Jet Feedback on kpc Scales: A Review

Abstract

Relativistic jets from AGN are an important driver of feedback in galaxies. They interact with their environments over a wide range of physical scales during their lifetime, and an understanding of these interactions is crucial for unraveling the role of supermassive black holes in shaping galaxy evolution. The impact of such jets has been traditionally considered in the context of heating large-scale environments. However, in the last few decades, there has been additional focus on the immediate impact of jet feedback on the host galaxy itself. In this review, we outline the development of various numerical simulations from the onset of research on jets to the present day, where sophisticated numerical techniques have been employed to study jet feedback, including a range of physical processes. The jets can act as important agents of energy injection into a host’s ISM, as confirmed in both observations of multi-phase gas as well as in simulations. Such interactions have the potential to impact the kinematics of the gas as well as star formation. We summarize recent results from simulations of jet feedback on kpc scales and outline the broader implications for observations and galaxy evolution.

1. Introduction

1.1. A Brief Overview of Classical AGN Feedback

Feedback from supermassive black holes (SMBH) in large early-type galaxies has been established as a major influencer of galaxy evolution [1,2]. However, the exact mechanism by which active galactic nuclei (AGN) affect the galaxy and its environment—and its implications on the galaxy’s properties—is still not settled. From a historical perspective, since the advent of X-ray observations of galaxy clusters, cooling flows of gas cooled via thermal Bremsstrahlung from the cluster environment [3] have been both postulated from theoretical modeling [4] and observationally confirmed [5,6]. However, the fate of the gas cooled below X-ray-emitting temperatures (≲1–2 keV) was left uncertain due to lack of distinct observational signatures [7,8]. This prompted considerations of re-heating of the gas by some mechanism with feedback from the AGN being a viable source [1,9]. The early concept of AGN feedback was primarily proposed to investigate two major implications: (a) the well-known $M-\sigma$ relation due to the co-evolution of the SMBH and the galaxy core [10] and (b) a heating mechanism to offset the over-cooling of the cluster cores [9,11]. These two different tracks eventually led to the evolution of the concept of dual-mode feedback by AGN: (a) Quasar or Establishment mode—related to the local impact of AGN-driven outflows and the co-evolution of the SMBH and galaxy mass—and (b) Radio or Maintenance mode—catering to the large-scale heating of gas reservoirs external to the galaxy and regulating galaxy growth by preventing cooling flows. In this dual-mode scenario, the role of relativistic jets has been largely confined to their impact on extra-galactic gas in the Radio/Maintenance mode, whereas non-relativistic winds in high-Eddington ratio systems have been considered to be the primary driver of Quasar/Establishment mode feedback. However, in recent decades, a large body of literature has demonstrated, from both theory and observations, that jets can have a significant impact on the ISM of the host galaxy. This makes the earlier dual-mode distinction ambiguous in some cases, requiring rethinking of the traditional definitions (see Harrison et al. 2024 [2] for a discussion).

1.2. Scope of the Current Review

Over the last few decades, there have been some excellent reviews on different aspects of the topic of relativistic jets and their feedback by various authors. However, their scopes and focuses have been different and often non-overlapping. Some of the recent comprehensive reviews in this domain can be placed in the following broad groups:

• Advances in the physics of relativistic jets themselves (e.g., Blandford et al. 2019 [12]) or their simulations (e.g., Marti 2019 [13], Komissarov and Porth 2021 [14], and Perucho 2023 [15]).
• Astrophysical implications of jets and outflows in general (e.g., Veilleux et al. 2020 [16] and Laha et al. 2021 [17]).
• AGN feedback and its implications (e.g., Fabian 2012 [1], Harrison 2017 [18], Morganti 2017 [19], Eckert et al. 2021 [20], Combes 2021 [21], Bourne and Yang 2023 [22], and Harrison and Ramos Almeida 2024 [2]).
• The varied nature of AGN sources and their radio-loud counterparts (such as Tadhunter 2016 [23], O’dea and Saikia 2021 [24], Hardcastle and Croston 2020 [25], and Baldi 2023 [26]).
• Gas in and around AGN host galaxies leading to feeding and feedback (e.g., Morganti and Oosterloo 2018 Morganti and Oosterloo [27], Storchi-Bergmann 2019 [28], Gaspari et al. 2020 [29], and Combes 2023 [30]).
• The episodic nature of AGN outbursts and duty cycles (e.g., Morganti 2017 [19]).

The above works provide broad overviews of the various complex astrophysical processes related to the topics of feedback and galaxy evolution. However, only a few detailed reviews have discussed the complex issues regarding the interactions of such outflows, specifically jets, with the host galaxy itself (such as Wagner et al. 2016 [31], Mukherjee et al. 2021 [32], Morganti et al. 2023 [33], and Krause et al. 2023 [34]). In this review, we discuss the simulation techniques developed over the past few decades for studying AGN jets in general and jet–ISM interaction in particular. We also summarize the status of observational studies of jet–ISM interaction and their implications for galaxy evolution. The review is not meant to be a comprehensive summary of all accumulated results to date. Rather, it highlights the major achievements in this field and their historical developments, to place them in the broader context of AGN feedback and galaxy evolution.

2. Modeling Jet-Driven Feedback at Galactic Scales

2.1. Jets in Homogeneous Medium

In the mid and late 1970s, there were several seminal theoretical models to explain the dynamics and emission from extra-galactic relativistic jets, such as the ‘twin-exhaust’ [35] and beam models [36], the Blandford–Znajek (B-Z) jet launch mechanism [37] and diffusive shock acceleration [38], which helped shape the future study of jets and non-thermal emission. Attempts at simulating such jet beams were made even at early stages as well, although with limited resolution [39]. The first detailed 2D simulations exploring the structures of hypersonic jet beams were published nearly simultaneously in 1982 by Yokosawa et al. [40] and Norman et al. [41], with the latter paper being more widely recognized in the literature. The Yokosawa et al. [40] paper showed that the nature of the jet beam (ballistic vs. turbulent) and formation of well-defined backflows depend on the jet and the contrast of density between the jet and ambient media. Norman et al. [41] presented a more detailed description of the structure of jet beams with features such as a working surface and backflow, as proposed in Blandford and Rees 1974 [35] (see Figure 1). These papers spawned several other numerical works that probed different aspects of the dynamics of supersonic jet beams, such as beamed synchrotron emission [42], 3D generalization [43,44,45,46], stability of slab jets [47], and MHD simulations [48,49]. Future works have built on the early success of such numerical simulations with larger domains, grid sizes and resolution, although true convergence of the cocoon and beam structures remain elusive [50,51] due to the small-scale structures generated with an increase in resolution.

The relativistic nature of jet flows had been inferred in the 1970s from observations of superluminal motion of jet knots in radio studies (e.g., [53,54,55,56,57]). Numerical simulations of steady-state jets with relativistic solvers had been presented as early as 1987 by Wilson [58]. Full-fledged dynamic simulations with relativistic solvers followed in the next decade e.g., [59,60,61,62,63,64,65]. A key focus of these simulations was to reconfirm the proposed model of the jet structure in the relativistic limit and explore the dependence of the jet’s dynamics on various properties of the jet. They established that the internal structures of relativistic jets show significant dependence on the Mach number of the jet beam, bulk Lorentz factor and internal pressure. Highly relativistic flows are more stable due to longer growth times of instabilities [66]. On the other hand, jets with progressively lower Mach numbers show markedly different behavior, varying from more internal structures in warm jets ($\mathcal{M}\sim 2$) to stable cocoons for hotter jets ($\mathcal{M}\lesssim 1.6$) [65]. This results either because small-scale perturbations are ill-resolved by the numerical grid or because KH instabilities couple poorly with the jet flow. Attempts at simulating magnetized relativistic jets have been made in tandem as well (e.g., [64,67,68,69]). However, such simulations received more momentum with the development of efficient high-resolution shock-capturing schemes in the late 1990s and early 2000s (see, for example, [70,71,72,73,74,75,76,77] and references therein).

In later years, advances in computational power and high-order numerical schemes (see Martí and Müller [78] for a review) have led to a wide range of AGN jet simulations. Such works have probed a diverse range of topics, such as the impact of fluid instabilities on the jet and cocoon structures (for some recent examples see [15,51,79,80,81,82,83,84,85]), the origin of turbulent structures and dynamics of lower-power FR-I jets (e.g., [86,87,88,89,90,91,92,93]), and the formation of their FR-II counterparts (such as [94,95,96]), to name a few. Another major focus has been to compare the jet dynamics with predictions from semi-analytical models of jet evolution (e.g., [97,98]). Several papers have proposed that jets undergo a self-similar expansion [94,98,99], although such an assumption may not hold for the entire life span of the jet [100,101], especially for the early phase of evolution [79]. In many cases, however, the general scaling laws predicted by Begelman and Cioffi [97], duly modified for a power-law ambient density profile, show a good agreement with simulations [79,94].

