Scalar Dissipation Research Articles

Dissipation at limited resolutions: power law and detection of hidden dissipative scales

Abstract Non-equilibrium systems, in particular, living organisms, are maintained by irreversible transformations of energy that drive diverse functions. Quantifying their irreversibility, as measured by energy dissipation, is essential for understanding the underlying mechanisms. However, existing techniques usually overlook experimental limitations, either by assuming full information or by employing a coarse-graining method that requires knowledge of the structure behind hidden degrees of freedom. Here, we study the inference of dissipation from finite-resolution measurements by employing a recently developed model-free estimator that considers both the sequence of coarse-grained transitions and the waiting time distributions: σ 2 = σ 2 ℓ + σ 2 t . The dominant term σ 2 ℓ originates from the sequence of observed transitions. We find that it scales with resolution following a power law. Comparing the scaling exponent with a previous estimator highlights the importance of accounting for flux correlations at lower resolutions. σ 2 t comes from asymmetries in waiting time distributions. It is non-monotonic in resolution, with its peak position revealing characteristic scales of the underlying dissipative process, consistent with observations in the actomyosin cortex of starfish oocytes. Alternatively, the characteristic scale can be detected in a crossover of the scaling of σ 2 ℓ . This provides a novel perspective for extracting otherwise hidden characteristic dissipative scales directly from dissipation measurements. We illustrate these results in biochemical models as well as complex networks. Overall, this study highlights the significance of resolution considerations in non-equilibrium systems, providing insight into the interplay between experimental resolution, entropy production and underlying complexity.

Measurement of the Taylor Microscale and the Effective Magnetic Reynolds Number in the Solar Wind With Cluster

AbstractWe use magnetic field data from the Cluster mission to estimate the value of the Taylor microscale and the effective magnetic Reynolds number in the interplanetary solar wind. Turbulent cascades can be characterized by the spatial scale at which dissipation begins to impact the local energy transfer, estimated by the Taylor microscale, as well as the separation between the injection and dissipation scales, estimated by the effective magnetic Reynolds number. Estimating the Taylor microscale requires measurements of the autocorrelation function at small separations. The Cluster spacecraft have exceptionally sensitive search coil magnetometers with high time resolution, making them ideal for measuring the Taylor microscale. We obtain a value of km; smaller than most previous measurements. We interpret this value as being smaller due to the higher time resolution, enabling the curvature of the autocorrelation function to be measured closer to the origin, giving a more accurate measurement. Combining the Taylor Microscale's computed value with concurrent correlation length measurements, we obtain a value of for the effective magnetic Reynolds number, which compares well to other observations. The four spacecraft of Cluster also allow directions transverse to the flow to be surveyed. The small separations (7 km) of Clusters 3 and 4 show that the Taylor microscale may vary as a function of direction to the mean magnetic field direction. The observed differences are small, requiring more observations to confirm this anisotropy.

Turbulence Revealed by Wavelet Transform: Power Spectrum and Intermittency for the Velocity Field of the Cosmic Baryonic Fluid

We use continuous wavelet transform techniques to construct the global and environment-dependent wavelet statistics, such as energy spectrum and kurtosis, to study the fluctuation and intermittency of the turbulent motion in the cosmic fluid velocity field with the IllustrisTNG simulation data. We find that the peak scale of the energy spectrum defines a characteristic scale, which can be regarded as the integral scale of turbulence, and the Nyquist wavenumber can be regarded as the dissipation scale. With these two characteristic scales, the energy spectrum can be divided into the energy-containing range, the inertial range, and the dissipation range of turbulence. The wavelet kurtosis is an increasing function of the wavenumber k, which first grows rapidly then slowly with k, indicating that the cosmic fluid becomes increasingly intermittent with k. In the energy-containing range, the energy spectrum increases significantly from z = 2 to 1, but remains almost unchanged from z = 1 to 0. We find that both the environment-dependent spectrum and kurtosis are similar to the global ones, and the magnitude of the spectrum is smallest in the lowest-density and largest in the highest-density environment, suggesting that the cosmic fluid is more turbulent in a high-density than in a low-density environment. In the inertial range, the energy spectrum’s exponent is steeper than both the Kolmogorov and Burgers exponents, indicating more efficient energy transfer compared to Kolmogorov or Burgers turbulence.

