ORCID Profile
0000-0002-1600-7552
Current Organisation
Princeton University
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Publisher: Oxford University Press (OUP)
Date: 13-03-2020
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 $\\mathcal {M}$.
Publisher: Oxford University Press (OUP)
Date: 11-12-2021
Abstract: Turbulence in the intracluster medium (ICM) is driven by active galactic nuclei (AGNs) jets, by mergers, and in the wakes of infalling galaxies. It not only governs gas motion but also plays a key role in the ICM thermodynamics. Turbulence can help seed thermal instability by generating density fluctuations, and mix the hot and cold phases together to produce intermediate temperature gas (104–107 K) with short cooling times. We conduct high resolution (3843–7683 resolution elements) idealized simulations of the multiphase ICM and study the effects of turbulence strength, characterized by fturb (0.001–1.0), the ratio of turbulent forcing power to the net radiative cooling rate. We analyse density and temperature distribution, litude and nature of gas perturbations, and probability of transitions across the temperature phases. We also study the effects of mass and volume weighted thermal heating and weak ICM magnetic fields. For low fturb, the gas is distribution is bimodal between the hot and cold phases. The mixing between different phases becomes more efficient with increasing fturb, producing larger amounts of the intermediate temperature gas. Strong turbulence (fturb ≥ 0.5) generates larger density fluctuations and faster cooling, The rms logarithmic pressure fluctuation scaling with Mach number $\\sigma _{\\ln {\\bar{P}}}^2\\approx \\ln (1+b^2\\gamma ^2\\mathcal {M}^4)$ is unaffected by thermal instability and is the same as in hydro turbulence. In contrast, the density fluctuations characterized by $\\sigma _s^2$ are much larger, especially for $\\mathcal {M}\\lesssim 0.5$. In magnetohydrodynamic runs, magnetic fields provide significant pressure support in the cold phase but do not have any strong effects on the diffuse gas distribution, and nature and litude of fluctuations.
Publisher: Oxford University Press (OUP)
Date: 25-08-2023
Abstract: Gas in the central regions of cool-core clusters and other massive halos has a short cooling time (≲ 1 Gyr). Theoretical models predict that this gas is susceptible to multiphase condensation, in which cold gas is expected to condense out of the hot phase if the ratio of the thermal instability growth time scale (tti) to the free-fall time (tff) is tti/tff ≲ 10. The turbulent mixing time tmix is another important time scale: if tmix is short enough, the fluctuations are mixed before they can cool. In this study, we perform high-resolution (5122 × 768–10242 × 1536 resolution elements) hydrodynamic simulations of turbulence in a stratified medium, including radiative cooling of the gas. We explore the parameter space of tti/tff and tti/tmix relevant to galaxy and cluster halos. We also study the effect of the steepness of the entropy profile, the strength of turbulent forcing and the nature of turbulent forcing (natural mixture vs. compressive modes) on multiphase gas condensation. We find that larger values of tti/tff or tti/tmix generally imply stability against multiphase gas condensation, whereas larger density fluctuations (e.g., due to compressible turbulence) promote multiphase gas condensation. We propose a new criterion min (tti/min (tmix, tff)) ≲ c2 × exp (c1σs) for when the halo becomes multiphase, where σs denotes the litude of logarithmic density fluctuations and c1 ≃ 6, c2 ≃ 1.8 from an empirical fit to our results.
Publisher: Informa UK Limited
Date: 06-04-2021
Publisher: MDPI AG
Date: 04-08-2021
Abstract: This study investigates young Korean children’s attitudes toward three English varieties: American English (AmE), Singapore English (SiE), and Korean English (KoE). A total of 42 Korean children participated in this study. For data analysis purposes, the results were categorized according to the children’s age and their experience of exposure to formal English learning. In addition to this, 30 Singaporean children were also involved in the study, and their results were compared with the results of the younger group of Korean children. A mixed methodological approach, which included a modified verbal guise technique appropriate for use with children and semi-structured interviews, was also adopted. The results show that 5-year-old Korean and Singaporean children do not prefer one specific variety of English more than the other varieties of English. However, this was not the case for 12-year-old Korean children. These older Korean children preferred AmE and SiE more than KoE, and the “speaker’s pronunciation” was considered to be the critical feature in determining these attitudes. The findings suggest that Korean children’s developing attitudes toward a particular variety of English emerge sometime during their elementary school years.
