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

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)

Observational activity HD – DSCT-Gamma Dor HD DSCT HD – Beta Cephei HD DSCT

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

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

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:

Read the data (RL) and show the light curve (SL) Original light curve of m rl DATA FILE? m 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

Fast Fourier Transformation (FF), show the spectrum (SS) Spectrum and spectral window generated at the same time Original spectrum of m and spectral window of the run ff MAXIMUM FREQUENCY: MINIMUM FREQUENCY: 0 MAXIMUM FREQUENCY: E E-03 NFFT: NUMBER OF STEPS: MINIMUM: fmax= E-02 ss LAST SPECTRUM LAST WINDOW 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

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

Comparison of spectra (CS) Original spectrum and prewhitened by the trend cs LAST SPECTRUM LAST WINDOW 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

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)= a( 1)= sig= 0.2% fi( 1)= residual: > pw

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

Determination of the dominant mode in m 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= a= f= a= f= a= f= a= f= a= f= a= f= a= f= a= 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 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)= a( 1)= sig= 0.2% fi( 1)= residual:

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

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

Change of the system parameters from a single track to 58 tracks, B=1000 to B=1 Sp A---MAXIMUM LENGTH OF GAPS B---MAXIMUM LENGTH OF SEGMENTS 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 E-01 B---MAXIMUM LENGTH OF SEGMENTS 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

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

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 F( 2)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F 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)= a( 1)= sig= 0.2% fi( 1)= f( 2)= a( 2)= sig= 0.2% fi( 2)= residual:

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

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

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)

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

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)= f( 1)= a( 1)= sig= 0.2% fi( 1)= f( 2)= a( 2)= sig= 0.2% fi( 2)= f( 3)= a( 3)= sig= 0.6% fi( 3)= f( 4)= a( 4)= sig= 0.5% fi( 4)= f( 5)= a( 5)= sig= 1.2% fi( 5)= residual:

Original spectrum is compared to the residual spectrum

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

Test investigation by TiFrAn for Gamma Doradus, hybrid and SPB/Beta Cephei stars The different stars were selected on the classification list of Philippe: - m – Gamma Doradus - m – Gamma Doradus/ DSCT - m – Gamma Doradus - m – Gamma Doradus/DCST - m – SPB/Beta Cephei

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

m – real Gamma Doradus star c/d – there is no constant signal Group around c/d – two peaks are resolved colour varation shows that more peaks are in this region solution: test on synthetic data

m – 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

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

m – 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

m – Gamma Doradus/DCST Some trace of the orbital period Separated two groups between and 3-4 c/d Bad resoluiton inside the groups – remarkable amplitude variation

m – SPB/Beta Cephei Clear sign at the orbital period Frequencies with large amplitude are clearly seen

Thank you