I Fourier Series and Cepheid Variables

[no_drama_llama_77]

Summary:: If given a set of data points for the magnitude of a cepheid variable at a certain time, how can we use Fourier series to find the period of the cepheid variable from the equation of the light curve? Where can I find data points for M31_V1?

If given a set of data points for the magnitude of a cepheid variable at a certain time (JD), how can we use Fourier series to find the period of the cepheid variable?

I'm trying to do a math investigation (IB math investigation) on finding the period of the cepheid variable M31_V1 from data points for the magnitude of the cepheid variable at a certain time (JD). However, to find the equation of the light curve using Fourier series, the period must be given already right? How can I find the period then?

Also, I'm trying to plot the data points from the AAVSO (https://www.aavso.org/data-download/aavsodata_5f913c1d4f3f0.txt), but it seems like the points are not forming a curve. Can I find data points for the magnitude and JD of M31_V1 anywhere else?

UPDATE:
In dire need of Fourier Series help.
If anyone can please help me with understanding how to calculate the Fourier series based on the AAVSO raw data and the periods I've obtained from the spectral density graph gotten from coding, I will be very grateful.
(Read posts above)

Thank you so much T-T

 

[Vanadium 50]

From my calculations
Period for the left frequency: 502.3156753… days
Period for the right frequency: 31.38948703… days

A. Please watch the precision. You are not getting 11 digits here no matter what you do: that's 10 ms over the entire observing period.
B. Please wtach your units: the tick marks go from 0.005 Hz to 0.030 Hz. That's a period from 30 to 200 seconds. You can't see a 30 day period on this plot, nor distinguish it from 500 days.

If you sample every 2.4 hours, you can't see a 200 second effect. It's got to be noise.

 

[no_drama_llama_77]

A. Please watch the precision. You are not getting 11 digits here no matter what you do: that's 10 ms over the entire observing period.
B. Please wtach your units: the tick marks go from 0.005 Hz to 0.030 Hz. That's a period from 30 to 200 seconds. You can't see a 30 day period on this plot, nor distinguish it from 500 days.

If you sample every 2.4 hours, you can't see a 200 second effect. It's got to be noise.

A. I wasn't sure what the data uncertainty was, so I rounded my figures to 3 significant figures in my written report. Will that be appropriate?

B. When I apply the Lomb Scargle Periodogram to the data, does that mean my frequency is actually represented by the units (1/days) rather than the usual (1/seconds), since the AAVSO data measures the period using Julian dates (days)? I may have mislabelled my spectral density graph.
I obtained 502 frequency by dividing 1/0.00199078. I obtained 0.00199078 by estimating the coordinates of the second-highest peak on the left

 

[Vanadium 50]

A. I wasn't sure what the data uncertainty was, so I rounded my figures to 3 significant figures in my written report. Will that be appropriate?

Do you think so? That means you think you know the period to one part in a thousand. (And for that matter, that the period is stable to one part in a thousand)

When I apply the Lomb Scargle Periodogram to the data, does that mean my frequency is actually represented by the units (1/days) rather than the usual (1/seconds), since the AAVSO data measures the period using Julian dates (days)

If days are the input than 1/days is the output.

That said, I am still far from convinced that you are doing anything besides chasing fluctuations.
A. If you split the data into pre-1940 and post-1940 do you get the same answer?
B. If you fit even and odd data points do you get the same answer?

 

[Vanadium 50]

A paper has made observations on the period of M31_V1, and they obtained a period of 31.4 days. Therefore, I think the peak on the right is not noise but rather the closest to the correct period

"I got the same result as someone else, and therefore I must be right" is not the way we do science. People have gotten burned doing this.

 

[no_drama_llama_77]

Do you think so? That means you think you know the period to one part in a thousand. (And for that matter, that the period is stable to one part in a thousand)

I really don't know. The uncertainty is left blank.

That said, I am still far from convinced that you are doing anything besides chasing fluctuations.
A. If you split the data into pre-1940 and post-1940 do you get the same answer?
B. If you fit even and odd data points do you get the same answer?

I'm not because my math IA (an essay written for my math class for the IB) focuses more on the mathematical working and steps rather than the precision of the data I've collected from AAVSO. I would love to get my data as precise as possible but I don't have the time.

"I got the same result as someone else, and therefore I must be right" is not the way we do science. People have gotten burned doing this.

I understand; however, I am a high school student trying to write up my math investigation paper. The curriculum commends students for verifying their data with literature values for accuracy.

 

[no_drama_llama_77]

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[no_drama_llama_77]

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[no_drama_llama_77]

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[no_drama_llama_77]

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[no_drama_llama_77]

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