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Future ground-based telescopes, such as the 4-metre class facilities DKIST and EST, will dramatically improve on current capabilities for simultaneous multi-line polarimetric observations in a wide range of wavelength bands, from the near-ultraviolet to the near-infrared. As a result, there will be an increasing demand for fast diagnostic tools, i.e., inversion codes, that can infer the physical properties of the solar atmosphere from the vast amount of data these observatories will produce. The advent of substantially larger apertures, with the concomitant increase in polarimetric sensitivity, will drive an increased interest in observing chromospheric spectral lines. Accordingly, pertinent inversion codes will need to take account of line formation under general non-local thermodynamic equilibrium (NLTE) conditions. Several currently available codes can already accomplish this, but they have a common practical limitation that impairs the speed at which they can invert polarised spectra, namely that they employ numerical evaluation of the so-called response functions to changes in the atmospheric parameters, which makes them less suitable for the analysis of very large data volumes. Here we present DeSIRe (Departure coefficient aided Stokes Inversion based on Response functions), an inversion code that integrates the well-known inversion code SIR with the NLTE radiative transfer solver RH. The DeSIRe runtime benefits from employing analytical response functions computed in local thermodynamic equilibrium (through SIR), modified with fixed departure coefficients to incorporate NLTE effects in chromospheric spectral lines. This publication describes the operating fundamentals of DeSIRe and describes its behaviour, robustness, stability, and speed. The code is ready to be used by the solar community and is being made publicly available. © ESO 2022., C. Quintero Noda was supported by the EST Project Office, funded by the Canary Islands Government (file SD 17/01) under a direct grant awarded to the IAC on ground of public interest. This activity has also received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 739500. C. Quintero Noda also acknowledges the support of the ISAS/JAXA International Top Young Fellowship (ITYF) and the JSPS KAKENHI Grant Number 18K13596. This work was supported by ISAS/JAXA Small Mission-of-Opportunity program for novel solar observations and JSPS KAKENHI Grant Number JP18H05234. This work was supported by the Research Council of Norway through its Centres of Excellence scheme, project number 262622, and through grants of computing time from the Programme for Supercomputing. This work was supported by Fundação para a Cióncia e a Tecnologia (FCT) through the research grants UIDB/04434/2020 and UIDP/04434/2020. This work has also been supported by Spanish Ministry of Economy and Competitiveness through the project ESP-2016-77548-C5-1-R and RTI2018-096886-B-C53. D. Orozco Suárez also acknowledges financial support through the Ramón y Cajal fellowships. CITEUC is funded by National Funds through FCT-Foundation for Science and Technology (project: UID/Multi/00611/2013) and FEDER - European Regional Development Fund through COMPETE 2020 Operational Programme Competitiveness and Internationalization (project: POCI-01-0145-FEDER-006922). NSO is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under cooperative agreement with the National Science Foundation (NSF)., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

