Impact of AGN feedback on star formation

Thermal and radiative AGN feedback have a limited impact on star formation in high-redshift galaxies

Orianne Roos, Stéphanie Juneau, Frédéric Bournaud and Jared M. Gabor CEA-Saclay, 91190 Gif-sur-Yvette, France
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Abstract

The effects of Active Galactic Nuclei (AGNs) on their host-galaxies depend on the coupling between the injected energy and the interstellar medium (ISM). Here, we model and quantify the impact of long-range AGN ionizing radiation – in addition to the often considered small-scale energy deposition – on the physical state of the multi-phase ISM of the host-galaxy, and on its total Star Formation Rate (SFR). We formulate an AGN Spectral Energy Distribution matched with observations, which we use with the radiative transfer (RT) code Cloudy to compute AGN ionization in a simulated high-redshift disk galaxy. We use a high-resolution ( pc) simulation including standard thermal AGN feedback and calculate RT in post-processing. Surprisingly, while these models produce significant AGN-driven outflows, we find that AGN ionizing radiation and heating reduce the SFR by a few percent at most for a quasar luminosity ( erg s). Although the circum-galactic gaseous halo can be kept almost entirely ionized by the AGN, most star-forming clouds ( cm) and even the reservoirs of cool atomic gas ( cm) – which are the sites of future star formation (100 - 200 Myrs), are generally too dense to be significantly affected. Our analysis ignores any absorption from a putative torus, making our results upper limits on the effects of ionizing radiation. Therefore, while the AGN-driven outflows can remove substantial amounts of gas in the long term, the impact of AGN feedback on the star formation efficiency in the interstellar gas in high-redshift galaxies is marginal, even when long-range radiative effects are accounted for.

galaxies: active –– galaxies: high-redshift –– galaxies: star formation — ISM: clouds — methods: numerical — radiative transfer
slugcomment: draft version

1. Introduction

The impact of Active Galactic Nucleus (AGN) feedback on Star-Forming Galaxies (SFGs) remains an open question: contradictory answers are found in both simulations and observations. The amount of energy released by AGNs is theoretically high enough to blow all the gas out of their host-galaxies, or to maintain surrounding gas at high temperatures (Croton2006; Ciotti1997; Matsuoka2012a). Curran2012 also show that there is always a finite ultra-violet (UV) luminosity above which all the gas in a radio galaxy or quasar host is ionized, up to redshift . This makes AGNs good candidates to quench star formation (SF) through outflows and ionization (“quasar mode”), or through jets (“maintenance” or “radio” mode), which occurs in many simulations (e.g. Sijacki2007; Martizzi2012; Dubois2012; Dubois2013). Simulations also predict that galaxy mergers create starbursts and feed quasi-stellar objects (QSOs), which produce shock waves, expel the interstellar medium (ISM), and prevent it from falling back on the galaxy (e.g. DiMatteo2005; Hopkins2006; Li2007). However, mergers are rare and QSO phases are extreme events, and the gas expulsion depends on the coupling between the AGN and the ISM (e.g. DeBuhr2011). In contrast, other simulations show that AGN jets can trigger large-scale star formation by creating blast waves that compress the gaseous clouds of the interstellar/intergalactic medium (Gaibler2012; Dugan2014).

On the observational side, most X-ray selected AGNs up to redshift 3 are located in normal star-forming (main sequence) disk galaxies (Mullaney2012) and normal SFGs frequently host an AGN up to redshift  (Mullaney2012b; Juneau2013; Rosario2013c), which suggests limited AGN impact on star formation, under the assumption that their star formation history is steady (Elbaz2011). Nonetheless, there is evidence for AGN quenching local elliptical galaxies (Schawinski2007), or suppressing star formation without necessarily quenching it (Karouzos2014). At higher AGN luminosities, molecular outflows have been observed in local quasars (Feruglio2010) or Ultra-Luminous Infra-Red Galaxies (ULIRGs) (Cicone2014; Veilleux2013), however without necessarily affecting the Star Formation Rate (SFR) (Spoon2013). Finally, Keel2012 observed giant AGN-ionized clouds in low-redshift (mostly) interacting or merging galaxies, which could also impact the SFR of the hosts. On the other hand, there is observational evidence for AGNs triggering SF (e.g. Begelman1989; Graham1998; Klamer2004; Croft2006; Feain2007; Elbaz2009), and some studies show that the hosts of more powerful AGNs have higher nuclear SFR but similar global SFR as those of less powerful AGNs, up to intermediate redshift (Diamond-Stanic2012; LaMassa2013; Esquej2014). Finally, Hickox2014 take into account the rapid variability of AGNs and find that, averaged over a period of  Myr, star-forming galaxy hosts at least one active episode and long-term black hole accretion rate (BHAR) is perfectly correlated with the SFR of the host, reproducing the observed weak correlation between the AGN luminosity and the global SFR. A plausible explanation to this apparent discrepancy (both in simulations and observations) in the role of AGN feedback in star formation would be that AGN feedback works both ways, depending on the current accretion mode (Zinn2013), and on the timescale considered.

To determine if AGN feedback can reduce star formation, we need to know whether the gas expelled and/or ionized would have formed stars in the absence of AGN. In this paper, we will focus on the impact of thermal and radiative AGN feedback on the physical state of the gas, and therefore on its ability to form stars in a simulation representative of a high-redshift star-forming disk galaxy from Gabor2013b.

AGN feedback is often implemented in simulations in the form of local (at the resolution scale) deposition of energy (see Wurster2013a, for a comparison of five models of AGN feedback). It has recently been shown that such AGN feedback creates outflows without impacting the disk (e.g. Gabor2014). However, due to the lack of resolved small-scale observations of those mechanisms at high-redshift, the recipes remain quite arbitrary and do not have strong constraints on the scale at which energy should be re-injected.

