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Context: Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as best-fit solutions to these problems in specific situations, but their effectiveness and limitations are rarely discussed. Aims. We rigorously test the different implementations of solving the conductivity flux, in the massively-parallel magnetohydrodynamics code, Bifrost, with the aim of specifying the best scenarios for the use of each method. Methods: We compare the differences and limitations of explicit versus implicit methods, and analyse the convergence of a hyperbolic approximation. Among the tests, we use a newly derived 1st-order self-similar approximation to compare the efficacy of each method analytically in a 1D pure-thermal test scenario. Results: We find that although the hyperbolic approximation proves the most accurate and the fastest to compute in long-running simulations, there is no optimal method to calculate the mid-term conductivity with both accuracy and efficiency. We also find that the solution of this approximation is sensitive to the initial conditions, and can lead to faster convergence if used correctly. Hyper-diffusivity is particularly useful in aiding the methods to perform optimally. Conclusions: We discuss recommendations for the use of each method within more complex simulations, whilst acknowledging the areas of opportunity for new methods to be developed.

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic capabilities for studying the Sun, providing complementary insights through high spatial and temporal resolution at millimeter wavelengths. ALMA acts as a linear thermometer for atmospheric gas, aiding in understanding the solar atmosphere's structure, dynamics, and energy balance. Given the Sun's complex emission patterns and rapid evolution, high-cadence imaging is essential for solar observations. Snapshot imaging is required, though it limits available visibility data, making full exploitation of ALMA's capabilities non-trivial. Challenges in processing solar ALMA data highlight the need for revising and enhancing the solar observing mode. The ALMA development study High-Cadence Imaging of the Sun demonstrated the potential benefits of high cadence observations through a forward modelling approach. The resulting report provides initial recommendations for improved post-processing solar ALMA data and explores increasing the observing cadence to sub-second intervals to improve image reliability., Comment: ALMA Memo 628 summarising the results of the ESO-funded ALMA development study "High-cadence Imaging of the Sun", concluded in 2023 (74 pages, 53 figures)

The Ha line, one of the most studied chromospheric diagnostics, is a tracer for magnetic field structures, while its line core intensity provides an estimate of the mass density. The brightness temperatures from Atacama Large Millimetre-submm Array (ALMA) observations provide a complementary view of the activity and the thermal structure of stellar atmospheres. These two diagnostics together can provide insights into the physical properties of stellar atmospheres. In this paper, we present a comparative study between synthetic continuum brightness temperature maps for mm wavelengths (0.3 mm to 8.5 mm) and the width of the Ha 6565{\AA} line. The 3D radiative transfer codes Multi3D and Advanced Radiative Transfer (ART) are used to calculate synthetic spectra for the Ha line and the mm continua respectively, from an enhanced network atmosphere model with non-equilibrium hydrogen ionisation generated with the state-of-the-art 3D rMHD code Bifrost. We use Gaussian Point Spread Function (PSF) for simulating the effect of ALMA's limited spatial resolution and calculate the Ha vs. mm continuum correlations and slopes of scatter plots for the original and degraded resolution of the whole box, quiet sun and enhanced network patches separately. The Ha linewidth and mm brightness temperatures are highly correlated and the correlation is highest at a wavelength 0.8 mm i.e. ALMA Band 7. The correlation increases with decreased resolution. On the other hand, the slopes decrease with increasing wavelength. The degradation of resolution does not have a significant impact on the calculated slopes. With decreasing spatial resolution the standard deviations of the observables, Ha linewidth and brightness temperatures decrease and the correlations between them increase, but the slopes do not change significantly. Hence, these relations may prove useful to calibrate the mm continuum maps observed with ALMA., Comment: 20 pages, 26 figures

We used solar observations of a plage/enhanced network with the Atacama Large Millimeter/sub-millimeter Array (ALMA) in Band 3 and Band 6 together with synthetic continuum maps from numerical simulations with Bifrost at the same bands to carry out a detailed study of bright small-scale magnetic features. To this end, we have used an algorithm to automatically identify and trace the features within the field of view (FoV) of the observations and the simulation. We found 193 and 293 features in the Bands 3 and 6 observations, respectively. In the degraded simulation, the total number of features were 24 for Band 3 and 204 for Band 6. In the original simulation, the total number of features were 36 for Band 3 and 392 for Band 6. Based on the simulation, we confirm the magnetic nature of the features which exhibit an oscillatory behaviour in temperature, size and horizontal velocity. The average oscillation periods were of 30-99\,s for temperature, 37-92\,s for size and 37-78\,s for horizontal velocity. There are indications for the possible presence of transverse (kink) waves with average amplitude velocities of 2.1-5.0\,km\,s$^{-1}$. An anti-phase behaviour between temperature and size oscillations suggest the presence of compressible fast-sausage Magnetohydrodynamics (MHD) modes. Finally, we have estimated the flux of energy of the fast-sausage waves at the chromospheric heights sampled by ALMA as 453-1838\,W\,m$^{-2}$ for Band 3 and 3640-5485\,W\,m$^{-2}$ for Band 6. The decrease of wave energy-flux with height (from Band 6 to Band 3) could possibly suggest energy dissipation at chromospheric heights, thus wave heating, with the assumptions that the identified small-scale waves are typical at each band and they propagate upward through the chromosphere., Comment: 15 pages, 11 figures. Accepted for publication in Astronomy and Astrophysics. Abstract has been shorten to fulfil Arxiv requirements