Context. At present, an exponential growth in scientific data from current and upcoming solar observatories is expected. Most of the data consist of high spatial and temporal resolution cubes of Stokes profiles taken in both local thermodynamic equilibrium (LTE) and non-LTE spectral lines. The analysis of such solar observations requires complex inversion codes. Hence, it is necessary to develop new tools to boost the speed and efficiency of inversions and reduce computation times and costs. Aims. In this work we discuss the application of convolutional neural networks (CNNs) as a tool to advantageously initialize Stokes profile inversions. Methods. To demonstrate the usefulness of CNNs, we concentrate in this paper on the inversion of LTE Stokes profiles. We use observations taken with the spectropolarimeter on board the Hinode spacecraft as a test bench mark. First, we carefully analyse the data with the SIR inversion code using a given initial atmospheric model. The code provides a set of atmospheric models that reproduce the observations well. These models are then used to train a CNN. Afterwards, the same data are again inverted with SIR but using the trained CNN to provide the initial guess atmospheric models for SIR. Results. The CNNs allow us to significantly reduce the number of inversion cycles when used to compute initial guess model atmospheres ('assisted inversions'), therefore decreasing the computational time for LTE inversions by a factor of two to four. CNNs alone are much faster than assisted inversions, but the latter are more robust and accurate. CNNs also help to automatically cluster pixels with similar physical properties, allowing the association with different solar features on the solar surface, which is useful when inverting huge datasets where completely different regimes are present. The advantages and limitations of machine learning techniques for estimating optimum initial atmospheric models for spectral line inversions are discussed. Finally, we describe a python wrapper for the SIR and DeSIRe codes that allows for the easy setup of parallel inversions. The tool implements the assisted inversion method described in this paper. The parallel wrapper can also be used to synthesize Stokes profiles with the RH code. Conclusions. The assisted inversions can speed up the inversion process, but the efficiency and accuracy of the inversion results depend strongly on the solar scene and the data used for the CNN training. This method (assisted inversions) will not obviate the need for analysing individual events with the utmost care but will provide solar scientists with a much better opportunity to sample large amounts of inverted data, which will undoubtedly broaden the physical discovery space. © ESO 2021., All the network training and inference has been done using Keras with Tensorflow back-end. All the plots were done using matplotlib python package. This work has been supported by the Spanish Ministry of Economy and Competitiveness through projects ESP-201677548-C5-1-R and by Spanish Science Ministry "Centro de Excelencia Severo Ochoa" Program under grant SEV-2017-0709 and project RTI2018-096886-BC51. D. O. S. also acknowledges financial support through the Ramon y Cajal fellowship. CQN acknowledges the Research Council of Norway through its Centres of Excellence scheme, project number 262622. This work was supported by Fundacao para a Cioncia e a Tecnologia (FCT) through the research grants [UID/FIS/04434/2019,] UIDB/04434/2020 and UIDP/04434/2020.

This is an open access article, original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI., The magnetic field plays an essential role in the initiation and evolution of different solar phenomena in the corona. The structure and evolution of the 3D coronal magnetic field are still not very well known. A way to ascertain the 3D structure of the coronal magnetic field is by performing magnetic field extrapolations from the photosphere to the corona. In previous work, it was shown that by prescribing the 3D-reconstructed loops' geometry, the magnetic field extrapolation produces a solution with a better agreement between the modeled field and the reconstructed loops. This also improves the quality of the field extrapolation. Stereoscopy, which uses at least two view directions, is the traditional method for performing 3D coronal loop reconstruction. When only one vantage point of the coronal loops is available, other 3D reconstruction methods must be applied. Within this work, we present a method for the 3D loop reconstruction based on machine learning. Our purpose for developing this method is to use as many observed coronal loops in space and time for the modeling of the coronal magnetic field. Our results show that we can build machine-learning models that can retrieve 3D loops based only on their projection information. Ultimately, the neural network model will be able to use only 2D information of the coronal loops, identified, traced, and extracted from the extreme-ultraviolet images, for the calculation of their 3D geometry. © 2021. The Author(s). Published by the American Astronomical Society., Data are courtesy of NASA/SDO and the HMI science teams. I.C. acknowledges DFG-grant WI 3211/5-1. The HMI data are provided courtesy of NASA/SDO and the HMI science team. R.G. acknowledges financial support by the Portuguese Government through the Foundation for Science and Technology-FCT FEDER-European Regional Development Fund through COMPETE 2020-Operational Programme Competitiveness and Internationalization., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