Until now, long-range effects of AGN radiation are rarely included because simulations cannot afford both high resolution and a complete treatment of the radiative transfer (RT), due to the cost in terms of computational time and memory. For instance, Vogelsberger2013; Vogelsberger2014c, in their simulation Illustris, use the moving-mesh code AREPO to treat cosmological simulations including standard AGN and stellar feedback, plus a prescription for radiative electromagnetic AGN feedback. Also, Rosdahl2013 implemented RT into RAMSES (RAMSES-RT). However, the resolution of the ISM structure of a galaxy is degraded, and effects of ionization on small-scale structures such as Giant Molecular Clouds (GMCs) cannot be considered. The effect of long-range AGN radiation may however have a great impact on the structure of the ISM since most of AGN radiation is emitted in the optical, UV and X-ray wavelengths and is able to heat and/or ionize surrounding ISM, which could change the physical properties of the clouds (Proga2014). Furthermore, the fraction of ionizing photons emitted by the AGN that remains trapped in the ISM depends on the distribution of the gas into clumps (Yajima2014), and could in return change the properties of the ISM (Maloney1999) and of the AGN-driven winds (Dove2000). Many authors already attempted to predict such effects with simple models (see Section 2.3), but, due to the complexity of the ISM in a real galaxy and the broad wavelength range of observed AGN spectra, such models are not sufficient and RT calculations need to be performed.

To do that, we post-process the results of our high-resolution simulation with a complete treatment of the RT and study the large-scale effect of AGN ionization on star formation. Therefore, we are not able to treat coupling to longer-term dynamical effects, but the ISM structure of the high-redshift disk galaxy allows us to probe which ISM phases can be impacted as a function of the AGN luminosity. While it is known that very diffuse gas ( cm ; e.g. in the circum-galactic medium) can be entirely ionized by an AGN, and dense gas ( cm) is self-shielding (Liu2013), the impact of AGN radiation on other gas phases, such as atomic gas ( cm ; which will form stars on a timescale of a few hundreds of Myrs), has not been studied extensively. Moreover, the effects of a clumpy distribution of gas inside a dense galactic disk on the propagation of AGN radiation are hard to determine with a simple model. In Section 2, we describe the galaxy simulation and our method to predict the distribution of the gas photoionized by the AGN in the galaxy. Section 3 shows maps of heated/ionized gas, and star-forming regions, total reduction of SFR and fractions of the total mass and volume of the gas that is heated/ionized by the AGN. Finally, in Section 4 we study the dependence of the SFR reduction on the structure of the ISM, give clues about long-term effects on star formation and the typical size and density of ionized regions. Finally, we try to account for other sources of ionization (e.g. stars, UV background). Our conclusions are in Section 5.

2. Method

Using radiative tranfser calculations applied in post-processing to a high-resolution simulation of an isolated disk galaxy, we study the effects of photoionization by an AGN on the ISM. Our procedure allows us to quantify the impact of AGN radiation on the SFR of well-resolved star-forming clouds in the galactic disk. In this section we describe the hydrodynamic galaxy simulation, the AGN SED used as the only ionizing source (hypothesis discussed in Section 4.4), and the radiation transfer procedure.

2.1. Sample of simulated galaxy snapshots

The simulation, described fully by Gabor2013b, is an unstable clumpy disk representing an isolated disk galaxy with a well-resolved ISM (see e.g. Elmegreen2008, for a comparison of such clumps with observations). Such clumpy galaxies are predicted to efficiently fuel their central black hole (BH), resulting in frequent active phases (Bournaud2011), which is observationally supported up to intermediate redshift (Bournaud2012). The simulation is a cube of 50 kpc length using the adaptative mesh refinement (AMR) code RAMSES (Teyssier2002).

Stars, gas and dark matter are included. The total baryonic mass is M, and the gas fraction is initially set to  50 %. A cell is refined if its mass exceeds M, if there are more than 30 dark matter particles in the cell, or if the Jeans length is not resolved by at least 4 cell widths (Truelove1997). The maximal resolution of the simulation, taken as the size of the smallest cells, is about 6 pc. Thus, GMCs, where stars are supposed to form (Waller1987), are resolved. Star formation is allowed for cells denser than 100 m cm (see Appendix LABEL:subSection:threshold for discussion) and colder than  K (Renaud2012). A thermal model for supernovae (SNe) feedback is included (see Gabor2013b, for details). The distribution of clouds in the simulation depends on the numerical noise and is therefore stochastic. Furthermore, star formation contains a random module for the mass distribution of new stars, which will affect the mass, shape, size and movements of the clumps. Nevertheless, the simulations used all have the same statistical behaviour since they have the same probability density function (PDF) and power spectrum density (PSD) for gas density.

AGN feedback is twofold: gas is heated, diluted and pushed away by the AGN directly in the simulation (thermal AGN feedback) ; and RT is added afterwards in 6 successive snapshots of the simulation (AGN photoionization), using version 13.02 of Cloudy (last described by Ferland2013) to study the large-scale effect of AGN ionization on star formation. Thermal AGN feedback is based on Booth2009 and consists of local (10 pc-scale) energy re-deposition at a uniform pressure if it is sufficient to heat the gas to an average temperature of K, else energy is stored until the next time-step. Corrections to this method were added to prevent too high energy storage when the BH is embedded in very dense clumps. The maximum temperature allowed in the region where energy is re-deposited by the AGN is K. In the very infrequent case when this maximum temperature is reached, the radius of the re-deposition region is enlarged by a factor 1.25 until the temperature drops below the maximum temperature. When this happens, the radius is multiplied by a factor 2 on average. These prescriptions only apply to the very central region (10 pc-scale) of the galaxy and do not directly impact the large-scale gas structure and star formation in the intermediate and outer regions of the disk (see Section 2.2.2 of Gabor2013b, for details).

The simulation shows high-velocity AGN-driven outflows, with mass outflow rates between about 10 and 100 % of the SFR of the galaxy ( 30 M yr). These outflows are mostly hot and diffuse, and do not impact large scale ( pc) star formation within short (10 - 20 Myrs) time-scales (Gabor2014).

