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Electromotive force is an essential quantity in dynamo theory. During a coronal mass ejection (CME), magnetic helicity gets decoupled from the Sun and advected into the heliosphere with the solar wind. Eventually, a heliospheric magnetic transient event might pass by a spacecraft, such as the Helios space observatories. Our aim is to investigate the electromotive force, the kinetic helicity effect ($\alpha$ term), the turbulent diffusion ($\beta$ term) and the cross-helicity effect ($\gamma$ term) in the inner heliosphere below 1 au. We set up a one-dimensional model of the solar wind velocity and magnetic field for a hypothetic interplanetary CME. Because turbulent structures within the solar wind evolve much slower than this structure needs to pass by the spacecraft, we use a reduced curl operator to compute the current density and vorticity. We test our CME shock-front model against an observed magnetic transient that passes by the Helios-2 spacecraft. At the peak of the fluctuations in this event we find strongly enhanced $\alpha$, $\beta$ and $\gamma$ terms, as well as a strong peak in the total electromotive force. Our method allows us to automatically identify magnetic transient events from any in-situ spacecraft observations that contain magnetic field and plasma velocity data of the solar wind., Comment: 10 pages, 14 figures, published

We present Chandra and XMM-Newton X-ray observations of the Abell 3391/Abell 3395 intercluster filament. It has been suggested that the galaxy clusters Abell 3395, Abell 3391, and the galaxy group ESO-161 located between the two clusters, are in alignment along a large-scale intercluster filament. We find that the filament is aligned close to the plane of the sky, in contrast to previous results. We find a global projected filament temperature kT = $4.45_{-0.55}^{+0.89}$~keV, electron density $n_e=1.08^{+0.06}_{-0.05} \times 10^{-4}$~cm$^{-3}$, and $M_{\rm gas} = 2.7^{+0.2}_{-0.1} \times 10^{13}$~M$_\odot$. The thermodynamic properties of the filament are consistent with that of intracluster medium (ICM) of Abell 3395 and Abell 3391, suggesting that the filament emission is dominated by ICM gas that has been tidally disrupted during an early stage merger between these two clusters. We present temperature, density, entropy, and abundance profiles across the filament. We find that the galaxy group ESO-161 may be undergoing ram pressure stripping in the low density environment at or near the virial radius of both clusters due to its rapid motion through the filament., Comment: 13 Pages, 12 Figures, 5 Tables. Submitted to ApJ, comments are welcome

The Solar TErrestrial RElations Observatory (STEREO) and its heliospheric imagers (HI) have provided us the possibility to enhance our understanding of the interplanetary propagation of coronal mass ejections (CMEs). HI-based methods are able to forecast arrival times and speeds at any target and use the advantage of tracing a CME's path of propagation up to 1 AU. In our study we use the ELEvoHI model for CME arrival prediction together with an ensemble approach to derive uncertainties in the modeled arrival time and impact speed. The CME from 3 November 2010 is analyzed by performing 339 model runs that are compared to in situ measurements from lined-up spacecraft MESSENGER and STEREO-B. Remote data from STEREO-B showed the CME as halo event, which is comparable to an HI observer situated at L1 and observing an Earth-directed CME. A promising and easy approach is found by using the frequency distributions of four ELEvoHI output parameters, drag parameter, background solar wind speed, initial distance and speed. In this case study, the most frequent values of these outputs lead to the predictions with the smallest errors. Restricting the ensemble to those runs, we are able to reduce the mean absolute arrival time error from $3.5 \pm 2.6$ h to $1.6 \pm 1.1$ h at 1 AU. Our study suggests that L1 may provide a sufficient vantage point for an Earth-directed CME, when observed by HI, and that ensemble modeling could be a feasible approach to use ELEvoHI operationally., Comment: submitted to Space Weather

Plasma beta is an important and fundamental physical quantity in order to understand plasma dynamics, particularly in the context of magnetically active stars, because it tells about the domination of magnetic versus thermodynamic processes on the plasma motion. We estimate the value ranges of plasma beta in different regions within the solar atmosphere and we describe a possible mechanism that helps forming a penumbra. For that we evaluate data from a 3D magnetohydrodynamic model of the solar corona above a magnetically active region. We compare our results with previously established data that is based on magnetic field extrapolations and that was matched for some observations. Our model data suggest that plasma beta in the photosphere should be considered to be larger than unity outside of sunspots. However, in the corona we also find that the beta value range reaches lower than previously thought, which coincides with a recent observation. We present an idea based on a gravity-driven process in a high-beta regime that might be responsible for the formation of the penumbra around sunspot umbra, where the vertical field strength reaches a given threshold. This process would also explain counter-Evershed flows. Regarding the thermal and magnetic pressure within the mixed-polarity solar atmosphere, including non-vertical magnetic field and quiet regions, plasma beta may reach unity at practically any height from the photosphere to the outer corona., Comment: 5 pages, 2 figures, published

