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The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

The geometry of a coronal hole (CH) affects the density profile of the reflected part of an incoming global coronal wave (CW). In this study, we perform for the first time magnetohydrodynamic (MHD) simulations of fast-mode MHD waves interacting with CHs of different geometries, such as circular, elliptic, convex, and concave shapes. We analyse the influence these geometries have on the density profiles of the reflected waves and we generate the corresponding simulation-based time-distance plots. Within these time-distance plots we determine regions that exhibit specific density features, such as large reflected density amplitudes. In a further step, these interaction features can be compared to actual observed CW-CH interaction events which makes it possible to explain interaction parameters from the observed interaction events, such as the density structure of the reflected wave, which are usually difficult to comprehensively understand by only analysing the measurements. Moreover, we show that the interaction between a concave shaped CH and CWs, whose density profile include an enhanced as well as a depleted wave, can lead to reflected density amplitudes that are more than two times larger than the incoming ones. Another effect of the interplay between the constructive and destructive interference of the reflected wave parts is a strongly depleted region in the middle of the CW-CH interaction process. In addition, we show how important the choice of the path is that is used to generate the time-distance plots and how this choice affects the interpretation of the CW-CH interaction results., Comment: arXiv admin note: text overlap with arXiv:2308.08928

We provide a new scaling relation between $Y_{\text{SZ}}$, the integrated Sunyaev-Zeldovich signal and $M_{500}^{Y_{\text{X}}}$, the cluster mass derived from X-ray observations, using a sample of clusters from the Planck Early Sunyaev-Zeldovich (ESZ) catalogue observed in X-rays by Chandra, and compare it to the results of the Planck collaboration obtained from XMM-Newton observations of a subsample of the ESZ. We calibrated a mass bias on a subset of the Planck cosmological cluster sample using published weak-lensing data from CCCP and MENeaCS, for the new scaling relation as well as that from the Planck collaboration. We propose a novel method to account for selection effects and find a mass bias of $(1-b)=0.89\pm0.04$ for the Chandra-calibrated scaling relation, and $(1-b)=0.76\pm0.04$ for the XMM-Newton-calibrated scaling relation. We apply the scaling relations we derived to the full Planck cosmological cluster sample and obtain identical cosmological constraints regardless of the X-ray sample used, with $\sigma_8 =0.77\pm0.02$, $\Omega_m=0.31\pm0.02$, and $S_8= \sigma_8 \sqrt{\Omega_m / 0.3}=0.78\pm0.02$. We also provide constraints with a redshift evolution of the scaling relation fitted from the data instead of fixing it to the self-similar value. We find a redshift evolution significantly deviating from the self-similar value, leading to a higher value of $S_8=0.81\pm0.02$. We compare our results to those from various cosmological probes, and find that our $S_8$ constraints are competitive with the tightest constraints from the literature. When assuming a self-similar redshift evolution, our constraints are in agreement with most late-time probes and in tension with constraints from the CMB primary anisotropies. When relaxing the assumption of redshift evolution and fitting it to the data, we find no significant tension with results from either late-time probes or the CMB., Comment: 21 pages, 20 figures, accepted by A&A

Galaxy cluster number counts are an important probe to constrain cosmological parameters. One of the main ingredients of the analysis, along with accurate estimates of the clusters' masses, is the selection function, and in particular the completeness, associated to the cluster sample one is considering. Incorrectly characterising this function can lead to biases in the cosmological constraints. In this work, we want to study the completeness of the Planck cluster catalog, estimating the clusters' probability of detection in a realistic setting using hydrodynamical simulations. In particular, we probe the case in which the cluster model assumed in the detection method differs from the shape and profiles of true galaxy clusters. We create around 9000 images of the Sunyaev-Zel'dovich effect from galaxy clusters from the IllustrisTNG simulation, and use a Monte-Carlo injection method to estimate the completeness function. We study the impact of having different cluster pressure profiles, as well as that of complex cluster morphologies on the detection process. We find that the cluster profile has a significant effect on the completeness, with clusters with steeper profiles producing a higher completeness than ones with flatter profiles. We also show that cluster morphologies have small impact on the completeness, finding that elliptical clusters have slightly lower probability of detection with respect to spherically symmetric ones. Finally, we investigate the impact of a different completeness function on a cosmological analysis with cluster number counts, showing a shift in the constraints on $\Omega_m$ and $\sigma_8$ that lies in the same direction as the one driven by the mass bias., Comment: 13 pages, 12 figures. Submitted to A&A