We used two runs of the simulation with the same initial conditions, which develop a clumpy irregular ISM structure. The runs are identical until AGN feedback is shut down in one of them. This moment is defined as . After that, both runs evolved separately. SNe feedback remains in both runs. A series of 6 pairs of successive snapshots was studied, ranging from to 88 Myrs. Among all the snapshots studied, the maximum number density of hydrogen is  cm, due to both the spatial resolution and the temperature floor. Ionization was added to the snapshots of the simulation including AGN feedback, and the corresponding snapshots of the simulation with no AGN feedback were used to measure an uncertainty on the SFR. The ionization calculation is done on static snapshots of the simulation, and therefore the effect we see is instantaneous and indicates in which phases of the ISM the AGN radiation is absorbed, and whether it reaches high-density star-forming regions.

2.2. Realistic Seyfert SED

To study the effects of AGN radiation on the surrounding gas, we first require a realistic source spectral energy distribution (SED). In this work, we span a large range of wavelengths (from far infra-red (FIR) to X-rays), and match observational data in the wavelength domains of interest for this study. Hence, several bands of ionizing photons are taken into account (X-rays, extreme UV (EUV), UV), rather than a simple power-law model. We formulated such an AGN SED for use in Cloudy, as shown in Figure 1. The so-called “AGN spectrum” used in the study is composed of radiation from the AGN itself (accretion disk and corona) but also takes into account the emission of dust and clumps surrounding the AGN, which are not resolved in our simulation. The input spectrum is described in more detail in Appendix LABEL:appendix:spectra. It was adjusted to the observational mean SED of the inner region of Seyfert 1 galaxies described by Prieto2010.

We chose to model the AGN spectrum of an unobscured (Type 1) Seyfert galaxy, i.e. the spectrum coming out of the central region seen face-on. The AGN radiation is propagated isotropically – we neglect the partial absorption of UV and X-ray photons by a dusty torus that would occur according to the Unified Model (Urry1995). We make this assumption because the geometry and orientation of any such torus is unknown, and there are currently not enough resolved observations to be confident about them (Sales2014; RicciC2014; RicciTV2014b). Consequently, our results are upper limits to the instantaneous impact of AGN radiation on star-formation in high-z disk galaxies – including an obscuring torus would only decrease the amount of ionizing radiation emitted into the ISM.

We note here that the FIR part of the spectrum does not match the observations. Nonetheless, those photons are not of a great interest in this study because they cannot ionize gas. We also verified that the presence of emission lines in the Broad-Line Region (BLR) spectrum did not affect our further results.

The normalization of the SED we used to perform the analysis is set to explore three luminosity regimes, as shown in Table 1. The bolometric luminosities are not related to the AGN luminosity inferred from BHAR in the simulation and we analyze the effects of each luminosity separately. The lowest luminosity regime corresponds to the typical bolometric luminosity observed for an AGN in a M normal SFG, which is of a few  erg s at a redshift of (Mullaney2012b). Such AGNs are hosted by roughly 30 % of the standard main-sequence galaxies in the same mass range (Mullaney2012; Juneau2013). The second luminosity we used is reached by  10 % of all AGNs (Mullaney2012), which are hosted by  3 % of the SFGs. The last luminosity we studied corresponds to a QSO, which is quite uncommon in normal star-forming disks.

Mullaney2012b show that typical AGNs up to redshift 2 have an average BHAR to SFR ratio of . Considering the same definition of the BHAR:

 ˙MBH=(1−ϵ)Lbolϵc2, (1)

• where is the bolometric luminosity of the AGN, is the speed of light and is the radiative conversion efficiency, set to 0.1 (Merloni2004; Marconi2004); and an average SFR of 30  yr for the simulation, we find that our lower-luminosity regime has a BHAR to SFR ratio roughly corresponding to the observed average. The middle and higher-luminosity regimes are respectively 10 and 100 times above (see Table 1), which is consistent with them being less frequent.

As QSOs and lower-luminosity AGNs do not have the same SED shape, a radio-loud quasar-matched spectral energy distribution was also formulated, using the Elvis1994 mean SED as a reference. The results are insensitive to the choice of the SED, and therefore we used the Seyfert spectrum in all luminosity regimes. We note here that even more luminous quasars have been observed (e.g. Stern2014) but since they are even rarer than the QSOs we studied, they might not impact normal star-forming disk galaxies in general.

2.3. Expectations from simple models

Several simple models have been introduced by many authors to infer the effects of AGN radiation on their host galaxies. Some of them are addressed here. For instance, according to Proga2014, in optically thin clouds dominated by absorption opacity, radiation propagating through gas at constant density and pressure will uniformly heat the cloud, which will uniformly expand but will not be accelerated ; whereas for optically thin clouds dominated by scattering opacity, the radiation will uniformly accelerate the cloud away from the emitting source, without changing its size or shape, and inducing no mass loss. On the other hand, when a cloud is optically thick and is exposed to weak radiation, only a thin layer on the irradiated part of the cloud will be heated, inducing a slow mass loss. They find that BLR clouds – which are very dense ( cm ; Mattews1985), typically become optically thin in less than a sound-crossing time, are weakly accelerated, and that their structure, shape, and size change before they can travel a significant distance. A realistic ISM made of dense clumps and diffuse interclump medium would be a complex combination of the above trivial cases and RT needs to be treated in order to know the impact of AGN irradiation on such a realistic multi-phase ISM.

As another example, Curran2012 have shown that a UV luminosity of  W Hz erg s Hz is able to ionize the cold neutral medium (CNM) with gas densities typical of GMCs ( cm), up to  pc in the galactic disk, around the BH. For our three AGN luminosity regimes, we find  erg s Hz respectively. If we were using a constant density of  cm, we would thus expect the ionization front to be located at sub-kpc scale around the BH for gas temperatures between 20 and 2,000 K (see Table 1).

Finally, a simple calculation of the optical depth in the UV gives an even lower value of this radius: if the UV opacity is cm g (Cayatte1994; Schaye2001), the critical value of the column density above which the gas becomes self-shielding is 10 g cm. In this case, if the inner region close to the BH is at a uniform density of cm, the UV emission is expected to be blocked within the first pc.

