Revealing the physical properties of gas accreting to haloes in the EAGLE simulations
Ruby J. Wright, Claudia del P. Lagos, Chris Power, Camila A. Correa
MMNRAS , 1–23 (2020) Preprint 23 February 2021 Compiled using MNRAS L A TEX style file v3.0
Revealing the physical properties of gas accreting to haloes in theEAGLE simulations
Ruby J. Wright ★ , , Claudia del P. Lagos , , Chris Power , , Camila A. Correa International Centre for Radio Astronomy Research (ICRAR), University of Western Australia, Crawley, WA 6009, Australia ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D) Institute for Theoretical Physics Amsterdam, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
The inflow of cosmological gas onto haloes, while challenging to directly observe andquantify, plays a fundamental role in the baryon cycle of galaxies. Using the EAGLE suiteof hydrodynamical simulations, we present a thorough exploration of the physical propertiesof gas accreting onto haloes – namely, its spatial characteristics, density, temperature, andmetallicity. Classifying accretion as “hot” or “ cold” based on a temperature cut of 10 . K, wefind that the covering fraction ( 𝑓 cov ) of cold-mode accreting gas is significantly lower than thehot-mode, with 𝑧 = 𝑓 cov values of ≈
50% and ≈
80% respectively. Active Galactic Nuclei(AGN) feedback in EAGLE reduces inflow 𝑓 cov values by ≈ ≈ 𝑀 (cid:12) , and that variation in halo-scale gas accretion rates may offer a physicalexplanation for the enhanced scatter in the star-forming main sequence at low ( (cid:46) 𝑀 (cid:12) ) andhigh ( (cid:38) 𝑀 (cid:12) ) stellar masses. Our results highlight how gas inflow influences several halo-and galaxy-scale properties, and the need to combine kinematic and chemical data in order toconfidently break the degeneracy between accreting and outflowing gas in CGM observations. Key words: galaxies: formation – galaxies: evolution – galaxies: haloes
The baryon cycle – the interplay of gas inflow, outflow, and starformation at a galaxy and halo-level – plays a dominant role insetting the observable properties of galaxies over cosmic time. Theaccretion of gas onto dark matter haloes is a critical, yet a poorlyunderstood aspect of the galactic baryon cycle. The necessity of gasaccretion to regulate galaxy gas reservoirs has been supported bymany cosmological simulations (see Dekel et al. 2009; van de Voortet al. 2011; Lagos et al. 2014; Nelson et al. 2015; Correa et al. 2018b;Mitchell et al. 2020a; Wright et al. 2020). Observationally, however,the diffuse nature and weak kinematic signature of accreting IGMgas makes its direct detection an arduous pursuit (e.g. Tumlinsonet al. 2011; Sánchez Almeida 2017).In light of these challenges, observational studies have largelyused continuity arguments instead of direct detection to demonstratethe role smooth gas inflow (i.e. gas not accumulated via mergers)from the inter-galactic medium (IGM) in regulating galaxy proper- ★ E-mail: [email protected] ties (e.g. Davé et al. 2012; Lilly et al. 2013). For instance, it hasbeen established that the consumption timescale of galactic gas ismuch shorter than a Hubble time, and that continued smooth gas ac-cretion is required to sustain the observed cosmic star formation to 𝑧 = © a r X i v : . [ a s t r o - ph . GA ] F e b R. J. Wright et al. suggesting that these detections correspond to recycling gas that hadpreviously been ejected from the galaxy by stellar or Active GalacticNuclei (AGN)-driven outflows (see Marasco et al. 2012; Fraternaliet al. 2015; Sánchez Almeida 2017; Kacprzak et al. 2019).Numerical simulations have highlighted the fact that gas re-cycling on both galaxy- and halo-scales only represents part of thepicture of smooth gas inflow. Another key component is the gason “first-infall” to haloes and galaxies from the cosmic web, withinflow aided by the gravitational pull provided by the collapsingregions around haloes. Cosmological simulations have found thatgas on “first-infall” (that is, gas which has never been accretedonto a halo or galaxy previously) provides the majority of baryongrowth to haloes at all epochs (with the exception of group- andcluster-sized haloes at 𝑧 ≈ a priori assumption made in many studies in the absence of kinematic data,in which lower metallicity gas is assumed to trace inflowing gas,while higher metallicity gas traces the outflowing component (e.g.Kacprzak et al. 2012, 2015; Nielsen et al. 2020).Smooth accreting gas is also often classified into a “hot”-modeand a “cold”-mode. In haloes with mass exceeding ∼ 𝑀 (cid:12) ,gas on infall towards over-densities is expected to be shock-heated– an idea first explored in Rees & Ostriker (1977); White & Rees(1978); Binney (1977), and extended to the cold dark matter (CDM)paradigm in White & Frenk (1991). Hot-mode accretion typicallyrefers to gas that has been shock-heated and subsequently coolsradiatively to join the central galaxy, while cold-mode accretionrefers to the gas that accretes directly to the central galaxy in afilamentary manner, associated with the cosmic web. Numericalsimulations have since demonstrated that hot-mode and cold-modegas accretion can occur simultaneously, in a balance dependingprincipally on halo mass (Kereš et al. 2005; Dekel & Birnboim2006; Ocvirk et al. 2008; Dekel et al. 2009; van de Voort et al.2011; van de Voort & Schaye 2012; Nelson et al. 2013; Correa et al.2018a,b; Stern et al. 2020).A combination of observations and simulations have shownthat gas inflow has a measurable impact on the interstellar medium(ISM) of galaxies. Using SDSS data, Mannucci et al. (2010)and Lara-López et al. (2010) independently found a fundamentalplane (commonly referred to as the fundamental metallicity rela-tion, FMR) between the properties of stellar mass, star-formationrate (SFR), and inter-stellar medium (ISM) metallicity in galax-ies. Specifically, it was found that the scatter in the stellar mass-metallicity relation (MZR) at a fixed stellar mass correlates withSFR, with star-forming (quiescent) galaxies associated with low(high) metallicities. Pristine gas inflow provides a natural linkbetween metallicity and SFR, with accretion encouraging star-formation while simultaneously “diluting” the ISM with enoughlow-Z gas to reduce its bulk metal fraction (e.g. Kacprzak et al.2016).This idea has been supported by simulations, which have foundthat gas accretion onto galaxies regulates ISM metallicities. (Col-lacchioni et al. 2020; De Lucia et al. 2020; van Loon et al. 2021).An indirect tracer of this regulation is via the gas content of galax-ies. Simulations have shown that the scatter in the MZR is bettercorrelated with the gas content of galaxies rather than their SFR(e.g. Lagos et al. 2016; De Rossi et al. 2017; De Lucia et al. 2020. This is supported by observations, which find the atomic or molec-ular hydrogen content of galaxies to better describe the scatter inthe MZR than SFRs (e.g. Hughes et al. 2013; Bothwell et al. 2016;Brown et al. 2018).Gas inflow also leaves a measurable imprint on the CGM sur-rounding galaxies. Observations have found a bimodality in the az-imuthal angle of metal-line absorbers, with gas covering fractionsenhanced by 20 −
30% near the major and minor axes of galaxies(e.g. Bordoloi et al. 2011; Kacprzak et al. 2012, 2015). CGM gasdetected on the major and minor axes of galaxies is proposed tobe associated with co-planar, inflows and feedback-driven outflows,respectively; a conjecture which has been reproduced in large-scalesimulations (e.g. Stewart et al. 2011; van de Voort & Schaye 2012;Shen et al. 2012; Péroux et al. 2020). Assuming outflow winds aremetal enriched relative to inflows, one would then expect to find anazimuthal dependence on the metallicity of CGM absorbers (Lehneret al. 2016; Péroux et al. 2020). While a wide range of CGM metal-licities have been measured (with a range of > ≈ 𝑇 vir ) originatesfrom the virial shock-heating of gas accreting high-mass haloes( 𝑀 halo (cid:38) 𝑀 (cid:12) ; e.g. Rees & Ostriker 1977). A cold-phase of theCGM at ≈ K has also been observed, but its origins are less clear(e.g. Adelberger et al. 2003; Stocke et al. 2006; Lehner & Howk2011; Prochaska et al. 2013; Zhu et al. 2014; Werk et al. 2014;Heckman et al. 2017; Zahedy et al. 2019). Several origins of thiscool CGM phase have been proposed, namely pristine IGM accre-tion (e.g. simulation-based findings in van de Voort & Schaye 2012;Afruni et al. 2019, 2020), the condensation of hot halo gas (e.g.the empirical arguments of Voit 2018 and illustris-TNG findingsin Nelson et al. 2020), feedback-driven outflows (e.g. Bouché et al.2013; Borthakur et al. 2015; Anglés-Alcázar et al. 2017; Oppen-heimer et al. 2018; Hafen et al. 2019), and the stripping of satellitegalaxies in larger systems (e.g. Hafen et al. 2019 using the fire-2simulations). Afruni et al. (2019, 2020), using semi-analytic modelsand results from the COS-Halos and COS-GASS surveys, argue thatstar-formation driven outflows cannot account for the amount of coolgas in the CGM of observed haloes, pointing towards IGM accretionas the origin of this gas. Additionally, the radial variation of CGMproperties was explored in Fielding et al. (2020) using a number ofhydrodynamical simulations (as part of the smaug project). Theyfind that the properties of the outer-CGM (at (cid:38) . 𝑅 , crit ) areshaped by larger-scale processes, such as cosmological accretion,rather than galactic feedback which dominates the inner regions, (cid:46) . 𝑅 , crit . In any case, the wide range of observed metallici-ties and temperatures observed implies that the CGM is a diverse,multi-phase gas reservoir, making it an ideal laboratory to study theinfluence of cosmological inflows.Recent IFU-based studies of the CGM continue to improveour understanding of resolved CGM properties and kinematics (seeSchroetter et al. 2016; Nielsen et al. 2020, and references therein).New ways of probing the CGM continue to be proposed and tested,for instance using fast radio bursts (FRBs; Macquart et al. 2020),and observations of Ly 𝛼 and metal-lines in emission (see overviewand predictions in Lokhorst et al. 2019 and Augustin et al. (2019),who use the EAGLE simulations and dedicated zoom simulationsrespectively). Detecting CGM gas in emission is currently possibleat high redshifts ( 𝑧 (cid:38)
2) using ground-based telescopes – e.g. the
MNRAS , 1–23 (2020) he nature of gas accretion to haloes Very Large Telescope (VLT) or Keck – in conjunction with meth-ods of enhancing the signal (e.g. Steidel et al. 2011; Wisotzki et al.2018). This is also possible at lower redshift using space-based tele-scopes, such as the Hubble Space Telescope (HST; e.g. Hayes et al.2016). A promising future space-based endeavour is the LUVOIR(Large UV/Optical/Infrared Surveyor), slated to provide spectro-scopic sensitivity in the UV enhanced by 30 −
100 times comparedto the HST/Cosmic Origins Spectrograph instrument (The LUVOIRTeam 2019). With improvements in methodology and instrumenta-tion, it may become possible to distinguish different phases of theCGM based on spatially resolved properties; for instance differen-tiating between recycled and pristine inflow based on metallicitymeasurements.In this study we use the EAGLE suite of hydrodynamical sim-ulations to characterise the nature of gas accreting to haloes fromthe IGM. Specifically, we investigate its history, spatial character-istics, metallicity, density, and temperature in an effort to predictobservational signatures of accreting IGM gas, and its influenceon integrated galaxy and CGM properties. This paper is organisedas follows: in §2, we introduce (i) the EAGLE hydrodynamicalsimulation suite and the sub-grid models that are relevant to thisstudy, (ii) VELOCIraptor and TreeFrog: the phase-space struc-ture finder we use to identify bound haloes and substructures (andits accompanying halo merger tree generator), and (iii) chumm: thecode we use to calculate and analyse accretion rates onto haloes inEAGLE. §3 explores the spatial characteristics of gas accreting tohaloes over redshift; §4 explores the chemical enrichment of this gasas a function of halo mass and its position in density-temperaturephase space; and in §5 we discuss the influence of gas accretionrates on central galaxy and CGM properties. To conclude, in §6we summarise our findings and discuss the implications of our re-sults on semi-analytic models and observations, together with futurescientific directions.
