arXiv subjects

Prateek Sharma

Publications and source records attributed to Prateek Sharma.

At least 109 records · Page 6Linked to original sources

arXiv2013

Isotropic Heating of Galaxy Cluster Cores via Rapidly Reorienting AGN Jets

AGN jets carry more than sufficient energy to stave off catastrophic cooling of the intracluster medium (ICM) in the cores of cool-core clusters. However, in order to prevent catastrophic cooling, the ICM must be heated in a near-isotropic fashion and narrow bipolar jets with $P_{\rm jet}=10^{44-45}$ ergs/s, typical of radio AGNs at cluster centres, are inefficient at heating the gas in the transverse direction to the jets. We argue that due to existent conditions in cluster cores, the SMBHs will, in addition to accreting gas via radiatively inefficient flows, experience short stochastic episodes of enhanced accretion via thin discs. In general, the orientation of these accretion discs will be misaligned with the spin axis of the black holes and the ensuing torques will cause the black hole's spin axis (and therefore, the jet axis) to slew and rapidly change direction. This model not only explains recent observations showing successive generations of jet-lobes-bubbles in individual cool-core clusters that are offset from each other in the angular direction with respect to the cluster center, but also shows that AGN jets {\it can} heat the cluster core nearly isotropically on the gas cooling timescale. Our model {\it does} require that the SMBHs at the centers of cool-core clusters be spinning relatively slowly. Torques from individual misaligned discs are ineffective at tilting rapidly spinning black holes by more than a few degrees. Additionally, since SMBHs that host thin accretion discs will manifest as quasars, we predict that roughly 1--2 rich clusters within $z<0.5$ should have quasars at their centers.

astro-ph.CO↗

arXiv2012

Thermal Instability in Gravitationally-Stratified Plasmas: Implications for Multi-Phase Structure in Clusters and Galaxy Halos

We study the interplay among cooling, heating, conduction, and magnetic fields in gravitationally stratified plasmas using simplified, plane-parallel numerical simulations. Since the physical heating mechanism remains uncertain in massive halos such as groups or clusters, we adopt a simple, observationally-motivated prescription which enforces global thermal equilibrium when averaged over large scales. The plasma remains susceptible to local thermal instability, however, and cooling drives an inward flow of material. In contrast to previous results, we argue that the thermal stability of the plasma is independent of its convective stability. We find that the ratio of the cooling timescale to the dynamical timescale t_cool/t_ff controls the saturation of the thermal instability: when t_cool/t_ff < 1, the plasma develops extended multi-phase structure, whereas when t_cool / t_ff > 1 it does not. (In a companion paper, we show that the criterion for thermal instability in a spherical potential is somewhat less stringent, t_cool / t_ff < 10.) When thermal conduction is anisotropic with respect to the magnetic field, the criterion for multi-phase structure is essentially independent of the thermal conductivity of the plasma. Our criterion for local thermal instability to produce multi-phase structure is an extension of the cold vs. hot accretion modes in galaxy formation that applies at all radii in hot halos, not just to the virial shock. We show that this criterion is consistent with data on multi-phase gas in the ACCEPT sample of clusters; in addition, when t_cool / t_ff > 1, the net cooling rate to low temperatures and the mass flux to small radii are suppressed enough relative to models without heating to be qualitatively consistent with star formation rates and x-ray line emission in groups and clusters.

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arXiv2012

On the Structure of Hot Gas in Halos: Implications for the Lx-Tx Relation & Missing Baryons