The present work aims to validate the positions of solar filaments published in the Annals of Coimbra University Astronomical Observatory, currently the Geophysical and Astronomical Observatory of the University of Coimbra, corresponding to years 1929 to 1941. The published Stonyhurst positions were obtained by an original method devised in the early 20th century that used a spherical calculator instrument, a wood-made model of the Sun. We used the digital images of the original spectroheliograms to measure the positions of the filaments, and heliographic coordinates were determined with the routines implemented in the Python package Sunpy. The correlation coefficients between both sets of coordinates are positive and highly significant. The results validate the method used at the Coimbra observatory and the published data. We conclude that the Coimbra solar filament catalogues are reliable and can therefore be considered for future solar activity studies. © 2021, The Author(s), under exclusive licence to Springer Nature B.V., This study was partially supported by the Portuguese Government through the Foundation for Science and Technology-FCT, CITEUC Funds (project: ID/Multi/00611/2013), and FEDER-European Regional Development Fund through COMPETE 2020-Operational Programme Competitiveness and Internationalization (project: POCI-01-0145-FEDER-006922). Ana Lourencos work was supported by the project ReNATURE-Valuation of Endogenous Natural Resources in the Central Region (CENTRO-25 01-0145-FEDER-000007-BPD16)., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

Future ground-based telescopes will expand our capabilities for simultaneous multi-line polarimetric observations in a wide range of wavelengths, from the near-ultraviolet to the near-infrared. This creates a strong demand to compare candidate spectral lines to establish a guideline of the lines that are most appropriate for each observation target. We focused in this first work on Zeeman-sensitive photospheric lines in the visible and infrared. We first examined their polarisation signals and response functions using a 1D semi-empirical atmosphere. Then we studied the spatial distribution of the line core intensity and linear and circular polarisation signals using a realistic 3D numerical simulation. We ran inversions of synthetic profiles, and we compared the heights at which we obtain a high correlation between the input and the inferred atmosphere. We also used this opportunity to revisit the atomic information we have on these lines and computed the broadening cross-sections due to collisions with neutral hydrogen atoms for all the studied spectral lines. The results reveal that four spectral lines stand out from the rest for quiet-Sun and network conditions: Fe» I 5250.2, 6302, 8468, and 15 648 A. The first three form higher in the atmosphere, and the last line is mainly sensitive to the atmospheric parameters at the bottom of the photosphere. However, as they reach different heights, we strongly recommend using at least one of the first three candidates together with the Fe» I 15 648 A line to optimise our capabilities for inferring the thermal and magnetic properties of the lower atmosphere. © ESO 2021., C. Quintero Noda was supported by the EST Project Office, funded by the Canary Islands Government (file SD 17/01) under a direct grant awarded to the IAC on ground of public interest, and this activity has also received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 739500. This work was supported by the Research Council of Norway through its Centres of Excellence scheme, project number 262622, and through grants of computing time from the Programme for Supercomputing. P. S. Barklem received financial support from the Swedish Research Council. The Centre for Earth and Space Research of University of Coimbra is funded by National Funds through FCT – Foundation for Science and Technology (project: UID/MULTI/00611/2019) and FEDER – European Regional Development Fund through COMPETE 2020 – Operational Programme Competitiveness and Internationalization (project: POCI-01-0145-FEDER-006922). This work has been funded by the Spanish Ministry of Science and Innovation through project ESP-2016-77548-C5-1-R, including a percentage from FEDER funds, and through the Centro de Excelencia Severo Ochoa grant SEV-2017-0709 awarded to the Instituto de Astrofísica de Andalucía in the period 2018-2022. D. Orozco Suárez also acknowledges financial support through the Ramón y Cajal fellowships. This work was supported by the ISAS/JAXA Small Mission-of-Opportunity program for novel solar observations and the JSPS KAKENHI Grant Number JP18H05234.

