arXiv subjects

S. Peng Oh

Publications and source records attributed to S. Peng Oh.

At least 37 records · Page 2Linked to original sources

arXiv2023

Cosmic Ray Drag and Damping of Compressive Turbulence

While it is well-known that cosmic rays (CRs) can gain energy from turbulence via second order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping time $t_{\rm damp} \sim ρv^{2}/\dot{E}_{\rm CR} \propto E_{\rm CR}^{-1}$ becomes comparable to the turbulent cascade time. Magnetohydrodynamic (MHD) simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating at $\dot{E}_{\rm CR} \sim \tildeε$, where $\tildeε$ is the turbulent energy input rate. In that case, almost all the energy in large scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge-Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering of $E > 300$ GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large scale motions, with kinetic energy reduced by up to to an order of magnitude in realistic $E_{\rm CR} \sim E_{\rm g}$ scenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e. $\tildeε \gg ρv^{3}/L$.

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arXiv2023

Cooling driven coagulation

Astrophysical gases such as the interstellar-, circumgalactic- or intracluster-medium are commonly multiphase, which poses the question of the structure of these systems. While there are many known processes leading to fragmentation of cold gas embedded in a (turbulent) hot medium, in this work, we focus on the reverse process: coagulation. This is often seen in wind-tunnel and shearing layer simulations, where cold gas fragments spontaneously coalesce. Using 2D and 3D hydrodynamical simulations, we find that sufficiently large ($\gg c_{\rm s} t_{\rm cool}$), perturbed cold gas clouds develop pulsations which ensure cold gas mass growth over an extended period of time ($\gg r / c_{\rm s}$). This mass growth efficiently accelerates hot gas which in turn can entrain cold droplets, leading to coagulation. The attractive inverse square force between cold gas droplets has interesting parallels with gravity; the `monopole' is surface area rather than mass. We develop a simple analytic model which reproduces our numerical findings.

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arXiv2023

The Impact of Cosmic Rays on Thermal and Hydrostatic Stability in Galactic Halos

We investigate how cosmic rays (CRs) affect thermal and hydrostatic stability of circumgalactic (CGM) gas, in simulations with both CR streaming and diffusion. Local thermal instability can be suppressed by CR-driven entropy mode propagation, in accordance with previous analytic work. However, there is only a narrow parameter regime where this operates, before CRs overheat the background gas. As mass dropout from thermal instability causes the background density and hence plasma $β\equiv P_g/P_B$ to fall, the CGM becomes globally unstable. At the cool disk to hot halo interface, a sharp drop in density boosts Alfven speeds and CR gradients, driving a transition from diffusive to streaming transport. CR forces and heating strengthen, while countervailing gravitational forces and radiative cooling weaken, resulting in a loss of both hydrostatic and thermal equilibrium. In lower $β$ halos, CR heating drives a hot, single-phase diffuse wind with velocities $v \propto (t_\mathrm{heat}/t_\mathrm{ff})^{-1}$, which exceeds the escape velocity when $t_\mathrm{heat}/t_\mathrm{ff} \lesssim 0.4$. In higher $β$ halos, CR forces drive multi-phase winds with cool, dense fountain flows and significant turbulence. These flows are CR dominated due to "trapping" of CRs by weak transverse B-fields, and have the highest mass loading factors. Thus, local thermal instability can result in winds or fountain flows where either the heat or momentum input of CRs dominates.

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arXiv2023

Key Physical Processes in the Circumgalactic Medium

Spurred by rich, multi-wavelength observations and enabled by new simulations, ranging from cosmological to sub-pc scales, the last decade has seen major theoretical progress in our understanding of the circumgalactic medium. We review key physical processes in the CGM. Our conclusions include: (1) The properties of the CGM depend on a competition between gravity-driven infall and gas cooling. When cooling is slow relative to free fall, the gas is hot (roughly virial temperature) whereas the gas is cold (T~10^4 K) when cooling is rapid. (2) Gas inflows and outflows play crucial roles, as does the cosmological environment. Large-scale structure collimates cold streams and provides angular momentum. Satellite galaxies contribute to the CGM through winds and gas stripping. (3) In multiphase gas, the hot and cold phases continuously exchange mass, energy and momentum. The interaction between turbulent mixing and radiative cooling is critical. A broad spectrum of cold gas structures, going down to sub-pc scales, arises from fragmentation, coagulation, and condensation onto gas clouds. (4) Magnetic fields, thermal conduction and cosmic rays can substantially modify how the cold and hot phases interact, although microphysical uncertainties are presently large. Key open questions for future work include the mutual interplay between small-scale structure and large-scale dynamics, and how the CGM affects the evolution of galaxies.