Solar modelling has long been split into ''internal'' and ''surface'' modelling, because of the lack of tools to connect the very different scales in space and time, as well as the widely different environments and dominating physical effects involved. Significant efforts have recently been put into resolving this disconnect. We address the outstanding bottlenecks in connecting internal convection zone and dynamo simulations to the surface of the Sun, and conduct a proof-of-concept high resolution global simulation of the convection zone of the Sun, using the task-based DISPATCH code framework. We present a new `volleyball' mesh decomposition, which has Cartesian patches tessellated on a sphere with no singularities. We use our new entropy based HLLS approximate Riemann solver to model magneto-hydrodynamics in a global simulation, ranging between 0.655 -- 0.995 R$_\odot$, with an initial ambient magnetic field set to 0.1 Gauss. The simulations develop convective motions with complex, turbulent structures. Small-scale dynamo action twists the ambient magnetic field and locally amplifies magnetic field magnitudes by more than two orders of magnitude within the initial run-time., Comment: 12 pages, 9 figures, submitted to A&A. Movies available online

The ponderomotive force is suggested to be the main mechanism to produce the so-called first ionization potential (FIP) effect - the enrichment of low FIP elements observed in the outer solar atmosphere. It is well known that the ionization of these elements occurs within the chromosphere. Therefore, this phenomenon is intimately tied to the plasma state in the chromosphere and the corona. In addition, the chromosphere is a highly complex region with a large variation in the ion-neutral collision frequencies, and hydrogen and helium ionization is largely out of equilibrium. For this study, we combine IRIS observations, a single fluid 2.5D radiative magnetohydrodynamics (MHD) model of the solar atmosphere, including ion-neutral interaction effects and non-equilibrium (NEQ) ionization effects, and a novel multi-fluid multi-species (MFMS) numerical code (Ebysus). Nonthermal velocities of Si IV measured from IRIS spectra can provide an upper limit for the strength of any high-frequency Alfven waves. With the single-fluid model, we investigate the possible impact of NEQ ionization within the region where the FIP may occur and the plasma properties in those regions. These models suggest that regions with strong enhanced network and type II spicules are associated with the presence of large ponderomotive forces. From the plasma properties from the single-fluid MHD model and IRIS observations, we initialize our multi-fluid models to investigate the multi-fluid effects on the ponderomotive force associated with Alfven waves. Our multi-fluid analysis reveals that collisions and NEQ ionization effects dramatically impact the behavior of the ponderomotive force in the chromosphere, and existing theories may need to be revisited., Comment: Submitted to ApJ, 23 pages, 15 figures

The intensity of radiation at millimeter wavelengths from the solar atmosphere is closely related to the plasma temperature and the height of formation of the radiation is wavelength dependent. From that follows that the slope of the brightness temperature (T$_\mathrm{b}$) continuum, samples the local gradient of the gas temperature of the sampled layers in the solar atmosphere. We use solar observations from the Atacama Large Millimeter/sub-millimeter Array (ALMA) and perform estimations and prediction of the slope of the T$_\mathrm{b}$ continuum based on differences between synthetic observables at different ALMA receiver sub-bands (2.8-3.2 mm; band 3) and (1.20-1.31 mm; band 6) from a state-of-the-art 3D rMHD simulation. The slope of the continuum is coupled to the small-scale dynamics and a positive sign indicates an increase in temperature with height while a negative sign implies a decrease. Network patches are dominated by large positive slopes while quiet Sun region show a mixture of positive and negative slopes, much in connection to propagating shock waves and the temporal evolution of the slopes can therefore be used to identify shocks. The observability of the slope of brightness temperatures is estimated for angular resolutions corresponding to ALMA observations. The simulations also show that the radiation of both bands 3 and 6 can origin from several components at different heights simultaneously and that the delay of shock signatures between two wavelengths does not necessarily reflect the propagation speed, but could be caused by different rate of change of opacity of above-lying layers. The slope of the T$_\mathrm{b}$ continuum sampled at different ALMA receiver sub-bands serves as indicator of the slope of the local plasma temperature at the sampled heights in the atmosphere, which offers new diagnostic possibilities to measure the underlying physical properties., Comment: 14 pages, 12 figures with appendix of 2 pages and 1 figure. Accepted for publication in A&A