We present one-dimensional models of the hot gas in dark-matter halos, which both predict the existence of cool cores and explain their structure. Our models are directly applicable to semi-analytic models (SAMs) of galaxy formation. We have previously argued that filaments of cold (~10^4 K) gas condense out of the intracluster medium (ICM) in hydrostatic and thermal equilibrium when the ratio of the thermal instability timescale to the free-fall time $t_{TI}/t_{ff}$ falls below 5-10. This criterion corresponds to an upper limit on the density of the ICM and motivates a model in which a density core forms wherever $t_{TI}/t_{ff} \lesssim 10$. Consistent with observations and numerical simulations, this model predicts larger and more tenuous cores for lower-mass halos---while the core density in a cluster may be as large as ~ 0.1 cm^{-3}, the core density in the Galactic halo should not exceed ~ 10^{-4} cm^{-3}. We can also explain the large densities in smaller mass halos (galactic `coronae') if we include the contribution of the central galaxy to the gravitational potential. Our models produce a favorable match to the observational X-ray luminosity-temperature (Lx-Tx) relation. For halo masses $\lesssim 10^{13}$ Msun the core size approaches the virial radius. Thus, most of the baryons in such halos cannot be in the hot ICM, but either in the form of stars or in the form of hot gas beyond the virial radius. Because of the smaller mass in the ICM and much larger mass available for star formation, the majority of the baryons in low mass halos ($\lesssim 10^{13}$ Msun) can be expelled beyond the virial radius due to supernova feedback. This can account for the baryons `missing' from low mass halos, such as the Galactic halo.

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arXiv2012

Local 2D Particle-in-cell simulations of the collisionless MRI

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the rate of Coulomb collisions between particles is very small, making the disk evolve essentially as a collisionless plasma. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell (PIC) plasma simulations. In this initial study we focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field until the Alfvén velocity, v_A, is comparable to the speed of light, c (independent of the initial value of v_A/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the perpendicular pressure being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission -- from the radio to the gamma-rays -- of systems such as Sgr A*.

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arXiv2012

The Effects of Anisotropic Viscosity on Turbulence and Heat Transport in the Intracluster Medium

In the intracluster medium (ICM) of galaxy clusters, heat and momentum are transported almost entirely along (but not across) magnetic field lines. We perform the first fully self-consistent Braginskii-MHD simulations of galaxy clusters including both of these effects. Specifically, we perform local and global simulations of the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability (HBI) and assess the effects of viscosity on their saturation and astrophysical implications. We find that viscosity has only a modest effect on the saturation of the MTI. As in previous calculations, we find that the MTI can generate nearly sonic turbulent velocities in the outer parts of galaxy clusters, although viscosity somewhat suppresses the magnetic field amplification. At smaller radii in cool-core clusters, viscosity can decrease the linear growth rates of the HBI. However, it has less of an effect on the HBI's nonlinear saturation, in part because three-dimensional interchange motions (magnetic flux tubes slipping past each other) are not damped by anisotropic viscosity. In global simulations of cool core clusters, we show that the HBI robustly inhibits radial thermal conduction and thus precipitates a cooling catastrophe. The effects of viscosity are, however, more important for higher entropy clusters. We argue that viscosity can contribute to the global transition of cluster cores from cool-core to non cool-core states: additional sources of intracluster turbulence, such as can be produced by AGN feedback or galactic wakes, suppress the HBI, heating the cluster core by thermal conduction; this makes the ICM more viscous, which slows the growth of the HBI, allowing further conductive heating of the cluster core and a transition to a non cool-core state.

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arXiv2011

Turbulent Pressure Support in the Outer Parts of Galaxy Clusters

We use three-dimensional MHD simulations with anisotropic thermal conduction to study turbulence due to the magnetothermal instability (MTI) in the intracluster medium (ICM) of galaxy clusters. The MTI grows on timescales of ~1 Gyr and is capable of driving vigorous, sustained turbulence in the outer parts of galaxy clusters if the temperature gradient is maintained in spite of the rapid thermal conduction. If this is the case, turbulence due to the MTI can provide up to 5-30% of the pressure support beyond r_500 in galaxy clusters, an effect that is strongest for hot, massive clusters. The turbulence driven by the MTI is generally additive to other sources of turbulence in the ICM, such as that produced by structure formation. This new source of non-thermal pressure support reduces the observed Sunyaev-Zel'dovich (SZ) signal and X-ray pressure gradient for a given cluster mass and introduces a cluster mass and temperature gradient-dependent bias in SZ and X-ray mass estimates of clusters. This additional physics may also need to be taken into account when estimating the matter power spectrum normalization, sigma-8, through simulation templates from the observed amplitude of the SZ power spectrum.