Here we briefly outline our methodology in calculating accretionrates to haloes and classifying inflow channels. For a full overviewof our method (as well as temporal and resolution convergencetests), we refer the reader to Section 2 of Wright et al. (2020).
EAGLE simulations
The EAGLE (Evolution and Assembly of GaLaxies and their Envi-ronments) simulation suite (Schaye et al. 2015; Crain et al. 2015) isa collection of cosmological hydrodynamical simulations that fol-low the evolution of galaxies and cosmological structure down to 𝑧 =
0. The ANARCHY (Schaller et al. 2015) set of revisions, de-signed to correct for “classical” smoothed particle hydrodynamics(SPH) issues, were implemented in the GADGET-3 tree-SPH code(Springel 2005) to perform the EAGLE simulations over a varietyof periodic volumes and resolutions. EAGLE adopts the parame-ters of a Λ CDM universe from Planck Collaboration et al. (2014),with initial conditions outlined in Jenkins (2013). Sub-grid physicsmodels are included for important processes that occur on scalesbelow the resolution-scale of the simulation, including (i) radiativecooling and photoheating, (ii) star formation, (iii) stellar evolutionand enrichment, (iv) stellar feedback, and (v) supermassive blackhole (SMBH) growth and AGN feedback. Below, we provide a briefdescription of how these mechanisms are modelled in EAGLE.Photo-heating and radiative cooling are applied based on the work of Wiersma et al. (2009), including the influence of 11 ele-ments: H, He, C, N, O, Ne, Mg, Si, S, Ca, and Fe (Schaye et al. 2015).The UV and X-ray background described by Haardt & Madau (2001)is applied on each element individually. Since the EAGLE simula-tions do not provide the resolution to model cold, interstellar gas, adensity-dependent temperature floor (normalised to 𝑇 = ,
000 K at 𝑛 H = − cm − ) is imposed. To model star formation, a metallicity-dependent density threshold is set, above which star formation islocally permitted (Schaye et al. 2015). Gas particles are convertedto star particles stochastically, with the star formation rate based ona tuned pressure law (Schaye & Dalla Vecchia 2008), calibrated tothe work of Kennicutt (1998) at 𝑧 =
0. The energy feedback fromstar formation is treated with a thermal energy injection of 10 erg per type Ia supernovae (SNIa) event, the amount of which is afunction of the IMF adopted (Chabrier 2003). This is implementedin the form of a temperature boost to the surrounding particles of Δ 𝑇 SNe = . 𝐾 , based on the work of Dalla Vecchia & Schaye(2012). The number of stars heated is calculated using Equation 1,taken from Equation 8 in Schaye et al. (2015): (cid:104) 𝑁 heat (cid:105) ≈ . 𝑓 th (cid:18) Δ 𝑇 . K (cid:19) − , (1)where 𝑓 th is the fraction of the total amount of energy from corecollapse supernovae per unit stellar mass that is injected on average. 𝑓 th varies between set minimum and maximum values (see Table1), the value in this range calculated based on local inter-stellarmedium (ISM) properties.SMBHs are seeded in EAGLE when a DM halo exceeds a virialmass of 10 h − M (cid:12) , with the seed SMBHs having an initial massof 10 h − M (cid:12) . Subsequently, SMBHs can grow via Eddington-limited-accretion (Schaye et al. 2015), as well as mergers with otherSMBHs, according to work by Springel et al. (2005). Similar to stel-lar feedback, AGN feedback in EAGLE also involves the injectionof thermal energy into particles surrounding the SMBH in the formof temperature boost of Δ 𝑇 BH = K (in the reference physicsrun; Schaye et al. 2015). The rate of energy injection from AGNfeedback is determined using the SMBH accretion rate, and a fixedenergy conversion efficiency, as in Equation 2: Δ 𝐸 Δ 𝑡 = 𝜖 f 𝜖 r (cid:164) 𝑚 accr 𝑐 , (2)where (cid:164) 𝑚 accr is a modified Bondi-Hoyle accretion rate (see Equations9,10 in Schaye et al. 2015), and 𝜖 f 𝜖 r = . 𝑧 ≈ MNRAS , 1–23 (2020)
R. J. Wright et al.
Run Name 𝐿 box /cMpc 𝑁 part 𝑚 DM / M (cid:12) 𝑚 gas / M (cid:12) SPH 𝜖 /pkpc Δ 𝑇 SNe / K Δ 𝑇 AGN / K 𝑁 halo , 𝑧 = ( > 𝑀 (cid:12) ) L50-REF 50 752 . × . × anarchy 0 .
70 10 . . , . × . × anarchy 0 .
70 10 . N/A 74 , . × . × anarchy 0 .
70 N/A N/A 9 , . × . × gadget-2 0 .
70 10 . . , . × . × anarchy 0 .
35 10 . , Table 1.
Simulation parameters for the EAGLE runs utilised in this paper (Schaye et al. 2015; Crain et al. 2015). 𝐿 box is the comoving box size of the simulation; 𝑁 part refers to the number of DM particles (and initial number of gas particles); 𝑀 DM and 𝑀 gas refer to the masses of DM and gas particles in the simulationrespectively; SPH refers to the smoothed particle hydrodynamics scheme used; 𝜖 refers to the Plummer equivalent maximum gravitational smoothing length; Δ 𝑇 SN and Δ 𝑇 AGN are the heating temperatures adopted for stellar and AGN feedback; and 𝑁 field halo ( 𝑧 = ) describes the number of field haloes in each runat the final snapshot. VELOCIraptor and
TreeFrogWe identify haloes and subhaloes in the EAGLE runs using VE-LOCIraptor (Elahi et al. 2011, 2019a; Cañas et al. 2019), a 6Dfriends of friends (6D-FOF) structure finding algorithm. VELOCI-raptor first uses a 3D-FOF algorithm (Davis et al. 1985) to identifyfield haloes, and subsequently applies a 6D-FOF algorithm (includ-ing spatial and velocity information) in order to separate virialisedstructures (Elahi et al. 2019a). Once the 6D-FOF algorithm has beenrun over a 3D-FOF object, any nested density peaks will be identi-fied as “sub-haloes” of the parent halo. To link haloes through time,we use the halo merger tree code TreeFrog (Elahi et al. 2019b),developed to work on the outputs of VELOCIraptor. This codecompares the particles in haloes across multiple snapshots by cal-culating a “merit” based on the fraction of particles that are sharedby two (sub)haloes 𝑖 and 𝑗 at different times. chummIn order to calculate accretion rates onto haloes, we developed andused the code package chumm (Code for Halo AccUMulation ofMass, available at https://github.com/RJWright25/CHUMM ).Our method, which focuses on the build-up of matter on halo-scales,is outlined in detail in Wright et al. (2020). Like van de Voort et al.(2017) and Correa et al. (2018b), we calculate accretion over theinterval between adjacent EAGLE snapshots (29 snapshots from 𝑧 =
20 to 𝑧 = Δ 𝑡 ranging between ≈
250 Myrat minimum (at 𝑧 ≈ ≈ . 𝑧 ≈ . − . 𝑅 vir are selected as con-stituting a halo. For the purposes of this work, we exclusively usethe FOF-based classification of particles into haloes, meaning wemake no assumption about the morphology of haloes. In this paper,we only consider accretion rates to field haloes (i.e, not subhaloes),which may or may not contain substructure. To calculate accretionrates onto haloes at a snap 𝑛 , we identify accretion candidates as theparticles that exist in the halo at snap 𝑛 as per the definition above,but did not exist in the halo at snap 𝑛 −
1. The summed mass ofthese candidate particles, normalised by Δ 𝑡 = 𝑡 𝑛 − − 𝑡 𝑛 (where 𝑡 𝑛 represents the lookback time at snap 𝑛 ), constitutes the raw gross total accretion rate of the halo at snap 𝑛 . Accretion rates are split byparticle type, with the particle type categorised at the initial snap 𝑛 −
1, before undergoing any processing in the halo (such that gasparticles at snap 𝑛 − 𝑛 would be considered gas inflow, not stellar inflow).We subsequently categorise the nature of the inflow particles(their accretion “channel” or “mode”) based on (i) their host at snap 𝑛 −
1, and (ii) their processing history. The particle’s host at snap 𝑛 − “pre-processed” if it has existed in any halo (as definedby VELOCIraptor) up to and including snap 𝑛 − 𝑧 ≈ .
