Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

The On/Off Nature of Star-Planet Interactions

Evidence suggesting an observable magnetic interaction between a star and its hot Jupiter appears as a cyclic variation of stellar activity synchronized to the planet's orbit. In this study, we monitored the chromospheric activity of 7 stars with hot Jupiters using new high-resolution echelle spectra collected with ESPaDOnS over a few nights in 2005 and 2006 from the CFHT. We searched for variability in several stellar activity indicators (Ca II H, K, the Ca II infrared triplet, Halpha, and He I). HD 179949 has been observed almost every year since 2001. Synchronicity of the Ca II H & K emission with the orbit is clearly seen in four out of six epochs, while rotational modulation with P_rot=7 days is apparent in the other two seasons. We observe a similar phenomenon on upsilon And, which displays rotational modulation (P_rot=12 days) in September 2005, in 2002 and 2003 variations appear to correlate with the planet's orbital period. This on/off nature of star-planet interaction (SPI) in the two systems is likely a function of the changing stellar magnetic field structure throughout its activity cycle. Variability in the transiting system HD 189733 is likely associated with an active region rotating with the star, however, the flaring in excess of the rotational modulation may be associated with its hot Jupiter. As for HD 179949, the peak variability as measured by the mean absolute deviation for both HD 189733 and tau Boo leads the sub-planetary longitude by 70 degrees. The tentative correlation between this activity and the ratio of Mpsini to the planet's rotation period, a quantity proportional to the hot Jupiter's magnetic moment, first presented in Shkolnik et al. 2005 remains viable. This work furthers the characterization of SPI, improving its potential as a probe of extrasolar planetary magnetic fields.Comment: Accepted for publication in the Astrophysical Journa

Gamma-ray Timing of Redback PSR J2339-0533: Hints for Gravitational Quadrupole Moment Changes

We present the results of precision gamma-ray timing measurements of the binary millisecond pulsar PSR J2339$-$0533, an irradiating system of "redback" type, using data from the Fermi Large Area Telescope. We describe an optimized analysis method to determine a long-term phase-coherent timing solution spanning more than six years, including a measured eccentricity of the binary orbit and constraints on the proper motion of the system. A major result of this timing analysis is the discovery of an extreme variation of the nominal 4.6-hour orbital period $P_{\rm orb}$ over time, showing alternating epochs of decrease and increase. We inferred a cyclic modulation of $P_{\rm orb}$ with an approximate cycle duration of 4.2 years and a modulation amplitude of $\Delta P_{\rm orb}/ P_{\rm orb} = 2.3 \times 10^{-7}$. Considering different possible physical causes, the observed orbital-period modulation most likely results from a variable gravitational quadrupole moment of the companion star due to cyclic magnetic activity in its convective zone.Comment: 9 pages, 2 figure

The X-ray cycle in the solar-type star HD 81809

(abridged) Our long-term XMM-Newton program of long-term monitoring of a solar-like star with a well-studied chromospheric cycle, HD 81809 aims to study whether an X-ray cycle is present, along with studying its characteristics and its relation to the chromospheric cycle. Regular observations of HD 81809 were performed with XMM-Newton, spaced by 6 months from 2001 to 2007. We studied the variations in the resulting coronal luminosity and temperature, and compared them with the chromospheric CaII variations. We also modeled the observations in terms of a mixture of active regions, using a methodology originally developed to study the solar corona. Our observations show a well-defined cycle with an amplitude exceeding 1 dex and an average luminosity approximately one order of magnitude higher than in the Sun. The behavior of the corona of HD 81809 can be modeled well in terms of varying coverage of solar-like active regions, with a larger coverage than for the Sun, showing it to be compatible with a simple extension of the solar case.Comment: In press, Astronomy & Astrophysic

X-ray activity cycle on the active ultra-fast rotator AB Dor A? Implication of correlated coronal and photometric variability

