Star Cluster Photometry and the H-R Diagram

Transcription

1 Star Cluster Photometry and the H-R Diagram Contents Introduction Star Cluster Photometry... 1 Downloads... 1 Part 1: Measuring Star Magnitudes... 2 Part 2: Plotting the Stars on a Colour-Magnitude (H-R) Diagram... 7 Discussion... 8 Appendix A... 9 Appendix B M80 Worksheet NGC 2420 Worksheet Introduction Star Cluster Photometry Star clusters may be open clusters or globular clusters. Photometry means measurement of brightness. The Hertzsprung-Russell (H-R) or colour-magnitude diagram is used for understanding the properties of stars. Most stars occupy the region of the H-R diagram along a band called the main sequence. The main sequence includes stars of all masses, ranging from cool red dwarfs to massive blue giants. The colour of a star depends on temperature at the surface of the star. Colours range from red (3000 degrees) through yellow (6000 degrees) to white (7500 degrees) and blue (30000 degrees). Stars on the main sequence are fusing hydrogen into helium in their cores. This process occurs in stars for most of their lifetimes. The Sun is in the middle of the main sequence it is a middle-sized, middle-aged star. The next concentration of stars on the H-R diagram is the horizontal giant branch. These stars are fusing helium into carbon or heavier elements in the core and hydrogen into helium in a shell surrounding the core. This process occurs in older stars and causes them to swell up, making them brighter, but also cooler and redder at the surface. In this exercise, students will plot an H-R diagram for an open cluster and a globular cluster and identify the relative ages of these clusters from their locations on the H-R diagram. Brighter stars are the easiest to see and dominate the colour of a cluster as a whole. Young clusters will appear relatively blue (dominated by blue giants on the main sequence) and old clusters will appear relatively red (dominated by red giants on the horizontal branch). Downloads From here you can download everything you need to get you started with the Star Cluster Photometry project. 1. Download and install Makali i This software will allow you to make measurements of the brightness of individual stars. It will save measurements to a.csv (comma-separated values) file that can be opened in Excel. 2. Download the image and spreadsheet files Save these files to your hard drive in a new directory (e.g. StarClusterPhotometry): M80-B.fits and M80-V.fits are images of a globular cluster in blue (B) and green (V or visual) light. NGC2420-B.fits and NGC2420-V.fits are images of an open cluster in B and V. StarClusterPhotometry.xls is a blank spreadsheet into which data from the.csv files will be copied and pasted for the purpose of generating the colour-magnitude diagram. Page 1

2 Part 1: Measuring Star Magnitudes Read through all the instructions in Part 1 carefully before you start. The objects imaged by the Faulkes Telescope for this activity were the open cluster NGC 2420 and the globular cluster M80. To discover the ages of these clusters you need to measure the colours of the stars. Images of these clusters were taken through coloured filters: Blue and Visible (V green). You will see that the files have names like M80-B.fits. This example means that this image is of M80 and the B means it was taken through a blue filter (the image is of the blue light emitted by the stars). Images you will see are all black-andwhite, but the stars will have different relative brightness when imaged through different filters. To find the ages of these clusters you need to measure a blue (B) and a visible (V) magnitude (brightness) for as many stars as possible in each cluster. Steps are: Find a reference star in each image that has calibrated magnitudes in both colours (B ref and V ref ). Appendix A supplies these data and explains how you could do this yourself. Use these reference values to calibrate the reference star. Calibrate the magnitudes of all the measured stars in the image. Do this for both the B and V images for both clusters. Plot a graph to work out the relative ages of the two clusters. 1. Viewing the first image M80-B.fits Start with the M80 files, and it may be easier to work in teams. Once you have read through this information you can divide up the tasks and be more efficient. Open the program Makali i (Subaru Image Processor). Then in Makali i open the image M80-B.fits. The image you open will look like Figure 1. You may not see the whole image displayed but there will be scroll bars on the right and the bottom of the display. Important: It is possible to change the image size, but for this activity it is important that you DON T CHANGE THE IMAGE SIZE, as this would affect the measurements. Figure 1: M80-B.fits as seen naturally with white stars on a black sky background. The reference star for this image is circled. Only part of the image is visible. Other parts may be viewed using the scrollbars on your image in Makali i. You will compile a list of B and V values for many stars in this cluster so you will need to assign a number to each star as you go so you can match up their B and V values. Star 1 is marked in Figure 2. You will use a larger version of Figure 2 as a reference chart. The larger version is found on the M80 Worksheet, included at the end of this manual. Keep the worksheet handy as you read through these instructions. Page 2

