Direct statistical simulation of low-order dynamosystems

In this paper, we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third order and has cubic nonlinearities while the second has only quadratic nonlinearities and describes the interaction of convection and an aperiodically reversing magnetic field. We show how DSS can be used to solve for the statistics of these systems of equations both in the presence and the absence of stochastic terms, by truncating the cumulant hierarchy at either second or third order. We compare two different techniques for solving for the statistics: timestepping, which is able to locate only stable solutions of the equations for the statistics, and direct detection of the fixed points. We develop a complete methodology and symbolic package in Python for deriving the statistical equations governing the low-order dynamic systems in cumulant expansions. We demonstrate that although direct detection of the fixed points is efficient and accurate for DSS truncated at second order, the addition of higher order terms leads to the inclusion of many unstable fixed points that may be found by direct detection of the fixed point by iterative methods. In those cases, timestepping is a more robust protocol for finding meaningful solutions to DSS.

Latitudinal differential rotation in the solar analogues 16 Cygni A and B

Context. Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT and Kepler space missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect. Aims. Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed by Kepler and have therefore been extensively observed, with exquisite precision on their oscillation frequencies. Methods. We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form. Results. We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is 320 ± 269 nHz and 440−383+363 nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are 535 ± 75 nHz and 565−129+150 nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry. Conclusions. We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters.

Dynamo Processes Constrained by Solar and Stellar Observations

Our understanding of stellar dynamos has largely been driven by the phenomena we have observed of our own Sun. Yet, as we amass longer-term datasets for an increasing number of stars, it is clear that there is a wide variety of stellar behavior. Here we briefly review observed trends that place key constraints on the fundamental dynamo operation of solar-type stars to fully convective M dwarfs, including: starspot and sunspot patterns, various magnetism-rotation correlations, and mean field flows such as differential rotation and meridional circulation. We also comment on the current insight that simulations of dynamo action and flux emergence lend to our working knowledge of stellar dynamo theory. While the growing landscape of both observations and simulations of stellar magnetic activity work in tandem to decipher dynamo action, there are still many puzzles that we have yet to fully understand.

Stellar Magnetic Dynamos and Activity Cycles

Using a new uniform sample of 824 solar and late-type stars with measured X-ray luminosities and rotation periods we have studied the relationship between rotation and stellar activity that is believed to be a probe of the underlying stellar dynamo. Using an unbiased subset of the sample we calculate the power law slope of the unsaturated regime of the activity – rotation relationship as LX / Lbol ∝ Roβ, where β = − 2.70 ± 0.13. This is inconsistent with the canonical β = − 2 slope to a confidence of 5σ and argues for an interface-type dynamo. We map out three regimes of coronal emission as a function of stellar mass and age, using the empirical saturation threshold and theoretical super-saturation thresholds. We find that the empirical saturation timescale is well correlated with the time at which stars transition from the rapidly rotating convective sequence to the slowly rotating interface sequence in stellar spin-down models. This may be hinting at fundamental changes in the underlying stellar dynamo or internal structure. We also present the first discovery of an X-ray unsaturated, fully convective M star, which may be hinting at an underlying rotation - activity relationship in fully convective stars hitherto not observed. Finally we present early results from a blind search for stellar X-ray cycles that can place valuable constraints on the underlying ubiquity of solar-like activity cycles.

Stellar Magnetism and starspots: the implications for exoplanets

Stellar variability induced by starspots can hamper the detection of exoplanets and bias planet property estimations. These features can also be used to study star-planet interactions as well as inferring properties from the underlying stellar dynamo. However, typical techniques, such as ZDI, are not possible for most host-stars. We present a robust method based on spot modelling to map the surface of active star allowing us to statistically study the effects and interactions of stellar magnetism with transiting exoplanets. The method is applied to the active Kepler-9 star where we find small evidence for a possible interaction between planet and stellar magnetosphere which leads to a 2:1 resonance between spot rotation and orbital period.

Differential rotation and meridional flows in stellar convection zones

Differential rotation and meridional flow are key ingredients in flux transport dynamo models of the solar activity cycle. As the subsurface flow pattern is not sufficiently constrained by observations, it is a major source of uncertainty in solar and stellar dynamo models. We discuss the current mean field theory of stellar differential rotation and meridional flows and its predicitons for the Sun and stars on the lower main sequence.

Rotation and magnetism of solar-like stars: from scaling laws to spot-dynamos

The Sun is the archetype of magnetic star and its proximity coupled with very high accuracy observations has helped us understanding how solar-like stars (e.g with a convective envelope) redistribute angular momentum and generate a cyclic magnetic field. However most solar models have been so fine tuned that when they are applied to other solar-like stars the agreement with observations is not good enough. I will thus discuss, based on theoretical considerations and multi-D MHD stellar models, what can be considered as robust properties of solar-like star dynamics and magnetism and what is still speculative. I will derive scaling laws for differential rotation and magnetic energy as a function of stellar parameters, discuss recent results of stellar dynamo models and define the new concept of spot-dynamo, e.g. global dynamo that develops self-consistent magnetic buoyant structures that emerge at the surface.