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&

An all-optical buffer based on temporal cavity solitons operating at 10 Gb/s

We demonstrate the operation of an all-optical buffer based on temporal cavity solitons stored in a nonlinear passive fiber ring resonator. Unwanted acoustic interactions between neighboring solitons are suppressed by modulating the phase of the external laser driving the cavity. A new locking scheme is presented that allows the buffer to operate with an arbitrarily large number of cavity solitons in the loop. Experimentally, we are able to demonstrate the storage of 4536 bits of data, written all-optically into the fiber ring at 10 Gb/s, for 1 minute.Comment: 5 pages, 4 figure

Three-loop matching coefficients for hot QCD: Reduction and gauge independence

We perform an integral reduction for the 3-loop effective gauge coupling and screening mass of QCD at high temperatures, defined as matching coefficients appearing in the dimensionally reduced effective field theory (EQCD). Expressing both parameters in terms of a set master (sum-) integrals, we show explicit gauge parameter independence. The lack of suitable methods for solving the comparatively large number of master integrals forbids the complete evaluation at the moment. Taking one generic class of masters as an example, we highlight the calculational techniques involved. The full result would allow to improve on one of the classic probes for the convergence of the weak-coupling expansion at high temperatures, namely the comparison of full and effective theory determinations of the spatial string tension. Furthermore, the full result would also allow to determine one new contribution of order O(g**7) to the pressure of hot QCD.Comment: 19 pages, 2 figures. v2: new Section 6 discussing applications, to match journal versio

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

A new three-loop sum-integral of mass dimension two

We evaluate a new 3-loop sum-integral which contributes to the Debye screening mass in hot QCD. While we manage to derive all divergences analytically, its finite part is mapped onto simple integrals and evaluated numerically.Comment: 15 page

3-D unrestricted TDHF fusion calculations using the full Skyrme interaction

We present a study of fusion cross sections using a new generation Time-Dependent Hartree-Fock (TDHF) code which contains no approximations regarding collision geometry and uses the full Skyrme interaction, including all of the time-odd terms. In addition, the code uses the Basis-Spline collocation method for improved numerical accuracy. A comparative study of fusion cross sections for $^{16}O + ^{16,28}O$ is made with the older TDHF results and experiments. We present results using the modern Skyrme forces and discuss the influence of the new terms present in the interaction.Comment: 7 pages, 10 figure

Generic Modal Cut Elimination Applied to Conditional Logics

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics. For these, we obtain fully internalised calculi which are substantially simpler than those known in the literature, along with leaner proofs of cut elimination and complexity. In one case, conditional logic with modus ponens and conditional excluded middle, cut elimination and complexity were explicitly stated as open in the literature

Revisiting the cycle-rotation connection for late-type stars

We analyse the relation between the activity cycle length and the Rossby number and collected a sample of 44 main sequence stars with well-known activity cycle periods and rotation periods. We find a linear behaviour in the double-logarithmic relation between the Rossby number and cycle period. The bifurcation into a long and a short period branch is clearly real but it depends, empirically, on the colour index B-V, indicating a physical dependence on effective temperature and position on the main sequence. Furthermore, there is also a correlation between cycle length and convective turnover time with the relative depth of the convection zone. Based on this, we derive empirical relations between cycle period and Rossby number, and for the short period cycle branch relations, we estimate a scatter of the relative deviation between 14% and 28% on the long-period cycle branch. With these relations, we obtain a good match with the 10.3 yr period for the well known 11-year solar Schwabe cycle and a long-period branch value of 104 yr for the Gleissberg cycle of the Sun. Finally, we suggest that the cycles on the short-period branch appear to be generated in the deeper layers of the convective zone, while long-period branch cycles seem to be related to fewer deep layers in that zone. We show that for a broader B-V range, the Rossby number is a more suitable parameter for universal relation with cycle-rotation than just the rotation period alone. As proof, we demonstrate that our empirical stellar relations are consistent with the 11-year solar Schwabe cycle, in contrast to earlier studies using just the rotation period in their relations. Previous studies have tried to explain the cycle position of the Sun in the cycle-rotation presentation via other kinds of dynamo, however, in our study, no evidence is found that would suggest another type of dynamo for the Sun and other stars.Comment: 18 pages, 18 figures, accepted for publication in A&