Active longitudes

5.4 Active longitudes

Decades of continuous photometric monitoring of RS CVn stars revealed that large spots maintained their identities for years which was interpreted as a signature of one or two active longitudes similar to the distribution of solar energetic flares (Zeilik et al., 1988 ; Olah et al., 1988 ; Henry et al., 1995

; Jetsu, 1996 ). Whether such a structure has a preferred orientation with respect to the line of centres in a binary, and how long it survives, was a long debate (Hall, 1996 ). Berdyugina and Tuominen (1998

) showed that active longitudes on RS CVns are permanent but can continuously migrate in the orbital reference frame, and generally have no preferred orientation. The active longitudes are separated by 180° on average and differ in their activity level. Periodic switching of the dominant activity from one active longitude to the other results in a so-called flip-flop cycle (Berdyugina and Tuominen, 1998

) which is described in more detail in Section 6.2. A further analysis of photometric data confirmed the existence of active longitudes on RS CVn stars (Lanza et al., 1998a

; Rodonò et al., 2000 ).

Two active longitudes seem to be a conspicuous pattern of the stellar activity. In addition to RS CVn stars they have been found in the spot distribution on FK Com-type stars (Jetsu et al., 1993 , 1999 ; Korhonen et al., 2002 ) and very active young solar analogues (Berdyugina et al., 2002 ; Järvinen et al., 2005b ; Berdyugina and Järvinen, 2005 ). Two examples for the RS CVn star $σ$ Gem and young dwarf AB Dor are shown in Figure 11 .

Figure 11: Active longitudes, flip-flops, and sunspot-like cycles on the RS CVn star $σ$ Gem (Berdyugina and Henry, 2005

), young solar analogue AB Dor (Järvinen et al., 2005b

), and the Sun (Berdyugina and Usoskin, 2003

). The three plots upper panels show phases of spot concentrations (filled and open circles denote primary and secondary regions, respectively). The migration paths of active longitudes are emphasised by solid lines. Flip-flops are marked by vertical dashed lines. They occur when the primary region jumps to the opposite active longitude. For the Sun, only half-year average phases are shown and a linear drift of the active longitudes in the Carrington system is subtracted for better visibility. Lower panels in the plots show variations of the stellar brightness and sunspot area. Note that minimum brightness corresponds to maximum spotted area for both $σ$ Gem and AB Dor, in contrast to the Sun (e.g., Amado et al., 2001

The migration of active longitudes occurs with respect to the chosen reference frame. In binaries, this is usually the orbital ephemeris, while in single stars it represents an average epoch obtained over several years. If the migration is linear, a phase difference accumulates due to a constant difference between the assumed and true periods of the spot rotation. This is more common for binary components of RS CVn-type stars (Berdyugina and Tuominen, 1998 ). A non-linear migration suggests the presence of differential rotation and changes in mean spot latitudes as, e.g., on the Sun. Such a behaviour is typical for single stars, young solar type dwarfs, and FK Com-type giants (see Figure 11 ).

The analogy with solar active longitudes is further supported by the longitudinal distribution of sunspots (Berdyugina and Usoskin, 2003 ). Large sunspot groups in both Northern and Southern hemispheres are preferably formed around two active longitudes which are separated by 180° and persistent for at least 120 yr. Similar to young solar-type dwarfs, the two active longitudes on the Sun are long-lived quasi-rigid structures which are not fixed in any reference frame due to differential rotation. They continuously migrate, with a variable rate, with respect to the chosen reference frame (see Figure 11 ). In the Carrington system, the migration results in a phase lag of about 2.5 solar rotations per sunspot cycle. The migration of active longitudes is caused by changes in the mean latitude of the sunspot formation and differential rotation. Sunspots are first formed at higher latitudes and approach the equator as the solar cycle advances. In the Carrington reference frame the migration is more rapid at the beginning of the cycle and slows down towards the end. The migration pattern of the active longitudes bears, therefore, the information on both differential rotation and mean spot latitudes. This can be used for inferring stellar differential rotation and butterfly diagrams.