Interactions between global coronal waves (CWs) and coronal holes (CHs) reveal many interesting features of reflected waves and coronal hole boundaries (CHB) but have fairly been studied so far. Magnetohydrodynamic (MHD) simulations can help us to better understand what is happening during these interaction events, and therefore, to achieve a broader understanding of the parameters involved. In this study, we perform for the first time 2D MHD simulations of a CW-CH interaction including a realistic initial wave density profile that consists of an enhanced as well as a depleted wave part. We vary several initial parameters, such as the initial density amplitudes of the incoming wave, the CH density, and the CHB width, which are all based on actual measurements. We analyse the effects of different incident angles on the interaction features and we use the corresponding time-distance plots to detect specific features of the incoming and the reflected wave. We found that a particular combination of a small CH density, a realistic initial density profile and a sufficiently small incident angle leads to remarkable interaction features, such as a large density amplitude of the reflected wave with respect to the incoming one. The parameter studies in this paper provide a tool to compare time-distance plots based on observational measurements to those created from simulations and therefore enable us to derive interaction parameters from observed CW-CH interaction events that usually cannot be obtained directly. The simulation results in this study are augmented by analytical expressions for the reflection coefficient of the CW-CH interaction which allows us to verify the simulations results in an additional way. This work is the first of a series of studies aiming to finally reconstruct actual observed CW-CH interaction events by means of MHD-simulations.

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.

Due to its physical nature, the solar corona exhibits large spatial variations of intensity that make it difficult to simultaneously visualize the features present at all levels and scales. Many general-purpose and specialized filters have been proposed to enhance coronal images. However, most of them require the ad hoc tweaking of parameters to produce subjectively good results. Our aim was to develop a general purpose image enhancement technique that would produce equally good results, but based on an objective criterion. The underlying principle of the method is the equalization, or whitening, of power in the {\it \`a trous} wavelet spectrum of the input image at all scales and locations. An edge-avoiding modification of the {\it \`a trous} transform that uses bilateral weighting by the local variance in the wavelet planes is used to suppress the undesirable halos otherwise produced by discontinuities in the data. Results are presented for a variety of extreme ultraviolet (EUV) and white light images of the solar corona. The proposed filter produces sharp and contrasted output, without requiring the manual adjustment of parameters. Furthermore, the built-in denoising scheme prevents the explosion of high-frequency noise typical of other enhancement methods, without smoothing statistically significant small-scale features. The standard version of the algorithm is about two times faster than the widely used multiscale Gaussian normalization (MGN). The bilateral version is slower, but provides significantly better results in the presence of spikes or edges. Comparisons with other methods suggest that the whitening principle may correspond to the subjective criterion of most users when adjusting free parameters.

Context. Accurate detections of frequent small-scale extreme ultraviolet (EUV) brightenings are essential to the investigation of the physical processes heating the corona. Aims. We detected small-scale brightenings, termed campfires, using their morphological and intensity structures as observed in coronal EUV imaging observations for statistical analysis. Methods. We applied a method based on Zernike moments and a support vector machine classifier to automatically identify and track campfires observed by Solar Orbiter/Extreme Ultraviolet Imager (EUI) and SDO/AIA. Results. This method detected 8678 campfires (with length scales between 400 km and 4000 km) from a sequence of 50 High Resolution EUV telescope (HRIEUV) 174{\AA} images. From 21 near co-temporal AIA images covering the same field of view as EUI, we found 1131 campfires, 58% of which were also detected in HRIEUV images. In contrast, about 16% of campfires recognized in HRIEUV were detected by AIA. We obtain a campfire birthrate of 2*10-16m-2s-1. About 40% of campfires show a duration longer than 5 s, having been observed in at least two HRIEUV images. We find that 27% of campfires were found in coronal bright points and the remaining 73% have occurred out of coronal bright points. We detected 23 EUI campfires with a duration greater than 245 s. We found that about 80% of campfires are formed at supergranular boundaries, and the features with the highest total intensities are generated at network junctions and intense H I Lyman-{\alpha} emission regions observed by EUI/HRILya. The probability distribution functions for the total intensity, peak intensity, and projected area of campfires follow a power law behavior with absolute indices between 2 and 3. This self-similar behavior is a possible signature of self-organization, or even self-organized criticality, in the campfire formation process.

