Photometry of the Pleiades
Part 1: [10Points]
1.Define absolute magnitude M.
2.If m = M (m=V=visual magnitude) for a given star, how far would that star be from Earth? Use the formula:
d = 10 x 10(m-M)/5.
Explain the steps you went through to obtain the answer.
3.What would it tell you about the distance if m was greater than M?
4.What does it mean (in terms of distance) if your set of stars has apparent magnitudes (V or m) less than the corresponding stars on the H-R diagram of known absolute magnitude (Vabs or M)?
Part 2: [10 Points]
Imagine, you are an astronomer and NASA asked you to do some research on the Pleiades.
Use Stellarium to find the position of the Pleiades in the night sky. Next, you determine altitude and azimuth to quickly find them from your location. However, to communicate the position of the star cluster to your astronomer friend in San Francisco you use equatorial coordinates.
5.From your first inquiry, you record the following data:
Horizon coordinate system:
Date of Observation:
Location from where you observe the objects:
Insert a screenshot from Stellarium and indicate where the Pleiades are in the picture. Use the “Insert shapes” feature in MS Word to show the Pleiades in the screenshot.
Part III: [50 Points]
After determining the positon, you investigate actual data to calculate the cluster’s distance from Earth. You have two methods to perform an analysis of data gathered with a photometer attached to a telescope. The data have been made available to the scientific community in a database called the Hipparcos Catalog Vol. 5 (Go to page 358).
Open the Excel workbook and enter the required data for each listed star in Table 1 on the sheet named “Pleiades Data”.
You will need the visual magnitude V, parallax par (given in milli-arcseconds), and b-v the color index for each star.
Analysis method 1:
6.You calculate the distance for each star using the parallax value and record it in the table on your Excel worksheet. Maybe you remember from our last lab that distance d is 1/(parallax in arcseconds). Note that you need to convert the given parallax value into arcseconds before calculating the distance. The value in the catalog is in milli-arcseconds.
7.Once you know the distance you can calculate the absolute magnitude M for each star.
The relationship between a star’s apparent or visible magnitude and absolute magnitude is given by the expression
M = m – 5*( log d) + 5,
where m is the star’s apparent magnitude, M is the star’s absolute magnitude, and d is the distance to the star in parsecs.
[Copy and paste the completed table from your Spreadsheet here into this report]
8.Create an HR Diagram in your Excel workbook. Plot the calculated absolute magnitude M as a function of the color index b-v. Label your axes.
[Copy and paste the graph here into the report.]
Analysis method 2:
You will be making an H-R diagram using the visual or apparent magnitude V. Plot V as a function of b-v by adding the data series into the standard stars’ HR Diagram on the second sheet in your workbook. Now perform an HR diagram fit to determine the value m-M. The question is how much you need to shift your values up to match the standard stars’ diagram.
For example: the arrow indicates the distance modulus or m-M (visual magnitude – absolute magnitude)
9.[Copy and paste the graph from the spreadsheet here]
10.Determine the distance modulus m-M from the graph: Your value is….
11.Use this value to calculate the Distance of the cluster in parsec
D = 10 (m-M+5)/5
12.Where do the main sequence stars in this cluster lie with respect to the main sequence of stars of known absolute magnitude?
13.Is this cluster closer or farther than 10 parsecs away?
14.In 1958, H.L. Johnson and R.I. Mitchell calculated the distance to this cluster to about 410 light-years. (Parsec value times 3.26 gives you the value in lightyears). As a percentage, how does your calculated value compare? Show your work.
15.Do any of your stars seem to lie in the red giant part of the H-R diagram? If so, identify them by their RA and declination.
Conclusion question: [10 points]
Compare the two methods of finding distance. Identify strengths and weaknesses of these methods and explain assumptions you have made.