However, these models are valid in idealized conditions such as smoothed galactic profiles or single-band AGN SEDs. In this study, we demonstrate the effect of a broad observationally-matched AGN spectrum, coupled to AGN-driven winds, on a realistic multi-phase distribution of the ISM. Applied to a disk galaxy with turbulent multi-phase ISM, these predictions of the ionization radius can vary by an order of magnitude, since most of the gas volume in our high-resolution clumpy ISM has a density low enough not to be opaque to AGN radiation, while a few dense clumps are able to completely block the radiation – which can significantly change the escape fraction of photons emitted by the AGN.

Nonetheless, to account for dynamical effects such as mass loss or radiative pressure pushing clouds away, RT calculations need to be performed during the simulation, which is not the purpose of our post-processing treatment. However, the comparison between complete radiative treatment in post-processing and simplified but dynamical RT could help improve both methods, by developping accurate subgrid models.

2.4. Ionizing the simulated galaxy

We estimate the effects of AGN photoionization on the gas in the simulated galaxy under the assumption that our AGN SED emerges isotropically from the location of the black hole. We cast about 3,000 lines-of-propagation (LOPs) in all directions outward from the black hole, and calculate the radiative transfer along each LOP independently using Cloudy, a code designed to compute the radiative transfer and the atomic and molecular chemistry along 1-D lines.

2.4.1 LOP building

The first step of our analysis is to build the LOPs, as illustrated by the sketch in Figure 2. For each snapshot, LOPs are distributed as follows. The simulation box is sampled with 512 LOPs randomly cast into the entire box, plus 512 randomly cast LOPs restrained into the 30 degree half-opening angle cone of revolution perpendicular to the disk. In addition to that, the plane of the galactic disk is sampled with 512 randomly cast LOPs (see Figure 3a, right). Finally, two arbitrary planes of the simulation box, perpendicular to the galactic disk, are sampled with 768 LOPs each (see Figure 3a, left, for one of these planes with its 768 LOPs). A third of these lines are cast randomly into the entire plane, another third in the projection of the cone on the plane, and the remaining into the galactic disk. All points of a given LOP are initially separated by the size of the smallest cells (see Figure 2). As shown on the sketch, the positions of all points inside a given cell are then averaged so that only one LOP point is kept per cell and per LOP. For each LOP point, all relevant physical properties (gas density, temperature, etc.) are recorded. The hydrogen number density (hereafter, density) of the cell and its distance to the black hole are used to build the density profile along each LOP (see Figure 4 for two examples).

2.4.2 Cloudy computations

Before computing the RT, Cloudy interpolates the discrete density profile coming from the AMR simulation to get a continuous profile (see Figure 4). By comparing the size of the cells (Figure 3a) to their density (Figure 3b) and from the typical LOP profiles (Figure 4), we know that substructures, namely GMCs, are well sampled along the lines.

The Cloudy computation occurs on a static snapshot and the density profile does not change during the radiative transfer computation. The calculation stops either when the computed temperature along the line drops under 4,000 K, meaning that the rest of the line is not affected by the ionizing source ; or at the end of the line, in which case the line is totally ionized.

When calculating the one-dimensional RT along a single LOP, Cloudy treats the system as a spherically symmetric set of concentric shells (or zones), centered on the ionization source. These zones are dynamically determined with a local thermal equilibrium (LTE) criterion. Thus, the sampling of each line changes during the process, and depends on the AGN luminosity (see Figure 3c for the sampling at the end of the process for the typical AGN regime): the LOPs are sampled with higher density in regions where AGN radiation induces significant changes, while they are sampled with lower density where the physical properties are similar. The LOP regions where the Cloudy calculation did not occur (because the equilibrium temperature is below 4,000 K) keep the initial sampling.

In each zone, ionization processes (photo-ionization, collisions, charge transfer, etc.) and recombination processes (radiative and charge transfers, etc.) are balanced to compute the propagation of radiation along a given LOP, according to the input hydrogen number density profile, filling factor and radiation source, and gives the resulting SEDs and physical conditions (Ferland2013). The filling factor is set to 0.2 and accounts for the multi-phase gas distribution along the 2 other spatial dimensions in the sphere. In each sphere, the flux of the ionizing source is proportional to the inverse square of the distance to the source. To rebuild the galaxy, all computations are assembled using only the radial dependence, and interpolated. This pseudo-3D ray-tracing approach is similar to that used in Cloudy_3D (Morisset2006), now re-written in Python and renamed pyCloudy (pyCloudy). The reflection and scattering between two neighbouring LOPs are not considered explicitly. We assume that those phenomena are reproduced on average for the whole galaxy, since reflection and scattering are taken into account inside each individual sphere.

Lastly, the initial temperature along the lines is not used for the calculation, and the gas is considered initially neutral. We do not include the SNe and the UV background in the ionization process. However, they are implemented in the simulation, and from the value of the initial temperature in the cells, we know that they heat the halo and some regions in the disk: gas at T  K is likely to be ionized and some of the  K gas is possibly ionized. Such regions could then be transparent to AGN radiation. A test study on a series of LOPs shows that the transparency of such diffuse gas that could be already ionized by other sources has no impact on the effect of AGN radiation on star formation (see Section 4.4). Thus, transparent gas is conservatively neglected in the main study. Considering that the gas is initially neutral allows us to study the effect of AGN photo-ionization alone and confront our model of thermal feedback to the ability of the AGN to ionize gas. Here, as the AGN is able to ionize the cavities created by winds entirely, we assume that our model of AGN feedback (thermal + RT) is self-consistent.

