the telescope will eliminate the effect of Earth’s rotation and track a point in the sky of your choosing.

• Maneuvering the Telescope: The thin red square in the field of view indicates the finder of the telescope. Use the direction buttons to move the telescope such that a galaxy is centered in the finder. The “Slew Rate” indicates how fast the telescope will move. By clicking on it repeatedly you can change the slew rate to faster or slower settings. Once you have a galaxy centered within the finder, click on “Change View”. This will switch the finder with the instrument, a spectroscope, that will take the spectrum. In the field of view the red square changes to two parallel red lines that symbolize the narrow slit of the spectroscope. You may have to readjust the telescope so that the slit is centered on the brightest portion of the galaxy.

• Taking Data: There are a total of six fields of galaxies one of each you need to measure. Once you have adjusted the slit of the spectroscope to the desired position, click “Take Reading”. The window that opens up shows a graph plotting intensity vs. wavelength. When you click on “Start/Resume Count”, the spectrometer will start receiving data points which are instantly plotted on the graph. Clicking on “Stop Count” will stop the data taking and a continuous curve will be plotted through the data points. If you still cannot discern the H and K absorption lines (they are dips in the overall intensity) you can click on “Start/Resume Count” to continue taking data. The further away the galaxy the more “noisy” the data will look like. The data points will be more scattered and the absorption lines harder to discern. Fewer photons are coming in so you’ll have to wait longer to reach a certain number of photons (collect at least 50,000). The further away, the more redshifted the lines are which means they will move to longer wavelengths. When you are sure you can see the lines clear enough click on the minimum of each line to see its wavelength and intensity. From the data below the graph, record the object, photon count, apparent magnitude, and the wavelengths for the H and K lines. The K-line will be the one at shorter wavelength, the H-line at longer wavelength just to the right of the K-line. For the nearby galaxies, you may see a third line at even longer wavelengths called the “G” band (it results from the molecule methane). If you like you can click on “Record Data” and enter, save, and or print your data. Once you’re done with processing the data, click “Return” and a window will pop up to remind you that you’ll lose your spectrum when you return. If you have recorded your data at least on paper you can click “Ok”. To get to the next galaxy field you need to click on “Change View” to change your telescope back to the finder. This releases the “Field” option at the top menu bar which you now select. The field you just studied is still highlighted. Click on another one, then “Ok” and the next field will be loaded. You need to gather spectra from one galaxy in each field to fill in the table.

• Analyzing Data: You can assume that all the galaxies you see would be about equally luminous if you saw them side by side. Their differences in brightness are due to their distance from Earth. Take their absolute magnitude (M) to be 22. You’ll also need the rest wavelengths of the H and K lines of Calcium: 8 K = 3933.7D and 8 H = 3968.5D .

◦ In column 4 of the data table you will calculate the distance of the galaxies. You can use: M = m + 5 – 5logD, where M and m are absolute and apparent magnitudes, respectively, and D is the distance of the galaxy. You can solve this equation for D by subtracting m + 5 from both sides, divide by -5 and then use both sides as the exponent to base 10. The last step will remove the log and D will be isolated: 10(m + 5 -M)/5 = D. This will give you the distance in parsecs, pc.

◦ Column 5 requires the distance in Mpc. Use this conversion factor: 1Mpc = 106pc.

◦ In column 8 and 9 you calculate the recessional velocity of the galaxy based on the redshift of the wavelengths you measured for the H and K lines of Calcium. You can calculate the redshift for each line using ) 8 = 8 measured – 8 rest, then plug that into the formula for the Doppler Shift, v/c = ) 8 /8 rest. This can be solved for the recessional velocity by multiplying both sides by c: v = c ) 8 /8 rest.

◦ Column 10 is the average of column 8 and 9: vaverage = (vH + vK)/2.

◦ Graphing your data: use the graph on page 235 (last page of manual) to plot you data. The average recessional velocity values from column 10 are the values for the vertical axis and the distance values from column 5 go on the horizontal axis. Use a ruler and draw a straight line through the origin and as close to the majority of the data points as you can. DO NOT connect the dots.

◦ You must submit the completed graph. There are three ways you can get a copy of the completed graph to me: 1) send it through regular mail: c./o. Ulrike Lahaise, 3251 Panthersville Road, Decatur, GA 30034. 2) fax it to me: (404)244-5937, 3) scan it in and send it as an attachment to a private mail message.

◦ Calculation Hints for Answering Questions:

▪ Q1: The average value of the Hubble constant is the slope of your graph. Pick one point on the line that is easy to read, for example, where the line intersects gridlines. The other point is the origin (0,0). That makes it easy to calculate the slope as H = velocity value/distance value.

▪ Q2: Use the Hubble law to calculate the recessional velocity of a galaxy that is 800Mpc away: v = your value from Q1 x 800Mpc.

▪ Q3: Conversion of 800Mpc to km. Use the following conversion factors: M stands for Mega = 106, 1pc = 3.26ly, 1ly = 300,000km, 1 year = 3.15 x 107s.

▪ Q4: Knowing the distance and recessional velocity of the galaxy you can calculate how much time it needed to get to its current position. This is the time the universe has been in existence. You can use the simple relationship that distance = velocity x time or d = vt. Solving this for t by dividing both sides by v yields: t = d/v. Plug in your value from Q1 for v, your value from Q3 for d, and you get the age of the universe in seconds.

▪ Q5: Convert the age of the universe to years by using the conversion factor 1 year = 3.15 x 107s.

▪ Q6: Recalculate the age of the universe for galactic distances that are smaller by a factor of 10 with the same velocities. Think about it. All quantities you’ve calculated have been products or quotients. Changing one number by a factor of 10 will also change the others to either ten times smaller or larger. If your numbers are in scientific notation you can do that by changing the power of ten to one more or one less. You just need to figure out which way.

▪ The Hubble constant was calculated as the quotient of velocity in the numerator and distance in the denominator. The distance is going to be ten times smaller in the denominator.

▪ The age of the universe in seconds was calculated by dividing distance by velocity. This time the ten times smaller distance is in the numerator.

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▪ To convert into the age of the universe into years you just multiplied the age of the universe in seconds by a number. So, whatever change you made for the age of the universe in seconds will be the same for the age of the universe in years.