Context. Interpreting spectropolarimetric observations of the solar atmosphere takes much longer than the acquiring the data. The most important reason for this is that the model fitting, or "inversion", used to infer physical quantities from the observations is extremely slow, because the underlying models are numerically demanding. Aims. We aim to improve the speed of the inference by using a neural network that relates input polarized spectra to the output physical parameters. Methods. We first select a subset of the data to be interpreted and infer physical quantities from corresponding spectra using a standard minimization-based inversion code. Taking these results as reliable and representative of the whole data set, we train a convolutional neural network to connect the input polarized spectra to the output physical parameters (nodes, in context of spectropolarimetric inversion). We then apply the neural network to the various other data, previously unseen to the network. As a check, we apply the referent inversion code to the unseen data and compare the fit quality and the maps of the inferred parameters between the two inversions. Results. The physical parameters inferred by the neural network show excellent agreement with the results from the inversion, and are obtained in a factor of 105 less time. Additionally, substituting the results of the neural network back in the forward model, shows excellent agreement between inferred and original spectra. Conclusions. The method we present here is very simple for implementation and extremely fast. It only requires a training data set, which can be obtained by inverting a representative subset of the observed data. Applying these (and similar) machine learning techniques will yield orders of magnitude acceleration in the routine interpretation of spectropolarimetric data. © ESO 2020., We thank Andres Asensio Ramos, Christopher Osborne, Carlos Jose Diaz Baso, Mark Rast and Mark Cheung on discussions and suggestions that led to this investigation. Comments by Mom.cil Molnar, Shah Mohammad Badaouin and David Orozco Suarez greatly improved the manuscript. We also thank Tino Riethmuller and Matthias Rempel for providing us with the MURAM simulations. We thank the anonymous referee for their comments that significantly improved the manuscript. All the network training and inference has been done using Keras with Tensorflow package. All the plots were done using matplotlib python package. This work has been supported by the Spanish Ministry of Economy and Competitiveness through projects ESP-201677548-C5-1-R and by Spanish Science Ministry "Centro de Excelencia Severo Ochoa" Program under grant SEV-2017-0709 and project RTI2018-096886B-C51.

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited., Context. Studies of long-term solar activity and variability require knowledge of the past evolution of the solar surface magnetism. The archives of full-disc Ca II K observations that have been performed more or less regularly at various sites since 1892 can serve as an important source of such information. Aims. We derive the plage area evolution over the last 12 solar cycles by employing data from all Ca II K archives that are publicly available in digital form, including several as-yet-unexplored Ca II K archives. Methods. We analysed more than 290 000 full-disc Ca II K observations from 43 datasets spanning the period between 1892-2019. All images were consistently processed with an automatic procedure that performs the photometric calibration (if needed) and the limb-darkening compensation. The processing also accounts for artefacts affecting many of the images, including some very specific artefacts, such as bright arcs found in Kyoto and Yerkes data. Our employed methods have previously been tested and evaluated on synthetic data and found to be more accurate than other methods used in the literature to treat a subset of the data analysed here. Results. We produced a plage area time-series from each analysed dataset. We found that the differences between the plage areas derived from individual archives are mainly due to the differences in the central wavelength and the bandpass used to acquire the data at the various sites. We empirically cross-calibrated and combined the results obtained from each dataset to produce a composite series of plage areas. The 'backbone' approach was used to bridge the series together. We have also shown that the selection of the backbone series has little effect on the final composite of the plage area. We quantified the uncertainty of determining the plage areas with our processing due to shifts in the central wavelength and found it to be less than 0.01 in fraction of the solar disc for the average conditions found on historical data. We also found the variable seeing conditions during the observations to slightly increase the plage areas during the activity maxima. Conclusions. We provide the most complete so far time series of plage areas based on corrected and calibrated historical and modern Ca II K images. Consistent plage areas are now available on 88% of all days from 1892 onwards and on 98% from 1907 onwards. © T. Chatzistergos et al. 2020., The authors thank the observers at the Arcetri, Baikal, Big Bear, Brussels, Calern, Catania, Coimbra, Kanzelhohe, Kharkiv, Kenwood, Kislovodsk, Kodaikanal, Kyoto, Manila, Mauna Loa, McMathHulbert, Mees, Meudon, Mitaka, European Union's Horizon 2020 research and innovation program Mt Wilson, Pic du Midi, Rome, Sacramento Peak, San Fernando, Schauinsland, Teide, Upice, Valasske Mezi.ri.ci, Wendelstein, and Yerkes sites for all their work in carrying out the observing programs. We thank Isabelle Buale for all her e fforts to digitise the Meudon archive. We thank Je ff Kuhn and Cindy Maui for locating and sharing with us the Mees Ca II K data. We thank Satoru Ueno and Reizaburo Kitai for providing the Kyoto observations. We thank the anonymous referee for the constructive comments that improved this manuscript. We thank Ester Antonucci, Alexi Baker, Angie Cookson, Martina Exnerova, Bernhard Fleck, Detlef Groote, Laurent Koechlin, Libor Lenza, Mustapha Meftah, Werner Potzi, Roger Ulrich, John Varsik, and Hubertus Wohl for providing information about various Ca II K data. This work was supported by FP7 SOLID, and by the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea. This research has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 824135 (SOLARNET). The Coimbra researchers thank the project ReNATURE (CENTRO-01-0145-FEDER-000007-BPD16). We acknowledge the "Observateurs associes" for their commitment to image acquisition and processing; IRAP for the instrumental and database management; Universite de Toulouse, CNRS, and Fiducial for the funding. We acknowledge Paris Observatory for the use of spectroheliograms and the Royal Observatory of Belgium, Brussels for USET data. The Kanzelhohe Ca II K data were provided by the Kanzelhohe Observatory, University of Graz, Austria. ChroTel is operated by the Kiepenheuer-Institute for Solar Physics in Freiburg, Germany, at the Spanish Observatorio del Teide, Tenerife, Canary Islands. The ChroTel filtergraph has been developed by the Kiepenheuer-Institute in cooperation with the High Altitude Observatory in Boulder, CO, USA. We acknowledge www.observethesun.com and www.solarstation.ru for storing the Kislovodsk data. This work used data provided by the MEDOC data and operations centre (CNES/CNRS/Univ. Paris-Sud). The Kenwood observations used here are from lantern slides in the Division of History of Science and Technology at Yale University's Peabody Museum of Natural History (objects YPM HST.340744, HST.340745, HST.340747, and HST.340752). The Yerkes observations are courtesy of the University of Chicago Photographic Archive, Special Collections Research Center, University of Chicago Library. This research has made use of NASA's Astrophysics Data System.

