Period search in hungary mufran and tifran margit papar konkoly observatory budapest
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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

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Period search in hungary mufran and tifran margit papar konkoly observatory budapest
Period search in HungaryMuFrAn and TiFrAnMargit PaparóKonkoly Observatory, Budapest

Gamma Doradus Workshop, May 24-29, 2008, Nice


Hungarian asteroseismology group
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
Observational activity

HD 44195 – DSCT-Gamma Dor

HD 44283 - DSCT

HD 50844 - DSCT

HD 180642 – Beta Cephei


Period search programs
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
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 INFORMATIONH WRITE LS COEFFICIENTS-------WC QUIT-------------------------Q


Mathamatical algorithm used the basic is the same as in any other period search program
Mathamatical algorithm usedThe 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 m0102710988
Read the data (RL) and show the light curve (SL)Original light curve of m0102710988

  • rlDATA 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 1plot has been written to a.ps


Fast Fourier Transformation (FF), show the spectrum (SS)Spectrum and spectral window generated at the same timeOriginal 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-03NFFT: 65536 NUMBER OF STEPS: MINIMUM: 46165001 5001 1 1fmax= 1.20000E-02

  • ss LAST SPECTRUM----------------0 LAST WINDOW------------------1 SPECTRUM A------------------A SPECTRUM B------------------B SPECTRUM C------------------C SPECTRUM D------------------D1 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

  • lnNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED1 F( 1)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F0.01027 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


Comparison of spectra cs original spectrum and prewhitened by the trend
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------------------Dab 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
Parameter of frequency (LS)Prewhitened light curve by the trend frequency (PW)

  • lsNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED0 a( 0)=********* f( 1)= 0.009007 a( 1)=219.33072 sig= 0.2% fi( 1)= 89.30residual: 175.55481436325----->pw


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


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 MODEplot has been written to a.psf= 2.68999 a= 149.000f= 2.84481 a= 115.480f= 2.66389 a= 58.5009f= 2.91440 a= 42.4856f= 2.86916 a= 36.8989f= 2.80305 a= 33.9193f= 2.71432 a= 34.2917f= 2.64649 a= 29.4499

Determination of dominant mode

lnNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED1 F( 1)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F2.69038 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 140.0949689lsNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED0 a( 0)= 0.25069 f( 1)= 2.690581 a( 1)=149.84914 sig= 0.2% fi( 1)= 306.42residual: 140.09496887444

Determination of the dominant mode in m0102710988


Folded light curve by the dominant mode sf b version
Folded light curve by the dominant mode (SF – b version)

  • sf NORMAL PLOT--------------A FOLD THE DATA-----------Bb 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---------------Ba 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
Change of the system parametersfrom a single track to 58 tracks, B=1000 to B=1

  • Sp

  • A---MAXIMUM LENGTH OF GAPS 1000.000B---MAXIMUM LENGTH OF SEGMENTS 1000.000C---EPOCHA : 0.D---FORMAT IN TIME SERIES: TT XXS---SAVE SYSTEM VARIABLES NUMBER OF SEGMENTS: 0E---CHANGE ACTIVE SEGMENTSF---MANUAL CUTTING FOR SEGMENTSaNEW VALUE?.1A---MAXIMUM LENGTH OF GAPS 1.00000E-01B---MAXIMUM LENGTH OF SEGMENTS 1000.000C---EPOCHA : 0.D---FORMAT IN TIME SERIES: TT XXS---SAVE SYSTEM VARIABLES NUMBER OF SEGMENTS: 1E---CHANGE ACTIVE SEGMENTSF---MANUAL CUTTING FOR SEGMENTS


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


Multifrequency search for the two largest amplitude modes

lnNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED2 F( 1)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F2.690581 F( 2)=? TYPE 0 TO ENTER PERIOD TYPE -F TO GIVE THE NUMBER OF HARMONICS OF F2.84368 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

lsNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED0 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)= 23.96residual: 112.60969166981

Multifrequency search for the two largest amplitude modes


Fit by two frequencies as a single dataset and as 58 tracks 6th track hjd 2595
Fit by two frequenciesas 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 investigationWith given frequencies and amplitude any kind of synthetic data can be generated (MA)


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


Multifrequency search for 5 frequencies more low amplitude frequencies are shown
Multifrequency search for 5 frequenciesmore low amplitude frequencies are shown

  • lsNUMBER OF MAIN FREQUENCIES? 0 - PREVIOUSLY USED VALUES -1 - READ FREQUENCIES FROM FILE -N - KEEP THE FIRST N FREQUENCIES UNCHANGED0 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)= 118.11residual: 105.90738307820



Figure display separate window or data files for further representation
Figure display – separate windowor 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 INFORMATIONH WRITE LS COEFFICIENTS-------WC QUIT-------------------------Q


Test investigation by tifran for gamma doradus hybrid and spb beta cephei stars
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


Time frequency diagrams
Time-frequency diagrams SPB/Beta Cephei stars

  • 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


m0102710988 – real Gamma Doradus star SPB/Beta Cephei stars10-15 c/d – there is no constant signalGroup around 2.5-3 c/d – two peaks are resolvedcolour varation shows that more peaks are in this regionsolution: test on synthetic data

2.689092

0.009093

2.844412

2.913292

2.676806

2.805785


m0102739724 – Gamma Doradus/delta Scuti star SPB/Beta Cephei starsClear sign around the orbital period – amplitude is changingTwo 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


M0102739724 gamma doradus delta scuti star
m0102739724 – Gamma Doradus/delta Scuti star SPB/Beta Cephei stars

  • Continuous lines show the frequency values obtained in the traditional Fourier analyses


m0102755149 – Gamma Doradus SPB/Beta Cephei starsSign of the orbital period with lower intensityPartly resolved frequencies in the 2-3 c/d rangeSingle, 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


m0102790135 – Gamma Doradus/DCST SPB/Beta Cephei starsSome trace of the orbital periodSeparated two groups between 1.5-2.5 and 3-4 c/dBad resoluiton inside the groups – remarkable amplitude variation

1.862477

2.250655

2.971545

4.614975

4.781493

5.250662


m0102839234 – SPB/Beta Cephei SPB/Beta Cephei starsClear sign at the orbital periodFrequencies with large amplitude are clearly seen

3.528935

4.859924

5.912461

0.919464

1.821773

5.957922

6.402607

9.683105


Thank you
Thank you SPB/Beta Cephei stars


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