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic possibilities that complement other commonly used diagnostics for the study of our Sun. In particular, ALMA's ability to serve as an essentially linear thermometer of the chromospheric gas at unprecedented spatial resolution at millimetre wavelengths and future polarisation measurements have great diagnostic potential. Solar ALMA observations are therefore expected to contribute significantly to answering long-standing questions about the structure, dynamics and energy balance of the outer layers of the solar atmosphere. In this regard, current and future ALMA data are also important for constraining and further developing numerical models of the solar atmosphere, which in turn are often vital for the interpretation of observations. The latter is particularly important given the Sun's highly intermittent and dynamic nature that involves a plethora of processes occurring over extended ranges in spatial and temporal scales. Realistic forward modelling of the Sun therefore requires time-dependent three-dimensional radiation magnetohydrodynamics that account for non-equilibrium effects and, typically as a separate step, detailed radiative transfer calculations, resulting in synthetic observables that can be compared to observations. Such artificial observations sometimes also account for instrumental and seeing effects, which, in addition to aiding the interpretation of observations, provide instructive tools for designing and optimising ALMA's solar observing modes. In the other direction, ALMA data in combination with other simultaneous observations enables the reconstruction of the solar atmospheric structure via data inversion techniques. This article highlights central aspects of the impact of ALMA for numerical modelling for the Sun, their potential and challenges, together with selected examples., Comment: 32 pages, 7 figures. Accepted for publication in Frontiers in Astronomy and Space Sciences (Stellar and Solar Physics)

The Atacama Large Millimeter/sub-millimeter Array (ALMA) has provided us with an excellent diagnostic tool for studies of the dynamics of the Solar chromosphere, albeit through a single receiver band at one time presently. Each ALMA band consists of four sub-bands that are comprised of several spectral channels. To date, however, the spectral domain has been neglected in favour of ensuring optimal imaging, so that time-series observations have been mostly limited to full-band data products, thereby limiting studies to a single chromospheric layer. Here, we report the first observations of a dynamical event (i.e. wave propagation) for which the ALMA Band 3 data (centred at 3\,mm; 100\,GHz) is split into a lower and an upper sideband. In principle, this approach is aimed at mapping slightly different layers in the Solar atmosphere. The side-band data were reduced together with the Solar ALMA Pipeline (SoAP), resulting in time series of brightness-temperature maps for each side-band. Through a phase analysis of a magnetically quiet region, where purely acoustic waves are expected to dominate, the average height difference between the two side-bands is estimated as $73\pm16$~km. Furthermore, we examined the propagation of transverse waves in small-scale bright structures by means of wavelet phase analysis between oscillations at the two atmospheric heights. We find 6\% of the waves to be standing, while 54\% and 46\% of the remaining waves are propagating upwards and downwards, respectively, with absolute propagating speeds on the order of $\approx96$~km/s, resulting in a mean energy flux of $3800$\,W/m$^2$., Comment: 5 pages, 3 figures, Accepted for publication in Astronomy and Astrophysics Letters

Current models of the solar wind must approximate (or ignore) the small-scale dynamics within the solar atmosphere, however these are likely important in shaping the emerging wave-turbulence spectrum and ultimately heating/accelerating the coronal plasma. The Bifrost code produces realistic simulations of the solar atmosphere that facilitate the analysis of spatial and temporal scales which are currently at, or beyond, the limit of modern solar telescopes. For this study, the Bifrost simulation is configured to represent the solar atmosphere in a coronal hole region, from which the fast solar wind emerges. The simulation extends from the upper-convection zone (2.5 Mm below the photosphere) to the low-corona (14.5 Mm above the photosphere), with a horizontal extent of 24 Mm x 24 Mm. The twisting of the coronal magnetic field by photospheric flows, efficiently injects energy into the low-corona. Poynting fluxes of up to $2-4$ kWm$^{-2}$ are commonly observed inside twisted magnetic structures with diameters in the low-corona of 1 - 5 Mm. Torsional Alfv\'en waves are favourably transmitted along these structures, and will subsequently escape into the solar wind. However, reflections of these waves from the upper boundary condition make it difficult to unambiguously quantify the emerging Alfv\'en wave-energy flux. This study represents a first step in quantifying the conditions at the base of the solar wind using Bifrost simulations. It is shown that the coronal magnetic field is readily braided and twisted by photospheric flows. Temperature and density contrasts form between regions with active stirring motions and those without. Stronger whirlpool-like flows in the convection, concurrent with magnetic concentrations, launch torsional Alfv\'en waves up through the magnetic funnel network, which are expected to enhance the turbulent generation of magnetic switchbacks in the solar wind., Comment: Accepted to A&A. 22 Pages + Appendix. 20 Figures + 5 Appendix Figures