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arXiv2023

Cloudy with A Chance of Rain: Accretion Braking of Cold Clouds

Understanding the survival, growth and dynamics of cold gas is fundamental to galaxy formation. While there has been a plethora of work on `wind tunnel' simulations that study such cold gas in winds, the infall of this gas under gravity is at least equally important, and fundamentally different since cold gas can never entrain. Instead, velocity shear increases and remains unrelenting. If these clouds are growing, they can experience a drag force due to the accretion of low momentum gas, which dominates over ram pressure drag. This leads to sub-virial terminal velocities, in line with observations. We develop simple analytic theory and predictions based on turbulent radiative mixing layers. We test these scalings in 3D hydrodynamic simulations, both for an artificial constant background, as well as a more realistic stratified background. We find that the survival criterion for infalling gas is more stringent than in a wind, requiring that clouds grow faster than they are destroyed ($t_{\rm grow} < 4\,t_{\rm cc} $). This can be translated to a critical pressure, which for Milky Way like conditions is $P \sim 3000 {\rm k}_B {\rm K}\,{\rm cm}^{-3}$ . Cold gas which forms via linear thermal instability ($t_{\rm cool}/t_{\rm ff} < 1$) in planar geometry meets the survival threshold. In stratified environments, larger clouds need only survive infall until cooling becomes effective. We discuss applications to high velocity clouds and filaments in galaxy clusters.

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arXiv2023

Turbulent Reacceleration of Streaming Cosmic Rays

Subsonic, compressive turbulence transfers energy to cosmic rays (CRs), a process known as non-resonant reacceleration. It is often invoked to explain observed ratios of primary to secondary CRs at $\sim \rm GeV$ energies, assuming wholly diffusive CR transport. However, such estimates ignore the impact of CR self-confinement and streaming. We study these issues in stirring box magnetohydrodynamic (MHD) simulations using Athena++, with field-aligned diffusive and streaming CR transport. For diffusion only, we find CR reacceleration rates in good agreement with analytic predictions. When streaming is included, reacceleration rates depend on plasma $β$. Due to streaming-modified phase shifts between CR and gas variables, they are slower than canonical reacceleration rates in low-$β$ environments like the interstellar medium (ISM) but remain unchanged in high-$β$ environments like the intracluster medium (ICM). We also quantify the streaming energy loss rate in our simulations. For sub-Alfvénic turbulence, it is resolution-dependent (hence unconverged in large scale simulations) and heavily suppressed -- by an order of magnitude -- compared to the isotropic loss rate $v_{A} \cdot \nabla P_{\rm CR} / P_{\rm CR} \sim v_{A}/L_{0}$, due to misalignment between the mean field and isotropic CR gradients. Counterintuitively, and unlike acceleration efficiencies, CR losses are almost independent of magnetic field strength over $β\sim 1-100$ and are, therefore, not the primary factor behind lower acceleration rates when streaming is included. While this paper is primarily concerned with how turbulence affects CRs, in a follow-up paper (Bustard and Oh, in prep), we consider how CRs affect turbulence by diverting energy from the MHD cascade, altering the pathway to gas heating and steepening the turbulent power spectrum.