5) in the EAGLE simulation due to dataavailability – meaning that particles accreted prior to snap 9, if sub-sequently ejected and re-accreted, would be considered first-infall.As such, we restrict our analysis to 𝑧 (cid:46)
3, where there have beenadequate snapshots since 𝑧 ≈ . 𝑇 max ). Using a cutoff in 𝑇 max does notallow for post-feedback cooling, and could wrongly associate gasto the hot-mode of accretion when in reality the gas has cooled. Weexplore the distribution of 𝑇 max for accreting gas, and the necessityto allow for cooling, in Appendix A. We consider an accreting par- MNRAS000
3, where there have beenadequate snapshots since 𝑧 ≈ . 𝑇 max ). Using a cutoff in 𝑇 max does notallow for post-feedback cooling, and could wrongly associate gasto the hot-mode of accretion when in reality the gas has cooled. Weexplore the distribution of 𝑇 max for accreting gas, and the necessityto allow for cooling, in Appendix A. We consider an accreting par- MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes Inflow channel Classification type Description ColourTotal accretion N/A Particles identified as accreted: not part of FOF at snap 𝑛 − 𝑛 .First-infall accretion Particle history Particles identified as accreted from the field and never previously processed in a halo.Pre-processed accretion Particle history Particles identified as accreted from the field and previously processed in a halo.Merger accretion Particle history Particles identified as accreted that were in a separate halo at snap 𝑛 − 𝑛 temperature above 10 . K.Cold accretion Particle temperature Particles identified as accreted from the field with snap 𝑛 temperature below 10 . K. Table 2.
A summary of the decomposition of accreting particles into distinct inflow channels. The first-infall, pre-processed and merger channels are basedon the VELOCIraptor-generated particle history classifications in Wright et al. (2020), and the hot and cold- modes are based on post-accretion particletemperatures. ticle to be part of the hot-mode if it satisfies the temperature cutrequirement in Equation 3: 𝑇 post − shock ≥ . K , (3)where 𝑇 post − shock refers to the temperature of a particle post-accretion, at snap 𝑛 . The hot- and cold- modes of accretion arethen calculated as the summed masses of non-merger (smoothlyaccreted) particles meeting each criterion in Equations 4 and 5: (cid:164) 𝑀 cold = Σ 𝑖 𝑀 𝑖 ( 𝑇 post − shock < . K )/ Δ 𝑡, and (4) (cid:164) 𝑀 hot = Σ 𝑗 𝑀 𝑗 ( 𝑇 post − shock ≥ . K )/ Δ 𝑡. (5)Each of these inflow channel definitions, based either on particlehistory or particle temperature, are summarised in Table 2. In order to classify the spatial nature of inflow in each of the afore-mentioned channŁls, we define a “covering fraction”, 𝑓 cov , whichquantifies the extent to which inflow is isotropic in nature. The cov-ering fraction of a halo essentially corresponds the solid angle sig-nificantly occupied by accreting gas. More collimated/filamentaryinflow corresponds to low covering fractions ( 𝑓 cov → 𝑓 cov → 𝑓 cov , we use spherical coordinates to bin the spacearound each halo into 72 bins in solid angle: 12 in azimuth ( 𝜙 ) and6 in elevation ( 𝜃 ), all equally spaced. We impose no requirementon radial position of particles, and only consider their distributionin projected angular space about the halo center of mass. For eachof the 72 cells, 𝑖 , and for each inflow channel, 𝑗 , we determine the expected mass influx in each cell, (cid:104) (cid:164) 𝑚 𝑖, 𝑗 (cid:105) , if inflow were isotropicby scaling the total mass influx of that mode, (cid:164) 𝑀 𝑗 , by the solid angle, Ω 𝑖 , of each cell: (cid:104) (cid:164) 𝑚 𝑖, 𝑗 (cid:105) = (cid:164) 𝑀 𝑗 × Ω 𝑖 𝜋 . (6)We then classify a cell, 𝑖 , “occupied” or “covered” by inflow particlesof mode 𝑗 if the actual cell inflow rate (cid:164) 𝑚 𝑖, 𝑗 exceeds a minimumfraction, 𝑓 , of the expected isotropic inflow rate (cid:104) (cid:164) 𝑚 𝑖, 𝑗 (cid:105) : (cid:164) 𝑚 𝑖, 𝑗 ≥ 𝑓 × (cid:104) (cid:164) 𝑚 𝑖, 𝑗 (cid:105) , (7)where we select 𝑓 to be 0 .
1. We remark that altering this 𝑓 valuebetween 0 . − . 𝑗 is then calculated as the solid angle weighted fraction ofoccupied cells, as per Equation 8: 𝑓 cov , j = Σ 𝑖 Ω 𝑖 ( occupied , 𝑗 ) 𝜋 . (8) In order to ensure that the numerical value of 𝑓 cov is not driven bythe number of inflow particles, we only calculate 𝑓 cov for a mode 𝑗 if the inflow to that halo exceeds 10 particles (where then theminimum expected mass flux, 𝑓 × (cid:104) (cid:164) 𝑚 𝑖, 𝑗 (cid:105) , corresponds to at least1 accreted gas particle: at minimum ≈ / 𝑓 =
10 in each cell,and 10 × =
720 particles in total). This is the case for ≈ 𝑀 halo (cid:38) 𝑀 (cid:12) at all redshifts considered. The particleflux requirement only significantly reduces the number of haloeswe can calculate merger covering fractions for, where we couldonly use ≈
50% of the sample towards 𝑧 = In this Section, we investigate the link between the temperature,history, and spatial characteristics of gas accreting to haloes inEAGLE. We focus on the halo mass range 𝑀 halo (cid:38) 𝑀 (cid:12) , where,on average, inflow corresponds to a flux of more than 100 gasparticles over the designated time interval between each snapshot.We quantify and analyse gas inflow to these haloes from 𝑧 ≈ 𝑧 ≈
0. Wherever we take bins in halo and stellar mass, unlessotherwise stated, they are spaced in increments of 0 . We start by revisiting the gas accretion rates originally presented inWright et al. (2020), in which accreting particles were broken downinto being either first-infall, recycled, transfer, or merger-based inorigin. As described in Section 2.3 and Table 2, for the purposes ofthis work, we combine the recycled and transfer components intoone “pre-processed” mode, and add in a separate temperature-basedinflow classification, originally conceived in Correa et al. (2018a).In Figure 1, we illustrate the median gas accretion efficiencies, (cid:164) 𝑀 gas /( 𝑓 b 𝑀 halo ) , for each accretion channel as a function of halomass for (i) the original history-based classifications (top panels),and (ii) the new temperature-based classifications (bottom panels)at 𝑧 ≈ 𝑧 ≈ 𝑓 b implied by the results of Planck Collaboration et al. (2014), at Ω b / Ω m = . MNRAS , 1–23 (2020)
R. J. Wright et al.
Figure 1.
