Real or apparent? -- Period variations of Kepler and TESS RR Lyrae stars based on their O-C diagrams

Real or apparent? Period variations of Kepler and TESS RR Lyrae stars based on their O-C diagrams Benkő, J. M.1, Bódi, A.2, Plachy, E.1,3, Molnár, L.1,3 1Konkoly Observatory, HUN-REN Research Centre for Astronomy and Earth Sciences, Budapest, Hungary 2Department of Astrophysical Sciences, Princeton University, USA 3 ELTE Eötvös Loránd University, Institute of Physics and Astronomy, Budapest, Hungary Kepler non-Blazhko RRab stars Acknowledgments This poster includes data collected by the Kepler and TESS missions is provided by the NASA Science Mission Directorate. The research was partly supported by the 'SeismoLab' KKP-137523 Élvonal grant of the Hungarian Research, Development and Innovation Office (NKFIH) and by the NKFIH excellence grant TKP2021-NKTA64. RRc stars in the TESS Continuous Viewing Zone References Benkő, J. M. et al. (2014) ApJS 213, id.31 Benkő, J. M. et al. (2023) MNRAS 521, 443 Benkő, J. M. et al. (2025) A&A 697, A154 Forró, A. et al. (2020) ApJS 260, id.20 Koen, C. (2006) MNRAS 365, 489 Nemec, J. M. et al. (2013) ApJ 773, id.181 The main steps of the analysis (for the details see Benkő et al. 2025) Input Light curves for RRab stars and Blazhko RR Lyr stars, (Benkő et al. 2014, Forró et al. 2020) from the original Kepler field light curves for RRc stars from the TESS continuous viewing zone (Benkő et al. 2023) O-C diagrams calculated by the template fitting method (col. 1 in Fig 1 and Fig. 3) General statistical models by Koen (2006). Pi instantaneous period: - constant mean period - smooth real period variation - cycle to cycle (C2C) light curve variation + timing or phase error (= accuracy of the O-C values): ti = Ti + ei Three random variable: ξ, η, e, and three parameters: σξ, ση, σe Four models tested: M1 - Only phase noise (σe > 0, σξ = ση ) M2 - Phase noise + C2C variation (σe > 0, ση > 0, σξ = 0) M3 - Phase noise + real period variation (σe > 0, σξ > 0, ση = 0) M4 - Phase noise + period variation + C2C variation (σe > 0, ση > 0, σξ > 0) - For each model maximize the Gaussian log-likelihood function - Calculate both Bayesian and Akaike information criteria Output - Best fitting model - parameters: σξ, ση, σe - pseudo-residuals (≈ observed O-C minus fitted model O-C, see cols. 2 in Figs. 1 & 3). - 89% of RRab and 81% of RRc stars of the O-C curves can be explained assuming timing noise and C2C variation without true main period change. - The average C2C variation strength ση is one order of magnitude higher for RRc than RRab stars - C2C variation is dependent on the pulsation period: the effect is stronger for longer period (Figs. 2 & 4). A similar analysis is in progress for Kepler Blazhko stars as for non-Blazhko stars. Preliminary results - The averaged ση is even higher than that of RRc stars. This may be a natural explanation for the historically observed high amplitude irregular O-C variations - The strength of C2C variation ση and strength of FM variation in the Blazhko effect R is related (see Fig. 6) Results Kepler Blazhko stars 0 2 4 0.4 0.45 0.5 0.55 0.6 0.65 0.7 ση x 10−5 [d] P0 [d] −3 −2.5 −2 −1.5 −1 −0.5 0 [M/H] 0 2 4 5600 6000 6400 6800 ση x 10−5 [d] Teff [K] 1.5 2 2.5 3 log g [cm s2] 0 2 4 2.5 3 3.5 4 4.5 5 ση x 10−5 [d] ξt [km s−1] 4 6 8 10 12 14 16 18 20 νmac [km s−1] 0 1 2 3 0.25 0.3 0.35 0.4 ση x 10−4 [d] P1 [d] −3 −2.5 −2 −1.5 −1 −0.5 [Fe/H] 0 1 2 3 6500 7000 7500 ση x 10−4 [d] Teff [K] 3 3.5 4 log g [cm s2] −0.5 0.0 0.5 NR Lyr O -C diagrams −2.5 0.0 2.5 P.e0do -residuals 0.0 0.5 p=0.40 M2 Distributions 0 1 V715 Cyg −2.5 0.0 2.5 0.0 0.5 p=0.60 M4 0.0 0.5 V782 Cyg −2.5 0.0 2.5 0.0 0.5 p=0.45 M2 −0.25 0.00 0.25 V784 Cyg −2.5 0.0 2.5 0.0 0.5 p=0.89 M2 −0.25 0.00 0.25 KIC 6 100702 −2.5 0.0 2.5 0.0 0.5 p=0.29 M2 −0.5 0.0 NQ L1− −2.5 0.0 2.5 0.0 0.5 p=0.09 M2 −0.5 0.0 O -C [ x 10 −3 d FN Ly− −2.5 0.0 2.5 Standa−d −e.id0al 0.0 0.5 No−mali2ed No. p=0. 