Nonradial modes and Blazhko effect in Cepheids of the Large Magellanic Cloud

P. Moskalik¹, Z. Kolaczkowski^2,3

¹ Copernicus Astronomical Center, Warsaw, Poland

² Universidad de Concepcion, Concepcion, Chile

³ Astronomical Institute, University of Wroclaw, Wroclaw, Poland

We have conducted a systematic search for multiperiodicity in the Population I Cepheids of the LMC. The analysis has been based on OGLE-II photometry, suplemented with MACHO photometry when needed. Full results of this project are presented in Moskalik & Kolaczkowski 2008abc (arXiv:0807.0615; arXiv:0807.0623; arXiv:0809.0864).

• In 42 first overtone (FO) pulsators, which constitutes 9% of the FO sample, we have detected secondary frequencies corresponding to nonradial modes of oscillation. These stars are listed in Table 1. In the following we call them FO-ν Cepheids. Nonradial modes appear either very close to the primary (radial) pulsation frequency or at a high frequecy with a period ratio of 0.60-0.64.
  In Figs 1 and 2 we present several examples of both types of FO-ν Cepheids.
  In Fig. 3 we display distribution of frequency diferences between radial and nonradial modes on FO-ν Cepheids, and for comparison, in Blazhko RRc stars (from Nagy & Kovács 2006).
  In Fig. 4 we show distribution of amplitude ratio of nonradial to radial modes.
  Fig. 5 displays position of the FO-ν Cepheid on the LMC Cepheid P-L diagram.
  Figs 6 and 7 show period distribution of LMC FO Cepheids and the incedence rate of FO-ν Cepheids vs. first overtone period.
• In 22 FO Cepheids (5% of the sample) we have found residual power unresolved from the primary radial frequency. The power has remained unresolved even with much longer MACHO data. These stars are listed in Table 2. We call them FO-PC Cepheids.
• We have detected nonradial modes in 3 fundamental/first overtone double mode Cepehids (13% of the sample). These stars are listed in Table 3 and displayed in Fig. 8. We call them FU/FO-ν double mode Cepheids.
• Combined OGLE-II + MACHO sample of second/first overtone double mode Cepheids (FO/SO Cepheids) consistes of 107 objects. In 20 of these stars (19% of the sample) we have detectes well resolved secondary power around radial modes. These stars are listed in Table 4. In the following we call them Blazhko FO/SO double mode Cepheids. Typical frequency pattern in displayed in Fig. 9. In the vicinity of a radial mode we detect two secondary peaks located on the opposite sides of the primary (radial) frequency. Together with the primary peak they form and equally spaced triplet of frequencies. Such a structure is usually found around both radial modes. Both triplets have the same frequency separation. In several stars we have detected equally space quintuplets.
  In Fig. 10 we display several examples of triplets and quintuplest detected in Blazhko FO/SO Cepheids.
  Frequency pattern shown in Figs 9 and 10 corresponds to periodic modulation of amplitudes and phases of both radial modes. Both modes are modulated with a common period, which is always above 700 days. In Fig. 11 we present an example of such modulation.
  In Fig. 12 we show distribution of the modulation frequancy, 1/P_B. The low frequancy cut-off of this distribution is given by the frequency resolution of available data. The true physical cuf-off is not known.
• In 17 FO/SO Cepheids (16% of the sample) we have detected secondary power unresolved from the primary (radial) frequencies. We call thes stars FO/SO-PC Cepheids. They are listed in Table 5. FO/SO-PC Cepheids most likely experience the same type of periodic modulation as the Blazhko FO/SO Cepheids, but on timescales longer than the current data.
  Fig. 13 displays position of the Blazhko FO/SO Cepheids and FO/SO-PC Cepheids on the Petersen diagram.
  Figs 14 and 15 show period distribution of LMC FO/SO Cepheids and the incedence rate of Blazhko FO/SO Cepheids and FO/SO-PC Cepheids vs. first overtone period.

Fig 1. Prewhitened power spectra of sample of LMC FO-ν Cepheids with small |Δf|. Frequencies of removed radial modes indicated by dashed lines. [post script]	Fig 2. Prewhitened power spectra of sample of LMC FO-ν Cepheids with Pν/P1 = 0.60 - 0.64. Frequencies of removed radial modes indicated by dashed lines. [post script]
Fig 3. Distribution of frequency differences Δf = fν - f1 for LMC FO-ν Cepheids and for LMC RRc-BL stars (from Nagy & Kovács 2006). For RRc-BL variables with frequency triplets, only higher side peaks are taken into account. Shaded area marks variables with Pν/P1 = 0.60 - 0.64. [post script]	Fig 4. Distribution of amplitude ratios Aν/A1 for LMC FO-ν Cepheids. [post script]
Fig 5. WI index P-L diagram for LMC Cepheids. Dominant (radial) periods of FO-ν Cepheids are displayed with black symbols. [post script]	Fig 6. Distribution of radial mode periods for LMC first overtone (FO) Cepheids. Shaded red histogram represents FO-ν variables. [post script]
Fig 7. Incidence rate of LMC FO-ν Cepheids vs. first overtone period. [post script]	Fig 8. Power spectra of LMC FU/FO-ν double-mode Cepheids after prewhitening with frequencies of the two radial modes and their linear combinations. Removed radial frequencies indicated by dashed lines. [post script]
Fig 9. Prewhitened power spectrum of Blazhko FO/SO double-mode Cepheid SC1-44845. Frequencies of removed radial modes indicated by dashed lines. Lower panels display the fine structure around the radial modes. [post script]	Fig 10. Prewhitened power spectra of sample of LMC Blazhko FO/SO double-mode Cepheids. Frequencies of removed radial modes indicated by dashed lines. [post script]
Fig 11. Periodic modulation of amplitudes and phases of radial modes in Blazhko FO/SO double-mode Cepheid SC1-285275. First and second overtones are displayed with blue and red dots, respectively. The error bars are ± 1σ. Modulation period is P_B = 902day. [post script]	Fig 12. Distribution of modulation frequencies, Δf, for LMC Blazhko FO/SO double-mode Cepheids. [post script]
Fig 13. Petersen diagram for FO/SO double-mode Cepheids in the LMC. Cepheids with Blazhko effect and FO/SO-PC variables displayed with red and green dots, respectively. Remaining pulsators plotted with asterisks. [post script]	Fig 14. Distribution of first overtone periods of FO/SO double-mode Cepheids in the LMC. Red histogram represents Blazhko pulsators. Shaded green area marks FO/SO-PC variables. [post script]
Fig 15. Incidence rate of LMC Blazhko FO/SO Cepheids and FO/SO-PC Cepheids vs. first overtone period. Cepheids with Blazhko effect and FO/SO-PC variables displayed with red and green dots, respectively. [post script]