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Period Analysis for Three Pulsating Variable Stars Using Differential Aperture Photometry w/ PixInsight & RobPer

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#1 akulapanam

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Posted 15 June 2021 - 12:32 AM

I wanted to share the coolest project that I have done with my equipment so far; photometry using PixInsight and RobPer to determine periods/plot light curves for three variable stars. When I was putting this project together I noticed that not many people were taking advantage of the incredible functionality for photometry in PixInsight so I figured it might be helpful to post publicly. Happy to answer questions but on a high level this was my process:

 

1) Test equipment and determine exposure time. Basically we want to make sure we are not going to get saturated pixels for the target in question
2) Take a bunch of exposures over multiple nights. One of the stars, V0436 UMA, has a very short period (a matter of hours) and BF Ser a bit over a day. Other stars or objects you investigate may even have longer periods
3) Take flats and darks just like you would for your images
4) Calibrate your images (I used CCDStack here but PixInsight also works). Again same as you do for images
5) Run the AperturePhotometry script in PixInsight. Here you are going to want to play around a bit to ensure your aperture correctly fits the star. The AAVSO guide and PixInsight documentation are helpful here. PixInsight also offers a PSF option and an option to use a wavelet model for the background. I played around with these and both produce excellent results. You do need to pick the right comparison catalog for the next steps (Tycho or Gaia) and PixInsight will fetch information from Vizier for your spreadsheet
6) Next you will get a Excel sheet (really CSV file) which you will use to perform ensemble differential aperture photometry. I used Excel for this but I could have easily done everything in R. I used the formulas from the popular AstroimageJ tool (see documentation in paper below) but you could also use those in the AAVSO or other references. Note you want to choose a check star and then 4 or 5 comparison stars for your ensemble. You want to search for your stars on Simbad and VSX to check for signs of variability. Your comparison stars should be in roughly the same area of the image, have roughly the same magnitude, and have roughly the same color index. We also need to calculate measurement uncertainty
7) Now you want to export the measured light curve and uncertainty terms along with Julian date (PixInsight provides) into a CSV to determine period. For periodicity determination I used the RobPer R package. It has five different models for period fitted with four different regression algorithms. Three of the regression choices are "Robust" which means they are less sensitive to outliers than ordinary least squares. Fitting in RobPer requires 1 line of code. For the curves here I used m regression with a huber function + second-degree Fourier model. You can then plot the periodogram (see example) or use some code to determine most likely period. The periods I determined matched VSX almost exactly
8) Now we take the model parameters and make a pretty plot in Excel, R, Tableau, etc...

V0436 Uma Light Curve.png

AH Leo Light Curve.PNG

 

With a little bit of additional work you could also submit your data to AAVSO.

 

What about the fact that I used a Chroma G vs scientific V filter? The chart below shows the relationship between flux measured using PixInsight photometry and the Tycho 2 V magnitude.

Tycho-2 Magnitude vs. Flux.png

 

Note I have listed all exposures in March 28th for convenience but actual collection took place over March 28th, 30th, April 1st, and April 3rd.

RobPer - https://cran.r-proje...bPer/index.html
PixInsight - https://pixinsight.c...Photometry.html
AstroimageJ paper for formulas - https://arxiv.org/abs/1701.04817
The AAVSO Guide to CCD Photometry - https://www.aavso.or...ometryGuide.pdf

 

All images are also on Astrobin.  https://www.astrobin...2bxrrd/?nc=user


Edited by akulapanam, 15 June 2021 - 12:33 AM.