Coronal holes and active regions are typical magnetic structures found in the solar atmosphere. We propose several magnetohydrostatic equilibrium solutions that are representative of these structures in two dimensions. Our models include the effect of a finite plasma-$\beta$ and gravity, but the distinctive feature is that we incorporate a thermal structure with properties similar to those reported by observations. We developed a semi-analytical method to compute the equilibrium configuration. Using this method, we obtain cold and under-dense plasma structures in open magnetic fields representing coronal holes, while in closed magnetic configurations, we achieve the characteristic hot and over-dense plasma arrangements of active regions. Although coronal holes and active regions seem to be antagonistic structures, we find that they can be described using a common thermal structure that depends on the flux function. In addition to the force balance, the energy balance is included in the constructed models using an a posteriori approach. From the two-dimensional computation of thermal conduction and radiative losses in our models, we infer the required heating function to achieve energy equilibrium. We find that the temperature dependence on height is an important parameter that may prevent the system from accomplishing thermal balance at certain spatial locations. The implications of these results are discussed in detail., Comment: Accepted for publication in A&A

Context: Thermal non-equilibrium (TNE) produces several observables that can be used to constrain the spatial and temporal distribution of solar coronal heating. Its manifestations include prominence formation, coronal rain, and long-period intensity pulsations in coronal loops. The recent observation of abundant periodic coronal rain associated with intensity pulsations by Auch\`ere et al. allows to unify these two phenomena as the result of TNE condensation and evaporation cycles. On the other hand, many intensity pulsation events observed by Froment et al. show little to no coronal rain formation. Aims: Our goal is to understand why some TNE cycles produce such abundant coronal rain, while others produce little to no rain. Methods: We reconstruct the geometry of the event reported by Auch\`ere et al., using images from STEREO/SECCHI/EUVI and magnetograms from SDO/HMI. We then perform 1D hydrodynamic simulations of this event, for different heating parameters and variations of the loop geometry (9000 simulations in total). We compare the resulting behaviour to simulations of TNE cycles by Froment et al. that do not produce coronal rain. Results: Our simulations show that both prominences and TNE cycles (with and without coronal rain) can form within the same magnetic structure. We show that the formation of coronal rain during TNE cycles depends on the asymmetry of the loop and of the heating. Asymmetric loops are overall less likely to produce coronal rain, regardless of the heating. In symmetric loops, coronal rain forms when the heating is also symmetric. In asymmetric loops, rain forms only when the heating compensates the asymmetry., Comment: Accepted for publication in A&A. 15 pages, 8 figures

The 3D fine structure of the solar atmosphere is still not fully understood as most of the available observations are taken from a single vantage point. The goal of the paper is to study the 3D distribution of small-scale brightening events ("campfires") discovered in the EUV quiet Sun by the Extreme Ultraviolet Imager (EUI) aboard Solar Orbiter. We used a first commissioning data set acquired by the EUI's High Resolution EUV telescope on 30 May 2020 in the 174 {\AA} passband and we combined it with simultaneous data taken by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory in a similar 171 {\AA} passband. The two-pixel spatial resolution of the two telescopes is 400 km and 880 km, respectively, which is sufficient to identify the campfires in both data sets. The two spacecraft had an angular separation of around 31.5 degrees (essentially in heliographic longitude), which allowed for the 3D reconstruction of the campfire position. These observations represent the first time that stereoscopy was achieved for brightenings at such a small scale. Manual and automatic triangulation methods were used to characterize the campfire data. The height of the campfires is located between 1000 km and 5000 km above the photosphere and we find a good agreement between the manual and automatic methods. The internal structure of campfires is mostly unresolved by AIA; however, for a particularly large campfire, we were able to triangulate a few pixels, which are all in a narrow range between 2500 and 4500 km. The low height of EUI campfires suggests that they belong to the previously unresolved fine structure of the transition region and low corona of the quiet Sun. They are probably apexes of small-scale dynamic loops heated internally to coronal temperatures. This work demonstrates that high-resolution stereoscopy of structures in the solar atmosphere has become feasible.