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arXiv2011

Thermal Instability & the Feedback Regulation of Hot Halos in Clusters, Groups, and Galaxies

Observations of clusters and groups imply that such halos are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally-motivated heating prescriptions, we show that local thermal instability (TI) can produce a multi-phase medium---with ~ 10000 K cold filaments condensing out of the hot ICM---only when the ratio of the TI timescale in the hot plasma (t_{TI}) to the free-fall timescale (t_{ff}) satisfies t_{TI}/t_{ff} <~ 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling, and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of ~ 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling-flow is ~ 0.001 for clusters and decreases for lower mass halos; supernova heating may be energetically sufficient to balance cooling in galactic halos. We further argue that the ICM self-adjusts so that t_{TI}/t_{ff} >~ 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives t_{TI}/t_{ff} >~ 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminosity-temperature (L_X-T_X) relation. The high-velocity clouds observed in the Galactic halo can also be due to local TI producing multi-phase gas close to the virial radius.

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arXiv2011

Numerical Implementation of Streaming Down the Gradient: Application to Fluid Modeling of Cosmic Rays and Saturated Conduction

The equation governing the streaming of a quantity down its gradient superficially looks similar to the simple constant velocity advection equation. In fact, it is the same as an advection equation if there are no local extrema in the computational domain or at the boundary. However, in general when there are local extrema in the computational domain it is a non-trivial nonlinear equation. The standard upwind time evolution with a CFL-limited time step results in spurious oscillations at the grid scale. These oscillations, which originate at the extrema, propagate throughout the computational domain and are undamped even at late times. These oscillations arise because of unphysically large fluxes leaving (entering) the maxima (minima) with the standard CFL-limited explicit methods. Regularization of the equation shows that it is diffusive at the extrema; because of this, an explicit method for the regularized equation with $Δt \propto Δx^2$ behaves fine. We show that the implicit methods show stable and converging results with $Δt \propto Δx$; however, surprisingly, even implicit methods are not stable with large enough timesteps. In addition to these subtleties in the numerical implementation, the solutions to the streaming equation are quite novel: non-differentiable solutions emerge from initially smooth profiles; the solutions show transport over large length scales, e.g., in form of tails. The fluid model for cosmic rays interacting with a thermal plasma (valid at space scales much larger than the cosmic ray Larmor radius) is similar to the equation for streaming of a quantity down its gradient, so our method will find applications in fluid modeling of cosmic rays.

astro-ph.HE↗

arXiv2011

A Fast Semi-implicit Method for Anisotropic Diffusion

Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative temperatures for the anisotropic thermal diffusion equation. In a previous paper we proposed a monotonicity-preserving explicit method which uses limiters (analogous to those used in the solution of hyperbolic equations) to interpolate the temperature gradients at cell faces. However, being explicit, this method was limited by a restrictive Courant-Friedrichs-Lewy (CFL) stability timestep. Here we propose a fast, conservative, directionally-split, semi-implicit method which is second order accurate in space, is stable for large timesteps, and is easy to implement in parallel. Although not strictly monotonicity-preserving, our method gives only small amplitude temperature oscillations at large temperature gradients, and the oscillations are damped in time. With numerical experiments we show that our semi-implicit method can achieve large speed-ups compared to the explicit method, without seriously violating the monotonicity constraint. This method can also be applied to isotropic diffusion, both on regular and distorted meshes.

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arXiv2010

Time Dependent Models of Flares from Sagittarius A*

The emission from Sgr A*, the supermassive black hole in the Galactic Center, shows order of magnitude variability ("flares") a few times a day that is particularly prominent in the near-infrared (NIR) and X-rays. We present a time-dependent model for these flares motivated by the hypothesis that dissipation of magnetic energy powers the flares. We show that episodic magnetic reconnection can occur near the last stable circular orbit in time-dependent magnetohydrodynamic simulations of black hole accretion - the timescales and energetics of these events are broadly consistent with the flares from Sgr A*. Motivated by these results, we present a spatially one-zone time-dependent model for the electron distribution function in flares, including energy loss due to synchrotron cooling and adiabatic expansion. Synchrotron emission from transiently accelerated particles can explain the NIR/X-ray lightcurves and spectra of a luminous flare observed 4 April 2007. A significant decrease in the magnetic field strength during the flare (coincident with the electron acceleration) is required to explain the simultaneity and symmetry of the simultaneous lightcurves. Our models predict that the NIR and X-ray spectral indices differ by 0.5 and that there is only modest variation in the spectral index during flares. We also explore implications of this model for longer wavelength (radio-submm) emission seemingly associated with X-ray and NIR flares; we argue that a few hour decrease in the submm emission is a more generic consequence of large-scale magnetic reconnection than delayed radio emission from adiabatic expansion.

