Period search in HungaryMuFrAn and TiFrAn

Margit PaparóKonkoly 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 44195 – DSCT-Gamma Dor

HD 44283 - DSCT

HD 180642 – Beta Cephei

HD 50844 - 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

j

jjj

jjk

kk tsinmitcosmtfi2expmF

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:

k i

kiikiik,obs tf2sinBtf2cosAm

k i

ikiik,obs tf2cosAm

kcoskk

kk

jjkj

kkjk

jj

jjjcos

FFTt̂cosm̂t̂costwm

t̂costwmtcosmDFT

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 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-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------------------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 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

cs

LAST SPECTRUM----------------0

LAST WINDOW------------------1

SPECTRUM A------------------A *

SPECTRUM B------------------B *

SPECTRUM C------------------C

SPECTRUM D------------------D

ab 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 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• ln

NUMBER 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 140.0949689ls

NUMBER 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

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 parametersfrom a single track to 58 tracks, B=1000 to B=1

• Sp• A---MAXIMUM LENGTH OF GAPS 1000.000

B---MAXIMUM LENGTH OF SEGMENTS 1000.000C---EPOCHA : 0.D---FORMAT IN TIME SERIES: TT XXS---SAVE SYSTEM VARIABLES NUMBER OF SEGMENTS: 0E---CHANGE ACTIVE SEGMENTSF---MANUAL CUTTING FOR SEGMENTS

aNEW 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

• ln

NUMBER 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

• ls

NUMBER 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

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 frequenciesmore 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 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

Original spectrum is compared to the residual spectrum

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 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:

- m0102710988 – Gamma Doradus

- m0102739724 – Gamma Doradus/ DSCT

- m0102755149 – Gamma Doradus

- m0102790135 – Gamma Doradus/DCST

- m0102839234 – 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

m0102710988 – real Gamma Doradus star10-15 c/d – there is no constant signal

Group around 2.5-3 c/d – two peaks are resolvedcolour 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

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

m0102739724 – Gamma Doradus/delta Scuti star

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

m0102755149 – Gamma DoradusSign of the orbital period with lower intensity

Partly 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/DCSTSome trace of the orbital period

Separated 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 CepheiClear 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

Thank you