Capturing the inside-out quenching by black holes with far-infrared atomic line ratios
Shigeki Inoue, Hiroshi Matsuo, Naoki Yoshida, Hidenobu Yajima, Kana Moriwaki
MMNRAS , 1–15 (2020) Preprint 23 February 2021 Compiled using MNRAS L A TEX style file v3.0
Capturing the inside-out quenching by black holes with far-infraredatomic line ratios
Shigeki Inoue , (cid:63) , Hiroshi Matsuo , Naoki Yoshida , , , Hidenobu Yajima & Kana Moriwaki Center for Computational Sciences, University of Tsukuba, Ten-nodai, 1-1-1 Tsukuba, Ibaraki 305-8577, Japan Chile Observatory, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Advanced Technology Center, National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan Department of Physics, School of Science, The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan Research Center for the Early Universe, School of Science, The University of Tokyo, Bunkyo, Tokyo 113-0033, Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Chiba 277-8583, Japan
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We propose to use relative strengths of far-infrared fine structure lines from galaxies to characterise early phases of the inside-outquenching by massive black holes (BHs). The BH feedback is thought to quench star formation by evacuating the ambient gas.In order to quantify the feedback effect on the gas density in the galactic centres, we utilise the outputs of IllustrisTNG andIllustris simulations, which implement different BH feedback models. We devise a physical model of H II regions and computethe intensities of [O III ] and µ m lines. The line intensity ratio is sensitive to the local electron density, and thus can beused to measure the strength and physical extent of the BH quenching. If the BH feedback abruptly operates and expel the gaswhen it grows to a certain mass, as modelled in IllustrisTNG, the low-density gas yields relatively weak [O III ] line withrespect to µ m . In contrast, if the feedback strength and hence the local gas density are not strongly correlated with the BHmass, as in Illustris, the line ratio is not expected to vary significantly among galaxies with different evolutionary stages. Wefind these features are reproduced in the simulations. We also show that the line ratios are not sensitive to the aperture size formeasurement, and thus observations do not need to resolve the galactic centres. We argue that the integrated line ratios can beused to capture the onset of the inside-out quenching by BHs. Key words: methods: numerical – galaxies: evolution – galaxies: nuclei – quasars: supermassive black holes
A wide variety of physical processes occur in the central regions ofgalaxies through the co-evolution of galaxies and massive black holes(BHs). Detailed observations of galactic inner regions can thereforeprovide important clues to the evolutionary stages of the galaxies. Itis theoretically expected that, in massive galaxies in the high-redshiftUniverse, a large amount of gas is funnelled into the galactic centre,where the earliest episode of star formation should have taken place.There, the central BH can grow by accreting a large amount of gas,but the details of this process have not been elucidated (e.g. Inayoshiet al. 2020, and references therein). When there is a large amountof dense gas in the galactic centre, a massive BH can outshine asa quasar by accreting the ambient gas at a high rate. When the gasaround a BH is diffuse and the accretion rate is low, it can expel thegas from the galactic centre through various processes such as high-energy radiation and launching a jet. If the feedback effect of activegalactic nuclei (AGN) is strong enough to expel most of the gas fromthe galaxy, star formation activity there is effectively ‘quenched’, andthe galaxy evolves to a quiescent galaxy that consists of old and red (cid:63)
E-mail: [email protected] stars with little gas. Hence the AGN feedback plays a key role in theevolution of galaxies that host massive BHs.It is known that the star formation efficiencies of galaxies, i.e.ratios of stellar to halo masses, peaks at a halo mass of ∼ M (cid:12) ,and declines toward more massive galaxies (e.g. Silk & Mamon2012; Behroozi et al. 2019). This trend is often attributed to thefeedback by massive BHs. In a colour-magnitude diagram, quenchedgalaxies are generally found in a ‘red sequence’ as elliptical andlenticular galaxies, which is distinct from a ‘blue cloud’ consistingof star-forming galaxies. Several quenching mechanisms have beenproposed to transform galaxies from blue to red through the so-called‘green valley’ (e.g. Martig et al. 2009; Schawinski et al. 2014; Joshiet al. 2020), and the BH feedback is thought to be a major processthat shapes the colour bimodality of the local galaxies by quenchingstar formation in massive galaxies.Because the AGN feedback is driven by the central BH, star-formation quenching is expected to proceed from the galactic cen-tre first and then propagate outwards. This "inside-out" quenchingprocess would begin with lowering the gas densities in the centralregions, whereas the outer regions still sustain their star formationactivity with a sufficient amount of dense gas. Contrastingly, if thereare no massive BHs are or the feedback is insufficient, galaxies usu-ally have gas density profiles increasing towards the centre. There- © a r X i v : . [ a s t r o - ph . GA ] F e b S. Inoue et al. fore, measuring the gas density at the galactic centre may provide aprobe of the inside-out quenching by massive BHs. Namely, if a star-forming galaxy is observed to have a low gas density at the centre, itmay be a sign of the onset of the BH quenching of star formation.Although it is difficult to measure directly the gas densities byobservations especially for distant galaxies, one can use the intensityratio between a specific pair of emission lines to estimate the localelectron density. In the present study, we focus on the fine structurelines of doubly ionized oxygen at the wavelengths of and µ m (hereafter [O III ] and [O III ] ). The relative strength of [O III ] to (hereafter [O III ] / ) is sensitive to the electron density ofthe line emitting region owing to their different critical densities (e.g.Keenan & Aggarwal 1988). The [O III ] lines are detected in variousastronomical objects including low- and high-redshift galaxies (e.g.De Looze et al. 2014; Inoue et al. 2016; Novak et al. 2019). Weapply a physical model of the [O
III ] line emission to the output ofcosmological hydrodynamics simulations and examine whether ornot and how the BH feedback affects the line ratio.Since the detailed physics of BH formation and growth are notknow, and numerical simulations do not have a sufficient resolu-tion to reproduce the interaction between BHs and the surroundinggas, even the state-of-the-art cosmological simulations treat the for-mation, growth and feedback of BHs as sub-resolution models (seeSection 2.1). Unfortunately, there is not a well-established model ofBH feedback, and recent simulations adopt different numerical im-plementation, especially for massive BHs. The major purposes of ourstudy are to predict the line ratios of [O
III ] / for star-forminggalaxies using cosmological simulations and to show how charac-teristic features of BH feedback models are inferred from the lineratio.We utilise the outputs of the cosmological simulation of the NextGeneration Illustris (hereafter IllustrisTNG or TNG). Nelson et al.(2018b) show that IllustrisTNG reproduces well the colour bimodal-ity of galaxies observed in the local Universe thanks to its improvedmodel for BH feedback in massive galaxies. However, Hayward et al.(2020) postprocess the simulation data and model sub-millimetregalaxies (SMGs) at redshift z = , to show that TNG significantlyunderestimates the SMG luminosity function. They argue that theBH quenching in TNG appears to operate too early. It is thus im-portant to study in detail the feedback effects caused by the massiveBHs in the simulations. Using the two sets of simulations allows usto make a quantitative comparison; we apply the same analysis tothe original Illustris simulation (hereafter Illustris), in which the BHfeedback model is different from that of TNG. Hayward et al. (2020)also shows that Illustris can reproduce the luminosity function ofSMGs better than TNG. With our postprocessing model of the [O III ]lines, we can address how the differences in the BH feedback modelsaffect the line ratios. It is worth noting here that we do not aim atjudging which simulation is more realistic. We propose a method ordiagnostics to constrain BH models using observations of emissionlines from star-forming galaxies at low and high redshifts. The resultsof our study would eventually help to understand the behaviours ofBH quenching observationally, such as the dependence of the feed-back efficiency on BH mass and on other physical parameters in thereal Universe.Because far-infrared emission of atomic fine-structure lines is op-tically thin, their relative strengths can be used as a direct probe of thegas (electron) density of the emitting region. High-redshift quasars at z (cid:38) are bright in the line emission such as [O III ] and [N II ] and havebeen observed with Atacama Large Millimetre/submillimetre Array(ALMA). Our method using these line pairs could be applicable tosuch quasars in the early Universe. However, because there are no massive BHs at z (cid:38) in the above simulations, we demonstrate ourmethod with snapshot data at z ≤ .In Section 2, we describe the cosmological simulations of Illus-trisTNG and Illustris. In Section 3, we explain our models to computethe [O III ] lines from snapshot data of the simulations. We presentour results in Section 4 and discuss them in Section 5. We summarisethis study and draw our conclusions in Section 6.
