CZ LacertaeA Blazhko RR Lyrae starwith multiperiodic

modulationÁdám SÓDOR

Konkoly Observatoryof the HungarianAcademy of Sciences

2008.09.09., Wien, Österreich

JENAM 2008, Symposium 4

Asteroseismologyand Stellar Evolution

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TelescopeMultiperiodic modulationMultiperiodic modulation was suggested by earlier observations, e.g. by the MACHO and OGLE surveys.Several such stars were extensively observed first

by our RR Lyrae survey project.An example is our ongoing observation of V759 Cyg:

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TelescopeThe data of CZ LacertaePrevious observations

• Konkoly pe. observations (7 nights)• Bookmeyer (29 V data points)• Hipparcos epoch photometry

Our observations• 24” automatic telescope, CCD• 2 seasons: Sep 2004. – Dec 2005.• 4 bands: BV(RI)C

• 7000 – 8000 data points / bandReduction

• IRAF• ISIS Image Subtraction Method

(Alard 2000, A&AS, 144, 235)

Hipparcos epoch photometry on CZ Lac

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TelescopeLight curve – season 1V light curve of season 1 folded with P0 = 0.4322 d

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TelescopeLight curve – season 1V light curve of season 1shows a complex amplitude variation

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TelescopeFourier spectrum – season 1

Dirty spectrum

Clean spectrum

clean algorithm: Roberts et al. (1987, AJ, 93,

968)

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TelescopeFourier spectrum – season 1

frequency [c/d]

ampl

itude

[mag

]

1f0 2f0 3f0 4f0

Vicinity of k·f0 peaks in the clean Fourier spectrum

f0 = 2.31388 c/d

The two pairs of modulation peaks are similarly strong.

-fm1 +fm1

-fm2 +fm2

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TelescopeLight curve solution – season 1

frequency [c/d]

ampl

itude

[V m

ag]

1f0 2f0 3f0 4f0

Fit to the V light curve with 3 base frequenciesf 0 = 2.31388, fm1 = 0.054 c/d, fm2 = 0.067 c/dusing 72 linear combination harmonic componentsreduced r.m.s. = 15 mmagfm1 / fm2 = 0.80085 ± 0.00007 ≈ 4:5

-fm2/2 +fm2/2 +fm2-fm1-fm2+fm1 +fm1+fm2

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TelescopeLight curve – seasons 1 & 2V light curves of seasons 1 & 2 folded with P0 = 0.4322 d

season 1 season 2

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TelescopeLight curve – season 2V light curve of season 2also shows a complex amplitude variation

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TelescopeFourier spectrum – season 2

frequency [c/d]

ampl

itude

[mag

]

1f0 2f0 3f0 4f0

-fm1 +fm1-fm2 +fm2

Vicinity of k·f0 peaks in the clean Fourier spectrum

f0 = 2.31388 c/d

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TelescopeLight curve solution – season 2

frequency [c/d]

ampl

itude

[V m

ag]

1f0 2f0 3f0 4f0

Fit of the V light curve with 3 base frequenciesf 0 = 2.31388, fm1 = 0.053 c/d, fm2 = 0.070 c/dusing 69 linear combination harmonic componentsreduced r.m.s. = 12 mmag fm1 / fm2 = 0.762 ± 0.001 ≈ 3:4

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TelescopeChanges between the seasonsComparison of V light curve solutionsModulation frequencies and amplitudes changed

3f0season 1season 2

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TelescopeChanges between the seasonsChanges in the pulsation and modulation frequencies

Relative change of the pulsation frequency (f0 2 – f0 1)/f0 1 = (7 ± 2)·10-6

Relative change of the modulation frequencies (fm1 2 – fm1 1)/fm1 1 = –0.0181 ± 0.0003

(fm2 2 – fm2 1)/fm2 1 = +0.0328 ± 0.0011

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TelescopeChanges between the seasonsComparison of V light curve solutionsThe modulation component amplitudes at different pulsation harmonic orders season 1

season 2

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TelescopeChanges between the seasonsMean V light curves of season 1 and season 2The mean pulsation amplitude decreased 0.03 mag with the decreasing modulation amplitudes

season 1season 2

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TelescopeSummary & conclusionSummary

• CZ Lac is the first extensively observed Blazhko star with double periodic modulation.

• The frequency ratio of the two modulations changed from 4:5 to about 3:4.

• The modulation properties changed rapidly between the two seasons.

Conclusion• Multiperiodic modulation seems to be more unstable than the

monoperiodic ones.• Multiperiodic modulation renders earlier Blazhko models that

bind the modulation frequency to the rotation of the star invalid.• There is not yet any model that explains the multiperiodic

modulation.The multiperiodicity is one more property of Blazhko stars

that should be explained by any forthcoming model.