3 Figure 2: M80-B.fits, seen as astronomers view their images reversed with black stars on a white sky background. The reference star is circled and Star 1 is arrowed. When you make measurements on these images from now on it will probably be easier to view the images by selecting Grey Scale (Reverse) in the colour mode drop-down menu at the top left of the Makali i screen (see Figure 3). If that is not easy enough you could choose rainbow or another colour scheme. What extra information does rainbow give you? Figure 3: Grey Scale (Reverse) shows you black stars on a white background. Other options are also available. 2. Opening the photometry window Press and choose the Aperture button on the popup window. You should see something like Figure 4 on your screen and you will see your pointer is a target when you move it across the image. Important: Do not change any of the settings. Leave Radius on Auto and Search Centroid on 3 pixels. Figure 4: The photometry window Page 3

4 3. Measuring the reference star Using the mouse, centre your target pointer over the reference star (circled in Figures 1 and 2) and click once. You should now have some data for the reference star and you will see what is shown in Figure 5. The count value circled in the figure is count ref. Record this number on your worksheet. Figure 5: Measurement of data count for the reference star from M80-B.fits. 4. Measuring Star 1 Then place your target pointer over a different star in the cluster that you want to measure (use Star 1 labelled in Figure 2) and click once. Your data now looks like Figure 6. The count value circled in the figure is count star. Record this number on your worksheet. Figure 6: Measurement of data count for Star Calculating B magnitude of Star 1 Now you have the values count ref and count star. To calculate a blue magnitude (B star ) for Star 1, you need a formula that uses base-10 logs (log 10 or just log on a calculator). The equation is: B star = B ref! 2.5log count count You should be able to do this in your calculator and record the answer on your worksheet. Solution: B star = ! 2.5log = star ref This means that the star you have measured in the image above has a blue magnitude B = Cool, you ve done it!! Now read the next few steps to see what else you need to do and you ll find that there is an Excel spreadsheet to do all these calculations for you. Page 4

5 Note: you need to read all the instructions from Step 1 to 9 before you continue making star measurements. 6. Measuring more stars in M80-B.fits Now you need to repeat Step 4 above for as many stars as possible in M80-B.fits. 50 to 100 stars will produce a good H-R diagram. When you do this, make sure you don t go too close to the centre of the cluster where the light of many stars has blurred together and saturated the image. Write in the number of each star on the reference chart on your worksheet. Choose only stars that have distinct round images and are separated from other stars by a reasonable distance. If you think a measurement you make is not good you can press the remove button and delete it. Important: Stars will be numbered in order from 1 to however many you measure. This includes the reference star. Click on any line for Star 1 in the photometry window. Click Remove to delete the data for the reference star once you have recorded it on your worksheet. Then the stars you measure will have the same number that you assign them, i.e. Star 1 (from Figure 2) will be numbered 1 in the photometry window and in the.csv file. When you have finished measuring all your stars, click Print to save your data as a.csv file. This file will be named M80-B-Aperture.csv. This file will later be opened in Excel. You DO NOT need to calculate the magnitude for every star as in Step 5. Most of this will be done in Excel. 7. Measuring stars in M80-V.fits Repeat all the steps above for the visible image M80-V.fits, selecting stars in the same order using your labelled reference chart. Record data count values from Steps 3 and 4 on your worksheet. At Step 5, calculate the V magnitude of Star 1 using the equation: V star count = ! 2.5log count Important: You must carefully match the B and V values for each star in each image. The B value you measured for Star 1 must correspond with the V value for that same star. Using the reference chart in this document to write down which star is star 1, star 2, star 3, etc. is essential. Then the data will line up correctly when you start working with the spreadsheets. You should now have sets of B and V data for each image in two.csv files. 8. Calculating magnitudes of all the stars in Excel If you are thinking this activity is going to be a lot of boring calculations then think again! Open the spreadsheet called StarClusterPhotometry.xls. It has the above equations in it to do the calculations for you. You will also use it to plot your graph. Cells where you need to enter data are coloured yellow. Some cells contain formulas. You shouldn t change any of the formula cells at this stage. First you need to enter the B and V reference counts in cells J4 and J7, respectively. Then open M80-B-Aperture.csv, which should be in the same directory. You may need to display Files of type: All files (*.*) to see the file name. You will see many rows and columns of numbers. Your star numbers are in the first column. The counts you need should be way over in column Q under the heading Result Count. Highlight all the numbers in this column (the quick way is to click on the first number, press F8, then Ctrl + down arrow). Then Copy and Paste these numbers into the yellow cells in StarClusterPhotometry.xls, making sure the first entry is in cell C7 alongside the label for Star 1. When you have done this, you should see all the B magnitudes calculated under the heading B star. The first entry should match your manual calculation at Step 5. star ref Page 5

