The solar differential rotation in the 18th century

The sunspot drawings of Johann Staudacher of 1749--1799 were used to determine the solar differential rotation in that period. These drawings of the full disk lack any indication of their orientation. We used a Bayesian estimator to obtain the position angles of the drawings, the corresponding heliographic spot positions, a time offset between the drawings and the differential rotation parameter \delta\Omega, assuming the equatorial rotation period is the same as today. The drawings are grouped in pairs, and the resulting marginal distributions for \delta\Omega were multiplied. We obtain \delta\Omega=-0.048 \pm 0.025 d^-1 (-2.75^o/d) for the entire period. There is no significant difference to the value of the present Sun. We find an (insignificant) indication for a change of \delta\Omega throughout the observing period from strong differential rotation, \delta\Omega\approx -0.07 d^-1, to weaker differential rotation, \delta\Omega\approx-0.04 d^-1.Comment: 6 pages, 6 figures, accepted for Astronomy and Astrophysic

Nature of grand minima and maxima from fully non-linear Flux-Transport Dynamos

We aim to investigate the nature and occurrence characteristics of grand solar minimum and maximum periods, which are observed in the solar proxy records such as 10Be and 14C, using a fully non-linear Babcock-Leighton type flux-transport dynamo including momentum and entropy equations. The differential rotation and meridional circulation are generated from the effect of turbulent Reynolds stress and are subjected to back-reaction from the magnetic field. To generate grand minimum and maximum-like periods in our simulations, we used random fluctuations in the angular momentum transport process, namely the Lambda-mechanism, and in the Babcock-Leighton mechanism. To characterise the nature and occurrences of the identified grand minima and maxima in our simulations, we used the waiting time distribution analyses, which reflects whether the underlying distribution arises from a random or a memory-bearing process. The results show that, in majority of the cases, the distributions of grand minima and maxima reveal that the nature of these events originates from memoryless processes. We also found that in our simulations the meridional circulation speed tends to be smaller during grand maximum, while it is faster during grand minimum periods. The radial differential rotation tend to be larger during grand maxima, while it is smaller during grand minima. The latitudinal differential rotation on the other hand is found to be larger during grand minima.Comment: accepted for publication in Astrophysical Journa

Delayed Babcock-Leighton dynamos in the diffusion-dominated regime

Context. Solar dynamo models of Babcock-Leighton type typically assume the rise of magnetic flux tubes to be instantaneous. Solutions with high-magnetic-diffusivity have too short periods and a wrong migration of their active belts. Only the low-diffusivity regime with advective meridional flows is usually considered. Aims. In the present paper we discuss these assumptions and applied a time delay in the source term of the azimuthally averaged induction equation. This delay is set to be the rise time of magnetic flux tubes which supposedly form at the tachocline. We study the effect of the delay, which adds to the spacial non-locality a non-linear temporal one, in the advective but particularly in the diffusive regime. Methods. Fournier et al. (2017) obtained the rise time according to stellar parameters such as rotation, and the magnetic field strength at the bottom of the convection zone. These results allowed us to constrain the delay in the mean-field model used in a parameter study. Results. We identify an unknown family of solutions. These solutions self-quench, and exhibit longer periods than their non-delayed counterparts. Additionally, we demonstrate that the non-linear delay is responsible for the recover of the equatorward migration of the active belts at high turbulent diffusivities. Conclusions. By introducing a non-linear temporal non-locality (the delay) in a Babcock-Leighton dynamo model, we could obtain solutions quantitatively comparable to the solar butterfly diagram in the diffusion-dominated regime.Comment: 11 pages, 10 Figure

