Turbulence in stratified atmospheres: implications for the intracluster medium

ABSTRACT The gas motions in the intracluster medium (ICM) are governed by turbulence. However, since the ICM has a radial profile with the centre being denser than the outskirts, ICM turbulence is stratified. Stratified turbulence is fundamentally different from Kolmogorov (isotropic, homogeneous) turbulence; kinetic energy not only cascades from large to small scales, but it is also converted into buoyancy potential energy. To understand the density and velocity fluctuations in the ICM, we conduct high-resolution (10242 × 1536 grid points) hydrodynamical simulations of subsonic turbulence (with rms Mach number $\mathcal {M}\approx 0.25$) and different levels of stratification, quantified by the Richardson number Ri, from Ri = 0 (no stratification) to Ri = 13 (strong stratification). We quantify the density, pressure, and velocity fields for varying stratification because observational studies often use surface brightness fluctuations to infer the turbulent gas velocities of the ICM. We find that the standard deviation of the logarithmic density fluctuations (σs), where s = ln (ρ/ < ρ($z$) >), increases with Ri. For weakly stratified subsonic turbulence (Ri ≲ 10, $\mathcal {M}\lt 1$), we derive a new σs–$\mathcal {M}$–Ri relation, $\sigma _\mathrm{ s}^2=\ln (1+b^2\mathcal {M}^4+0.09\mathcal {M}^2 \mathrm{Ri} H_\mathrm{ P}/H_\mathrm{ S})$, where b = 1/3–1 is the turbulence driving parameter, and HP and HS are the pressure and entropy scale heights, respectively. We further find that the power spectrum of density fluctuations, P(ρk/ < ρ >), increases in magnitude with increasing Ri. Its slope in k-space flattens with increasing Ri before steepening again for Ri ≳ 1. In contrast to the density spectrum, the velocity power spectrum is invariant to changes in the stratification. Thus, we find that the ratio between density and velocity power spectra strongly depends on Ri, with the total power in density and velocity fluctuations described by our σs–$\mathcal {M}$–Ri relation. Pressure fluctuations, on the other hand, are independent of stratification and only depend on $\mathcal {M}$.

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New constraints on the mass bias of galaxy clusters from the power spectra of the thermal Sunyaev–Zeldovich effect and cosmic shear

Publications of the Astronomical Society of Japan ◽

10.1093/pasj/psz147 ◽

2020 ◽

Vol 72 (2) ◽

Cited By ~ 3

Author(s):

Ryu Makiya ◽

Chiaki Hikage ◽

Eiichiro Komatsu

Keyword(s):

Power Spectrum ◽

Galaxy Clusters ◽

Cosmological Parameters ◽

Power Spectra ◽

Matter Density ◽

Density Fluctuations ◽

Microwave Background ◽

Mass Bias ◽

Cosmic Shear ◽

Hydrodynamical Simulations

Abstract The thermal Sunyaev–Zeldovich (tSZ) power spectrum is a powerful probe of the present-day amplitude of matter density fluctuations, and has been measured up to $\ell \approx 10^3$ from the Planck data. The largest systematic uncertainty in the interpretation of this data is the so-called “mass bias” parameter B, which relates the true halo mass to the mass proxy used by the Planck team as $M\,_{\rm 500c}^{\rm Planck}=M\,_{\rm 500c}^{\rm true}/B$. Since the power spectrum of the cosmic weak lensing shear is also sensitive to the amplitude of matter density fluctuations via $S_8\equiv \sigma _8 \Omega _{\rm m}^{\alpha }$ with $\alpha \sim 0.5$, we can break the degeneracy between the mass bias and the cosmological parameters by combining the tSZ and cosmic shear power spectra. In this paper, we perform a joint likelihood analysis of the tSZ power spectrum from Planck and the cosmic shear power spectrum from Subaru Hyper Suprime-Cam. Our analysis does not use the primordial cosmic microwave background (CMB) information. We obtain a new constraint on the mass bias as $B = 1.37 ^{+0.15}_{-0.23}$ or $(1-b) = B^{-1}=0.73^{+0.08}_{-0.13}$ ($68\%$ confidence limit), for $\sigma _8 < 0.9$. This value of B is lower than that needed to reconcile the tSZ data with the primordial CMB and CMB lensing data, i.e., $B = 1.64 \pm 0.19$, but is consistent with the mass bias expected from hydrodynamical simulations, $B = 1.28 \pm 0.20$. Thus our results indicate that the mass bias is consistent with the non-thermal pressure support from mass accretion of galaxy clusters via the cosmic structure formation, and that the cosmologies inferred from the tSZ and the cosmic shear are consistent with each other.

