AGN feedback in state-of-the-art cosmological simulations
Observations allow us to appreciate how AGN feedback develops with different mechanisms (for instance inflating bubbles or launching outflows), with different appearances, in a variety of systems. Besides, it is a recurrent process, with each AGN burst leaving a clear signature in the system. Additional evidence which adds complexity to the comprehension and modelling of AGN feedback is the presence of multiphase gas in and around galaxies. Multiwavelength observations reveal the presence of gas spanning a wide range of densities, temperatures, and ionisation states in galaxies. Multiphase gas is present not only in spiral galaxies, which are systems rich in cold gas, but also in ellipticals and in the innermost regions of galaxy groups and clusters, which are environments known to be dominated by X-ray emitting, hot gas.
Observations ([276] ,[277] among other works) also provide evidence for different regimes of BH accretion and feedback. In a simplified context, the AGN activity operates through (at least) two distinct phases: radiative or quasar mode, and kinetic or radio mode ([278] for a review). The radio-mode is characterized by large radio jets generating hot X-ray cavities, whereas in the quasar-mode the emission is dominated by the accretion disc, and feedback energy is mainly radiated away. This distinction has been theoretically modelled [273] by describing AGN feedback with two components: radiation and mechanical outflows ([279] considered three different regimes for BH accretion in their model). In these models, the amount of energy associated with each component depends on the Eddington ratio $f_{Edd}$ (see §3.15). Not only are simple theoretical models like the two aforementioned ones supported by observations, but they are also corroborated by other independent analytical models ([280] and references therein), which showed how it is possible to associate different BH accretion rates to changes in the radiative efficiency and to transitions to different types of accretion discs. In addition, observations [281] ,[282] suggest that the radiative efficiency does not only correlates with the BH accretion rate, but also with the BH mass (see also [272] ).
However, a two-mode AGN feedback is only an approximation to the smooth transition which is observed (e.g., [276] ,[283] ) and also theoretically expected (e.g., [284] ,[285] ,[280] ,[286] ). Reality is in fact more complex than the aforementioned simplified frameworks, and AGN feedback operates through a variety of modes, which often occur simultaneously. Among the main AGN feedback mechanisms, there is the preventive (or preventative) mode, where feedback prevents the gas from being accreted or from effectively cooling; the ejective mode, in which gas is removed from the innermost regions of forming structures where SF occurs; AGN feedback can suppress the SF efficiency, mainly via turbulence and ISM heating; it can operate via radiation pressure on dust, which clears out gas from the BH vicinity; or AGN can act in the maintenance mode, by keeping quiescent an already quenched system. Besides all the aforementioned modes in which BH feedback is negative, i.e. it produces an overall suppression of the SFR, AGN feedback can also be positive and locally enhance the SF efficiency for a given period of time, mainly via ISM overpressurization. Different regimes have to be accounted for to address the overall AGN feedback problem, always considering that AGN and their host galaxies are embedded in a DM halo.
Another key characteristic of AGN is that it develops across a large dynamical range of scales, and that it impacts on the evolution of gas with a range of densities and temperatures. This can occur from nuclear scales to galaxy cluster scales, moving through the ISM, the CGM, the intra-group medium and the ICM. This large range in spatial scales corresponds to an equivalently wide range in temporal scales (e.g., [287] ).
State-of-the-art cosmological simulations are still far from fully capturing the complexity. Starting from the seminal works by [242] ,[241] , a number of prescriptions for modelling AGN feedback have been conceived to account for SMBH feedback in cosmological simulations. Following the two aforementioned papers, many simulations assume that the AGN feedback energy that a SMBH accreting at a rate $\dot{M}_{\bullet}$ releases per unit time can be cast as: $$ \dot{E} = \epsilon_f \epsilon_r \dot{M_\bullet} c^2,
$$ where $\epsilon_r$ and $\epsilon_f$ are the radiative and the feedback efficiencies, respectively.
A constant value for the radiative efficiency $\epsilon_r$ is often used. It is often set to $0.1$ [241] ,[141] , which corresponds to the mean value for the radiatively efficient accretion onto a non-spinning, Schwarzschild BH [288] ,[289] ,[290] . Recent works (e.g., [142] ,[291] ) included a BH spin-dependent $\epsilon_r$.
The feedback efficiency $\epsilon_{f}$ quantifies the fraction of energy radiated from the BH which is actually coupled to the. Values commonly assumed in cosmological simulations span the range $\sim 10^{-4} - 0.2$ (e.g., [292] ,[293] ,[294] ,[35] ,[295] ,[139] ,[296] ). This efficiency is often tuned in order to match the normalisation of the BH to stellar mass relation [231] ,[238] . The value of $\epsilon_{f}$ can be either constant (e.g., [241] ,[41] , or dependent on the AGN mode. Motivated by the observational evidence of more powerful outflows associated with SMBHs accreting at lower rate [273] ,[279] ,[297] , [298] introduced a steep transition of the feedback efficiency between quasar-mode and radio-mode, (see also [299] ,[300] ,[35] ,[268] ,[141] ,[44] ). Even within the same (radio) mode, $\epsilon_{f}$ can change according to the ISM density [301] ,[139] .
AGN feedback energy can be deposited by means of different numerical prescriptions: either purely in the form of thermal or kinetic energy, or it can be used to inject bubbles, or according to different channels depending on e.g., the BH accretion rate. Among the several possible AGN feedback models, it is worth highlighting a number of schemes that modern cosmological simulations adopt.
Following the original idea of [242] ,[241] , the AGN feedback energy can be simply dumped thermally: in this way, the BH distributes the AGN feedback energy (eq. feedback_energy_old) to nearby resolution elements, possibly in a kernel-weighted fashion. The thermal energy received is used to increase the internal energy of particles or cells surrounding the BH, which increase their temperature as a consequence. While being overall effective, this simple prescription often turns out to be inefficient and does not succeed at reproducing the variety of observations currently available at different redshift. Nonetheless, this prescription is still widely used in cosmological simulations, that often adopt it to describe the quasar-mode feedback only, along with a complementary model for lower BH accretion rates. As an example, [268] ,[35] ,[141] ,[139] ,[142] ,[145] rely on this model to describe the quasar-mode feedback in their simulations.
Indeed, in the Magneticum and in the SLOW simulation suites, they assume a two-mode AGN feedback: for high BH accretion rates, i.e. $f_{Edd} > 0.01$, SMBHs experience a quasar phase and release thermal energy in the surrounding. On the other hand, they model the radio-mode feedback ($f_{Edd} < 0.01$) through energy deposition by hot bubbles (following [302] ,[299] ). In these simulations, radiative and feedback efficiencies are free parameters. Specifically, $\epsilon_{f}$ is increased by a factor of 4 during the radio-mode feedback with respect to the quasar phase. Interestingly, in a subset of the Magneticum simulations [272] , they explore a different scenario for a two-mode AGN feedback, where hot bubbles are replaced by outflows. However, due to the limited resolution, the latter mechanical channel is numerically implemented as thermal feedback.
While the Illustris simulation [268] ,[40] implements AGN feedback in a similar way to Magneticum (i.e. thermal feedback for $f_{Edd} > 0.05$ and bubble-like feedback below), the Illustris-TNG simulation substantially improves the modelling of the mechanical component of the BH feedback [301] ,[139] . Indeed, besides adding a BH mass dependence to the BH accretion rate threshold which distinguishes between quasar and radio mode, they explicitly model kinetic winds in the radio mode, by adding momentum with random injection directions to selected gas cells (see [301] for details). Interestingly, both Illustris and Illustris-TNG include a radiative (electro-magnetic) AGN feedback via a phenomenological model. This latter feedback channel modifies the net cooling rates of halo gas. Even though it operates whatever the $\dot{M}_{\bullet}$, it proved effective only for BH accretion rates close to Eddington.
The EAGLE simulations [41] adopt a stochastic thermal feedback scheme, where accumulated AGN feedback is injected only when enough to heat the surrounding ISM up to an sufficiently-high temperature ($T \sim 10^{8.5} \div 10^9$ K), similarly as for the case of stellar feedback (see Secton §3.14). This choice is also the fiducial option in the reference runs of the FLAMINGO suite [6] , although they foresee the possibility to adopt instead a jet-mode, kinetic AGN feedback. In the latter case, should jets be on, they are launched according to the BH spin direction. AGN feedback in these two simulation suites [41] ,[6] is always one-mode.
Simba simulation [303] ,[44] ,[304] includes a two-mode AGN feedback: a radiative and a jet mode. BHs in the radio mode ($f_{Edd} > 0.02$) promote AGN winds, with velocity proportional to the BH mass, that do not alter the temperature of the outflowing gas. During the jet-mode (for low $f_{Edd}$ and if $M_{\bullet} > 10^{7.5}$ M$_\odot$), the temperature of the gas involved in outflows is instead raised to the virial temperature of the halo. Both types of winds are produced via momentum input. When the jet-mode is active, there is an additional heating channel, namely the X-ray feedback: it releases energy into the BH surrounding gas, which is supposed to originate from X-rays of the accretion disk.
In the (New)Horizon-AGN [300] ,[305] ,[141] ,[142] AGN feedback features two modes, depending on the BH accretion rate. During the radio mode, the BH powers jets, continuously releasing mass, momentum, and total energy into the gas. On the other hand, only thermal energy in supplied to the gas cells within a sphere centred on the BH when it is in quasar mode. As for the jet mode, BH jets are bipolar, launched with a constant velocity, and they deposit mass, momentum and energy within a cylinder. In the New Horizon-AGN simulation, radiative and feedback efficiencies are BH spin-dependent (both in quasar and radio mode).
Fig. 12 summarises the numerical prescriptions that some modern cosmological simulations adopt to model BH growth, AGN feeding and feedback. The six sketches in the aforementioned figure aim at providing a simplified yet immediate understanding and comparison among the various models.
The compilation of prescriptions for AGN feedback listed above is far from being complete. Other works which is worth mentioning include e.g., [306] ,[140] ,[307] ,[308] ,[309] .
A few remarks on AGN feedback modelling in simulations follow, about: $(i)$ model parameter calibration; $(ii)$ the simplification underlying many of the state-of-the art models; and $(iii)$ comparison among different models.
Subgrid physics and in particular free parameters of the models, are usually tuned to reproduce observables. This is especially true for AGN feedback efficiencies (i.e. $\epsilon_{f}$ and $\epsilon_{r}$). The majority of cosmological simulations calibrate free parameters (possibly within ranges suggested by theory or phenomenology or data) by attempting to reproduce a number of observables. The most popular examples are the BH to stellar mass relation [231] ,[238] and the galaxy stellar mass function (GSMF, e.g. [310] ), usually at redshift $z=0$. Other calibration targets include: the galaxy mass-size relation, baryon or gas mass fractions, metallicity-mass and luminosity-mass relations. We refer the reader to [226] for a more extended discussion. Common strategies to model calibration consist in performing a fit to selected data sets (e.g. EAGLE), to exploit trends in comparison to some observations (e.g. Magneticum, Illustris), to profit from machine learning (e.g. FLAMINGO) or from comparison to previous/scaled-down versions of similar simulations.
There are as well different approaches when resolution changes. Weak convergence (as opposite to strong convergence, see [41] ) is usually preferred, and for different numerical resolutions it is common practice to adapt at least a few values of the model parameters.
However, the choice of the observational data sets adopted for calibration does not impact parameter tuning only. Rather, it allows to understand the performance of different simulation predictions against various observations. For instance, the Magneticum simulation succeeds at reproducing the physical properties of the ICM and of the intra-group medium better than other simulations (see [311] for an example), while simulations like Illustris-TNG, Simba and EAGLE usually outperform the competition as for predicting final properties of the galaxy population. This mainly stems from the calibration targets, i.e. ICM and stellar metallicity content, plus X-ray luminosity-mass relation for the Magneticum simulation versus GSMF and galaxy mass-size in the others.
z = 2
z = 0
Among the many assumptions underlying any sub-grid model, one simplification consists in accepting that little is known about how AGN feedback energy couples with different phases of the ISM. [270] investigate how relevant it is to distribute AGN feedback energy to the individual phases of the ISM. Within the MUPPI sub-resolution model [155] ,[135] , they show the impact of supplying feedback energy to hot or cold gas only, of evenly providing the two phases with BH feedback energy, and of coupling AGN feedback energy to the hot and cold gas according to their physical properties (i.e. the covering factor of cold clouds). They find that the numerical prescriptions adopted to couple AGN feedback energy to the ISM phases affect final BH and host galaxy properties (see Fig. 13). Interestingly, they assume that AGN feedback energy is used either to increase the hot gas temperature, or to evaporate molecular gas, instead of e.g. producing a deviation from the equilibrium solution of multiphase particles [241] .
Finally, assessing the differences among different models for AGN feeding and feedback is not straightforward. We refer the interested reader to [312] for a reference comparative study where the impact of various prescriptions for BH seeding, AGN feeding and feedback has been addressed. Different implementations are tested with the same cosmological simulation also in the CAMELS project [313] . Here, Fig. 14 (along with the associated movie) provides evidence of how various sub-grid models adopted in some state-of-the-art cosmological simulations predict differences as for the energy distribution and the evolution of the IGM/CGM.
评论