Testing the fitting
- First we wanted to test that the function we are fitting is actually normalised.
- The skewed Gaussian function is:
- Below are some skewed Gaussians for different skews:
- A normalized function would have values between 0 and 1, but here the values are between 0 and 14. This is because the function is summed over all columns and rows.
- If one looks at an individual column, it can be seen that the function is indeed normalised.
- Middle column:
- At the far columns one can see:
- Also, the formula was extracted from this reference ( doi: 10.1093/biomet/83.4.715 ) which derives a normalized skewed bivariate Gaussian.
- We wanted to look at a good star and see how the fit looks like in as much detail as possible, as the summation along rows and columns seems to distort the details of fitting.
- The fit is done by minimizing the
in the following way:
- So we fit for 9 parameters.
- We do not integrate, instead we evaluate the function at the pixel and multiply by pixel area.
- Column by column the fit looks like this:
- The plot parameters are shown below:
|
0.0509 |
|
33.5 |
|
33.8 |
|
5.021 |
|
5.373 |
|
-1.184 |
|
-1.384 |
|
0.0014 |
|
1.71e+06 |
|
3222 |
Degrees of freedom |
3591 |
- Found its magnitude using two methods, integration of the Gaussian and multiplication of two parameters:
- Method 1 gave magnitude = -8.4647927462328827
- Method 2 gave magnitude = -8.4647927466101169
- So they are equivalent to 9 decimal places.
- Therefore we shall use the second method as integration might slow the analysing down, also it would be easier to find the errors using method 2.
Matching stars between images
- Used Pythagoras to estimate the closest star image to image. Only used stars whose
were between 0.5 <
< 1.5
- Went through images and found the image with highest number of stars.
- This was the base image that all other images were compared to.
- It worked fine for images in focus and blue filter since they were taken close enough in time for individual stars to not have moved much.
- In red filter however, there was double matching, when more than one star was matched to the same base star as shown below:

- Improved the algortihm by:
- first calculate the minimum distances, some of them will be wronged as stars will be wrongly matched.
- Use those matches to work out the median x and y shifts.
- Then check between matches if the x and y shifts match the median x and y shifts to 1 pixel, if they do its a match.
- Below is the same red image and matches:
HR diagram for Cr39
- Using the matching and ML fits we got the following HR diagrams:
- The stars in V-R HR that seem to have the same V-R are indexed 26 and 27. The star with V close to -8 is indexed 2, it appeared 3 times. Star with V close to -7.5 appeared 3 times.
- The HR diagrams are terrible.
- From SIMBAD they should look like this:
--
ElenaCukanovaite - 14 Feb 2016
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Topic revision: r4 - 19 Feb 2016 - DavidHadden