2.4.3 Output parameters for a given cell

Temperature

The final temperature of a given cell containing at least one Cloudy point is defined as the maximum between the average equilibrium temperature of the Cloudy points in the cell (corresponding to the temperature gas would reach if it was not externally re-heated), and the initial temperature of the cell111If the RT calculation returns a lower temperature, it means that a mechanism other than AGN photoionization (e.g. UV background, SNe, compressive motions, etc.) is already heating the gas at a temperature higher than what the AGN ionization can provide and so these other sources will dominate.. For the points where the computation did not occur (because the temperature on the line dropped under 4,000 K), the assumed temperature is the initial temperature. The latter is not necessarily equal to the equilibrium temperature given by Cloudy because gas is constantly heated by thermal AGN and stellar feedback in the simulation. The instantaneous relative temperature change is defined as:

 RTC=Tfinal−TinitialTinitial, (2)

where is the initial temperature of the cell in the simulation (before RT), and is the final temperature of the cell defined above. Regions with % (or ) are considered not heated.

Star Formation Rate

A cell is star-forming and has a non-zero value of the SFR if its temperature is below  K and its density is above a threshold of 10 m cm (hereafter, m will be implicitly assumed). This value distinguishes diffuse gas and dense star-forming clumps and is chosen arbitrarily and independently of the density threshold in the simulation. It is varied in Appendix LABEL:subSection:threshold. The SFR in each cell is computed according to the Schmidt-Kennicutt law (Kennicutt1998) :

 SFRi=ϵ √32G3π ρNiVi if~{}Tiρthr, (3)

where is the mass density of cell , its volume and its temperature before or after RT. The Kennicutt index N is equal to 1.5 and the efficiency is 1 %. and are respectively the temperature and density thresholds for star formation defined above. The SFR per cell is limited to a maximum value, computed to account for the fact that molecular clouds generally do not turn more than 30 % of their gas into stars during their 10 - 100 Myrs lifetime (Matzner2000; Elmegreen2002; Renaud2012). The final SFR of the simulated galaxy is the sum of the individual values – interpolated as described below, and is compared: (1) to the initial SFR of the simulation including AGN feedback, (2) to the SFR of the reference simulation, where AGN feedback is shut down. Option (1) allows to measure the impact of ionization feedback alone, while option (2) allows to measure the impact of all types of AGN feedback on the SFR.

Neutral fraction of hydrogen

As for the temperature, the fraction of neutral hydrogen in a given cell is defined by averaging the values of all LOP points inside the cell. LOP regions where RT did not occur are assumed to be neutral. A cell is considered ionized if the neutral fraction of hydrogen is smaller than 10 %. The fraction of neutral hydrogen, unlike temperature, does not take into account the other heating/ionizing sources (such as stars).

2.4.4 Interpolation onto the simulation box

About 3,000 lines-of-propagation were cast in the simulation box. Even though the box is relatively well covered with LOPs, and due to the Cloudy resampling in LTE zones, all AMR cells in the snapshots do not necessarily contain a LOP point. Thus, values of the physical properties output by Cloudy (temperature, ionization fraction, etc.) need to be interpolated in order to apply to the whole simulation box.

We use the fact that the Jeans length has to be resolved by at least 4 neighbouring cells in the simulation (see Section 2.1) – and therefore their properties are alike – and assume all cells containing no LOP point neighbouring a processed cell222A cell containing either one (or more) LOP point where the Cloudy computation occured, or one point from LOP regions where the Cloudy computation stopped before the end (because there was no further effect of the ionizing radiation). Two percent of the cells (in mass and in number) contain at least 1 Cloudy point. within a radius of 4 times the cell size have the same output parameters. With this method, 20 % of the total number of cells for each snapshot – equivalent to 20 % of the total gas mass in the simulation box (galaxy and gaseous halo) – have known post-RT physical properties. We call these cells “4-neighbouring cells”.

To get the values of the physical properties for the entire grid of the simulation, the properties of the “4-neighbouring cells” are corrected with respect to the joint histogram of density and cell size. We assume that cells at a given density and a given radius in the galactic disk or gaseous halo are similarly affected by the AGN. Due to the geometry of the simulated galaxy (a disk with a vertical exponential density profile in a diffuse gaseous halo) and the mass criterion of the refinement, the size of the cells (see Figure 3a) increases when going away from the galactic disk. This naturally ensures a good sampling of the outer gaseous halo, since fewer LOPs per unit angle are needed to cross larger cells. In a few cases, some density bins are not sampled by the “4-neighbouring cells” criterion, which is enlarged to 8 neighbouring cells.

3. Results

The aim of this work is to switch on the AGN located at the center333As the central BH of the galaxy slightly moves during the simulation (Gabor2013b), we use the exact position of the BH particle of the simulation, not the geometrical center of the simulation box. of the simulated galaxy, probe how far gas is ionized by the AGN and whether many star-forming regions are heated and/or ionized and prevented from forming stars. In this section, we compare the ionization, temperature, and SFR of the gas before our RT calculations to those after the RT calculations for the three AGN luminosity regimes presented in Section 2.2.

3.1. Maps of the ionized galaxy

After propagating AGN radiation throughout the galaxy, the ionization state of the gas and its new temperature are known, and the new SFRs are computed for all cells. Gas density is the same before and after RT (see Section 2.4). Figures 5 and 6 show edge-on and face-on views of a representative snapshot, and zooms on the central regions are displayed in Figures 7 and 8. Each map is a thin slice of the simulation box, centered on the BH. The maps for some other snapshots are available in Appendix LABEL:appendix:maps.

We will first focus on the effect of the lowest AGN luminosity on the galaxy, namely the first two columns of each figure. The impact of the higher luminosities are discussed in next section. The ionization panels of the disk seen edge-on at both large (Figure 5) and small (Figure 7) scales show that the AGN radiation escaping the galaxy has a typical bi-conical shape, as observed by Muller-Sanchez2011 (see Section 4.3 for discussion).

In the central region of the disk, gas at densities of about 10 cm is heated by roughly a factor of ten, though the effect is invisible at kpc-scale. Dense clumps are only slightly heated on the illuminated side but shield themselves and the material behind them. At approximately 500 pc around the BH in the disk, even directly illuminated diffuse gas is not impacted. In the upper outer part of the gaseous halo, and in some diffuse spots above and under the disk, very diffuse gas ( cm is relatively inefficiently heated () by the AGN. These outer heated regions relatively resemble the upper outer part of the ionization cone. It is however important to note that a complete “temperature cone” similar to the ionization cone does not appear here since the measurement of the final temperature takes into account the initial temperature in the simulation (in which gas is already heated by thermal AGN and SNe feedback, etc.), whereas ionization is only based on the radiative transfer due to the AGN radiation (which assumes the gas was previously neutral, see Section 2.4). We therefore see that the effect of AGN heating dominates the other kinds of feedback only in the outer parts of the halo, or in diffuse regions around the galactic disk, near the BH.