The median gas accretion efficiency, (cid:164) 𝑀 gas /( 𝑓 b 𝑀 halo ) , of each inflow mode in Table 2, as a function of halo mass at 𝑧 ≈ 𝑧 ≈ th − th percentile range spread in gasaccretion efficiency for L50-REF as error bars (excluding the merger-mode), and the bootstrap-generated 95% confidence interval (CI) error on the median forL50-REF as shaded regions. reference physics run, dashed lines represent results from the L50-NOAGN run, and the dotted lines correspond to results from theL25-NOFB run. Additionally, the 16 th − th (1 𝜎 ) percentile range isshown with errorbars, and the bootstrap-generated 95% confidenceinterval error on the median (from 100 resamples using a randomlyselected half of the appropriate population) is illustrated as a shadedregion for the L50-REF reference run exclusively.Concentrating first on the L50-REF reference physics run(solid lines), at 𝑧 ≈ 𝑀 halo (cid:46) . 𝑀 (cid:12) , and pre-processed accretion dominates abovethis transition mass. The contribution of mergers to mass growth isubiquitously small, but increases with halo mass to be within 1 dexof the first-infall and pre-processed modes at 𝑀 halo (cid:38) 𝑀 (cid:12) .If we compare this breakdown to that between the hot and cold-modes of accretion in the bottom left panel, we see qualitative sim-ilarity between cold and first-infall channels, as well as the hotand pre-processed channel - in that cold accretion dominates for 𝑀 halo (cid:46) 𝑀 (cid:12) , and above this transition mass, hot-mode accre-tion takes over. While we find these similarities between the first-infall (pre-processed) and cold (hot) modes of accretion, we are notclaiming that these causally or physically linked: rather, we argue that the similarities are driven by a set of physical processes definedby similar halo mass transition scales. In the case of the breakdownbetween first-infall and pre-processed accretion, we show in Wrightet al. (2020) that the pre-processed mode increases in flux with halomass as haloes become massive enough to attract previously ejectedparticles (either from one of the halo’s progenitors, or an unrelatedhalo). Conversely, in the hot/cold-mode case, the contribution ofthe hot-mode increases with halo mass as haloes become massiveenough to efficiently shock heat the accreting gas (e.g. Katz et al.2003; Kereš et al. 2005, 2009; Ocvirk et al. 2008; van de Voort et al.2011). Note that we explore the relationship between the tempera-ture and history-based inflow classifications in Figure 2, which wediscuss further below.At 𝑧 ≈
2, we see that first-infall accretion channel exceeds pre-processed accretion for all halo masses, with a roughly constant off-set of ≈ . ≈ . 𝑀 (cid:12) . We also find that cold-mode accretiondominates over hot-mode accretion for the full halo mass range, withthe hot accretion channel increasing with halo mass to nearly meetthe relatively constant cold-mode efficiency at 𝑀 halo ≈ . 𝑀 (cid:12) . MNRAS000
2, we see that first-infall accretion channel exceeds pre-processed accretion for all halo masses, with a roughly constant off-set of ≈ . ≈ . 𝑀 (cid:12) . We also find that cold-mode accretiondominates over hot-mode accretion for the full halo mass range, withthe hot accretion channel increasing with halo mass to nearly meetthe relatively constant cold-mode efficiency at 𝑀 halo ≈ . 𝑀 (cid:12) . MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes The rise in contribution of hot-mode accretion with halo mass is un-surprising, given the increased importance of virial shock-heating(Rees & Ostriker 1977; Birnboim & Dekel 2003; Kereš et al. 2009),however Correa et al. (2018a) show in EAGLE that other physicalprocesses are also required to explain gas accreting above halo virialtemperatures.Focusing on the influence of sub-grid physics, we note anincrease in 𝑧 ≈ 𝑀 (cid:12) - a direct consequence of the lack of stellar feedback, asdiscussed in Wright et al. (2020). At 𝑧 ≈
2, we find that while thefirst-infall mode in the L25-NOFB run is consistent with L50-REF,the pre-processed mode appears to be suppressed due to the lackof mechanisms to eject particles from haloes (for subsequent pre-processed re-accretion). At 𝑧 ≈
2, we note that hot-mode accretionin the L25-NOFB run is strongly enhanced relative to L50-REF,which we explore further in the discussion of Figure 2. We notethat the influence of AGN feedback on accretion modes is minimal,with only a slight increase in total accretion rates for haloes between10 𝑀 (cid:12) and 10 . 𝑀 (cid:12) at 𝑧 ≈ 𝑓 hot fractions for both modesincrease with halo mass at both 𝑧 ≈ 𝑧 ≈
2, in a similarfashion to total hot accretion fractions presented in Correa et al.(2018b). Focusing on reference physics (solid lines), we find thatthe pre-processed mode is systematically “hotter” than the first-infall mode, with an offset in median hot fraction of 10% for haloesbelow 𝑀 halo ≈ 𝑀 (cid:12) at both 𝑧 ≈ 𝑧 ≈
2. We remark that thebootstrapped error on the respective medians do not overlap below 𝑀 halo ≈ 𝑀 (cid:12) at each redshift, meaning we consider this to be asignificant and real difference in the temperature of first-infall andpre-processed accreting gas.The bottom panels of Figure 2 show the converse of the upperpanels: instead of the fraction of particles accreting hot for eachhistory-based inflow classification, we show the fraction of particlesaccreting for the first time ( 𝑓 first infall , or 𝑓 FI ), broken down into gasaccreting via the hot and cold channels of inflow.At 𝑧 ≈
0, we see a trend for 𝑓 FI for both hot- and cold- modesto decrease with halo mass from ≈
75% at 𝑀 halo ≈ . 𝑀 (cid:12) to ≈
50% at 𝑀 halo ≈ . 𝑀 (cid:12) (in line with the global shift towardsrecycled and transferred baryonic accretion found in Wright et al.2020, Figure 6). Embedded in this global trend, we see a significantdisparity between the hot- and cold-mode unprocessed fractions forhaloes in the mass range 10 𝑀 (cid:12) (cid:46) 𝑀 halo (cid:46) 𝑀 (cid:12) - with 𝑓 FI ofhot-accreting gas being ≈
20% lower than cold-accreting gas. In thishalo mass range, cold-accreting gas is significantly more likely tobe on first-infall than to have been previously processed. Above thishalo mass range, 𝑓 FI is similar for the hot- and cold- modes, thoughwe remind the reader that the cold-mode is also heavily suppressedin this regime at 𝑧 ≈ 𝑧 ≈
2, the differences between hot- and cold-mode 𝑓 FI arequalitatively similar to those found 𝑧 ≈ 𝑓 FI remain at ≈
70% for the full halo mass range (slightly higher thanat 𝑧 ≈ 𝑓 FI values in the mass range 10 . 𝑀 (cid:12) (cid:46) 𝑀 halo (cid:46) . 𝑀 (cid:12) , with cold-accreted particles ≈
10% more likely to be on first-infall compared to being pre-processed. The spread in 𝑓 FI is lower for both hot- and cold- modes at 𝑧 ≈
2, however thereis still overlap between the percentile ranges for the full halo massrange.Shifting focus away from the L50-REF run, we can use theL50-NOAGN and L25-NOFB curves in Figure 2 to investigate therole of feedback in altering hot-accretion fractions and first-infallfractions. We remind the reader that in Figure 1, we found enhancedhot accretion in the L25-NOFB run relative to reference physics. Inthe top panels of Figure 2, we show that the median hot fraction ofboth the first-infall and pre-processed modes in the L25-NOFB runis significantly increased, particularly at 𝑧 ≈ ≈
20% more prominent than in L50-REF for 𝑀 halo (cid:38) . 𝑀 (cid:12) ,with raw total accretion rates otherwise very similar.Upon investigation, we attribute the enhanced hot fraction ofaccretion in L25-NOFB to two factors. Firstly, we find that thebaryon fraction of haloes in the L25-NOFB run are larger than inL50-REF and L50-NOAGN run, and that this baryonic componentis less radially extended than L50-NOAGN/REF haloes at a givenmass. We consequently argue that the compact, gas-rich halo envi-ronment in L25-NOFB facilitates efficient shock heating of accret-ing gas. Secondly, we find that that the non-merger component ofaccreting to haloes in the L25-NOFB run is heavily metal-depletedrelative to reference physics (see Figure 5, top panels). The lowmetallicity of accreting gas extends cooling times after virial heat-ing - meaning that less accreting gas is able to cool below 10 . Kshortly after accretion, as would be required to be classified as“cold”.The lack of metal-enriched accreting gas in L25-NOFB (com-pared to L50-REF) is a likely consequence of the lack of stellar-feedback driven outflows, which can act to enrich the CGM sur-rounding galaxies and haloes. With these outflows, accreting gaswhich has been previously processed (for instance, gas which hasbeen ejected from a halo and is subsequently re-accreting) is morelikely to have been enriched, and gas on first-infall is more likely tohave been enriched when in contact with the outskirts of the haloenvironment prior to accretion. We explore these ideas further in§4. We find that AGN feedback plays a sub-dominant role inregulating hot accretion fractions at 𝑧 ≈
0, however at 𝑧 ≈ 𝑀 halo ≈ 𝑀 (cid:12) . At maximum, we see a difference of ≈ 𝑀 halo ≈ . 𝑀 (cid:12) . This could be a result of slightlyhigher halo baryon fractions and a more compact baryonic profilesin the L50-NOAGN run at this halo mass, facilitating more efficientshock-heating of the accreting gas. The increase accretion hot frac-tions in L50-NOAGN are specifically a result of increase hot-modeaccretion in relation to the cold-mode, which remains fairly simi-lar between L50-NOAGN and L50-REF. This suggests that AGNfeedback preferentially suppresses hot-mode accretion as opposedto the cold-mode, which we discuss further in §3.2. Using the accretion classifications presented in Table 2 and statis-tically measured in Figure 1, we now investigate and quantify thespatial characteristics of gas accreting to haloes in EAGLE basedon the parameters in Section 2.4.We visualise the gas accreting to 3 example haloes at of dif-ferent mass at 𝑧 ≈
0, and their progenitors at 𝑧 ≈
2, in Figure 3. Wechoose these 3 haloes to demonstrate the nature of accreting gas for
MNRAS , 1–23 (2020)
R. J. Wright et al.
Figure 2.