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arXiv2022

Turbulent Heating in a Stratified Medium

There is considerable evidence for widespread subsonic turbulence in galaxy clusters, most notably from {\it Hitomi}. Turbulence is often invoked to offset radiative losses in cluster cores, both by direct dissipation and by enabling turbulent heat diffusion. However, in a stratified medium, buoyancy forces oppose radial motions, making turbulence anisotropic. This can be quantified via the Froude number ${\rm Fr}$, which decreases inward in clusters as stratification increases. We exploit analogies with MHD turbulence to show that wave-turbulence interactions increase cascade times and reduces dissipation rates $ε\propto {\rm Fr}$. Equivalently, for a given energy injection/dissipation rate $ε$, turbulent velocities $u$ must be higher compared to Kolmogorov scalings. High resolution hydrodynamic simulations show excellent agreement with the $ε\propto {\rm Fr}$ scaling, which sets in for ${\rm Fr} < 0.1$. We also compare previously predicted scalings for the turbulent diffusion coefficient $D \propto {\rm Fr}^2$ and find excellent agreement, for ${\rm Fr} < 1$. However, we find a different normalization, corresponding to stronger diffusive suppression by more than an order of magnitude. Our results imply that turbulent diffusion is more heavily suppressed by stratification, over a much wider radial range, than turbulent dissipation. Thus, the latter potentially dominates. Furthermore, this shift implies significantly higher turbulent velocities required to offset cooling, compared to previous models. These results are potentially relevant to turbulent metal diffusion (which is likewise suppressed), and to planetary atmospheres.

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arXiv2022

Survival and mass growth of cold gas in a turbulent, multiphase medium

Astrophysical gases are commonly multiphase and highly turbulent. In this work, we investigate the survival and growth of cold gas in such a turbulent, multi-phase medium using three-dimensional hydrodynamical simulations. Similar to previous work simulating coherent flow (winds), we find that cold gas survives if the cooling time of the mixed gas is shorter than the Kelvin-Helmholtz time of the cold gas clump (with some weak additional Mach number dependence). However, there are important differences. Near the survival threshold, the long-term evolution is highly stochastic, and subject to the existence of sufficiently large clumps. In a turbulent flow, the cold gas continuously fragments, enhancing its surface area. This leads to exponential mass growth, with a growth time given by the geometric mean of the cooling and the mixing time. The fragmentation process leads to a large number of small droplets which follow a scale-free $\mathrm{d} N/\mathrm{d} m \propto m^{-2}$ mass distribution, and dominate the area covering fraction. Thus, whilst survival depends on the presence of large `clouds', these in turn produce a `fog' of smaller droplets tightly coupled to the hot phase which are probed by absorption line spectroscopy. We show with the aid of Monte-Carlo simulations that the simulated mass distribution emerges naturally due to the proportional mass growth and the coagulation of droplets. We discuss the implications of our results for convergence criteria of larger scale simulations and observations of the circumgalactic medium.

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arXiv2021

A Model for Line Absorption and Emission from Turbulent Mixing Layers

Turbulent mixing layers (TMLs) are ubiquitous in multiphase gas. They can potentially explain observations of high ions such as O VI, which have significant observed column densities despite short cooling times. Previously, we showed that global mass, momentum and energy transfer between phases mediated by TMLs is not sensitive to details of thermal conduction or numerical resolution. By contrast, we show here that observables such as temperature distributions, column densities and line ratios are sensitive to such considerations. We explain the reason for this difference. We develop a prescription for applying a simple 1D conductive-cooling front model which quantitatively reproduces 3D hydrodynamic simulation results for column densities and line ratios, even when the TML has a complex fractal structure. This enables sub-grid absorption and emission line predictions in large scale simulations. The predicted line ratios are in good agreement with observations, while observed column densities require numerous mixing layers to be pierced along a line of sight.

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arXiv2021

The Cosmic Ray Staircase: the Outcome of the Cosmic Ray Acoustic Instability

Recently, cosmic rays (CRs) have emerged as a leading candidate for driving galactic winds. Small-scale processes can dramatically affect global wind properties. We run two-moment simulations of CR streaming to study how sound waves are driven unstable by phase-shifted CR forces and CR heating. We verify linear theory growth rates. As the sound waves grow non-linear, they steepen into a quasi-periodic series of propagating shocks; the density jumps at shocks create CR bottlenecks. The depth of a propagating bottleneck depends on both the density jump and its velocity; ΔP_c is smaller for rapidly moving bottlenecks. A series of bottlenecks creates a CR staircase structure, which can be understood from a convex hull construction. The system reaches a steady state between growth of new perturbations, and stair mergers. CRs are decoupled at plateaus, but exert intense forces and heating at stair jumps. The absence of CR heating at plateaus leads to cooling, strong gas pressure gradients and further shocks. If bottlenecks are stationary, they can drastically modify global flows; if their propagation times are comparable to dynamical times, their effects on global momentum and energy transfer are modest. The CR acoustic instability is likely relevant in thermal interfaces between cold and hot gas, as well as galactic winds. Similar to increased opacity in radiative flows, the build-up of CR pressure due to bottlenecks can significantly increase mass outflow rates, by up to an order of magnitude. It seeds unusual forms of thermal instability, and the shocks could have distinct observational signatures.