We present a statistical analysis of power distribution of oscillations in a plage region in active region NOAA AR12651, observed jointly with ALMA (Atacama Large Millimeter/Submillimeter Array), IRIS (Interface Region Imaging Spectrograph), and SDO (Solar Dynamics Observatory). We employ coordinated ALMA Band-6 (1.25 mm) brightness temperature maps, IRIS Slit-Jaw Images in 2796 {\AA} passband, and observations in six passbands (1600 {\AA}, 304 {\AA}, 131 {\AA}, 171 {\AA}, 193 {\AA} and 211 {\AA}) of AIA (Atmospheric Imaging Assembly) onboard SDO. We perform Lomb-Scargle transforms to study the distribution of oscillation power over the observed region by means of dominant period maps and power maps. We study spatial association of oscillations through the atmosphere mapped by the different passbands, with focus on the correlation of power distribution of ALMA oscillations with others. We do not observe any significant association of ALMA oscillations with IRIS and AIA oscillations. While the global behavior of ALMA dominant oscillations shows similarity with that of transition region and coronal passbands of AIA, the ALMA dominant period maps and power maps do not show any correlation with those from the other passbands. The spatial distribution of dominant periods and power in different period intervals of ALMA oscillations is uncorrelated with any other passband. We speculate the non-association of ALMA oscillations with those of IRIS and AIA be due to significant variations in the height of formation of the millimeter continuum observed by ALMA. Additionally, the fact that ALMA directly maps the brightness temperature, in contrast to the intensity observations by IRIS and AIA, can result in the very different intrinsic nature of the ALMA oscillations compared to the IRIS and AIA oscillations., Comment: Accepted for publication in A&A; abstract abridged to meet arXiv requirements

Interferometric observations of the Sun with ALMA provide valuable diagnostic tools for studying the small-scale dynamics of the solar atmosphere. Estimations of the observability of the small-scale dynamics as a function of spatial resolution for regions with different characteristic magnetic field topology facilitate a more robust analysis of ALMA observations of the Sun. A 3D model of the solar atmosphere from the MHD code Bifrost was used to produce high-cadence observables at mm and submm wavelengths. The synthetic observables for receiver bands 3-10 were degraded to the angular resolution corresponding to ALMA observations with different configurations of the interferometric array from the most compact C1, to the more extended C7. The observability of the small-scale dynamics was analyzed in each case. The analysis was thus also performed for predicting the potential of future capabilities. The minimum resolution required to study the typical small spatial scales in the solar chromosphere depends on the characteristic properties of the target region. Here, a range from quiet Sun to enhanced network loops is considered. Limited spatial resolution affects the observable signatures of dynamic small-scale brightening events in the form of reduced brightness temperature amplitudes, potentially leaving them undetectable, and even shifts in the times at which the peaks occur of up to tens of seconds. Conversion factors between the observable brightness amplitude and the original amplitude in the fully resolved simulation are provided that can be applied to observational data in principle, but are subject to wavelength-dependent uncertainties. Predictions of the typical appearance at the different combinations of receiver band, array configuration, and properties of the target region are conducted., Comment: 17 pages, 12 figures, 1 table and appendix of 8 pages with 6 figures and 2 tables. Accepted for publication in Astronomy and Astrophysics

In December 2016, the Atacama Large Millimeter/submillimeter Array (ALMA) carried out the first regular observations of the Sun. These early observations and the reduction of the respective data posed a challenge due to the novelty and complexity of observing the Sun with ALMA. The difficulties with producing science-ready time-resolved imaging products in a format familiar and usable by solar physicists based on the measurement sets delivered by ALMA had so far limited the availability of such data. With the development of the Solar ALMA Pipeline (SoAP), it has now become possible to routinely reduce such data sets. As a result, a growing number of science-ready solar ALMA datasets is now offered in the form of Solar ALMA Science Archive (SALSA). So far, SALSA contains primarily time series of single-pointing interferometric images at cadences of one or two seconds. The data arrays are provided in FITS format. We also present the first version of a standardised header format that accommodates future expansions and fits within the scope of other standards including the ALMA Science Archive itself and SOLARNET. The headers also include information designed to aid the reproduction of the imaging products from the raw data. Links to co-observations, if available, with a focus on those of the Interface Region Imaging Spectrograph (IRIS), are also provided. SALSA is accompanied by the Solar ALMA Library of Auxiliary Tools (SALAT) that contains IDL and Python routines for convenient loading and quick-look analysis of SALSA data., Comment: New figure. Minor edits. Web archive is up and ready to use. Manuscript waiting review