Simulations of large-scale jets have been further driven by efforts to understand the impact of jets on cluster scale environment and the resultant non-thermal emission (e.g., [102,103,104,105,106,107,108,109,110]). Such studies have given detailed results of the dynamics of large-scale jets, energy transfer to the environment, evolution of synchrotron surface brightness and polarization characteristics as a function of jet length. These have further motivated simulation-based scaling laws relating the synchrotron power to the jet’s mechanical power [111]. In recent years, simulations of jets have also been utilized to address other science goals such as production of ultra-high-energy cosmic rays from shocks driven by jets [112,113,114], impact of multi-species fluid on jet dynamics and emission (e.g., [115,116,117]), jet precession and production of X-shaped structures ([118,119,120,121,122,123,124]), impact of in situ particle acceleration of non-thermal electrons (e.g., [125,126,127,128,129,130,131,132]), etc., demonstrating the diverse areas of interest on this topic.

2.2. Jets in Inhomogeneous Medium

2.2.1. Non-Relativistic Simulations

The early phase: The earliest suggestion of jets interacting with intervening gas clouds was proposed as early as 1979, to explain the observed variability of jet emission [133] or the knots in the jet of M87 [57]. Although future works revealed such knots in M87 [134,135,136,137,138] and in others, such as Cen A, to arise from mechanisms related to hydrodynamics of the jet itself [139,140,141,142], static shocks in Cen A have still been attributed to possible obstructions in the jet’s path (e.g., from dense clouds) [143]. Later, in the 1990s, studies of Gigahertz-Peaked Spectrum (GPS), Compact Steep Spectrum (CSS) or Compact Symmetric object (CSO) [24,144,145,146], further renewed interest in the jet’s impact on its dense environment. Free-free absorption by intervening ionized gas, either as swept-up matter in the forward shock or pre-existing clouds engulfed by the evolving bubble of a radio jet [145,147], was proposed to explain the turnover in the radio spectrum of such sources. This motivated several theoretical simulations to probe the evolutionary stages of a jet through the host’s ISM, as further outlined below.

Jet-single cloud interactions: Some of the earliest 2D simulations of jets drilling through an inhomogeneous ISM were by DeYoung 1993 [148] and Steffen et al. 1997 [149], who considered a random distribution of spherical (or point-like) dense structures to mimic an inhomogeneous ISM. However, several key aspects of the physics of jet–ISM interaction were first elucidated by simpler configurations of jets piercing an oblique density discontinuity [150,151,152]. These papers highlighted that such interactions can tilt the jet’s Mach disc and disrupt the regular jet-cocoon structure into turbulent vortices. These results gave an early hint of disruption of the jet beam, which was further demonstrated by more complex simulations later on.

Similarly, other works have explored the impact of jets on individual spherical clouds, (e.g., [153,154,155,156,157,158]), or on multiple randomly distributed clouds (e.g., [158,159]), an extension of the DeYoung [148] setup. These so called ‘cloud-crushing’ simulations1 were an important first step in understanding how jets propagate through an inhomogeneous ISM, besides addressing other related questions, such as the origin of bent radio jets (wide-angle tailed sources) or asymmetric hybrid jet morphologies, etc. Subsequent studies included increasingly complex physical processes such as atomic and molecular cooling [170,171], idealized set-ups of shear layers and mixing [172], self-gravity and star formation [173,174], and realistic morphological models of inhomogeneous molecular clouds [175,176].

Resolved simulations of jet–cloud interaction are insightful in providing the details of how the jets/outflows are affected by the presence of a cloud [152,154,177,178], and more importantly, the various evolutionary stages of the clouds themselves (e.g., see Figure 2). Since they focus on a single cloud, such simulations often have sufficient resolution (at least ≳120 volume elements required across a cloud for convergence [168,169]) to capture the different fluid instabilities operating at jet-cloud interfaces [170,175,176], which otherwise become difficult to follow on global scales. Recent works have also included upgraded models of star formation [175,176] to quantify the positive/negative feedback that may result from the radiative shocks driven inside such clouds by the AGN outflows. However, a limitation of such individual jet–cloud simulations is that they do not probe the global impact on the ISM at larger scales, and the evolutionary stages of the jet through the inhomogeneous medium.

The first studies of Jets in fractal inhomogeneous medium: A separate line of simulations probed the passage of jets through a large-scale inhomogeneous ISM, a more realistic depiction than the early works of DeYoung [148], Steffen et al. [149]. Although such simulations have relatively moderate resolution (∼10–20 cells across a cloud [179,180]) than the previously mentioned single jet–cloud works, they probe the global impact of the outflow on the turbulent structures in the central few kpc of the galaxy. Hence, such studies are a bridge between the highly resolved jet–ISM interaction of single clouds and large-scale cosmological simulations with much poorer resolutions [∼100 pc], which cannot capture the internal structures of molecular clouds in any detail.

A key new detail of such simulations was the use of a fractal density distribution as a realistic model of the ISM. Two-dimensional simulations of jets through a fractal ISM were first introduced in the early 2000s [181,182]. The first detailed 3D simulations were presented in Sutherland and Bicknell 2007 ([52], hereafter SB07), where a non-relativistic jet was injected through a two-phase ISM. This was a pioneering paper in many aspects. It laid the technical foundation for several future publications and also elucidated the basic evolutionary stages of a jet breaking out through an inhomogeneous ISM. These studies were later improved upon by relativistic simulations of jet–ISM interaction, summarized in the next section (Section 2.2.2).

Other non-relativistic jet–ISM simulations with improved physics: Besides the SB07 study, several other papers have explored different aspects of jet–ISM interaction through non-relativistic simulations. In one such series, Gaibler et al. (2011,2012), [183,184] and Dugan et al. (2014,2017) [173,185], simulated jet feedback on a large inhomogeneous gas disk (∼30 $\mathrm{k}\mathrm{p}\mathrm{c}$), in contrast to the smaller disks (∼1–2 kpc) considered in other studies [52,180,186,187]. However, the larger scales necessitated a more modest resolution of $\Delta x\sim$67 pc, which was more than 10 times poorer than that of other similar simulations. Nonetheless, these simulations truly probed the global impact of an AGN jet on a large-scale disk. They outlined several important results, such as (a) asymmetric jet morphologies due to local density inhomogeneities [183], (b) large-scale compression-driven positive feedback [184], (c) a ring-shaped region with enhanced SFR surrounding the central cavity, (d) appearance of hyper-velocity stars with strong non-circular velocities [185], (e) comparison of jet vs. wind-driven feedback, and (f) impact of jet orientation [173] on feedback efficiency, a precursor to the later study by Mukherjee et al. [180]. The simulations provided observational predictions of active jet–ISM interaction, and provided diagnostics to identify past such activities in the form of disturbed stellar kinematics. While the above papers considered a preexisting fractal density as an initial condition, other recent works have also explored the generation of a self-consistent inhomogeneous ISM by stellar feedback, before jet launch (e.g., [188]). However, most of the above studies have only performed hydrodynamic simulations. Only a handful of papers [188,189] have explored the impact of magnetic fields on jet–cloud interaction, which remains an area to be explored in the future.

In recent years, a more self-consistent treatment of evolution jets within their environment has been carried out in another series of publications (e.g., Fiacconi et al. [190], Talbot et al. [191,192,193]). These works presented a novel sub-grid prescription for black hole accretion and ejection, based on a thin accretion disk model, duly accounting for variation of the accretion disk’s mass and the angular momentum exchange between the in-falling gas, the black hole and the accretion disk. The jet power is determined by the Blandford–Znajek mechanism, with the efficiency parameterized from GRMHD results [190,191]. The innovative model has been employed to study the mutual evolution of jets and a sub-kpc circum-nuclear disk (of radius ∼70 pc and height ∼9 pc) [191,192], as well as larger kpc scale gas disks [193]. The Talbot et al. [191,192] studies probed outflows from lower-mass black holes (∼${10}^6 M_{\odot }$), with jets of low kinetic power (∼${10}^{42} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$), whereas higher-power jets were explored in the subsequent paper [193].

Although the parameter space explored in these simulations is more representative of Seyfert galaxies than typical massive radio-loud AGN, the qualitative results are similar to other studies of jet–ISM interaction (see Section 3 for a general summary). However, one of the key outcomes of the Talbot et al. [192] work, not well explored in earlier simulations, is the self-consistent evolution of the jet angular momentum, including reorientation of an inclined jet, driven by the Bardeen–Peterson effect. The simulations also predicted significant cold ($T<{10}^4$ K) outflows from the circum-nuclear disk, with increased rates for inclined jets, in good agreement with observations [194,195]. Although the authors did not find significant evolution of the black hole spin during a single outburst, the generality of the method makes it suitable for implementation in large-scale cosmological simulations. This has been demonstrated in Talbot et al. [193], where the framework was used to trace black hole growth and feedback over cosmic time.