Publisher: Oxford University Press (OUP)
Date: 27-11-2021
Abstract: The central regions of cool-core galaxy clusters harbour multiphase gas, with gas temperatures ranging from $10$ to $10^7\\, \\mathrm{K}$. Feedback from active galactic nuclei jets prevents the gas from undergoing a catastrophic cooling flow. However, the exact mechanism of this feedback energy input is unknown, mainly due to the lack of velocity measurements of the hot-phase gas. However, recent observations have measured the velocity structure functions (VSFs) of the cooler molecular (${\\sim} 10\\, \\mathrm{K}$) and Hα filaments (${\\sim} 10^4\\, \\mathrm{K}$) and used them to indirectly estimate the motions of the hot phase. In the first part of this study, we conduct high-resolution (3843–15363 resolution elements) simulations of homogeneous isotropic subsonic turbulence, without radiative cooling. We analyse the second-order velocity structure functions (VSF2) in these simulations and study the effects of varying spatial resolution, the introduction of magnetic fields, and the effect of projection along the line of sight (LOS) on it. In the second part of the study, we analyse high-resolution (7683 resolution elements) idealized simulations of multiphase turbulence in the intracluster medium from the companion study Mohapatra et al. We compare the VSF2 for both the hot ($T\\sim 10^7\\, \\mathrm{K}$) and cold ($T\\sim 10^4\\, \\mathrm{K}$) phases and find that their litude depends on the density contrast between the phases. They have similar scaling with separation, but introducing magnetic fields steepens the VSF2 of only the cold phase. We also find that projection along the LOS steepens the VSF2 for the hot phase and mostly flattens it for the cold phase.
Publisher: Oxford University Press (OUP)
Date: 18-11-2020
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.
Publisher: Oxford University Press (OUP)
Date: 02-2019
DOI: 10.1093/MNRAS/STZ328
Publisher: Oxford University Press (OUP)
Date: 07-07-2023
Abstract: It has been shown that the gas velocities within the intracluster medium (ICM) can be measured by applying the novel XMM–Newton EPIC-pn energy scale calibration, which uses instrumental Cu Kα as reference for the line emission. Using this technique, we have measured the velocity distribution of the ICM for clusters involving AGN feedback and sloshing of the plasma within the gravitational well (Virgo and Centaurus) and a relaxed one (Ophiuchus). We present a detailed study of the kinematics of the hot ICM for these systems. First, we compute the velocity probability distribution functions (PDFs) from the velocity maps. We find that for all sources, the PDF follows a normal distribution, with a hint of a multimodal distribution in the case of Ophiuchus. Then, we compute the velocity structure function (VSF) for all sources in order to study the variation with scale as well as the nature of turbulence in the ICM. We measure a turbulence driving scale of ∼10–20 kpc for the Virgo cluster, while the Ophiuchus cluster VSF reflects the absence of strong interaction between the ICM and a powerful Active Galactic Nucleus (AGN) at such spatial scales. For the former, we compute a dissipation time larger than the jet activity cycle, thus indicating that a more efficient heating process than turbulence is required to reach equilibrium. This is the first time that the VSF of the hot ICM has been computed using direct velocity measurements from X-ray astronomical observations.
Publisher: Oxford University Press (OUP)
Date: 14-06-2022
Abstract: Supernova explosions, active galactic nuclei jets, galaxy–galaxy interactions, and cluster mergers can drive turbulence in the circumgalactic medium (CGM) and the intracluster medium (ICM). However, the exact nature of turbulence forced by these sources and its impact on the different statistical properties of the CGM/ICM and their global thermodynamics is still unclear. To investigate the effects of different types of forcing, we conduct high-resolution (10083 resolution elements) idealized hydrodynamic simulations with purely solenoidal ( ergence-free) forcing, purely compressive (curl-free) forcing, and natural mixture forcing (equal fractions of the two components). The simulations also include radiative cooling. We study the impact of the three different forcing modes (sol, comp, and mix) on the morphology of the gas, its temperature and density distributions, sources and sinks of enstrophy, i.e. solenoidal motions, as well as the kinematics of hot (∼107 K) X-ray emitting and cold (∼104 K) H α emitting gas. We find that compressive forcing leads to stronger variations in density and temperature of the gas as compared to solenoidal forcing. The cold phase gas forms large-scale filamentary structures for compressive forcing and misty, small-scale clouds for solenoidal forcing. The cold phase gas has stronger large-scale velocities for compressive forcing. The natural mixture forcing shows kinematics and gas distributions intermediate between the two extremes, the cold-phase gas occurs as both large-scale filaments and small-scale misty clouds.
No related grants have been discovered for Rajsekhar Mohapatra.