New Astronomy 15 (2010) 274–281 Contents lists available at ScienceDirect New Astronomy journal homepage: www.elsevier.com/locate/newast Differential rotation of some HK-Project stars and the butterfly diagrams M.M. Katsova a, M.A. Livshits b, W. Soon c, S.L. Baliunas c, D.D. Sokoloff d,* a Sternberg State Astronomical Institute, Moscow State University, Moscow, Russia b Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of Russian Academy of Sciences, Troitsk, Moscow Region, Russia c Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA d Physical Department, Moscow State University, Moscow, Russia article info abstract Article history: We analyze the long-term variability of the chromospheric radiation of 20 stars monitored in the course Received 10 June 2009 of the HK-Project at the Mount Wilson Observatory. We apply the modified wavelet algorithm for this set Received in revised form 13 August 2009 of gapped time series. Besides the mean rotational periods for all these stars, we find reliable changes of Accepted 13 August 2009 the rotational periods from year to year for a few stars. Epochs of slower rotation occur when the activity Available online 20 August 2009 level of the star is high, and the relationship repeats again during the next maximum of an activity cycle. Communicated by P.S. Conti Such an effect is traced in two stars with activity cycles that are not perfectly regular (but labeled ‘‘Good” under the classification in [Baliunas, S.L., Donahue, R.A., Soon, W.H., Horne, J.H., Frazer, J., Woodard- PACS: Eklund, L., Bradford, M., Rao, L.M., Wilson, O.C., Zhang, Q. et al., 1995. ApJ 438, 269.]) but the two stars have 97.10.Kc 97.20.Jg mean activity levels exceed that of the Sun. The averaged rotational period of HD 115404 is 18.5 days but 96.60.Q sometimes the period increases up to 21.5 days. The sign of the differential rotation is the same as the 96.60.P Sun’s, and the value DX=hXi¼À0:14: For the star HD 149661, this ratio is À0.074. Characteristic changes 97.10.Jb of rotational periods occur over around three years when the amplitude of the rotational modulation is 97.10.Qh large. These changes can be transformed into latitude-time butterfly diagrams with minimal a priori 95.75.Wx assumptions. We compare these results with those for the Sun as a star and conclude that epochs when surface inhomogeneities rotate slower are synchronous with the reversal of the global magnetic dipole. Keywords: Stellar rotation Ó 2009 Elsevier B.V. All rights reserved. Late-type stars Solar activity 1. Introduction Common sense would suggests that the observed bulk phenom- ena above can hardly be only manifested in the Sun. One expects to Solar cycle is something more then a quasi-periodic variation of find something similar on solar-type stars. A comparison between solar activity. The mean latitude of sunspots and active regions as a various details of the structure of propagating activity waves and whole varies in step with the cycle. Change of latitudinal position a more direct confrontation with corresponding distinctions in stel- of sunspots with time – Maunder’s ‘‘Butterfly Diagram” shows that lar hydrodynamics in various solar-type stars appear to be able to a physical process underlying solar activity cycles can be presented open new avenues for a further understanding of the solar and stel- as the propagation of activity waves from middle latitudes to the lar dynamos. In fact, spotty stellar activity as well as stellar chromo- solar equator. The less superficial understanding of the activity spheric and coronal emissions cycles are known for several decades. waves nature is suggested on one hand by the concept of extended One could imagine that observations will provide for theory a rich solar cycle which can be revealed by various tracers of solar activ- sample of stars with various spatial configurations of stellar activity ity and presents the whole shape of the variable solar activity as waves (or confirm that the solar configuration is the only one possi- several activity waves located in various latitudinal belts. These ble) while theory tries to explain the observed phenomenology. In waves propagate mainly equatorwards however some of them practice, however, we are only at the beginning of this research goal. (say, the wave of filaments) propagate polarwards. On the other The point is that one needs a systematic monitoring of stellar hand, solar dynamo theory considers the activity waves as mani- activity for a given star at the timescale of a decade (typical length festations of the waves of quasi-stationary magnetic field and sug- of a cycle) to push forward any research progress. The available gests an excitation mechanism for these waves. bulk of inverse Doppler images of stellar surfaces presents usually only stellar activity at particular phases and do not allow to com- bine them in a butterfly