PHYS133 Lab 7 Goals: Measure brightness of various stars in the Pleiades star cluster in two different wavelength bands. Create an HR diagram based on the data taken. Use the distance modulus to determine the distance to the cluster. Convert the apparent rotation rate of the Sun into the sidereal rate of rotation of the Sun. Explore how the rotation rate of the Sun depends on latitude. What You Turn In: Your HR Diagram. Calculations to determine the distance to the cluster. Answers to the questions in this manual. Background Reading: Background reading for this lab can be found in your text book (specifically, Chapters 12 and 13) and the notes for the course. Equipment provided by the lab: Computer with Internet Connection Project CLEA program VIREO Equipment provided by the student: Pen Calculator UDel Physics 1 of 10 Fall 2017
Background: Photmetry is the measurement of how much light (i.e. how many photons) are received in a given period of time. This is the most accurate way to determine the brightness of objects. Photometry is classically (and most accurately) done with a photomultiplier attaced to a telescope. This works by the photoelectric effect, which was first explained by Albert Einstein (for which he received his Nobel Prize). What happens is when a discrete particle of light, called a photon, strikes a senstive plate, the plate emits an electron which is accelerated through a series of electric fields. This creates a small but measurable electric current which is what is the output which is directly proportional to the light received. So, we can use the photomultiplier to tell us how bright an object is. What is more interesting, is that we can place filters before the light strikes the photomultiplier. The computer program you will use is a realistic simulation of a UBV (Ultraviolet/Blue/Visual) photometer attached to a moderate sized research telescope. The telescope is controlled by a computer that allows you to move from star to star and make measurements. Different filters (Ultraviolet, Blue and Visual) are selected for each observation, and the integration time (the length of time the photometer samples the starlight) may be adjustable. The computer also does much of the busy work needed to convert photon counts into apparent magnitude and provides an estimate of the quality of the collected data. You will use this instrument to collect data on 24 stars in the region of the Pleiades star cluster. The apparent magnitudes will be measured for each star, in each of three colors. We will assume all of these stars are approximately the same distance away. This is a necessary and reasonable assumption because all of the stars are members of the same cluster. If we did not make this general assumption, the apparent magnitudes of the stars would also depend on their individual distances, an effect we cannot easily take into account in this lab. From this information, you will plot a Hertzsprung Russell (H R) diagram which will display the apparent magnitude of the cluster of stars as a function of their color index. The color index, B V, is the apparent blue magnitude (B) minus the apparent visual magnitude (V). For your H R diagram, plot the calculated B V data on the horizontal x axis, and apparent magnitude on the vertical y axis using graph paper. Recall that the dimmer a star is, the greater the apparent magnitude number. Bright stars have a small apparent magnitude number; in fact, very bright stars actually have negative apparent magnitudes. Plot your y axis in such a way that zero magnitude is at the top, and 25th magnitude (a very dim star indeed) is at the bottom. The x axis should range from 0.4 on the left to 1.8 at the right. Figure 1 is an example of the H R diagram. Figure 1 a. Paper Graph b. Plastic Graph The H-R Diagram UDel Physics 2 of 10 Fall 2017
Lay out your graph as shown at the bottom of the previous page in Figure 1 (a). Expand this miniature example so it occupies most of a sheet of paper. Be sure the y axis runs from 0 at the top to 25 at the bottom as shown in the example. Creating too small a graph will make it difficult to plot the data accurately. It is very important that the scales be identical on both graphs. You will then align the main sequence with absolute magnitudes to plotted stars. Knowing the apparent and absolute magnitude of a star, you can determine its distance (in parsecs) from the equation: d 5/5 10 m M (1) where m = the apparent magnitude, M = the absolute magnitude, d = the distance in parsecs This is known as the Distance Modulus. Procedure Open the CLEA lab titled VIREO by double clicking on the Icon labeled VIREO. 1. Click on File > Login. Enter the names of each group member and click OK and then YES. 2. Click on File > Run s of Star Clusters. 3. Click on Telescopes > Optical and access the 0.4m telescope. 4. On the Main screen select File > Cluster Data and then click on File. a. Select View/Select Cluster from list b. Select a cluster to view (e.g. M45 Pleiades) from the list and the click Selection > Add Cluster to Current Hot List, then click List > Close. c. You can click Cancel at this point. 5. Open the Dome and Turn the Telescope Control Panel On. UDel Physics 3 of 10 Fall 2017