Finally, only a thin layer (up to 40 pc for 10 cm ; 15 pc for 10 cm) on the illuminated side of the star-forming regions is heated above the temperature threshold, and most of the ionized regions were not initially forming stars anyway. The remaining star-forming regions shield themselves from the radiation starting approximately at 10 cm. Around 100 pc away from the BH, even the diffuse star-forming regions remain. The density threshold for SFR is 10 cm, but more diffuse clumps would not be self-shielding from the AGN radiation, and would contribute negligibly to the total SFR of the galaxy (see discussion in Appendix LABEL:subSection:threshold).

All snapshots (see Appendix LABEL:appendix:maps) show roughly the same behaviour, except #6, where the BH is embedded into a very dense clump of gas (n 10 cm). In this case, AGN radiation is blocked within the central clump and regions that could be affected by the AGN are below the resolution limit. Snapshot #3 shows both behaviours, since a dense clump just above the BH blocks the radiation above the disk, but not on the other side. Thus, the distribution of the gas into clumps has an important impact on the propagation of the AGN radiation, sometimes preventing it from escaping at all.

3.2. Dependence on AGN luminosity

In this section, we investigate the effect of increasing AGN luminosities (right two columns of Figures 5, 6, 7 and 8). As expected, the higher the luminosity, the more extended the ionized and/or heated regions, and the more star-forming regions are suppressed.

In the halo, diffuse gas at 10 cm and 10 K is heated at 10 K in the standard AGN regime, and at 10 and 10 K in the strong AGN and QSO regimes. At small scale in the disk, 10 cm gas is heated from 10 to 10 K in the normal AGN regime, at approximately 500 pc around the BH. Denser gas or gas located further in the disk is not heated. In the strong AGN regime, gas with the same density and temperature is also heated, but to a higher degree (10 K) and further away from the BH (up to 1 kpc). In the QSO regime, the effect is even more important: diffuse 10 K gas is heated to 10 K, within up to 10 kpc around the BH, thanks to the diffuse interclump medium allowing the QSO radiation to go past the inner kiloparsec. However, the densest clouds ( cm) are not heated and shield the gas behind them. The clumpy distribution of gas in the ISM is responsible for the high variability of the maximal radius at which gas is heated by the AGN in the disk, which cannot be probed with smooth density profiles.

As AGN luminosity increases, star-forming regions are suppressed further from the BH. In the strong AGN regime, diffuse star-forming regions close to the BH and not shielded by dense clumps are destroyed up to 300 pc away in the disk. In the QSO regime, this distance increases to 1 kpc and only the cm star-forming regions survive at the center. However, most of the SFR lies in the densest star-forming clouds, which are not affected by the AGN radiation.

Snapshot #6 (AGN embedded in a dense clump, see Appendix LABEL:appendix:maps) shows a more extreme behaviour. Even if AGN radiation escapes the central clump and an ionization cone is visible in the strong AGN and QSO regimes, the reduction of SFR is nearly zero whatever the luminosity of the AGN. This, once again, shows that gas ionized is mainly not initially star-forming, even at high AGN luminosity.

The idea that star-forming gas is mostly left unaffected even in the strong AGN and QSO regimes is also well presented by the temperature versus relative temperature change diagrams (see Figure 9). The temperature represented is the initial temperature (before RT) and only the gas in the central region of the box – defined as the cylinder of radius 2 kpc and height 4 kpc centered on the BH, is shown. All cells with  % are considered not heated and are shown in the first bin (). The demarcation line between gas forming stars before RT and remaining below the temperature threshold for star formation after the RT process, and gas forming stars before RT but crossing the temperature threshold after RT is defined as:

 Tinitial=TthrRTC+1, (4)

where , and are the quantities defined above. Star-forming gas above the demarcation line defined in Equation 4 is prevented from forming stars due to AGN ionization. Figure 9 clearly shows that, even though a greater amount of gas is heated to a higher degree when increasing the AGN luminosity, the bulk of the star-forming gas is not heated enough by AGN radiation to exceed the temperature threshold for star formation.

In summary, increasing AGN luminosity indeed heats a greater amount of gas with densities reaching 10 cm above the temperature threshold for star formation. However, given the low density of the gas in most affected regions, we expect the decrease of the total SFR due to photoionization to be relatively small, as quantified below.

3.3. Reduction of the total SFR

We estimate the global effects of AGN photoionization by summing the SFRs of all cells in the simulation, and calculating total ionized/heated mass and volume fractions (see Section 3.4). Figure 10 shows the evolution of the total SFR as a function of time for the simulation without AGN feedback and the simulation including AGN feedback before and after ionization. Here the density threshold for star formation is 10 cm (see Appendix LABEL:subSection:threshold for other thresholds). The slow decrease is due to gas consumption over time – as no new gas is added to the simulation box.

The difference between the SFR without AGN feedback and the SFR with only thermal AGN feedback (before RT) arises due to the fluctuations of the SFR in the simulation, which is highly dependent on the distribution of gas into clumps. As this distribution is stochastic (see Section 2.1), short-term variation and a difference of a few percent between two simulation runs are not surprising and AGN feedback – if it does play a role in this change – is probably not the main driving mechanism. Similarly, the SFR with thermal AGN feedback being greater than the SFR without AGN feedback is most likely due to a random event, and is not necessarily a sign of positive AGN feedback (SF-triggering).