6 ASISTM Faulkes Telescope - Deep Space in the Classroom Then open M80-V-Aperture.csv and copy and paste your data into StarClusterPhotometry.xls in the yellow column starting at cell E7, as above. Note: When you have completed this you will see that the spreadsheet has calculated a B-V value for each star. 9. Measuring stars in Open Cluster NGC 2420 Now you need to repeat the process for the open cluster NGC 2420 (see Figures 7 and 8). The images you will use are NGC2420-B.fits and NGC2420-V.fits. You will see there is a separate worksheet in the Excel spreadsheet file for the calculations for this cluster. You will also need the NGC 2420 Worksheet. Note: Once you have lots of B and V magnitudes for M80 and NGC 2420 you can move on to Part 2. Figure 7: This image shows the whole cluster NGC Your image (Figure 8) is the area within the white box. The reference star is circled. Image Credit: WIYN / NOAO / NSF Figure 8: This image displays the file NGC2040-B.fits and shows the centre of the cluster within the white box in Figure 7. The reference star is circled. Figure 9: This shows you what your screen should look like once you have measured 100 stars. Page 6

7 Part 2: Plotting the Stars on a Colour-Magnitude (H-R) Diagram Read through all the instructions in Part 2 carefully before you continue. The spreadsheet should have calculated B-V values for all your stars in M80 and NGC B-V values are a quantitative measure of the colour of the star and the number B-V is called the colour index. Colour index values generally range from -0.6 to Question: Can you work out at which end of the colour-index scale you would find a red star and where you would find a blue star? Answer: Blue stars (more blue light than green light) have B-V values that are closer to zero or negative and red stars (more green light than blue light) have larger positive B-V values. If this is surprising to you, take a look at the magnitude scale below. Notice that on the magnitude scale, bright stars have small or negative magnitudes and faint stars have large positive magnitudes. The reason the scale works this way is because originally the brightest naked-eye stars were referred to as first magnitude. The limit of naked-eye visibility is about sixth magnitude. You can see fainter stars with a telescope. The magnitudes the spreadsheet calculates should all be somewhere around the magnitude of the reference star or fainter. In the magnitude scale, the closer to 0 the number is, the brighter the star is. Most or all of the stars should be fainter than the reference star and their magnitudes should be larger positive numbers (the magnitude scale is shown in Figure 10). Figure 10: The magnitude scale for stars. 1. Plotting data for M80 Astronomers make an assumption that all the stars in a cluster are at approximately the same distance, so their different brightnesses are due only to how much light they emit, not due to them being at different distances. You can therefore plot the apparent V star vs. B-V to obtain a meaningful Colour-Magnitude diagram (very similar to an H-R diagram) for the cluster. To plot the data, go to the M80 tab in the StarClusterPhotometry.xls file. Delete any dodgy B-V and V values (where the cell shows #NUM!). You may plot negative values, but you may prefer to delete these later for a neater plot. Click on the first number in the B-V column, press F8 and highlight all the numbers in that column and the adjacent V star column. Then click on the Chart Wizard icon and work through the steps, naming the series M80, giving titles to the chart and the axes, and saving the chart as a new sheet in the file. For more help with plotting, or if using Excel 2007 refer to the Basic Modules: Charts in Excel 2003 or Excel Plotting data for NGC 2420 With your plot displayed, click on the Chart Wizard icon again, go Next and click on the Series tab. Add another series, selecting your data for NGC You may have to select the x-data and y-data separately. 3. Analysis This diagram will allow you to compare the ages of the two clusters by comparing the colours of the stars in the clusters. Generally, young stars are more blue and old stars are more red, so the younger cluster will have smaller (bluer) B-V values and the older cluster will have Page 7