We present a machine learning framework to simulate realistic galaxies for the Euclid Survey. The proposed method combines a control on galaxy shape parameters offered by analytic models with realistic surface brightness distributions learned from real Hubble Space Telescope observations by deep generative models. We simulate a galaxy field of $0.4\,\rm{deg}^2$ as it will be seen by the Euclid visible imager VIS and show that galaxy structural parameters are recovered with similar accuracy as for pure analytic S\'ersic profiles. Based on these simulations, we estimate that the Euclid Wide Survey will be able to resolve the internal morphological structure of galaxies down to a surface brightness of $22.5\,\rm{mag}\,\rm{arcsec}^{-2}$, and $24.9\,\rm{mag}\,\rm{arcsec}^{-2}$ for the Euclid Deep Survey. This corresponds to approximately $250$ million galaxies at the end of the mission and a $50\,\%$ complete sample for stellar masses above $10^{10.6}\,\rm{M}_\odot$ (resp. $10^{9.6}\,\rm{M}_\odot$) at a redshift $z\sim0.5$ for the wide (resp. deep) survey. The approach presented in this work can contribute to improving the preparation of future high-precision cosmological imaging surveys by allowing simulations to incorporate more realistic galaxies., Comment: 22 pages, 21 figures (6 in appendinx). Accepted for publication to A&A. Change in the title for Euclid submission chronology coherence. Few changes for clarification

The goal of this paper is to study the smallest brightening events observed in the EUV quiet Sun. We use commissioning data taken by the EUI instrument onboard the recently launched Solar Orbiter mission. On 2020 May 30, EUI was situated at 0.556AU from the Sun. Its HRIEUV telescope 17.4nm passband reached an exceptionally high two-pixel spatial resolution of 400km. The size and duration of small-scale structures is determined in the HRIEUV data, while their height is estimated from triangulation with the simultaneous SDO/AIA data. This is the first stereoscopy of small scale brightenings at high resolution. We observed small localised brightenings ("campfires") in a quiet Sun region with lengthscales between 400km and 4000km and durations between 10 and 200s. The smallest and weakest of these HRIEUV brightenings have not been observed before. Simultaneous HRILYA observations do not show localised brightening events, but the locations of the HRIEUV events correspond clearly to the chromospheric network. Comparison with simultaneous AIA images shows that most events can also be identified in the 17.1nm, 19.3nm, 21.1nm, and 30.4nm passbands of AIA, although they appear weaker and blurred. DEM analysis indicates coronal temperatures peaking at log(T)~6.1-6.15. We determined the height of a few campfires, which is between 1000 and 5000km above the photosphere. We conclude that "campfires" are mostly coronal in nature and are rooted in the magnetic flux concentrations of the chromospheric network. We interpret these events as a new extension to the flare/microflare/nanoflare family. Given their low height, the EUI "campfires" could be a new element of the fine structure of the transition region/low corona: apexes of small-scale loops that are internally heated to coronal temperatures., Comment: 12 pages, 14 figures

Context: Long-period intensity pulsations were recently detected in the EUV emission of coronal loops, and have been attributed to cycles of plasma evaporation and condensation driven by thermal non-equilibrium (TNE). Numerical simulations that reproduce this phenomenon also predict the formation of periodic flows of plasma at coronal temperatures along some of the pulsating loops. Aims: In this paper, we aim at detecting these predicted flows of coronal-temperature plasma in pulsating loops. Methods: To this end, we use time series of spatially resolved spectra from the EUV imaging spectrometer (EIS) onboard Hinode, and track the evolution of the Doppler velocity in loops in which intensity pulsations have previously been detected in images of SDO/AIA. Results: We measure signatures of flows that are compatible with the simulations, but only in a fraction of the observed events. We demonstrate that this low detection rate can be explained by line of sight ambiguities, combined with instrumental limitations such as low signal to noise ratio or insufficient cadence., Comment: Accepted for publication in A&A. 16 pages, 16 figures