Probing the physics of star formation (ProPStar)

Context. Turbulence is a key component of molecular cloud structure. It is usually described by a cascade of energy down to the dissipation scale. The power spectrum for subsonic incompressible turbulence is ∝k−5/3, while for supersonic turbulence it is ∝k−2. Aims. We determine the power spectrum in an actively star-forming molecular cloud, from parsec scales down to the expected magnetohydrodynamic (MHD) wave cutoff (dissipation scale). Methods. We analyzed observations of the nearby NGC 1333 star-forming region in three different tracers to cover the different scales from ∼10 pc down to 20 mpc. The largest scales are covered with the low-density gas tracer 13CO (1–0) obtained with a single dish, the intermediate scales are covered with single-dish observations of the C18O (3–2) line, while the smallest scales are covered in H13CO+ (1–0) and HNC (1–0) with a combination of NOEMA interferometer and IRAM 30m single-dish observations. The complementarity of these observations enables us to generate a combined power spectrum covering more than two orders of magnitude in spatial scale. Results. We derive the power spectrum in an active star-forming region spanning more than 2 decades of spatial scales. The power spectrum of the intensity maps shows a single power-law behavior, with an exponent of 2.9 ± 0.1 and no evidence of dissipation. Moreover, there is evidence that the power spectrum of the ions to have more power at smaller scales than the neutrals, which is opposite to the theoretical expectations. Conclusions. We show new possibilities for studying the dissipation of energy at small scales in star-forming regions provided by interferometric observations.

A residence time-based concept for modeling and analyzing the impact of diffusion on auto-ignition processes with thermal stratification

A meticulous definition of the residence time (also referred to as the fluid age) in the context of auto-ignition in a thermally stratified gas has demonstrated that the age can be considered as a level-set function, which allows the tracking of a self-ignition front propagating. In order to avoid the difficulty of defining the boundary and initial conditions for this age, which can be seen as fluid birth, a normalized age is introduced. Meticulous derivation of the equation revealed additional terms related to the scalar dissipation rates and the gradient in the composition space of the auto-ignition delay. To validate this model equation, two canonical configurations were proposed: one representing a hot spot self-igniting with significant thermal diffusion and the other where a self-ignition front propagates at an almost constant speed. The analysis, based on the normalized age of the particles, reveals the impact of thermal diffusion on the acceleration or deceleration of particle aging. In certain instances, a particle rejuvenation mechanism through thermal diffusion has been identified. Furthermore, this work demonstrates the capacity of the normalized residence time field to map transitions between auto-ignition and laminar flame. Finally, the different cases studied were classified in an auto-ignition/diffusion diagram based on three non-dimensional characteristic numbers, which highlighted five combustion regimes.

Effect of H[formula omitted] addition on NH[formula omitted] flame structure and dynamics in a mixing layer

Hydrogen addition has been widely used to improve the combustion performance of low-reactivity fuels such as NH3. In this study, a series of two-dimensional NH3/H2 flames in mixing layers were investigated numerically. The aim is to assess and interpret the effects of H2 addition on the structure and dynamics of ammonia flames. Detailed chemistry and transport models were considered in the simulations. It was shown that for pure hydrogen or ammonia flames, a classical tribrachial structure was observed. The non-premixed branch in the tribrachial flame of NH3 combustion features high heat release rate (HRR), while the two premixed branches are weak. The mixture fraction corresponding to the maximum HRR of NH3 combustion is significantly lower than the stoichiometric mixture fraction. When blending ammonia with hydrogen, a tetrabrachial flame structure consisting of two premixed branches and two non-premixed branches was observed, where one non-premixed branch corresponds to the reaction of NH3, while the other is formed due to the reaction of H2. It was suggested that the formation of the tetrabrachial flame is related to the preferential diffusion of hydrogen. After decreasing artificially the diffusivity of hydrogen to suppress the preferential diffusion effect, the flame exhibits only three branches with the merging of the two non-premixed branches. By analyzing the flame dynamics at the leading edge, it was found that the flame speed (Sd∗) is negatively correlated with the flame stretch (κ) and scalar dissipation rate (χ), with Sd∗ decreasing almost linearly with κ or χ, consistent with previous studies of methane and hydrogen flames. As the H2 concentration is increased, the values of Sd∗ increase due to the enhanced reactivity.