Context. Penumbral microjets (PMJs) is the name given to elongated jet-like brightenings observed in the chromosphere above sunspot penumbrae. They are transient events that last from a few seconds to several minutes, and their origin is presumed to be related to magnetic reconnection processes. Previous studies have mainly focused on their morphological and spectral characteristics, and more recently on their spectropolarimetric signals during the maximum brightness stage. Studies addressing the temporal evolution of PMJs have also been carried out, but they are based on spatial and spectral time variations only. Aims. Here we investigate, for the first time, the temporal evolution of the polarization signals produced by short-lived PMJs (lifetimes < 2 min) to infer how the magnetic field vector evolves in the upper photosphere and mid-chromosphere. Methods. We use fast-cadence spectropolarimetric observations of the Ca II 854.2 nm line taken with the CRisp Imaging Spectropolarimeter at the Swedish 1 m Solar Telescope. The weak-field approximation (WFA) is used to estimate the strength and inclination of the magnetic field vector. By separating the Ca II 854.2 nm line into two different wavelength domains to account for the chromospheric origin of the line core and the photospheric contribution to the wings, we infer the height variation of the magnetic field vector. Results. The WFA reveals larger magnetic field changes in the upper photosphere than in the chromosphere during the PMJ maximum brightness stage. In the photosphere, the magnetic field inclination and strength undergo a transient increase for most PMJs, but in 25% of the cases the field strength decreases during the brightening. In the chromosphere, the magnetic field tends to be slightly stronger during the PMJs. Conclusions. The propagation of compressive perturbation fronts followed by a rarefaction phase in the aftershock region may explain the observed behavior of the magnetic field vector. The fact that such behavior varies among the analyzed PMJs could be a consequence of the limited temporal resolution of the observations and the fast-evolving nature of the PMJs. © 2020 ESO., This work has been funded by the Spanish Ministry of Science and Innovation through project RTI2018-096886-B-C51, including a percentage from FEDER funds, and through the Centro de Excelencia Severo Ochoa grant SEV-2017-0709 awarded to the Instituto de Astrofísica de Andalucía in the period 2018–2022. The Swedish 1 m Solar Telescope is operated on the island of La Palma by the Institute for Solar Physics of Stockholm University in the Spanish Observatory del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. The Institute for Solar Physics is supported by a grant for research infrastructures of national importance from the Swedish Research Council (registration number 2017-00625).

