### 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.

• We fitted this star:
• 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

Topic attachments
I Attachment Action Size Date Who Comment
png 001_50.png manage 81.8 K 14 Feb 2016 - 19:13 ElenaCukanovaite
png 003_150.png manage 103.2 K 14 Feb 2016 - 19:13 ElenaCukanovaite
png 005_250.png manage 82.2 K 14 Feb 2016 - 19:13 ElenaCukanovaite
png B_V_simbad.png manage 49.3 K 18 Feb 2016 - 20:28 ElenaCukanovaite
png V_R_simbad.png manage 34.0 K 18 Feb 2016 - 20:28 ElenaCukanovaite
png complete_fit.png manage 111.7 K 14 Feb 2016 - 19:21 ElenaCukanovaite
png crop.png manage 58.4 K 14 Feb 2016 - 19:21 ElenaCukanovaite
png red_first.png manage 513.4 K 18 Feb 2016 - 19:50 ElenaCukanovaite
png red_second.png manage 96.4 K 18 Feb 2016 - 20:06 ElenaCukanovaite
png red_second_closeup.png manage 39.7 K 18 Feb 2016 - 20:06 ElenaCukanovaite
png summed.png manage 139.6 K 14 Feb 2016 - 19:13 ElenaCukanovaite

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Topic revision: r4 - 19 Feb 2016 - DavidHadden

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