We propose and employ a novel empirical method for determining chromospheric plage regions, which seems to better isolate plage from its surrounding regions compared to other methods commonly used. We caution that isolating plage from its immediate surroundings must be done with care in order to successfully mitigate statistical biases that, for instance, can impact quantitative comparisons between different chromospheric observables. Using this methodology, our analysis suggests that 1.25 mm wavelength free-free emission in plage regions observed with ALMA/Band6 may not form in the low chromosphere as previously thought, but rather in the upper chromospheric parts of dynamic plage features (such as spicules and other bright structures), i.e., near geometric heights of transition region temperatures. We investigate the high degree of similarity between chromospheric plage features observed in ALMA/Band6 (at 1.25 mm wavelength) and IRIS/Si IV at 1393\r{A}. We also show that IRIS/Mg II h and k is not as well correlated with ALMA/Band6 as was previously thought, and we discuss the discrepancies with previous works. Lastly, we report indications for chromospheric heating due to propagating shocks supported by the ALMA/Band6 observations., Comment: 35 pages, 8 figures, 3 online movies and 1 Appendix. Accepted for publication in the Astrophysical Journal. This preprint is a companion paper to the replacement of arXiv:2005.12717

Solar observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA) facilitate studying the atmosphere of the Sun at chromospheric heights at high spatial and temporal resolution at millimeter wavelengths. ALMA intensity data at mm-wavelengths are used for a first detailed systematic assessment of the occurrence and properties of small-scale dynamical features in the quiet Sun. ALMA Band 3 data (~ $3$ mm / $100$ GHz) with spatial resolution ~ $1.4$ - $2.1$ arcsec and a duration of ~ $40$ min are analysed together with SDO/HMI magnetograms. The temporal evolution of the mm-maps is studied to detect pronounced dynamical features which are connected to dynamical events via a k-means clustering algorithm. The physical properties of the resulting events are studied and it is explored if they show properties consistent with propagating shock waves. For this purpose, observable shock wave signatures at mm wavelengths are calculated from one- and three-dimensional model atmospheres. There are 552 dynamical events detected with an excess in brightness temperature ($\Delta T_\text{b}$) of at least $\geq 400$ K. The events show a large variety in size up to ~ $9$ arcsec, amplitude $\Delta T_\text{b}$ up to ~ $1200$ K with typical values between ~ $450$ - $750$ K and lifetime at FWHM of $\Delta T_\text{b}$ between ~ $43$ - $360$ s, with typical values between ~ $55$ - $125$ s. Furthermore, many of the events show signature properties that suggest that they are likely produced by propagating shock waves. There are a lot of small-scale dynamic structures detected in the Band 3 data, even though the spatial resolution sets limitations of the size of events that can be detected. The amount of dynamic signatures in the ALMA mm data is very low in areas with photospheric footpoints with stronger magnetic fields, which is consistent with the expectation for propagating shock waves., Comment: Accepted for publication in Astronomy & Astrophysics, 17 pages, 15 figures

By direct measurements of the gas temperature, the Atacama Large Millimeter/sub-millimeter Array (ALMA) has yielded a new diagnostic tool to study the solar chromosphere. Here we present an overview of the brightness-temperature fluctuations from several high-quality and high-temporal-resolution (i.e., 1 and 2 sec cadence) time series of images obtained during the first two years of solar observations with ALMA, in Band 3 and Band 6, centred at around 3 mm (100 GHz) and 1.25 mm (239 GHz), respectively. The various datasets represent solar regions with different levels of magnetic flux. We perform Fast Fourier and Lomb-Scargle transforms to measure both the spatial structuring of dominant frequencies and the average global frequency distributions of the oscillations (i.e., averaged over the entire field of view). We find that the observed frequencies significantly vary from one dataset to another, which is discussed in terms of the solar regions captured by the observations (i.e., linked to their underlying magnetic topology). While the presence of enhanced power within the frequency range 3-5 mHz is found for the most magnetically quiescent datasets, lower frequencies dominate when there is significant influence from strong underlying magnetic field concentrations (present inside and/or in the immediate vicinity of the observed field of view). We discuss here a number of reasons which could possibly contribute to the power suppression at around 5.5 mHz in the ALMA observations. However, it remains unclear how other chromospheric diagnostics (with an exception of Halpha line-core intensity) are unaffected by similar effects, i.e., they show very pronounced 3-min oscillations dominating the dynamics of the chromosphere, whereas only a very small fraction of all the pixels in the ten ALMA data sets analysed here show peak power near 5.5 mHz., Comment: Accepted for publication in Philosophical Transactions of the Royal Society A, 29 pages, 12 figures