We utilise publicly available data sets of IllustrsTNG and Illustris.The details of the simulations are presented on the respective websites , and in related papers including Nelson et al. (2018a), Wein-berger et al. (2017) and Pillepich et al. (2018) for IllustrisTNG,and Vogelsberger et al. (2014a,b), Genel et al. (2014) and Sijackiet al. (2015) for Illustris. Both simulations are performed with an N -body/moving-mesh hydrodynamics code Arepo (Springel 2010;Weinberger et al. 2020). The sub-resolution physics such as gas cool-ing, star formation and supernovae implemented are essentially thesame in the simulations. The main differences between the TNGand Illustris are in their BH feedback models and implementationof magneto-hydrodynamics (see Section 2.1). Although only TNGincludes the effects of magnetic fields, Pakmor et al. (2017) showthat the presence of magnetic fields hardly affects the formation his-tory of the simulated galaxies. This study focuses on the runs ofTNG100-1 and Illustris-1 for the IllustrisTNG and Illustris simu-lations, respectively. Their resolutions and sizes of the simulatedvolumes are hardly different. Their simulation boxes have comovingside lengths of (cid:39)
110 Mpc , and the mass-resolutions for dark matterand gas are (cid:39) and . × M (cid:12) . Hence, the comparison betweenTNG100-1 and Illustris-1 is expected to extract physical influencesby their different BH feedback models.In the simulations, dense gas cells with ρ cell > n H , SF = . − are converted to stellar particles according to a stochastic model ofstar formation. The mass-resolution of a stellar particle is thereforecomparable to that of the parent gas cell. Star formation rate (SFR)is calculated as ˙ m star = f M m cell t SF (1)where m cell is a mass of the parent cell, f M is the mass fractionof cold gas computed with a model of Yepes et al. (1997, see alsoSpringel & Hernquist 2003), and the star-formation time-scale t SF is approximated as a free-fall time within the cell: t SF ≡ / √ G ρ cell .A stellar particle is assumed to have the initial mass function (IMF)of Chabrier (2005). Type-II supernovae (SNe) are triggered immedi-ately following the star formation, and a feedback model of Springel& Hernquist (2003) is adopted to represent stellar feedback effects.Type-Ia SNe and asymptotic giant branch stars eject mass and metalsinto nearby gas cells.Gravitationally bound structures are identified with the friend-of-friend and SUBFIND grouping algorithms (e.g. Springel et al.2001). In this study, the total masses and SFRs are computed foreach SUBFIND group (galaxy). When a single galaxy hosts multipleBHs, we define the most massive one to be the representative BHof the galaxy and consider its mass to be the BH mass, M BH , of thegalaxy. , 1–15 (2020) apturing inside-out quenching The details of the BH model of IllustrisTNG and Illustris aredescribed in Weinberger et al. (2017) and Sijacki et al. (2007,2015), respectively. Briefly, BHs are seeded with the initial massof M seed = . × M (cid:12) when their friend-of-friend host haloesreach M FOF = . × M (cid:12) in TNG, whereas the correspondingmasses are M seed = . × M (cid:12) and M FOF = . × M (cid:12) inIllustris. The seed BHs are placed at the potential centres of theirhost haloes and move together with them. The BHs increase theirmasses by accreting the surrounding gas at rates ˙ M Bondi given by theBondi–Hoyle–Lyttleton formula limited by the Eddington rate ˙ M Edd ,i.e. ˙ M BH = min ( ˙ M Bondi , ˙ M Edd ) . In computing ˙ M Bondi , IllustrisTNGdoes not use an artificial boost factor nor take into account relativevelocity between the BH and ambient gas unlike Illustris.In both the simulations, the BH model assumes two feedbackmodes according to whether the Eddington ratios ˙ M Bondi / ˙ M Edd arehigher or lower than a critical value χ . An important point in our studyis that TNG and Illustris adopt different definitions of χ . IllustrisTNGassumes χ to be a function of M BH as χ = min (cid:34) χ (cid:18) M BH M (cid:12) (cid:19) β , . (cid:35) , (2)where χ = . and β = . , whereas Illustris sets a constant valueof χ = . . When ˙ M Bondi / ˙ M Edd > χ , an inefficient thermal feed-back mode called "quasar mode" is switched on in both simulations.When ˙ M Bondi / ˙ M Edd < χ , the BH feedback model largely differ be-tween TNG and Illustris. In TNG, the criterion given by equation (2)quadratically increases with M BH until M BH reaches . M (cid:12) . Onthe other hand, the Eddington ratio scales as ˙ M Bondi / ˙ M Edd ∝ M BH if the properties of ambient gas do not change. The transition of theBH feedback is thus closely linked to M BH in TNG. This modellingmakes M BH a determinant quantity to switch between the two feed-back modes, and massive BHs with M BH (cid:38) . M (cid:12) are mostly inthe low-accretion mode (see Section 4.1.1).In the quasar mode with ˙ M Bondi / ˙ M Edd > χ , a BH distributes ther-mal energies to nearby gas cells, given as ˙ E qsr = ε qsr L BH , where thethermal coupling efficiencies are ε qsr = . and . in IllustrisTNGand Illustris, respectively. The bolometric luminosity is given by L BH = ε r ˙ M BH c with radiative efficiency ε r = . , where c is thespeed of light. This high-accretion mode occurs essentially in thesame manner between the two simulations.In TNG, a BH in the low-accretion mode with ˙ M Bondi / ˙ M Edd < χ injects momenta to nearby gas cells (‘kinetic mode’, Weinbergeret al. 2017). The energy-injection rate in this mode is given as ˙ E kin = ε kin ˙ M BH c with the efficiency ε kin = . . The injection per time-step ˙ E kin ∆ t is accumulated in time, and the integrated energy is releasedevery time it exceeds a certain threshold given by equation (13) ofWeinberger et al. (2017). The accumulation makes the BH feedbackstrong enough to blow out the gas around the BH to halo regions.Since the kinetic energy injected as momentum is not convertedquickly to thermal energy that is lost by gas cooling, the kineticmode can cause efficient feedback in galaxies with massive BHs.In Illustris, the low-accretion mode with ˙ M Bondi / ˙ M Edd < χ injects When M BH > . M (cid:12) , χ is limited to 0.1 according to equation (2). As long as M BH < . M (cid:12) , a BH growing at a constant Eddington rationecessarily reaches the condition of ˙ M Bondi / ˙ M Edd < χ at a certain M BH , whenthe BH feedback is switched to the low-accretion mode. If gas around a BH has a hydrogen number density lower than n H = − cm − , the efficiency scales linearly with the local density as ε kin = min ( n H / n H , SF , . ) . thermal energies to gas within a ‘bubble’ region in the galaxy (‘radiomode’, Sijacki et al. 2007). The injected thermal energy into thebubble is given as E rad = ε rad δ BH M BH c , where ε rad = . . Theinjection is operated every time the BH increments its mass by δ BH = from M BH at the previous injection. The bubble is randomlylocated within a certain distance from a BH, and therefore the thermalenergy is injected effectively by avoiding the high-density region atthe galactic centre where the injected energy can be quickly radiatedaway.The low-accretion modes are the main driver of the quenchingprocess in massive galaxies in both the simulations although theirmodels are largely different. We expect that characteristic featuresof the distinct BH feedback models can be found in galaxies thathost massive BHs while still forming stars actively. We focus on theearly stage of the BH quenching occurring in massive, star-forminggalaxies. III ] LINE MODEL
It is well known that a combination of far-infrared emission lines canbe used to estimate the local election density of the line emitting re-gion. Although we consider specifically the line ratio of [O
III ] / in this study, other pairs such as [N II ] lines at and µ m (e.g. Zhao et al. 2016; Doherty et al. 2020) can also be the densityindicator (see also Section 5.1). Far-infrared fine structure lines areuseful to observationally study the density structure of high-redshiftgalaxies, in which the inside-out quenching driven by massive BHscan be occuring. Because the [O
III ] lines are mainly emitted from H II regions aroundyoung massive stars, we devise a physical model of H II regions andimplement in each gas cell in the simulations. We first evaluate thefollowing physical quantities; a typical lifetime of a H II region t HII and the characteristic mass of a star cluster M cl . We assume thatthe star cluster is the dominant radiation source that forms the H II region. Note that M cl is defined as the initial mass of a cluster. Thenumber of H II regions within a single gas cell is estimated as N HII = ˙ m star t HII M cl , (3)where ˙ m star is an SFR of a cell, given by equation (1). We set theparameters to be t HII = (e.g. Krumholz 2017; Fukushimaet al. 2020) and M cl = M (cid:12) . We allow N HII to be less than 1, i.e. acomputational cell covers only a fraction of a star-forming region. Weassume that ˙ m star is constant during t HII , and that the cluster stellarpopulation is represented by time-integrated Chabrier IMF evolvedover t HII . We consider the metallicity of the stars to be the same asthat of its parent gas cell. From these quantities, we compute thespectral energy distribution (SED) of a star cluster using PÉGASE.2(Fioc & Rocca-Volmerange 1999), and calculate the production rateof ionizing photons, ˙ N ph , with energies higher than . .Since the spatial resolutions of star-forming gas cells with ρ cell > n H , SF = . − are in the order of ∼ –