Although chromospheric activity cycles have been studied in a larger number of late-type stars for quite some time, very little is known about coronal activity-cycles in other stars and their similarities or dissimilarities with the solar activity cycle. While it is usually assumed that cyclic activity is present only in stars of low to moderate activity, we investigate whether the ultra-fast rotator AB Dor, a K dwarf exhibiting signs of substantial magnetic activity in essentially all wavelength bands, exhibits a X-ray activity cycle in analogy to its photospheric activity cycle of about 17 years and possible correlations between these bands. We analysed the combined optical photometric data of AB Dor A, which span ~35 years. Additionally, we used ROSAT and XMM-Newton X-ray observations of AB Dor A to study the long-term evolution of magnetic activity in this active K dwarf over nearly three decades and searched for X-ray activity cycles and related photometric brightness changes. AB Dor A exhibits photometric brightness variations ranging between 6.75 < Vmag < 7.15 while the X-ray luminosities range between 29.8 < log LX [erg/s] < 30.2 in the 0.3-2.5 keV. As a very active star, AB Dor A shows frequent X-ray flaring, but, in the long XMM-Newton observations a kind of basal state is attained very often. This basal state probably varies with the photospheric activity-cycle of AB Dor A which has a period of ~17 years, but, the X-ray variability amounts at most to a factor of ~2, which is, much lower than the typical cycle amplitudes found on the Sun.Comment: 10 page

Magnitude-range brightness variations of overactive K giants

We study three representative, overactive spotted K giants (IL Hya, XX Tri, and DM UMa) known to exhibit V-band light variations between 0.65-1.05 mags. Our aim is to find the origin of their large brightness variation. We employ long-term phase-resolved multicolor photometry, mostly from automatic telescopes, covering 42 yr for IL Hya, 28 yr for XX Tri, and 34 yr for DM UMa. For one target, IL Hya, we present a new Doppler image from NSO data taken in late 1996. Effective temperatures for our targets are determined from all well-sampled observing epochs and are based on a V-I_C color-index calibration. The effective temperature change between the extrema of the rotational modulation for IL Hya and XX Tri is in the range 50-200 K. The bolometric flux during maximum of the rotational modulation, i.e., the least spotted states, varied by up to 39% in IL Hya and up to 54% in XX Tri over the course of our observations. We emphasize that for IL Hya this is just about half of the total luminosity variation that can be explained by the photospheric temperature (spots/faculae) changes, while for XX Tri it is even about one third. The long-term, 0.6 mag V-band variation of DM UMa is more difficult to explain because little or no B-V color index change is observed on the same timescale. Placing the three stars with their light and color variations into H-R diagrams, we find that their overall luminosities are generally too low compared to predictions from current evolutionary tracks. A change in the stellar radius due to strong and variable magnetic fields during activity cycles likely plays a role in explaining the anomalous brightness and luminosity of our three targets. At least for IL Hya, a radius change of about 9% is suggested from m_bol and T_eff, and is supported by independent vsin(i) measurements.Comment: 13 pages, 8 figures, accepted in A&

Quantum properties of a cyclic structure based on tripolar fields

The properties of cyclic structures (toroidal oscillators) based on classical tripolar (colour) fields are discussed, in particular, of a cyclic structure formed of three colour-singlets spinning around a ring-closed axis. It is shown that the helicity and handedness of this structure can be related to the quantum properties of the electron. The symmetry of this structure corresponds to the complete cycle of ${2/3}\pi$-rotations of its constituents, which leads to the exact overlapping of the paths of its three complementary coloured constituents, making the system dynamically colourless. The gyromagnetic ratio of this system is estimated to be g$\approx 2$, which agrees with the Land\'e g-factor for the electron.Comment: 11 pages, 4 figures, journal versio

Cycle frequency in standard Rock-Paper-Scissors games: Evidence from experimental economics

The Rock-Paper-Scissors (RPS) game is a widely used model system in game theory. Evolutionary game theory predicts the existence of persistent cycles in the evolutionary trajectories of the RPS game, but experimental evidence has remained to be rather weak. In this work we performed laboratory experiments on the RPS game and analyzed the social-state evolutionary trajectories of twelve populations of N=6 players. We found strong evidence supporting the existence of persistent cycles. The mean cycling frequency was measured to be $0.029 \pm 0.009$ period per experimental round. Our experimental observations can be quantitatively explained by a simple non-equilibrium model, namely the discrete-time logit dynamical process with a noise parameter. Our work therefore favors the evolutionary game theory over the classical game theory for describing the dynamical behavior of the RPS game.Comment: 7 Page, 3 figure; Keyword: Rock-Paper-Scissors game; cycle; social state; population dynamics; evolutionary trajector