Scaling relations are very useful tools for estimating unknown stellar quantities. Within this framework, eclipsing binaries are ideal for this goal because their mass and radius are known with a very good level of accuracy, leading to improved constraints on the models. We aim to provide empirical relations for the mass and radius as function of luminosity, metallicity, and age. We investigate, in particular, the impact of metallicity and age on those relations. We used a multi-dimensional fit approach based on the data from DEBCat, an updated catalogue of eclipsing binary observations such as mass, radius, luminosity, effective temperature, gravity, and metallicity. We used the {PARAM web interface for the Bayesian estimation of stellar parameters, along with} the stellar evolutionary code MESA to estimate the binary age, assuming a coeval hypothesis for both members. We derived the mass and radius-luminosity-metallicity-age relations using 56 stars, {with metallicity and mass in the range -0.34, Comment: 8 pages, 9 figures, Accepted for publication on Astronomy and Astrophysics

S. Jafarzadeh et. al., ©2017 The American Astronomical Society. All rights reserved. We present observations of transverse oscillations in slender Ca ii H fibrils (SCFs) in the lower solar chromosphere. We use a 1 hr long time series of high- (spatial and temporal-) resolution seeing-free observations in a 1.1 Å wide passband covering the line core of Ca ii H 3969 Å from the second flight of the Sunrise balloon-borne solar observatory. The entire field of view, spanning the polarity inversion line of an active region close to the solar disk center, is covered with bright, thin, and very dynamic fine structures. Our analysis reveals the prevalence of transverse waves in SCFs with median amplitudes and periods on the order of 2.4 ± 0.8 km s−1 and 83 ± 29 s, respectively (with standard deviations given as uncertainties). We find that the transverse waves often propagate along (parts of) the SCFs with median phase speeds of 9 ± 14 km s−1. While the propagation is only in one direction along the axis in some of the SCFs, propagating waves in both directions, as well as standing waves are also observed. The transverse oscillations are likely Alfvénic and are thought to be representative of magnetohydrodynamic kink waves. The wave propagation suggests that the rapid high-frequency transverse waves, often produced in the lower photosphere, can penetrate into the chromosphere with an estimated energy flux of ≈15 kW m−2. Characteristics of these waves differ from those reported for other fibrillar structures, which, however, were observed mainly in the upper solar chromosphere., The German contribution to Sunrise and its reflight was funded by the Max Planck Foundation, the Strategic Innovations Fund of the President of the Max Planck Society (MPG), DLR, and private donations by supporting members of the Max Planck Society, which is gratefully acknowledged. The Spanish contribution was funded by the Ministerio de Economía y Competitividad under Projects ESP2013-47349-C6 and ESP2014-56169-C6, partially using European FEDER funds. The HAO contribution was partly funded through NASA grant number NNX13AE95G. This work was partly supported by the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea.

The stellar mass-luminosity relation (MLR) is one of the most famous empirical "laws", discovered in the beginning of the 20th century. MLR is still used to estimate stellar masses for nearby stars, particularly for those that are not binary systems, hence the mass cannot be derived directly from the observations. It's well known that the MLR has a statistical dispersion which cannot be explained exclusively due to the observational errors in luminosity (or mass). It is an intrinsic dispersion caused by the differences in age and chemical composition from star to star. In this work we discuss the impact of age and metallicity on the MLR. Using the recent data on mass, luminosity, metallicity, and age for 26 FGK stars (all members of binary systems, with observational mass-errors, 7 pages, 4 figures, 1 table, accepted in Astrophysics and Space Science