Observations at millimetre wavelengths provide a valuable tool to study the small scale dynamics in the solar chromosphere. We evaluate the physical conditions of the atmosphere in the presence of a propagating shock wave and link that to the observable signatures in mm-wavelength radiation, providing valuable insights into the underlying physics of mm-wavelength observations. A realistic numerical simulation from the 3D radiative Magnetohydrodynamic (MHD) code Bifrost is used to interpret changes in the atmosphere caused by shock wave propagation. High-cadence (1 s) time series of brightness temperature (T$_\text{b}$) maps are calculated with the Advanced Radiative Transfer (ART) code at the wavelengths $1.309$ mm and $1.204$ mm, which represents opposite sides of spectral band~$6$ of the Atacama Large Millimeter/submillimeter Array (ALMA). An example of shock wave propagation is presented. The brightness temperatures show a strong shock wave signature with large variation in formation height between $\sim0.7$ to $1.4$ Mm. The results demonstrate that millimetre brightness temperatures efficiently track upwardly propagating shock waves in the middle chromosphere. In addition, we show that the gradient of the brightness temperature between wavelengths within ALMA band $6$ can potentially be utilised as a diagnostics tool in understanding the small-scale dynamics at the sampled layers., Comment: 16 pages, 6 figures. Accepted for publication in Philosophical Transactions A of the Royal Society

We report detection of oscillations in brightness temperature, size, and horizontal velocity of three small bright features in the chromosphere of a plage/enhanced-network region. The observations, which were taken with high temporal resolution (i.e., 2-sec cadence) with the Atacama Large Millimeter/submillimeter Array (ALMA) in Band 3 (centred at 3 mm; 100 GHz), exhibit three small-scale features with oscillatory behaviour with different, but overlapping, distributions of period on the order of, on average, $90 \pm 22$ s, $110 \pm 12$ s and $66 \pm 23$ s, respectively. We find anti-correlations between perturbations in brightness temperature and size of the three features, which suggest the presence of fast sausage-mode waves in these small structures. In addition, the detection of transverse oscillations (although with a larger uncertainty) may suggest as well the presence of Alfv\'enic oscillations which are likely representative of kink waves. This work demonstrates the diagnostic potential of high-cadence observations with ALMA for detecting high-frequency magnetohydrodynamic waves in the solar chromosphere. Such waves can potentially channel a vast amount of energy into the outer atmosphere of the Sun., Comment: 16 pages, 8 figures, 2 tables. Accepted for publication in Philosophical Transactions of the Royal Society A

The solar atmosphere is composed of many species which are populated at different ionization and excitation levels. The upper chromosphere, transition region, and corona are nearly collisionless. Consequently, slippage between, for instance, ions and neutral particles, or interactions between separate species, may play important roles. We have developed a 3D multi-fluid and multi-species numerical code (Ebysus) to investigate such effects. Ebysus is capable of treating species (e.g., hydrogen, helium, etc) and fluids (neutrals, excited and ionized elements) separately, including non-equilibrium ionization, momentum exchange, radiation, thermal conduction, and other complex processes in the solar atmosphere. Treating different species as different fluids leads to drifts between different ions and an electric field that couples these motions. The coupling for two ionized fluids can lead to an anti-phase rotational motion between them. Different ionized species and momentum exchange can dissipate this velocity drift, i.e., convert wave kinetic energy into thermal energy. High frequency Alfv\'en waves driven by, e.g., reconnection thought to occur in the solar atmosphere, can drive such multi-ion velocity drifts., Comment: 18 pages, 9 figures, 2 tables, Accepted to be published in ApJ

We present observations of the solar chromosphere obtained simultaneously with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Interface Region Imaging Spectrograph (IRIS). The observatories targeted a chromospheric plage region of which the spatial distribution (split between strongly and weakly magnetized regions) allowed the study of linear-like structures in isolation, free of contamination from background emission. Using these observations in conjunction with a radiative magnetohydrodynamic 2.5D model covering the upper convection zone all the way to the corona that considers non-equilibrium ionization effects, we report the detection of an on-disk chromospheric spicule with ALMA and confirm its multithermal nature., Comment: 29 pages, 9 figures, Accepted for publication in the Astrophysical Journal. This version replaces the previous submission, which is now split into two companion papers

