Master's thesis International Master's Programme in Space Science Time series analysis of long-term photometry of the RS CVn star IM Pegasi Victor S, olea May 2013 Tutor: Doc. Lauri Jetsu Censors: Prof. Alexis Finoguenov Doc. Lauri Jetsu University of Helsinki Department of Physics P.O. Box 64 (Gustaf Hallstr¨ omin¨ katu 2a) FIN-00014 University of Helsinki Helsingin yliopisto | Helsingfors universitet | University of Helsinki Tiedekunta/Osasto | Fakultet/Sektion | Faculty Laitos | Institution | Department Faculty of Science Department of Physics Tekij¨a | F¨orfattare | Author Victor S, olea Ty¨on nimi | Arbetets titel | Title Time series analysis of long-term photometry of the RS CVn star IM Pegasi Oppiaine | L¨aro¨amne | Subject International Master's Programme in Space Science Ty¨on laji | Arbetets art | Level Aika | Datum | Month and year Sivum¨a¨ar¨a | Sidoantal | Number of pages Master's thesis May 2013 31 Tiivistelm¨a | Referat | Abstract We applied the Continuous Period Search (CPS) method to 23 years of V-band photometric data of the spectroscopic binary star IM Pegasi (primary: K2-class giant; secondary: G{ K-class dwarf). We studied the short and long-term activity changes of the light curve. Our modelling gave the mean magnitude, amplitude, period and the minima of the light curve, as well as their error estimates. There was not enough data to establish whether the long-term changes of the spot distribution followed an activity cycle. We also studied the differential rotation and detected that it was significantly stronger than expected, k ≥ 0:093. This result is based on the assumption that the law of solar differential rotation is valid also for IM Peg. We detected two long-lived active longitudes, rotating with a mean d d period of 24 :59, which is slightly slower that the rotation period of the star PW = 24 :6488. These two active longitudes were present during the whole observation period. There were also three abrupt activity shifts, in 1989, 1992 and 1993. Avainsanat | Nyckelord | Keywords Methods: data analysis; Stars: activity, individual (IM Pegasi), rotation, starspots S¨ailytyspaikka | F¨orvaringsst¨alle | Where deposited Kumpula Science Library Muita tietoja | ¨ovriga uppgifter | Additional information Contents 1 Introduction 1 1.1 The activity of the Sun ............................. 1 1.2 Variable stars of type RS CVn ......................... 2 1.3 The star IM Pegasi ............................... 2 2 Observations 5 3 The continuous period search 8 4 Long-term activity changes 11 5 Differential rotation 16 6 Active longitudes 19 7 Conclusions 22 References 23 A The data and its format 27 B CPS test results 28 i Chapter 1 Introduction 1.1 The activity of the Sun The Sun, being the closest star to us, has been observed extensively for centuries. Sunspots have been observed since the invention of the telescope. Schwabe began in 1826 the first systematic observations of sunspots. He determined later the length of the sunspot cycle to be approximately 11 years long (Schwabe 1843). However, the lengths of the observed cycles have varied between 8 and 15 years. Gleissberg (1945) noticed that the number of sunspots during these cycles oscillates with a period of approximately 80 years (the so-called Gleissberg cycle). The activity has sometimes been very low or even ceased altogether: one such period was the Maunder Minimum, lasting approximately between 1645 and 1715. This coincided with an unusually cold weather on Earth, the so-called "Little Ice Age". The cause of sunspots was discovered in the beginning of the 20th century: Hale (1908) proposed a solar magnetic field as an explanation. Solar magnetic activity is also the cause of several other phenomena, such as flares or the very high temperature of the chromosphere and corona above the visible photosphere. At the beginning of each activity cycle, pairs of sunspots of opposing magnetic polarity form at higher latitudes on both hemispheres (but usually not more than 45◦ from the equator). As the cycle proceeds, they form at lower and lower latitudes. The plot of the latitudinal positions of these pairs as a function of time gives the well- known "butterfly diagram". The magnetic field polarity of the leading and trailing sunspot pairs changes at the end of each cycle. It has been observed that the solar luminosity varies by 0:1% during the sunspot cycle. Willson and Hudson (1991) showed that the maximum luminosity is reached at the sunspot maximum. There are also similar variations in the intensity of several spectral emission lines, for example in the chromospheric Ca II H & K emission lines. It is thus an obvious question to ask whether other stars also exhibit similar cycles and whether spots can be observed (directly or indirectly) on other stellar surfaces. It 1 CHAPTER 1. INTRODUCTION 2 is not an impossible task, since detecting luminosity changes, like those in the Sun, is within the capabilities of modern instruments. 