Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Beyond small-scale transients: a closer look at the diffuse quiet solar corona

Within the quiet Sun corona imaged at 1 MK, much of the field of view consists of diffuse emission that appears to lack the spatial structuring that is so evident in coronal loops or bright points. We seek to determine if these diffuse regions are categorically different in terms of their intensity fluctuations and spatial configuration from the more well-studied dynamic coronal features. We analyze a time series of observations from Solar Orbiter's High Resolution Imager in the Extreme Ultraviolet to quantify the characterization of the diffuse corona at high spatial and temporal resolutions. We then compare this to the dynamic features within the field of view, mainly a coronal bright point. We find that the diffuse corona lacks visible structuring, such as small embedded loops, and that this is persistent over the 25 min duration of the observation. The intensity fluctuations of the diffuse corona, which are within +/-5%, are significantly smaller in comparison to the coronal bright point. Yet, the total intensity observed in the diffuse corona is of the same order as the bright point. It seems inconsistent with our data that the diffuse corona is a composition of small loops or jets or that it is driven by discrete small heating events that follow a power-law-like distribution. We speculate that small-scale processes like MHD turbulence might be energizing the diffuse regions, but at this point we cannot offer a conclusive explanation for the nature of this feature.Comment: Accepted for publication in A&A. 10 pages, 8 figure

On the irrationality measure function in average

We study asymptotics for the intergal of irrationality measure functions.Comment: Summary in English, fulltext in Russia

Prominence eruption observed in He II 304 Å up to >6 R⊙ by EUI/FSI aboard Solar Orbiter⋆

Aims. We report observations of a unique, large prominence eruption that was observed in the He II 304 Å passband of the Extreme Ultraviolet Imager/Full Sun Imager telescope aboard Solar Orbiter on 15–16 February 2022. Methods. Observations from several vantage points – Solar Orbiter, the Solar-Terrestrial Relations Observatory, the Solar and Heliospheric Observatory, and Earth-orbiting satellites – were used to measure the kinematics of the erupting prominence and the associated coronal mass ejection. Three-dimensional reconstruction was used to calculate the deprojected positions and speeds of different parts of the prominence. Observations in several passbands allowed us to analyse the radiative properties of the erupting prominence. Results. The leading parts of the erupting prominence and the leading edge of the corresponding coronal mass ejection propagate at speeds of around 1700 km s−1 and 2200 km s−1, respectively, while the trailing parts of the prominence are significantly slower (around 500 km s−1). Parts of the prominence are tracked up to heights of over 6 R⊙. The He II emission is probably produced via collisional excitation rather than scattering. Surprisingly, the brightness of a trailing feature increases with height. Conclusions. The reported prominence is the first observed in He II 304 Å emission at such a great height (above 6 R⊙)

Small-scale EUV features as the drivers of coronal upflows in the quiet Sun

Context. Coronal upflows in the quiet Sun are seen in a wide range of features, including jets and filament eruptions. The in situ measurements from Parker Solar Probe within ≈0.2 au have demonstrated that the solar wind is highly structured, showing abrupt and near-ubiquitous magnetic field reversals (i.e., switchbacks) on different timescales. The source of these structures has been associated with supergranular structures on the solar disc. This raises the question of whether there are additional small coronal features that contribute energy to the corona and produce plasma that potentially feeds into the solar wind. / Aims. During the Solar Orbiter first science perihelion, high-resolution images of the solar corona were recorded using the Extreme Ultraviolet High Resolution Imager (HRIEUV) from the Extreme Ultraviolet Imager (EUI). The Hinode spacecraft was also observing at the same location providing coronal spectroscopic measurements. Combining the two datasets allows us to determine the cause of the weak upflows observed in the quiet Sun and the associated activity. / Methods. We used a multi-spacecraft approach to characterise regions of upflows. The upflows were identified in the Fe XII emission line by the Hinode EUV Imaging Spectrometer (EIS). We then used imaging data from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO/AIA) and the High Resolution Imagers (HRI) from EUI on board the Solar Orbiter to identify coronal features and magnetic field data from the SDO Helioseismic and Magnetic Imager (HMI). Interface Region Imaging Spectrograph (IRIS) observations were also used to understand the photospheric and chromospheric driving mechanisms. / Results. We have identified two regions of coronal upflows in the quiet Sun, with respective sizes and lifetimes of (20 Mm2, 20 min) and (180 Mm2, several hours), which are contrasting dynamic events. Both examples show weak flux cancellation, indicating that the source of the upflows and enhancements is related to the magnetic field changes. The first event, a larger upflow region, shows velocities of up to −8.6 km s−1 at the footpoint of a complex loop structure. We observe several distinct extreme ultraviolet (EUV) features including frequent loop brightenings and plasma blobs travelling along closed coronal loops. The second upflow region has velocities of up to −7.2 km s−1. Within it, a complex EUV feature that lasts for about 20 min can be seen. This main feature has several substructures. During its appearance, a clear mini-filament eruption takes place at its location, before the EUV feature disappears. / Conclusions. Two features, with contrasting properties, show upflows with comparable magnitudes. The first event, a complex loop structure, shares several similarities with active region upflows. The second one, a complex small-scale feature that could not have been well resolved with previous instruments, triggered a cascade of events, including a mini-filament that lead to a measurable upflow. This is remarkable for an EUV feature that many instruments can barely resolve. The complexity of the two events, including small loop brightenings and travelling plasma blobs for the first and EUV small-scale loops and mini-filament for the second one would not have been identifiable as the sources of upflow without an instrument with the spatial resolution of HRIEUV at this distance to the Sun. These results reinforce the importance of the smallest-scale features in the Sun and their potential relevance for and impact on the solar corona and the solar wind