Top panels: The median hot fraction (defined by the temperature cut in Equation 3) of inflow gas for the first-infall and pre-processed modes as afunction of halo mass at 𝑧 ≈ 𝑧 ≈ 𝑓 hot value of 0 . 𝑓 FI value of 0 . (i) dwarf-mass haloes: 𝑀 halo ( 𝑧 = ) ≈ . 𝑀 (cid:12) , (ii) Milky Way(MW)-mass haloes: 𝑀 halo ( 𝑧 = ) ≈ . 𝑀 (cid:12) , and (ii) group-masshaloes: 𝑀 halo ( 𝑧 = ) ≈ . 𝑀 (cid:12) .Gas accreting to the 10 . 𝑀 (cid:12) halo at 𝑧 ≈ ≈ ≈ ≈ 𝑧 ≈ 𝑧 ≈
2, we find that the halo has a similar breakdown betweenfirst-infall and pre-processed inflow ( ≈
71% compared to ≈ . 𝑀 (cid:12) halo at 𝑧 ≈ ≈
90% hot in nature, withonly 10% being accreted via the cold-mode. There is no mergercontribution to the mass growth of the halo at this snapshot, with accreting gas roughly evenly split between gas on first-infall to ahalo ( ≈ ≈ 𝑧 ≈ 𝑧 ≈ ≈ . 𝑀 (cid:12) halo at 𝑧 ≈ 𝑅 , fed by a numberof filaments. The vast majority of recently accreted gas is hot innature, with ≈
97% having been heated upon entering the halo. Thenon-merger component is dominated by pre-processed gas ( ≈ ≈ 𝑧 ≈ ≈
35% cold-mode and ≈
56% hot-mode, the remaining ≈ ≈ MNRAS000
56% hot-mode, the remaining ≈ ≈ MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes Figure 3.
A visualisation of the gas surrounding 3 example haloes at 𝑧 ≈ 𝑧 ≈ ≈ . 𝑀 (cid:12) (“dwarf-mass”, top panels), a halo at ≈ . 𝑀 (cid:12) (“Milky Way-mass”, middle panels), and a halo at ≈ . 𝑀 (cid:12) (“group-mass”, bottom panels).Gas is coloured by log-scaled density, and averaged velocity vectors are overlayed with white arrows. Additionally, the virial sphere for each halo is circled inwhite, and the breakdown of accreting gas (which had entered the halo at the previous snap) into its constituent channels is quantified and quoted as a percentageof total inflow mass. Visualisations were produced with the yt package (Turk et al. 2011).MNRAS , 1–23 (2020) R. J. Wright et al. particles which had been pre-processed ( ≈ 𝑧 ≈ 𝑧 ≈ 𝑧 ≈ 𝑧 ≈ 𝑓 cov ,introduced in Equation 8), we illustrate the redshift evolution of thespatial distribution of halo-scale accreting matter for each accretionmode in Figure 4. To ensure 𝑓 cov is not sensitive to the numberof particles accreting (and is exclusively a reflection of the spatial distribution of accreting matter), we only include haloes at each snapthat are (i) in the mass range 10 𝑀 (cid:12) < 𝑀 halo < 𝑀 (cid:12) , and (ii)have accreted at least 10 gas particles since the previous snapshot.We impose the latter for each of the accretion modes individually,meaning the halo sample for each curve is not identical. Within theimposed mass range, an accretion flux of ≥ gas particles occursin at least ≈
95% of haloes for all non-merger accretion modes (at allsnapshots). The particle flux requirement only significantly reducesthe number of haloes we can calculate merger covering fractionsfor, where we could only use ≈
50% of the sample towards 𝑧 = 𝑧 =
0. This indicates a shift from more filamentary, colli-mated inflow towards a more isotropic distribution, consistent withthe qualitative picture painted in Figure 3. The first-infall and pre-processed modes possess a median covering fraction of at least 0 . 𝑓 cov parameter compared to first-infall accretion by ≈
20% over the majority of the redshift range. The median valuesprove to be significantly different based on the bootstrap-generatederror ranges, indicating that particles on first-infall to a halo aresignificantly more likely to come in the form of more collimatedinflow compared to particles which had been previously accretedand ejected by a halo. Qualitatively, this aligns with the scenarioof first-infall particles originating from cosmic web filaments. Thecovering fraction of first-infall accretion reaches a maximum at 𝑧 ≈ ≈
70% compared to the ≈
90% of the pre-processedmode. Unsurprisingly, the covering fraction of inflow from merg-ers is comparatively very low ( ≈ 𝑓 cov values in the top panel. Unlike the first-infall mode,we don’t find any significant evolution of cold-mode covering frac-tions with redshift, with cold-mode 𝑓 cov remaining at a roughlyconstant value of ≈ >
60% found for the
Figure 4.
The median covering fraction, 𝑓 cov (as defined in Equation 8),of accreting gas in haloes with 10 𝑀 (cid:12) < 𝑀 halo < 𝑀 (cid:12) as a functionof redshift. We show 𝑓 cov individually for each accretion mode in Table 2(with history-based classification in the top panel, and temperature basedclassification in the bottom panel), requiring at least 1000 particles accretedfor each mode for a halo to be analysed). 𝑓 cov is shown for the L50-REFrun (solid lines), the L50-NOAGN run (dashed lines), and the L25-NOFBrun (dotted lines). We also include the bootstrap-generated 95% confidenceinterval error on the median for L50-REF as shaded regions. first-infall mode. Similar to the pre-processed mode, the hot-modeof accretion reaches a maximum 𝑓 cov value of ≈
90% at 𝑧 ≈ 𝑓 cov for the cold and hot-modes is not necessar-ily expected. The qualitative picture that has been discussed in theliterature tends to connect the hot-mode with isotropic accretion,with correspondingly large covering fractions, and cold-mode withhighly collimated accretion, with much smaller covering fractions.We show here that the picture is more complicated than this, and infact the covering fraction of cold-mode is quite large (albeit alwayssmaller than that of the hot-mode) across the whole redshift rangestudied. hot-mode accretion, on the other hand, shows significantredshift evolution of its covering fraction, and at 𝑧 ≈ . MNRAS000
90% at 𝑧 ≈ 𝑓 cov for the cold and hot-modes is not necessar-ily expected. The qualitative picture that has been discussed in theliterature tends to connect the hot-mode with isotropic accretion,with correspondingly large covering fractions, and cold-mode withhighly collimated accretion, with much smaller covering fractions.We show here that the picture is more complicated than this, and infact the covering fraction of cold-mode is quite large (albeit alwayssmaller than that of the hot-mode) across the whole redshift rangestudied. hot-mode accretion, on the other hand, shows significantredshift evolution of its covering fraction, and at 𝑧 ≈ . MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes ences the spatial distribution of accreting gas in this halo mass range.In the absence of AGN feedback (L50-NOAGN), we see a signifi-cant enhancement (by ≈ − 𝑓 cov values sitting near the 84 th percentile in 𝑓 cov values from L50-REF across the full redshift range for these modes. In Wright et al.(2020), we show that AGN activity can modulate accretion ratesin this mass regime by ≈ 𝑓 cov , the behaviour of the L25-NOFB run is similarto the L50-NOAGN run for the pre-processed, first-infall and hotchannels of accretion. In contrast, focusing on the cold-mode, wenote that covering fractions of cold-mode accreting matter decreaseby ≈
20% in the absence of stellar feedback for the full redshift rangeanalysed. In EAGLE, Correa et al. (2018a) show that stellar feedbackhas a considerable influence on the amount of hot gas in the halo.They show for haloes at 𝑀 halo ≈ 𝑀 (cid:12) that a doubling of stellarfeedback strength leads to a increase in the gas mass fraction by afactor of 1 .
3, and that a halving of stellar feedback strength reducesthe gas mass fraction by a factor 2 .
5. We suggest that the presenceof a hot gaseous corona maintained by stellar feedback causes coldinflow gas to become less collimated as it approaches a halo, therebyincreasing the covering fraction, 𝑓 cov , of gas accreting via this modein L50-NOAGN and L50-REF compared to L25-NOFB. This doesnot influence the already heated and less collimated hot-mode.We remark that in Appendix B, we check the “weak conver-gence” (see Schaye et al. 2015 for explanation) of our covering frac-tions, and find that 𝑓 cov values from the L25-RECAL run are largelyconsistent (within uncertainty) with L50-REF covering fractionsover cosmic time. We also investigate the influence of SPH schemeon our 𝑓 cov calculations, and find that using an older, GADGET-likeSPH implementation (without the improved Pressure-SPH scheme)produces systematically lower accretion covering fractions (see Fig-ure B1). In this Section, we investigate the metallicity of gas accreting tohaloes in EAGLE, in particular the level of enrichment for gasaccreting via different inflow channels (as described in Table 2).We also remark that when we refer to the “integrated” metallic-ity of the matter accreting to a halo, we calculate the total massaccreted in metals normalised by the total mass accreted in gas: 𝑍 int = (cid:164) 𝑀 metals / (cid:164) 𝑀 gas = Σ 𝑖 ( 𝑍 𝑖 × 𝑀 𝑖 )/ Σ 𝑖 ( 𝑀 𝑖 ) , summing over allaccreted particles 𝑖 . This measurement is typically skewed towardshigher values of log ( 𝑍 / 𝑍 (cid:12) ) compared to the median metallicityof individual accreting particles. Figure 5 shows the median integrated metallicity of accretion chan-nels as a function of halo mass for first-infall and pre-processedparticles at 𝑧 ≈ 𝑀 halo ≈ M (cid:12) to10 . M (cid:12) , the metallicity of the first-infall mode is significantlydepleted relative to the pre-processed mode by ≈ − − . < log ( 𝑍 / 𝑍 (cid:12) ) < − .
