The goal of this project is to determine the age and distance of M11 and compare it to results which were obtained by a group I worked with during the summer 2001 COSMOS Math and Science program at UCSC.
I analyzed digital images of M11 in the blue and visual filters. I later went on to receive two new sets of data from the 24î Yerkes telescope. One set was taken in a twenty second exposure and the other was a thirty second exposure. I would need a standard star to find the relative magnitudes of the other stars, so I searched the internet using google and failing to find anything tangible emailed Stuart, a UCSC graduate student, who sent me a standard star map of M11.
Equipped with a map of the standard stars. I began a search which involved manipulating the image to match the view of the standard star map. I choose standard star #899. Due to a pixel error I manually documented the counts of each pixel in the vicinity of the star. Using averages I determined a good estimate for the brightness. Stuart suggested I find three other standards to determine if the outcome was consistent. I went on to find eight standard stars, of which only six were to be used.
I created graphs of the color index of the stars(blue magnitude-visual magnitude), versus their visual magnitudes. By comparing the graph with a Yale Isochrone model I was able to determine its age and distance. Afterwards I was able to make Absolute Magnitude graphs by using the differences in the turnoff points.
The standard star #899 was throwing the results off; whereas, the other standards were within 2% agreement, so it was discounted. The standard star #1329 was not visible in the 20s and 30s images so it was also discounted from the total data.
The summer results suggested M11 is 275 million years old and 1,900 parsecs or 6,200 light years away. The results from the original images suggest that M11 is 200 million years old and 1,649 parsecs or 5,375 light years away. The results from both the 20s and 30s images suggested that M11 was also 200 million years old; however the distances varied wildly. The large variations in distance seem to be due to the differences in the magnitudes of the standard stars.
1) Look carefully at digital images to discover pixel errors using Image Processing. Subtract sky and line up the axes of both images.
2) Search internet to find standard stars(with known magnitudes in the B and V filters).
3)Match views of the cluster so that images match up.
4)Search for standard stars. Preferably find the brightest standard stars.
5)Once standard stars are found whether on the internet or from a really nice graduate student from UCSC, it is time to find them inside of the images.
6)Use the Find option in the Image Processing software to find all the stars in the image. At first I had it find 200 stars. Than I had Find search for as many stars as it could find, which was a little over 400 in the originaldata, 500 in the 20s data, and 900 in the 30s data.
7)Search through the star positions in the blue filter image and the visual filter image and pair them up within a pixel difference. Any stars that are similar but just a little over 1 pixel difference in either the y or x axis were counted, but a star was used to differentiate the pair.
8) From the original data 135 pairs were found initially and the second star survey revealed only 171 pairs. The 20s image data revealed 292 and the 30 image data revealed 366 star pairs. Take these pairs and use an Excel document to list them. The standard star is not counted in the star surveys so it should be placed at the top of the list. Add a star to the pairs that are just slightly over one pixel off on the x or the y axis.
9)The counts measured using the Find option are the brightnesses, so they are plugged into the spreadsheet in their respective b and v columns.
10)The use of the HOU formula that converts brightness, which is counts, to magnitude involves the standard stars apparent magnitude in one filter plus 2.5*Log(standard stars brightness in that same filter/individual stars brightness of that same filter).
11)Create a separate volume that will be the B magnitude minus the V magnitude. Begin experimenting with Chart Wizard function. Graph the B-V index versus the Apparent magnitude(V Magnitude). Reverse the order of the axis and adjust graphs.
12)Adjust the V magnitude and the B-V columns to accommodate the dust tha reddens the digital images in Visual because of the great distance of the Wild Duck Cluster. That is to say subtract 1.37 from the V Magnitude column and .34 from the B-V column. Graph this result.
13)When the graphs are finished, import the isochrone data from Cosmos Research guidance web page. Graph the isochrones of 100, 200, and 400 million years old. Create graphs that have the same change in y and the same change in x. Place the three isochrones on the same graph.
14)Compare the isochrones to discover which one matches the shape of the graphs for each individual standard star. The difference between the Absolute Magnitude and the Apparent Magnitude is measured on the y axis of the isochrone and the standard stars graph, and is used in the distance formula from the HOU binder; a.k.a. the antilog[(distance modulus+5)/d]. Analyze data and throw out the standard that is not in agreement. Take the magnitude difference measured above and adjust the graphs to find the Absolute Magnitude vs. Color Index graph.
15)The formula above gives the distance to the Wild Duck Cluster.
The initial distance was found to be 1,649 parsecs away from Earth from the original data. The distance suggested by the 20s and 30s data is for standards #660 and #992 to be 24,185 parsecs away and for standards #1261, #898, and #979 is 1,626 parsecs away and standard#1223 was the only one with the distance of 5,517 parsecs away. Its age was judged to be 200 million years old. The age suggested from the 20s and 30s data is judged to be 200 million years old. The numbers may be affected by several factors, including the following: the previous numbers used were derived during a summer project in which different software was used, each data set had a different amount of pairs, the distance differences seem to be paired up by the standard starís visual magnitudes. The distances grew larger as the standard starís visual magnitude increased, which means as the stars brightness decreased the distance increased.