We present an initial study of one of the first ALMA Band 3 observations of the Sun with the aim to characterise the diagnostic potential of brightness temperatures measured with ALMA on the Sun. The observation covers 48min at a cadence of 2s targeting a Quiet Sun region at disk-centre. Corresponding time series of brightness temperature maps are constructed with the first version of the Solar ALMA Pipeline (SoAP) and compared to simultaneous SDO observations. The angular resolution of the observations is set by the synthesized beam (1.4x2.1as). The ALMA maps exhibit network patches, internetwork regions and also elongated thin features that are connected to large-scale magnetic loops as confirmed by a comparison with SDO maps. The ALMA Band 3 maps correlate best with the SDO/AIA 171, 131 and 304 channels in that they exhibit network features and, although very weak in the ALMA maps, imprints of large-scale loops. A group of compact magnetic loops is very clearly visible in ALMA Band 3. The brightness temperatures in the loop tops reach values of about 8000-9000K and in extreme moments up to 10 000K. ALMA Band 3 interferometric observations from early observing cycles already reveal temperature differences in the solar chromosphere. The weak imprint of magnetic loops and the correlation with the 171, 131, and 304 SDO channels suggests though that the radiation mapped in ALMA Band 3 might have contributions from a larger range of atmospheric heights than previously assumed but the exact formation height of Band 3 needs to be investigated in more detail. The absolute brightness temperature scale as set by Total Power measurements remains less certain and must be improved in the future. Despite these complications and the limited angular resolution, ALMA Band 3 observations have large potential for quantitative studies of the small-scale structure and dynamics of the solar chromosphere., Comment: 14 pages, 9 figures; accepted for publication in A&A

The thermal structure of the chromosphere is regulated through a complex interaction of various heating processes, radiative cooling, and the ionization degree of the plasma. Here we study the impact on the thermal properties of the chromosphere when including the combined action of non-equilibrium ionization (NEI) of hydrogen and helium and ion-neutral interaction effects. We have performed a 2.5D radiative magnetohydrodynamic simulation including ion-neutral interaction effects by solving the generalized Ohm's law (GOL) as well as NEI for hydrogen and helium using the Bifrost code. The GOL equation includes ambipolar diffusion and the Hall term. We compare this simulation with another simulation that computes the ionization in local thermodynamic equilibrium (LTE) including ion-neutral interaction effects. Our numerical models reveal substantial thermal differences in magneto-acoustic shocks, the wake behind the shocks, spicules, low-lying magnetic loops, and the transition region. In particular, we find that heating through ambipolar diffusion in shock wakes is substantially less efficient, while in the shock fronts themselves it is more efficient, under NEI conditions than when assuming LTE., Comment: 14 pages, 8 Figures, Accepted to be published in ApJ

High-energy particles enter the solar atmosphere from Galactic or solar coronal sources, producing an "albedo'' source from the quiet Sun, now observable across a wide range of photon energies. The interaction of high-energy particles in a stellar atmosphere depends essentially upon the joint variation of the magnetic field and the gas, which heretofore has been characterized parametrically as P ~ B^alpha with P the gas pressure and B the magnitude of the magnetic field. We re-examine that parametrization by using a self-consistent 3D MHD model (Bifrost) and show that this relationship tends to P ~ B^{2.9+-0.1} based on the visible portions of the sample of open-field flux tubes in such a model, but with large variations from point to point. This scatter corresponds to the strong meandering of the open-field flux tubes in the lower atmosphere, which will have a strong effect on the prediction of the emission anisotropy (limb brightening). The simulations show that much of the open flux in coronal holes originates in weak-field regions within the granular pattern of the convective motions seen in the simulations., Comment: Preprint prepared for submission to MNRAS

The aim of this study is to demonstrate how the logarithmic millimeter continuum gradient observed using the Atacama Large Millimeter/submillimeter Array (ALMA) may be used to estimate optical thickness in the solar atmosphere. We discuss how using multi-wavelength millimeter measurements can refine plasma analysis through knowledge of the absorption mechanisms. Here we use sub-band observations from the publicly available science verification (SV) data, whilst our methodology will also be applicable to regular ALMA data. The spectral resolving capacity of ALMA SV data is tested using the enhancement coincident with an X-ray Bright Point (XBP) and from a plasmoid ejection event near active region NOAA12470 observed in Band 3 (84-116 GHz) on 17/12/2015. We compute the interferometric brightness temperature light-curve for both features at each of the four constituent sub-bands to find the logarithmic millimetre spectrum. We compared the observed logarithmic spectral gradient with the derived relationship with optical thickness for an isothermal plasma to estimate the structure's optical thicknesses. We conclude, within 90% confidence, that the stationary enhancement has an optical thickness between $0.02 \leq \tau \leq 2.78$, and that the moving enhancement has $0.11 \leq \tau \leq 2.78$, thus both lie near to the transition between optically thin and thick plasma at 100 GHz. From these estimates, isothermal plasmas with typical Band 3 background brightness temperatures would be expected to have electron temperatures of $\sim 7370 - 15300$ K for the stationary enhancement and between $\sim 7440 - 9560$ K for the moving enhancement, thus demonstrating the benefit of sub-band ALMA spectral analysis., Comment: To appear in ApJ

