1. Period search in Hungary MuFrAn and TiFrAn Margit Paparó Konkoly Observatory, Budapest Gamma Doradus Workshop, May 24-29, 2008, Nice

2. Hungarian Asteroseismology Group Paparó Margit Csubry Zoltán Benkő József Kolláth Zoltán Szabados László Szabó Róbert Sódorné, Bognár Zsófia PiStA (Molnár László, Plachy Emese, Pápics Péter, Kerekes Gyöngyi, Már András, Bokor Eszter, Sztankó Nándor + Verebélyi Erika, Olle Hajnalka, Györffy Ákos)

3. Observational activity HD 44195 – DSCT-Gamma Dor HD 44283 - DSCT HD 180642 – Beta Cephei HD 50844 - DSCT

4. Period search programs MuFrAn – Multi Frequency Analysis Developed by Zoltán Kolláth for period search and graphical display TiFrAn – Time Frequency Analysis Developed by Z. Kolláth and Z. Csubry for time-dependent frequency analysis

5. Menu of MuFrAn READ LIGHT CURVE------------ RL DFT------------------------- DF WRITE LIGHT CURVE--------- -WL ZOOM-FFT-------------------- FF REFRESH THE DATA------------- R LS FIT (LINEAR)------------- LS READ SPECTRUM--------------- RS SVD FIT-------------------- SVD WRITE SPECTRUM------------- WS LS FIT (NONLINEAR)---------- LN SHOW THE LIGHT CURVE------ SL PREWHITENING---------------- PW SHOW THE FIT----------------- SF MAKE SYNTHETIC DATA---------MS SHOW THE SPECTRUM-----------SS TEST AMPLITUDES------------- MA COMPARE THE SPECTRA-------- CS SYSTEM PARAMETERS----------- SP MOVE THE SPECTRUM ----------- M ------------------------------ READ LS COEFFICIENTS-------- RC DISPLAY THIS INFORMATION H WRITE LS COEFFICIENTS------- WC QUIT------------------------- Q

6. Mathamatical algorithm used The basic is the same as in any other period search program FFT: j: unevenly sampled, k: evenly sampled DFT: LS: LN:

7. Read the data (RL) and show the light curve (SL) Original light curve of m0102710988 rl DATA FILE? m0102710988.dat -----> sl CURSOR SHOULD BE ON THE FIGURE! n -- SHOW THE NEXT SEGMENT s -- CHANGE ACTIVE/INAVTIVE STATUS OF SEGMENT w -- WRITE THE PLOT TO FILE (a.ps) q -- QUIT THIS MODE MOUSE: RIGHT -- QUIT THIS MODE 1 1 plot has been written to a.ps

8. Fast Fourier Transformation (FF), show the spectrum (SS) Spectrum and spectral window generated at the same time Original spectrum of m0102710988 and spectral window of the run ff MAXIMUM FREQUENCY: 17.7338 MINIMUM FREQUENCY: 0 MAXIMUM FREQUENCY: 20 7.47100E-03 3.52435E-03 NFFT: 65536 NUMBER OF STEPS: MINIMUM: 4616 5001 5001 1 1 fmax= 1.20000E-02 ss LAST SPECTRUM----------------0 LAST WINDOW------------------1 SPECTRUM A------------------A SPECTRUM B------------------B SPECTRUM C------------------C SPECTRUM D------------------D 1 CURSOR SHOULD BE ON THE FIGURE! s -- SAVE THE CURSOR FREQUENCY FOR LS FIT IT ERASES THE PREVIOUSLY USED FREQUENCIES! a -- ADD THE CURSOR FREQUENCY FOR LS FIT l -- SET MINIMUM FREQUENCY r -- SET MAXIMUM FREQUENCY p -- PRINT FREQUENCY AND AMPLITUDE w -- WRITE THE PLOT TO FILE (a.ps) q -- QUIT THIS MODE MOUSE: MIDDLE -- PRINT FREQUENCY AND AMPLITUDE RIGHT -- QUIT THIS MODE

9. Determination of the trend frequency by iteration (LN) Folded light curve by the trend frequency, the continuous line is subtracted in the prewhitening process ln NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 1 F( 1)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F 0.01027 0.0102700 175.7066116 0.0091429 175.5562698 0.0090131 175.5548171 0.0090074 175.5548144 0.0090072 175.5548144 0.0090072 175.5548144 0.0090072 175.5548144

10. Comparison of spectra (CS) Original spectrum and prewhitened by the trend cs LAST SPECTRUM----------------0 LAST WINDOW------------------1 SPECTRUM A------------------A * SPECTRUM B------------------B * SPECTRUM C------------------C SPECTRUM D------------------D a b CURSOR SHOULD BE ON THE FIGURE! s -- SAVE THE CURSOR FREQUENCY FOR LS FIT IT ERASES THE PREVIOUSLY USED FREQUENCIES! a -- ADD THE CURSOR FREQUENCY FOR LS FIT l -- SET MINIMUM FREQUENCY r -- SET MAXIMUM FREQUENCY p -- PRINT FREQUENCY AND AMPLITUDE w -- WRITE THE PLOT TO FILE (a.ps) q -- QUIT THIS MODE MOUSE: MIDDLE -- PRINT FREQUENCY AND AMPLITUDE RIGHT -- QUIT THIS MODE