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arXiv2010

Can conduction induce convection? The non-linear saturation of buoyancy instabilities in dilute plasmas

We study the effects of anisotropic thermal conduction on low-collisionality, astrophysical plasmas using two and three-dimensional magnetohydrodynamic simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable for either sign of the temperature gradient: the heat-flux-driven buoyancy instability (HBI) operates when the temperature increases with radius while the magnetothermal instability (MTI) operates in the opposite limit. In contrast to previous results, we show that, in the presence of a sustained temperature gradient, the MTI drives strong turbulence and operates as an efficient magnetic dynamo (akin to standard, adiabatic convection). Together, the turbulent and magnetic energies contribute up to ~10% of the pressure support in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5% of rho c_s^3. These findings are robust even in the presence of an external source of strong turbulence. Our results on the nonlinear saturation of the HBI are consistent with previous studies but we explain physically why the HBI saturates quiescently by re-orienting the magnetic field (suppressing the conductive heat flux through the plasma), while the MTI saturates by generating sustained turbulence. We also systematically study how an external source of turbulence affects the saturation of the HBI: such turbulence can disrupt the HBI only on scales where the shearing rate of the turbulence is faster than the growth rate of the HBI. In particular, our results provide a simple mapping between the level of turbulence in a plasma and the effective isotropic thermal conductivity. We discuss the astrophysical implications of these findings, with a particular focus on the intracluster medium of galaxy clusters.

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arXiv2010

Turbulence in Galaxy Cluster Cores: a Key to Cluster Bimodality?

We study the effects of externally imposed turbulence on the thermal properties of galaxy cluster cores, using three-dimensional numerical simulations including magnetic fields, anisotropic thermal conduction, and radiative cooling. The imposed "stirring" crudely approximates the effects of galactic wakes, waves generated by galaxies moving through the intracluster medium (ICM), and/or turbulence produced by a central active galactic nucleus. The simulated clusters exhibit a strong bimodality. Modest levels of turbulence, ~100 km/s (~10% of the sound speed), suppress the heat-flux-driven buoyancy instability (HBI), resulting in an isotropically tangled magnetic field and a quasi-stable, high entropy, thermal equilibrium with no cooling catastrophe. Thermal conduction dominates the heating of the cluster core, but turbulent mixing is critical because it suppresses the HBI and (to a lesser extent) the thermal instability. Lower levels of turbulent mixing (approximately less than 100 km/s) are insufficient to suppress the HBI, rapidly leading to a thermal runaway and a cool-core cluster. Remarkably, then, small fluctuations in the level of turbulence in galaxy cluster cores can initiate transitions between cool-core (low entropy) and non cool-core (high entropy) states.

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arXiv2010

Thermal Instability with Anisotropic Thermal Conduction and Adiabatic Cosmic Rays: Implications for Cold Filaments in Galaxy Clusters