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The anisotropy of the power spectrum in periodic cosmological simulations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab874 ◽

2021 ◽

Vol 503 (4) ◽

pp. 5638-5645

Author(s):

Gábor Rácz ◽

István Szapudi ◽

István Csabai ◽

László Dobos

Keyword(s):

Dark Matter ◽

Power Spectrum ◽

Large Scale ◽

Cold Dark Matter ◽

Initial Conditions ◽

Power Spectra ◽

Cosmological Simulations ◽

Spherical Collapse ◽

Lower Amplitude ◽

Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

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Kinetic field theory: Non-linear cosmic power spectra in the mean-field approximation

SciPost Physics ◽

10.21468/scipostphys.10.6.153 ◽

2021 ◽

Vol 10 (6) ◽

Author(s):

Matthias Bartelmann ◽

Johannes Dombrowski ◽

Sara Konrad ◽

Elena Kozlikin ◽

Robert Lilow ◽

...

Keyword(s):

Field Theory ◽

Power Spectrum ◽

Mean Field ◽

Power Spectra ◽

Field Approximation ◽

Density Fluctuations ◽

Mean Field Approximation ◽

Non Linear ◽

Two Parameters ◽

Kinetic Field

We use the recently developed Kinetic Field Theory (KFT) for cosmic structure formation to show how non-linear power spectra for cosmic density fluctuations can be calculated in a mean-field approximation to the particle interactions. Our main result is a simple, closed and analytic, approximate expression for this power spectrum. This expression has two parameters characterising non-linear structure growth which can be calibrated within KFT itself. Using this self-calibration, the non-linear power spectrum agrees with results obtained from numerical simulations to within typically \lesssim10\,\%≲10% up to wave numbers k\lesssim10\,h\,\mathrm{Mpc}^{-1}k≲10hMpc−1 at redshift z = 0z=0. Adjusting the two parameters to optimise agreement with numerical simulations, the relative difference to numerical results shrinks to typically \lesssim 5\,\%≲5%. As part of the derivation of our mean-field approximation, we show that the effective interaction potential between dark-matter particles relative to Zel’dovich trajectories is sourced by non-linear cosmic density fluctuations only, and is approximately of Yukawa rather than Newtonian shape.

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The lensing properties of subhaloes in massive elliptical galaxies in sterile neutrino cosmologies

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3068 ◽

2019 ◽

Vol 491 (1) ◽

pp. 1295-1310 ◽

Cited By ~ 4

Author(s):

Giulia Despali ◽

Mark Lovell ◽

Simona Vegetti ◽

Robert A Crain ◽

Benjamin D Oppenheimer

Keyword(s):

Dark Matter ◽

Power Spectrum ◽

Galaxy Formation ◽

Cold Dark Matter ◽

Distribution Density ◽

Sterile Neutrino ◽

Power Spectra ◽

Mass Function ◽

Elliptical Galaxies ◽

Hydrodynamical Simulations

ABSTRACT We use high-resolution hydrodynamical simulations run with the EAGLE model of galaxy formation to study the differences between the properties of – and subsequently the lensing signal from – subhaloes of massive elliptical galaxies at redshift 0.2, in Cold and Sterile Neutrino (SN) Dark Matter models. We focus on the two 7 keV SN models that bracket the range of matter power spectra compatible with resonantly produced SN as the source of the observed 3.5 keV line. We derive an accurate parametrization for the subhalo mass function in these two SN models relative to cold dark matter (CDM), as well as the subhalo spatial distribution, density profile, and projected number density and the dark matter fraction in subhaloes. We create mock lensing maps from the simulated haloes to study the differences in the lensing signal in the framework of subhalo detection. We find that subhalo convergence is well described by a lognormal distribution and that signal of subhaloes in the power spectrum is lower in SN models with respect to CDM, at a level of 10–80 per cent, depending on the scale. However, the scatter between different projections is large and might make the use of power spectrum studies on the typical scales of current lensing images very difficult. Moreover, in the framework of individual detections through gravitational imaging a sample of ≃30 lenses with an average sensitivity of $M_{\rm {sub}} = 5 \times 10^{7}\, {\rm M}_{\odot}$ would be required to discriminate between CDM and the considered sterile neutrino models.