diagram. * Corresponding author. E-mail addresses: [email protected] (M.M. Katsova), [email protected] On the other hand, the available bulk of stellar activity moni- (D.D. Sokoloff). tored using the Ca II chromospheric emission H and K lines by 1384-1076/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2009.08.003 M.M. Katsova et al. / New Astronomy 15 (2010) 274–281 275 the Mount Wilson Observatory’s HK-Project1. The project was pear to be contradictory to some extent that we failed to get a but- started in the middle of 1960’s by Olin Wilson to search for activity terfly diagram for stars with the most pronounced cycles (i.e., those cycles of other stars. Thanks to the realization of this project we pos- labeled ‘‘Excellent”) which probably do not carry those long-lasting sess at present the unique observations of long-term variability of activity tracers. the chromospheric radiation for many late-type stars. Presumably, For less pronounced cycles (i.e., labeled ‘‘Good”) we find two when magnetically active areas are present on the surface of the star examples (HD 115404 and HD 149661) where the attempt looks and/or the overall magnetic activity is stronger, the H and K Ca II promising so we get stellar butterfly diagrams. We note however emission flux increases. that the quality of butterfly diagram is significantly better (more The HK-Project deals with integral quantities representing stel- confident) in HD 115404 than for HD 149661. lar activity but was not directed, initially, to a reconstruction of its Also note that the present analysis follows the previous one spatial characteristics. The situation is not completely hopeless. (Katsova and Livshits, 2006) which focused on the status of solar This paper makes an attempt to reconstruct the temporal-latitudi- activity among processes in those late-type stars with activity nal (butterfly) diagram of stellar activity using the bulk chromo- spheric emission data series from the HK-Project. Surely, it would be beneficial for experts in inverse Doppler images to reor- ganize their research strategies in order to improve on the science (a) demands and goals described above. The first successful result of this type, adopting bulk photometry data series, has been pre- sented by Berdyugina and Henry (2007) for the binary system HR 1099 RS CVn. Our aim here is to perform similar analysis for single stars from the HK-Project. The key idea for the analysis can be presented as follows. Be- cause we can’t resolve the stellar disk, we cannot measure the lat- itude of active regions. However, we can monitor the change in rotation period with time. Baliunas et al. (1985) first proposed to determine the rotation rate for the stars of HK-Project using Fou- rier analysis and they recognized that the rotational periods of some stars vary from one observational season to another on time- scale of about 3 years. Of course, we presume that the angular momentum of the rotation of a star as a whole is conserved. A nat- ural interpretation of the result is to connect the variations with a redistribution of the emitting volume in course of stellar cycle and (b) differential rotation of chromospheric inhomogeneities. Frick et al. (1997) improved the idea and developed a wavelet method for a consistent representation of time-frequency characteristics of stel- lar activity. We applied this new method in this paper. Another starting point for our analysis is a classification scheme for cyclic chromospheric activity as suggested by Baliunas et al. (1995). That paper classified star activity into several classes depending on how pronounced the cyclicity is. The classification ranges from ”Excellent” to ”Good”, ”Fair” and ”Poor”. If a star activ- ity record is too variable to reveal a cyclic component, it is denoted as ”Variable”. A straightforward interpretation of variations of stellar rotation rate from one observational season to another is that the activity belt varies its latitude according to the phase of its cycle. We per- form the above analysis with data records covering time intervals longer than the activity cycles. We show that at least for two stars, (c) the variations of rotation rate demonstrate a regular behaviour which appears consistent with the latitude migration interpreta- tion. Anticipating the stellar rotation curve to be similar to the so- lar one we recalculate the rotation variations isolated into the latitudes of the activity belt at various phases of the cycle to arrive at a stellar butterfly diagram. Our method demands quite a lot from a star activity record for which we are going to reconstruct stellar butterfly diagram. We need a pronounced surface activity tracer (a long-lived spot or something like an active longitude) which exists on the time scales of the activity cycle in order to obtain the rotation rate with accu- racy sufficient for our aims.