Mon. Not. R. Astron. Soc. 000, 1–8 (2002) Printed 31 March 2021 (MN LATEX style file v2.2) First observations of W Virginis stars with K2: detection of period doubling E. Plachy1⋆, L. Moln´ar1, M. I. Jurkovic1,2, R. Smolec3, P. A. Moskalik3, A. P´al1,4, L. Szabados1, R. Szab´o1 1Konkoly Observatory, MTA CSFK, Konkoly Thege Mikl´os ´ut 15-17, H-1121 Budapest, Hungary 2Astronomical Observatory of Belgrade, Volgina 7, 11 060 Belgrade, Serbia 3Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warszawa, Poland 4E¨otv¨os Lor´and University, P´azm´any P´eter s´et´any 1/A, H-1117 Budapest, Hungary Accepted. Received; in original form ABSTRACT We present the first analysis of W Vir stars observed by the Kepler space telescope in the K2 mission. Clear cycle-to-cycle variation were detected in the light curves of KT Sco and the globular cluster member M80-V1. While the variations in the former star seems to be irregular on the short time scale of the K2 data, the latter appears to experience period doubling in its pulsation. Ground-based colour data confirmed that both stars are W Vir-type pulsators, while a comparison with historical photo- metric time-series data revealed drastic period changes in both stars. For comparison we reexamine ground-based observations of W Vir, the prototype of the class, and conclude that it shows period doubling instead of mode beating. These results sup- port the notion that nonlinear dynamics plays an important role in the pulsation of W Virginis-type stars. Key words: stars: variables: Cepheids 1 INTRODUCTION and space-based photometry revealed that RR Lyrae stars may show it in their light curves as well (Szab´oet al. 2010; W Virginis stars are population II, low mass stars that Smolec et al. 2015). likely undergo blueward loops away from the asymptotic arXiv:1610.05488v1 [astro-ph.SR] 18 Oct 2016 giant branch due to helium shell flashes (Gingold 1976; The most promising explanation of PD involves nonlin- Wallerstein 2002). They represent the intermediate period ear dynamics, where period doubling bifurcation naturally (P =∼4–20 d) subclass of the Type II Cepheid variables, be- occurs at certain parameter combinations of the system. tween the BL Her and RV Tau stars. We note, however, that The early hydrodynamical models (Kov´acs & Buchler 1988; the boundaries between the subclasses are not well-defined Moskalik & Buchler 1990) already predicted nonlinear phe- (Welch 2012). Most Type II Cepheids pulsate in the radial nomena in W Vir stars: PD and even chaos was presented. fundamental mode, showing more irregularities towards the The bifurcation, e.g., the destabilisation of the single-period longer periods. In the light curves of RV Tau stars irreg- limit cycle was caused by half-integer resonances between ularities are observed in addition to the period doubling the fundamental mode and the first overtone (3:2 resonance) (PD), the alternation of lower- and higher-amplitude cycles or the second overtone (5:2 resonance). Recent theoretical that characterize this subtype. But PD is not universally calculations suggest that 7:2 resonance with the third and observed in the P > 20 d period range, and appears in 9:2 resonance with the fourth overtone are also plausible but a few stars with shorter periods too (Wils & Otero 2008; only for narrower parameter ranges (Smolec 2016). Two PD Soszy´nski et al. 2011). The possibility of PD was mentioned domains were identified: one contains the BL Her type and but rejected by Templeton & Henden (2007) in their study the short-period W Vir stars in the period range of ∼2-6.5 d, of the prototype star W Vir. PD can be also found among while the other appears at periods longer than P > 9.5 d. BL Her stars (Soszy´nski et al. 2011; Smolec et al. 2012), Large ground- and space-based surveys have potential to map these domains, although the former are limited by accuracy, and the latter by small sample size per mission ⋆ E-mail: [email protected] so far. The only Type II Cepheid observed from space, the c 2002 RAS 2 E. Plachy et al. BL Her subtype CoRoT 0659466327 is outside the theoreti- cal PD domains with its 1.542353 d period, and indeed does not show cycle-to-cycle variation (Poretti et al. 2015). For- tunately, the K2 mission will build up a large collection of variable stars, including hundreds of Type II Cepheid stars in the coming years (Plachy et al. 2016). In this paper we report the analysis of the first space observations of W Vir-type stars: KT Sco, a field star, and M80-V1, a member of the globular cluster M80. h m s ◦ ′ ′′ KT Sco (α2000.0 = 16 11 14.90, δ2000.0 = −16 51 40. 