2.2.2. Relativistic Simulations

Why relativistic hydrodynamics? A drawback of using a non-relativistic framework for simulating AGN jets that are inherently relativistic in their bulk flows is the difference in the momentum exchange with the external environment. The momentum conservation equation in relativistic hydrodynamics is

$${\displaystyle \frac{\partial }{\partial t}}\left({\gamma }^2\rho h\mathbf{v}\right)+\nabla ·\left({\gamma }^2\rho h\mathbf{v}\mathbf{v}+\mathbf{I}p\right)=0,$$

(1)

where $\rho h=\rho c^2+\rho ϵ+p$ is the relativistic enthalpy, $\rho ϵ$ the internal energy, and $\mathbf{I}$ an identity tensor. The Lorentz factor of the flow velocity is $\gamma$. For a jet with a given rest-frame density, pressure and bulk velocity, a relativistic formulation implies higher momentum imparted by the jet beam, at least by a factor of ${\gamma }^2$. For example, the difference (${\gamma }^2-1$) becomes ∼10% even for mildly relativistic flows of $\beta \sim 0.3c$ ($\gamma \sim 1.05$). Thus, non-relativistic fluid dynamics will undervalue the momentum imparted by the jet. Of course, the total energy flux of a relativistic and non-relativistic jet, with identical fluid parameters, is not the same. Hence, non-relativistic simulations of jets have often employed an equivalent jet beam by fixing the jet pressure, velocity and injection radius to values suited for a non-relativistic simulation, but deriving the jet density to match the total energy flux. The relations between the densities for such an equivalent non-relativistic (${\rho }_{\mathrm{nr}}$) and its relativistic counterpart (${\rho }_r$) were derived by Komissarov and Falle [196] as

$${\rho }_{\mathrm{nr}}=2{\rho }_r{\gamma }^2\left({\displaystyle \frac{\gamma }{\gamma +1}}+{\displaystyle \frac{1}{\chi }}\right),\chi ={\displaystyle \frac{\rho c^2}{\rho ϵ+p}}={\displaystyle \frac{(\Gamma -1)}{\Gamma }}{\displaystyle \frac{\rho c^2}{p}},$$

(2)

where $\chi$ is the ratio of the rest mass energy and the non-relativistic part of the rest-frame enthalpy ($\rho h-\rho c^2$). Equation (2) shows that a flux-matched non-relativistic jet has a higher density, and hence a heavier jet. This results in narrower jet cocoons, faster jet propagation, higher mach numbers [65,196] and lower cavity pressures [197] than that of relativistic jets. Thus, irrespective of the choice of initial jet parameters, whether done by strictly ignoring relativistic effects, or by deriving effective jet parameters by matching fluxes, the momentum balance is strongly affected by the neglect of relativistic solvers while evolving AGN jets [14,65,196]. However, the accuracy of the momentum exchange is crucial for the physics of jet–ISM interaction and the implications for local-scale AGN feedback effects by the jets. This necessitates the usage of relativistic solvers in simulations of jet feedback.

Relativistic Jets in a static fractal ISM: The first such simulations were presented in Wagner and Bicknell 2011 [179] and later expanded with a larger set of simulations in Wagner et al. 2012 [198], which probed different volume filling factors of the dense gas. These simulations modeled a relativistic jet ploughing through a static fractal ISM [52], immersed in a constant-density background halo. The simulations did not have an external gravitational field of the galaxy. The dense ISM was assumed to be distributed spherically, unlike SB07 [52], who considered a disk. The suite of simulations probed several different parameters of the simulations relevant for studying jet–ISM interaction, such as (i) jet power: ${10}^{43}$–${10}^{46} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$, (ii) mean cloud density: ${10}^2$–${10}^3 {\mathrm{c}\mathrm{m}}^{-3}$, (iii) volume filling factor2: $f_V\sim$ 0.027–0.4 and (iv) cloud sizes: 10–50 pc (see Table 2 of Wagner et al. [198]). All the simulations were run for a jet of $\gamma =10$ and $\chi =1.6$ (see Equation (2)).

These simulations, along with SB07 [52], were the first to explicitly identify the various stages of a jet’s evolution, as it channels through an inhomogeneous ISM (see Section 3.1 for more details). They examined the effect of the jet on ablation and acceleration of ISM clouds, the dynamics of the jet-driven bubble, and the resulting impact on ISM energetics, placing these processes in the broader context of AGN feedback in galaxies. These results provided definitive proof that jets can significantly impact the host’s ISM, which has been further expanded upon and confirmed in future simulations. Additionally, these papers highlighted two other impacts of jets, not often highlighted in other studies:

• Moderately powerful jets ($P_{\mathrm{jet}}\gtrsim {10}^{43} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$) can potentially clear an ISM with small-sized clouds ($\lambda \lesssim$ 10–20 pc). Such jets are capable of driving outflows with mean radial velocities higher than the stellar velocity dispersion, even for modest values of Eddington ratios ($\eta =P_{\mathrm{jet}}/L_{\mathrm{Edd}}\sim {10}^{-4}$–${10}^{-3}$), thereby indicating successful negative feedback. In contrast, sufficiently accelerating larger clouds, such as Giant Molecular Clouds (GMCs hereafter) with sizes of ≳50 pc [199,200,201], require substantially higher Eddington ratio ($\eta \gtrsim$ 0.01–0.1) and jet powers ($P_{\mathrm{jet}}\gtrsim {10}^{45} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$). This suggests that such cases require more efficient outbursts from a larger mass SMBH to power global outflows. Thus, larger clouds enhance jet confinement and are also more resilient to ablation, as also confirmed in later works [186].
• The jets were found to provide a strong mechanical advantage (i.e., a value greater than unity), which is defined as the ratio of total outward momentum of the clouds to the momentum imparted by the jet until a given time (e.g., $P_{\mathrm{jet}}t/c$). This enhancement arises because the high-pressure bubble created by the jet accelerates the clouds in addition to the direct ram pressure of the flow. This is similar to the high-momentum boost conjectured for the energy conserving phase of a general AGN-driven outflow [202,203]. The temporal evolution of the mechanical advantage correlates with the fraction of kinetic energy transferred to the ISM, peaking at ∼20–30%, which was later refined to slightly lower values by future simulations [186]. Overall, these results indicate strong coupling of the jet with the ISM.

Jet–ISM interaction in dynamic environments: The earlier studies were extended by four subsequent papers—Mukherjee et al. 2016 [186], Bicknell et al. 2018 [204], Mukherjee et al. 2018a [205] and Mukherjee et al. 2018b [180]—which had several new developments: (i) an external gravitational potential (double isothermal) with a hydrostatic atmosphere, which enabled more accurate estimates of gas kinematics (see Section 3.3), (ii) initialization of the ISM with a turbulent velocity dispersion along with the fractal density, which added further realism to the setups and enabled successful comparison with observations (see Section 4). These simulations have formed the primary benchmark for studies of jet–ISM interactions in recent years.

The papers listed above mainly considered high-power jets ($P_{\mathrm{jet}}\sim {10}^{44}$–${10}^{46} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$). Tanner and Weaver 2022 [187] extended such simulations to a broader range of powers, including simulations with very low jet powers ($P_{\mathrm{jet}}\lesssim {10}^{42} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$), compared to what was previously explored. While these simulations broadly recovered the earlier results [180], one key distinction was that the higher-power jets ($P_{\mathrm{jet}}\gtrsim {10}^{44} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$) were not efficiently confined and found to eventually drill through the ISM. In contrast, lower-power jets were more prone to disruption and breakup. Such confinement of low-power jets likely results from the weaker jet momentum flux due to the lower jet density and pressure, which in turn causes longer cloud ablation and jet confinement time scales (see Appendix A for a discussion on jet confinement). Similar results have also been reported in more recent non-relativistic simulations [206].

3. Summary of Key Results

Although results of different simulations may vary due to different choices of jet parameters, the ambient medium or micro-physics, a common set of general outcomes can be ascertained. In the following sections, we outline the broad summary of some general conclusions and the key results of the simulations of jet–ISM interaction.

3.1. Evolutionary Stages of the Jet Through an Inhomogeneous Medium

In general, one can identify a common set of evolutionary phases of a jet moving through as gas-rich ISM (first presented in [52]). This is illustrated in Figure 3.

• The Confined phase: The jet remains confined within the clumpy ISM (∼0.5–1 kpc), resulting in the formation of a flood-channel scenario (see right panel of Figure 1). The jet plasma is diverted to low density channels through the clouds, through which it percolates into the ISM. The jet beam’s forward progress is temporarily halted. However, the backflows from the stalled jet disperse its energy over a quasi-spherical volume. This creates a highly pressurized energy-driven bubble, enclosed by a forward shock, sweeping through the ambient medium. Simulations find that the timescale of such a confined phase can last from a few hundred kilo-years to ∼2 Myr, and depends on various factors, such as the jet power, the density of the ambient medium and the spatial extent of the dense gas. In fact, low-power jets may remain confined for a long time, without ever evolving to the later stages [186,187,198,206]. An approximate analytical treatment of the duration of confinement is presented in Appendix A. Since these conditions can vary significantly between different galaxies, the impact of the jet and the efficiency of coupling with the ISM can have a wide variation as well.
• Jet breakout phase: In this phase, the jet and its resultant hemispherical bubble break free from the dense ISM and evolve further. Although free from the confines of the ISM, the jet-driven bubble can still indirectly impact the dense gas in the galaxy. The bubble remains over-pressurized and eventually engulfs the ISM. The combined impact of the bubble and backflows from the tip of the jet drives shocks into clouds away from the jet axis. This enhances turbulence [180] and impacts star formation in the inner few kpc of the galaxy [180,207,208]. Eventually, at late times, as the bubble’s pressure decreases due to its expansion, the impact on the dense ISM is weakened.
• The classical phase: Beyond the breakout phase, the jet carves a clear path through the ISM. Subsequent energy flows have less impact on the ISM. The jet-head proceeds into the low-density stratified halo gas. Beyond this point, the dynamics of the jet are similar to the conventional models of jet propagation into a static homogeneous medium. The dynamics of the ISM and perturbed velocity dispersion of the clouds start to decay back to the pre-jet levels [208].

Of the above stages, the confined phase is of primary interest in the context of AGN feedback. During the confined phase, there can be strong coupling of the jet with the dense gas, which would result in a significant transfer of the jet’s energy flux into the ISM (e.g., ∼10–20% for the simulations presented in [186,198]) in the form of kinetic energy, which creates local outflows and also heats the gas via radiative shocks. The efficiency of such an interaction depends on the following parameters:

1.

The volume filling factor of the dense gas ($f_V$).

2.

Jet’s orientation with respect to the ISM morphology, with jets inclined to a gas disk showing more coupling with the ISM (${\theta }_j$).

3.

Jet power ($P_j$).

4.

Mean density of the clouds in the ISM ($n_c$).

Thus, the efficiency of jet-driven feedback on kpc scales depends on a four-dimensional parameter space. The maximal impact, of course, is for a high-power jet, directly oriented into a dense ISM (e.g., jets pointed into a gas disk [180,205,209]), having clouds with high mean density, which results in longer confinement of the jet. More detailed discussion on the impact of parameters 1, 3 and 4 on jet confinement is discussed later in Appendix A. However, the interactions can also be gentle if one of the parameters is weak, even though others are prominent. For example, although NGC 3100 [210] hosts a moderately powerful jet ($P_j\sim {10}^{44} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$) along with a dense gas disk observed in CO 1-0, the impact of the jet on the disk’s kinematics is minimal. This is likely due to weak jet–disk coupling, arising from the relative orientation of the jet away from the disk’s plane. However, on the other hand, several detailed spatially resolved observations have uncovered more telltale smoking gun signatures of the strong impact of the jet on the confining ISM, as discussed later in Section 4.

3.2. Global Impact on the ISM

Simulations of jets through the inhomogeneous ISM have strongly supported that jets can cause a large-scale effect on the central few kpcs of the galaxy, contrary to earlier beliefs that such thin collimated structures are less important in the global context [211]. There are again three distinct types of impact of the jet, which has varied effects on the ISM.

1.

Direct impact of jet-beam (≲1 kpc): Clouds directly along the path of the jet are strongly affected by the flow and are eventually destroyed. Such an interaction influences the evolution of both the clouds and the jet. For large clouds that may nearly cover the jet’s width (e.g., a GMC of size $\gtrsim 50$ pc), the jet is strongly decelerated until the cloud moves away from its path, or is completely disintegrated. The region of such impact is usually confined to ≲1 kpc, where the jet beam and its ensuing backflow directly interact with the ISM. This region experiences much higher turbulent velocity dispersion and density enhancement [208] due to stronger ram pressure-driven shocks. In addition, the stronger interaction in the central region also results in mass removal and formation of a cavity [180,184,208]. However, simulations that better resolve the cloud structures show that such cavities are not completely devoid of dense gas [205,209]. Strands of dense cloud cores compressed to high densities by radiative shocks remain embedded inside such cavities and are slowly ablated by the jet-driven flows [180,205].

2.

Indirect impact by energy bubble (≳1 kpc): As discussed in Section 3.1, the energy of the confined jet spreads out in the form of an expanding energy bubble and sweeps through the ISM. The nature of this indirect coupling of the jet and the ambient gas depends on the evolutionary phase of the jet (see Section 3.1). During the jet-confinement phase, the forward shock of the energy bubble sweeps through the ISM. The embedded clouds face a steady radial outflow of the jet plasma, which is re-directed in lateral directions, away from the jet axis, through the flood-channel mechanism. This results in outward radial flows inside the ISM. In the jet-breakout phase and beyond, the jet expands beyond the immediate confines along its path and the over-pressured cocoon engulfs the ISM. This is more prominent for gas disks, as shown in the right panel of Figure 3. Such indirect interactions are responsible for more large-scale impact of the jet, beyond the central 1 kpc. This raises the velocity dispersion of the gas and also shock heats a large volume of the ISM [212,213]. Inclined jets that remain strongly confined within the ISM [173,180,187,205] are more agents of feedback, as the decelerated jet-head allows plasma to spread and create widespread radial flows.

The fact that jets can, in principle, affect a volume of the ISM larger than their apparent width near their launch axis has strong implications for AGN feedback. This demonstrates that jets can create strong global outflows, impact gas kinematics and star formation rate of the galaxy, as further discussed below.

3.3. Impact on ISM Kinematics

As discussed above, the jets can affect a significant fraction of the ISM during the confined and breakout phase, which results in fast multiphase outflows [52,173,186,187,192,198,205]. The extent of the interaction and nature of the outflows depend on the four key factors listed in Section 3.1. We list below some of the broad major inferences that can be drawn from these theoretical simulations.

3.3.1. Multi-Phase Outflow

In a realistic system, one would expect a wide range of gas phases to co-exist: (a) dilute hot gas in the halo of galaxies, (b) dense gas collisionally ionized by shocks or photoionized by radiation from a central source like AGN [212] or shock precursors [214], (c) warm molecular gas likely representing cooling fronts of shocks or turbulence that have penetrated the dense gas [215,216], (d) cold dense molecular gas [217,218], and (e) neutral (e.g., HI) gas [33]. However, most simulations consider a single fluid system and do not explicitly track the chemical evolution of the constituents of the gas, due to the computational complexities. Although some recent works have started some preliminary investigations to model differences in composition [15,219,220] in jet-gas simulations, such efforts are still in their infancy.

Nonetheless, simulations that can resolve the density sub-structures inside an inhomogeneous ISM can track the variation of density, temperature and velocity structures of the fluid, which act as a proxy for the different phases [205,212,221]. Some theoretical papers have attempted to understand the multi-phase nature of the ISM and disentangle the relative contributions of different gas properties in the outflows by evaluating 2D histograms [176,186] or analyzing the simulations based on temperature thresholds [192]. A better representation of the multi-dimensional nature of the phase space is shown in Figure 4, where the mass distribution is represented in terms of the three primary variables of interest, viz. density (n), temperature (T) and the outward radial velocity ($v_r$) representing the outflowing gas. The corresponding 2D distributions obtained by summing along each axis of the 3D distribution are plotted on the right. However, the summed 2D distributions often fail to capture the variation in the phase space visible in the 3D image. The plot is for the last panel of Figure 14 of simulation D from Mukherjee et al. [180], which corresponds to a jet of power $P_j={10}^{45} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$, launched at ${45}^{\circ }$ to the axis of the disk.

Several distinct identifiable regions have been highlighted in the 3D figure (Figure 4).

• Cloud cores: There is collection of mass at $T\sim 1000$ K, with high densities near the left face of the 3D figure. This corresponds to the cores of the clouds, with a temperature near the cooling floor of the simulation ($T={10}^3$ K). The clouds have some positive radial velocity ($v_r\lesssim 100 {\mathrm{k}\mathrm{m} \mathrm{s}}^{-1}$), which likely is a mixture of the turbulent bulk velocity of the clouds injected at the beginning of the simulation and also mild acceleration after jet–ISM interaction.
• Dense warm outflow: There is a collection of mass in Figure 4 that is shifted from the cloud cores, extending from $T\sim {10}^3$ K to $T\sim {10}^4$ K in temperature, $v_r\sim$ 100–1000 ${\mathrm{k}\mathrm{m} \mathrm{s}}^{-1}$ in velocity and density of $n\gtrsim 100 {\mathrm{c}\mathrm{m}}^{-3}$. This phase corresponds to the dense shock-heated gas accelerated to high velocities that has now cooled. This phase has the highest mass amongst all of the outflowing gas and is the dominant contributor to the kinetic energy budget of the outflows. In observational studies, this phase would correspond to the warm molecular gas [215,222,223,224] or the cold gas outflows [217,221,225], as modeled in Mukherjee et al. [205].
  However, one must note that the lack of explicit chemical evolution and molecular cooling (however, see [219,220] for recent updates) in these simulations limits quantitative comparison with such observed phases. Nonetheless, the distinct feature in the above phase space diagram qualitatively indicates the multi-phase nature of the ISM shocked by jets and the probable location of the dense molecular phase in the 3D phase space of the simulated gas distribution.
• Shocked cloud layers: Beyond the dense warm phase, there is another distinct, but small, collection of mass, peaking between $T\sim {10}^4$–${10}^5$ K, and at a lower density ($n\sim$ 10–100${ \mathrm{c}\mathrm{m}}^{-3}$) than the dense warm phase. The temperature range above corresponds to the peak of the cooling curve. This phase is composed of the outskirts of the clouds being shocked by the enveloping pressure bubble or shocked dense cloud-lets ablated from large clouds [180,213]. It accounts for the majority of the observed emission in optical lines used as diagnostics of shock ionization, such as [OII], [OIII], [SII], etc. [205,213]. It should be noted that the mass represented in this phase is small compared to the dense phase. Hence, masses of ionized gas inferred from such shocked gas are often lower limits to the total ISM mass, which is often difficult to estimate due to the lack of multi-wavelength coverage.
• Hot tenuous outflow: The jet-driven outflows push out the gas ablated from the clouds in a tenuous hot form ($n\lesssim 10 {\mathrm{c}\mathrm{m}}^{-3}$, $T>{10}^6$ K). This manifests as an elongated tail in the phase-space distributions of Figure 3, which extends to very low densities and high velocities. Such a hot, tenuous gas can potentially be observed in X-ray wavebands [52]. However, detecting the soft thermal X-rays from shocked regions, with sufficient spatial resolution to distinguish them from the central nucleus, is challenging, owing to photoionizing radiation from the AGN. Nonetheless, such X-rays from shocked gas have been tentatively confirmed in several sources, e.g., 3C 171 [226], 3C 305 [227], PKS 2152-69 [228], B2 0258+35 [229]. A broader review of such cases, including both jetted and non-jetted AGN, is presented in Fabbiano and Elvis [230].

3.3.2. Galactic Fountain

Although the jets can launch strong local outflows, a blow-out of the major fraction of the ISM, as often required by semi-analytical models of AGN feedback [9,11], is not obtained in many of simulations discussed above. Studies investigating resolution dependence of cosmological simulations have shown that simulations with higher resolution retain more gas in the galaxy [231]. Hence, simulations that better resolve denser ISM structures [180,186], including those with non-relativistic AGN winds [232,233], find it difficult to clear out the galaxy. The total mass weighted mean velocities are, in fact, negative in some cases [186]. Although some recent large-scale simulations have shown strong outflows (sometimes reaching up to ∼100 kpc [193]), a fraction of the uplifted gas falls back at later stages. However, it must be noted that the above results depend on various conditions of the ISM, such as the mean density, cloud sizes, efficiency of ablation [31,180], etc., and the power of the outflow. Low-density clouds with smaller sizes may be pushed out with higher efficiency. Nonetheless, denser ISM in general provides stronger resistance to large-scale ejection.

The discussion above indicates that although jet feedback simulations can cause strong localized outflows, a significant fraction of the ISM may remain within the gravitational potential of the host galaxy. This is best demonstrated by the escape fraction plot in Figure 20 of Mukherjee et al. [186]. It shows that only ≲10% of the ISM moves beyond the central few kpc. Such outflows, without escape, will give rise to galactic fountains, where the expelled gas is expected to be recycled within the galaxy’s confines [186].

3.3.3. Turbulent Velocity Dispersion

A key focus of local AGN feedback studies in both observational and theoretical domains has been to understand the influence of AGN-driven outflows on the turbulence of the ISM. Resolved simulations of jet–ISM interactions have shown that as the jet-driven bubble sweeps over the central few kpc of the ISM, it can significantly raise the velocity dispersion by an order of magnitude from its initial value. However, this seems to depend on the phase of the gas. For example, Mukherjee et al. [180] show that hotter shock ionized gas ($T>{10}^4$ K) will have higher-velocity dispersion (∼400–600 ${\mathrm{k}\mathrm{m} \mathrm{s}}^{-1}$) than the colder component (≲100 ${\mathrm{k}\mathrm{m} \mathrm{s}}^{-1}$). This is because the shocks progress very slowly within the dense cores. The primary impact of the jet-driven bubble is on the ablated cloudlets stripped from the larger clouds. Random bulk motions of such clouds add to the velocity dispersion. However, the dense gas is not completely undisturbed. Detailed comparisons of the kinematics of dense gas in galaxies such as IC 5063 [217] and B2-0258 [221,234] with simulations [180,205,213] have shown excellent correspondence with observed gas kinematics. An interesting new feature identified in both simulations [205,213] and observations [235,236,237,238,239] is the appearance of high-velocity dispersion in directions perpendicular to the jet. Such features are conjectured to arise from deceleration of a jet strongly inclined into the gas disk, resulting in outflows of plasma both along the minor axis following the path of least resistance [205,213], as well as into the plane of the gas disk [240]. A combined effect of both types of motions is predicted to result in such apparent enhanced widths perpendicular to the jet [213,240].

3.4. Impact on Star Formation Rate

One of the primary motivations of AGN feedback studies has been to understand the impact of AGN-driven outflows on the instantaneous and long-term star formation rate (SFR) of galaxies. In simulations, star formation rates have been predominantly estimated as

$$SFR=ϵ{\displaystyle \frac{\rho }{t_{\mathrm{ff}}}};t_{\mathrm{ff}}={\left({\displaystyle \frac{3\pi }{32G\rho }}\right)}^{1/2},$$

(3)

where $ϵ$ is often assumed to be a constant efficiency factor (≲0.01) and $t_{\mathrm{ff}}$ is the local free-fall time. Both negative and positive feedback scenarios have been predicted by simulations. Since estimates of star formation rates only depend on the gas density, a reduction in SFR can be achieved either by removing gas from a galaxy’s potential or by ablating dense clouds to lower densities. Similarly, SFR can be enhanced by shock-driven compression of gas [31]. Some large-scale simulations that probe maintenance mode feedback using self-consistent modeling of feedback cycles and star formation have demonstrated that AGN outflows can suppress star formation (e.g., for some recent works, see [22,241,242], and references therein). However, many of these studies often are unable resolve a preexisting dense inhomogeneous ISM of the host galaxy. Gas removal, and hence reduction in SFR via mass loss, is also more effective for the lower resolutions [231] in such studies, as compared to simulations discussed earlier. Properly testing the impact of outflows on a dense inhomogeneous ISM, thus, necessitates resolving the structures on the scales of molecular clouds (∼50–100 pc).

Spatially resolved simulations of jet-ISM interaction have predicted a central cavity (hence negative feedback) surrounded by a ring of SFR-enhanced region due to compression of gas in the immediate rim of the cavity [173,180,184,188]. Strong compression from the ensuing pressure bubble can potentially promote star formation in extended regions of the galaxy as well [184,207]. Such theoretical predictions of positive feedback compliment some observed sources, especially where star forming streams are found to align with outflows [243,244,245,246]. Additionally, several radio-loud galaxies are known to have significantly reduced SFR [222,247]. The nature of the density structures also determine how the outflows impact the SFR. Low-density, smaller clouds are easily ablated, resulting in negative feedback [31,193]. On the other hand, simulations with higher gas densities, similar to the dense cores of molecular clouds ($n\gtrsim 100 {\mathrm{c}\mathrm{m}}^{-3}$), are more resilient [232,233] and often show enhancement of SFR [184]. Such diverse results should be explained by a single self-consistent model of star formation.

In a recent study, Mandal et al. [208] proposed a new method to estimate the SFR in simulations that resolve turbulent gas structures. The work applies the well known theoretical framework of turbulence-regulated star formation in molecular clouds [248,249] to estimate the SFR in AGN feedback simulations. The model duly accounts for the variation of local free-fall time as a function of the gas density, the virial parameter (${\alpha }_{\mathrm{vir}}=2E_{\mathrm{kin}}/E_{\mathrm{grav}}$) and the Mach number of the gas ($\mathcal{M}$). Only those regions whose Jean’s length is lower than the sonic scale (${\lambda }_J={\left(\pi c_s^2/\left(G\rho \right)\right)}^{1/2}\lesssim {\lambda }_s$) are considered to be gravitationally unstable to form stars. The sonic scale is defined as the length scale at which the turbulent velocity dispersion is lower than the local sound speed. At scales higher than the sonic scale, the turbulent pressure offsets the gravitational collapse. The above criteria yield a density threshold for star formation that depends on the properties of the local turbulence, which is a significant upgrade from the simplistic gas-density based prescription outlined above.

The turbulence-regulated method has been used in post-processing to estimate the SFR of jet–ISM interaction simulations by Mandal et al. [208]. In a departure from either pure positive or negative feedback, the above approach with improved micro-physics reveals some new aspects. (i) There is a mild global reduction in SFR during the onset of the jet–ISM interaction, (ii) inefficient positive feedback occurs in the inner regions directly impacted by the jet, and hence, they encounter both jet-driven compression as well as enhanced turbulence, (iii) the ISM goes through a sequence of evolutionary phases in the Kennicutt–Schmidt (KS) plot, until the jet breakout, beyond which the turbulent velocities return to pre-jet levels. Although in its infancy, the inclusion of a turbulence-regulated star formation model in large-scale simulations shows promise in addressing several existing issues related to the impact of AGN feedback processes on SFR.

In addition to turbulence, other factors such as photo-ionization from the central AGN have also been considered as a potential source of preventing star formation. Post-process analysis of some jet-feedback simulations has found that AGN-driven photoionization does not significantly affect the SFR, for the chosen parameters of their studies [212,250]. However, this is a largely unexplored domain which requires more work, with detailed inputs of gas chemistry [251] for more definitive results.

4. Observational Implications

As outlined in Section 1.2, several reviews have summarized the observational evidence and implications of AGN feedback. We refer the reader to Harrison and Ramos Almeida [2], which is a more recent addition to the series. However, in the following sections, we briefly summarize the observational results related to jet–ISM interaction in particular, which is a narrower focus than the broad discussions presented earlier.

4.1. Observations of Jet–ISM Interactions

Evidence of jet–ISM interactions was presented even in the early days of studies of relativistic jets in galaxies. One of the first such reports was in 1972 [252], which conjectured that a “nuclear explosion” had expelled ionized gas co-located with radio-emitting ridges in NGC 4258. The authors at that time had discounted the idea that relativistic electrons were streamed directly from the nucleus, as the concept of non-thermal plasma moving at bulk relativistic speeds was still not well-developed. Future studies of this well-studied galaxy have now established that it harbors radio jets which are co-planar with the gas disk and strongly interact with the ISM [253,254,255]. Later, in the early 1980s, several galaxies were found to have radio emission co-spatial with ionized gas emission (e.g., 3C 66B, 3C 31, NGC 315, 3C 449 [256], 3C 277.3 [257], 3C 305 [258], 3C 171 [259], 3C 293 [260], 3C 310 with a proposed radio bubble from a trapped jet [261], etc.). The spectra of such sources often revealed elevated kinematics of the ionized gas and depolarization of radio emission, all of which was indicative of jet–ISM interaction.

Later on, several other papers reported alignment of radio and optical/UV emission in multiple sources [262,263,264,265]. Such observations presented evidence of widespread prevalence of jet–ISM interaction in general and also possible signatures of positive feedback, if the UV emission was from newly formed stars (see reviews by McCarthy [266] and O’Dea and Saikia [24]). However, further analysis revealed possible contamination of the observed UV emission by two sources: (i) radiation from the central AGN, either through scattering from dust or direct photoionization, (ii) nebular continuum emission [23,267,268,269,270]. Only in a small fraction of such sources did young stars contribute to the UV budget [23]. Thus, it remains unclear whether such alignments can be considered to be strong signatures of jet-induced star formation. More recent results, such as Duggal et al. [246], have expanded on this, with observations of spatially extended UV knots, a few kpc away from the central nucleus, confirming the possibility of the presence of young stars. However, more work is needed to ascertain the extent of AGN contribution in such systems.

In recent years, better access to spatially resolved sensitive observations has resulted in a large collection of multi-wavelength and multi-phase observations of jet–ISM interaction (see Figure 5 for an example). A collection of sources has been presented in

Table A1. A selection of cases with observations of jet–gas interaction. The second column mentions the major gas phase where outflows/feedback effects are observed. The label Ionized in general denotes standard emission lines in optical bands, with some having data at other frequencies such as IR and X-rays. WH2 in the molecular phase denotes warm H2.

	Source/Survey	Gas Phase	Comments and References
1	J1430 (Tea Cup), J1509, J1356, part of the QSOFEED survey	Molecular (CO, WH2, PAH), Ionized (Optical+Xrays)	Part of a sample of 48 Type-2 Seyferts (44 detected in radio) with several examples of well defined jetted system driving outflows. [240,395,396,397,398,399,400]
2	NGC 5929	Molecular (WH2), Ionized (FeII)	Outflows perpendicular to the jet axis. [236,401]
3	QFeedS survey	Molecular (CO), Ionized	A survey of 42 sources [298], many radio-quiet [298,402] but showing jet-like features (∼88% cases [299]) and dense gas (for 17 sources [300,301]). Multi-wavelength studies of feedback performed for a subset of sources, including outflows perpendicular to the jet. [237,238,403]
4	NGC 5972	Ionized	Detection of jet-induced shocks. [404]
5	3C 293 (UGC 8782)	Molecular (WH2), Atomic (HI absorption), Ionized	[405,406,407,408,409]
6	IC 5063	Molecular (CO, WH2), Ionized (IR/optical+X-rays)	A very well studied source with a jet strongly inclined into a kpc-scale disk. Shows outflow perpendicular to the jet. [217,410,411,412,413,414]
7	NGC 5643, NGC 1068, NGC 1386, NGC 1365	Ionized	Part of the MAGNUM survey, also including IC 5063. Several of these sources show outflow perpendicular to the jet. [235,415,416]
8	NGC 3393	Molecular (CO), Ionized (Optical+X-rays)	[417,418,419]
9	NGC 7319 in Stephan’s quintet	Molecular (CO), Ionized	A well studied group of 5 interacting galaxies with one showing prominent jet–ISM interaction. [420,421]
10	3C 326	Molecular (CO, WH2), Ionized	Early evidence of strong jet-induced turbulence, refined with better spatial resolution (JWST) to uncover in situ outflows [222,422,423,424]
11	GATOS survey	Molecular (CO), Ionized	A survey of dusty CND of 19+ Seyferts [195,425]. Several show very prominent jet–ISM interaction, reported as part of this survey and also from other multi-wavelength observations. [426,427,428,429]
12	WIDE-AEGIS-2018003848	Ionized	Detection of strong shock from emission line modelling, likely powered by the radio jet. [430]
13	B2 0258+35 (NGC 1167)	Molecular (CO), Ionized (X-ray)	A confirmed detection of jet clearing the central kpc of dense gas. Tentative confirmation of thermal X-rays. [221,229,234,278]
14	NGC 3100, IC 1531, NGC 3557	Molecular (CO, tentative HCO+)	A subset from a survey of 11 LERGs, showing evidence of only mild jet–ISM interaction, in spite of potential conditions available for more stronger effects observed elsewhere. [210,431,432,433]
15	NGC 1052	Ionized	Prominent ionized bubble along the galaxy’s minor axis, blown by a jet inclined towards a nuclear gas disk, besides detection of large-scale disturbed kinematics and shocks. [434,435,436,437]
16	NGC 3079	Radio (deceleration of knots), Ionized	A well studied source with prominent gas filaments from nuclear outflows [438]. Observed pc-scale jet–ISM interaction [439,440], which may power the large-scale outflow [441,442].
17	XID2028	Molecular (CO), Ionized	Co-spatial collimated molecular, ionized jet-driven outflows outflow piercing gas shells (≳6 kpc) from the nucleus. [443,444]
18	4C 31.04	Ionized, Neutral	CSS source with $\sim 100$ pc jet but large-scale (∼0.3–2 kpc) shocked gas. [216,225]
19	NGC 3998	Radio	Indirect evidence of jet–medium interaction from radio emission. [445]
20	NGC 4579 (Messier 58)	Molecular (CO, WH2, PAH), Ionized	[446]
21	IRAS 10565+2448	Molecular (CO), Atomic (HI emission+absorption), Ionized	[447]
22	4C 41.17	Molecular (CO), Ionized	A $z=3.792$ galaxy associated with positive feedback [245,448]
23	PKS 1549-79	Molecular (CO), Ionized, Atomic (HI absorption)	Nuclear molecular outflow, extended ionized outflow. [449,450]
24	Sub sample of 9 sources from the southern 2 Jy sample [451]	Ionized	Broad integrated outflowing emission lines ($v_{\mathrm{out}}\gtrsim 800{ \mathrm{k}\mathrm{m} \mathrm{s}}^{-1}$, FWHM $\gtrsim 700{ \mathrm{k}\mathrm{m} \mathrm{s}}^{-1}$) driven by jets. [452]
25	3C 273	Molecular (CO), Ionized	Expanding jet-driven cocoon impinging on a gas disk. [453]
26	HE 1353-1917, HE0040-1105	Ionized	Nuclear-scale jet-driven outflow. Part of the CARS survey. [454,455]
27	4C 12.50 (F13451+1232)	Molecular (CO, WH2), Ionized	Strong jet-driven nuclear (≲100 pc) outflow [456,457,458], but not on large scales[459].
28	TNJ 1338-1942	Ionized	Jet impact on extra-galactic gas cloud with extreme kinematics. [460,461,462]
29	NGC 6328 (PKS 1718-649)	Molecular (CO)	GPS source with pc-scale jet interacting with ambient gas. [463]
30	PKS 0023-26	Molecular (CO)	[464]
31	HzRG-MRC 0152-209 (Dragonfly galaxy)	Molecular (CO)	Molecular outflow (jet/AGN-driven) perpendicular to the jet, with indications of jet–ISM interaction at small scales. [465]
32	ESO 420-G13	Molecular (CO), Ionized	[466]
33	Jet-driven HI outflows (including 3C 236, 3C 305, 3C 459, OQ 208)	Molecular (CO), Atomic (HI absorption)	[467,468,469,470]
34	NGC 4258 (Messier 106)	Molecular (WH2), Ionized, X-rays	Detection of shocks and turbulence induced by jets. [253,254,255]
35	Molecular Hydrogen Emission line Galaxies (MOHEG)	Molecular (WH2)	A sample of 17 Radio-Loud galaxies with detections of warm H2 lines and indications of jet-driven shocks. [471]
36	PKS B1934-63	Ionized, WH2	Compact GPC source with ionized outflow but not in molecular phase. [472]
37	Cen A (NGC 5128)	Molecular (CO)	Jet-induced inefficient star formation in filaments along the jet. [473,474]
38	Cygnus A	Molecular (WH2, PAH), Ionized	High velocity ∼6 kpc-scale outflow driven by jet. [475]
39	SINFONI survey of RLAGN	Molecular (WH2), Ionized	A survey of 33 powerful RLAGN, confirming widespread jet-driven extreme gas kinematics. [223,224,476]
40	NGC 6951	Ionized	[477]
41	PKS 2152-69	Ionized (Optical+X-rays)	Highly ionized gas cloud 8 kpc from the galaxy impacted by a jet. [228,478,479].
42	PKS PKS2250-41	Ionized	Interaction of a jet with gas in a companion galaxy. [480,481,482]
43	IRAS 00183-7111	Molecular	Jet–ISM interaction in a ULIRG [483]
44	J165315.06+234943.0 (Beetle)	Ionized	Detection of extreme gas kinematics up to 46 kpc from the galaxy due to shocks from a jet in a radio-quiet quasar [484].

of Appendix B, along with comments on the nature of the interaction where applicable. These sources show signs of interaction of a jet with the ambient gas, such as spatially resolved outflows and/or enhanced velocity dispersion of the gas. The list is not meant to be a complete collection of all observed cases, but a representative sample showing the diverse nature of observations of jet–ISM interaction. In many cases, however, the central AGN is also energetically capable of driving the observed outflows. However, several factors, especially resolved spatial morphology of the gas kinematics and jet, support the jet-driven feedback scenario.

Besides spatially resolved studies of individual galaxies, several papers have explored observations of jets driving outflows in larger samples of radio-loud galaxies (e.g., [271,272,273,274], etc.). Such studies confirm the widespread prevalence of jet-driven outflows influencing their host. This is further extended by the discovery of ionized outflows in the “red geyser” galaxies, which comprise up to ∼10% of the local quiescent population of massive galaxies [275]. Star formation has been ruled out as the source of radio emission in such systems [276]. The favored interpretation is that the outflows are powered by jets [277], as the AGN luminosity is inadequate. Additionally, several well resolved sources have jet-like morphologies [277]. If jets are indeed powering such outflows, it would imply that low-power AGN jets play an important role in galaxy evolution, as predicted in some earlier works [186,221].

To summarize, the observations discussed above strongly support the results of the spatially resolved simulations outlined in the earlier part of this review. Such observations are further augmented by predictions of observable signatures of jet–ISM interaction from simulations, such as models for ionized gas kinematics by Meenakshi et al. 2022b [213]. Direct comparison of observations with simulations has been very fruitful for several sources in recent years, e.g., IC 5063 [205], 4C 31.04 [216], B2 0258+35 [221,229,234,278], 2MASSX J23453269-044925 [247,279], Tea Cup galaxy [240], etc. This highlights the growing synergy between studies exploring spatially resolved simulations and their observational counterparts.

4.2. Implications for Compact and Peaked Spectrum Sources (CSS/GPS/CSO)

Observational studies of systems with compact jets such as Compact Symmetric Objects (CSO) [280], High Frequency Peakers (HFP) [281], GHz-Peaked Spectrum (GPS) [282], Compact Steep Spectrum (CSS) [24] are directly related to the topic confined, young radio jets discussed in this review. The origin and nature of such compact radio sources, which are often characterized by a peaked radio spectrum, are still debated in the literature. It remains unclear if they are (a) young evolving sources or (b) jets trapped by the host’s ISM [24,146]. Source ages inferred from synchrotron spectral studies [283] or kinematic age estimates from VLBI studies [284] favor the former, young-jet scenario. However, such short confinement times can also be due to the powerful ($P_{1.4} \mathrm{G}\mathrm{H}\mathrm{z}\gtrsim {10}^{25}{\mathrm{W}\mathrm{H}\mathrm{z}}^{-1}$) nature of these jets [284,285] and do not rule out jet–ISM interaction. There is evidence to suggest that such galaxies are gas-rich, e.g., (i) high rotation measures [24,146,282,286,287], (ii) high X-ray column depths [288,289,290] that are well correlated with HI gas distribution [291,292], implying a common origin of both phases, (iii) enhanced IR emission indicating presence of reprocessed dust emission [285,293,294], etc. There are also direct detections of atomic and molecular gas in many such systems, as described in reviews by O’Dea [146], Fanti [295] and O’Dea and Saikia [24]. Recent observations [296] have also uncovered strong ionized outflows in a large number of such systems with compact jets, indicating strong coupling of the jet with the gas, as predicted by simulations (see Section 3.3.1).

Hence, given the abundance of possibilities of jet–ISM interaction in these systems, such galaxies may indeed follow the evolutionary sequence outlined in Section 3.1 and remain confined for some duration while within the host’s potential. Approximate analytical estimates of jet confinement timescales are presented in Appendix A. Besides the traditional peaked spectrum sources, recent surveys have uncovered a large sample of compact FR0 sources [26,297], where the jet remains compact. Compact jet-like systems have also been found in resolved radio images of radio-quiet systems as well [298,299]. Long confinement times ($\tau \gtrsim 5$ Myr) of low-power jets ($P_j\lesssim {10}^{41} {\mathrm{e}\mathrm{r}\mathrm{g} \mathrm{s}}^{-1}$), even for modest mean densities of the ISM clouds ($n_c\sim {10}^2$–${10}^3$), can explain the compactness of such sources. Indeed, molecular gas has been detected in several such galaxies with compact radio emission [300,301]. This makes such sources ideal test beds for investigating the physical processes of jet–ISM interaction discussed in this review.

5. Concluding Perspectives

This review outlines the development of numerical simulations of relativistic jets propagating through their environment, with a particular focus on jet–ISM interaction. In addition, the observational implications of such processes have also been discussed. The last few decades have seen a very prominent growth of studies in this domain. This is in contrast to earlier general skepticism (e.g., see the arguments in Section 1 of Ostriker et al. [211]) regarding the impact of jets in the Establishment phase of AGN feedback. However, as discussed in this review, such perceptions are starting to change. Some of the major points that have emerged in this context are summarized below.

5.1. Are Radio-Loud AGNs Gas-Rich?

One of the major concerns regarding the role of jets in their host galaxies was whether radio-loud galaxies have sufficient gas to be affected by jets in the first place. The traditional view has been that in the nearby universe, powerful radio jets are usually found in early-type galaxies (ETGs), which were considered to be gas-poor. However, systematic surveys of such systems have uncovered a significant fraction (∼25% [302]) to host dense gas, with higher fractions for radio-loud AGN (≳34% [303]). A summary of the various surveys can be found in Table 4 of Tadhunter et al. [303]. The recent review by Ruffa and Davis 2024 [304] gives more details on the properties of molecular gas in the local ETG. Interestingly, the fraction of radio-loud galaxies containing molecular gas and the estimated $H_2$ masses (${10}^7$–${10}^{10}{M}_{H2}$) have been found to increase with redshift [305]. Thus, dense gas is present in a significant fraction of radio galaxies, raising the possibility for jet-driven feedback if jets couple significantly with the ISM.

5.2. Radio-Detected Fraction of AGN?

Earlier studies of AGN populations had demonstrated that the radio-detected fraction of AGN reaches up to ∼30% for high-mass galaxies [306,307]. Though small, this is non-negligible. More recent sensitive radio surveys [308] have extended these studies to lower radio luminosities Although the higher fractions result from inclusion of weaker AGN, whose radio powers are lower by an order of magnitude, such results support the widespread presence of radio activity in galaxies. Furthermore, it is important to note that the traditional definition of “radio-loudness”, inferred from correlations of [OIII] and 1.4 GHz radio luminosity, does not imply radio “silence”. As demonstrated in recent surveys [298,299], a significant fraction of traditional “radio-quiet” sources may harbor nuclear radio emission driven by an AGN, and more specifically, a jet. They may also demonstrate jet–ISM interaction, as shown in Figure 5 [237].

5.3. Large-Scale Impact on the Host Galaxy?

Although the apparent beams of radio jets are often found to be thin, collimated structures, their large-scale influence has been well demonstrated by both simulations and observations, as outlined in this review. The observed size of a jet in radio wavelengths may often under-represent its wider impact (e.g., in 4C 31.04 [216], and several other sources in Appendix B), as the jet plasma is broken into low-density streams during the flood-channel phase of its evolution. However, even though the jet’s impact may extend beyond its immediate confines, in most cases, the disturbances are restricted to the central few kpc of the galaxy. Though non-negligible, there needs to be better proof for a wider-scale impact, to confirm/discard the predictions from simulations.

Observations have now firmly established that jets can drive multi-phase outflows in the central few kpc of galaxies, in line with predictions from simulations (see Section 4). The broad line widths of such outflowing gas, due to turbulent gas motions, indicate the jet’s ability to strongly affect the kinematics of the ambient gas. However, the long-term implications of such activity for galaxy evolution, particularly in relation to star formation, remain an open question. Although several prominent radio-loud sources show a deficiency of star formation rate [222,245], the ubiquitousness of such jet-driven negative feedback has been questioned in other recent studies. For example, Molyneux et al. [301] find that jets do not significantly disturb the molecular gas at larger scales in their observed sample of galaxies. Even though recent theoretical studies, such as the turbulence-regulated star formation framework, predict that jets can regulate SFR over large scales, such models are still in their infancy. Furthermore, the following two points should be noted while assessing the impact of AGN on the star formation rate and galaxy’s mass assembly: (a) a given jet/AGN feedback episode may not have an instantaneous impact on the SFR, as the star formation time scales may differ from the dynamical times, (b) impacts from repeated jet/AGN activity will accumulate over time and jointly affect the galaxy’s growth. For more detailed discussions, see Sections 2.1, 5 and 6 of the reviews [2]. Hence, more systematic studies of the long-term impact of jets in particular, and AGN in general, are needed in the future to answer these questions.

