CZ LacertaeCZ LacertaeA Blazhko RR Lyrae starA Blazhko RR Lyrae starwith multiperiodic with multiperiodic

modulationmodulationÁdámÁdám SÓDOR SÓDOR

Konkoly Konkoly ObservatoryObservatoryof the Hungarianof the HungarianAcademy of SciencesAcademy of Sciences

20020088.0.099..0909.., Wien, , Wien, ÖsterreichÖsterreich

JENAM 2008, JENAM 2008, Symposium 4Symposium 4

AsteroseismologyAsteroseismologyand Stellar Evolutionand Stellar Evolution

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TelescopeMultiperiodic 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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Previous 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 / band

Reduction

• IRAF

• ISIS Image Subtraction Method (Alard 2000, A&AS, 144, 235)

Hipparcos epoch photometry on CZ Lac

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TelescopeV light curve of season 1 folded with P0 = 0.4322 d

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TelescopeV light curve of season 1

shows a complex amplitude variation

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Dirty spectrum

Clean spectrum

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

968)

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frequency [c/d]

ampl

itude

[m

ag]

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.

--ffm1m1 ++ffm1m1

--ffm2m2 ++ffm2m2

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frequency [c/d]

ampl

itude

[V

mag

]

1f0 2f0 3f0 4f0

Fit to the V light curve with 3 base frequencies

f 0 = 2.31388, fm1 = 0.054 c/d, fm2 = 0.067 c/d

using 72 linear combination harmonic components

reduced r.m.s. = 15 mmag

ffm1m1 / / ffm2 m2 = 0.80085 ± 0.00007 ≈ 4:5= 0.80085 ± 0.00007 ≈ 4:5

--ffm2m2/2/2 ++ffm2m2/2/2 ++ffm2m2--ffm1m1--ffm2m2++ffm1m1 ++ffm1m1++ffm2m2

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TelescopeV light curves of seasons 1 & 2 folded with P0 = 0.4322 d

season 1 season 2

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TelescopeV light curve of season 2

also shows a complex amplitude variation

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frequency [c/d]

ampl

itude

[m

ag]

1f0 2f0 3f0 4f0

--ffm1m1 ++ffm1m1--ffm2m2 ++ffm2m2

Vicinity of k·f0 peaks in the clean Fourier spectrum

f0 = 2.31388 c/d

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frequency [c/d]

ampl

itude

[V

mag

]

1f0 2f0 3f0 4f0

Fit of the V light curve with 3 base frequencies

f 0 = 2.31388, fm1 = 0.053 c/d, fm2 = 0.070 c/d

using 69 linear combination harmonic components

reduced r.m.s. = 12 mmag

ffm1m1 / / ffm2 m2 = 0.762 ± 0.001 ≈ 3:4= 0.762 ± 0.001 ≈ 3:4

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TelescopeComparison of V light curve solutionsModulation frequencies and amplitudes changed

3f0season 1season 2

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TelescopeChanges in the pulsation and modulation frequencies

Relative change of the pulsation frequency

(f0 2 – f0 1)/f0 1 = (7 (7 ±± 2) 2)··1010-6-6

Relative change of the modulation frequencies

(fm1 2 – fm1 1)/fm1 1 = –0.0181 –0.0181 ±± 0.0003 0.0003

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

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TelescopeComparison of V light curve solutionsThe modulation component amplitudes at different pulsation harmonic orders

season 1season 2

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TelescopeMean V light curves of season 1 and season 2

The mean pulsation amplitude decreased 0.03 mag

with the decreasing modulation amplitudesseason 1season 2

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TelescopeSummary

• 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.

TThe multiperiodicity is one more propertyhe multiperiodicity is one more property of Blazhko stars of Blazhko stars

that should be explainedthat should be explained by any forthcoming model. by any forthcoming model.