100 pc in the runs ofTNG100-1 and Illustris-1, star-forming regions are not resolved inthe simulations. The actual physical density in a star-forming regionis therefore expected to be significantly higher than the cell density ρ cell . We adopt a model for interstellar matter (ISM) used in Inoueet al. (2020), where a gas cell is considered to consist of cold andwarm neutral media (CNM and WNM) with their density contrast of MNRAS000
100 pc in the runs ofTNG100-1 and Illustris-1, star-forming regions are not resolved inthe simulations. The actual physical density in a star-forming regionis therefore expected to be significantly higher than the cell density ρ cell . We adopt a model for interstellar matter (ISM) used in Inoueet al. (2020), where a gas cell is considered to consist of cold andwarm neutral media (CNM and WNM) with their density contrast of MNRAS000 , 1–15 (2020)
S. Inoue et al. ρ CNM / ρ WNM = (Wolfire et al. 1995). The ISM model considersthat the CNM and WNM are in pressure equilibrium due to thebalance between (unresolved) SN feedback and thermal instability bycooling (Springel & Hernquist 2003). According to the ISM model,we can compute a density and volume of the CNM for each gas cell.The density enhancement factors are estimated to be ρ CNM / ρ cell ∼ – depending on cell density (see figure 1 of Inoue et al. 2020).Although the CNM and WNM are unresolved in the simulations,stars are actually expected to form in the CNM. We therefore considerthat all H II regions reside in CNM, and the gas density inside theH II regions is approximated to be ρ CNM for each cell.To compute the line emission of [O
III ] based on the above modelfor H II regions, we use a method described in Moriwaki et al. (2018).Assuming the density within an H II region to be uniform, a Ström-gren sphere forming the H II region has a radius of r S = (cid:18) N ph π n α B (cid:19) , (4)where α B is the case-B hydrogen recombination coefficient, and weassume a constant value of α B = . × − cm s − . Consideringa fully ionized state, the electron number density n e is equal to thehydrogen number density estimated for the H II region by the aboveISM model: ρ CNM . In all snapshots of both simulations, we confirmthat the total volume of the Strömgren spheres, π r N HII / , does notexceed a volume of CNM in any star-forming cell with ρ cell > n H , SF with the above parameter settings. Eventually, the volume-averagedionization parameter inside r S is given as U = c (cid:32) N ph n e α π (cid:33) . (5)In the plane-parallel case, the ionization parameter at an inner surfaceof the H II region becomes U in = U .For the H II region modelled above, we adopt a spectral synthesiscode Cloudy (version 17.02 of the code last described in Ferlandet al. 2017) designed to simulate conditions in ISM. For our Cloudymodel, we input an SED of the radiation source, ionization parameter U in , density n e , metallicity Z of gas, and redshift z that sets the tem-perature of the cosmic microwave background. The SED is computedwith PÉGASE.2 for our star cluster model. For the IllustrisTNG sim-ulation, we use an oxygen-based metallicity: Z ≡ Z (cid:12) y O / y O , (cid:12) where Z (cid:12) and y O , (cid:12) are the solar metallicity and oxygen abundance. Thistreatment is motivated by the fact that the [O III ] lines are more sensi-tive to oxygen abundance than the total metallicity. Since the originalIllustris simulation does not have information on oxygen abundance,we use a metallicity assigned to a gas cell as a proxy. At each redshift z , we generate a look-up table of line intensities of [O III ] , [O III ] and H α as a function of the three parameters of U in , n e and Z inlogarithmic spacing of .
48 dex , although U in depends only on n e ata given Z (see below). The line emission of H α is used for parametercalibration (see below). The look-up table covers the whole parame-ter space that the star-forming gas cells in the simulations can have.We estimate the line intensities of each gas cell from the tabulatedvalues multiplied by N HII . We assume that low-density cells with ρ cell < n H , SF do not emit any radiation since they do not form stars.In this study, we do not take into account dust attenuation.In our model described above, the properties of a Strömgren sphereare determined by an SED of a central star cluster and a local density Although the coefficient α B actually depends on temperature of free elec-trons, we adopt the value estimated at K . Figure 1.
Line rations of [O
III ] with respect to [O III ] computed withour model described in Section 3.1, as functions of electron density n e fordifferent metallicities Z . We here adopt our fiducial values of t HII = and M cl = M (cid:12) . Figure 2.
Correlation between H α luminosities and SFRs. The magenta dotsindicate the galaxy-integrated values at redshift z = in IllustrisTNG. Al-though all galaxies in the simulation are plotted, their distribution highlyconcentrates along a linear relation. The black dotted line shows the observa-tional result of Kennicutt (1998). n e , and the SED depends on Z , t HII and M cl . Hence, if we fix t HII and M cl , U in becomes a function of n e at a given Z . Fig. 1 illustratesthe line ratios of [O III ] / computed with our model, as functionsof n e for different Z . The line ratios monotonically increase with n e and hardly depend on Z (see also Fig. B3 in Appendix B). Thus,[O III ] / is expected to be an observational tracer of a localdensity in a star-forming region. Combining it with the fact thatintensities of the [O III ] lines are nearly proportional to SFR (seebelow and e.g. De Looze et al. 2014), [O
III ] / measured withinan aperture can be used to estimate the averaged gas density weightedby SFR. Fig. 2 shows relationship between the galaxy-integrated SFRs andthe modelled H α luminosities of all galaxies at redshift z = in Illus-trisTNG. With the fiducial values of t HII = and M cl = M (cid:12) , MNRAS , 1–15 (2020) apturing inside-out quenching Figure 3.
Correlation between luminosities of [O
III ] and SFRs of allgalaxies in TNG at redshift z = . The colour codes indicate the numbers ofgalaxies in each bin, increasing from blue to red in logarithmic scales. Thestraight lines show correlations observed by De Looze et al. (2014) for thefive types of galaxies: dwarfs, star burst (SB) galaxies, active galactic nuclei(AGNs), ultraluminous infrared galaxies (ULIRG) and high-redshift (high- z )galaxies. our result is in agreement with the observed relation of Kennicutt(1998). Our result for Illustris also shows the same consistency withthe observations. We confirm that this result hardly depends on red-shift or cluster mass in the ranges from z = to and from M cl = to M (cid:12) . The H α luminosities increase with t HII and deviate fromthe observed relation if t HII (cid:38) . Accordingly, hereafter we argueour results with the fiducial values of t HII = and M cl = M (cid:12) .Fig. 3 is the same as Fig. 2 but for luminosities of [O III ] insteadof H α . Our result is in agreement with observations of De Loozeet al. (2014) for dwarf and high-redshift galaxies although the dis-tribution of the simulated galaxies appears to be slightly below theobserved relation for AGNs and also below the relations for star-burstand ultraluminous infrared galaxies. The correlation of the modelled[O III ] and SFR little depends on M cl or evolves with redshift z . Wefind no systematic differences of the correlation in Fig. 3 betweenthe star-forming and quiescent galaxies or between BHs in the high-and low-accretion modes. We find essentially the same result withIllustris. We show our results for IllustrisTNG in Section 4.1. First, in Section4.1.1, we address characteristic features of the inside-out quenchingprocesses caused by massive BHs in the simulation, i.e. depletionof central gas by the kinematic feedback. Next, in Section 4.1.2, weshow how the modelled [O
III ] emission reflects the gas distributionaffected by the BH quenching. In Section 4.2, we follow the samecourse but show the results for Illustris. When M cl (cid:46) M (cid:12) , we find that the total volumes of the Strömgrenspheres can exceed the CNM volumes in some cells. We consider that M cl (cid:38) M (cid:12) would be too large for a typical cluster mass. Figure 4.
