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Multi-mode, non-radial and modulated pulsation of RR Lyrae stars and Cepheids

project	OPUS, DEC-2012/05/B/ST9/03932
funding	Polish National Science Center, NCN
PI	Radosław Smolec
Co-Is	Paweł Moskalik
	Wojciech Dziembowski
	Henryka Netzel
dates	01.2013 - 08.2016, finished

Jump to project highlights, refereed publications, conference contributions, and presentations.

Project Highlights

• New classes of double-periodic pulsation among RR Lyrae stars

  Analysis of the OGLE data for fundamental mode RR Lyrae stars (RRab) led to the discovery of the new forms of beat pulsation. In Smolec et al. (2016) we report the discovery of four long period beat pulsators. In the Petersen diagram below, they are marked with open squares. Linear pulsation models show that these might be the most extreme, longest period RRd stars - stars that pulsate simultaneously in the radial fundamental mode and the radial first overtone. Other interesting group of RRd stars is marked with open circles. These are Blazhko RRd stars we have discussed below. Analysis of the Magellanic Cloud photometry led to the discovery of more such objects, which we now call anomalous RRd stars - see Soszyński, Smolec, Dziembowski, et al. (2016). We proposed that this peculiar form of pulsation may be caused by the parametric resonance between the three radial modes: 2ν_1O=ν_F+ν_2O. Finally, in the paper by Prudil, Smolec, Skarka and Netzel (2017) we report the discovery of the most intriguing group - marked with open triangles in the figure. Original classification for most of these stars is RRab. Light curve shape for these stars is very peculiar, however - in between the shape typical for RRab and RRc stars. The additional periodicity is too short to be associated with the radial first overtone. Nature of these variables remains unknown.

  

  Petersen diagram for new groups of double-periodic RR Lyrae stars.

• New model for double-periodic, first overtone classical pulsators

  In Dziembowski (2016), we propose a new model explaining the double-periodic pulsation in classical pulsators with dominant radial first overtone and additional shorter periodicity, P_x, which is in the (0.60, 0.65)P_1O range. We studied these stars within our project in detail, both RR Lyrae stars (see e.g. Netzel, Smolec & Moskalik, 2015) and classical Cepheids (Smolec & Śniegowska, 2016). In the Petersen diagram these stars form sequences, as illustrated in the Figure below. In some of these stars, additional variability, with period equal to 2P_x, is detected. In the Petersen diagram, these stars are not distributed uniformly among the sequences: most of them are in the top sequence (RR Lyr stars) or in the middle sequence (Cepheids). This fully supports the proposed model, in which the variability at 2P_x is associated with non-radial modes of l=7-9 as indicated in the Figure. Observed amplitudes of these modes are very low due to geometric cancellation effect; often too low to directly detect non-radial mode in the observations. Detections are most common for l=8, as here the geometric cancellation is weaker than for l=7 and l=9. Variability at P_x on the other hand, corresponds to the harmonic of the non-radial mode which, thanks to geometric and non-linear effects, has typically higher observed amplitude and is more easy to detect.

  

  Petersen diagram for first overtone RR Lyr stars and first overtone Cepheids with additional periodicity in the (0.60, 0.65)P_1O range. Filled symbols mark the stars in which variability at 2P_x (non-radial mode) was also detected.

• Blazhko Effect - on-line gallery of light curve changes

  http://users.camk.edu.pl/smolec/blazhko/

• Discovery of a new group of double-periodic RR Lyrae stars

  Our analysis of the OGLE-IV photometry for the Galactic bulge RRc stars led to the discovery of the new group of double-periodic variables. Except of the first overtone mode we detect additional, longer period mode; the characteristic period ratio, P_1O/P_X falls around 0.686. We detect such modes in 11 OGLE RRc stars. The same period ratio was detected in one of the stars observed by Kepler space telescope, that we analysed in Moskalik et al. (2015). These stars are marked with red diamonds in the Petersen diagram below. Comparison with RRd stars (small blue symbols) indicates that additional period is longer than period of the fundamental mode (which is not detected in these stars). Hence, additional mode must be non-radial, of gravity or mixed character. Read more in our paper Netzel, Smolec & Dziembowski, MNRAS Letters (2015).

  

  Petersen diagram for double-periodic RR Lyrae stars. The newly discovered group is represented by red diamonds. Other stars discovered/analysed by our group are: majority of the 0.61-stars (magenta symbols; Netzel, Smolec & Moskalik (2015), Moskalik et al. (2015)) and modulated RRd stars analysed in Smolec et al. (2015) (encircled RR stars).