Observations of the cores of nearby galaxy clusters show H$α$ and molecular emission line filaments. We argue that these are the result of {\em local} thermal instability in a {\em globally} stable galaxy cluster core. We present local, high resolution, two-dimensional magnetohydrodynamic simulations of thermal instability for conditions appropriate to the intracluster medium (ICM); the simulations include thermal conduction along magnetic field lines and adiabatic cosmic rays. Thermal conduction suppresses thermal instability along magnetic field lines on scales smaller than the Field length ($\gtrsim$10 kpc for the hot, diffuse ICM). We show that the Field length in the cold medium must be resolved both along and perpendicular to the magnetic field in order to obtain numerically converged results. Because of negligible conduction perpendicular to the magnetic field, thermal instability leads to fine scale structure in the perpendicular direction. Filaments of cold gas along magnetic field lines are thus a natural consequence of thermal instability with anisotropic thermal conduction. Nonlinearly, filaments of cold ($\sim 10^4$ K) gas should have lengths (along the magnetic field) comparable to the Field length in the cold medium $\sim 10^{-4}$ pc! Observations show, however, that the atomic filaments in clusters are far more extended, $\sim 10$ kpc. Cosmic ray pressure support (or a small scale turbulent magnetic pressure) may resolve this discrepancy: even a small cosmic ray pressure in the diffuse ICM, $\sim 10^{-4}$ of the thermal pressure, can be adiabatically compressed to provide significant pressure support in cold filaments. This is qualitatively consistent with the large population of cosmic rays invoked to explain the atomic and molecular line ratios observed in filaments.

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arXiv2009

Anisotropic Thermal Conduction and the Cooling Flow Problem in Galaxy Clusters

We examine the long-standing cooling flow problem in galaxy clusters with 3D MHD simulations of isolated clusters including radiative cooling and anisotropic thermal conduction along magnetic field lines. The central regions of the intracluster medium (ICM) can have cooling timescales of ~200 Myr or shorter--in order to prevent a cooling catastrophe the ICM must be heated by some mechanism such as AGN feedback or thermal conduction from the thermal reservoir at large radii. The cores of galaxy clusters are linearly unstable to the heat-flux-driven buoyancy instability (HBI), which significantly changes the thermodynamics of the cluster core. The HBI is a convective, buoyancy-driven instability that rearranges the magnetic field to be preferentially perpendicular to the temperature gradient. For a wide range of parameters, our simulations demonstrate that in the presence of the HBI, the effective radial thermal conductivity is reduced to less than 10% of the full Spitzer conductivity. With this suppression of conductive heating, the cooling catastrophe occurs on a timescale comparable to the central cooling time of the cluster. Thermal conduction alone is thus unlikely to stabilize clusters with low central entropies and short central cooling timescales. High central entropy clusters have sufficiently long cooling times that conduction can help stave off the cooling catastrophe for cosmologically interesting timescales.

astro-ph.CO↗

arXiv2008

Spherical Accretion with Anisotropic Thermal Conduction

We study the effects of anisotropic thermal conduction on magnetized spherical accretion flows using global axisymmetric MHD simulations. In low collisionality plasmas, the Bondi spherical accretion solution is unstable to the magnetothermal instability (MTI). The MTI grows rapidly at large radii where the inflow is subsonic. For a weak initial field, the MTI saturates by creating a primarily radial magnetic field, i.e., by aligning the field lines with the background temperature gradient. The saturation is quasilinear in the sense that the magnetic field is amplified by a factor of $\sim 10-30$ independent of the initial field strength (for weak fields). In the saturated state, the conductive heat flux is much larger than the convective heat flux, and is comparable to the field-free (Spitzer) value (since the field lines are largely radial). The MTI by itself does not appreciably change the accretion rate $\dot M$ relative to the Bondi rate $\dot M_B$. However, the radial field lines created by the MTI are amplified by flux freezing as the plasma flows in to small radii. Oppositely directed field lines are brought together by the converging inflow, leading to significant resistive heating. When the magnetic energy density is comparable to the gravitational potential energy density, the plasma is heated to roughly the virial temperature; the mean inflow is highly subsonic; most of the energy released by accretion is transported to large radii by thermal conduction; and the accretion rate $\dot M \ll \dot M_B$. The predominantly radial magnetic field created by the MTI at large radii in spherical accretion flows may account for the stable Faraday rotation measure towards Sgr A* in the Galactic Center.

