(Upper Panels) Magnetic field strength slice at t = 0.2 Gyr (left), 0.5 Gyr (middle), and 0.8 Gyr (right) for the MPG-MHD run. Magnetic fields concentrate along the jet axis, while they decline in strength at larger radii. (Lower Panels) Thin slice showing the kinetic to thermal energy ratio in the CGM for the MHD multiphase galaxy (M_{200} ~ 4x10^{13} Msun) run at the same times as upper panels. As time progresses the jet cone becomes more and more kinetically dominated, showing that the rise in magnetif field strength along jet axis is providing addition collimation to the jets allowing it to travel farther before thermalising.[Prasad et al., 2026, MNRAS, 545, 1]

(Top panels) jet power (Pjet ) and X-ray luminosity (0.5 – 7 keV) as functions of time for simulations of the Single Phase Galaxy (M_{200} ~ 4x10^13 Msun; left), Multiphase Galaxy (M_{200}~4x10^{13} Msun; middle), and Brightest Cluster Galaxy ( M_{200, halo} ~ 7x10^{14} Msun; right) with AGN feedback. Gray lines show instantaneous jet power , and solid lines with changing color with time show jet power smoothed on a 20 Myr timescale. Dashed lines show radiative losses from the inner 10 kpc (blue) and inner 30 kpc (green). All three simulations self-regulate but exhibit two different feedback modes: a high power mode (~ 10^43 - 10^44 ergs/s) capable of altering the central r < 30 kpc, and a low power mode (~ 10^41 - 10^42 ergs/s) that cannot compensate for cooling in the halos of the MPG or BCG. (Bottom panels) Ratio of SN Ia heating to radiative cooling as a function of radius every 150 Myr during the evolution of each halo. In the SPG (left), AGN feedback promptly lowers the atmosphere’s density, enabling SN Ia heating to exceed radiative cooling from ∼0.5 to ∼5kpc. That state corresponds in time to the steady low power mode of self-regulation. The high power feedback mode in the MPG (middle) expands the galactic atmosphere, lowering its X-ray luminosity until SN Ia heating becomes comparable to radiative cooling near ∼1 kpc. AGN feedback then switches to a low-power mode that is insuf cient to replace radiative losses within ∼30 kpc, causing feedback to revert to a high-power mode at 1.2 Gyr, when radiative cooling once again exceeds SN Ia heating everywhere. In the BCG simulation (right), radiative cooling rapidly exceeds SNIa heating everywhere, fueling only the high power feedback mode. [Prasad et al., 2020, ApJ, 905, 50]

Time-averaged mass flow rates inside and outside of the jet-driven bipolar outflow during the full 1.5 Gyr simulation period for the Single Phase Galaxy (left) and Multiphase Galaxy (right) simulations. Here, we define the jet cone to be the region within θ=30° around the jet axis. Blue lines show the net gas mass that flows through radius 'r' within the jet cone. Red lines show the net gas mass that ows through radius 'r' outside of the jet cone. AGN feedback in these simulations drives large-scale circulation that generally flows outward along the jet axis and inward along directions far from the jet axis. The mean circulation rate at ∼10 kpc is ∼1 Msun/yr in the SPG simulation and∼ 30 Msun/yr in the MPG simulation. [Prasad et al., 2022, ApJ, 932, 18]

Angle-averaged, emissivity-weighted (for 0.5–10 keV) and scaled entropy (top left panel), TkeV (top right panel), cooling time (tcool, lower left panel), and tcool/tff (lower right panel) radial profiles of four epochs from our simulation (red and blue curves). In our simulations, at t = 1.93 and 2.62 Gyr (solid curves), the simulated cluster is in the intense cooling phase of the cooling cycle while t = 1.95 and 2.64 Gyr (dashed curves) marks the end of the cooling cycle and the beginning of the jet outburst phase. The observed profiles for Phoenix (McDonald et al. 2019) and a pure cooling flow for a Phoenix mass model based on read-off from figs 10 and 11 of McDonald et al. (2019) are the solid black line with circle markers and solid magenta line respectively . The cyan shaded region represent the 50 per cent scatter around the observed Phoenix values. The profiles are scaled to their characteristic values indexed to r_200(M_200, z) (assuming WMAP cosmology): K_200(z) ≡ T_{keV,200}(z)n_{e,200}(z)−2/3; T_200(z) ≡ GM_{200}μmp/[2r_200(z)k_B]; t_{cool,200}(z) ≡ 1.5μ_{e}μ_{i}m_{p}k_{B}T_{200}(z)/[200μf_{b}ρ_{cr}(z)*Cooling_fn(T_{200})]; and t_{ff,200} ≡ sqrt[2r_{200}(z)/g_{200}(z)], where g_{200}(z)= GM_{200}/(r_{200})^2. Here, the symbols have their usual meaning. Once the differences in mass and redshift between the Phoenix cluster and our simulated cluster are accounted for through rescaling, simulation profiles at t = 2.62 Gyr are in excellent agreement with the Phoenix results. [Prasad et al., 2020, MNRAS, 495, 594]