Differential rotation decay in the radiative envelopes of CP stars

Stars of spectral classes A and late B are almost entirely radiative. CP stars are a slowly rotating subgroup of these stars. It is possible that they possessed long-lived accretion disks in their T Tauri phase. Magnetic coupling of disk and star leads to rotational braking at the surface of the star. Microscopic viscosities are extremely small and will not be able to reduce the rotation rate of the core of the star. We investigate the question whether magneto-rotational instability can provide turbulent angular momentum transport. We illuminate the question whether or not differential rotation is present in CP stars. Numerical MHD simulations of thick stellar shells are performed. An initial differential rotation law is subject to the influence of a magnetic field. The configuration gives indeed rise to magneto-rotational instability. The emerging flows and magnetic fields transport efficiently angular momentum outwards. Weak dependence on the magnetic Prandtl number (~0.01 in stars) is found from the simulations. Since the estimated time-scale of decay of differential rotation is 10^7-10^8 yr and comparable to the life-time of A stars, we find the braking of the core to be an ongoing process in many CP stars. The evolution of the surface rotation of CP stars with age will be an observational challenge and of much value for verifying the simulations.Comment: 8 pages, 11 figures; submitted to Astron. & Astrophy

Inconsistency of the Wolf sunspot number series around 1848

Aims. Sunspot number is a benchmark series in many studies, but may still contain inhomogeneities and inconsistencies. In particular, an essential discrepancy exists between the two main sunspot number series, Wolf (WSN) and group (GSN) sunspot numbers, before 1848. The source of this discrepancy has so far remained unresolved. However, the recently digitized series of solar observations in 1825-1867 by Samuel Heinrich Schwabe, who was the primary observer of the WSN before 1848, makes such an assessment possible. Methods. We construct sunspot series, similar to WSN and GSN, but using only Schwabe's data. These series, called WSN-S and GSN-S, respectively, were compared with the original WSN and GSN series for the period 1835-1867 to look for possible inhomogeneities. Results. We show that: (1) The GSN series is homogeneous and consistent with the Schwabe data throughout the entire studied period; (2) The WSN series decreases by roughly ~20% around 1848 caused by the change of the primary observer from Schwabe to Wolf and an inappropriate individual correction factor used for Schwabe in the WSN; (3) This implies a major inhomogeneity in the WSN, which needs to be corrected by reducing its values by 20% before 1848; (4) The corrected WSN series is in good agreement with the GSN series. This study supports the earlier conclusions that the GSN series is more consistent and homogeneous in the earlier part than the WSN series.Comment: Published as: Leussu, R., I.G. Usoskin, R. Arlt and K. Mursula, Inconsistency of the Wolf sunspot number series around 1848, Astron. Astrophys., 559, A28, 201

Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and red giant stars. Under the assumption of local angular momentum conservation, the core contraction and envelope expansion occurring at the end of the main sequence would result in a much larger internal differential rotation than observed. This suggests that angular momentum redistribution must be taking place in the interior of these stars. Aims. We investigate the physical nature of the angular momentum redistribution mechanisms operating in stellar interiors by constraining the efficiency of post-main sequence rotational coupling. Methods. We model the rotational evolution of a 1.25 Msun star using the Yale Rotational stellar Evolution Code. Our models take into account the magnetic wind braking occurring at the surface of the star and the angular momentum transport in the interior, with an efficiency dependent on the degree of internal differential rotation. Results. We find that models including a dependence of the angular momentum transport efficiency on the radial rotational shear reproduce very well the observations. The best fit of the data is obtained with an angular momentum transport coefficient scaling with the ratio of the rotation rate of the radiative interior over that of the convective envelope of the star as a power law of exponent ~3. This scaling is consistent with the predictions of recent numerical simulations of the Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular momentum transport process whose efficiency varies during the stellar evolution through a dependence on the level of internal differential rotation is required to explain the observed post-main sequence rotational evolution of low-mass stars.Comment: 8 pages, 6 figures; accepted for publication in Astronomy & Astrophysic

Sunspot group tilt angle measurements from historical observations

Sunspot positions from various historical sets of solar drawings are analysed with respect to the tilt angles of bipolar sunspot groups. Data by Scheiner, Hevelius, Staudacher, Zucconi, Schwabe, and Spoerer deliver a series of average tilt angles spanning a period of 270 years, additional to previously found values for 20th-century data obtained by other authors. We find that the average tilt angles before the Maunder minimum were not significantly different from the modern values. However, the average tilt angles of a period 50 years after the Maunder minimum, namely for cycles 0 and 1, were much lower and near zero. The normal tilt angles before the Maunder minimum suggest that it was not abnormally low tilt angles which drove the solar cycle into a grand minimum.Comment: accepted by Advances in Space Researc