Obtaining the Full Unitarity Triangle from B -> pi K Decays

We present a method of obtaining the entire unitarity triangle from measurements of B -> pi K decay rates alone. Electroweak penguin amplitudes are included, and are related to tree operators. Discrete ambiguities are removed by comparing solutions with independent experimental data. The theoretical uncertainty in this method is rather small, in the range 5--10%.Comment: 4 pages, RevTeX, no figures. Clarifying remarks and references adde

A coupled 2 x 2D Babcock-Leighton solar dynamo model. II Reference dynamo solutions

In this paper we complete the presentation of a new hybrid 2 × 2D flux transport dynamo (FTD) model of the solar cycle based on the Babcock–Leighton mechanism of poloidal magnetic field regeneration via the surface decay of bipolar magnetic regions (BMRs). This hybrid model is constructed by allowing the surface flux transport (SFT) simulation described in Lemerle et al. to provide the poloidal source term to an axisymmetric FTD simulation defined in a meridional plane, which in turn generates the BMRs required by the SFT. A key aspect of this coupling is the definition of an emergence function describing the probability of BMR emergence as a function of the spatial distribution of the internal axisymmetric magnetic field. We use a genetic algorithm to calibrate this function, together with other model parameters, against observed cycle 21 emergence data. We present a reference dynamo solution reproducing many solar cycle characteristics, including good hemispheric coupling, phase relationship between the surface dipole and the BMR-generating internal field, and correlation between dipole strength at cycle maximum and peak amplitude of the next cycle. The saturation of the cycle amplitude takes place through the quenching of the BMR tilt as a function of the internal field. The observed statistical scatter about the mean BMR tilt, built into the model, acts as a source of stochasticity which dominates amplitude fluctuations. The model thus can produce Dalton-like epochs of strongly suppressed cycle amplitude lasting a few cycles and can even shut off entirely following an unfavorable sequence of emergence events

Modélisation hybride du cycle d’activité solaire : évolution couplée du flux magnétique photosphérique et de la dynamo interne