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arXiv2021

Radiative Mixing Layers: Insights from Turbulent Combustion

Radiative mixing layers arise wherever multiphase gas, shear, and radiative cooling are present. Simulations show that in steady state, thermal advection from the hot phase balances radiative cooling. However, many features are puzzling. For instance, hot gas entrainment appears to be numerically converged despite the scale-free, fractal structure of such fronts being unresolved. Additionally, the hot gas heat flux has a characteristic velocity $v_{\rm in} \approx c_{\rm s,cold} (t_{\rm cool}/t_{\rm sc,cold})^{-1/4}$ whose strength and scaling are not intuitive. We revisit these issues in 1D and 3D hydrodynamic simulations. We find that over-cooling only happens if numerical diffusion dominates thermal transport; convergence is still possible even when the Field length is unresolved. A deeper physical understanding of radiative fronts can be obtained by exploiting parallels between mixing layers and turbulent combustion, which has well-developed theory and abundant experimental data. A key parameter is the Damköhler number ${\rm Da} = τ_{\rm turb}/t_{\rm cool}$, the ratio of the outer eddy turnover time to the cooling time. Once ${\rm Da} > 1$, the front fragments into a multiphase medium. Just as for scalar mixing, the eddy turnover time sets the mixing rate, independent of small scale diffusion. For this reason, thermal conduction often has limited impact. We show that $v_{\rm in}$ and the effective emissivity can be understood in detail by adapting combustion theory scalings. Mean density and temperature profiles can also be reproduced remarkably well by mixing length theory. These results have implications for the structure and survival of cold gas in many settings, and resolution requirements for large scale galaxy simulations.

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arXiv2021

Thermal Instabilities and Shattering in the High-Redshift WHIM: Convergence Criteria and Implications for Low-Metallicity Strong HI Absorbers

Using a novel suite of cosmological simulations zooming in on a Mpc-scale intergalactic sheet or "pancake" at z~3-5, we conduct an in-depth study of the thermal properties and HI content of the warm-hot intergalactic medium (WHIM) at those redshifts. The simulations span nearly three orders of magnitude in gas-cell mass, from ~(7.7x10^6-1.5x10^4)Msun, one of the highest resolution simulations of such a large patch of the inter-galactic medium (IGM) to date. At z~5, a strong accretion shock develops around the main pancake following a collision between two smaller sheets. Gas in the post-shock region proceeds to cool rapidly, triggering thermal instabilities and the formation of a multiphase medium. We find neither the mass, nor the morphology, nor the distribution of HI in the WHIM to be converged at our highest resolution. Interestingly, the lack of convergence is more severe for the less dense, more metal-poor, intra-pancake medium (IPM) in between filaments and far from any star-forming galaxies. As the resolution increases, the IPM develops a shattered structure, with ~kpc scale clouds containing most of the HI. From our lowest to highest resolution, the covering fraction of metal-poor (Z<10^{-3}Zsun) Lyman-limit systems (NHI>10^{17.2}/cm^2) in the IPM at z~4 increases from (3-15)%, while that of Damped Lyman-alpha Absorbers (NHI>10^{20}/cm^2) with similar metallicity increases threefold, from (0.2-0.6)%, with no sign of convergence. We find that a necessary condition for the formation of a multiphase, shattered structure is resolving the cooling length, lcool=cs*tcool, at T~10^5K. If this scale is unresolved, gas "piles up" at these temperatures and cooling to lower temperatures becomes very inefficient. We conclude that state-of-the-art cosmological simulations are still unable to resolve the multi-phase structure of the low-density IGM, with potentially far-reaching implications.