We present the optimal reconstruction of the thermal Sunyaev-Zel'dovich (tSZ) effect signal based on the combination of a heterogeneous dataset consisting of ACT and Planck data, with different numbers of channels, angular resolutions and noise levels. We combine both datasets using two different approaches, a Matched Multi-Filter (MMF) technique and an optimised Internal Linear Combination (ILC). We show that when applying the MMF to the combination of ACT and Planck data, the size-flux degeneracy is reduced and the signal-to-noise of clusters detected with their SZ signal improves by up to a factor of three. In the case of the optimised ILC method, we show that the tSZ map is reconstructed with a resolution of $\sim 1.5$ arcmin. This is more than a factor two improvement compared with the Planck resolution, and with a very good control of noise, i.e. limited only by the intrinsic noise of the individual experiments. The combination of ACT and Planck data offers a unique opportunity to improve on the study of the pressure profiles and to study substructure in clusters through their tSZ., Comment: 10 pages, 10 figures

We study interplanetary coronal mass ejections (ICMEs) measured by probes at different heliocentric distances (0.3-1AU) to investigate the propagation of ICMEs in the inner heliosphere and determine how the generic features of ICMEs change with heliospheric distance. Using data from the MESSENGER, Venus Express and ACE spacecraft, we analyze with the superposed epoch technique the profiles of ICME substructures, namely the sheath and the magnetic ejecta. We determine that the median magnetic field magnitude in the sheath correlates well with ICME speeds at 1 AU and we use this proxy to order the ICMEs at all spacecraft. We then investigate the typical ICME profiles for three categories equivalent to slow, intermediate and fast ICMEs. Contrary to fast ICMEs, slow ICMEs have a weaker solar wind field at the front and a more symmetric magnetic field profile. We find the asymmetry to be less pronounced at Earth than at Mercury, indicating a relaxation taking place as ICMEs propagate. We also find that the magnetic field intensities in the wake region of the ICMEs do not go back to the pre-ICME solar wind intensities, suggesting that the effects of ICMEs on the ambient solar wind last longer than the duration of the transient event. Such results provide an indication of physical processes that need to be reproduced by numerical simulations of ICME propagation. The samples studied here will be greatly improved by future missions dedicated to the exploration of the inner heliosphere, such as Parker Solar Probe and Solar Orbiter., Comment: 63 pages, 8 figures, Accepted for publication in Journal of Geophysical Research - Space physics

Star-formation activity is a key property to probe the structure formation and hence characterise the large-scale structures of the universe. This information can be deduced from the star formation rate (SFR) and the stellar mass (Mstar), both of which, but especially the SFR, are very complex to estimate. Determining these quantities from UV, optical, or IR luminosities relies on complex modeling and on priors on galaxy types. We propose a method based on the machine-learning algorithm Random Forest to estimate the SFR and the Mstar of galaxies at redshifts in the range 0.01

Long-period EUV pulsations, recently discovered to be common in active regions, are understood to be the coronal manifestation of thermal non-equilibrium (TNE). The active regions previously studied with EIT/SOHO and AIA/SDO indicated that long-period intensity pulsations are localized in only one or two loop bundles. The basic idea of this study is to understand why. For this purpose, we tested the response of different loop systems, using different magnetic configurations, to different stratifications and strengths of the heating. We present an extensive parameter-space study using 1D hydrodynamic simulations (1,020 in total) and conclude that the occurrence of TNE requires specific combinations of parameters. Our study shows that the TNE cycles are confined to specific ranges in parameter space. This naturally explains why only some loops undergo constant periodic pulsations over several days: since the loop geometry and the heating properties generally vary from one loop to another in an active region, only the ones in which these parameters are compatible exhibits TNE cycles. Furthermore, these parameters (heating and geometry) are likely to vary significantly over the duration of a cycle, which potentially limits the possibilities of periodic behavior. This study also confirms that long-period intensity pulsations and coronal rain are two aspects of the same phenomenon: both phenomena can occur for similar heating conditions and can appear simultaneously in the simulations., Comment: 26 pages, 17 figures, accepted for publication in The Astrophysical journal