• Analysis of the Blazhko effect discovered in RRd stars

  Recently, the OGLE team announced the discovery of the Blazhko effect in a few double-mode RR Lyrae stars (RRd stars, Soszynski et al. 2014). We have analysed the effect in detail and found all together 15 stars that show the effect. Exemplary light curves with the clear signature of the modulation are shown below. Majority of the stars have untypical period ratios - see the Petersen diagram below, in which modulated stars are marked with diamonds. Modulation is typically multiperiodic. Both radial modes may be modulated with the same period. More commonly however, dominant modulation for the fundamental mode has different period than dominant modulation for the first overtone. Quite often modulation of only one mode is detected in the data. Pulsation properties of all analysed stars are non-stationary. Read more in Smolec et al. (2015a).

  

  Exemplary light curves for the three modulated RRd stars over the five observing seasons of OGLE-IV. From top to bottom: OGLE-BLG-RRLYR-06283, -07393, and -05762.

  

  Petersen diagram for the OGLE Galactic bulge RRd sample. Modulated stars are marked with diamonds. Triangle marks other interesting target: triple-mode RR Lyrae star with period doubling, discussed in detail in Smolec et al. (2015b).

• 147 new members of a double-mode radial-non-radial RR Lyrae pulsators

  We report the discovery of 147 new members of the new class of double periodic RR Lyrae stars with characteristic period ratio of 0.61. The stars were detected in the OGLE-III Galactic bulge photometry and increase the number of known stars of this type by a factor of 6. Still the new stars constitute only 3 per cent of the OGLE-III Galactic bulge RRc sample, while space photometry indicates that the phenomenon should be common in RRc stars. The low detection rate is due to small amplitudes of the additional signal (mmag range) and relatively large noise level inherent to ground based observations. In the Petersen diagram we detect a tight progression with period ratios clustering around 0.618 and a signature of the second sequence with slightly larger period ratio. See figure below and read more in Netzel, Smolec & Moskalik (2015).

  

  Petersen diagram showing the location of the newly discovered double-periodic stars (crosses) compared with the models assuming simultaneous excitation of third and first radial overtones (top part) and fourth and first radial overtones (bottom part). The stars are located in-between the models, hence the additional mode cannot be a radial mode. Models were computed with the Warsaw pulsation codes of Smolec & Moskalik (2008).

• Analysis of space photometry for RRc stars. New group of double-periodic RRc stars

  We have analysed the Kepler space photometry for the first overtone RR Lyrae stars (RRc stars). In all stars the additional shorter period variability is detected, with characteristic period ratios of the two modes, P_x/P_1O, around 0.61. Such stars were also detected earlier, in the ground-based photometry and in the space photometry gathered by MOST and CoRoT. Nearly all RRc stars observed from space show the additional mode - the phenomenon must be common. Sub-harmonics of the additional signal are present in the frequency spectrum. Amplitudes and phases of the additional mode and of its subharmonics show a pronounced quasi-periodic variation. Read more in Moskalik et al. (2015).

  

  Frequency spectra for the four analysed Kepler RRc stars after prewhitening with the frequency of the first overtone, f₁. Additional mode is denoted with f₂, its subharmonics are marked with red arrows, while combination frequencies are marked with blue arrows (top panel). In all spectra frequency is normalized by f₁.

