Paofits teaching Material: Worksheet of Draw hr diagram of Star Cluster N




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AOFITS Teaching Material: Worksheet of Draw HR Diagram of Star Cluster - No.3
1. Notes

  1. This guide uses FITS images of an open cluster NGC 1912 and a globular cluster NGC 362 with their sky values set to zero.

  2. Use ‘Auto’ photometry function of Makali`i, use statistics of STAR.

  3. In drawing the CM diagram using Excel macro, sets the vertical axis to be in the unit of absolute magnitude.

2. This guide is available for Makali`i ver 1.0 or later.


3. Preparation

  1. Install Makali`i (license registration, if necessary).

  2. Download FITS images of open cluster (N1912Bs.fits, N1912Vs.fits).

Download FITS images of globular cluster (NGC0362B3.fits, NGC0362V3.fits).

  1. Download whole-area image of open cluster NGC 1912 (NGC1912_30x30.gif).

Download whole-area image of globular cluster NGC 362 (NGC0362_30x30.gif).

  1. Download a macro for drawing CM diagram (NGC1912ABS_e.xls, NGC0362ABS_e.xls), and set security level to allow the macro.

  2. Download theoretical stellar evolution curves (RIRON_e.xls).

  3. Teacher should work through once before the class day, from a point of student’s view.

  4. If students should have time to get acquainted with handling Makali`i, have some time.

  5. Read the teacher’s guide thoroughly.

4. Corresponding to the National Curriculum Guidelines in Japan (Heisei 15 version)

Senior High School Earth Science I

(2) Atmosphere, Ocean, and Universe

Earth Science II

(4) Extensive Studies


5. Class plan

1st period: Introduction, explanation of the work, seeing image data carefully (or starting the photometry)

2nd period: Doing photometry earnestly, output to CSV file (from CSV to CM diagram, running the Excel macro)

3rd period: Discussion based on the CM diagram


Stellar Evolution

- Draw CM Diagram of Star Clusters -
1. Purpose
Draw CM diagram of an open and a globular clusters, then discuss about the stellar evolution.
2. Outline
Take apparent magnitude of stars on the vertical axis, and take color (or spectral type) on the horizontal axis. The plot with these axes is called CM (or HR) diagram. In this work, draw CM diagram of an open cluster and a globular cluster, read the characteristics, and discuss about the stellar evolution.
3. Data
The image frames of the open cluster NGC 1912 that you will investigate were taken by the camera of 2kCCD aboard the Kiso Schmidt Telescope. NGC1912B.fits was taken with B (blue) filter, and NGC1912V.fits was taken with V (green) filter. Both have the same field of view. N1912Bs.fits and N1912Vs.fits are about one-fourth sections of NGC1912B.fits and NGC1912V.fits, respectively. This work uses the trimmed images.

Filter

(center wavelength)



B

(430.0 nm)



V

(540.7 nm)



Whole-area image

NGC1912B.fits

NGC1912V.fits

Trimmed image

N1912Bs.fits

N1912Vs.fits

The image frames of the globular cluster NGC 362 that you will investigate were taken by the camera of WFPC2 aboard the Hubble Space Telescope. The WFPC2 consists of four CCD chips. Four frames of NGC0362B1.fits to NGC0362B4.fits were taken with B (blue) filter, and four frames of NGC0362V1.fits to NGC0362V4.fits were taken with V (green) filter. NGC0362B3.fits and NGC0362V3.fits have the same field of view.



Filter

(center wavelength)



B

(430.0 nm)



V

(540.7 nm)



1st plane

NGC0362B1.fits

NGC0362V1.fits

2nd plane

NGC0362B2.fits

NGC0362V2.fits

3rd plane

NGC0362B3.fits

NGC0362V3.fits

4th plane

NGC0362B4.fits

NGC0362V4.fits


4. Method
4-1. Choose a cluster that you will investigate
Choose either an open cluster (NGC 1912) or a globular cluster (NGC 362). The procedure for the analysis is the same for both clusters, so in the explanations below, simply it is described like B image and V image. For the open cluster, N1912Bs.fits and N1912Vs.fits are B and V images, for the globular cluster, NGC0362B3.fits and NGC0362V3.fits are B and V images, respectively.
4-2. Open B and V images


  1. Start Makali`i. Widen the Makali`i window to the whole size by clicking center button of the upper right corner of the window.

  2. Open ‘Open image file’ pop-up by clicking ‘Open’ button or selecting ‘File’ > ‘Open’ in the menu bar.

  3. Select B image in a folder that teacher specifies, then click ‘Open’. Similarly, open V image as well.

  4. Activate B image, then press ‘Window’ > ‘Tile Vertically’ in the menu bar.

  5. You should pick up stars including faint ones carefully. To show the faint stars clearly, slide black and while triangle indicators in the menu bar, with a histogram shown by pressing ‘View’ > ‘Contrast’, if necessary. You can also change color mode by selecting ‘View’ > ‘Color Mode’, and choose log-scale viewing or not by pressing ‘View’ > ‘Log Scale’.

  6. Write blow color mode, log-scale on or off, minimum and maximum levels for the best viewing.




Image

Color mode

Log scale

Min. level

Max. level

Open cluster

N1912Bs.fits




on / off







N1912Vs.fits




on / off







Globular cluster

NGC0362B3.fits




on / off







NGC0362V3.fits




on / off









4-3. Inspect One Star Carefully


  1. Select one star in B image, and write below coordinates and count value. Similarly, write below them for V image. The values are shown in the upper left when you put the pointer on the star image.