We report on the discovery of periodic coronal rain in an off-limb sequence of {\it Solar Dynamics Observatory}/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6~hr) intensity pulsations of coronal loops of the sort described by Auchere et al. (2014) and Froment et al. (2015, 2017). These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation / condensation cycles resulting from a state of thermal nonequilibrium (TNE). The fluctuations around coronal temperatures produce the intensity pulsations of loops, and rain falls along their legs if thermal runaway cools the periodic condensations down and below transition-region (TR) temperatures. This scenario is in line with the predictions of numerical models of quasi-steadily and footpoint heated loops. The presence of coronal rain -- albeit non-periodic -- in several other structures within the studied field of view implies that this type of heating is at play on a large scale., Comment: By mistake, this article was originally submitted as a replacement (version v4) of arXiv:1608.03789. This latter was then replaced with a correct v5 (identical to v3) The present paper was then properly submitted as a new submission (this version)

Galaxy clusters play a crucial role in constraining cosmological parameters. Cluster detection and characterization have therefore become an important field of modern cosmology. In this work, we aim at constructing reasonably representative composite luminosity function of cluster members in the WISE survey that can be used in the future as an input in matching algorithms for cluster detection. We use a sample of massive clusters from the redMaPPer catalog to match the positions of the WISE sources. We build the composite luminosity function of the WISE members in different redshift bins. We find that galaxy cluster members have a characteristic composite luminosity function, with a clear change in the slope at a given magnitude apparent $M^{*}$, which becomes fainter with increasing redshift. The best-fit bright-end slope $\beta$ is compatible with a constant value of $3.54$ with no clear trend with redshift, while the faint-end slope $\alpha$ is remarkably different, ranging from $2$ to $3$. We present the first characterization of the composite luminosity function of the WISE counterparts of redMaPPer cluster members and in this way we provide an element for building cluster detection techniques based on matching algorithms., Comment: 8 pages, 7 figures, 6 tables, resubmitted to A&A after first referee report

The Differential Emission Measure (DEM) analysis is one of the most used diagnostic tools for solar and stellar coronae. Being an inverse problem, it has limitations due to the presence of random and systematic errors. We present in theses series of papers an analysis of the robustness of the inversion in the case of AIA/SDO observations. We completely characterize the DEM inversion and its statistical properties, providing all the solutions consistent with the data along with their associated probabilities, and a test of the suitability of the assumed DEM model. While Paper I focused on isothermal conditions, we now consider multi-thermal plasmas and investigate both isothermal and multithermal solutions. We demonstrate how the ambiguity between noises and multi-thermality fundamentally limits the temperature resolution of the inversion. We show that if the observed plasma is multi-thermal, isothermal solutions tend to cluster on a constant temperature whatever the number of passbands or spectral lines. The multi-thermal solutions are also found to be biased toward near isothermal solutions around 1 MK. This is true even if the residuals support the chosen DEM model, possibly leading to erroneous conclusions on the observed plasma. We propose tools to identify and quantify the possible degeneracy of solutions, thus helping the interpretation of DEM inversion., Comment: 24 pages, 12 figures

DEM analysis is a major diagnostic tool for stellar atmospheres. But both its derivation and its interpretation are notably difficult because of random and systematic errors, and the inverse nature of the problem. We use simulations with simple thermal distributions to investigate the inversion properties of SDO/AIA observations of the solar corona. This allows a systematic exploration of the parameter space and using a statistical approach, the respective probabilities of all the DEMs compatible with the uncertainties can be computed. Following this methodology, several important properties of the DEM inversion, including new limitations, can be derived and presented in a very synthetic fashion. In this first paper, we describe the formalism and we focus on isothermal plasmas, as building blocks to understand the more complex DEMs studied in the second paper. The behavior of the inversion of AIA data being thus quantified, and we provide new tools to properly interpret the DEM. We quantify the improvement of the isothermal inversion with 6 AIA bands compared to previous EUV imagers. The maximum temperature resolution of AIA is found to be 0.03 log Te, and we derive a rigorous test to quantify the compatibility of observations with the isothermal hypothesis. However we demonstrate limitations in the ability of AIA alone to distinguish different physical conditions., Comment: 22 pages, 8 figures