8 larger (redder) B-V values. Give it a try, removing any values that look dodgy by deleting them from the spreadsheet, and then compare your graph with the example in Appendix B (note that the y-axis in the example has values in reverse order bright stars at the top and faint stars at the bottom). What trends can you observe in your diagram and what can you conclude about the age of the two clusters? Discussion The colour of a star is due to the temperature of its outer atmosphere. Relatively cool stars are orange or red and hot stars are white or blue. The temperature of a star s outer layers is determined by how much energy a star is giving out and how far the star s outer layers are from the centre of the star. Stars in open clusters are young (typically less than a few 100 million years old) so their stars are relatively small (i.e. the surface is nearer the core, making the surface hotter). This means there are many stars that appear blue. Stars in globular clusters, on the other hand, are old (typically billions of years) so their stars are large because they have expanded in their old age (i.e. the surface is far from the core, making the surface cooler) so their stars appear more orange or red. You can see in your plot that the stars in the open cluster have lower colour indexes and therefore are more blue in colour. This supports the idea that these stars are from an open cluster, since open clusters contain relatively young stars which are relatively blue in colour. So the identification of NGC 2420 as an open cluster seems reasonable. The stars in the globular cluster cover a much larger range of colours and many of them are quite red indicating that they are old. Note: The graph of the stars from M80 is complicated by the fact that M80 contains stars called blue stragglers. These are thought to be stars that have formed when two stars collide and they appear blue when they should have already aged and turned red. Figure 11 shows a clearer example of the colour-magnitude diagram for an open and globular cluster. You can see that as a cluster ages its stars move to the right on the diagram. Figure 11: Colour-Magnitude Diagram Congratulations! You have now done the work an astronomer might do as part of their research. Most people will never experience doing something that a professional scientist does in their job. Well done. Page 8

9 Appendix A Finding B and V reference values for stars To find reference magnitudes for a star in each image: 1. Open the image in Makali i. 2. Place your pointer in the centre of the brightest single star in the image and record its RA and DEC that are shown in the middle of the screen above the image. These are the coordinates of the star in the sky. This is like finding latitude and longitude for your position on the Earth s surface. 3. Visit the astronomical database Vizier at: input the RA and DEC you have found and click Find Data (see Figure 11). This will return a very long list of object details. If you wish, you can refine the search by changing the Target radius (arrowed in the figure) to something smaller, say 5 arcsec. Figure 12: The Vizier query form enter coordinates under Target Name ( ) or Position and click Find Data. Narrow the search by changing the Target radius (e.g. you could use 1 arcmin or 5 arcsec). You can search the list using Find (Ctrl + F) and entering the RA to the first decimal point as shown in Figure 12. If your search does not show the magnitudes in the band you require, keep looking until you have been through the whole list! The list contains data from many catalogues. You will probably be able to find a set of B and V reference magnitudes for the star you are interested in. If not, choose another star. Page 9

10 Figure 13: Finding the correct star and magnitude details. Notes: The reference star for the M80 images is circled in Figure 1 and has coordinates: RA 16h17m08.15s and Dec It has the calibrated magnitudes: B ref = 12.89, V ref = and R ref = The B and V values are used for this project. The reference star for the NGC 2420 images is circled in Figure 7 and has coordinates: RA 7h38m24.2s and Dec It has calibrated magnitudes: B ref = and V ref = Page 10

11 Appendix B Sample Excel Plot Page 11

12 ASISTM Faulkes Telescope - Deep Space in the Classroom M80 Worksheet M80-B.fits M80 V data M80 B data Record countref here: Record countref here: Record countstar here: Record countstar here: Calculate the V magnitude of Star 1 using the following formula and Vref = Calculate the B magnitude of Star 1 using the following formula and Bref = Bstar = Bref! 2.5 log count star countref Vstar = Vref! 2.5 log Vstar = Bstar = Page 12 count star countref

13 NGC 2420 Worksheet NGC2420-B.fits NGC 2420 B data NGC 2420 V data Record count ref here: Record count ref here: Page 13