5. The disparity between the first-infalland pre-processed channels is physically intuitive: particles whichhave not been processed in a halo prior to accretion are far less likelyto be enriched compared to those that have previously been accretedonto a halo. We remark to the reader that these history-based clas-sifications of inflow channel yield a much stronger separation inthe metallicities of their populations compared to the negligibledifference noted between temperature-based (hot- and cold-mode)classifications, which we consequently have not included in Figure5. The low metallicities (log ( 𝑍 / 𝑍 (cid:12) ) (cid:46) −
2) of the first-infallchannel, together with the low contamination by stellar-feedbackaffected gas illustrated in Figure A1 give us confidence in our classi-fication scheme. Despite being very metal poor, first-infall particlesare not necessarily pristine (i.e., they do not have zero metallicity).Upon investigation, we found that in most haloes, the majority of thefirst-infall particles do possess zero metallicity, but the addition of asmall sample of slightly enriched particles can drastically increasethe value of 𝑍 int : the sum of all accreted mass in metals divided bythe total mass accreted. The finite cadence of the simulation outputsused, as well as the lower mass resolution limit of VELOCIraptor,may also lead to a small number of particles wrongly being classedas unprocessed.We also note a trend of increasing inflow enrichment withincreasing halo mass for each of the included accretion channels.Upon investigation, we argue that this is the result of pre-accretionenrichment - where particles are enriched prior to formally enteringthe halo environment. We find that the metallicity profiles of highermass haloes are more extended (even relative to their size) comparedto less massive haloes, meaning that gas can be enriched beforecrossing the FOF boundary of larger haloes.We now consider the influence of sub-grid physics on the en-richment of accreting gas, based on the alternative physics curvesshown in Figure 5. Comparing the L50-REF and L50-NOAGNruns, we see fairly similar behaviour over halo mass and redshift,indicating that AGN feedback does not heavily influence accretingmetallicities. The exception to this statement is that pre-processedgas in the L50-NOAGN run appears marginally less enriched com-pared to the L50-REF run for haloes with mass between 10 . 𝑀 (cid:12) and 10 𝑀 (cid:12) at 𝑧 ≈
0. The pre-processed accreting gas in this massregime is mostly recycling gas from the main progenitor (see Wrightet al. 2020). In L50-REF, some of this gas will likely correspond tothe metal-enriched central ISM gas expelled due to AGN feedback,given this mass range is that previously associated with AGN-drivenoutflows (Davies et al. 2019b; Oppenheimer et al. 2020). The ad-ditional source of metal-rich recycling gas in L50-REF comparedto L50-NOAGN potentially offers an explanation for the marginalincrease in pre-processed accreting metal content.Unlike the L50-NOAGN run, we see very notable changesin accreting metallicities when investigating the L25-NOFB runcompared to L50-REF. First-infall and pre-processed accreting gas
MNRAS , 1–23 (2020) R. J. Wright et al.
Figure 5.
The integrated metallicity (prior to accretion) of halo-accretinggas as a function of halo mass for the history-based inflow modes, excludingthe heavily enriched merger-mode. To guide the reader’s eye, we also includethe integrated metallicity of all accreting gas (essentially a weighted averageof the pre-processed and first-infall mode) in the L50-REF run in grey. Inthis figure we quote the metallicities at 𝑧 ≈
0, and consider redshift evolutionin Figure 6. The metallicities are shown for multiple EAGLE runs, namelythe L50-REF run (solid lines), the L50-NOAGN run (dashed lines), and theL25-NOFB run (dotted lines). We also include the 16 th − th percentilerange spread in accreting metallicity for L50-REF as error bars, and thebootstrap-generated 95% confidence interval error on the median for L50-REF as shaded regions. in the L25-NOFB run is metal-poor relative to accreting gas inthe L50-REF and L50-NOAGN runs, the difference being the lackof stellar feedback. This depletion is particularly clear in the pre-processed mode, which shows reduced metal content by up to ≈ − 𝑧 ≈ 𝑀 halo (cid:46) 𝑀 (cid:12) ).Similar to the influence of enriched AGN-driven outflows wediscuss above, we argue that it is the lack of circum-halo enrichedmatter that drives the depletion of accreting matter in this run.In runs with stellar feedback, out-flowing gas in stellar feedbackdriven winds normally acts to deliver enriched material to the CGM.In the absence of these outflows, the CGM and gas at the halointerface is seldom enriched by the central galaxy - meaning thatboth first-infall and pre-processed accreting gas is less likely to haveever been enriched. In other words, we argue that the spatial scaleof metal enrichment from galaxies in the L25-NOFB run is moreconcentrated to the galaxy-scale, and does not influence the largerscales from which halo-accreting gas originates. Comparatively, gasaccreting at the halo-scale in L50-REF and L50-NOAGN is muchmore likely to have previously been enriched.In Figure 6, we concentrate on the redshift evolution of accret-ing metallicities in the reference L50-REF run for a MW-like halomass band between 10 and 10 . 𝑀 (cid:12) . We include the first-infall(blue) and pre-processed (green) modes, together with the integratedmetallicity of all accreting gas in grey (including the first-infall, pre-processed and merger components). For reference, we also comparethese inflow metallicities to halo-bound gas reservoirs, namely the Figure 6.
The pre-accretion integrated metallicity of first-infall (blue), pre-processed (green) and all accreting gas (grey) as a function of scale factor forhaloes between 10 𝑀 (cid:12) and 10 . 𝑀 (cid:12) in L50-REF only. For comparison,in the same mass sample we also include the integrated metal content of haloCGMs (yellow) and central galaxy ISMs (hot pink) as defined in the text.For each line, we include the 16 th − th percentile range spread in accret-ing metallicity as error bars, and the bootstrap-generated 95% confidenceinterval error on the median as shaded regions. metal content of the CGM (yellow) and central galaxy ISM (hotpink). For the purposes of this work, we follow the definition ofCorrea et al. (2018b) in defining the ISM as gas within a radius of0 . × 𝑅 of a halo’s most bound particle (which we assume toreside in the central galaxy), that have either (a) a non-zero SFR, or(b) are part of the atomic phase of the ISM with 𝑛 H > . − and 𝑇 < K. To define the CGM, we use all FOF particles outsidethe central 0 . × 𝑅 of the halo, subtracting the particles fromany nested subhaloes in the host (so as to avoid including the ISMgas associated with satellite galaxies).Previously, galaxy gas metallicities at 𝑀 ★ ≈ . 𝑀 (cid:12) (cor-responding roughly to the illustrated halo mass range) have beenmeasured to evolve from 12 + log ( O / H ) ≈ . 𝑧 = ≈ . 𝑧 = ≈ . ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ − . 𝑧 ≈ ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ . 𝑧 ≈ . ≈ . ( 𝑍 CGM / 𝑍 (cid:12) ) ≈ − . − . 𝑧 ≈ ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ . 𝑧 ≈ . ≈ . − . ≈ MNRAS000
The pre-accretion integrated metallicity of first-infall (blue), pre-processed (green) and all accreting gas (grey) as a function of scale factor forhaloes between 10 𝑀 (cid:12) and 10 . 𝑀 (cid:12) in L50-REF only. For comparison,in the same mass sample we also include the integrated metal content of haloCGMs (yellow) and central galaxy ISMs (hot pink) as defined in the text.For each line, we include the 16 th − th percentile range spread in accret-ing metallicity as error bars, and the bootstrap-generated 95% confidenceinterval error on the median as shaded regions. metal content of the CGM (yellow) and central galaxy ISM (hotpink). For the purposes of this work, we follow the definition ofCorrea et al. (2018b) in defining the ISM as gas within a radius of0 . × 𝑅 of a halo’s most bound particle (which we assume toreside in the central galaxy), that have either (a) a non-zero SFR, or(b) are part of the atomic phase of the ISM with 𝑛 H > . − and 𝑇 < K. To define the CGM, we use all FOF particles outsidethe central 0 . × 𝑅 of the halo, subtracting the particles fromany nested subhaloes in the host (so as to avoid including the ISMgas associated with satellite galaxies).Previously, galaxy gas metallicities at 𝑀 ★ ≈ . 𝑀 (cid:12) (cor-responding roughly to the illustrated halo mass range) have beenmeasured to evolve from 12 + log ( O / H ) ≈ . 𝑧 = ≈ . 𝑧 = ≈ . ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ − . 𝑧 ≈ ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ . 𝑧 ≈ . ≈ . ( 𝑍 CGM / 𝑍 (cid:12) ) ≈ − . − . 𝑧 ≈ ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ . 𝑧 ≈ . ≈ . − . ≈ MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes average CGM metallicities closely over redshift, with a very slighlysteeper gradient. This concordance is consistent with a picture wherethe pre-processed inflow material had previously been accreted intothe CGM of progenitor haloes, and subsequently recycled.As seen in Figure 5, the first-infall mode is significantly de-pleted in metal content than the pre-processed mode. The inte-grated metallicity of this already depleted mode appears to de-crease slightly towards 𝑧 =
0, from log ( 𝑍 int / 𝑍 (cid:12) ) ≈ − . 𝑧 ≈ ( 𝑍 int / 𝑍 (cid:12) ) ≈ − . 𝑧 ≈ .