6. The telescope control panel will open (see below) a. You must turn Tracking On in order to have the telescope stay pointed at the same place in the sky (i.e. compensate for the Earth s rotation). b. You can move the telescope by pressing the N, W, S, or E buttons. c. By default your are looking through the finder scope, you can change this by switching the View (right hand side). The central red box in the Finder view shows the field of view of your telescope. The small circle in Telescope view shows what data will be taken. d. There are various instruments for taking data. We will use the Photometer. 7. Move the telescope to its first target by selecting Slew > Observation Hot List > Select from List. The stars from the cluster you added will be listed. a. Right Click on target star and choose Slew to Selection. b. Click OK in the Sky Coordinates box and confirm the slew. This moves the telescope to the target star. 8. Switch from Finder to telescope view. The star should be centered in the Photometer. 9. Access the Photometer. a. You will need to move the telescope to a blank portion of sky to get a background sky count (why?) b. You can leave the Integration time at 1s, but you should change the number of integrations to 5. This means it will make five one second measurements. UDel Physics 4 of 10 Fall 2017
c. You will need to make a sky count for the B and V filters. This only needs to be done once. Select the appropriate filter and click Start. d. You now have a sky reading which is the level of background brightness that will automatically be removed from the brightness of your objects. e. Slew back to the target and take B and V filter photometry for these objects. The computer will automatically convert the actual amount of photons counted (the brightness in raw counts), subtract out the sky value and then convert to the magnitude scale: m B F B F V 2.5log mv 2.5log F B,0 F V,0 Where the flux observed in the B and V bands (F B and F V ) is compared to the standard for a star of zero magnitude (F B,0 and F V,0 ) as shown. f. Use the File > Data > Record/Review to save the data. g. Slew to the next object on your list and repeat the photometry. You will not need to do the sky again, just get the B and V photometry of each star in the list. h. Complete the B and V photometry for at least 25 stars (should take less than thirty minutes). i. Watch out for more than one star is inside the photometry circle. You will either need to change the aperture size or skip it. (Why?) 10. Close the photometry window 11. Go to Tools > Results Editor > Observational Results and Save your data to a file in case the system has a problem. If the PC needs to be rebooted, copy/email this file elsewhere so you do not need to go through the data taking procedure again. 12. Print out our data table to include with your lab (Tools > Results Editor > Observational Results) This will conclude the data taking part of the lab. UDel Physics 5 of 10 Fall 2017
Analysis 1. On the main window, select Tools > HR Diagram Analysis. The system will automatically plot the brightness (in visual magnitude in the V band) vs. the (B magnitude V magnitude) value. Remember from class that B V color gives the difference in light coming in from the blue band and green bands. As can be seen in the diagram to the right, more light passes through the B band than the V band for the star shown. However, this is temperature dependent, so if we make the reasonable assumption that the photosphere of the star can be approximated by a blackbody. This temperature is approximated by Ballesteros formula: 4600K 1 1 T 0.92( BV ) 1.7 0.92( BV ) 0.62 In practice, we can just make the horizontal axis the B V magnitude values. 2. You will now see an HR diagram akin to that shown to the right. Yours will be different depending on the cluster you have chosen! 3. Select Tools > Zero Age Main Sequence. A main sequence curve appears. You can use the scroll bars on the right and bottom to align this as carefully as you can to your plotted data. 4. Record the V MV value on your data sheet. This is the difference between visual magnitude and absolution magnitude of your stars in the V band. 5. Use this value to calculate the distance to your cluster using the distance modulus: 5/5 10 m d M where m M is the value recorded in step 4 and the resulting distance is in parsecs. 6. Compare this to a value for the distance to the cluster you find from some resource (online, book, etc.) make sure you include your source. UDel Physics 6 of 10 Fall 2017
7. Use the Tools > Isochrones tool to determine the age of your cluster by when the main sequence turnoff occurs. a. Use all three parameters Log(age/yr), Adjust B V and Metallicity to find the best fit for the cluster s age. b. Record this value (given in Gyr) in the upper right box. 8. Looking at your HR diagram, there are clearly some stars off in the Red giant/supergiant range. Identify them by using the B V color and V magnitudes. Print out your data tables, diagrams and analysis and attach to your Write up! UDel Physics 7 of 10 Fall 2017
Names: Section: Date: 1. Name of your star cluster (should not be the Pleiades unless directed by your TA:. 2. Prior to turning on tracking, answer the following question: The Earth rotates to the and the stars drift to the. 3. Sky Readings: Filter B V Mean Sky (Counts/sec) 5/5 4. Using the distance modulus equation, 10 m d M, in the Introduction to calculate the distance to the cluster in parsecs. Then convert your answer to light years. Show all work in the space provided. V M v = m M Distance to cluster: parsecs UDel Physics 8 of 10 Fall 2017
Distance to cluster: light years 5. Possible Red Giant Stars: Star ID RA DEC 6. Are there any other curious stars in your HR diagram. If so note them and describe what they most probably are and your reasons for those conclusions. UDel Physics 9 of 10 Fall 2017
7. What is the age for your cluster and the parameters used to find it? Log(age/yr) Adjusted B V Metallicity Cluster Age 8. Using only your graphs and results, calculate the apparent magnitude of the Sun if it were located in the Pleiades cluster. Explain your procedure in a narrative, and show all your math. HINT: You ll need the absolute magnitude of the Sun. The Sun is a type G2 star with a B V of about +0.62. Now, you can use the clear plastic graph to estimate its absolute magnitude. MAKE SURE YOU ATTACH ALL DATA SHEETS AND GRAPHS UDel Physics 10 of 10 Fall 2017