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

The Thermal Environment of the Fiber Glass Dome for the New Solar Telescope at Big Bear Solar Observatory

The New Solar Telescope (NST) is a 1.6-meter off-axis Gregory-type telescope with an equatorial mount and an open optical support structure. To mitigate the temperature fluctuations along the exposed optical path, the effects of local/dome-related seeing have to be minimized. To accomplish this, NST will be housed in a 5/8-sphere fiberglass dome that is outfitted with 14 active vents evenly spaced around its perimeter. The 14 vents house louvers that open and close independently of one another to regulate and direct the passage of air through the dome. In January 2006, 16 thermal probes were installed throughout the dome and the temperature distribution was measured. The measurements confirmed the existence of a strong thermal gradient on the order of 5 degree Celsius inside the dome. In December 2006, a second set of temperature measurements were made using different louver configurations. In this study, we present the results of these measurements along with their integration into the thermal control system (ThCS) and the overall telescope control system (TCS).Comment: 12 pages, 11 figures, submitted to SPIE Optics+Photonics, San Diego, U.S.A., 26-30 August 2007, Conference: Solar Physics and Space Weather Instrumentation II, Proceedings of SPIE Volume 6689, Paper #2

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

Ca II 8542 \AA\ brightenings induced by a solar microflare

We study small-scale brightenings in Ca II 8542 \AA\ line-core images to determine their nature and effect on localized heating and mass transfer in active regions. High-resolution 2D spectroscopic observations of an active region in the Ca II 8542 \AA\ line were acquired with the GFPI attached to the 1.5-meter GREGOR telescope. Inversions of the spectra were carried out using NICOLE. We identified three brightenings of sizes up to 2"x2". We found evidence that the brightenings belonged to the footpoints of a microflare (MF). The properties of the observed brightenings disqualified the scenarios of Ellerman bombs or IRIS bombs. However, this MF shared some common properties with flaring active-region fibrils or flaring arch filaments (FAFs): (1) FAFs and MFs are both apparent in chromospheric and coronal layers according to the AIA channels, and (2) both show flaring arches with lifetimes of about 3.0-3.5 min and lengths of about 20". The inversions revealed heating by 600 K at the footpoint location in the ambient chromosphere during the impulsive phase. Connecting the footpoints, a dark filamentary structure appeared in the Ca II line-core images. Before the start of the MF, the spectra of this structure already indicated average blueshifts, meaning upward motions of the plasma along the LOS. During the impulsive phase, these velocities increased up to -2.2 km/s. Downflows dominated at the footpoints. However, in the upper photosphere, slight upflows occurred during the impulsive phase. Hence, bidirectional flows are present in the footpoints of the MF. Conclusions: We detected Ca II brightenings that coincided with the footpoint location of an MF. The MF event led to a rise of plasma in the upper photosphere, both before and during the impulsive phase. Excess mass, previously raised to at most chromospheric layers, slowly drained downward along arches toward the footpoints of the MF.Comment: Accepted for publication in Astronomy & Astrophysics, 13 pages, 6 figures, 1 online movi

Periods implying almost all periods, trees with snowflakes, and zero entropy maps

Let $X$ be a compact tree, $f$ be a continuous map from $X$ to itself, $End(X)$ be the number of endpoints and $Edg(X)$ be the number of edges of $X$. We show that if $n>1$ has no prime divisors less than $End(X)+1$ and $f$ has a cycle of period $n$, then $f$ has cycles of all periods greater than $2End(X)(n-1)$ and topological entropy $h(f)>0$; so if $p$ is the least prime number greater than $End(X)$ and $f$ has cycles of all periods from 1 to $2End(X)(p-1)$, then $f$ has cycles of all periods (this verifies a conjecture of Misiurewicz for tree maps). Together with the spectral decomposition theorem for graph maps it implies that $h(f)>0$ iff there exists $n$ such that $f$ has a cycle of period $mn$ for any $m$. We also define {\it snowflakes} for tree maps and show that $h(f)=0$ iff every cycle of $f$ is a snowflake or iff the period of every cycle of $f$ is of form $2^lm$ where $m\le Edg(X)$ is an odd integer with prime divisors less than $End(X)+1$

Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations