Investigating a model of optimized active galactic nucleus feedback

Abstract

The feedback heating from active galactic nuclei (AGNs) in massive galaxies and galaxy clusters can be thought of as a naturally occurring control system which plays a significant role in regulating both star formation rates and the X-ray luminosity of the surrounding hot gas. In the simplest case, negative feedback can be viewed as a system response that is 'optimized' to minimize deviations from equilibrium, such that the system rapidly evolves towards a steady state. However, a general solution of this form appears to be incompatible with radio observations which indicate intermittent AGN outbursts. Here, we explore an energetically favourable scenario in which feedback is required to both balance X-ray gas cooling and minimize the sum of the energy radiated by the gas and the energy injected by the AGN. This specification is equivalent to ensuring that AGN heating balances the X-ray gas cooling with the minimum black hole growth. It is shown that minimum energy heating occurs in discrete events and not at a continuous, constant level. Furthermore, systems with stronger feedback experience proportionally more powerful heating events, but correspondingly smaller duty cycles. Interpreting observations from this perspective would imply that stronger feedback occurs in less-massive objects -elliptical galaxies rather than galaxy clusters. One direct consequence of this effect would be that AGN heating events are sufficiently powerful to expel hot gas from the gravitational potential of a galaxy, but not a galaxy cluster, which is consistent with theoretical explanations for the steepening of the L X -T relation at temperatures below 1-2 keV.

Self-regulated growth of supermassive black holes by a dual jet-heating active galactic nucleus feedback mechanism: methods, tests and implications for cosmological simulations

“…As a result of this accumulation of energy, BHs release a comparable amount of energy to the Δ M d = 0 case (simulation 128L25J) but in a shorter amount of time, allowing for fewer but stronger AGN luminosity bursts. Thus, BHs can more easily self‐regulate with smaller duty cycles (Pope 2011).…”

“…Alternative approaches based on the injection of cosmic rays have also been explored . These cosmological simulations have successfully reproduced relationships between BH masses and galaxy properties (Sijacki et al 2007;Di Matteo et al 2008;Booth & Schaye 2009, 2011, and suppressed the cooling catastrophe in groups and clusters of galaxies (Khalatyan et al 2008;Puchwein, Sijacki & Springel 2008;McCarthy et al 2010McCarthy et al , 2011. Recently, AGN feedback associated with BH growth has been introduced in adaptive mesh refinement (AMR) cosmological re-simulations of a galaxy cluster with the RAMSES code.…”

Investigating the properties of active galactic nucleus feedback in hot atmospheres triggered by cooling-induced gravitational collapse

“…Best et al 2005; Shabala et al 2008). In addition, as demonstrated in Pope (2011), periodic heating can supply the energy required to balance gas cooling, with minimum effort. Thus, periodic AGN activity appears to be an energetically favourable heating strategy.…”

Why and when is internally driven AGN feedback energetically favoured?

“…Any differential equation of this type would be highly uncertain. Indeed, it was for this reason that Pope () used a different approach: to find a Lagrangian function that yielded periodic episodes of feedback heating that were in approximate agreement with the observations of Best et al (), Best () and Shabala et al (). Notably, the Lagrangian that provided the best agreement with observations favoured minimum energy output from the system which, in turn, favours a scenario in which time‐averaged heating balances cooling.…”

“…Using equation , we can express the minimum output energy integral from Pope () in terms of the GFE, where is the rate of change of the total GFE with respect to time. For a system that is evolving steadily and quasistatically, we assume that , while [1 − ( v / c s ) 2 ] changes sign as a result of (i) the work done by gravity and (ii) feedback, such that over long times (and many sign switches), .…”