Distribution of the total SFRs and stellar masses of galaxies in TNGat redshifts z = , , and . In each panel, the SFMS is indicated with theblack dashed line. At a given M star , the boundary between star-forming andquenched galaxies (the magenta solid line) is defined to be an SFR at the offset ∆ MS = − . σ SFR from the SFMS, where σ SFR is the averaged dispersion ofSFRs (see Appendix A). The colour codes indicate the numbers of galaxiesin each bin, increasing from blue to red in logarithmic scales.
Figure 5.
Projected maps of surface gas densities in two examples of star-forming galaxies in TNG at z = . They have cavities in gas distributionaround BHs. The orientations of the discs are not exactly face-on or edge-on.The left and right galaxies have M BH = . and . × M (cid:12) , M star = . and . × M (cid:12) and SFRs of and
35 M (cid:12) yr − , respectively. To sample star-forming galaxies from the simulation data, we definea star-formation main sequence (SFMS: correlation between the totalstellar masses M star and SFRs) in each snapshot. We use a methodproposed by Donnari et al. (2019) to both simulations, describe themethod in Appendix A. Fig. 4 illustrates the distribution of M star and SFRs of galaxies in IllustrisTNG, and the black dashed linedelineates the SFMS defined at each redshift. The magenta solid lineis the boundary between star-forming and quiescent galaxies, and thisstudy samples those above the boundary as star-forming galaxies.Fig. 5 exemplifies two star-forming galaxies in IllustrisTNG at MNRAS000
35 M (cid:12) yr − , respectively. To sample star-forming galaxies from the simulation data, we definea star-formation main sequence (SFMS: correlation between the totalstellar masses M star and SFRs) in each snapshot. We use a methodproposed by Donnari et al. (2019) to both simulations, describe themethod in Appendix A. Fig. 4 illustrates the distribution of M star and SFRs of galaxies in IllustrisTNG, and the black dashed linedelineates the SFMS defined at each redshift. The magenta solid lineis the boundary between star-forming and quiescent galaxies, and thisstudy samples those above the boundary as star-forming galaxies.Fig. 5 exemplifies two star-forming galaxies in IllustrisTNG at MNRAS000 , 1–15 (2020)
S. Inoue et al.
Figure 6.
Radial profiles of face-on gas surface densities of the star-forming galaxies in IllustrisTNG at redshift z = . The left and right pan-els show galaxies in the BH-mass ranges of log ( M BH / M (cid:12) ) > . and < log ( M BH / M (cid:12) ) < . In each panel, the thick line delineates the stackedprofile among 128 galaxies selected randomly in the BH-mass range, and theshaded region indicates the range of ± σ . The thin lines delineate profiles of12 individual galaxies selected randomly. The left panel shows that the gasdensities decrease towards the central BHs in the galaxies with the high BHmasses. redshift z = . Both have BHs more massive than M (cid:12) and highSFRs. With molecular gas modelling of Inoue et al. (2020), thesegalaxies are found to be the first and eighth brightest galaxies inCO(1-0) emission in TNG100-1. These galaxies have ‘cavities’ intheir gas distributions at the galactic centres (see also Terrazas et al.2020). Fig. 6 indicates gas surface density distributions Σ gas , whichare the face-on radial profiles stacked among 128 galaxies randomlyselected in the ranges of log ( M BH / M (cid:12) ) > . (left panel) and < log ( M BH / M (cid:12) ) < (right panel). The galaxies with massive BHsshow Σ gas decreasing towards their galactic centres, whereas thosewith less massive BHs have nearly exponential profiles in which Σ gas is generally the highest at the centre. Nelson et al. (2019) havealso shown that massive galaxies with M star (cid:38) . M (cid:12) indicateSFRs decreasing in their central regions in the TNG50 simulation(see also Donnari et al. 2021). Thus, central gas densities can besignificantly affected by the feedback of massive BHs in star-forminggalaxies in TNG. Such characteristic features may be consistent withobservations of green-valley galaxies (see Section 5.2).Fig. 7 shows relationship between M BH and gas densities aroundthe BHs for the star-forming galaxies in IllustrisTNG. The densitiesaround BHs abruptly decrease at M BH ∼ . M (cid:12) , which is con-sistent with the presence of the cavities shown in Fig. 5 and the leftpanel of Fig. 6. In Fig. 7, the red and blue dots correspond to galaxieswhose BHs are in the high- and low-accretion modes, and most of themassive BHs in the low-accretion mode (blue dots) are surroundedby low-density gas. Hence, the depletion of the central gas is causedby the kinetic feedback of the low-accretion mode in TNG, ratherthan other mechanisms such as stellar feedback and consumption ofgas by star formation.Previous studies using the IllustrisTNG simulation have alsoshown similar results. Terrazas et al. (2020) show the averagedgas densities within galaxies to significantly decrease in those with M BH (cid:38) . M (cid:12) at z = since energies injected by the kineticfeedback of the low-accretion mode exceed binding energies in thegalaxies. They propose, therefore, that galaxies whose BHs reachthe critical M BH are suddenly quenched and abruptly decrease theirspecific SFRs (see also Weinberger et al. 2018). Weinberger et al.(2017) show that the critical BH mass at which the feedback modesare switched is M BH ∼ – . M (cid:12) , does not significantly vary Figure 7.
Gas densities n H around BHs as functions of M BH for the star-forming galaxies in IllustrisTNG at redshifts z = , , and . The redand blue dots correspond to BHs whose feedback is in the high- and low-accretion modes. The ordinates n H are cell densities ρ cell averaged over thenearest ± cells around the BHs with a spline kernel, but in the units ofnumber of hydrogen atoms per cubic centimetre. with redshift in the case of the fiducial settings of IllustrisTNG .However, Terrazas et al. (2020) perform similar simulations but withdifferent parameter settings and feedback models, demonstrate thatthe critical M BH depends on the BH models and parameters therein. [ O III ] line ratios and black hole masses Our result suggests that, if we observe the [O
III ] lines from thesimulated galaxies in TNG, the large difference of the central gasdensities between galaxies whose M BH are are higher and lower thanthe critical M BH ∼ . M (cid:12) can be inferred. To model the [O III ] lineemission, we adopt our method described in Section 3 to snapshotsof TNG at redshifts z = , , and .Fig. 8 shows our results of modelled line ratios of [O III ] / asfunctions of M BH for the star-forming galaxies in IllustrisTNG. Inthe left set of four panels, the [O III ] / ratios are measured withintwo-dimensional apertures of R = centred on their BHs, whereline-of-sight orientations of the galaxies are at random. The coloursof the dots indicate unattenuated luminosities of [O III ] integratedwithin the apertures. In TNG, no BHs are in the low-accretion modeat high redshifts z (cid:38) (see Fig. 7). At redshift z = , [O III ] / appears to increase with M BH although the scatter is large, whichmeans that more massive BHs are embedded within gas with higherdensities. The higher gas densities around more massive BHs are alsoreflected in stronger emission of [O III ] which indicates higherSFRs within the apertures. In the following snapshots at z = , and , similar trends are only seen for galaxies hosting less massiveBHs with M BH (cid:46) . M (cid:12) . It is noteworthy that the line ratios of In TNG100-1, no BHs are in the low-accretion mode in redshifts z (cid:38) .Therefore, the redshift-dependence of the critical M BH is unclear above z ∼ .MNRAS , 1–15 (2020) apturing inside-out quenching Figure 8.