11 M2 −0.5 0.0 KIC 7030715 −2.5 0.0 2.5 0.0 0.5 p=0.96 M2 −1 0 V349 L1− −2.5 0.0 2.5 0.0 0.5 p=0.55 M2 −2 0 V368 L1− −2.5 0.0 2.5 0.0 0.5 p=0.52 M2 0 2 V1510 C1g −2.5 0.0 2.5 0.0 0.5 p=0.10 M2 0 1 V894 C1g −2.5 0.0 2.5 0.0 0.5 p=0.68 M2 500 1000 1500 0.0 0.5 KIC 9658012 BJD − 2454833 0 100 200 300 400 −2.5 0.0 2.5 N0mbe− of O − C point. −2.5 0.0 2.5 0.0 0.5 p=0.34 M2 Standa−d −e.id0al −1 0 1 [SHM2017] J282.06827+62.45832 Resid. l O -Cs −2.5 0.0 2.5 Pse.do-+esid. ls 0.0 0.5 p=0.54 M2 Dis-+ib.-ions −1 0 1 G i DR2 5476969341269561344 −2.5 0.0 2.5 0.0 0.5 p=0.65 M3 −2.5 0.0 G i DR2 1650042086261498880 −2.5 0.0 2.5 0.0 0.5 p=0.26 M4 −0.5 0.0 0.5 G i DR2 5280964179391935616 −2.5 0.0 2.5 0.0 0.5 p=0.61 M2 −2 0 [SHM2017] J280.68767+58.39747 −2.5 0.0 2.5 0.0 0.5 p=0.87 M2 −0.5 0.0 0.5 2MASS J04274606-6202513 −2.5 0.0 2.5 0.0 0.5 p=0.41 M2 0.0 2.5 O-C [ x 10 −3 d] G i DR2 5264448926328694272 −2.5 0.0 2.5 Snd +d +esid. l 0.0 0.5 No+m lized No. p=0.42 M2 −0.25 0.00 0.25 G i DR2 5486632674089049472 −2.5 0.0 2.5 0.0 0.5 p=0.26 M3 −0.5 0.0 0.5 G i DR2 4628067852624828672 −2.5 0.0 2.5 0.0 0.5 p=0.80 M2 0.0 0.5 G i DR2 5285349822037246464 −2.5 0.0 2.5 0.0 0.5 p=0.59 M2 −2.5 0.0 2.5 HD 270239 −2.5 0.0 2.5 0.0 0.5 p=0.87 M2 −0.5 0.0 GSC 04450-00308 −2.5 0.0 2.5 0.0 0.5 p=0.49 M2 0 100 200 300 −2.5 0.0 2.5 [SHM2017] J281.12439+66.86821 BJD − 2458325; BJD − 2458684 0 100 200 300 400 −2.5 0.0 2.5 N.mbe+ of O − C poin-s −2.5 0.0 2.5 0.0 0.5 p=0.39 M2 Snd +d +esid. l Quantitative modeling of O-C diagrams of RR Lyrae stars Fig. 2 Strength of C2C variation as a function of the main period P0 and physical parameters metallicity [M/H], effective temperature Teff, log g, micro-turbulence ξt and macro-turbulence νmac for Kepler RRab stars. The stars with no additional frequencies, f1 and f2 frequencies are plotted as filled circles, rectangles and triangles, respectively. The green line shows the significant correlation between period and ση. The physical parameters are taken from the work of Nemec et al. (2013) where they were determined based on high-resolution spectra. Fig. 4 Parameter ση characterizing the C2C variation for the stars of the RRc sample as a function of the main pulsation period P1, metallicity [Fe/H], effective temperature Teff, and log g. The different symbols show the additional frequency content of the stars. The physical parameters were calculated from the Gaia DR3 data. Fig. 5 Relation between the fundamentalised period Pfund, and the effective temperature for the stars in our sample. Red rectangles: RRab stars, blue circles: RRc stars. 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 3.74 3.76 3.78 3.8 3.82 3.84 3.86 3.88 3.9 3.92 Pfund [d] log Teff Fig. 1 Quantitative analysis of O-C diagrams of Kepler non-Blazhko RRab stars (excerpt, for all figures see: Benkő et al. 2025) First column: O-C diagrams. Note: there are very different vertical scales shown in each panel. Second column: Pseudo-residuals associated with the best statistical model. Third column: Normalized distribution of pseudo-residual values (blue histograms) compared to the standard normal distribution (orange curves). In the upper right corner of the panels, the resulting optimal model (M1-M4) is indicated. In the upper left corner, the p-value of the normality test is given. Fig. 3 Quantitative analysis of O-C diagrams of TESS non-Blazhko RRc stars (excerpt, for all figures see: Benkő et al. 2025) First column: O-C diagrams calculated from the phase variation functions of Benkő et al. (2023), from which the short-period signals are pre-whitened. Second and third columns are the same as in Fig. 1 above. Period Teff Efficiency of convection C2C variation is caused by (?) or connected with (?) turbulent convection Fig. 6 Parameter ση characterizing the C2C variation of the Blazhko sample as a function of the strength of FM variation R: where Ai are the Fourier amplitudes of all the frequencies associated with Blazhko effect in the O-C spectra Question or comment? Let me know! [email protected] Blazhko effect strong C2C variation ? 0 1 2 3 4 5 6 0 10 20 30 40 50 60 ση x10−3 [d] R [min]