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The impact of the observed baryon distribution in haloes on the total matter power spectrum

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz3446 ◽

2019 ◽

Vol 492 (2) ◽

pp. 2285-2307 ◽

Cited By ~ 11

Author(s):

Stijn N B Debackere ◽

Joop Schaye ◽

Henk Hoekstra

Keyword(s):

Dark Matter ◽

Power Spectrum ◽

Gas Content ◽

Total Power ◽

X Ray ◽

Hot Gas ◽

Matter Power Spectrum ◽

Hydrodynamical Simulations ◽

Halo Masses ◽

The Impact

ABSTRACT The interpretation of upcoming weak gravitational lensing surveys depends critically on our understanding of the matter power spectrum on scales $k \lt 10\, {h\, {\rm Mpc}^{-1}}$, where baryonic processes are important. We study the impact of galaxy formation processes on the matter power spectrum using a halo model that treats the stars and gas separately from the dark matter distribution. We use empirical constraints from X-ray observations (hot gas) and halo occupation distribution modelling (stars) for the baryons. Since X-ray observations cannot generally measure the hot gas content outside r500c, we vary the gas density profiles beyond this radius. Compared with dark matter only models, we find a total power suppression of $1\, {\mathrm{per\ cent}}$ ($5\, {\mathrm{per\ cent}}$) on scales $0.2\!-\!1\, {h\, {\rm Mpc}^{-1}}$ ($0.5\!-\!2\, {h\, {\rm Mpc}^{-1}}$), where lower baryon fractions result in stronger suppression. We show that groups of galaxies ($10^{13} \lt m_{\mathrm{500c}} / (h^{-1}\, \mathrm{M}_{\odot }) \lt 10^{14}$) dominate the total power at all scales $k \lesssim 10\, {h\, {\rm Mpc}^{-1}}$. We find that a halo mass bias of $30\, {\mathrm{per\ cent}}$ (similar to what is expected from the hydrostatic equilibrium assumption) results in an underestimation of the power suppression of up to $4\, {\mathrm{per\ cent}}$ at $k=1\, {h\, {\rm Mpc}^{-1}}$, illustrating the importance of measuring accurate halo masses. Contrary to work based on hydrodynamical simulations, our conclusion that baryonic effects can no longer be neglected is not subject to uncertainties associated with our poor understanding of feedback processes. Observationally, probing the outskirts of groups and clusters will provide the tightest constraints on the power suppression for $k \lesssim 1\, {h\, {\rm Mpc}^{-1}}$.

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Modelling baryonic physics in future weak lensing surveys

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1714 ◽

2019 ◽

Vol 488 (2) ◽

pp. 1652-1678 ◽

Cited By ~ 17

Author(s):

Hung-Jin Huang ◽

Tim Eifler ◽

Rachel Mandelbaum ◽

Scott Dodelson

Keyword(s):

Power Spectrum ◽

Cosmological Parameters ◽

Power Spectra ◽

Principal Component ◽

Weak Lensing ◽

Survey Statistics ◽

Simulated Likelihood ◽

Pca Method ◽

Hydrodynamical Simulations ◽

Parameter Constraints

Abstract Modifications of the matter power spectrum due to baryonic physics are one of the major theoretical uncertainties in cosmological weak lensing measurements. Developing robust mitigation schemes for this source of systematic uncertainty increases the robustness of cosmological constraints, and may increase their precision if they enable the use of information from smaller scales. Here we explore the performance of two mitigation schemes for baryonic effects in weak lensing cosmic shear: the principal component analysis (PCA) method and the halo-model approach in hmcode. We construct mock tomographic shear power spectra from four hydrodynamical simulations, and run simulated likelihood analyses with cosmolike assuming LSST-like survey statistics. With an angular scale cut of ℓmax < 2000, both methods successfully remove the biases in cosmological parameters due to the various baryonic physics scenarios, with the PCA method causing less degradation in the parameter constraints than hmcode. For a more aggressive ℓmax = 5000, the PCA method performs well for all but one baryonic physics scenario, requiring additional training simulations to account for the extreme baryonic physics scenario of Illustris; hmcode exhibits tensions in the 2D posterior distributions of cosmological parameters due to lack of freedom in describing the power spectrum for $k \gt 10\ h^{-1}\, \mathrm{Mpc}$. We investigate variants of the PCA method and improve the bias mitigation through PCA by accounting for the noise properties in the data via Cholesky decomposition of the covariance matrix. Our improved PCA method allows us to retain more statistical constraining power while effectively mitigating baryonic uncertainties even for a broad range of baryonic physics scenarios.

