Linear regression of light curve section

Affiliation

American Association of Variable Star Observers (AAVSO)

Sun, 03/05/2023 - 03:37

Hi,

According to VSX, BX Leo has a period of 8.7 hours and there was only one observation, so I decided to observe the target for an hour - just a section of the light curve. The variable did have a higher magnitude standard deviation than the 2 check stars throughout the observing period (0.023 vs. 0.016 and 0.014). I also did linear regression of the target's and check stars' data points - with the target having a slope of -2.064 (brightening) and R^2 of 0.742; check 1 has slope of 0.519 and R^2 of 0.104; and check 2 has a slope of 0.693 and R^2 of 0.229.

Has anyone used linear regression to analyze a section of the light curve (approximates a line)? I was wondering if computing and comparing the standard deviations of the target and check stars, coupled with linear regression models to get the slope to determine direction of variability - whether steady, brightening or fading - at a particular section of the light curve is a worthwhile activity if the observer has limited observing time.

Thanks,

Raymund

TRE

Affiliation

American Association of Variable Star Observers (AAVSO)

Tue, 03/07/2023 - 04:14

Looks like a fun one

Yes, just one data point in the database. No comps in a 60 minute FOV. VSX yields a 0.7 magnitude photographic magnitude.

You could spend a season observing it through all your filters. Bug the comp team for some close-in comps. See if you can really consistently see an amplitude of 0.2 or 0.7 at magnitude 11 over a period of months with your equipment.

You can apply the linear regression to any set of random data. But if you want to see what's happening out there, nothing beats a good light curve, carefully measured by you, and left in the database for future generations of OC fans.

I may do a BVI of this one next year. Nothing more fun than populating a light curve in the AAVSO DB and playing it back with VSTAR at the end of it's season.

The moving average that you mentioned in another post is helpful as long as the averaging period is much shorter than parts of the light curve that are changing rapidly. It is possible to artificially flatten the peaks and troughs by averaging over 30 minutes on an eight hour curve. But sliding-stack-averaging does produce less noisy data. I see you are using CV which is fine to measure a period.

Ray

Roy_Axelsen_ARX

Affiliation

Variable Stars South (VSS)

Wed, 03/08/2023 - 00:58

Time series over one or more nights

"See if you can really consistently see an amplitude of 0.2 or 0.7 at magnitude 11 over a period of months with your equipment."

With such a short period most if not all of one cycle could be captured by time series photometry during one night with good horizons. Just a few nights might do.

Roy

raymundang

Affiliation

American Association of Variable Star Observers (AAVSO)

Wed, 03/08/2023 - 03:35

Hi Roy,

Unfortunately, I do…

Hi Roy,

Unfortunately, I do not have enough observing time for a complete light curve - almost 9 hours. Hoping to observe at least 3 to 4 hours to catch the rise. If not, maybe a shorter observing run. A horizontal slope would mean either maximum or minimum since the target would not be brightening or fading at that particular section.

Raymund

raymundang

Affiliation

American Association of Variable Star Observers (AAVSO)

Wed, 03/08/2023 - 03:28

Hi Ray,

Yes, will continue…

Hi Ray,

Yes, will continue to monitor this target. I did not use a comp star. I was using ASTAP which has ensemble photometry using GAIA DR3. Initially doing CV, but now trying out TG filter as well to focus on one channel.

VSX states rise of 3.5h (RR Lyrae type). The slope I got was -2.064, multiplied by (3.5 / 24) should yield 0.301 magnitude change. I think I was just after the start of the rise period - so the regression line is not yet too steep.

If there's limited observing time, applying linear regression would be a nice way to estimate which part of the light curve you're observing. But you'd need to have one or two check stars to apply linear regression as well for comparison - plus compare standard deviation of the entire data points if checking just a section of the curve.

On the moving stack, I agree. If the target is changing rapidly, the method would average out/flatten some interesting phenomena in the light curve. I did 5 minutes total integration with 2-minute interval per data point to smoothen and increase SNR.

Raymund