(Left Panel) Mass-weighted and angle-averaged radial profile for electron density with time (t = 0–1.0 Gyr) with a 10 Myr cadence for hot+cold-mode AGN feedback run with accretion efficiency ϵ = 0.01 for a A2029 analog cluster (M_{200}~10^{15} Msun). Plots show that the cluster core density (r < 30 kpc) maintains the initial density profile for the initial t∼ 300 Myr unlike the fiducial run as the hot-mode AGN feedback causes the AGN activity to switch on at the start of the simulation preventing the gas from accumulating in the core. (Right Panel) Total jet power (P_{jet}; solid blue line) averaged over δt = 10 Myr with time for the hot + cold-mode run. A red dashed line shows the hot-mode jet power, P_{Bondi} (= ϵ \dot{M}_{Bondi} c^2 ), with time for accretion efficiency ϵ = 0.01, same as the cold-mode feedback. The background cyan line represents the instantaneous total injected P_{jet} with time. Plots show that hot-mode AGN activity is enabled from the beginning of the simulation and dominates over the cold-mode feedback for most of the simulation run time. [Prasad et al., 2024, MNRAS, 531, 259]

The evolution of various quantities like kinetic energy density (ergs/cm^3), magnetic energy density (ergs/cm^3), the minimum and maximum temperature in the computational domain (T_{min} and T_{max}) with time using different methods for anisotropic conduction to study the local TI. Explicit (red solid line), sub-cycling (green solid line) and RKL-2 (black solid line) methods show similar time evolution, but AAG-STS (blue dashed line) starts to deviate in the non-linear stage. Notice the numerous spikes in Tmax and Tmin for AAG-STS, which are symptoms of numerical instability that blows up the code at 0.87 Gyr. These plots show that RKL-STS is a more robust method for modelling anisotropic conduction. Caveat : We impose a numerical temperature floor when the temperature becomes negative. [Vaidya B., Prasad D. et al., 2017, MNRAS, 472, 3147]

Velocity-radius distribution of the cold gas (T < 5x10^4 K) mass averaged from 1 to 4 Gyr. The right panel shows the v_{\phi} - r for the rotationally dominant gas and the left panel shows the v_{r} - r for the radially dominant gas. There is a lack of infalling high velocity cold gas clouds, showing that observed high velocity cold gas clouds in the intracluster medium are outflows caused by the AGN jets. In our hydro simulations, we see formation of rotationally supported galactic size disc which get decoupled from the feedback cycle. Such discs are observed in a few cool-core clusters like Hydra with similar rotational velocities. [Prasad et al., 2015, ApJ, 811, 108]

Average mass-weighted ⟨lz/|l|⟩ (bottom panel) and rms ⟨lz^2 /|l|2⟩^{1/2} (top panel) of cold gas crossing the inner boundary as a function of time for the fiducial NFW run. The dashed red lines are for all the cold gas crossing the inner boundary. The purple dot–dashed lines with stars show the average orientation of cold gas with |l| < 10^{28} cm^2/s and solid blue lines are for |l| <10^{29} cm^2/s. The orientation of cold gas with |l| < 10^28 cm^2/s changes on a short time-scale compared to the other two cases showing the stochastic nature of the low angular momentum cold gas which feeds the super massive black hole fueling powerful AGN outbursts. [Prasad et al., 2017, MNRAS, 471, 1531]

Molecular gas mass in centres of cool groups and clusters, ob- tained using CO observations, as a function of the SMBH mass. The filled circles represent detections and the triangles are upper limits. The cluster temperature is represented by colour (obtained from Cavagnolo et al. 2009, ApJS, 182, 12). There is a large scatter in the molecular gas mass for a given SMBH mass. Three vertical lines on extreme right denote the range of cold gas mass in our three simulations (measured from 1 Gyr till the end of the run, without accounting for cold gas depletion). A vertical line and an upper limit in extreme left are obtained from the simulations of Li et al., 2015, ApJ, 811, 73 with their feedback efficiency of 0.01 and 0.001. Star formation would help in reducing the total cold gas mass in the domain. [Prasad et al., 2017, MNRAS, 471, 1531]

(Left panel) The emissivity-weighted line-of-sight velocity dispersion (LOSVD), with time for 2–8 keV plasma (a proxy for Fe XXV line emission) and for 0.5–10 keV plasma within 30–60 kpc of the cool-core cluster run. The solid lines (the blue line is parallel to the jet direction, while the red line is perpendicular to the jet direction) represent the LOSVD for 2–8 keV gas. Dashed lines (the green line is perpendicular to the jet direction, while the magenta line is parallel to the jet direction) show the LOSVD for 0.5–10 keV gas. The horizontal purple dashed line marks the turbulent velocity in the ICM of Perseus Cluster as measured by Hitomi [Hitomi Collaboration, 2016, Nature, 535, 117]. (Right panel) The probability distribution function (PDF) of the emissivity-weighted line-of- sight velocity for the 2–8 keV gas. The solid black line and dotted–dashed magenta line are the time-averaged PDF between 1 and 4 Gyr along and perpendicular to the jet axis, respectively. The red and blue lines (the solid line is parallel, and the dotted–dashed line is perpendicular to the jet axis) show the PDF at t = 2.35 Gyr and t=2.1 Gyr, respectively. These times correspond to a trough and a peak in the LOSVD as seen in the left panel. [Prasad et al., 2018, ApJ, 863, 62]