La dynamo magnétohydrodynamique (MHD) solaire requière un mécanisme de régénération cyclique du champ magnétique poloïdal global, que la force de Coriolis peut fournir, mais dont l'échelle spatiale et le lieu d'occurence restent encore incertains malgré un siècle d'analyse théorique et quelques décennies de simulation numérique. Tandis que les modèles en champs moyens axisymétriques et certains modèles tridimensionnels (3D) globaux trouvent cette source dans un excès d'hélicité aux petites échelles convectives, les modèles de type Babcock-Leighton (BL) proposent plutôt que le mécanisme dominant soit directement dû à la torsion des boucles de flux ascendantes responsables de l'émergence des régions magnétiques bipolaires (BMR) (et de la formation des taches) à la surface du Soleil. Nous optons ici pour cette seconde classe de modèles, en une approche plutôt phénoménologique permettant de reproduire au mieux les observations, dans une représentation fidèle et compréhensible des processus physiques en cause aux multiples échelles spatio-temporelles, mais tout en cherchant à conserver une efficacité d'exécution numérique qui permette des analyses poussées et répétées. D'une part, une modélisation bidimensionnelle (2D) de la surface solaire (simulation d'évolution du flux de surface ou SFT) est requise afin de rendre compte des observations de l'émergence, du transport et de la diffusion du flux magnétique photosphérique. D'autre part, les tendances globales du patron d'émergence indiquent une structure ordonnée, approximativement axisymétrique, du champ magnétique dans la zone convective, ce qui requière donc minimalement une modélisation dynamo 2D dans le plan méridien. En combinant directement ces deux configurations minimales requises, nous élaborons un nouveau modèle dynamo BL couplé 2 x 2D: l'émergence probabiliste des BMR à partir du champ magnétique interne fournissant le terme source à la SFT, et le résultat de la SFT servant de terme source à la dynamo interne. Afin d'en faire un modèle le plus près possible du Soleil réel, une double calibration est effectuée, à l'aide d'un algorithme génétique, afin d'obtenir des valeurs optimales (avec barres d'incertitudes) pour 18 paramètres libres: (1) le résultat de la SFT est comparé à une carte magnétographique de surface (Lemerle et al, 2015, ApJ, 810, 78), et (2) le résultat de la dynamo interne est comparé au ``diagramme papillon'' des BMR observées (Lemerle & Charbonneau, 2017, ApJ, 834, 133). Nous obtenons ainsi un modèle dynamo BL couplé 2 x 2D qui sait reproduire plusieurs comportements solaires: émergence de BMR aux basses latitudes respectant les statistiques observées, trainées magnétiques unipolaires aux moyennes latitudes, accumulation adéquate de flux aux pôles au minimum d'activité, fort couplage hémisphérique, corrélation à potentiel prédictif entre amplitude du dipôle en fin de cycle et amplitude du cycle d'activité suivant, fluctuations d'amplitude à long terme, phases d'arrêts tel le minimum de Maunder, etc. Le travail encore en cours au Groupe de Recherche en Physique solaire (GRPS) montre que cette dynamo est hautement sujette aux fluctuations stochastiques dues à la spécificité de la série d'émergences, que, par ailleurs, ce sont de telles fluctuations qui parfois entraînent la dynamo vers une phase d'arrêt, qu'un mécanisme dynamo secondaire doit être présent pour subséquemment redémarrer le système, mais que, malgré cette stochasticité intrinsèque, un fort potentiel prédictif, éventuellement de l'ordre d'un cycle d'activité entier, est envisageable.The solar magnetohydrodynamical (MHD) dynamo requires a mechanism of cyclic regeneration for the global poloidal magnetic field, that can be provided by the Coriolis force, but for which spatial scale and location remain uncertain despite a century of theoretical analysis and decades of numerical simulations. While axisymmetric mean fields and global 3D models find this source in an excess of helicity at small convective scales, Babcock–Leighton (BL)-type models rather suggest that the dominant mechanism is due to the torsion of rising flux loops ultimately responsible for the emergence of bipolar magnetic regions (BMRs) (and formation of sunspots) at the surface of the Sun. We opt here for this second class of models, in a phenomenological approach that seeks to optimally reproduce observations, while accurately and intelligibly accounting for the physical processes that occur at multiple spatial and temporal scales, while also maintaining a numerical efficiency that allows for detailed and extended analyses. On one hand, a two-dimension (2D) modeling of the solar surface (namely surface flux transport (SFT)) is required to account for the observed emergence, transport, and diffusion of photospheric magnetic flux. On the other hand, the globally structured, roughly axisymmetric, magnetic fields in the convection zone, as inferred by the shape of the emergence patterns (the “butterfly diagram”), minimally require a 2D dynamo modeling in the meridional plane. Combining these two minimal configurations allows us to build a new coupled 2 × 2D BL dynamo model, where the probabilistic emergence of BMRs from deep toroidal field provides a source for the SFT, and the output of the SFT in turn provides a source for the internal dynamo. In order to make this model most closely solar-like, a double calibration is performed, through a genetic algorithm, to obtain optimal values (with error estimates) for 18 free parameters: (1) the SFT results are compared with magnetographic maps of the solar surface (Lemerle et al, 2015, ApJ, 810, 78), and (2) the internal dynamo results are compared with the observed “butterfly diagram” of BMRs (Lemerle & Charbonneau, 2017, ApJ, 834, 133). We thus obtain a coupled 2 x 2D BL dynamo model that consistently reproduces several solar features: low-latitude BMR emergences that follow observed statistics, mid-latitude unipolar flux strips, suitable polar cap flux at activity minima, strong hemispheric coupling, forecast-enabling correlations between amplitude of the axial dipole at cycle minima and amplitude of the subsequent cycle, long term amplitude fluctuations, occurence of grand minima (like the Maunder minimum), etc. Work still in progress at the Groupe de Recherche en Physique solaire (GRPS) shows that this dynamo is highly subjected to stochastic fluctuations due to the specific realization of random emergence series, that it is these fluctuations that sometimes bring the dynamo into a descending phase toward a grand minimum, that a second order dynamo mechanism must exist to subsequently restart the system, but that, despite this inherent stochasticity, the model provides a strong predictive capability, possibly of the order of a full activity cycle

