RR Lyrae stars

 

Simulation

A complex dataset was generated. Double mode RR Lyrae stars with realistic periods and amplitudes (fundamental mode and first overtone) were simulated at the same time with characteristic behaviour of Blazhko RR Lyrae stars (showing triplets around one of the mean peak) and with one possible low amplitude non-radial mode.

The following frequencies and amplitudes were used in the simulation:


Frequency
[c/d]		Sinus amplitude
[mag]		Cosinus amplitude
[mag]		 
2.000.100.20- fundamental mode
2.150.010.02- side peak of Blazhko
1.850.020.01- side peak of Blazhko
3.300.300.10- first overtone
3.150.010.03- non-radial mode (lower amplitude)

The amplitude of the simulated light curve is ±0.5 magnitude.

Analysis

As a first step the spectral window was finally checked, what gives the special behaviour of the data distribution over the continuous 150 day run with 8 minutes sampling time. It gives the half width of the main peak and the fine structure of the spectra. Numerically it is the following:


PeaksFrequency
[c/d]		Half width
[c/d]		Amplitude
[mag]
mean00.004161
1. side0.01 0.2155
2. side0.0166 0.129
3. side0.0233 0.093
4. side0.02997 0.073
5. side0.0366 0.059

The spectal window is given in the first panel of the figure (download in PS).

The steps of frequency search:


 Frequency
[c/d]		Amplitude
[mag]		Phase
[deg]
1. stepf1 = 1.999990.2238526.87
2. stepf1 = 2.0000.2238426.60
 f2 = 3.3000.3158671.50
3. stepf1 = 2.000.2236126.57
 f2 = 3.300.3162371.57
 f3 = 3.150.0316218.43
 f4 = 1.850.0223663.43
 f5 = 2.150.0223626.56

As we see from the accepted values we have got back precisely the frequencies that we used in the generation of the synthetic data set. However, the residual spectrum shows values at 6.55x10-7 mag amplitudo level with a regular structure.

In the residual spectrum peaks are seen at:


Frequency
[c/d]		Amplitude
[10-7mag]
3.30086.5
0.90175.2
4.69845.3
2.29994.1
1.49603.5
2.31001.7

Warning: if we are looking for pulsation with amplitude on 10-6 mag level (solar type pulsation) then we can recognize false peaks because of the precision of the calculation.

Light curves: