1. CZ Lacertae A Blazhko RR Lyrae star with multiperiodic modulation Ádám SÓDOR Konkoly Observatory of the Hungarian Academy of Sciences 2008.09.09., Wien, Österreich JENAM 2008, Symposium 4 Asteroseismology and Stellar Evolution

2. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Multiperiodic 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:

3. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope 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

4. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope V light curve of season 1 folded with P 0 = 0.4322 d

5. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope V light curve of season 1 shows a complex amplitude variation

6. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Dirty spectrum Clean spectrum clean algorithm: Roberts et al. (1987, AJ, 93, 968)

7. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope frequency [c/d] amplitude [mag] 1f01f0 2f02f0 3f03f0 4f04f0 Vicinity of k·f 0 peaks in the clean Fourier spectrum f 0 = 2.31388 c/d The two pairs of modulation peaks are similarly strong. -f m1 +f m1 -f m2 +f m2

8. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope frequency [c/d] amplitude [V mag] 1f01f0 2f02f0 3f03f0 4f04f0 Fit to the V light curve with 3 base frequencies f 0 = 2.31388, f m1 = 0.054 c/d, f m2 = 0.067 c/d using 72 linear combination harmonic components reduced r.m.s. = 15 mmag f m1 / f m2 = 0.80085 ± 0.00007 4:5 -f m2 /2 +f m2 /2 +f m2 -f m1 -f m2 +f m1 +f m1 +f m2

9. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope V light curves of seasons 1 & 2 folded with P 0 = 0.4322 d season 1season 2

10. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope V light curve of season 2 also shows a complex amplitude variation

11. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope frequency [c/d] amplitude [mag] 1f01f0 2f02f0 3f03f0 4f04f0 -f m1 +f m1 -f m2 +f m2 Vicinity of k·f 0 peaks in the clean Fourier spectrum f 0 = 2.31388 c/d

12. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope frequency [c/d] amplitude [V mag] 1f01f0 2f02f0 3f03f0 4f04f0 Fit of the V light curve with 3 base frequencies f 0 = 2.31388, f m1 = 0.053 c/d, f m2 = 0.070 c/d using 69 linear combination harmonic components reduced r.m.s. = 12 mmag f m1 / f m2 = 0.762 ± 0.001 3:4

13. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Comparison of V light curve solutions Modulation frequencies and amplitudes changed 3f03f0 season 1 season 2

14. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Changes in the pulsation and modulation frequencies Relative change of the pulsation frequency (7 ± 2)·10 -6 (f 0 2 – f 0 1 )/f 0 1 = (7 ± 2)·10 -6 Relative change of the modulation frequencies –0.0181 ± 0.0003 (f m1 2 – f m1 1 )/f m1 1 = –0.0181 ± 0.0003 +0.0328 ± 0.0011 (f m2 2 – f m2 1 )/f m2 1 = +0.0328 ± 0.0011

15. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Comparison of V light curve solutions The modulation component amplitudes at different pulsation harmonic orders season 1 season 2

16. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Mean V light curves of season 1 and season 2 The mean pulsation amplitude decreased 0.03 mag with the decreasing modulation amplitudes season 1 season 2

17. Ádám SÓDOR CZ Lac JENAM 2008 Asteroseismology and Stellar Evolution Telescope Summary 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.