Figure 10 clearly shows that the impact of RT on the total SFR of the simulation with feedback is small at all luminosities. As the final SFR is based on the final post-RT temperature (defined as the maximum between the Cloudy temperature and the initial temperature, see Section 2.4), it takes into account the effect of the thermal AGN and stellar feedback implemented in the simulation even though theses sources are not considered for the RT computation itself. Thus, we conclude that, not only does RT change the SFR marginally compared to other feedback models444All simulations include SNe feedback. but also, in this particular simulation, the change in SFR due to all kinds of AGN feedback is not significant.

Figure 11 shows the relative reduction of the SFR due to the radiative transfer, as a function of the AGN luminosity. It is defined as :

 Δrel=∣∣SFRfinal − SFRinitial∣∣SFRinitial, (5)

where is the SFR of the simulated galaxy with thermal AGN feedback before computation of the RT and is the SFR after computation of the RT. The total values of the SFR – both before and after RT – were corrected the same way to account for the resampling induced by the Cloudy computation (see Section 2.4). We see that the effect is indeed very small, and though there is an increasing trend at higher luminosities, the overall effect is marginal: a maximum of a few percent in the QSO regime, for the snapshots with the most diffuse inner regions. The lowest curve corresponds to snapshot #6, where no effect is visible on the maps. In the standard AGN regime, the final SFR of this snapshot, which is a rare configuration, is not reduced at all.

We conclude that adding instantaneous AGN photoionization feedback to a simulation containing thermal AGN feedback and stellar feedback changes the SFR of the whole galaxy by only a few percent at most. Moreover, this reduction is much smaller than the difference in SFR between two runs of the same simulation with and without thermal AGN feedback – which represents the fluctuations of the SFR due to the stochastic distribution of clouds – and shows that AGN feedback does not have a significant impact on the SFR on short time-scales.

3.4. Fractions of heated and/or ionized gas

From the small reduction of the SFR, we expect the gas mass fraction that is heated or ionized by the AGN to be small. Figure 12 shows the volume and mass fractions of the gas in the galactic disk (2 kpc-thick layers on each side of the median plane of the box) that is ionized by the AGN, as a function of the luminosity. The ratios are defined as follows:

 mion=Mionized, correctedMtotal, % corrected ; vion=Vionized, correctedVtotal, corrected (6)

As for Equation 5, both the pre- and post-RT parameters are those of the simulation with AGN feedback respectively before and after photoionization, and were corrected the same way to account for the resampling due to the Cloudy computation. We consider gas to be ionized if its neutral hydrogen fraction is below 10 %. Contributions from OB stars and SNe or thermal AGN feedback are not included since Cloudy computes the RT as if the BH was the only ionizing source and the gas was initially neutral (see Section 2.4). Given that the halo is initially set in the simulation to have very diffuse gas ( cm), the halo component is highly ionized by the AGN, but would be easily ionized by another source such as OB stars and SNe feedback or UV background (see Section 4.4 for discussion). The simulation is not designed to study the gaseous halo properties and one would need to account for cosmological context or at least close environment and satellites. Restraining the study to the gas in the disk reduces this effect but does not cancel it entirely and thus this value shows an upper limit to the amount of neutral gas that could be ionized by an AGN.

We see that even though the fraction of volume ionized by the AGN is large (from 5 to 40 % in all representative snapshots depending on the luminosity regime), the corresponding mass fraction is low: from 0.1 to 3 % at most. This confirms the intuition that, even though some regions that are ionized have a large spatial extent, they are not significant contributors to the total mass of the galaxy, and therefore to the total SFR.

Figure 13 shows the heated mass and volume fractions of gas in the disk. The ratios are similar to Equation 6. Gas is heated if the equilibrium temperature given by Cloudy is greater than the initial temperature in the simulation, meaning that the AGN ionization alone is able to heat the cell above the temperature at which it has been heated by all the other kinds of feedback (thermal AGN and stellar) in the simulation. Thus, heated gas takes into account the “feedback history” of the snapshot (contrarily to ionized gas) and traces the regions where heating due to the AGN photoionization outweighs the other kinds of feedback. However, the behaviour is very similar to that of ionized gas, and even when the photoionization has a stronger effect than the other forms of feedback together, the SFR is only slightly impacted because most of the affected gas is not initially star-forming.

4. Discussion

In the following, we discuss the dependence of our results on the structure of the ISM. We also deduce a trend for the 100 Myr-scale effects on star-formation and develop our study of the ionization cones. Finally, we try to account for the gas that would already be ionized by other sources before applying RT.

4.1. Role of ISM structure

The profiles used in the LOPs have complex structures with large contrasts between the clump and inter-clump densities (see Figure 4). In order to study the role of the ISM structure on the propagation of AGN radiation, we used Cloudy to calculate the propagation of the three AGN regimes we used before along homogeneous lines-of-propagation, using the inner and outer radii of a typical LOP in the plane of the disk, and the same filling factor (see Figure 14). We compared the resulting neutral hydrogen fractions to that of a typical LOP in the plane of the disk (as shown in black in Figure 4), whose mean density is 40 cm. We only show the typical AGN and QSO luminosities, and note that the strong AGN case is intermediate, as expected.

The ionization profile of the LOP inside the plane of the disk used in the main study is located between those of the constant LOP at 10 cm and at 1 cm, whereas its mean density is  cm. For all constant profiles (except for the 10 cm in the typical AGN regime), the radius at which gas becomes less than 10 % ionized is larger than for the main study LOP, showing that ionization and heating by the AGN goes deeper in the disk than for the typical disk plane LOP. However in the uniform-density case, the ionization fraction decreases smoothly whereas that of the main study LOP is not monotonic and regions of highly ionized gas are found far in the disk in the strong QSO regime (see Section 4.3). Such spikes correspond to diffuse interclump regions that are ionized by the AGN. In the QSO regime, they are located at radii up to kpc in the disk (see Figure 6). This suggests that typical high-redshift disk galaxies are on average dense enough to screen AGN radiation, and that holes between the dense clumps are necessary for radiation to go past the inner kiloparsecs.

A smooth exponential density profile enclosing the same mass as the simulated galaxy gave similar results.