Distribution of the line ratios of [O
III ]52 to [O
III ]88 and BH masses in the star-forming galaxies at redshifts z = , , and in IllustrisTNG. Theline ratios are measured within a two-dimensional aperture of R = centred on the BHs (left) and those covering the entire galaxies (right). The colours ofthe plotted dots indicate the luminosities of [O III ] integrated within the apertures. Note that the colour scales are different between the panels. [O III ] / suddenly decrease at M BH ∼ . M (cid:12) , and the [O III ] luminosities within the 3-kpc aperture are weak in the galaxies with M BH (cid:38) . M (cid:12) . In comparing Figs. 8 with 7, it is obvious that thedrop of [O III ] / at M BH ∼ . M (cid:12) coincides with the transitionfrom the high- to low-accretion modes of the BH feedback in TNG.Namely, the drop of [O III ] / reflects the depletion of central gasdensities by the kinematic feedback of massive BHs: the early phaseof the inside-out quenching.The right set of panels of Fig. 8 shows [O III ] / measuredwithin apertures covering the whole galaxies, and the ratios are notsignificantly different from those measured within the 3-kpc aper-tures. This is because, for galaxies with M BH (cid:46) . M (cid:12) , their SFRdistributions are compact, and their central regions inside R = are therefore dominant in their [O III ] emission. For galaxies with M BH (cid:38) . M (cid:12) , on the other hand, their central gas densitiesare significantly lowered by the kinematic feedback, and thereforemainly their outer regions contribute to the total SFRs and [O III ]emission. However, such outer gas is not dense enough to raisethe integrated [O
III ] / . It can be deduced from the result thatthe galaxy-integrated [O III ] is high in the galaxies with massiveBHs of M BH (cid:38) . M (cid:12) , unlike in the case of the 3-kpc apertures.Thus, from the above result, we predict that the abrupt decrease of[O III ] / is observed at the critical BH mass of M BH ∼ . M (cid:12) if the BH model implemented in IllustrisTNG is accurate. In addi-tion, the similarity between [O III ] / measured within the 3-kpcand galaxy-integrated apertures means that observations for the lineratios do not need to resolve the central regions of galaxies (althoughsee below).Although BH masses have been measured in a substantial num-ber of galaxies, determinations of M BH basically require differentobservations independent from measurements for the [O III ] lines. Ithas been known that M BH correlates with stellar velocity dispersions(VDs) of spheroidal components of galaxies: the M – σ relation (e.g.Ferrarese & Merritt 2000; Gebhardt et al. 2000; Marziani & Sulentic 2012, and references therein). This implies that more massive BHsgenerally reside in more massive galaxies although there are scattersto some extent in the correlation. It may be expected that the largemasses of galaxies can enlarge not only stellar VDs but also gaseousones. We compute the second-moment of [O III ] emission as σ [ O III ] = (cid:82) l cell ( v los − v los ) d S (cid:82) l cell d S , (6)where l cell and v los are [O III ] luminosity and line-of-sight ve-locity of a single gas cell, and the integrals in the denominatorand numerator cumulate gas cells within the observational aper-tures. The mean velocity v los is measured within the aperture: v los = (cid:82) l cell v los d S / (cid:82) l cell d S . We consider that equation (6) corre-sponds to a VD weighted by [O III ] luminosity.Fig. 9 shows the distribution of σ [ O III ] and M BH in IllustrisTNG.In the case of the 3-kpc apertures (the left set of panels), although thegalaxies in the high-accretion mode (the red dots) indicate the cor-relation between their σ [ O III ] and M BH , those in the low-accretionmode (the blue dots) have significantly lower σ [ O III ] than the ex-trapolation of the correlation. In the case of the galaxy-integratedapertures (the right set of panels), on the other hand, σ [ O III ] ap-pears to correlate with M BH regardless of the BH feedback modes.We infer that BHs in the kinematic mode blow out gas around thegalactic centres to outer regions and would significantly reduce dy-namical masses inside the 3-kpc apertures. Hence, virialised VDsinside result in low values at a given M BH above the criticalmass M BH ∼ . M (cid:12) . The galaxy-integrated apertures capture allgas belonging to the galaxies although σ [ O III ] would be biased tohigh-SFR regions. Since BH masses are thought to correlate with thetotal masses of the galaxies, the galaxy-integrated σ [ O III ] reflectingthe total mass still holds the correlation. From this result, we ex-pect that M BH can be replaced with σ [ O III ] if the galaxy-integratedapertures are applied.Fig. 10 shows the line ratios of [O III ] / as functions of σ [ O III ] MNRAS000
III ] / . It can be deduced from the result thatthe galaxy-integrated [O III ] is high in the galaxies with massiveBHs of M BH (cid:38) . M (cid:12) , unlike in the case of the 3-kpc apertures.Thus, from the above result, we predict that the abrupt decrease of[O III ] / is observed at the critical BH mass of M BH ∼ . M (cid:12) if the BH model implemented in IllustrisTNG is accurate. In addi-tion, the similarity between [O III ] / measured within the 3-kpcand galaxy-integrated apertures means that observations for the lineratios do not need to resolve the central regions of galaxies (althoughsee below).Although BH masses have been measured in a substantial num-ber of galaxies, determinations of M BH basically require differentobservations independent from measurements for the [O III ] lines. Ithas been known that M BH correlates with stellar velocity dispersions(VDs) of spheroidal components of galaxies: the M – σ relation (e.g.Ferrarese & Merritt 2000; Gebhardt et al. 2000; Marziani & Sulentic 2012, and references therein). This implies that more massive BHsgenerally reside in more massive galaxies although there are scattersto some extent in the correlation. It may be expected that the largemasses of galaxies can enlarge not only stellar VDs but also gaseousones. We compute the second-moment of [O III ] emission as σ [ O III ] = (cid:82) l cell ( v los − v los ) d S (cid:82) l cell d S , (6)where l cell and v los are [O III ] luminosity and line-of-sight ve-locity of a single gas cell, and the integrals in the denominatorand numerator cumulate gas cells within the observational aper-tures. The mean velocity v los is measured within the aperture: v los = (cid:82) l cell v los d S / (cid:82) l cell d S . We consider that equation (6) corre-sponds to a VD weighted by [O III ] luminosity.Fig. 9 shows the distribution of σ [ O III ] and M BH in IllustrisTNG.In the case of the 3-kpc apertures (the left set of panels), although thegalaxies in the high-accretion mode (the red dots) indicate the cor-relation between their σ [ O III ] and M BH , those in the low-accretionmode (the blue dots) have significantly lower σ [ O III ] than the ex-trapolation of the correlation. In the case of the galaxy-integratedapertures (the right set of panels), on the other hand, σ [ O III ] ap-pears to correlate with M BH regardless of the BH feedback modes.We infer that BHs in the kinematic mode blow out gas around thegalactic centres to outer regions and would significantly reduce dy-namical masses inside the 3-kpc apertures. Hence, virialised VDsinside result in low values at a given M BH above the criticalmass M BH ∼ . M (cid:12) . The galaxy-integrated apertures capture allgas belonging to the galaxies although σ [ O III ] would be biased tohigh-SFR regions. Since BH masses are thought to correlate with thetotal masses of the galaxies, the galaxy-integrated σ [ O III ] reflectingthe total mass still holds the correlation. From this result, we ex-pect that M BH can be replaced with σ [ O III ] if the galaxy-integratedapertures are applied.Fig. 10 shows the line ratios of [O III ] / as functions of σ [ O III ] MNRAS000 , 1–15 (2020)
S. Inoue et al.
Figure 9.
Correlations between M BH and the second-moments of [O III ] lines at redshifts z = , , and in IllustrisTNG. In the left and right sets of panels,the 3-kpc and galaxy-integrated apertures are applied to compute σ [ O III ] . As in the Fig. 7, the red and blue bots indicate galaxies whose BH feedback is in thehigh- and low accretion modes. Figure 10.
Same as Fig. 8 but with σ [ O III ] instead of M BH on the abscissas. for IllustrisTNG. As we expect above, since σ [ O III ] does not corre-late with M BH above the critical BH mass in the case of the 3-kpcapertures, the drop of [O III ] / is not clearly seen in the left setof panels. On the other hand, in the case of the galaxy-integratedapertures, the abrupt decrease of [O III ] / is still apparent at σ [ O III ] ∼
200 km s − although it is less clear than in Fig. 8. Thus,if we use observational apertures large enough to cover nearly theentire regions of galaxies, we may be able to use the second-moment of [O III ] instead of M BH in searching for the drop of [O III ] / .These two quantities can be obtained from the same spectroscopicobservations. As we mention in Section 2.1, the Illustris simulation is largely dif-ferent from TNG in the low-accretion mode of the BH feedback.