R. Gafeira et. al., ©2017 The American Astronomical Society. All rights reserved. We report the detection of oscillations in slender Ca ii H fibrils (SCFs) from high-resolution observations acquired with the Sunrise balloon-borne solar observatory. The SCFs show obvious oscillations in their intensity, but also their width. The oscillatory behaviors are investigated at several positions along the axes of the SCFs. A large majority of fibrils show signs of oscillations in intensity. Their periods and phase speeds are analyzed using a wavelet analysis. The width and intensity perturbations have overlapping distributions of the wave period. The obtained distributions have median values of the period of 32 ± 17 s and 36 ± 25 s, respectively. We find that the fluctuations of both parameters propagate in the SCFs with speeds of ${11}_{-11}^{+49}$ km s−1 and ${15}_{-15}^{+34}$ km s−1, respectively. Furthermore, the width and intensity oscillations have a strong tendency to be either in anti-phase or, to a smaller extent, in phase. This suggests that the oscillations of both parameters are caused by the same wave mode and that the waves are likely propagating. Taking all the evidence together, the most likely wave mode to explain all measurements and criteria is the fast sausage mode., The German contribution to Sunrise and its reflight was funded by the Max Planck Foundation, the Strategic Innovations Fund of the President of the Max Planck Society (MPG), DLR, and private donations by supporting members of the Max Planck Society, which are gratefully acknowledged. The Spanish contribution was funded by the Ministerio de Economía y Competitividad under Projects ESP2013-47349-C6 and ESP2014-56169-C6, partially using European FEDER funds. The HAO contribution was partly funded through NASA grant No. NNX13AE95G. This work was partly supported by the BK21 plus program through the National Research Foundation (NRF) funded by the Ministry of Education of Korea. S.J. receives support from the Research Council of Norway.

The increased amount of information provided by ongoing missions such as the Solar Dynamics Observatory (SDO) represents a great challenge for the understanding of basic questions such as the internal structure of sunspots and how they evolve with time. Here, we contribute with the exploitation of new data, to provide a better understanding of the separate growth and decay of sunspots, umbra and penumbra. Using fuzzy sets to compute separately the areas of sunspot umbra and penumbra, the growth and decay rates for active regions NOAA 11117, NOAA 11428, NOAA 11429, and NOAA 11430 are computed, from the analysis of intensitygrams obtained by the Helioseismic and Magnetic Imager onboard SDO. A simplified numerical model is proposed for the decay phase, whereby an empirical irrotational and uniformly convergent horizontal velocity field interacting with an axially symmetric and height invariant magnetic field, reproduces the large-scale features of the much more complex convection observed inside sunspots., 14 pages, 6 figures, accepted on Solar Physics

Ever since the very first photometric studies of Centaurs and Kuiper Belt Objects (KBOs) their visible color distribution has been controversial. That controversy gave rise to a prolific debate on the origin of the surface colors of these distant icy objects of the Solar System. Two different views attempt to interpret and explain the large variability of colors, hence surface composition. Are the colors mainly primordial and directly related to the formation region, or are they the result of surface evolution processes? To date, no mechanism has been found that successfully explains why Centaurs, which are escapees from the Kuiper Belt, exhibit two distinct color groups, whereas KBOs do not. In this letter, we readdress this issue using a carefully compiled set of B-R colors and H({\alpha}) magnitudes (as proxy for size) for 253 objects, including data for 10 new small objects. We find that the bimodal behavior seen among Centaurs is a size related phenomenon, common to both Centaurs and small KBOs, i.e. independent of dynamical classification. Further, we find that large KBOs also exhibit a bimodal behavior of surface colors, albeit distinct from the small objects and strongly dependent on the `Haumea collisional family' objects. When plotted in B-R, H({\alpha}) space, the colors of Centaurs and KBOs display a peculiar N shape., Comment: To appear in Astronomy & Astrophysics. 12 pages (including 6 pages of appendix), 2 figures, 3 tables