HOU Year 2 Exercise: the H-R diagram

 NGC 6939

 M67

M16

Pal 5

Warning! these exercises require a fair amount of persistence and patience in addition to bringing together almost all of the HOU skills learned in Year 1 and 2 Workshops.

NGC 6939

1) Download the following 2 open cluster images from the HOU (old) image archive [St. Mary's, Nova Scotia site]:

    6939B1.fts (a B-filtered image)
    6939G1.fts (a V-filtered image)

    If you are using Netscape, depress the Shift key and then click with the left mouse button to download;
    if you are using Internet Explorer, click with the right mouse button, and then select Save File As;
    in either case you may need to change the extension of the file... it should not be .txt

2) Open both images in HOU

3) The two images needed to be shifted by a small amount in x and y so that any given star has exactly
the same coordinates on the two images.  Determine, perform, and record the shift that you made.

4) Use Find to measure the x and y positions and the Counts value of all stars higher than sky + 8x deviation on the G image.  (Empty the Results box before doing this for the later convenience in saving the results to a text file that will load into Excel.)

5) Save the results file as a .txt file.

6) Open Excel and open the Gresults.txt file.

7) Repeat steps 4-6 for the B image and save the results in a separate .txt file.

8) Cut and paste the 2nd .txt file data into the 1st .txt file.  Note that all stars recorded in the G image's text file will not necessarily show up in the B image's text file (and vice versa).  You will have to hand delete any stars that dont show up in both OR go back and use aperture to measure the coutns total of any stars that weren't found in one of the Find commands done in steps 4/7 above.

9) The star located at x = 386 and y = 181 in the original B image is a standard star and has the following standard magnitudes:  B = 11.874 and V = 11.247.
Use the same method as in the HOU activity: Measuring the Color of Stars with Images to determine
the B and V magnitudes from your Counts data.  Use the power of the spreadsheet to do the magnitude calculations!

10) After you have calculated both the B and V magnitudes for each star, create another spreadsheet column that calculates the B-V magnitude for each star.  Note: for later convenience, it would useful to have the B-V column to the left of the V magnitude column; Excel always chooses the leftmost column of the two columns selected to become the x-axis and the rightmost column to be the y-axis.

11) Plot the H-R diagram of the cluster; in order to create an embedded graph in Excel:

a) select the column of numbers that will become the y axis (select only the V numbers by clicking the mouse and dragging over only numbers; do not include any blank cells or cells with text; do not select the whole column by clicking on the top letter of the column)
b) hold CTRL down and with the mouse, select the column numbers that will become the x axis (these are the B-V magnitude numbers)
(at this point, both columns should be highlighted)
c) click on Chart Wizard
d) click on XY Scatter Graph
e) choose type of graph. etc.

(after the graph is finished, remember that to reverse the vertical axis, so that the V magnitude axis increases downward!  in some versions of Excel, you can right click on the vertical axis and select "reverse axis scale")

12) By comparing the V magnitudes (often denoted m by astronomers) of stars on your H-R diagram with the absolute magnitudes (often denoted M by astronomers) of the same B-V stars on a standard H-R diagram, find the distance to the cluster using the magnitude of the inverse-square law formula:

                                            d  =  10((m-M+5)/5)  pc

13) Search the ADS data base for a published H-R diagram of NGC 6939 in the astronomical literature.
How does your H-R diagram (and cluster distance) compare with professionally published data?

If you are lazy pressed for time, click here for an H-R diagram found in this manner.

You will notice that our H-R diagram has only the brighter stars in the cluster; much of the lower portion of the published diagram's main sequence is missing.  Perhaps if we asked the Find command in step 4 above to select stars that are Sky + 6xdeviation (or + 4xdeviation) we would have a greater number of fainter stars and thus more closely match the published H-R diagram.  On the other hand, the process (particularly matching the stars in the B and V images) would take much longer.

14) The age of a cluster is given by

                tage  =  1010 years (Mt.o.p./Msun)-3

where Mt.o.p.  is the Mass of the star just beginning to leave the Main Sequence and head toward the Red Giant branch.  To determine the mass of the star just leaving the Main Sequence, use this table to correlate color index and mass for main sequence stars.
 
 

M67

1) Download the following 2 open cluster images from Vivian's Explorations page

    m67b20best000312.fts  (a B-filtered image)
    m67v08best000312.fts  (a V-filtered image)

    If you are using Netscape, depress the Shift key and then click with the left mouse button to download;
    if you are using Internet Explorer, click with the right mouse button, and then select Save File As;
    in either case you may need to change the extension of the file... it should not be .txt

The star labeled as 1 and located at x = 373 and y = 353 in the original B image and at x = 187   and y = 361 is a standard star and has the following standard magnitudes:  B = 11.1 and V = 10.51.
Use the same method as in the HOU activity: Measuring the Color of Stars with Images to determine
the B and V magnitudes from your Counts data.  Use the power of the spreadsheet to do the magnitude calculations!

Otherwise the procedure is the same as for NGC 6939

M16

  Download the B and V images and instructions for the cluster M16 from the RAAP group at UCSB
    the images come in a zipped file; the instructions in a .doc file

    again, same procedure as above

PAL 5

1) Use the MAST Catalog search on the SDSS data archive: click here

2) type in Pal 5 in the Target Name space (Pal 5 is a globular cluster in our galaxy) and click on Get Coordinates
    (coordinates should then be filled on the RA and Dec boxes)

3) type in 3 arcmin in the Radius box; select Star in the Object box; then click on Search
    (an alternative is to use a smaller radius; for example, a radius of 1.5 arcminutes returns 159 stars;
        it is easier to see the main sequence, but the horizontal branch is not well-defined)

4) the SDSS query should return with 823 stars

5) click on  Download to save the results as  Comma-separated-value file (which can be opened in Excel)

6) open the data file in Excel; there will be 823 stars listed with their magnitudes in 5 colors (u, g, r, i, z)

7) since an H-R diagram is a plot of one magnitude vs color index (a difference in magnitudes), we need to create the color index g - r  ;
    to do this insert a blank column in between the columns for the g magnitude and the r magnitude in order to calculate and list the
    g-r color index

8) type in the formula    =$K2-$M2 into the L2 box (a g-r value of 0.36 will then be returned);
    then drag down on the lower right corner to fill in all the values of the g-r color index in the L column

9) then plot the g magnitude vs the g-r color (see instructions under NGC6939 above, step 11) to get the HR diagram