X-ray emitting gaseous coronae around massive galaxies are a basic prediction of galaxy formation models. Although the coronae around spiral galaxies offer a fundamental test of these models, observational constraints on their characteristics are still scarce. While the presence of extended hot coronae has been established around a handful of massive spiral galaxies, the short X-ray observations only allowed for measurements of the basic characteristics of the coronae. In this work, we utilize deep XMM-Newton observations of NGC 6753 to explore its extended X-ray corona in unprecedented detail. Specifically, we establish the isotropic morphology of the hot gas, suggesting that it resides in hydrostatic equilibrium. The temperature profile of the gas shows a decrease with increasing radius: it drops from $kT\approx0.7$ keV in the innermost parts to $kT\approx0.4$ keV at 50 kpc radius. The temperature map reveals the complex temperature structure of the gas. We study the metallicity distribution of the gas, which is uniform at $Z\approx0.1$ Solar. This value is about an order of magnitude lower than that obtained for elliptical galaxies with similar dark matter halo mass, hinting that the hot gas in spiral galaxies predominantly originates from external gas inflows rather than from internal sources. By extrapolating the density profile of the hot gas out to the virial radius, we estimate the total gas mass and derive the total baryon mass of NGC 6753. We conclude that the baryon mass fraction is $f_{\rm b} \approx 0.06$, implying that about half of the baryons are missing., Comment: 12 pages, 10 figures, typos corrected, accepted for publication in ApJ

To understand the essential physics needed to reproduce magnetic reconnection events in 2.5-D particle-in-cell (PIC) simulations, we revisit the Geospace Environmental Modeling (GEM) setup. We set up a 2-D Harris current sheet (that also specifies the initial conditions) to evolve the reconnection of antiparallel magnetic fields. In contrast to the GEM setup, we use a much smaller initial perturbation to trigger the reconnection and evolve it more self-consistently. From PIC simulation data with high-quality particle statistics we study a symmetric reconnection site, including separatrix layers, as well as the inflow and the outflow regions. The velocity distribution functions (VDFs) of electrons have a fine structure and vary strongly depending on their location within the reconnection setup. The goal is to start cataloging multidimensional fine-structured electron velocity distributions showing different reconnection processes in the Earth's magnetotail under various conditions. This will enable a direct comparison with observations from, e.g., the NASA Magnetospheric MultiScale (MMS) mission, to identify reconnection-related events. We find regions with strong non-gyrotropy also near the separatrix layer and provide a refined criterion to identify an electron diffusion region in the magnetotail. The good statistical significance of this work for relatively small analysis areas reveals the gradual changes within the fine structure of electron VDFs depending on their sampling site., Comment: 17 pages, 11 figures, published

We present the joint analysis of the X-ray and SZ signals in A2319, the galaxy cluster with the highest signal-to-noise ratio in Planck maps and that has been surveyed within our XMM Cluster Outskirts Project (X-COP). We recover the thermodynamical profiles by the geometrical deprojection of the X-ray surface brightness, of the SZ comptonization parameter, and an accurate and robust spectroscopic measurements of the temperature. We resolve the clumpiness of the density to be below 20 per cent demonstrating that most of this clumpiness originates from the ongoing merger and can be associated to large-scale inhomogeneities. This analysis is done in azimuthally averaged radial bins and in eight independent angular sectors, enabling us to study in details the azimuthal variance of the recovered properties. Given the exquisite quality of the X-ray and SZ datasets, we constrain at $R_{200}$ the total hydrostatic mass, modelled with a NFW profile, with very high precision ($M_{200} = 9.76 \pm 0.16^{stat.} \pm 0.31^{syst.} \times 10^{14} M_\odot$). We identify the ongoing merger and how it is affecting differently the gas properties in the resolved azimuthal sectors. We have several indications that the merger has injected a high level of non-thermal pressure in this system: the clumping free density profile is above the average profile obtained by stacking Rosat observations; the gas mass fraction exceeds the expected cosmic gas fraction beyond $R_{500}$; the pressure profile is flatter than the fit obtained by the Planck collaboration; the entropy profile is flatter than the mean one predicted from non-radiative simulations; the analysis in azimuthal sectors has revealed that these deviations occur in a preferred region of the cluster. All these tensions are resolved by requiring a relative support of about 40 per cent from non-thermal to the total pressure at $R_{200}$., Comment: 20 pages, 16 figures. Accepted for publication by A&A. Comments welcome

The main result of the present theoretical paper is an original decomposition formula for the proximal operator of the sum of two proper, lower semicontinuous and convex functions $f$ and $g$. For this purpose, we introduce a new operator, called $f$-proximal operator of $g$ and denoted by $\mathrm{prox}^f_g$, that generalizes the classical notion. Then we prove the decomposition formula $\mathrm{prox}_{f+g} = \mathrm{prox}_f \circ \mathrm{prox}^f_g$. After collecting several properties and characterizations of $\mathrm{prox}^f_g$, we prove that it coincides with the fixed points of a generalized version of the classical Douglas-Rachford operator. This relationship is used for the construction of a weakly convergent algorithm that computes numerically this new operator $\mathrm{prox}^f_g$, and thus, from the decomposition formula, allows to compute numerically $\mathrm{prox}_{f+g}$. It turns out that this algorithm was already considered and implemented in previous works, showing that $\mathrm{prox}^f_g$ is already present (in a hidden form) and useful for numerical purposes in the existing literature. However, to the best of our knowledge, it has never been explicitly expressed in a closed formula and neither been deeply studied from a theoretical point of view. The present paper contributes to fill this gap in the literature. Finally we give an illustration of the usefulness of the decomposition formula in the context of sensitivity analysis of linear variational inequalities of second kind in a Hilbert space., Comment: To appear in Journal of Convex Analysis, 2018