1. This systematically drags downthe average integrated metallicity of all accreting gas (grey line)from that of the pre-processed mode by ≈ . − . ≈ . − . ≈ − . 𝑍 / 𝑍 (cid:12) (cid:46) − . ) in the CGM is likely tobe accreting and on first-infall, gas which has been ejected from agalaxy will likely possess metallicity degenerate with that of return-ing pre-processed gas. This highlights the importance of kinematicinformation in observations to delineate between accreting and out-going material in the CGM of haloes. Figure 7 illustrates the pre-accretion phase diagram (that is, thedensity and temperature of gas at the snapshot prior to accretion)of all gas particles accreting to haloes in the mass range 10 <𝑀 halo / M (cid:12) < . for 𝑧 ≈ 𝑧 ≈ 𝑧 ≈ − cm − < 𝑛 H < − cm − , and in the temperature range10 K < 𝑇 gas < K. This is a small subset of the full parameterspace, and corresponds to the warm/hot phase of the inter-galacticmedium (WHIM). In this region of the parameter space we observeintermediate metallicities, log ( 𝑍 acc / 𝑍 (cid:12) ) ≈ − −
2, which cor-responds to an non-trivial superposition of all 3 accretion modes(see bottom left panel).If we concentrate on the low metallicity population of accretingmatter, corresponding to bluer regions in the top panels of FigureFigure 7, we see a fairly well defined distribution in phase space. Themajority of low-metallicity accreting gas (log ( 𝑍 acc / 𝑍 (cid:12) ) (cid:46) − − < 𝑛 H / cm − < − (at thepeak of the bulk population) and 10 . < 𝑇 gas / K < (slightlycooler than the bulk population). This region of phase diagram isvery well correlated with the first-infall accretion mode in the bottompanel, and concurs with our findings in Section 3.1 and Figure 2which indicate that first-infall accretion is marginally cooler onaverage than the pre-processed and merger channels of inflow.We also observe a low metallicity "tail" extending towards theequation of state, forming a near linear and tight sequence from ( 𝑛 H , 𝑇 ) = ( − cm − , . K) to ( − cm − , K ) . This popu-lation corresponds to the metal-poor cooling of pristine gas priorto joining the star-forming equation of state. The same low-Z tailin the bottom panel is dominated by the merger-mode of inflow -simply meaning that there are few particles cooling and reaching densities above 𝑛 H = − cm − outside existing haloes (see alsoSchaller et al. 2015, Figure 7).Extending away from the blue, low-Z population that we dis-cuss above - there is a well defined concentric gradient outwardstowards higher metallicities. Solar and super-solar metallicitiescharacerise the accreting gas above 10 K, and also dominate thepopulation above 𝑛 H = − cm − (with the exception of the afore-mentioned tight low-Z cooling tail). At both redshifts, we observea hot and dense population of enriched accreting gas in the regionwhere 𝑛 H (cid:38) − cm − and 𝑇 (cid:38) . K. When we investigatedthe 𝑇 max values associated with this population, we noted a distinctpeak at 𝑇 max = . K - indicating that these particles have beenheated by stellar feedback events (this being the prescribed Δ 𝑇 SNe in EAGLE). In the bottom panels, we find that a combination ofpre-processed and merger channels of accretion contribute in thisregion of the phase diagram. The pre-processed portion likely cor-responds to particles which have been ejected from their halo viastellar feedback, and later re-accreted.One clear difference between the two redshifts shown is that wefind an extension of the low-metallicity population towards highertemperatures at 𝑧 ≈
2. The mass-weighted median metallicity ofall accreting gas increases from log ( 𝑍 / 𝑍 (cid:12) ) = − . 𝑧 ≈ ( 𝑍 / 𝑍 (cid:12) ) = − . 𝑧 ≈
0, where more particles are accretingvia the enriched pre-processed mode (see Wright et al. 2020). Wealso find that the overall pre-accretion temperature histogram ofaccreting gas becomes distinctly bi-modal at 𝑧 ≈ 𝑧 ≈
0, with the higher redshiftsnapshot showing a stronger peak at 𝑇 acc ≈ . K. This lower tem-perature population correlates with the more dominant cold-modeof gas accretion at higher redshift, and hosts a non-trivial breakdownof metallicities and inflow modes - increasing in metallicity withincreasing density, and simultaneously showing a shift from first-infall, to pre-processed, to merger-mode prevalence with increasingdensity. In addition, the high- 𝑛 H tail of the density distribution at 𝑧 ≈ Λ -CDM mass-growth scenario.Our results show that the different accretion modes do prefer-entially populate different regions of the three dimensional spacebetween density, temperature, and metallicity. However, there issome level of overlap between those regions, and hence by the po-sition of a particle in this three-dimensional space, one can onlysuggest the most likely accretion mode. Gas accretion rates have been proposed to be a primary regulatorof both galaxy star formation rates (SFRs) and gas metallicitiesin equilibrium models (e.g. Davé et al. 2012; Lilly et al. 2013).De Lucia et al. (2020), using the semi-analytic model GAEA, andCollacchioni et al. (2020) and van Loon et al. (2021), using EA-GLE, show that gas accretion rates onto galaxies are correlatedwith the scatter in their predicted stellar mass - ISM metallicityrelations (ISM MZR). The physical reasoning behind this modu-lation is that low-Z, relatively pristine (low-Z) inflow can act to“dilute” the metallicity of the ISM. Since gas accretion rates ontogalaxies depend strongly on the gas accretion rate onto haloes (Davéet al. 2012; Mitchell et al. 2020a), we here explore how halo-scalegas accretion rates modulate the properties of their central galaxies
MNRAS , 1–23 (2020) R. J. Wright et al.
Figure 7.
The pre-accretion phase ( 𝑛 H − 𝑇 ) plane for gas accreting to haloes of mass 10 < 𝑀 halo / M (cid:12) < . at 𝑧 ≈ 𝑧 ≈ 𝑛 H and 𝑇 (“M” corresponding to merger-origin particles, “PP” corresponding to pre-processed particles, and “FI” referring to first-infallparticles). Also shown are the PDFs of 𝑛 H and 𝑇 for accreting particles, in the top panels split into 3 equally log-spaced bins of metallicity and in the bottompanels split into different accretion modes. We also show the fraction of each 𝑛 H and 𝑇 bin occupied by each metallicity/inflow mode categorisation. Eachpanel has an inset at the bottom left indicating the mass-weighted median accreting temperatures and densities, and at the top left of each panel, we quote thetotal number of gas particles accreted onto haloes in the given mass range. In the top panels, integrated and median accreting metallicities are quoted inset atthe top right, while in the bottom panels, the fraction of mass delivered by each inflow mode are quoted at the top of each panel. and circum-galactic media. In particular, we investigate (i) the ISMMZR and halo mass - CGM metallicity relation (CGM MZR) in5.1, and (ii) the stellar mass - specific SFR (sSFR) relation in §5.2.We frequently use the notation Δ 𝑥 i to represent the excessvalue of quantity 𝑥 for object 𝑖 relative to the median. We nominally compute Δ 𝑥 𝑖 relative to the median of 𝑥 for a given value of secondquantity, 𝑦 as: Δ 𝑥 i | 𝑦 = log (cid:18) 𝑥 𝑖 ˜ 𝑥 | 𝑦 𝑖 (cid:19) , (9) MNRAS000
The pre-accretion phase ( 𝑛 H − 𝑇 ) plane for gas accreting to haloes of mass 10 < 𝑀 halo / M (cid:12) < . at 𝑧 ≈ 𝑧 ≈ 𝑛 H and 𝑇 (“M” corresponding to merger-origin particles, “PP” corresponding to pre-processed particles, and “FI” referring to first-infallparticles). Also shown are the PDFs of 𝑛 H and 𝑇 for accreting particles, in the top panels split into 3 equally log-spaced bins of metallicity and in the bottompanels split into different accretion modes. We also show the fraction of each 𝑛 H and 𝑇 bin occupied by each metallicity/inflow mode categorisation. Eachpanel has an inset at the bottom left indicating the mass-weighted median accreting temperatures and densities, and at the top left of each panel, we quote thetotal number of gas particles accreted onto haloes in the given mass range. In the top panels, integrated and median accreting metallicities are quoted inset atthe top right, while in the bottom panels, the fraction of mass delivered by each inflow mode are quoted at the top of each panel. and circum-galactic media. In particular, we investigate (i) the ISMMZR and halo mass - CGM metallicity relation (CGM MZR) in5.1, and (ii) the stellar mass - specific SFR (sSFR) relation in §5.2.We frequently use the notation Δ 𝑥 i to represent the excessvalue of quantity 𝑥 for object 𝑖 relative to the median. We nominally compute Δ 𝑥 𝑖 relative to the median of 𝑥 for a given value of secondquantity, 𝑦 as: Δ 𝑥 i | 𝑦 = log (cid:18) 𝑥 𝑖 ˜ 𝑥 | 𝑦 𝑖 (cid:19) , (9) MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes Figure 8.
Top 4 panels: The stellar mass - ISM metallicity relation in L50-REF coloured by excess gas accretion efficiency (at fixed stellar mass, Δ (cid:164) 𝑀 gas | 𝑀 ★ - upper panels), and 16 th − th percentile range in ISM metallicities and excess gas accretion rates (lower panels). The bins in ISM metallicity are spaced inincrements of 0 . Δ (cid:164) 𝑀 gas | 𝑀 halo - upper panels) and 16 th − th percentile range in CGM metallicities and excess gas accretion rates (lower panels). The bins in CGM metallicityare spaced in increments of 0 . 𝑧 ≈ 𝑧 ≈
2. The hatched regions show thebootstrap-generated 95% confidence interval error on the median for L50-REF in each relevant panel, and the parameter space is only coloured where there areat least 5 objects in each 2D bin.MNRAS , 1–23 (2020) R. J. Wright et al.
Figure 9.