5.4. AGN Winds and Jets

The current review primarily discusses the feedback from relativistic jets on their host galaxies. However, the major agent of direct feedback on the host, so far, has been considered to be driven by non-relativistic winds. This is primarily because of the smaller fraction of powerful radio-loud galaxies as compared to AGN [308]. The possibility of the central AGN powering large-scale outflows was proposed in the early 1980s by analytical works such as Weymann et al. 1982 [309], Schiano 1985, 1986 [310,311], etc. Such ideas were brought to the focus of cosmological models by the later seminal paper of Silk and Rees [10], and other subsequent recent works [202,203,312,313,314]. Although the origin of such a wind can be due to radiation pressure from the AGN or an accretion disk-driven MHD wind (see Section 4.2 of Faucher-Giguère and Quataert [203] for a discussion), at large scales (≳1 kpc), the wind can be treated as a mechanical outflow. Earlier studies assumed that efficient inverse-Compton cooling from the AGN radiation field will render the wind to be momentum-driven close to the AGN, while at larger distances (≳1 kpc), it was expected to be energy conserving [202,312]. However, Faucher-Giguère and Quataert [203] have shown that inefficient cooling of the protons is expected to create a two-temperature plasma and result in an energy-conserving flow at all scales. The authors showed that this explained the observed momentum boosts in many systems.

Such analytical models have mostly focused on an idealized, spherically symmetric ISM being cleared by the AGN-driven wind. Realistic simulations of AGN winds clearing an inhomogeneous galaxy have been less explored so far, with only a few recent papers highlighting such interactions (e.g., Wagner et al. 2013 [315], Gabor and Bournard 2014 [232], Hopkins et al. 2016 [316], Bieri et al. 2017 [317], Costa et al. 2018 [318], Costa et al. 2020 [233], Ward et al. 2024 [319], etc.). Some of the general conclusions of such simulations are similar to the multi-phase jet–ISM interaction simulations discussed above. (a) The nuclear outflows can have large-scale impact, generating shocks and multi-phase outflows. (b) They generate a nuclear cavity and can potentially deplete a fraction of the dense gas cores of star-forming fuel. (c) A complete blow-out of the dense cloud cores in the ISM is often not tenable and depends on the nature of the ISM. These conclusions support the current proposition that the interaction of a jet with the dense ISM resembles the Quasar/Establishment mode of feedback, which has hitherto been primarily attributed to AGN winds. However, direct quantitative comparison of such jetted vs. non-jetted outflows of similar powers has not been widely carried out (see [209,242] for some exceptions). The difference between jets and winds as feedback agents needs to be better quantified through systematic comparisons in the future.

From the observational perspective, powerful winds and jets have distinctly different signatures. AGN winds are characterized by fast outflowing ionized gas [320,321,322], whereas powerful jets have collimated radio emission. However, given the discussion in the earlier part of the review on how jets can also drive multi-phase outflows, and also since AGN winds can also result in synchrotron emission via shocks [323,324], the distinctions are often blurred in radio-detected AGN. Identifying the physical origin of such outflows and the origin of the radio emission itself is a rapidly evolving topic of research [325].

A decade back, synchrotron emission from traditional radio-quiet quasars was considered to arise from shocks driven by the AGN winds [323,326]. However, several recent results of large-scale radio surveys have also leaned towards a jet origin of the radio emission [273,327,328,329]. This has been further supported with clear identification of collimated jet-like morphologies in resolved radio observations of compact radio-quiet galaxies [298,299]. More detailed observational campaigns as well as theoretical developments are required to disentangle such degeneracies. Recent simulations of [129] have attempted to address this to some extent by modeling properties of the synchrotron emission from both jets and winds. However, emission morphologies, especially at coarser resolutions, do not provide very clear distinctions. Polarization signatures were found to be different between the two processes, but more work needs to be carried out to provide more concrete predictions.

5.5. Need for Theoretical Improvements

As outlined in the review, recent simulation efforts have reached high levels of sophistication and realism in modeling jet–ISM interaction and its impact on galaxy evolution. However, there do remain several lacunae that need improvement.

1.

Higher resolution and longer simulations: A primary drawback of the kpc-scale simulations of jet–ISM interaction is the inability to resolve cooling length scales at the outer surface of dense clouds. For example, as outlined in Appendix A of Meenakshi et al. [213], the typical cooling length3 in multi-phase simulations of Mukherjee et al. [180] ranges from ∼0.014 to 1 pc, well below the resolution of the simulations. Achieving such resolutions will require an order of magnitude increase in current resources, which remains a challenging task. Such resolutions are also necessary to better understand the shock–cloud interaction, as demonstrated in Figure 2. Such intricate substructures of the cloudlets are not resolved in current simulations.

Besides the need for better resolutions, most of the simulations in this domain have been carried out for only a few Myr, due to the limitations of computational time requirements. However, this explores only a very short phase of the jet and galaxy’s lifetime. Larger-scale studies exploring the jet-driven heating–cooling feedback cycles [22,331,332,333] have explored longer run times of up to a Gyr. However, they do not resolve the multi-phase gas structures internal to the ISM. Future efforts have to explore at least a few tens of Myr of run time, with self-consistent injection of AGN power, to account for at least one duty cycle of the AGN. Such simulations would require larger computational resources, which are expected to become available in the near future.

2.

Better chemistry of gas phases: Existing simulations can be further updated with models that more accurately capture the micro-physics of these systems. One such area is the treatment of the chemistry of ionized and molecular gas phases and other species, such as dust. In most numerical codes, a single fluid prescription is adopted, where the cooling of collisionally ionized gas is derived from pre-computed tables that depend on the total gas densities and temperatures. Only a few works have included more sophisticated treatments of multi-species fluids [220,251], an area that requires significant improvement in the future. In addition to this, the impact of photoionizing radiation from the central AGN has been largely unexplored in large-scale simulations of AGN feedback, barring a few works [209,212,250,317]. Although well explored for studying cloud dynamics in broad line regions or close to wind launch zones (e.g., see [334,335,336], and references therein), their effect on larger kpc-scale simulations is yet to be fully explored.

3.

Magnetic fields: Another ill-explored parameter is the effect of magnetic fields on shock–cloud dynamics and star formation. Very few simulations of jet–ISM interaction have included the evolution of magnetic fields [188,189]. Magnetic fields can potentially change the nature of shock–cloud interaction by affecting Kelvin–Helmholtz growth rates. They will also affect the estimates of turbulence-regulated star formation rates [249], and should be explored in more detail.

4.

Cosmic ray feedback: Another key ingredient overlooked in the current literature is the effect of cosmic rays on the fluid dynamics of jet–ISM interaction, in particular, and AGN feedback in general. Jet–cloud interfaces undergoing diffusive shock acceleration are expected to be active sites for the production of high-energy cosmic rays. Such cosmic rays will provide additional momentum and pressure to the fluid, which would in turn affect the local dynamics of the gas. This has been tentatively explored in some cases, for example, in IC 5063 [337]. Inclusion of cosmic ray diffusion and heating in MHD simulations in general [338,339,340,341,342] and studies of galaxy evolution and jet simulations in particular [343,344,345,346,347,348] is being actively pursued by several groups. However, their impact is yet to be investigated in the context of multi-phase AGN feedback.

5.

Jet composition, plasma processes and instabilities: Most of the simulations of large-scale relativistic jets do not explicitly account for plasma composition, which can influence the nature of the solution but is numerically challenging to implement (see Section 8.2.1 of Martí and Müller [78]). Only a handful of works have explored these issues. Some studies have used a modified EOS incorporating fixed ratios of leptonic and hadronic components in an otherwise single fluid description [117,349,350]. Other recent works have used a more sophisticated two-temperature fluid treatment including electron–ion interaction, which is modeled in a sub-grid framework [115,116]. However, such attempts are still in their infancy for jet simulations, although active development is on-going in other related domains (e.g., [351,352]).

Besides jet microphysics, another overlooked domain is the impact of small-scale plasma processes in general and MHD instabilities in particular. Accounting for plasma effects in large-scale jets is understandably difficult, due to the large separation of scales. Nonetheless, particle-in-cell studies of idealized jets or shear layers [353,354,355,356,357,358] have demonstrated the importance of considering fundamental plasma effects such as Weibel, two-stream instabilities, etc. (see Meli and Nishikawa 2021 [359] for a detailed review). Although sophisticated simulations have been performed to investigate particle acceleration of non-thermal electrons by relativistic shocks [360] or reconnection processes [361], the broader impact of such plasma processes on jet dynamics and emission requires further scrutiny.

Regarding large-scale fluid instabilities, it is well known that Kelvin–Helmholtz [362,363,364,365], current-driven instabilities (CDIs) [51,366,367,368,369,370], or a mixture of the two, can operate in relativistic jets [82,91,371,372,373]. Linear stability analyses of such instabilities find the growth rates to depend on various jet parameters such as the bulk Lorentz factor [374], jet magnetization and magnetic pitch parameter [66,375], jet’s rotation [376,377], jet opening angle [378,379], etc. Such instabilities can have strong implications for jet collimation and turbulence, which would in turn impact the various morphological classifications of jets (see Costa et al. [84] for an example). Spatially resolved observations of helical structures in jets or their ridge-lines have also hinted towards the presence of such MHD processes in a few sources, such as 3C 273 [380,381,382], M 87 [383,384,385], S5 0836+710 [86,386,387], NGC 315 [388,389], 3C 279 [390], 3C 84 [391], etc. Although several large-scale simulations have well demonstrated the onset and impact of such instabilities (e.g., [79,90,378,392]), more work is needed to unravel how such MHD processes affect jet dynamics and their non-thermal emission.