In this paper we investigate the sensitivity analysis of parameterized nonlinear variational inequalities of second kind in a Hilbert space. The challenge of the present work is to take into account a perturbation on all the data of the problem. This requires special adjustments in the definitions of the generalized first- and second-order differentiations of the involved operators and functions. Precisely, we extend the notions, introduced and thoroughly studied by R.T. Rockafellar, of twice epi-differentiability and proto-differentiability to the case of a parameterized lower semi-continuous convex function and its subdifferential respectively. The link between these two notions is tied to Attouch's theorem and to the new concept, introduced in this paper, of convergent supporting hyperplanes. The previous tools allow us to derive an exact formula of the proto-derivative of the generalized proximity operator associated to a parameterized variational inequality, and deduce the differentiability of the associated solution with respect to the parameter. Furthermore, the derivative is shown to be the solution of a new variational inequality involving semi- and twice epi-derivatives of the data. An application is given to parameterized convex optimization problems involving the sum of two convex functions (one of them being smooth). The case of smooth convex optimization problems with inequality constraints is discussed in details. This approach seems to be new in the literature and open several perspectives towards theoretical and computational issues in nonlinear optimization.

The aim of the present paper is to contribute to the development of the study of Cauchy problems involving Riemann-Liouville and Caputo fractional derivatives. Firstly existence-uniqueness results for solutions of non-linear Cauchy problems with vector fractional multi-order are addressed. A qualitative result about the behavior of local but non-global solutions is also provided. Finally the major aim of this paper is to introduce notions of fractional state-transition matrices and to derive fractional versions of the classical Duhamel formula. We also prove duality theorems relying left state-transition matrices with right state-transition matrices.

Successive releases of Planck data have demonstrated the strength of the Sunyaev--Zeldovich (SZ) effect in detecting hot baryons out to the galaxy cluster peripheries. To infer the hot gas pressure structure from nearby galaxy clusters to more distant objects, we developed a parametric method that models the spectral energy distribution and spatial anisotropies of both the Galactic thermal dust and the Cosmic Microwave Background, that are mixed-up with the cluster SZ and dust signals. Taking advantage of the best angular resolution of the High Frequency Instrument channels (5 arcmin) and using X-ray priors in the innermost cluster regions that are not resolved with Planck, this modelling allowed us to analyze a sample of 61 nearby members of the Planck catalog of SZ sources ($0 < z < 0.5$, $\tilde{z} = 0.15$) using the full mission data, as well as to examine a distant sample of 23 clusters ($0.5 < z < 1$, $\tilde{z} = 0.56$) that have been recently followed-up with XMM-Newton and Chandra observations. We find that (i) the average shape of the mass-scaled pressure profiles agrees with results obtained by the Planck collaboration in the nearby cluster sample, and that (ii) no sign of evolution is discernible between averaged pressure profiles of the low- and high-redshift cluster samples. In line with theoretical predictions for these halo masses and redshift ranges, the dispersion of individual profiles relative to a self-similar shape stays well below 10 % inside $r_{500}$ but increases in the cluster outskirts., Comment: 12 pages, 10 figures

We propose a method to map the temperature distribution of the hot gas in galaxy clusters that uses resolved images of the thermal Sunyaev-Zel'dovich (tSZ) effect in combination with X-ray data. Application to images from the New IRAM KIDs Array (NIKA) and XMM-Newton allows us to measure and determine the spatial distribution of the gas temperature in the merging cluster MACS J0717.5+3745, at $z=0.55$. Despite the complexity of the target object, we find a good morphological agreement between the temperature maps derived from X-ray spectroscopy only -- using XMM-Newton ($T_{\rm XMM}$) and Chandra ($T_{\rm CXO}$) -- and the new gas-mass-weighted tSZ+X-ray imaging method ($T_{\rm SZ}$). We correlate the temperatures from tSZ+X-ray imaging and those from X-ray spectroscopy alone and find that $T_{\rm SZ}$ is higher than $T_{\rm XMM}$ and lower than $T_{\rm CXO}$ by $\sim 10\%$ in both cases. Our results are limited by uncertainties in the geometry of the cluster gas, contamination from kinetic SZ ($\sim 10\%$), and the absolute calibration of the tSZ map ($7\%$). Investigation using a larger sample of clusters would help minimise these effects., Comment: Accepted in AA, 8 pages, 4 figures, 1 table