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Determining the period of a Cepheid variable in the shortest time possible

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oopfan
oopfan's picture
Determining the period of a Cepheid variable in the shortest time possible

Hypothetically, if the resources of AAVSO were not available to me nor a suitable reference, is there an algorithm that I could follow to estimate the period of a Cepheid variable with just a couple nights of data? Said agorithm should yield more precision as more data was captured.

Thank you,

Brian Morgan

(MBDA)

arx
arx's picture
Determining the period of a Cepheid variable ...

Hi Brian,

I'm not an expert on Cepheids, but I do work with periods of delta Scuti stars.

If all you can get is a couple of nights' data, the only way that I could see that you could do this would be to have a pretty good idear of what the period was to start with. Otherwise, since Cepheid periods vary from a few days to many days, I don't see how it could be possible.

If you had a pretty good idea of the period, and if you had time series data, on two or three nights, from the same steepish part of the light curve, you could fit a linear or polynomial function to each of the sets of data, calculate the 'precise' time of a certain magnitude, them simply calculate the difference between the times of the observations. From your 'pretty good knowledge' of what the period was, you could then, hopefully, do a more precise calculation of the period.

I would assume that you would need to have a cepheid with a fairly short period to do this, otherwise the slow rate of change of magnitude with time during one night be a problem.

The other necessary ingredient for this method would be a regular light curve.

I would be interested to hear if there is any other way to approach the problem.

Roy Axelsen (ARX)

oopfan
oopfan's picture
Perhaps FFT

Hi Roy,

Thanks for your reply. Sorry for the delayed response. I need to check my email notification settings.

I was fortunate to get clear skies last night so I set out to measure BZ Cyg and VZ Cyg. VSP lists the periods at 10.141932 and 4.864453 days, respectively. It amazes me that it is known to 6 decimal places.

Since the light curves are periodic my first thought was to use discrete Fourier analysis. My limited practical experience with FFT's tell me, however, that the light needs to be sampled at regular intervals. That is not always possible given the weather. Perhaps one could use quadratic regression to "fill in" a missed observation.

I find it to be all very interesting! Thanks again.

Brian

 

arx
arx's picture
Date Compensated Discrete Fourier Transform (DCDFT)

Hi Brian,

Sorry for the delay. I agree that FFT is not suitable for variable star data with gaps.

However, DCDFT is, and is available if such packages as the AAVSO's VStar package, and I think Peranso.

The limiting factor would be your requirement that you wish to work with only a couple of nights' data. I don't believe that would be sufficient for such analysis.

Roy

oopfan
oopfan's picture
VStar and Peranso

Thank you, Roy. I will definitely look into it.

Brian

HQA
HQA's picture
cepheid period measurement

Hi Brian,

Classical Cepheids have periods from about 1 day to about 100 days, with the majority in the 3-10day range.  They have a variety of light curve shapes, though most follow the classical asymmetric fast-rise, slow-fade from maximum shape.  A couple of nights is insufficient to measure the period (you don't come close to even covering the light curve once), though you can probably get a rough idea by eyeball-fitting a typical light curve template to the measurements.

There are numerous period-determination methods used for pulsating stars.  Some of these are implemented in the AAVSO's VStar program.  Other software programs include Peranso and Period98.

The reason the period can be quoted with such high precision is because the light curve is highly repeatable - they are almost clocks in most cases.  So if you determine one maxima to within a few seconds on one pulsation, and then wait a year and do it again, you can use the 365-day separation between the two times of maxima to further refine the period.  Many Cepheids have been followed for decades, providing an even longer baseline over which to determine the period.

I also recommend reading John Percy's book, Understanding Variable Stars, to get a better understanding of these fascinating stars!

Arne

oopfan
oopfan's picture
Thank you, Dr. Henden.

Thank you, Dr. Henden, I will look into Dr. Percy's book. Many years ago, I purchased your book "Astronomical Photometry" that you co-authored with Dr. Kaitchuck in 1990. Freshman year 1976 at University of Arizona the class spent several weeks touching upon Photometry at Steward Observatory. I didn't fully understand the importance of color transforms back then! Thank you.

Brian

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