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arXiv2020

Non-Kolmogorov turbulence in multiphase intracluster medium driven by cold gas precipitation and AGN jets

AGN feedback is responsible for maintaining plasma in global thermal balance in extended halos of elliptical galaxies and galaxy clusters. Local thermal instability in the hot gas leads to the formation of precipitating cold gas clouds that feed the central supermassive black holes, thus heating the hot gas and maintaining global thermal equilibrium. We perform three dimensional MHD simulations of self-regulated AGN feedback in a Perseus-like galaxy cluster with the aim of understanding the impact of the feedback physics on the turbulence properties of the hot and cold phases of the ICM. We find that, in general, the cold phase velocity structure function (VSF) is steeper than the prediction from Kolmogorov's theory. We attribute the physical origin of the steeper slope of the cold phase VSF to the driving of turbulent motions primarily by the gravitational acceleration acting on the ballistic clouds. We demonstrate that, in the pure hydrodynamical case, the precipitating cold filaments may be the dominant agent driving turbulence in the hot ICM. The arguments in favor of this hypothesis are that: (i) the cold phase mass dominates over hot gas mass in the inner cool core; (ii) hot and cold gas velocities are spatially correlated; (iii) both the cold and hot phase velocity distributions are radially biased. We show that, in the MHD case, the turbulence in the ambient hot medium (excluding the jet cone regions) can also be driven by the AGN jets. The driving is then facilitated by enhanced coupling due to magnetic fields of the ambient gas and the AGN jets. In the MHD case, turbulence may thus be driven by a combination of AGN jet stirring and filament motions. We conclude that future observations, including those from high spatial and spectral resolution X-ray missions, may help to constrain self-regulated AGN feedback by quantifying the multi-temperature VSF in the ICM.

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arXiv2020

Is Multiphase Gas Cloudy or Misty?

Cold $T \sim 10^{4}$K gas morphology could span a spectrum ranging from large discrete clouds to a fine `mist' in a hot medium. This has myriad implications, including dynamics and survival, radiative transfer, and resolution requirements for cosmological simulations. Here, we use 3D hydrodynamic simulations to study the pressure-driven fragmentation of cooling gas. This is a complex, multi-stage process, with an initial Rayleigh-Taylor unstable contraction phase which seeds perturbations, followed by a rapid, violent expansion leading to the dispersion of small cold gas `droplets' in the vicinity of the gas cloud. Finally, due to turbulent motions, and cooling, these droplets may coagulate. Our results show that a gas cloud `shatters' if it is sufficiently perturbed out of pressure balance ($δP/P\sim 1$), and has a large final overdensity $χ_{\mathrm{f}}\gtrsim 300$, with only a weak dependence on the cloud size. Otherwise, the droplets reassemble back into larger pieces. We discuss our results in the context of thermal instability, and clouds embedded in a shock heated environment.

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arXiv2020

Fluid Simulations of Cosmic Ray Modified Shocks

We consider cosmic ray (CR) modified shocks with both streaming and diffusion in the two-fluid description. Previously, numerical codes were unable to incorporate streaming in this demanding regime, and have never been compared against analytic solutions. First, we find a new analytic solution highly discrepant in acceleration efficiency from the standard solution. It arises from bi-directional streaming of CRs away from the subshock, similar to a Zeldovich spike in radiative shocks. Since fewer CRs diffuse back upstream, this results in a much lower acceleration efficiency, typically $\sim 10\%$ as opposed to $\sim 50\%$ found in previous analytic work. At Mach number $\gtrsim 10$, the new solution bifurcates into 3 branches, with efficient, intermediate and inefficient CR acceleration. Our two-moment code (Jiang & Oh 2018) accurately recovers these solutions across the entire parameter space probed, with no ad hoc closure relations. For generic initial conditions, the inefficient branch is the most robust and preferred solution. The intermediate branch is unstable, while the efficient branch appears only when the inefficient branch is not allowed (for CR dominated or high plasma $β$ shocks). CR modified shocks have very long equilibration times ($\sim 1000$ diffusion time) required to develop the precursor, which must be resolved by $\gtrsim 10$ cells for convergence. Non-equilibrium effects, poor resolution and obliquity of the magnetic field all reduce CR acceleration efficiency. Shocks in galaxy scale simulations will generally contribute little to CR acceleration without a subgrid prescription.