On EMEC Instability in Bi‐Kappa Distributed Space Plasmas Under the Influence of Parallel DC Electric Field

ABSTRACTEMEC waves driven by kinetic anisotropies and suprathermal particles are expected to play an important role at dissipative scales in the solar wind and planetary magnetospheres. Moreover, the correlation of EMEC waves with electric field magnitude and direction can be a tool to probe the inner magnetosphere. Thus, in this manuscript, we present the study of EMEC waves driven by temperature anisotropy in bi‐Kappa distributed space plasmas in the presence of a parallel DC electric field. The dispersion equation bearing the influence of electric field and suprathermal particles followed by the analytical expressions for wave frequency and wave growth rate is derived. The general dispersion equation is solved numerically to unveil the effect of suprathermal particles, temperature anisotropy, and the magnitude of the electric field on growth rate as well as the domain of unstable wave numbers, and the obtained numerical outcomes are compared with those of the bi‐Maxwellian model. Moreover, the maximum growth rates for EMEC waves have also been obtained.

A Comparative Study of the Hydrogen Auto-Ignition Process in Oxygen–Nitrogen and Oxygen–Water Vapor Oxidizer: Numerical Investigations in Mixture Fraction Space and 3D Forced Homogeneous Isotropic Turbulent Flow Field

In this paper, we analyze the auto-ignition process of hydrogen in a hot oxidizer stream composed of oxygen–nitrogen and oxygen–water vapor with nitrogen/water vapor mass fractions in a range of 0.1–0.9. The temperature of the oxidizer varies from 1100 K to 1500 K and the temperature of hydrogen is assumed to be 300 K. The research is performed in 1D mixture fraction space and in a forced homogeneous isotropic turbulent (HIT) flow field. In the latter case, the Large Eddy Simulation (LES) method combined with the Eulerian Stochastic Field (ESF) combustion model is applied. The results obtained in mixture fraction space aim to determine the most reactive mixture fraction, maximum flame temperature, and dependence on the scalar dissipation rate. Among others, we found that the ignition in H2-O2-H2O mixtures occurs later than in H2-O2-N2 mixtures, especially at low oxidizer temperatures. On the other hand, for a high oxidizer temperature, the ignitability of H2-O2-H2O mixtures is extended, i.e., the ignition occurs for a larger content of H2O and takes place faster. The 3D LES-ESF results show that the ignition time is virtually independent of initial conditions, e.g., randomness of an initial flow field and turbulence intensity. The latter parameter, however, strongly affects the flame evolution. It is shown that the presence of water vapor decreases ignitability and makes flames more prone to extinction.

MURCA driven bulk viscosity in neutrino trapped baryonic matter

We examine bulk viscosity, taking into account trapped neutrinos in baryonic matter, in the context of binary neutron star mergers. Following the merging event, the binary star can yield a remnant compact object with densities up to 5 nuclear saturation density and temperature up to 50 MeV resulting in the retention of neutrinos. We employ two relativistic mean field models, NL3 and DDME2, to describe the neutrino-trapped baryonic matter. The dissipation coefficient is determined by evaluating the Modified URCA interaction rate in the dense baryonic medium, and accounting for perturbations caused by density oscillations. We observe the resonant behavior of bulk viscosity as it varies with the temperature of the medium. The bulk viscosity peak remains within the temperature range of ∼13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim 13$$\\end{document}–50 MeV, depending upon the underlying equation of states and lepton fractions. This temperature range corresponds to the relevant domain of binary neutron star mergers. We also note that in presence of neutrinos in the medium the bulk viscosity peak shifts towards higher temperature and the peak value of bulk viscosity also changes. The time scale of viscous dissipation is dictated by the beta-off-equilibrium susceptibilities derived from the nuclear equation of state. The resulting viscous decay time scale ranges from 32–100 ms, which aligns with the order of magnitude of the post-merger object’s survival time in some specific scenarios.

Spectral energy transfer on complex networks: a filtering approach

The spectral analysis of dynamical systems is a staple technique for analyzing a vast range of systems. But beyond its analytical utility, it is also the primary lens through which many physical phenomena are defined and interpreted. The turbulent energy cascade in fluid mechanics, a dynamical consequence of the three-dimensional Navier–Stokes equations in which energy “cascades” from large injection scales to smaller dissipation scales, is a well-known example that is precisely defined only in reciprocal space. Related techniques in the context of networked dynamical systems have been employed with great success in deriving reduced order models. But what such techniques gain in analytical tractability, they often lose in interpretability and locality, as the lower degree of freedom system frequently contains information from all nodes of the network. Here, we demonstrate that a network of nonlinear oscillators exhibits spectral energy transfer facilitated by an effective force akin to the Reynolds stress in turbulence, an example of an emergent higher order interaction. Then, introducing a filter-based decomposition motivated by large eddy simulation, we show that such higher order interactions can be localized to individual nodes and study the effects of local topology on such interactions.

Effects of combustion progress variable and Karlovitz number on the scalar dissipation rate of turbulent premixed hydrogen-enriched methane–air flames: An experimental study

The scalar dissipation rate plays a key role in the modeling of turbulent premixed flames. Despite the above, our knowledge concerning the effects of several parameters, such as the combustion progress variable, Karlovitz number, and fuel composition on the scalar dissipation rate requires to be developed. This is carried out experimentally here. Two mixtures, methane–air (Lewis number of unity) and hydrogen-enriched methane–air (Lewis number of 0.8), are examined. Three passive (perforated plates) and one active turbulence generators are used, leading to a wide range of turbulence intensities with the corresponding Karlovitz number changing from 0.1 to 34.5. The hot-wire anemometry and the Rayleigh scattering techniques are used separately to study the background non-reacting turbulent flow and the reacting scalar dissipation rate, respectively. Three models that are available in the literature for estimating the Favre-averaged scalar dissipation rate are experimentally assessed. Using experimental results obtained in this study, it is shown that moving from fresh reactants towards combustion products increases the above modeling parameters by 2–3 times, depending on the tested Lewis number. For each tested Lewis number, empirical formulations that include the effects of both the Karlovitz number and combustion progress variable on the modeling parameters are proposed. Care must be taken in extending the proposed models of the present study to test conditions that are not examined here.

Modeling of Soot Emission in Turbulent Diffusion Flames Impinging on a Cold Surface

ABSTRACT A hydrocarbon flame impinging on a cold surface produces an enhanced soot emission compared to the identical free flame. Cooking with biomass fuels is one practical process where soot emissions due to flame impingement has important environmental and health consequences. This problem was examined in a simplified system in which a turbulent non-premixed ethylene flame impinged on a cold surface. Previous experiment on this configuration examined the influence of a number of parameters on soot emission. The present paper uses numerical modeling to investigate the mechanism of soot emission enhancement in this configuration. Variations in the height of the surface above the fuel jet inlet showed going through a maximum, replicating the data. Since soot behavior can be affected by both thermal quench and flow field disruption, we decoupled the processes by replacing the cold surface with an adiabatic surface. These results indicated that most of the emission enhancement was due to the flow field disruption and not due to thermal quench. The modeling suggests that the presence of the surface changes the scalar dissipation rate, which influences C2H2 concentration, a key species in the soot surface growth process. Specifically, the surface causes a spike in the scalar dissipation rate adjacent to the surface, which significantly influences C2H2 concentration and results in increased soot production. The surface also forces the flame to spread radially, allowing more O2 to penetrate the flame immediately, enhancing the soot oxidation process. The combination of the enhanced soot production and oxidation produces the observed behavior.

Modified and generalized single-element Maxwell viscoelastic model.

In this Letter, the single-element Maxwell model is generalized with respect to the wave vector and extended with a correction function that measures the reduced viscous response. This model has only two free parameters and avoids the attenuation-frequency locking present in the original model. Through molecular simulations it is shown that the model satisfactory predicts the transverse dynamics of the binary Lennard-Jones system at different temperatures, as well as water and toluene at ambient conditions. The correction function shows that the viscous response is significantly reduced compared to the predictions of the original Maxwell model and that there exists a characteristic length scale of minimum dissipation.

Scaling of turbulence-forced capillary waves

We simulate the propagation of capillary waves at the interface between two liquid layers of equal density, viscosity and thickness, which flow in stratified conditions inside a turbulent Poiseuille channel. This setup gives us the possibility to single out the effect of inertia and surface tension – in isolation from gravity – on the propagation of interfacial capillary waves. Numerical simulations, which are based on a combined pseudo spectral/phase field method, are run keeping the shear Reynolds number constant, Reτ=300, and considering four different values of the Weber number: We=0.5, We=1.0, We=1.5 and We=2.0. In the present case, waves are naturally forced by turbulence over a broad range of scales, from the larger ones, whose size is of order of the channel height h, down to the smaller dissipative scales. We show that, by increasing the Weber number, the interface is deformed more vigorously, and is prone to sustain the propagation of waves over a broader range of scales. Upon computation of the power spectra of wave elevation, we show that the behavior of waves agrees with the theoretical predictions given by the weak wave turbulence theory, which predicts a decay Sη(k)∼k−4 in the inertial regime, followed by a steeper decay at large k, in the surface-tension-dominated regime. We clearly show that the transition between the inertial and the surface-tension-dominated regime is pushed towards larger k by increasing the Weber number. In addition, we show that the two-dimensional frequency–wavenumber spectra of the wave elevation – the dispersion relation – is in good agreement with well established theoretical prediction, ω(k)∼k3/2, and that the range of validity of such prediction broadens for increasing Weber number.

On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.

BxC Toolkit: Generating Tailored Turbulent 3D Magnetic Fields

Turbulent states are ubiquitous in plasmas, and the understanding of turbulence is fundamental in modern astrophysics. Numerical simulations, which are the state-of-the-art approach to the study of turbulence, require substantial computing resources. Recently, attention shifted to methods for generating synthetic turbulent magnetic fields, affordably creating fields with parameter-controlled characteristic features of turbulence. In this context, the BxC toolkit was developed and validated against direct numerical simulations (DNSs) of isotropic turbulent magnetic fields. Here, we demonstrate novel extensions of BxC to generate realistic turbulent magnetic fields in a fast, controlled, geometric approach. First, we perform a parameter study to determine quantitative relations between the BxC input parameters and the desired characteristic features of the turbulent power spectrum, such as the extent of the inertial range, its spectral slope, and the injection and dissipation scale. Second, we introduce in the model a set of structured background magnetic fields, B 0, as a natural and more realistic extension to the purely isotropic turbulent fields. Third, we extend the model to include anisotropic turbulence properties in the generated fields. With all these extensions combined, our tool can quickly generate any desired structured magnetic field with controlled, anisotropic turbulent fluctuations, faster by orders of magnitude with respect to DNSs. These can be used, e.g., to provide initial conditions for DNSs or easily generate synthetic data for many astrophysical settings, all at otherwise unaffordable resolutions.

Geometry, Dissipation, Cooling, and the Dynamical Evolution of Wind-blown Bubbles

Bubbles driven by energy and mass injection from small scales are ubiquitous in astrophysical fluid systems and essential to feedback across multiple scales. In particular, O stars in young clusters produce high-velocity winds that create hot bubbles in the surrounding gas. We demonstrate that the dynamical evolution of these bubbles is critically dependent upon the geometry of their interfaces with their surroundings and the nature of heat transport across these interfaces. These factors together determine the amount of energy that can be lost from the interior through cooling at the interface, which in turn determines the ability of the bubble to do work on its surroundings. We further demonstrate that the scales relevant to physical dissipation across this interface are extremely difficult to resolve in global numerical simulations of bubbles for parameter values of interest. This means the dissipation driving evolution of these bubbles in numerical simulations is often of a numerical nature. We describe the physical and numerical principles that determine the level of dissipation in these simulations; we use this, along with a fractal model for the geometry of the interfaces, to explain differences in convergence behavior between hydrodynamical and magnetohydrodynamical simulations presented here. We additionally derive an expression for momentum as a function of bubble radius expected when the relevant dissipative scales are resolved and show that it still results in efficiently cooled solutions, as postulated in previous work.

Implications of Using Scalar Forcing to Sustain Reactant Mixture Stratification in Direct Numerical Simulations of Turbulent Combustion

A recently proposed scalar forcing scheme that maintains the mixture fraction mean, root-mean-square and probability density function in the unburned gas can lead to a statistically quasi-stationary state in direct numerical simulations of turbulent stratified combustion when combined with velocity forcing. Scalar forcing alongside turbulence forcing leads to greater values of turbulent burning velocity and flame surface area in comparison to unforced simulations for globally fuel-lean mixtures. The sustained unburned gas mixture inhomogeneity changes the percentage shares of back- and front-supported flame elements in comparison to unforced simulations, and this effect is particularly apparent for high turbulence intensities. Scalar forcing does not significantly affect the heat release rates due to different modes of combustion and the micro-mixing rate within the flame characterised by scalar dissipation rate of the reaction progress variable. Thus, scalar forcing has a significant potential for enabling detailed parametric studies as well as providing well-converged time-averaged statistics for stratified-mixture combustion using Direct Numerical Simulations in canonical configurations.

Probing the physics of star formation (ProPStar)

Context. Electron fraction and cosmic-ray ionization rates in star-forming regions are important quantities in astrochemical modeling and are critical to the degree of coupling between neutrals, ions, and electrons, which regulates the dynamics of the magnetic field. However, these are difficult quantities to estimate. Aims. We aim to derive the electron fraction and cosmic-ray ionization rate maps of an active star-forming region. Methods. We combined observations of the nearby NGC 1333 star-forming region carried out with the NOEMA interferometer and IRAM 30 m single dish to generate high spatial dynamic range maps of different molecular transitions. We used the DCO+ and H13CO+ ratio (in addition to complementary data) to estimate the electron fraction and produce cosmic-ray ionization rate maps. Results. We derived the first large-area electron fraction and cosmic-ray ionization rate resolved maps in a star-forming region, with typical values of 10−65 and 10−16.5 s−1, respectively. The maps present clear evidence of enhanced values around embedded young stellar objects (YSOs). This provides strong evidence for locally accelerated cosmic rays. We also found a strong enhancement toward the northwest region in the map that might be related either to an interaction with a bubble or to locally generated cosmic rays by YSOs. We used the typical electron fraction and derived a magnetohydrodynamic (MHD) turbulence dissipation scale of 0.054 pc, which could be tested with future observations. Conclusions. We found a higher cosmic-ray ionization rate compared to the canonical value for N(H2) = 1021−1023 cm−2 of 10−17 s−1 in the region, and it is likely generated by the accreting YSOs. The high value of the electron fraction suggests that new disks will form from gas in the ideal-MHD limit. This indicates that local enhancements of ζ(H2), due to YSOs, should be taken into account in the analysis of clustered star formation.

Toward mapping turbulence in the intra-cluster medium

Context. Future X-ray observatories with high spectral resolution and imaging capabilities will enable measurements and mappings of emission line shifts in the intracluster medium (ICM). Such direct measurements can serve as unique probes of turbulent motions in the ICM. Determining the level and scales of turbulence will improve our understanding of the galaxy cluster dynamical evolution and assembly, together with a more precise evaluation of the non thermal support pressure budget. This will allow for more accurate constraints to be placed on the masses of galaxy clusters, among other potential benefits. Aims. In this view, we implemented the methods presented in the previous instalments of our work to characterising the turbulence in the intra-cluster medium in a feasibility study with the X-ray Integral Field Unit (X-IFU) on board the future European X-ray observatory, Athena. Methods. From idealized mock observations of a toy model cluster, we reconstructed the second-order structure function built with the observed velocity field to constrain the turbulence. We carefully accounted for the various sources of errors to derive the most realistic and comprehensive error budget within the limits of our approach. With prior assumptions on the dissipation scale and power spectrum slope, we constrained the parameters of the turbulent power spectrum model through the use of Markov chain Monte Carlo (MCMC) sampling. Results. With a very long exposure time, a favourable configuration, and a prior assumption of the dissipation scale, we were able to retrieve the injection scale, velocity dispersion, and power spectrum slope, with 1σ uncertainties for better than ∼15% of the input values. We demonstrated the efficiency of our carefully set framework to constrain the turbulence in the ICM from high-resolution X-ray spectroscopic observations, paving the way for more in-depth investigation of the optimal required observing strategy within a more restrictive observational setup with the future Athena/X-IFU instrument.