2, V = 12.48 mag) first appeared as an unclassified variable star in the list of Guthnick & Prager (1934), but was ap- parently neglected afterwards. It was finally classified as a W Vir star with the advent of automated variability surveys (Pojmanski 2002; Hoffman, Harrison & McNamara h m s 2009). The variation of M80-V1 (α2000.0 = 16 16 52.60, ◦ ′ ′′ δ2000.0 = −22 57 15. 9, V = 13.42 mag) was discovered by Bailey (1902) in his extensive work on globular clus- ter variables. The star was later identified as a long-period Cepheid pulsating in the fundamental mode and it was reg- ularly monitored during the 20th century (Sawyer 1942; Wehlau et al. 1984; Wehlau, Sawyer Hogg & Butterworth 1990; Nemec, Nemec & Lutz 1994; Kopacki 2003). We note Figure 1. The K2 stamp EPIC 200004389 that contains M80-V1 that M80 belongs to the old population of globular clusters, (EPIC 204281168). Red circle marks the aperture we used for the ± with an age of 12.4 1.1 Gyr and an average metallicity photometry. The dashed circle marks EPIC 204287127 that we in the range of [Fe/H] = –1.47 and –1.75 (Salaris & Weiss used for comparison. 2002; Mar´ın-Franch et al. 2009). Details of the observations and data reduction are given in Section 2. Section 3 presents the light curve analysis, the decadal period changes, and colour-magnitude diagrams for 12.25 12.25 both stars. In Section 4 re-analyse the star W Vir, and dis- r=2.5px cuss the PD interpretation of its pulsation behaviour. Fi- nally we summarise our results in Section 5. 12.3 12.3 r=3px Kp (mag) 12.35 12.35 2 OBSERVATIONS AND DATA REDUCTION r=2px 12.4 12.4 Both stars were observed with the Kepler space telescope 17 18 19 20 21 22 23 24 82 83 84 85 86 87 88 89 during Campaign 2 of the K2 mission which lasted for 78.8 BJD−2456880 (d) BJD−2456880 (d) days, between August 23 and November 10, 2014. KT Sco Figure 2. Details of the photometry of M80-V1 with different (EPIC 205546706) was observed as a regular target, while apertures. Left and right panels show the first and last pulsation M80-V1 (EPIC 204281168, GSC 06793–01005) was included maxima. The small jumps are caused by the attitude changes of in the superstamp covering the globular cluster M80. Data Kepler. The r = 2 px aperture is strongly affected by the jumps were collected in long cadence mode (29.4 min sampling) in towards the end. The r = 3 px aperture is more affected at the both cases. beginning of the campaign. Photometry was obtained as follows. In the case of KT Sco, we used the pyke software to create a custom target pixel mask for the star that contains the movements of the lated with the motions of the centroid of the star, and then PSF caused by the drift of the telescope (Still & Barclay restored the assumed astrophysical component. 2012). Since the spacecraft has only two working reaction In the case of M80-V1 the dense stellar field required a wheels, the radiation pressure from the Sun causes it to ro- tighter mask with pyke to avoid contamination, but this in tate around the third axis (Howell et al. 2014). These move- turn prevented us from covering the movements of the field. ments are controlled with the onboard thrusters in every 6 h, So we chose to apply a traditional aperture photometry us- but the images of the stars traverse between different pixels ing the fitsh software (P´al 2012). Fitsh is a fully open that leads to systematics in the flux measurements. Beside source astronomical data reduction and analysis software these movements, the pointing of Kepler was adjusted by ∼2 package, containing standalone binaries that are utilised via pixels after the 50th cadence of the campaign that we also UNIX shell scripts. It has been used to extract the K2 ob- accommodated in the pixel mask. The variations of KT Sco servations of very faint RR Lyrae stars within the nearby were slow enough to separate the astrophysical signal from dwarf galaxy Leo IV (Moln´ar et al. 2015). the characteristic jumps caused by the correction manoeu- M80 was covered with four 50×50 px stamps. First we vres. We applied the self-flat-fielding (SFF) task of pyke to registered the frames of the stamp containing M80-V1 to the residual light curve to remove the flux variations corre- the same reference system. Then we extracted light curves c 2002 RAS, MNRAS 000, 1–8 W Vir stars with K2 3 100 12.5 12.5 12.6 12.6 KT Sco 80 12.7 12.7 60 12.8 12.8 40 Kp (mag) 12.9 Kp (mag) 12.9 13 13 20 BJD-2456880 (d) 13.1 13.1 0 0 20 40 60 80 100 0 0.25 0.5 0.75 1 1.25 1.5 BJD-2456880 (d) Pulsation phase (P = 13.16325 d) 100 12.2 12.2 12.4 12.4 M80-V1 80 12.6 12.6 60 12.8 12.8 40 Kp (mag) 13 Kp (mag) 13 13.2 13.2 20 BJD-2456880 (d) comp: EPIC 204287127 13.4 13.4 0 0 20 40 60 80 100 0 0.25 0.5 0.75 1 1.25 1.5 BJD-2456880 (d) Pulsation phase (P = 16.27989 d) Figure 3.