MNRAS , 1–15 (2020) apturing inside-out quenching Figure 11.
Same as Fig. 7 but for the star-forming galaxies at z = in Illustris.The red and green dots correspond to BHs whose feedback is in the high-and low-accretion modes, respectively. Note that the criterion χ to switchthe feedback modes and the implementation of the low-accretion mode arelargely different from those of IllustrisTNG (see Section 2.1). Figure 12.
Radial profiles of face-on gas surface densities of the star-forminggalaxies with M BH > M (cid:12) in Illustris at redshift z = . The left and rightpanels show galaxies whose BHs are in the low- and high-accretion modes.Note that there are only a small number of galaxies in the high-accretionmode at z = . Although the thick line in the left panel delineates the stackedprofile among 128 galaxies selected randomly, that in the right panel samplesonly 54 galaxies. The shaded region indicates the range of ± σ . The thinlines delineate individual profiles of 12 galaxies selected randomly. Instead of the kinematic feedback in TNG, Illustris adopts the ther-mal feedback designed to reproduce AGN bubbles to the BHs whoseEddington ratios are below the constant criterion χ = . (see Sec-tion 2.1). Therefore, the expected line ratios can differ between thetwo simulations, and their comparison may give us clues to constrainBH models and their parameters.As is done for TNG in Section 4.1.1, we extract star-forminggalaxies distributing along the SFMS in each snapshot and show theSFMSs in Appendix A. For the star-forming galaxies, Fig. 11 showsthe relationships between M BH and gas densities around the BHs.In contrast with TNG (Fig. 7), the gas densities around BHs little change and weakly increase with M BH in Illustris, and the transitionof BH feedback between the high- and low-accretion modes does notappear to significantly affect the gas densities. In addition, there isnot a characteristic value of M BH to switch the feedback modes inIllustris. Unlike in TNG, no galaxies have BHs with M BH (cid:38) . M (cid:12) at redshift z = in Illustris. This is because galaxies hosting suchmassive BHs are quenched after z = and drop off from the SFMS(see Fig. A1). They are no longer classified as star-forming galaxiesand excluded from our analysis. This behaviour is also due to thedifferent feedback model for the low-accretion mode in Illustris.Fig. 12 shows face-on radial profiles of Σ gas of the star-forminggalaxies with M BH > M (cid:12) at z = , where the left and rightpanels illustrate those of galaxies in the low- and high-accretionmodes. The stacked profiles are similar between galaxies in thelow- and high-accretion modes although those in the low-accretionmode have slightly lower Σ gas in their central regions. Note that thesample selection in Fig. 12 is different from that in Fig. 6. How-ever, these selections are essentially consistent since all BHs with log ( M BH / M (cid:12) ) > . and few BHs with < log ( M BH / M (cid:12) ) < arein the low-accretion mode in Fig. 6. The influence of the BH feedbackon the central gas densities is thus largely different between TNG andIllustris because of their different modellings for the feedback, es-pecially the low-accretion modes and the switching criteria χ . Asshown above, the low-accretion mode in the Illustris simulation isnot influential on gas distribution.Fig. 13 shows the relationship between M BH and [O III ] / forthe star-forming galaxies in Illustris. As expected from Figs. 11 and12, there is no clear drop of [O III ] / at any M BH , and the line ra-tios continuously increase with M BH although the scatters are large aswell as in TNG. The galaxy-integrated values (right) of [O III ] / are not significantly different from those measured within the 3-kpcapertures (left). Thus, we predict that abrupt decrease of [O III ] / is not observed at any M BH if the BH model of Illustris is accurate.Accordingly, the difference of the BH models in the simulations,especially the low-accretion modes of the feedback, is expected tosignificantly impact the line ratios of [O III ] / measured in star-forming galaxies hosting massive BHs. From these results, we pro-pose that observations for [O III ] / can constrain the BH modelsimplemented in simulations. As in the case of TNG (Fig. 8), the in-tegrated [O III ] / does not significantly depend on aperture size.The reason can be deduced from Fig. 12; the averaged profiles of Σ gas are approximately flat up to R ∼
10 kpc , and most of the [O
III ]lines are emitted from gas with similar densities.Fig. 14 shows the correlations between M BH and σ [ O III ] for thestar-forming galaxies in Illustris. In the distributions, there is noclear segregation between galaxies in the high- and low-accretionmodes. In comparing the left and right panels, the values of σ [ O III ] hardly depend on aperture size although the VDs are slightly higherin the case of the galaxy-integrated apertures at redshift z = . TheVDs weighted by [O III ] are clearly correlated with M BH althoughscatters are quite large at z = . It is noteworthy that, in the left setof panels, σ [ O III ] measured in the 3-kpc apertures also correlatewith M BH even in the range of M BH (cid:38) . M (cid:12) in Illustris. This isclearly different from the result of TNG shown in Fig. 10 where thecorrelation disappears above the critical mass M BH (cid:38) . M (cid:12) . Itimplies that measuring σ [ O III ] with small observational aperturesfor galaxies hosting massive BHs may be useful to study the impactof AGN on their central gas, and the absence of the correlation athigh M BH may be taken as a sign of the inside-out quenching.Fig. 15 shows the relationship between σ [ O III ] and [O III ] / .Due to the correlations between σ [ O III ] and M BH , Fig. 15 appearssimilar to Fig. 13, where the line ratios increase with the VDs without MNRAS000
III ]lines are emitted from gas with similar densities.Fig. 14 shows the correlations between M BH and σ [ O III ] for thestar-forming galaxies in Illustris. In the distributions, there is noclear segregation between galaxies in the high- and low-accretionmodes. In comparing the left and right panels, the values of σ [ O III ] hardly depend on aperture size although the VDs are slightly higherin the case of the galaxy-integrated apertures at redshift z = . TheVDs weighted by [O III ] are clearly correlated with M BH althoughscatters are quite large at z = . It is noteworthy that, in the left setof panels, σ [ O III ] measured in the 3-kpc apertures also correlatewith M BH even in the range of M BH (cid:38) . M (cid:12) in Illustris. This isclearly different from the result of TNG shown in Fig. 10 where thecorrelation disappears above the critical mass M BH (cid:38) . M (cid:12) . Itimplies that measuring σ [ O III ] with small observational aperturesfor galaxies hosting massive BHs may be useful to study the impactof AGN on their central gas, and the absence of the correlation athigh M BH may be taken as a sign of the inside-out quenching.Fig. 15 shows the relationship between σ [ O III ] and [O III ] / .Due to the correlations between σ [ O III ] and M BH , Fig. 15 appearssimilar to Fig. 13, where the line ratios increase with the VDs without MNRAS000 , 1–15 (2020) S. Inoue et al.
Figure 13.
Same as Fig. 8 but for the Illustris simulation.
Figure 14.
Same as Fig. 9 but for the Illustris simulation. the drop of [O
III ] / at any σ [ O III ] . Thus, if the BH feedbackmodel of Illustris is accurate, measurements of M BH can be replacedwith those of σ [ O III ] . In comparing with the result of TNG (Fig. 10),the presence/absence of the abrupt drop of [O III ] / at σ [ O III ] ∼
200 km s − is a noticeable difference that could be used to constraintheoretical models of BH feedback. We have shown good correlation of M BH with σ [ O III ] , but M BH appears to be a better quantity to characterise the impact of the BHfeedback on [O III ] / in star-forming galaxies. Suppose that weobservationally measure [O III ] / of star-forming galaxies withvarious BH masses, and suppose that the BH masses are known. Fromour results for TNG discussed in Section 4.1, we can infer whetherthere is a characteristic value of M BH to quench star formation around MNRAS , 1–15 (2020) apturing inside-out quenching Figure 15.