Beyond the disk: EUV coronagraphic observations of the Extreme Ultraviolet Imager on board Solar Orbiter

Context. Most observations of the solar corona beyond 2 R consist of broadband visible light imagery carried out with coronagraphs. The associated diagnostics mainly consist of kinematics and derivations of the electron number density. While the measurement of the properties of emission lines can provide crucial additional diagnostics of the coronal plasma (temperatures, velocities, abundances, etc.), these types of observations are comparatively rare. In visible wavelengths, observations at these heights are limited to total eclipses. In the ultraviolet (UV) to extreme UV (EUV) range, very few additional observations have been achieved since the pioneering results of the Ultraviolet Coronagraph Spectrometer (UVCS). Aims. One of the objectives of the Full Sun Imager (FSI) channel of the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter mission has been to provide very wide field-of-view EUV diagnostics of the morphology and dynamics of the solar atmosphere in temperature regimes that are typical of the lower transition region and of the corona. Methods. FSI carries out observations in two narrowbands of the EUV spectrum centered on 17.4 nm and 30.4 nm that are dominated, respectively, by lines of FeIX/X (formed in the corona around 1 MK) and by the resonance line of HeII (formed around 80 kK in the lower transition region). Unlike previous EUV imagers, FSI includes a moveable occulting disk that can be inserted in the optical path to reduce the amount of instrumental stray light to a minimum. Results. FSI detects signals at 17.4 nm up to the edge of its field of view (7 R), which is about twice further than was previously possible. Operation at 30.4 nm are for the moment compromised by an as-yet unidentified source of stray light. Comparisons with observations by the LASCO and Metis coronagraphs confirm the presence of morphological similarities and differences between the broadband visible light and EUV emissions, as documented on the basis of prior eclipse and space-based observations. Conclusions. The very-wide-field observations of FSI out to about 3 and 7 R, without and with the occulting disk, respectively, are paving the way for future dedicated instruments

Beyond the disk: EUV coronagraphic observations of the Extreme Ultraviolet Imager on board Solar Orbiter

Most observations of the solar corona beyond 2 Rs consist of broadband visible light imagery from coronagraphs. The associated diagnostics mainly consist of kinematics and derivations of the electron number density. While the measurement of the properties of emission lines can provide crucial additional diagnostics of the coronal plasma (temperatures, velocities, abundances, etc.), these observations are comparatively rare. In visible wavelengths, observations at these heights are limited to total eclipses. In the VUV range, very few additional observations have been achieved since the pioneering results of UVCS. One of the objectives of the Full Sun Imager (FSI) channel of the EUI telescope on board the Solar Orbiter mission has been to provide very wide field-of-view EUV diagnostics of the morphology and dynamics of the solar atmosphere in temperature regimes that are typical of the lower transition region and of the corona. FSI carries out observations in two narrowbands of the EUV spectrum centered on 17.4 nm and 30.4 nm that are dominated, respectively, by lines of Fe IX/X (formed in the corona around 1 MK) and by the resonance line of He II (formed around 80 kK in the lower transition region). Unlike previous EUV imagers, FSI includes a moveable occulting disk that can be inserted in the optical path to reduce the amount of instrumental stray light to a minimum. FSI detects signals at 17.4 nm up to the edge of its FOV (7~Rs), which is about twice further than was previously possible. Comparisons with observations by the LASCO and Metis coronagraphs confirm the presence of morphological similarities and differences between the broadband visible light and EUV emissions, as documented on the basis of prior eclipse and space-based observations. The very-wide-field observations of FSI are paving the way for future dedicated instruments

