Hello,
I am an undergraduate student in Massachusetts researching candidate exoplanets. However, my current focus has been to create a Python code that uses linear regression to see whether a star has variability. This is to help me in finding good reference stars which are consistent in magnitude so that I may have better results when doing photometry in a FOV in which the Variable Star Plotter does not indicate reference stars. I am basing this code on an article/paper which Kevin B. Paxson wrote for JAAVSO Volume 38 titled "Differential Ensemble Photometry by Linear Regression." (It's in the second part if you look for it on the website). I would typically ask an author for clarification on their work, but I have just recently found out that Paxson has unfortunately passed on as of 2015. And so, I'd like to relay my question to anyone here who may be willing to dig into and answer.
In Paxson's paper, he has the reader create an Excel file that allows the reader to input data to create a linearly regressed plot to help identify variable stars. In the Excel file, he has a column where he puts in the Johnson V sequence magnitude for each star. If you refer to the article, it's on step 7 of the process for making the Excel spreadsheet. Could anyone please tell me what this means and where he got the values for these stars? I've personally been using VizieR to get these magnitudes for the V filter, but I feel that he was getting his data from somewhere else.
Best,
Caleb Derochea
Hi Caleb,
From what I understand from your post, you are taking a single frame and seeing whether the Johnson V magnitude for a comparison star falls on a straight line with other comp stars. The reference Johnson V magnitudes usually come from the photometric sequence shown for a variable star using VSP. Note two things:
- the sequence may be from multiple sources, with offsets. At the 0.01-0.03mag level, these should agree, but there may be outliers in the "truth".
- you need to transform your instrumental values, because differences between your filter and the standard system might cause discrepancies, especially for bluer or redder comp stars
- you need to do this on multiple nights to find the stars that vary, as opposed to just having an offset.
Usually the way to find variable stars is to take multiple images, extract all of the stars, and then for each star, determine mean and standard deviation. Then plotting standard deviation vs. mean will give a plot with a basic exponential shape - low standard deviation for bright stars, increasing exponentially as you go to fainter stars. It is a very nice display of Poisson statistics. Then look for the stars that lie above this curve - larger error compared with similar stars of equivalent magnitude. Those are the ones to investigate.
Arne
Hello Arne,
Thank you for answering!
My primary concern is if using the magnitudes from VizieR of the same filter (V) that I made my observations with is an acceptable reference in terms of finding variable stars via linear regression. And, if not, where else would I be able to find an acceptable reference for star magnitudes in FOVs that don't have known reference stars in the variable star plotter.
In my project, I use ensemble photometry (in which I do use many pictures taken over a night or a few nights... or, in the case of variable stars, a few weeks) to find the mean instrumental magnitudes of the stars within the FOV and compare them to known magnitudes via linear regression. As Paxson had said in the article I had referenced, more stars used in this process allows for more accuracy.
This is primarily to be used for things like finding a star that doesn't vary in magnitude throughout an observation period, meaning someone can use it as a (temporary) reference star (temporary meaning "it may or may not be a variable star over a period of time, but it doesn't vary outside of a certain tolerance during my observations for this exoplanet transit so I can use it as a reference"). It's a sort of workaround for doing photometry in a FOV without any known reference stars when you want accurate data (which was something I ran into doing research on candidate exoplanets). Although just using ensemble photometry, in general, allows astronomers to use FOVs with unknown reference stars, finding and using stars within the same FOV that you know don't vary over an observation period will enable you to be more confident in your final data (again, like for exoplanet transits).
Essentially, I am using ensemble photometry of multiple stars over a period of time, finding the means of each star's instrumental magnitude, and using linear regression to compare the instrumental magnitude of each star with their accepted magnitude (in the same filter type) based on information I find via VizieR. I then omit the star with a magnitude that is the most off from the line of best fit and see if I can get an R^2 value as close to 1 as possible. I then use the standard error of estimates to get a value to use for my error bars and then I add the omitted star back in, with the error bars, to see if the error bars of the star I had omitted pass the line of best fit. If it does, I consider it to be good enough to use for photometry on the main target. If it doesn't, I don't use it as a reference star.
Based on the things you have mentioned, here are some observations I have made about my research project, as well as potential clarifications of what I am attempting to do with said project:
- You mentioned the discrepancies in the magnitudes, especially with the filters being used. We (at the BSU observatory) use a V filter for exoplanetary observations since that seems to be a commonly used filter for exoplanet transit detection, and I use the V mag values from VizieR. However, I am not sure if that is a reliable way to get the magnitudes of the stars in my FOVs.
- You mentioned something about offsets. I am not entirely sure what you mean about "offsets," but I am assuming you are talking about the difference in magnitudes between the "true" value and the instrumental value (e.g. assume two of my instrumental means are 14.0 and 12.8, while VizieR says they're 16.2 and 15.0, respectively). (Please let me know whether I am right in this assumption or if you meant something else.) I have been assuming that the offset in the value from the instrumental mag and the VizieR mag have been consistent, but that assumption is possibly flawed in retrospect. That's surely something I plan to look into.
- You mentioned something about plotting the standard deviation versus the mean and Poisson statistics. I will certainly be looking more into that to see how my data compares to that method of variable star detection.
I hope this clarifies what I am attempting to do in this project.
Caleb