Same as Fig. 10 but for the Illustris simulation. the galactic centres. If the BH feedback is suddenly ‘switched on’to a highly efficient mode at a certain M BH , and efficiently expelsthe gas from the central region in the manner implemented in TNG,[O III ] / is expected to drop abruptly at the BH mass as shown inFig. 8. IllustrisTNG predicts the drop to occur at M BH ∼ . M (cid:12) .However, if the efficiency of the BH feedback depends on propertiesother than M BH , the variation of [O III ] / would not be clear andthe line ratio may change gradually with M BH . If the BH feedbackis not efficient enough to drastically reduce the central gas densityas in Illustris, [O III ] / would not decrease with M BH . In fact,as shown in Fig. 13, Illustris predicts the line ratio to continuouslyincrease with M BH for the star-forming galaxies, although with largescatter. Based on the results, we expect that observations of galaxiesat redshifts z (cid:46) may allow us to make direct comparison with thesimulations.If we assume that the BH feedback expels the central gas as repro-duced in IllustrisTNG, a low (high) line ratio of [O III ] / impliesthe presence (absence) of a BH massive enough to trigger quench-ing the star formation activity in the galaxy. Unfortunately, for thismethod to work in practice, one needs a prior knowledge on thecharacteristic M BH for quenching and on weather M BH is a primaryquantity to cause the inside-out depletion of gas.In IllustrisTNG, the critical value of M BH ∼ . M (cid:12) varies littlewith redshift as shown in Figs .7 and 8 (see also Weinberger et al.2017; Terrazas et al. 2020). At z (cid:38) , the central BHs are still smallin mass, and none of them is in the low-accretion modes in TNG.Massive BHs with M BH (cid:38) M (cid:12) have, however, been actuallyobserved in galaxies at z (cid:38) (Marziani & Sulentic 2012, and ref-erences therein). It would be interesting to observe [O III ] / forsuch high-redshift galaxies hosting massive BHs. Low line ratios, ifmeasured, are indicative of low gas densities in the galaxies, whichin turn suggest early phases of the inside-out quenching processesdriven by BHs. The [O III ] lines emitted at z (cid:38) are redshifted tosubmillimetre wavelengths, and ALMA can detect the line emission.The capability of ALMA for detecting the [O III ] lines from suchhigh-redshift galaxies have already been suggested from theoretical models (e.g. Inoue et al. 2014; Arata et al. 2020), and ALMA hasindeed observed [O
III ] of galaxies at z (cid:38) (e.g. Inoue et al. 2016;Hashimoto et al. 2018; Novak et al. 2019). An analytic model of Yanget al. (2021) suggests that the high-redshift galaxy SXDF-NB1006-2 at z = . is a promising first target for [O III ] measurements.Clearly, using [O III ] / as diagonostics of BH feedback is realisticwith ALMA.The fine structure line diagnostics we propose here is not limitedto [O III ] / . The line ratio of [N II ] to µ m is also apromising density tracer (e.g. Zhao et al. 2016; Doherty et al. 2020),and the two lines can be used essentially in the same way. ALMAcan detect the [N II ] lines from high-redshift galaxies (e.g. Novaket al. 2019). The [O III ] line ratios significantly increase with density n e in the range 10 (cid:46) n e (cid:46) cm − , where the logarithmic gradient [ d ln ([ O III ] / ) / d ln n e ] > . . The [N II ] / ratio is a sen-sitive probe at relatively lower densities from n e ∼ to ∼ cm − with [ d ln ([ N II ] / ) / d ln n e ] > . (e.g. Doherty et al. 2020).For a recently discovered quasar at z = . with M BH = × M (cid:12) , Novak et al. (2019) report detection of emission lines ofvarious ions and molecules with ALMA. Although their observationslack [O III ] , they observe the [N II ] lines at and µ m witha large aperture diameter of
13 kpc , and place a lower limit of theline ratio to be [N II ] / > . . The line ratio indicate the localdensity of the emitting region n e (cid:38)
180 cm − . It should be noted thatthe galaxy-integrated line ratio cannot be directly converted to thelocal density in this case. Using their model for photodissociationregions, they also derive an upper limit of the local density for thequasar to be n H (cid:46) × cm − . Since there are no such massiveBHs at z (cid:38) in TNG or Illustris simulations, we cannot performdirect comparison. Instead, let us compare the observation with thesimulated galaxies at z (cid:46) shown in Fig. 7. Even the lower limit of n H ∼
180 cm − appears to be significantly higher than the centraldensities of galaxies with M BH (cid:38) M (cid:12) in IllustrisTNG. On theassumption that the physical conditions are similar, this may implythat inside-out quenching has not begun in the quasar host galaxy at z = . . Hashimoto et al. (2019) observe two quasars with M BH ∼ MNRAS000
180 cm − appears to be significantly higher than the centraldensities of galaxies with M BH (cid:38) M (cid:12) in IllustrisTNG. On theassumption that the physical conditions are similar, this may implythat inside-out quenching has not begun in the quasar host galaxy at z = . . Hashimoto et al. (2019) observe two quasars with M BH ∼ MNRAS000 , 1–15 (2020) S. Inoue et al. M (cid:12) at z = . using ALMA and detect bright [O III ] emission.They also find physically more extended emission than their dustcontinua, suggesting large-scale star formation activity. It would beinteresting to investigate whether the extended [O III ] is relevantto the inside-out quenching in the quasars by observing [O III ] andthe [N II ] lines in the future.For physically extended objects such as high-redshift galaxies, in-terferometers such as ALMA often take a strategy to enhance thesensitivity at the sacrifice of spatial resolution by shrinking the ar-rangement of the telescope arrays. Then the central regions of galax-ies are not resolved. It is encouraging that the correlations between[O III ] / and M BH are hardly different between the cases withthe 3-kpc and galaxy-integrated apertures (Figs. 8 and 13). The di-agnostics we propose here do not require a high spatial resolution if M BH is known. Fortunately, as shown in Figs. 10 and 14, M BH maybe replaced with the second-moments σ [ O III ] if the aperture size islarge enough to cover the entire star-forming regions. Some green-valley galaxies have been observed to have lower den-sities of molecular gas. They also show low SFRs in their centralregions, surrounded by outer disc regions with higher densities andSFRs (Lin et al. 2017; Brownson et al. 2020, see also Ellison et al.2021). Kalinova et al. (2021) classify local galaxies into variousquenching stages according to the morphology of the H α emissionmap, and find that the ‘centrally-quiescent’ galaxies reside in thegreen valley. They argue that their sample galaxies that are on theway to ‘red-sequence’ generally begin to cease their star formationfrom the centres. The observations and the interpretation are consis-tent with the inside-out quenching process, which is possibly drivenby the central BHs. It is also consistent with the cavity and the reversetrend in Σ gas shown in Figs. 5 and 6 for TNG. It is not clear, however,whether the transition is closely related with the BH mass; it maywell be that all galaxies evolve similarly toward completely quenchedstates.Terrazas et al. (2020) give similar prediction to ours. Using Illus-trisTNG, they show that galaxies at z = are suddenly quenched bythe kinematic feedback of BHs at M BH ∼ . M (cid:12) , and abrupt tran-sition from star-forming to quiescent galaxies is seen in diagramsof M BH , M star and specific SFR. They compare the simulated andobserved galaxies at z = using the diagrams, and find that, for ob-served galaxies, the transition from star-forming to quiescent statesoccurs roughly at M BH ∼ M (cid:12) . However, the transition is not assharp as in TNG, and star-forming and quiescent galaxies coexist ina wide range of M BH ∼ – M (cid:12) . Their result does not point toa clear critical M BH for the transition in the observed galaxies. Thequenching process by BH feedback is thought to depend not only on M BH but also on other physical parameters. Accordingly, we spec-ulate that, at least for local galaxies, the line ratios of [O III ] / may not indicate the abrupt decrease at M BH ∼ . M (cid:12) . However,we note that our samples taken from the simulations are star-forminggalaxies. Our result for TNG shows that the drop of [O III ] / is seen in the star-forming galaxies where their massive BHs havestarted quenching the galaxies. Because the line ratio traces local gasdensity rather than the total star formation rate, the diagnostics withthe line ratios could more directly deduce in which galaxies the BHquenching operates. III ] emission from AGN
Our model considers [O
III ] emission from H II regions whose energysources are young star clusters. A luminous AGN can also radiatehigh-energy photons and thus can be an energy source for the [O III ]emission of gas in the galactic centre. This means that our modelcan possibly underestimate the absolute luminosities of the [O
III ]lines. Since our main conclusions are based on the relative strengthof the [O