A Coupled 2 × 2D Babcock–Leighton Solar Dynamo Model. I. Surface Magnetic Flux Evolution

The need for reliable predictions of the solar activity cycle motivates the development of dynamo models incorporating a representation of surface processes sufficiently detailed to allow assimilation of magnetographic data. In this series of papers we present one such dynamo model, and document its behavior and properties. This first paper focuses on one of the model's key components, namely surface magnetic flux evolution. Using a genetic algorithm, we obtain best-fit parameters of the transport model by least-squares minimization of the differences between the associated synthetic synoptic magnetogram and real magnetographic data for activity cycle 21. Our fitting procedure also returns Monte Carlo-like error estimates. We show that the range of acceptable surface meridional flow profiles is in good agreement with Doppler measurements, even though the latter are not used in the fitting process. Using a synthetic database of bipolar magnetic region (BMR) emergences reproducing the statistical properties of observed emergences, we also ascertain the sensitivity of global cycle properties, such as the strength of the dipole moment and timing of polarity reversal, to distinct realizations of BMR emergence, and on this basis argue that this stochasticity represents a primary source of uncertainty for predicting solar cycle characteristics

Physical Models for Solar Cycle Predictions

The dynamic activity of stars such as the Sun influences (exo)planetary space environments through modulation of stellar radiation, plasma wind, particle and magnetic fluxes. Energetic solar-stellar phenomena such as flares and coronal mass ejections act as transient perturbations giving rise to hazardous space weather. Magnetic fields – the primary driver of solar-stellar activity – are created via a magnetohydrodynamic dynamo mechanism within stellar convection zones. The dynamo mechanism in our host star – the Sun – is manifest in the cyclic appearance of magnetized sunspots on the solar surface. While sunspots have been directly observed for over four centuries, and theories of the origin of solar-stellar magnetism have been explored for over half a century, the inability to converge on the exact mechanism(s) governing cycle to cycle fluctuations and inconsistent predictions for the strength of future sunspot cycles have been challenging for models of the solar cycles. This review discusses observational constraints on the solar magnetic cycle with a focus on those relevant for cycle forecasting, elucidates recent physical insights which aid in understanding solar cycle variability, and presents advances in solar cycle predictions achieved via data-driven, physics-based models. The most successful prediction approaches support the Babcock-Leighton solar dynamo mechanism as the primary driver of solar cycle variability and reinforce the flux transport paradigm as a useful tool for modelling solar-stellar magnetism

Analysis of Mars Global Surveyor magnetic data : crustal and time-dependent external magnetic fields

In this thesis, Mars Global Surveyor mapping-phase magnetic data are used to derive a combined spherical harmonic model of both Martian crustal and time-dependent external magnetic fields.A 60-degree spherical harmonic model of the crustal magnetic anomalies is first isolated, by averaging of in-shadow data over 0.5° x 0.5° latitude and longitude bins, and covariance analysis between multiple independent models. This model is then subtracted, separately, from day-side and night-side measurements. External residual data are expended in terms of now time-dependent 30-degree spherical harmonics, using 1 year and 1/2 year periods, and with separate internal and external radial dependencies. Independent Fourier series expansions allow to validate the temporal variations of the preceding model.As a result, I obtain, along with the crustal anomaly maps, the spatial distribution of the external fields, their steady-state features, and the amplitude maps of their yearly and half a year variations, separately for day and night sides of Mars. Although the maxima of the temporal amplitudes show good correlations with the strong crustal anomalies, there are significant differences between them.Keywords. covariance analysis, crustal anomalies, magnetic anomalies, magnetic field, magnetosphere, Mars, Mars Global Surveyor, spherical harmonics, temporal amplitude