We conclude that the ISM structure plays a major role in the propagation of AGN radiation since holes explain that ionization often reaches large distances in the disk or in the halo, whereas dense clumps are not necessary to explain the low ionized mass fraction, since the average density is high enough for the gas to be self-shielding.

4.2. Long-term effects on star formation

Long-term effects on star formation can be deduced from our instantaneous study by looking at the HI reservoirs in the envelope of GMCs and in the atomic clouds around them (“proto-GMCs”), which are composed of 0.3 - 10 cm ISM (Dobbs2008).

Indeed, the first step to launch star formation is to form a dense cloud of molecular gas (a GMC) out of diffuse ISM. Such GMCs are believed to be created by spiral-wave-induced shocks (Heyer1998; Dobbs2008b), and live about 15 - 40 Myrs (Murray2011), until they are disrupted by the stars that formed inside them and their envelope is dispersed (Elmegreen2007a). In the absence of external heating, those 0.3 - 10 cm regions form proto-GMCs which gradually fall under  K. These are likely to collapse due to shocks and create new GMCs, which in turn induce the formation of new stars in the next 100 - 200 Myrs, and the cycle continues.

However, if this gas phase is maintained hot or ionized by the AGN, it cannot cool down and collapse and future star formation is suppressed on a time-scale shorter than that necessary to refuel the interclump medium with cold infalling gas. The instantaneous effect of the three luminosity regimes on atomic gas is computed the same way as before (see Section 3.4) but accounts only for the gas at densities 0.3 - 10 cm and is displayed in Table 2.

From Table 1, AGN radiation is emitted at  erg s about 30 % of the time, and at  erg s about 3 % of the time, considering an AGN duty cycle of .

Instantaneously, the heating/ionization of the GMCs due to the AGN in such regimes is negligible (see Table 2), and therefore it is highly unlikely that cumulative effects will become important in the following 100 - 200 Myrs and thus no star formation quenching is expected. Even if the AGN were emitting 100 % of the time, the results would not change for both the typical and strong AGNs. However, in the case where a QSO would be emitting for an extended period of time because of, e.g., a merger, GMCs would more likely be impacted and cumulative effects could significantly reduce future star formation.

The longer-term ( Myrs - 1 Gyr) SFR evolution depends on the ability of the AGN to keep the gaseous halo warm or ionized. Indeed, keeping the halo hot over an extended period of time could prevent inflows from reaching the disk and starve the galaxy by suppressing its gas supplies (Dubois2012). However, the simulation we used is an isolated galaxy and its initial gaseous halo is not designed to be realistic and thus we cannot predict whether the AGN is able to quench the galaxy on a time-scale of a few Gyrs.

4.3. Distribution of ionized gas

This section focuses on the ionization maps in Figures 5, 6, 7 and 8. In the typical AGN regime, the inner part of the disk surrounding the AGN is ionized up to 50 - 700 pc, depending on the location of the nearest dense clumps ( cm), which shield themselves, block the AGN radiation and protect the diffuse material behind them. The galactic disk remains neutral at larger scale. The LOPs that do not cross dense clumps are ionized until the end, meaning that the material in the halo is not able to stop the radiation. However, this simulation was not designed to have a realistic gaseous halo and is not in its cosmological context.

At small scales around the black hole, the limit between neutral and ionized gas goes from 1 - 10 cm in the typical AGN regime, to 10 and 100 cm in the strong AGN and QSO regimes respectively. With increasing AGN luminosity, the distance at which clumps are able to shield the diffuse regions behind them is larger, allowing ionization to go further within the disk. Though, it does not affect the densest clumps or the disk itself, which remains neutral.

In the strong AGN and QSO regimes, not only are the ionized regions more extended, but also the fraction of remaining neutral hydrogen is smaller by a factor  10 - 100 in the regions that were already ionized in the typical AGN regime. In the QSO regime, ionized spots are visible at large scale within the disk (up to 8 kpc from the BH), though SFR is not impacted since those regions are mostly not initially star-forming.

Clearly, the impact of AGN photo-ionization is greater than expected for a simple model (see Section 2.3), showing that the multi-phase distribution of the gas plays a key role in the propagation of AGN radiation: while dense clumps can block the ionizing radiation at a very small scale-length depending on their distance to the BH, AGN radiation is allowed to propagate past the inner kiloparsecs thanks to the diffuse interclump medium. The morphology of the galaxy may also be of great importance, since the calculation done by Curran2012 reproduces observations of (most likely) elliptical radio galaxies and quasar hosts (Curran2006a; Curran2008a) up to redshift 3, but fails to reproduce the propagation of AGN radiation in a simulated star-forming disk at redshift .

Ionized gas (AGN ionization only) and heated gas (AGN ionization stronger than thermal AGN and SNe feedback) have distinct distributions, showing that, in the simulation presented here, AGN ionization itself does not overwhelm all other forms of feedback and ionization from other sources – at least instantaneously – for the three luminosity regimes.

Yet, our study reproduces the observed biconical shape of AGN emission (see Figure 5), even though the propagation of AGN light is isotropic. This shows that the simulated ISM is able to collimate the AGN radiation to some degree. These ionization cones may be larger-scale analogs to those predicted by the AGN Unified Model of Urry1995. Furthermore, as the AGN is the only ionizing source, we show that other sources of ionization such as stars are not needed for AGN radiation to escape the galaxy, which is consistent with AGNs being the main drivers of ionization cones. Accounting for these other sources of ionization would only favor the escape of photons emitted by the AGN.

The bases of the cones are not circular and are not necessarily centered on the BH . Their shape depends a lot on the cloud distribution. With a higher AGN luminosity, the ionization cones are wider and their basis is larger, which is in broad agreement with Hainline2013 in the sense that the size of the Narrow-Line Regions (NLRs) increases with AGN luminosity. Finally, the inclination of the cones with respect to the galaxy spin axis decreases for a higher AGN luminosity. The diffuse and almost entirely ionized gaseous halo may also be consistent with the observations of nearly circular NLRs in radio-quiet quasars by Liu2013b.

4.4. Other sources of ionization

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