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arXiv2019

How cold gas continuously entrains mass and momentum from a hot wind

The existence of fast moving, cold gas ubiquitously observed in galactic winds is theoretically puzzling, since the destruction time of cold gas is much smaller than its acceleration time. In previous work, we showed that cold gas can accelerate to wind speeds and grow in mass if the radiative cooling time of mixed gas is shorter than the cloud destruction time. Here, we study this process in much more detail, and find remarkably robust cloud acceleration and growth in a wide variety of scenarios. Radiative cooling, rather than the Kelvin-Helmholtz instability, enables self-sustaining entrainment of hot gas onto the cloud via cooling-induced pressure gradients. Indeed, growth peaks when the cloud is almost co-moving. The entrainment velocity is of order the cold gas sound speed, and growth is accompanied by cloud pulsations. Growth is also robust to the background wind and initial cloud geometry. In an adiabatic Chevalier-Clegg type wind, for instance, the mass growth rate is constant. Although growth rates are similar with magnetic fields, cloud morphology changes dramatically, with low density, magnetically supported filaments which have a small mass fraction but dominate by volume. This could bias absorption line observations. Cloud growth from entraining and cooling hot gas can potentially account for the cold gas content of the CGM. It can also fuel star formation in the disk as cold gas recycled in a galactic fountain accretes and cools halo gas. We speculate that galaxy-scale simulations should converge in cold gas mass once cloud column densities of ${\rm N} \sim 10^{18} \ {\rm cm^{-2}}$ are resolved.

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arXiv2019

Simulations of radiative turbulent mixing layers

Radiative turbulent mixing layers should be ubiquitous in multi-phase gas with shear flow. They are a potentially attractive explanation for the high ions such as OVI seen in high velocity clouds and the circumgalactic medium (CGM) of galaxies. We perform 3D MHD simulations with non-equilibrium (NEI) and photoionization modeling, with an eye towards testing simple analytic models. Even purely hydrodynamic collisional ionization equilibrium (CIE) calculations have column densities much lower than observations. Characteristic inflow and turbulent velocities are much less than the shear velocity, and the layer width $h \propto t_\mathrm{cool}^{1/2}$ rather than $h \propto t_\mathrm{cool}$. Column densities are not independent of density or metallicity as analytic scalings predict, and show surprisingly weak dependence on shear velocity and density contrast. Radiative cooling, rather than Kelvin-Helmholtz instability, appears paramount in determining the saturated state. Low pressure due to fast cooling both seeds turbulence and sets the entrainment rate of hot gas, whose enthalpy flux, along with turbulent dissipation, energizes the layer. Regardless of initial geometry, magnetic fields are amplified and stabilize the mixing layer via magnetic tension, producing almost laminar flow and depressing column densities. NEI effects can boost column densities by factors of a few. Suppression of cooling by NEI or photoionization can in principle also increase OVI column densities, but in practice is unimportant for CGM conditions. To explain observations, sightlines must pierce hundreds or thousands of mixing layers, which may be plausible if the CGM exists as a `fog' of tiny cloudlets.

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arXiv2019

Plasma 2020 - Intracluster Medium Plasmas

Galaxy clusters are the largest and most massive bound objects resulting from cosmic hierarchical structure formation. Baryons account for somewhat more than 10% of that mass, with roughly 90% of the baryonic matter distributed throughout the clusters as hot ($T>1$ keV), high-$β$, very weakly collisional plasma; the so-called "intracluster medium" (ICM). Cluster mergers, close gravitational encounters and accretion, along with violent feedback from galaxies and relativistic jets from active galactic nuclei, drive winds, gravity waves, turbulence and shocks within the ICM. Those dynamics, in turn, generate cluster-scale magnetic fields and accelerate and mediate the transport of high-energy charged particles. Kinetic-scale, collective plasma processes define the basic character and fundamental signatures of these ICM phenomena, which are observed primarily by X-ray and radio astronomers.

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