1.2 Variable stars of type RS CVn Hall (1976) defined a new class of variable stars, which he named RS CVn stars. These stars, like their prototype star RS Canum Venaticorum (HD 114519), are close binaries with a massive F–K-class giant and a G–M-class subgiant or dwarf. The variability in the V-band usually has an amplitude of lower than 0m:6. The main characteristics of this class are: • Photometrical variability caused by starspots • Active chromosphere: presence of chromospheric Ca II H & K and Hα emission lines, as well as X-ray and UV emission • Fast synchronous rotation and orbital motion, with variations in the rotation period • Orbital periods between 1 and 14 days. Those with periods over two weeks are referred to as "the long-period class". The members of these binaries are close to each other, tidally locked and therefore rotate fast. As a consequence of their fast rotation, they display strong magnetic ac- tivity, which is observed e.g. as large starspots. These characteristics make RS CVn stars interesting targets for light curve modelling. 1.3 The star IM Pegasi IM Peg (HR 8703, HD 216489) is a long-period spectroscopic binary of RS CVn type. It was already included in the first survey of Hall (1976). It has a visual magnitude V = 5m:6 (Strassmeier et al. 1997). The K2 III primary exhibits strong starspot ac- tivity (Berdyugina et al. 1999; Berdyugin et al. 2006; Marsden et al. 2005). It has an estimated mass of 1:8 0:2M⊙, an effective surface temperature of about 4500 K and a radius of at least 12 R⊙ (Strassmeier et al. 1997). There is, however, disagreement about the spectral class of the unseen secondary. Berdyugina et al. (1999) considered it to be a K0 dwarf, while Berdyugin et al. (2006) suggested that it is a G2 dwarf. No eclipses have been observed, i.e. the inclination of the orbital plane is not close ◦ to 90 . Strassmeier et al. (1997) reported an orbital period Porb = 24:65 days and a photometric period Pphot = 24:4 days. Additionally, they observed some seasonal variations in the photometric period: for the 1993-94 observing season its mean was CHAPTER 1. INTRODUCTION 3 25:19 0:39 days, for the 94-95 season 24:108 0:081 days, and for the 95-96 season 24:498 0:030 days. This gave a long-term average of Pphot = 24:4936 0:0024 days between 1978-1996. However, they did not find signs of regular long-term Pphot changes. IM Peg has a long observational history. This means that the orbital parameters and several other physical characteristics have been determined accurately, e.g. by Marsden et al. (2005). We have collected the following physical parameters of IM Peg into Table 1.1: effective surface temperature (Teff ), rotational velocity (v sin i), photometric period (Pphot), light curve amplitude (A), the radius (R) and spectral class of the primary. There is a good agreement between the results of the different authors in Table 1.1. For example, the following photometric observations of IM Peg have been made: • Between October 1983 and March 1987 with the 10 inch Automatic Photoelec- tric Telescope in Phoenix, Arizona and Mt. Hopkins, Arizona, 275 observations in standard Johnson UVB photometry (Strassmeier et al. 1989) • 218 observations between November 1993 and June 1996 with the 0.75 m Ama- deus APT at Mt. Hopkins, Arizona, and 111 observations with the 0.8 m Catania APT on Mt. Etna, Italy (Strassmeier et al. 1997) • Between 1996 and 2001 with the 0,75 m Amadeus Automatic Photoelectric Telescope at Mt. Hopkins, Arizona (Ribárik et al. 2003) In this thesis, we will analyze 23 years of photometric observations of IM Peg made with the 40 cm Vanderbilt/Tennessee State Automatic Photoelectric Telescope (APT) at Fairborn Observatory, Arizona. CHAPTER 1. INTRODUCTION 4 Reference Teff V sin i Pphot Amplitude R Spectral Class −1 [K] [km s ] [d] [mag] [R⊙] 1 24.643 2 4265 3 24.4248 0.16 K1 III-IV 4 24.6 K0 5 4250 24.65 K1 III 6 24.39 K1 III-IV 7 24 24.4 12 K1 III 8 4200 24.547 9 36 24.6 10 24.43 0.156 11 4420 24 24.349 K1 III 12 28.1 13.6 13 28.2 24.45 0.22-0.4 >13.6 K2 II-III 14 4450 26.5 24.6488 13.3 K2 III Table 1.1: Physical parameters of IM Peg: The references are: 1. Lucy and Sweeney (1971), 2. Gottlieb and Bell (1972), 3. Herbst (1973), 4. Spangler et al. (1977), 5. Glebocki and Stawikowski (1979), 6. Eaton et al. (1983), 7. Fekel et al. (1986), 8.