11. Parameter of frequency (LS) Prewhitened light curve by the trend frequency (PW) ls NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 0 a( 0)=********* f( 1)= 0.009007 a( 1)=219.33072 sig= 0.2% fi( 1)= 89.30 residual: 175.55481436325 -----> pw

12. Set up maximum and minimum frequencies Cut from left (l) and from right (r), mark frequency and amplitude values

13. Determination of the dominant mode in m0102710988 Peaks in the original spectrum CURSOR SHOULD BE ON THE FIGURE! s -- SAVE THE CURSOR FREQUENCY FOR LS FIT IT ERASES THE PREVIOUSLY USED FREQUENCIES! a -- ADD THE CURSOR FREQUENCY FOR LS FIT l -- SET MINIMUM FREQUENCY r -- SET MAXIMUM FREQUENCY p -- PRINT FREQUENCY AND AMPLITUDE w -- WRITE THE PLOT TO FILE (a.ps) q -- QUIT THIS MODE MOUSE: MIDDLE -- PRINT FREQUENCY AND AMPLITUDE RIGHT -- QUIT THIS MODE plot has been written to a.ps f= 2.68999 a= 149.000 f= 2.84481 a= 115.480 f= 2.66389 a= 58.5009 f= 2.91440 a= 42.4856 f= 2.86916 a= 36.8989 f= 2.80305 a= 33.9193 f= 2.71432 a= 34.2917 f= 2.64649 a= 29.4499 Determination of dominant mode ln NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 1 F( 1)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F 2.69038 2.6903800 140.1152661 2.6906078 140.0953178 2.6905779 140.0949748 2.6905818 140.0949690 2.6905813 140.0949689 2.6905814 140.0949689 2.6905814 140.0949689 2.6905814 140.0949689 ls NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 0 a( 0)= 0.25069 f( 1)= 2.690581 a( 1)=149.84914 sig= 0.2% fi( 1)= 306.42 residual: 140.09496887444

14. Folded light curve by the dominant mode (SF – b version) sf NORMAL PLOT--------------A FOLD THE DATA-----------B b CURSOR SHOULD BE ON THE FIGURE! w -- WRITE THE PLOT TO FILE (a.ps) q -- QUIT THIS MODE MOUSE: RIGHT -- QUIT THIS MODE

15. Normal plot of the fitted light curve (SF – a version) System parameters are changed to shorter segments (58 night). Fit with the dominant mode, with a single frequency sf NORMAL PLOT------------------A FOLD THE DATA---------------B a CURSOR SHOULD BE ON THE FIGURE! n -- SHOW THE NEXT SEGMENT s -- CHANGE ACTIVE/INAVTIVE STATUS OF SEGMENT w -- WRITE THE PLOT TO FILE (a.ps) q -- QUIT THIS MODE MOUSE: RIGHT -- QUIT THIS MODE

16. Change of the system parameters from a single track to 58 tracks, B=1000 to B=1 Sp A---MAXIMUM LENGTH OF GAPS 1000.000 B---MAXIMUM LENGTH OF SEGMENTS 1000.000 C---EPOCHA : 0. D---FORMAT IN TIME SERIES: TT XX S---SAVE SYSTEM VARIABLES NUMBER OF SEGMENTS: 0 E---CHANGE ACTIVE SEGMENTS F---MANUAL CUTTING FOR SEGMENTS a NEW VALUE?.1 A---MAXIMUM LENGTH OF GAPS 1.00000E-01 B---MAXIMUM LENGTH OF SEGMENTS 1000.000 C---EPOCHA : 0. D---FORMAT IN TIME SERIES: TT XX S---SAVE SYSTEM VARIABLES NUMBER OF SEGMENTS: 1 E---CHANGE ACTIVE SEGMENTS F---MANUAL CUTTING FOR SEGMENTS

17. Dominant mode has been removed Comparison of spectra before and after prewhitening by the dominnant mode

18. Multifrequency search for the two largest amplitude modes ln NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 2 F( 1)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F 2.690581 F( 2)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F 2.84368 2.6905810 2.8436800 112.8348904 2.6908623 2.8444599 112.6115903 2.6908235 2.8443985 112.6097113 2.6908285 2.8444034 112.6096919 2.6908279 2.8444030 112.6096917 2.6908280 2.8444030 112.6096917 2.6908280 2.8444030 112.6096917 2.6908280 2.8444030 112.6096917 ls NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 0 a( 0)= 0.08401 f( 1)= 2.690828 a( 1)=151.22834 sig= 0.2% fi( 1)= 304.63 f( 2)= 2.844403 a( 2)=117.75338 sig= 0.2% fi( 2)= 23.96 residual: 112.60969166981