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arXiv2007

Electron Heating in Hot Accretion Flows

Local (shearing box) simulations of the nonlinear evolution of the magnetorotational instability in a collisionless plasma show that angular momentum transport by pressure anisotropy ($p_\perp \ne p_\parallel$, where the directions are defined with respect to the local magnetic field) is comparable to that due to the Maxwell and Reynolds stresses. Pressure anisotropy, which is effectively a large-scale viscosity, arises because of adiabatic invariants related to $p_\perp$ and $p_\parallel$ in a fluctuating magnetic field. In a collisionless plasma, the magnitude of the pressure anisotropy, and thus the viscosity, is determined by kinetic instabilities at the cyclotron frequency. Our simulations show that $\sim 50$ % of the gravitational potential energy is directly converted into heat at large scales by the viscous stress (the remaining energy is lost to grid-scale numerical dissipation of kinetic and magnetic energy). We show that electrons receive a significant fraction ($\sim [T_e/T_i]^{1/2}$) of this dissipated energy. Employing this heating by an anisotropic viscous stress in one dimensional models of radiatively inefficient accretion flows, we find that the radiative efficiency of the flow is greater than 0.5% for $\dot{M} \gtrsim 10^{-4} \dot{M}_{Edd}$. Thus a low accretion rate, rather than just a low radiative efficiency, is necessary to explain the low luminosity of many accreting black holes. For Sgr A* in the Galactic Center, our predicted radiative efficiencies imply an accretion rate of $\approx 3 \times 10^{-8} M_\odot {\rm yr^{-1}}$ and an electron temperature of $\approx 3 \times 10^{10}$ K at $\approx 10$ Schwarzschild radii; the latter is consistent with the brightness temperature inferred from VLBI observations.

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arXiv2007

Faraday Rotation in Global Accretion Disk Simulations: Implications for Sgr A*

These Faraday rotation calculations of hot, thick accretion flows are motivated by the measured steady rotation measure (RM) of $\approx -6 \times 10^5$ rad m$^{-2}$ from Sgr A*. In our numerical simulations, the quasi-steady state structure of the accretion flow, and the RM it produces, depends on the initial magnetic field. In spite of this dependence, we can draw several robust conclusions about Faraday rotation produced by geometrically thick accretion disks: i) the time averaged RM does not depend that sensitively on the viewing angle, but the stability of the RM can. Equatorial viewing angles show significant variability in RM (including sign reversals), while polar viewing angles are relatively stable if there is a large scale magnetic field threading the disk at large radii. ii) Most of the RM is produced at small radii for polar viewing angles while all radii contribute significantly near the midplane of the disk. Our simulations confirm previous analytic arguments that the accretion rate onto Sgr A* must satisfy $\dot M_{\rm in} \ll \dot M_{\rm Bondi} \sim 10^{-5} \mpy$ in order to not over-produce the measured RM. We argue that the steady RM $\approx -6 \times 10^5$ rad m$^{-2}$ from Sgr A* has two plausible explanations: 1) it is produced at $\sim 100$ Schwarzschild radii, requires $\dot{M}_{\rm in} \approx 3 \times 10^{-8} M_\odot$ yr$^{-1}$, and we view the flow at an angle of $\sim 30^\circ$ relative to the rotation axis of the disk; in our simulations, the variation in RM across a finite-sized source is sufficient to depolarize the emission below $\approx$ 100 GHz, consistent with observations. 2) Alternatively, the RM may be produced in the relatively spherical inflowing plasma near the circularization radius at $\sim 10^3-10^4$ Schwarzschild radii.

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arXiv2007

Preserving Monotonicity in Anisotropic Diffusion

We show that standard algorithms for anisotropic diffusion based on centered differencing (including the recent symmetric algorithm) do not preserve monotonicity. In the context of anisotropic thermal conduction, this can lead to the violation of the entropy constraints of the second law of thermodynamics, causing heat to flow from regions of lower temperature to higher temperature. In regions of large temperature variations, this can cause the temperature to become negative. Test cases to illustrate this for centered asymmetric and symmetric differencing are presented. Algorithms based on slope limiters, analogous to those used in second order schemes for hyperbolic equations, are proposed to fix these problems. While centered algorithms may be good for many cases, the main advantage of limited methods is that they are guaranteed to avoid negative temperature (which can cause numerical instabilities) in the presence of large temperature gradients. In particular, limited methods will be useful to simulate hot, dilute astrophysical plasmas where conduction is anisotropic and the temperature gradients are enormous, e.g., collisionless shocks and disk-corona interface.

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