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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 Lacertae
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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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 1
shows 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
[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.
-fm1 +fm1
-fm2 +fm2
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TelescopeLight curve solution – season 1
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
fm1 / 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 2
also shows a complex amplitude variation
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TelescopeFourier spectrum – season 2
frequency [c/d]
ampl
itude
[m
ag]
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
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
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 1season 2
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TelescopeChanges between the seasonsMean 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 & 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.