Solar observations with the Atacama Large Millimeter/submillimeter Array (ALMA) provide us with direct measurements of the brightness temperature in the solar chromosphere. We study the temperature distributions obtained with ALMA Band 6 (in four sub-bands at 1.21, 1.22, 1.29, and 1.3 mm) for various areas at, and in the vicinity of, a sunspot, comprising quasi-quiet and active regions with different amounts of underlying magnetic fields. We compare these temperatures with those obtained at near- and far-ultraviolet (UV) wavelengths (and with the line-core intensities of the optically-thin far-UV spectra), co-observed with the Interface Region Imaging Spectrograph (IRIS) explorer. These include the emission peaks and cores of the Mg II k 279.6 nm and Mg II h 280.4 nm lines as well as the line cores of C II 133.4 nm, O I 135.6 nm, and Si IV 139.4 nm, sampling the mid-to-high chromosphere and the low transition region. Splitting the ALMA sub-bands resulted in an slight increase of spatial resolution in individual temperature maps, thus, resolving smaller-scale structures compared to those produced with the standard averaging routines. We find that the radiation temperatures have different, though somewhat overlapping, distributions in different wavelengths and in the various magnetic regions. Comparison of the ALMA temperatures with those of the UV diagnostics should, however, be interpreted with great caution, the former is formed under the local thermodynamic equilibrium (LTE) conditions, the latter under non-LTE. The mean radiation temperature of the ALMA Band 6 is similar to that extracted from the IRIS C II line in all areas with exception of the sunspot and pores where the C II poses higher radiation temperatures. In all magnetic regions, the Mg II lines associate with the lowest mean radiation temperatures in our sample. These will provide constraints for future numerical models., Comment: Accepted for publication in the Astronomy & Astrophysics journal

Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem. Some of the most popular and general methods proposed for this problem involve solving generalised least squares (GLS) equations with non-diagonal noise weights given by a block-diagonal matrix with Toeplitz blocks. In this work we study new map-making solvers potentially suitable for applications to the largest anticipated data sets. They are based on iterative conjugate gradient (CG) approaches enhanced with novel, parallel, two-level preconditioners. We apply the proposed solvers to examples of simulated non-polarised and polarised CMB observations, and a set of idealised scanning strategies with sky coverage ranging from nearly a full sky down to small sky patches. We discuss in detail their implementation for massively parallel computational platforms and their performance for a broad range of parameters characterising the simulated data sets. We find that our best new solver can outperform carefully-optimised standard solvers used today by a factor of as much as 5 in terms of the convergence rate and a factor of up to $4$ in terms of the time to solution, and to do so without significantly increasing the memory consumption and the volume of inter-processor communication. The performance of the new algorithms is also found to be more stable and robust, and less dependent on specific characteristics of the analysed data set. We therefore conclude that the proposed approaches are well suited to address successfully challenges posed by new and forthcoming CMB data sets., Comment: 19 pages // Final version submitted to A&A

Spherical Harmonic Transforms (SHT) are at the heart of many scientific and practical applications ranging from climate modelling to cosmological observations. In many of these areas new, cutting-edge science goals have been recently proposed requiring simulations and analyses of experimental or observational data at very high resolutions and of unprecedented volumes. Both these aspects pose formidable challenge for the currently existing implementations of the transforms. This paper describes parallel algorithms for computing SHT with two variants of intra-node parallelism appropriate for novel supercomputer architectures, multi-core processors and Graphic Processing Units (GPU). It also discusses their performance, alone and embedded within a top-level, MPI-based parallelisation layer ported from the S2HAT library, in terms of their accuracy, overall efficiency and scalability. We show that our inverse SHT run on GeForce 400 Series GPUs equipped with latest CUDA architecture ("Fermi") outperforms the state of the art implementation for a multi-core processor executed on a current Intel Core i7-2600K. Furthermore, we show that an MPI/CUDA version of the inverse transform run on a cluster of 128 Nvidia Tesla S1070 is as much as 3 times faster than the hybrid MPI/OpenMP version executed on the same number of quad-core processors Intel Nahalem for problem sizes motivated by our target applications. Performance of the direct transforms is however found to be at the best comparable in these cases. We discuss in detail the algorithmic solutions devised for major steps involved in the transforms calculation, emphasising those with a major impact on their overall performance, and elucidates the sources of the dichotomy between the direct and the inverse operations.