III ] lines, they may not be significantly affected by the influ-ence by an AGN on their absolute luminosities. We note that AGNscan enhance the overall [O
III ] emission from inner regions in thegalaxy. In this case, the integrated line ratio is more contributed fromthe emission from the central density, which strongly reflects theefficiency of BH quenching. Although hard photons emitted froman AGN likely increases the ionization parameter U in of the ISM,the line ratio hardly depends on the ionization parameter. In Ap-pendix B, we show that the contribution of AGN radiation to thetotal [O III ] emission is expected to be insignificant in most of thesimulated galaxies. We consider that our results for [O
III ] / arenot compromised by the uncertainty in the actual U in . The relative strength of a specific pair of line emission such as[O
III ] and [O III ] is used to estimate the local gas density ofstar-forming regions where the lines are emitted. By postprocessingthe outputs of the cosmological simulations of IllustrisTNG and Il-lustris, we model emission of the [O III ] lines from the simulatedgalaxies in a large cosmological volume from z = to .In galaxies hosting massive BHs, if the BH feedback and star-formation quenching proceeds efficiently in an "inside-out" fashion,the central gas densities are significantly lowered. If the BH quench-ing is inefficient, the gas densities are expected to be higher towardsthe centres. Such a difference of the central gas densities can beprobed by the line ratio of [O III ] / measured in the galaxies.Detecting and identifying both the lines can help extracting the in-formation of the physical properties of galactic centres affected bythe BH feedback.For star-forming galaxies in IllustrisTNG, we find that [O III ] / weakly increases with M BH with a large scatter but abruptly decreasesat M BH ∼ . M (cid:12) . The drop of the line ratios is due to the transitionfrom high- to low-accretion modes of the BH feedback. The lineratios do not significantly depend on aperture size to integrate the[O III ] lines. In addition, we find that the second-moments of [O
III ] correlate with M BH if the aperture sizes are sufficently large. Hence,in the diagrams of [O III ] / and σ [ O III ] , the abrupt drop of[O III ] / is still seen at a VD of σ [ O III ] ∼
200 km s − . However,if small apertures are applied to measure σ [ O III ] , the correlationbetween σ [ O III ] and M BH disappears above the critical mass M BH ∼ . M (cid:12) due to the strong feedback of the massive BHs in TNG.Models of the BH feedback are, however, largely different amongsimulations. In Illustris, we find that the line ratios continuously in-crease with M BH , and the drop of [O III ] / does not appear atany M BH . This is because the transition from high- to low-accretionmodes of the feedback model in Illustris does not significantly af-fect the central gas densities in star-forming galaxies. The second-moments σ [ O III ] correlate with M BH regardless of the feedbackmodes of BHs and the aperture sizes. Thus, the correlations of[O III ] / with M BH and σ [ O III ] among star-forming galaxiesare expected to reflect the efficiency of the BH feedback.Based on the simulation results, we propose that observing MNRAS , 1–15 (2020) apturing inside-out quenching [O III ] / for star-forming galaxies with massive BHs can be usedas diagnostics for accuracy of BH models implemented in simu-lations. If [O III ] / is low in a galaxy with a massive BH, thegalaxy may be at an early stage of the inside-out quenching by theBH. We have shown that [O III ] / hardly depends of aperturesize, and thus observations do not need to resolve the central re-gions of galaxies to apply our diagnostics, even if the aperture sizeis as large as covering the entire galaxies. ALMA is capable of ob-serving [O III ] / and other line ratios such as [N II ] / forhigh-redshift galaxies at z (cid:38) . Measuring the line ratios for distantgalaxies with massive BHs will provide us with important clues toknow on how the BH feedback operates in the galaxies. ACKNOWLEDGEMENTS
We thank Takuya Hashimoto and Ken-ichi Tadaki for their fascinat-ing discussion and helpful suggestion. This study was supported byNational Astronomical Observatory of Japan (NAOJ) ALMA Sci-entific Research Grant Number 2019-11A. HY receives the fund-ing from Grant-in-Aid for Scientific Research (No. 17H04827 and20H04724) from the Japan Society for the Promotion of Science(JSPS). The numerical computations presented in this paper werecarried out on the analysis servers and the general-purpose PC clus-ter at Center for Computational Astrophysics, NAOJ.
DATA AVAILABILITY
The data underlying this article will be shared on reasonable requestto the corresponding author.
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APPENDIX A: STAR-FORMATION MAIN SEQUENCE
In Section 4.1.1, we use the method of Donnari et al. (2019) to definean SFMS and to sample star-forming galaxies in each snapshot.Although Donnari et al. (2019) have proposed various methods todetermine an SFMS, here we describe the one we use in this study.We assume a power-low relation between M star and SFRs of galaxies, log ˙ M star = A log M star + B , (A1)where M star and ˙ M star are the total stellar mass and instantaneousSFR of a gravitationally bound structure detected with SUBFIND.We divide galaxies into stellar-mass bins with intervals of . inthe range from M star = to . M (cid:12) and compute the medianvalue Q SFR and standard deviation σ SFR of logarithmic SFRs in eachbin. We then exclude the galaxies whose SFRs are lower than Q SFR − . σ SFR , re-compute Q SFR and σ SFR and iterate this procedure untilconvergence. Using the converged Q SFR of the bins, we eventually
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MNRAS000 , 1–15 (2020) S. Inoue et al.
Figure A1.
Same as Fig. 4 but for the Illustris simulation. determine the constants A and B in equation (A1) by the least squaresmethod. We set the boundary between star-forming and quenchedgalaxies to be at . σ SFR below equation (A1) for all stellar masses,where σ SFR is the median of σ SFR .Fig. A1 shows the same result as Fig. 4 but for Illustris. Generally,the offset of the boundary from the SFMS, . σ SFR , decreases withredshift and is smaller than in all snapshots in both simulations.Donnari et al. (2019, 2020) have argued the dependence of estimatedfractions of quenched galaxies and relationship with the colour bi-modality on their methods to determine SFMSs in IllustrisTNG.
APPENDIX B: INFLUENCE BY RADIATION FROMBLACK HOLES
We estimate the contribution from the central AGN as a power sourceto the galaxy-integrated [O
III ] emission. It is difficult to accuratelycompute the line emission since we need to know the emergent SEDof an AGN which generally has unresolved small-scale structuressuch as torus. We thus resort to estimating a bolometric luminosityof the BH and compare it with the total bolometric luminosity ofstars that form H II regions in a galaxy.We follow a popular model of AGN that assumes the bolometricluminosity is given by L BH = ε r ˙ M BH c for ˙ M BH ≥ . M Edd , (cid:16) ˙ M BH ˙ M Edd (cid:17) ε r ˙ M Edd c for ˙ M BH < . M Edd , (B1)where ε r = . which is consistent with the value used in the simu-lations (Churazov et al. 2005; Hirschmann et al. 2014; Weinbergeret al. 2018). The bolometric luminosities of star clusters are com-puted with PÉGASE.2 in the same way as in our model of the [O III ]lines (see Section 3.1).For the star-forming galaxies in IllustrisTNG and Illustris, FigsB1 and B2 show the ratios of the galaxy-integrated bolometric lu-minosities of star clusters with respect to L BH of the most massiveBHs in the galaxies. In both the simulations, most of the galaxieshave ratios higher than unity, suggesting that the net radiation energy Figure B1.
The total bolometric luminosity of star clusters, L cl , normalizedby that of the most massive BH, L BH , as a function of M BH . We use thegalaxy sample in IllustrisTNG. The colours of the plotted dots indicate thegalaxy-integrated [O III ] luminosities. Figure B2.
Same as Fig. B1 but for Illustris. released from the star clusters is generally larger than that from BHsin the galaxies. We thus consider that BHs in the simulations are lesssignificant sources for the [O
III ] lines.Even if the bolometric luminosity of an AGN is insignificant, itcan emit hard photons and may increase the ionization parametersof star-forming regions. To evaluate the influence on [O
III ] / , MNRAS , 1–15 (2020) apturing inside-out quenching Figure B3.
Same as Fig. 1 but changing U in independently from n e . Theupper and lower lines delineate the results with Z = Z (cid:12) and Z = . (cid:12) . we compute the line ratios with our Cloudy model described inSection 3.1 by manually changing the parameter U in . Fig. B3 showsthe dependence of the computed [O III ] / on U in in the cases with Z = Z (cid:12) and Z = . (cid:12) . The line intensity ratio does not stronglydepend on U in , and therefore our conclusions in the main text basedon [O III ] / are not significantly affected by considering the AGNradiation contribution. This paper has been typeset from a TEX/L A TEX file prepared by the author. MNRAS000