Extreme-ultraviolet fine structure and variability associated with coronal rain revealed by Solar Orbiter/EUI HRIEUV and SPICE

CONTEXT: Coronal rain is the most dramatic cooling phenomenon of the solar corona. Recent observations in the visible and UV spectrum have shown that coronal rain is a pervasive phenomenon in active regions. Its strong link with coronal heating through the thermal non-equilibrium (TNE) a-thermal instability (TI) scenario makes it an essential diagnostic tool for the heating properties. Another puzzling feature of the solar corona in addition to the heating is its filamentary structure and variability, particularly in the extreme UV (EUV). AIMS: We aim to identify observable features of the TNE-TI scenario underlying coronal rain at small and large spatial scales to understand the role it plays in the solar corona. METHODS: We used EUV datasets at an unprecedented spatial resolution of 240 km from the High Resolution Imager (HRI) in the EUV (HRIEUV) of the Extreme Ultraviolet Imager (EUI) and SPICE on board Solar Orbiter from the perihelion in March and April 2022. RESULTS: EUV absorption features produced by coronal rain are detected at scales as small as 260 km. As the rain falls, heating and compression is produced immediately downstream, leading to a small EUV brightening that accompanies the fall and produces a fireball phenomenon in the solar corona. Just prior to impact, a flash-like EUV brightening downstream of the rain, lasting a few minutes, is observed for the fastest events. For the first time, we detect the atmospheric response to the impact of the rain on the chromosphere, and it consists of upward-propagating rebound shocks and flows that partly reheat the loop. The observed widths of the rain clumps are 500a-±a-200 km. They exhibit a broad velocity distribution of 10a-a-A-150 km sa-1and peak below 50 km sa-1. Coronal strands of similar widths are observed along the same loops. They are co-spatial with cool filamentary structure seen with SPICE, which we interpret as the condensation corona transition region. Prior to the appearance of the rain, sequential loop brightenings are detected in gradually cooler lines from coronal to chromospheric temperatures. This matches the expected cooling. Despite the large rain showers, most cannot be detected in AIA 171 in quadrature, indicating that line-of-sight effects play a major role in the visibility of coronal rain. The AIA 304 and SPICE observations still reveal that only a small fraction of the rain can be captured by HRIEUV. CONCLUSIONS: Coronal rain generates EUV structure and variability over a wide range of scales, from coronal loops to the smallest resolvable scales. This establishes the major role that TNE-TI plays in the observed EUV morphology and variability of the corona

EUV fine structure and variability associated with coronal rain revealed by Solar Orbiter/EUI HRIEUV and SPICE

Coronal rain is the most dramatic cooling phenomenon of the solar corona and an essential diagnostic tool for the coronal heating properties. A puzzling feature of the solar corona, besides the heating, is its EUV filamentary structure and variability. We aim to identify observable features of the TNE-TI scenario underlying coronal rain at small and large spatial scales, to understand the role it plays in the solar corona. We use EUV datasets at unprecedented spatial resolution of ~240 km from EUI/HRIEUV and SPICE of Solar Orbiter from the spring 2022 perihelion. EUV absorption features produced by coronal rain are detected at scales as small as 260 km. As the rain falls, heating and compression is produced immediately downstream, leading to a small EUV brightening accompanying the fall and producing a "fireball" phenomenon. Just prior to impact, a flash-like EUV brightening downstream of the rain, lasting a few minutes is observed for the fastest events. For the first time, we detect the atmospheric response to the rain's impact on the chromosphere and consists of upward propagating rebound shocks and flows partly reheating the loop. The observed widths of the rain clumps are 500 +- 200 km. They exhibit a broad velocity distribution of 10 - 150 km s^-1, peaking below 50 km s^-1. Coronal strands of similar widths are observed along the same loops co-spatial with cool filamentary structure, which we interpret as the CCTR. Matching with the expected cooling, prior to the rain appearance sequential loop brightenings are detected in gradually cooler lines from corona to chromospheric temperatures. Despite the large rain showers, most cannot be detected in AIA 171 in quadrature, indicating that LOS effects play a major role in coronal rain visibility. Still, AIA 304 and SPICE observations reveal that only a small fraction of the rain can be captured by HRIEUV.Comment: Astronomy & Astrophysics; 32 Pages, 24 Main Figures, Appendi