Image

x coordinate

y coordinate

Count value

Open cluster

N1912Bs.fits










N1912Vs.fits










Globular cluster

NGC0362B3.fits










NGC0362V3.fits













  1. In which of B or V images does the star you chose above appear brighter? Is the star a blue-colored star, or red-colored one?


4-4. Photometry One Star
The count value you inspected above is brightness at a certain pixel, not for the star’s whole brightness. The star’s whole brightness is measured as follows.


  1. Activate B image.

  2. Press ‘Open’ button, or click ‘Processing’ > ‘Photometry’. If you see a pop-up saying ‘Select of Photometry Mode’, then choose ‘Aperture’.

  3. Select ‘Auto’ for Radius setting in the Aperture Photometry window.

  4. Minimize the Aperture Photometry window so that you can see the star that you chose.

  5. Move a circle cursor showing the photometry aperture. Select the star that you chose, and left-click.

  6. Write below center coordinates and count shown in STAR line (not Count value in the third line).

  7. Do the same thing for V image. If the Aperture Photometry window hide the working area, drag the window to the below.




Image

x coordinate

y coordinate

Count in STAR

Open cluster

N1912Bs.fits










N1912Vs.fits










Globular cluster

NGC0362B3.fits










NGC0362V3.fits










  • In this work, we do not use values in SKY line.




  1. Is the star a blue-colored one or a red-colored one? Is your judgment the same as that in the previous section?
    If a larger value is for V image, the star is a red-colored one.




  • Before going forward, quite Makalii for a time, then start again Makalii.


4-5. Photometry Many Stars
You will photometry about 100 stars for both B and V images. Adjust the viewing so that you can see faint stars as well.

Magnifying by two may help you work easily. Find Zoom up icon in the upper left of the Makalii window; it has a picture of magnifier with a plus mark. Clicking once the icon makes the image size twice. But you can not see the whole area at a time, so scroll the image upper, lower, to the right and the left, and pick up all stars in the image.

It is good to choose stars in B and V images in pair, but you do not have to check so much. You will have a program in Excel that can sort the star pairing. Therefore, if you happen to pick up different star, do not stop and go ahead.

If your working area is hidden by the Aperture Photometry window, drag it to the blow.




  1. Sketch roughly the image in a box below.




  1. Point out by an arrow where you think it is the center of the cluster. Why do you think so? Write the reason in the margin.




  1. Write values so as to see faint stars as well.




Image

Color mode

Log scale

Min. level

Max. level

Open cluster

N1912Bs.fits




on / off







N1912Vs.fits




on / off







Globular cluster

NGC0362B3.fits




on / off







NGC0362V3.fits




on / off










  1. Photometry as many stars as possible. Note that you should choose stars that are seen in both images, that you should not choose stars that blend to neighboring stars, and stars that lie near the edge of the frame. You should also pick up faint stars as well as bright ones.

4-6. In the Case of Interruption
If the time is no enough, you may interrupt the work. Save the image with other name, then information about stars you chose is also saved. You can resume the work later.
4-7. Save the Results
After finishing photometry, click ‘Print’ in the Aperture Photometry window.

If teacher instructs nothing, simply click ‘Save’.
4-8. Draw CM Diagram Using Excel
Open an Excel file for drawing CM diagram, NGC1912ABS_e.xls for open cluster or NGC0362ABS_e.xls for globular cluster. The file contains a program of macro. Excel will ask you if you activate macro or not.

Activate macro.

Press a button ‘(1) Read B-band CSV file’. A pop-up for the setting is coming. Check in ‘Total count’ for the option of ‘Data for magnitude calculation’. Use a default value of 0.3 pixel for ‘Allowance for centroid difference’. Click ‘OK’ after confirming above settings. Then read the B-band photometry data, ‘*****-Aperture.csv’ (***** is file name of the image, for example, NGC0362B3). Similarly, press a button ‘(2) Read V-band CSV file’, and read the V-band photometry data, ‘*****-Aperture.csv’.

Then press a button ‘(3) Indentify stars, calc V & B-V’. Here, the program automatically check star data in B and V each other, within an allowance of difference in centroid position set by ‘Allowance of centroid difference’. Then it calculates magnitudes and colors. It may take some time, and the window is flickering due to the calculation. The calculation ends when the flickering stops.

Then, go to drawing the plot. Press a button ‘(4) CM diagram’. You will see a CM diagram in newly-generated sheet.


  • Depending on settings at your school, you may not see extensions of file name such as .xls or .csv.

Print the plot.


5. Discussion: Print out the CM diagram and discuss your result.
Q
.1. Decide which type is your CM diagram, referring diagrams below. Write names to parts in your diagram.
Q.2. Compare results by classmates who investigated open cluster data or globular cluster data. Exchange comments.

    1. Mention as many points as possible which are similar to and different from each other.

    2. Compare absolute magnitude of the turn-off point.

    3. Consider that the difference in part upper than the turn-off point is the shift in the horizontal direction. What characteristic of stars makes this shift?

    4. Since the energy generation system changes as the star ages, a star evolves from a protostar to a main-sequence star, a red-giant star, and a white dwarf. Which do you think is older, the open cluster or the globular cluster? Why do you conclude that?

Q.3. Compare derived CM diagram and theoretical curve. Estimate age of cluster you investigated.



  1. Estimation of the age.

Why do you guess so?


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