19. Fit by two frequencies as a single dataset and as 58 tracks (6th track – HJD 2595 )

20. Fit of JD 2615 and 2617 nights (26 and 28 tracks) Both the high and low amplitude tracks are well- fitted by two frequencies

21. Make synthetic light curve (MS) The fit is written in a separate data file for possible further investigation With given frequencies and amplitude any kind of synthetic data can be generated (MA)

22. Residual spectrum after prewhitening with two frequencies and comparison to the residual spectrum after prewhitening with one frequency

23. Multifrequency search for 5 frequencies more low amplitude frequencies are shown ls NUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED 0 a( 0)= 0.08827 f( 1)= 2.689101 a( 1)=162.35323 sig= 0.2% fi( 1)= 324.90 f( 2)= 2.844410 a( 2)=116.97104 sig= 0.2% fi( 2)= 23.56 f( 3)= 2.913291 a( 3)= 37.11501 sig= 0.6% fi( 3)= 57.67 f( 4)= 2.676770 a( 4)= 47.79147 sig= 0.5% fi( 4)= 301.66 f( 5)= 2.805789 a( 5)= 20.35828 sig= 1.2% fi( 5)= 118.11 residual: 105.90738307820

24. Original spectrum is compared to the residual spectrum

25. Figure display – separate window or data files for further representation READ LIGHT CURVE------------ RL DFT------------------------- DF WRITE LIGHT CURVE--------- -WL ZOOM-FFT-------------------- FF REFRESH THE DATA------------- R LS FIT (LINEAR)------------- LS READ SPECTRUM--------------- RS SVD FIT-------------------- SVD WRITE SPECTRUM------------- WS LS FIT (NONLINEAR)---------- LN SHOW THE LIGHT CURVE------ SL PREWHITENING---------------- PW SHOW THE FIT----------------- SF MAKE SYNTHETIC DATA---------MS SHOW THE SPECTRUM-----------SS TEST AMPLITUDES------------- MA COMPARE THE SPECTRA-------- CS SYSTEM PARAMETERS----------- SP MOVE THE SPECTRUM ----------- M ------------------------------ READ LS COEFFICIENTS-------- RC DISPLAY THIS INFORMATION H WRITE LS COEFFICIENTS-------WC QUIT------------------------- Q

26. Test investigation by TiFrAn for Gamma Doradus, hybrid and SPB/Beta Cephei stars The different stars were selected on the classification list of Philippe: - m0102710988 – Gamma Doradus - m0102739724 – Gamma Doradus/ DSCT - m0102755149 – Gamma Doradus - m0102790135 – Gamma Doradus/DCST - m0102839234 – SPB/Beta Cephei

27. Time-frequency diagrams Upper panel: the original light curve Middle panel: larger range in frequency Bottom panel: smaller range in frequency Interpretation of colours: give the amplitude value in that moment from red to blue Intensity of colour: shows the variability of the amplitude in time Source: real variablity or interferency of unsolved modes Short Term Fourier-Transform- light curve is weihgted with a Gauss curve as large halfwitdth as a length of some cycles Wider Gauss- more precise frequency resolution but worse time resolution At some part the colour code is modified to display the weaker structure

28. m0102710988 – real Gamma Doradus star 10-15 c/d – there is no constant signal Group around 2.5-3 c/d – two peaks are resolved colour varation shows that more peaks are in this region solution: test on synthetic data 2.689092 0.009093 2.844412 2.913292 2.676806 2.805785

29. m0102739724 – Gamma Doradus/delta Scuti star Clear sign around the orbital period – amplitude is changing Two groups are shown but with small amplitude – frequencies are resolved 1.273618 1.594065 1.851901 1.998287 4.348190 4.155921 3.749123 3.779358 3.451291

30. m0102739724 – Gamma Doradus/delta Scuti star Continuous lines show the frequency values obtained in the traditional Fourier analyses

31. m0102755149 – Gamma Doradus Sign of the orbital period with lower intensity Partly resolved frequencies in the 2-3 c/d range Single, fully resolved frequency at 1.7 c/d – amplitude seems to vary 2.636558 1.672298 2.297127 2.493420 2.557315 2.776238 2.819488 2.977274

32. m0102790135 – Gamma Doradus/DCST Some trace of the orbital period Separated two groups between 1.5-2.5 and 3-4 c/d Bad resoluiton inside the groups – remarkable amplitude variation 1.862477 2.250655 2.971545 4.614975 4.781493 5.250662

33. m0102839234 – SPB/Beta Cephei Clear sign at the orbital period Frequencies with large amplitude are clearly seen 3.528935 4.859924 5.912461 0.919464 1.821773 5.957922 6.402607 9.683105

34. Thank you