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Turbulent density and pressure fluctuations in the stratified intracluster medium

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3564 ◽

2020 ◽

Vol 500 (4) ◽

pp. 5072-5087

Author(s):

Rajsekhar Mohapatra ◽

Christoph Federrath ◽

Prateek Sharma

Keyword(s):

Surface Brightness ◽

Isotropic Turbulence ◽

Pressure Fluctuations ◽

Density Fluctuations ◽

Turbulence Theory ◽

Intracluster Medium ◽

Stratified Turbulence ◽

Hydrodynamic Simulations ◽

Pressure Scale ◽

Parameter Ranges

ABSTRACT Turbulent gas motions are observed in the intracluster medium (ICM). The ICM is density-stratified, with the gas density being highest at the centre of the cluster and decreasing radially outwards. As a result of this, Kolmogorov (homogeneous, isotropic) turbulence theory does not apply to the ICM. The gas motions are instead explained by anisotropic stratified turbulence, with the stratification quantified by the perpendicular Froude number (Fr⊥). These turbulent motions are associated with density and pressure fluctuations, which manifest as perturbations in X-ray surface brightness maps of the ICM and as thermal Sunyaev–Zeldovich effect (SZ) fluctuations, respectively. In order to advance our understanding of the relations between these fluctuations and the turbulent gas velocities, we have conducted 100 high-resolution hydrodynamic simulations of stratified turbulence (2562 × 384–10242 × 1536 resolution elements), in which we scan the parameter space of subsonic rms Mach number ($\mathcal {M}$), Fr⊥, and the ratio of entropy and pressure scale heights (RPS = HP/HS), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations (σs, where s = ln (ρ/$\langle$ρ$\rangle$)), $\mathcal {M}$, and Fr⊥, which covers both the strongly stratified (Fr⊥ ≪ 1) and weakly stratified (Fr⊥ ≫ 1) turbulence regimes: $\sigma _{\rm s}^2=\ln (1+b^2\mathcal {M}^4+0.10/(\mathrm{Fr}_\perp +0.25/\sqrt{\mathrm{Fr}_\perp })^2\mathcal {M}^2R_{\rm PS})$, where b ∼ 1/3 for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations σ(ln P/ < P >) are independent of stratification and scale according to the relation $\sigma _{(\ln {\bar{P}})}^2=\ln (1+b^2\gamma ^2\mathcal {M}^4)$, where $\bar{P}=P/\left\langle P \right\rangle $ and γ is the adiabatic index of the gas. We have tested these scaling relations to be valid over the parameter ranges $\mathcal {M} = 0.01$–0.40, Fr⊥ = 0.04–10.0, and RPS = 0.33–2.33.

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hmcode-2020: improved modelling of non-linear cosmological power spectra with baryonic feedback

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab082 ◽

2021 ◽

Vol 502 (1) ◽

pp. 1401-1422

Author(s):

A J Mead ◽

S Brieden ◽

T Tröster ◽

C Heymans

Keyword(s):

Power Spectrum ◽

Equations Of State ◽

Power Spectra ◽

Acoustic Oscillation ◽

Worst Case ◽

Wide Range ◽

Non Linear ◽

Hydrodynamical Simulations ◽

Energy Equations ◽

The Impact

ABSTRACT We present an updated version of the hmcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of baryon-acoustic oscillation (BAO) damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an root mean square (RMS) error of 2.5 per cent across a range of cosmologies, scales $k \lt 10\, h\, \mathrm{Mpc}^{-1}$, and redshifts z < 2. The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors occur at z ≃ 2, or for cosmologies with unusual dark energy equations of state. This represents a significant improvement over previous versions of hmcode, and over other popular fitting functions, particularly for massive-neutrino cosmologies with high neutrino mass. We also present a simple halo model that can be used to model the impact of baryonic feedback on the power spectrum. This six-parameter physical model includes gas expulsion by active galactic nuclei (AGN) feedback and encapsulates star formation. By comparing this model to data from hydrodynamical simulations, we demonstrate that the power spectrum response to feedback is matched at the <1 per cent level for z < 1 and $k\lt 20\, h\, \mathrm{Mpc}^{-1}$. We also present a single-parameter variant of this model, parametrized in terms of feedback strength, which is only slightly less accurate. We make code available for our non-linear and baryon models at https://github.com/alexander-mead/HMcode and it is also available within camb and soon within class.

