Digitization of sunspot drawings by Sp\"orer made in 1861-1894

Most of our knowledge about the Sun's activity cycle arises from sunspot observations over the last centuries since telescopes have been used for astronomy. The German astronomer Gustav Sp\"orer observed almost daily the Sun from 1861 until the beginning of 1894 and assembled a 33-year collection of sunspot data covering a total of 445 solar rotation periods. These sunspot drawings were carefully placed on an equidistant grid of heliographic longitude and latitude for each rotation period, which were then copied to copper plates for a lithographic reproduction of the drawings in astronomical journals. In this article, we describe in detail the process of capturing these data as digital images, correcting for various effects of the aging print materials, and preparing the data for contemporary scientific analysis based on advanced image processing techniques. With the processed data we create a butterfly diagram aggregating sunspot areas, and we present methods to measure the size of sunspots (umbra and penumbra) and to determine tilt angles of active regions. A probability density function of the sunspot area is computed, which conforms to contemporary data after rescaling.Comment: 10 pages, 8 figures, accepted for publication in Astronomische Nachrichten/Astronomical Note

Estimating meteor rates using Bayesian inference

A method for estimating the true meteor rate lambda from a small number of observed meteors n is derived. We employ Bayesian inference with a Poissonian likelihood function. We discuss the choice of a suitable prior and propose the adoption of Jeffreys prior, P(lambda)=lambda^-0.5, which yields an expectation value E(lambda) = n+0.5 for any n >= 0. We update the ZHR meteor activity formula accordingly, and explain how 68%- and 95%-confidence intervals can be computed.Peer reviewe

First solar butterfly diagram from Schwabe's observations in 1825-1867

The original sunspot observations by Heinrich Samuel Schwabe of 1825-1867 were digitized and a first subset of spots was measured. In this initial project, we determined more than 14 000 sunspot positions and areas comprising about 11% of the total amount of spots available from that period. The resulting butterfly diagram has a typical appearance, but with evident north-south asymmetries.Comment: 3 pages, 1 figure, Proceedings of IAU symposium 273, Physics of Sun and star spots, Ventura, California 22-26 August 201

Nonlinear dynamo models using quasi-biennial oscillations constrained by sunspot area data

Contex: Solar magnetic activity exhibits variations with periods between 1.5--4 years, the so-called quasi-biennial oscillations (QBOs), in addition to the well-known 11-year Schwabe cycles. Solar dynamo is thought to be the responsible mechanism for generation of the QBOs. Aims: In this work, we analyse sunspot areas to investigate the spatial and temporal behaviour of the QBO signal and study the responsible physical mechanisms using simulations from fully nonlinear mean-field flux-transport dynamos. Methods: We investigated the behaviour of the QBOs in the sunspot area data in full disk, and northern and southern hemispheres, using wavelet and Fourier analyses. We also ran solar dynamos with two different approaches to generating a poloidal field from an existing toroidal field, Babcock-Leighton and turbulent $\alpha$ mechanisms. We then studied the simulated magnetic field strengths as well as meridional circulation and differential rotation rates using the same methods. Results: The results from the sunspot areas show that the QBOs are present in the full disk and hemispheric sunspot areas and they show slightly different spatial and temporal behaviours, indicating a slightly decoupled solar hemispheres. The QBO signal is generally intermittent and in-phase with the sunspot area data, surfacing when the solar activity is in maximum. The results from the BL-dynamos showed that they are neither capable of generating the slightly decoupled behaviour of solar hemispheres nor can they generate QBO-like signals. The turbulent $\alpha$-dynamos, on the other hand, generated decoupled hemispheres and some QBO-like shorter cycles. Conclusions: In conclusion, our simulations show that the turbulent $\alpha$-dynamos with the Lorentz force seems more efficient in generating the observed temporal and spatial behaviour of the QBO signal compared with those from the BL-dynamos

3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $\Gamma_{\alpha_1}^{\alpha_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $\Gamma_{\alpha_1}^{\alpha_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $\Gamma_{\alpha_1}^{\alpha_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.Comment: 18 pages, 15 figures, 6 tabula

Reconstruction of the Solar Activity from the Catalogs of the Zurich Observatory

Catalogs of the Zurich Observatory contain positional information on sunspots, prominences and faculae in late 19th and early 20th centuries. This database is given in handwritten tabular form and was not systematically analysed earlier. It is different from the sunspot number time series made in Zurich and was obtained with a larger telescope. We trained a neural-network model for handwritten text recognition and present the database of reconstructed coordinates. The database obtained connects the earlier observations by Sp\"orer with later programs of the 20th century and supplements the sunspot-group catalogs of the Royal Greenwich Observatory. We also expect that the presented machine-learning approach and its deep capabilities will motivate the processing of a wide bulk of astronomical data, which is still given in non-digitized form or as plain scanned images