Refereed Publications

• Smolec, R., Moskalik, P., Kałużny, J., Pych, W., Różyczka, M., Thompson, I.B.; RR Lyrae stars in NGC 6362; MNRAS, 467, 2349 (2017); PDF, arXiv:1702.02172
• Prudil, Z., Smolec, R., Skarka, M., Netzel, H.; Peculiar double-periodic pulsation in RR Lyrae stars of the OGLE collection. II. Short-period stars with dominant radial fundamental mode; MNRAS, 465, 4074 (2017); ADS, PDF, arXiv:1701.00751
• Plachy, E., Molnar, L., Jurkovic, M.I., Smolec, R., Moskalik, P., Pal, A., Szabados, L., Szabo, R.; First observations of W Virginis stars with K2: detection of period doubling; MNRAS, 465, 173 (2017); ADS, PDF, arXiv:1610.05488
• Soszyński, I., Smolec, R., Dziembowski, W.A., Udalski, A., Szymański, M.K., Wyrzykowski, L., Ulaczyk, K., Poleski, R., Pietrukowicz, P., Kozłowski, S., Skowron, D., Skowron, J., Mroz, P., Pawlak, M.; Anomalous Double-Mode RR Lyrae Stars in the Magellanic Clouds; MNRAS, 463, 1332 (2016); ADS, PDF, arXiv:1608.00576
• Smolec, R., Prudil, Z., Skarka, M., Bąkowska, K.; Peculiar double-periodic pulsation in RR Lyrae stars of the OGLE collection. I. Long-period stars with dominant radial fundamental mode; MNRAS, 461, 2934 (2016); ADS, PDF, arXiv:1606.06928
• Smolec, R., Śniegowska, M.; Non-radial pulsation in first overtone Cepheids of the Small Magellanic Cloud; MNRAS, 458, 3561 (2016); ADS, PDF, arXiv:1603.01042
• Kurtz, D.W. Bowman, D.M., Ebo, S.J., Moskalik, P., Handberg, R., Lund, M.N.; EPIC 201585823, a rare triple-mode RR Lyrae star discovered in K2 mission data; MNRAS, 455, 1237 (2016); PDF, arXiv:1510.03347
• Netzel, H., Smolec, R., Moskalik, P.; Double-mode radial-non-radial RR Lyrae stars. OGLE-IV photometry of two high cadence fields in the Galactic bulge; MNRAS, 453, 2022 (2015); ADS, PDF, arXiv:1507.08414
• Molnar, L., Szabo, R., Moskalik, P., Nemec, J.M., Guggenberger, E., Smolec, R., Poleski, R., Plachy, E., Kolenberg, K., Kollath, Z.; An RR Lyrae family portrait: 33 stars observed in Pisces with K2-E2; MNRAS, 452, 4283 (2015); ADS, PDF, arXiv:1507.04714
• Evans N.R., Berdnikov L., Lauer J., Morgan D., Nichols J., Gunther H.M., Gorynya N., Rastorguev A., Moskalik P.; Binary Properties from cepheid Radial Velocities (CRaV); AJ, 150, 13 (2015); PDF, arXiv:1505.05823
• Netzel, H., Smolec, R., Dziembowski, W.; Discovery of a new group of double-periodic RR Lyrae stars in the OGLE-IV photometry; MNRAS Lett., 451, L25 (2015); ADS, PDF, arXiv:1504.05765
• Smolec, R., Soszyński, I., Udalski, A., Szymański, Pietrukowicz, P., Skowron, J., Kozłowski, S., Poleski, R., Moskalik, P., Skowron, D. et al.; Intriguing triple-mode RR Lyrae star with period doubling; MNRAS, 447, 3873 (2015); ADS, PDF, arXiv:1411.2908
• Smolec, R., Soszyński, I., Udalski, A., Szymański, Pietrukowicz, P., Skowron, J., Kozłowski, S., Poleski, R., Skowron, D., Pietrzyński, G. et al.; Blazhko-type modulation in the double-mode RR Lyrae stars of the OGLE Galactic bulge collection; MNRAS, 447, 3756 (2015); ADS, PDF, arXiv:1411.2447
• Moskalik, P., Smolec, R., Kolenberg, K., Molnar, L., Kurtz, D.W., Szabo, R., Benko, J.M., Nemec, J.M., Chadid, M., Guggenberger, E. et al.; Kepler photometry of RRc stars: peculiar double-mode pulsations and period doubling; MNRAS, 447, 2348 (2015); ADS, PDF, arXiv:1412.2272
• Netzel, H., Smolec, R., Moskalik, P.; Double-mode radial-non-radial RR Lyrae stars in the OGLE photometry of the Galactic bulge; MNRAS, 447, 1173 (2015); ADS, PDF, arXiv:1411.3155
• Daszyńska-Daszkiewicz, J., Dziembowski, W., Jerzykiewicz, M., Handler, G.; Oscillation modes in the rapidly rotating slowly pulsating B-type star μ Eridani, MNRAS, 446, 1438-1448 (2015); PDF, arXiv:1410.6283
• Soszyński, I., Dziembowski, W., Udalski, A., Szymański, M.K., Kubiak, M. et al.; OGLE-BLG-RRLYR-12245: An RR Lyrae Star that Switched from a Double- to Single-Mode Pulsation, Acta Astron., 64, 1-9 (2014); PDF, arXiv:1403.6476
• Nemec, J.M., Cohen, J.G., Ripepi, V., Derekas, A., Moskalik, P., Sesar, B., Chadid, M., Bruntt, H.; Metal Abundances, Radial Velocities, and Other Physical Characteristics for RR Lyrae Stars in The Kepler Field, ApJ, 773, 181 (2013); PDF, arXiv:1307.5820
• Mosser, B., Dziembowski, W., Belkacem, K., Goupil, M.J., Michel, E., Samadi, R., Soszyński, I., Vrard, M., Elsworth, Y., Hekker, S., Mathur, S.; Period-luminosity relations in evolved red giants explained by solar-like oscillations, A&A, 559, A137 (2013); PDF, arXiv:1310.0839
• Pietrukowicz, P., Dziembowski, W., Mroz, P., Soszyński, I., Udalski, A., Poleski, R., Szymański, M.K., Kubiak, M. et al.; Large Variety of New Pulsating Stars in the OGLE-III Galactic Disk Fields, Acta Astron., 63, 379-404 (2013); PDF, arXiv:1311.5894
• Marconi, M., Molinaro, R., Bono, G., Pietrzyński, G., Gieren, W., Pilecki, B., Stellingwerf, R. F., Graczyk, D., Smolec, R., Konorski, P., Suchomska, K., Górski, M., Karczmarek, P.; The Eclipsing Binary Cepheid OGLE-LMC-CEP-0227 in the Large Magellanic Cloud: Pulsation Modeling of Light and Radial Velocity Curves, ApJ Lett., 768, L6 (2013); PDF, arXiv:1304.0860

Conference Publications

• Dziembowski, W.; Nonradial oscillations in classical pulsating stars. Predictions and discoveries, in Communications from the Konkoly Observatory (2016), 105, 23; arXiv; RRL2015: High-precision studies of RR Lyrae stars, Visegrad, 19-22 October 2015; www
• Smolec, R.; On period ratios in modulated double-mode RR Lyrae stars, in Communications from the Konkoly Observatory (2016), 105, 69; arXiv; RRL2015: High-precision studies of RR Lyrae stars, Visegrad, 19-22 October 2015; www
• Netzel, H., Smolec, R., Moskalik, P.; Nonradial modes in RR Lyrae stars from the OGLE Collection of Variable Stars, in Communications from the Konkoly Observatory (2016), 105, 31; arXiv; RRL2015: High-precision studies of RR Lyrae stars, Visegrad, 19-22 October 2015; www
• Smolec, R., Bąkowska, K.; Light-curve changes over the Blazhko cycle in RR Lyrae stars, in Communications from the Konkoly Observatory (2016), 105, 215; RRL2015: High-precision studies of RR Lyrae stars, Visegrad, 19-22 October 2015; www
• Smolec, R., Netzel, H., Soszyński, I.; RR Lyrae stars: New discoveries in the OGLE data, in Astronomy in Focus, XXIXB, E14 (2016); doi; Proc. of the IAU General Assembly XXIX, Focus Meeting 17: Advances in Stellar Physics from Asteroseismology, Honolulu, 3-14 August 2015; www
• Smolec, R.; The Blazhko Effect, in Proc. of the Polish Astron. Soc., 3, 22-30 (2016); arXiv; XXXVII Meeting of the Polish Astronomical Society, Poznań, 7-10 September 2015; www
• Netzel, H., Smolec, R.; Non-radial Pulsations in RR Lyrae Stars from the OGLE Collection, in Proc. of the Polish Astron. Soc., 3, 36-41 (2016); arXiv; XXXVII Meeting of the Polish Astronomical Society, Poznań, 7-10 September 2015; www
• Bąkowska, K., Smolec, R.; RR Lyrae stars with Blazhko modulations in the OGLE collection, in Proc. of the Polish Astron. Soc., 3, 48-50 (2016); arXiv; XXXVII Meeting of the Polish Astronomical Society, Poznań, 7-10 September 2015; www
• Smolec, R.; Survey of hydrodynamic RR Lyrae models, in EPJ Web of Conferences, 101, 06059 (2015); PDF; The Space Photometry Revolution, CoRoT Symposium 3, Kepler KASC-7 joint meeting, Toulouse, 6-11 July 2014; www
• Smolec, R.; Two unusual, radially pulsating stars, in Proc. of the Polish Astron. Soc., 1, 65-70 (2014); PDF; XXXVI Polish Astronomical Society Meeting, Warszawa, 11-15 September 2013; www
• Moskalik, P.; Multi-mode oscillations in classical Cepheids and RR Lyrae-type stars; IAUS 301, p. 249 (2014); PDF, arXiv:1401.7271; IAU Symposium No. 301: Precision Asteroseismology: Celebration of the Scientific Opus of Wojtek Dziembowski, Wroclaw, 19-23 August 2013; www
• Smolec, R.; Mode selection in pulsating stars; IAUS 301, p. 265 (2014); PDF, arXiv:1309.5959; IAU Symposium No. 301: Precision Asteroseismology: Celebration of the Scientific Opus of Wojtek Dziembowski, Wroclaw, 19-23 August 2013; www
• Szewczuk, W., Daszyńska-Daszkiewicz, J., Dziembowski, W.; Interpretation of the oscillation spectrum of HD 50230 - a failure of richness; IAUS 301, p. 109 (2014); PDF, arXiv:1311.2818; IAU Symposium No. 301: Precision Asteroseismology: Celebration of the Scientific Opus of Wojtek Dziembowski, Wroclaw, 19-23 August 2013; www

Presentations

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