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Sub-ion scale measurements of compressible turbulence in the solar wind MMS Observations

10.5194/egusphere-egu2020-6815 ◽

2020 ◽

Author(s):

Owen Roberts ◽

Rumi Nakamura ◽

Yasuhito Narita ◽

Justin Holmes ◽

Zoltan Voros ◽

...

Keyword(s):

Magnetic Field ◽

Solar Wind ◽

Power Spectrum ◽

Electron Density ◽

Field Measurements ◽

Small Region ◽

Density Fluctuations ◽

Compressible Turbulence ◽

Density Spectrum ◽

Spacecraft Potential

<p>Compressible plasma turbulence is investigated at sub ion scales using both the Fast Plasma Investigation instrument on the Magnetospheric MultiScale mission as well as using calibrated spacecraft potential. The data from FPI allow inertial and a small region of sub-ion scales to be investigated before the instrumental noise becomes significant near 3Hz. In this work we give a detailed description of the spacecraft potential and how it is calibrated such that it can be used the measure the electron density. The key advantage of using the calibrated spacecraft potential is that a much higher time resolution is possible when compared to the direct measurement. This allows a measurement down to 40Hz for a measurement of the electron density. This is an improvement of an additional decade in scale. Using a one hour interval of solar wind burst mode data the power spectrum of the density fluctuations is measured from the inertial range to the sub ion range. At inertial scales the density spectrum shows similarities with the magnetic field power spectrum with a characteristic Kolmogorov like power law. In between the ion inertial and kinetic scales there is a brief flattening in the spectra before steepening in the sub ion range to a spectral index comparable to the trace magnetic field fluctuations. The morphology if the density spectra can be explained by either a cascade of Alfv\'en waves and slow waves at large scales and kinetic Alfv\'en waves at sub ion scales, or by the presence of the hall effect. Using electric field measurements the two hypotheses are tested.</p>

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On the ion-inertial-range density-power spectra in solar wind turbulence

Annales Geophysicae ◽

10.5194/angeo-37-183-2019 ◽

2019 ◽

Vol 37 (2) ◽

pp. 183-199 ◽

Cited By ~ 2

Author(s):

Rudolf A. Treumann ◽

Wolfgang Baumjohann ◽

Yasuhito Narita

Keyword(s):

Solar Wind ◽

Source Region ◽

Power Spectra ◽

Density Fluctuations ◽

Inertial Range ◽

Wave Number ◽

Mean Flow ◽

Pressure Balance ◽

Density Spectrum ◽

Velocity Turbulence

Abstract. A model-independent first-principle first-order investigation of the shape of turbulent density-power spectra in the ion-inertial range of the solar wind at 1 AU is presented. Demagnetised ions in the ion-inertial range of quasi-neutral plasmas respond to Kolmogorov (K) or Iroshnikov–Kraichnan (IK) inertial-range velocity–turbulence power spectra via the spectrum of the velocity–turbulence-related random-mean-square induction–electric field. Maintenance of electrical quasi-neutrality by the ions causes deformations in the power spectral density of the turbulent density fluctuations. Assuming inertial-range K (IK) spectra in solar wind velocity turbulence and referring to observations of density-power spectra suggest that the occasionally observed scale-limited bumps in the density-power spectrum may be traced back to the electric ion response. Magnetic power spectra react passively to the density spectrum by warranting pressure balance. This approach still neglects contribution of Hall currents and is restricted to the ion-inertial-range scale. While both density and magnetic turbulence spectra in the affected range of ion-inertial scales deviate from K or IK power law shapes, the velocity turbulence preserves its inertial-range shape in the process to which spectral advection turns out to be secondary but may become observable under special external conditions. One such case observed by WIND is analysed. We discuss various aspects of this effect, including the affected wave-number scale range, dependence on the angle between mean flow velocity and wave numbers, and, for a radially expanding solar wind flow, assuming adiabatic expansion at fast solar wind speeds and a Parker dependence of the solar wind magnetic field on radius, also the presumable limitations on the radial location of the turbulent source region.

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