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#2 NJScope

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Posted 20 June 2021 - 11:18 AM

Akulapanam:

Thank you for sharing your initial experience with acquiring light curve data from some pulsating variables and then trying to find oscillation

periods using a variety of deconvolution methods.   For those on a limited budget, the open source program AstroImageJ is a suitable substitute

for PixInsight/CCDStack to calibrate fits files and generate time, magnitude and mag_err data for period analysis.  Where possible, I normally use

APASS values for the comparison stars.  There are quite a few in the same FOV as V436 UMa and BF Ser.  I'm not familiar with the RobPer R package

but there are at least two other open source programs that can be used to perform a period analysis on pulsating variables.   The first is

Period04  which can run on MacOS, Windows and Linux, while the second, Famias

runs on Linux and MacOS.  It is important to use Heliocentric Julian Date (HJD) and not Julian Date

(JD) during period analysis particularly if you are planning to combine your results with others taken at different locations and times of the

year. Most pulsating stars do not oscillate at one frequency.  Many "High Amplitude Delta Scuti" (HADS) variables have a fundamental (f0)

pulsation mode along with multiple harmonics (2f0, 3f0, etc) whereas others ring in a much more complex manner (eg f0, f1, f0+f1, 2f0 etc).  V436

UMa appears to be a HADS variable whereas BF Ser is considered an "above horizontal branch subtype 1 ((AHB1) pulsating variable that would be

expected to have much more complex pulsation modes. Since the data you provided has a fairly short timeline, it is difficult to see these differences.  Unless you used a method called "pre-whitening" I suspect that your fits only represent the fundamental mode of pulsation.  The LC data from BF Ser are incomplete so that modeling will have great uncertainty.  The best chance to dig for additional pulsation modes would be to acquire much more data on both targets. PM me if you need help with your research.

 

Kevin


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#3 akulapanam

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Posted 20 June 2021 - 05:19 PM

Akulapanam:
Thank you for sharing your initial experience with acquiring light curve data from some pulsating variables and then trying to find oscillation
periods using a variety of deconvolution methods. For those on a limited budget, the open source program AstroImageJ is a suitable substitute
for PixInsight/CCDStack to calibrate fits files and generate time, magnitude and mag_err data for period analysis. Where possible, I normally use
APASS values for the comparison stars. There are quite a few in the same FOV as V436 UMa and BF Ser. I'm not familiar with the RobPer R package
but there are at least two other open source programs that can be used to perform a period analysis on pulsating variables. The first is
Period04 which can run on MacOS, Windows and Linux, while the second, Famias
runs on Linux and MacOS. It is important to use Heliocentric Julian Date (HJD) and not Julian Date
(JD) during period analysis particularly if you are planning to combine your results with others taken at different locations and times of the
year. Most pulsating stars do not oscillate at one frequency. Many "High Amplitude Delta Scuti" (HADS) variables have a fundamental (f0)
pulsation mode along with multiple harmonics (2f0, 3f0, etc) whereas others ring in a much more complex manner (eg f0, f1, f0+f1, 2f0 etc). V436
UMa appears to be a HADS variable whereas BF Ser is considered an "above horizontal branch subtype 1 ((AHB1) pulsating variable that would be
expected to have much more complex pulsation modes. Since the data you provided has a fairly short timeline, it is difficult to see these differences. Unless you used a method called "pre-whitening" I suspect that your fits only represent the fundamental mode of pulsation. The LC data from BF Ser are incomplete so that modeling will have great uncertainty. The best chance to dig for additional pulsation modes would be to acquire much more data on both targets. PM me if you need help with your research.

Kevin

Thanks for taking a look!

A couple points:

-yep definitely could use more data

-there are definitely more pulsation modes I didn’t capture with limited data. One of the nice things about RobPer is that you get the periodogram so you can see additional harmonics. Some good examples are in the RobPer documentation. As you noted there are lots of good packages here although most are not robust which could be a problem if you have lots of outliers

-converting to HJD can be done via script in PixInsight

-the big advantages I see of using PixInsight over AstroimageJ is that you can incorporate photometry into your normal astro image workflow, it supports psf photometry, it supports wavelet background estimation, and you can align & extract all sources from your stack of images in one pass into a csv

Edited by akulapanam, 20 June 2021 - 05:20 PM.



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