Revisiting the connection between magnetic activity, rotation period, and convective turnover time for main-sequence stars

The connection between stellar rotation, stellar activity, and convective turnover time is revisited with a focus on the sole contribution of magnetic activity to the Ca II H&K emission, the so-called excess flux, and its dimensionless indicator R$^{+}_{\rm{HK}}$ in relation to other stellar parameters and activity indicators. Our study is based on a sample of 169 main-sequence stars with directly measured Mount Wilson S-indices and rotation periods. The R$^{+}_{\rm{HK}}$ values are derived from the respective S-indices and related to the rotation periods in various $B-V$-colour intervals. First, we show that stars with vanishing magnetic activity, i.e. stars whose excess flux index R$^{+}_{\rm{HK}}$ approaches zero, have a well-defined, colour-dependent rotation period distribution; we also show that this rotation period distribution applies to large samples of cool stars for which rotation periods have recently become available. Second, we use empirical arguments to equate this rotation period distribution with the global convective turnover time, which is an approach that allows us to obtain clear relations between the magnetic activity related excess flux index R$^{+}_{\rm{HK}}$, rotation periods, and Rossby numbers. Third, we show that the activity versus Rossby number relations are very similar in the different activity indicators. As a consequence of our study, we emphasize that our Rossby number based on the global convective turnover time approaches but does not exceed unity even for entirely inactive stars. Furthermore, the rotation-activity relations might be universal for different activity indicators once the proper scalings are used.Comment: 13 pages, 7 figures, accepted for publication in A&

Retardation of Particle Evaporation from Excited Nuclear Systems Due to Thermal Expansion

Particle evaporation rates from excited nuclear systems at equilibrium matter density are studied within the Harmonic-Interaction Fermi Gas Model (HIFGM) combined with Weisskopf's detailed balance approach. It is found that thermal expansion of a hot nucleus, as described quantitatively by HIFGM, leads to a significant retardation of particle emission, greatly extending the validity of Weisskopf's approach. The decay of such highly excited nuclei is strongly influenced by surface instabilities

Basal Chromospheric Flux and Maunder Minimum-type Stars: The quiet-Sun Chromosphere as a Universal Phenomenon

Aims: We demonstrate the universal character of the quiet-Sun chromosphere among inactive stars (solar-type and giants). By assessing the main physical processes, we shed new light on some common observational phenomena. Methods: We discuss measurements of the solar Mt. Wilson S-index, obtained by the Hamburg Robotic Telescope around the extreme minimum year 2009, and compare the established chromospheric basal Ca II K line flux to the Mt. Wilson S-index data of inactive ("flat activity") stars, including giants. Results: During the unusually deep and extended activity minimum of 2009, the Sun reached S-index values considerably lower than in any of its previously observed minima. In several brief periods, the Sun coincided exactly with the S-indices of inactive ("flat", presumed Maunder Minimum-type) solar analogues of the Mt. Wilson sample; at the same time, the solar visible surface was also free of any plages or remaining weak activity regions. The corresponding minimum Ca II K flux of the quiet Sun and of the presumed Maunder Minimum-type stars in the Mt. Wilson sample are found to be identical to the corresponding Ca II K chromospheric basal flux limit. Conclusions: We conclude that the quiet-Sun chromosphere is a universal phenomenon among inactive stars. Its mixed-polarity magnetic field, generated by a local, "fast" turbulent dynamo finally provides a natural explanation for the minimal soft X-ray emission observed for inactive stars. Given such a local dynamo also works for giant chromospheres, albeit on larger length scales, i.e., l ~ R/g, with R and g as stellar radius and surface gravity, respectively, the existence of giant spicular phenomena and the guidance of mechanical energy toward the acceleration zone of cool stellar winds along flux-tubes have now become traceable.Comment: 6 pages, 4 figures; Astronomy & Astrophysics (Research Note), in pres

Ground states versus low-temperature equilibria in random field Ising chains

We discuss with the aid of random walk arguments and exact numerical computations the magnetization properties of one-dimensional random field chains. The ground state structure is explained in terms of absorbing and non-absorbing random walk excursions. At low temperatures, the magnetization profiles follow those of the ground states except at regions where a local random field fluctuation makes thermal excitations feasible. This follows also from the non-absorbing random walks, and implies that the magnetization length scale is a product of these two scales. It is not simply given by the Imry-Ma-like ground state domain size nor by the scale of the thermal excitations.Comment: 7 pages LaTeX, 8 eps-figures include

Geometric, Variational Integrators for Computer Animation

We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details

Matching small β\beta functions using centroid jitter and two beam position monitors

Matching to small beta functions is required to preserve emittance in plasma accelerators. The plasma wake provides strong focusing fields, which typically require beta functions on the mm-scale, comparable to those found in the final focusing of a linear collider. Such beams can be time consuming to experimentally produce and diagnose. We present a simple, fast, and noninvasive method to measure Twiss parameters in a linac using two beam position monitors only, relying on the similarity of the beam phase space and the jitter phase space. By benchmarking against conventional quadrupole scans, the viability of this technique was experimentally demonstrated at the FLASHForward plasma-accelerator facility.Comment: 8 pages, 7 figure

Local effective dynamics of quantum systems: A generalized approach to work and heat

By computing the local energy expectation values with respect to some local measurement basis we show that for any quantum system there are two fundamentally different contributions: changes in energy that do not alter the local von Neumann entropy and changes that do. We identify the former as work and the latter as heat. Since our derivation makes no assumptions on the system Hamiltonian or its state, the result is valid even for states arbitrarily far from equilibrium. Examples are discussed ranging from the classical limit to purely quantum mechanical scenarios, i.e. where the Hamiltonian and the density operator do not commute.Comment: 5 pages, 1 figure, published versio