Top panels: the relationship between excess gas accretion rate (at fixed stellar mass, Δ (cid:164) 𝑀 gas | 𝑀 ★ ) and excess central ISM metallicity ( Δ 𝑍 ISM | 𝑀 ★ )in L50-REF for 2 bins of central galaxy stellar mass: log ( 𝑀 ★ / 𝑀 (cid:12) ) ∈ [ , ) , and [ , . ) . Bottom panels: the relationship between excess gasaccretion rate (at fixed halo mass, Δ (cid:164) 𝑀 gas | 𝑀 halo ) and excess CGM metallicity ( Δ 𝑍 CGM | 𝑀 halo ) in L50-REF for 3 bins of halo mass: log ( 𝑀 halo / 𝑀 (cid:12) ) ∈[ , ) , [ , ) , and [ , ) . Left panels show these relations at 𝑧 ≈
0, while right panels show the relations at 𝑧 ≈
2. Error bars correspond to 16 th − th percentile ranges, and shaded regions show the bootstrap-generated 95% confidence interval error on the median. where ˜ 𝑥 | 𝑦 𝑖 is the median value of 𝑥 at 𝑦 ≈ 𝑦 𝑖 . Put simply, Δ 𝑥 i | 𝑦 describes the log-space excess value of 𝑥 for object 𝑖 compared towhat would be expected of 𝑥 from the object’s 𝑦 value. Here, we investigate the dependence of the (i) ISM MZR and (ii)CGM MZR on halo-scale gas accretion rates using reference EA-GLE physics. We remind the reader that we use VELOCIraptor(and not SUBFIND) to find haloes in EAGLE, and thus our re-sults are not identical to what would be obtained from the publiccatalogues outlined in McAlpine et al. (2016). We find, regardless,that our population statistics agree very well with these data (seeFigure 2 of Wright et al. 2020, comparing our accretion catalogueto Correa et al. 2018b). To compute ISM and CGM properties, weadopt the definitions outlined in § 4.1.The top panels of Figure 8 show ISM metallicity as a functionof 30 kpc aperture stellar mass (the
ISM MZR ) in the L50-REF runfor 𝑧 ≈ 𝑧 ≈
2, with the parameter space coloured by the mediangas accretion rate excess for a given stellar mass ( Δ (cid:164) 𝑀 gas | 𝑀 ★ ). These gas accretion rates include the contribution from all inflow modes.The panels below these illustrate the deviation of the 16 th and84 th percentile values for ISM metallicity (black) and the samespread in associated halo-scale gas accretion rates (grey). We notebefore continuing that the ISM MZR produced by reference EAGLEphysics is is known to be too flat relative to observations below 𝑀 ★ ≈ . 𝑀 (cid:12) (Schaye et al. 2015), however our work focuseson analysing the origin of the scatter in the relation (and not itsabsolute normalisation). We also note that the scatter in the gas-phase metallicity of high stellar-mass galaxies in EAGLE is higherthan observed due to sampling issues, with such objects typicallyquenched and therefore containing few star-forming gas particles(Schaye et al. 2015).At 𝑧 ≈ ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ 𝑀 ★ ≈ 𝑀 (cid:12) to ≈ . 𝑀 ★ ≈ 𝑀 (cid:12) . We find that the scatter in the relation varies slightly withstellar mass, with a peak at 𝑀 ★ ≈ 𝑀 (cid:12) (of ≈ . 𝑀 ★ ≈ 𝑀 (cid:12) (of ≈ . 𝑧 ≈
2, the MZR issteeper, with metallicity increasing from log ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ − . 𝑀 ★ ≈ 𝑀 (cid:12) to ≈ − . 𝑀 ★ ≈ 𝑀 (cid:12) , flattening abovethis mass. The spread decreases with stellar mass until just below MNRAS000
2, the MZR issteeper, with metallicity increasing from log ( 𝑍 ISM / 𝑍 (cid:12) ) ≈ − . 𝑀 ★ ≈ 𝑀 (cid:12) to ≈ − . 𝑀 ★ ≈ 𝑀 (cid:12) , flattening abovethis mass. The spread decreases with stellar mass until just below MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes 𝑀 ★ ≈ 𝑀 (cid:12) , increasing above this mass range for the mostmassive galaxies.At both redshifts, we find a clear trend with the scatter inISM metallicity being negatively correlated with halo-scale gasaccretion. This confirms that the ISM MZR modulation by thegalaxy-scale gas accretion is in large part driven by the halo scalegas accretion. While we observe this correlation with total accretionrates, we find that the trend remains when using the first-infall orpre-processed modes individually. This is due to the accretion fromboth these modes being metal depleted relative to the ISM, even inthe case of pre-processing (see Figure 5), meaning the gas is able todilute its metal content.Moving to a different scale, the bottom coloured panels ofFigure 8 show instead the CGM MZR in the L50-REF run, againcoloured by Δ (cid:164) 𝑀 gas | 𝑀 halo , including the contribution from all modesof inflow. At both redshifts, the metallicity of the CGM is lower thanthe ISM by ≈ . − 𝑧 ≈
0, the CGM MZR shows a slightminimum at 𝑀 halo ≈ 𝑀 (cid:12) of 𝑍 CGM ≈ − . 𝑍 (cid:12) , and above thismass scale, 𝑍 CGM increases modestly with halo mass, eventuallyflattening above 𝑀 halo ≈ . 𝑀 (cid:12) at 𝑍 CGM ≈ − . 𝑍 (cid:12) . At 𝑧 ≈ 𝑍 CGM increases monotonically with halo mass, from ≈ − . 𝑍 (cid:12) ata halo mass of ≈ 𝑀 (cid:12) to ≈ − . 𝑍 (cid:12) at ≈ . 𝑀 (cid:12) . We remindthe reader that that the metallicity of the CGM closely mimics theaverage pre-processed accreting gas metallicity at both redshifts(see Figure 6), albeit with less variation in 𝑍 CGM compared to 𝑍 PP at a given halo mass.Unlike the ISM MZR, at 𝑧 ≈ 𝑍 CGM de-creases monotonically with increasing halo mass from ≈ 𝑀 halo ≈ 𝑀 (cid:12) to ≈ . 𝑀 halo ≈ 𝑀 (cid:12) . At 𝑧 ≈ ≈ . 𝑧 ≈
0, for haloes below10 𝑀 (cid:12) , CGM metal content is strongly correlated with halo-scalegas accretion rates at fixed halo mass - with higher inflow ratesassociated with lower CGM metallicities. The same trend is evidentat 𝑧 ≈
2, across an overall smaller spread in 𝑍 CGM for a given halomass.We find a very strong gradient in excess gas accretion rate( Δ (cid:164) 𝑀 gas | 𝑀 halo ) across the scatter in 𝑍 CGM at fixed halo mass, below 𝑀 halo ≈ 𝑀 (cid:12) at 𝑧 ≈
0, and below 𝑀 halo ≈ . 𝑀 (cid:12) at 𝑧 ≈ 𝑍 FI (cid:46) − 𝑍 (cid:12) ) into the CGM, and allowing for itsdilution in a similar fashion as discussed in the gas of the ISM.We explore the mass dependence of CGM dilution further in thediscussion around Figure 9.We explore the driving nature of gas accretion in moderatingISM and CGM metallities more explicitly in Figure 9. In each panel,the x-axes correspond to the excess gas accretion rate (at fixed stellarmass for the ISM, and fixed halo mass for the CGM), and the y-axes in the top (bottom) panels correspond to the excess metallicityof the ISM (CGM) for a given stellar (halo) mass, showing therelationship for a number of bins in stellar (halo) mass. We choose totake two bins in stellar mass, in the ranges log ( 𝑀 ★ / 𝑀 (cid:12) ) ∈ [ , ) and [ , . ) respectively, which we refer to “low-mass” centralsand “high-mass” centrals respectively. These bins are chosen to beconsistent with the stellar-mass binning in Figure 11, motivated in§ 5.2. Our bins in halo mass to correspond to the regimes exploredin Figure 3 - (i) dwarf-mass haloes, (ii) MW-like haloes, and (iii)group-mass haloes.Focusing on the ISM-scale, we find a clear and significant negative correlation between excess total gas accretion and excessISM metal content for both low- and high-mass central galaxies.The gradient of the relation remains very similar between massbins, with high-mass galaxies spanning a smaller dynamic rangein gas accretion excess, particularly at 𝑧 ≈
2. On average, for afactor of 10 increase in gas accretion, we find an associated changein instantaneous ISM metallicity content of − . ≈ . 𝑀 (cid:12) ≤ 𝑀 halo < 𝑀 (cid:12) , ascan be qualitatively seen in Figure 9. While the correlation onlyappears significant for the dwarf halo mass range, this halo massbin exhibits a steeper gradient than we found at the ISM-scale at 𝑧 ≈
0. The dynamic range spanned in gas accretion is greatest forthis low-mass bin, particularly at 𝑧 ≈
0, aiding the establishmentof the anti-correlation above. For a factor of 10 increase in gasaccretion efficiency, on average we find a change in CGM metalcontent of ≈ − . ≈ 𝑧 ≈ 𝑧 ≈
2, below halo masses of 10 𝑀 (cid:12) , it is the first-infall mode that dominates accretion rates (see Figure 1) - bringingplentiful low-Z gas into the CGM (see Figure 5), and allowing forits dilution. Upon investigation, we also note that at low halo mass,newly accreted matter corresponds to a significant portion of theCGM mass (e.g. at 𝑧 ≈ 𝑀 (cid:12) haloes, ≈
50% of the CGM isnewly accreted gas), while in higher mass systems, newly accretedgas tends to make a smaller contribution to the CGM (e.g. at 𝑧 ≈ 𝑀 (cid:12) haloes, ≈
25% of the CGM is newly accreted gas). Thishighlights the dynamic nature of the CGM reservoir, with largefractions of its gas being renewed within a dynamical timescale.We remark that in the lower mass range, we also find thatthe accreting gas is, on average, more metal rich when accretionrates are lower (not shown). However, with the first-infall mode stilldominating, these increased metallicities are still below 10 − 𝑍 (cid:12) .Thus, we attribute the increase in 𝑍 CGM in low accretion rate haloesto the lack of pristine inflow, rather than the slight increase in averageaccretion metal content associated with low accretion rates.Above 𝑀 halo ≈ 𝑀 (cid:12) , the trend for CGM dilution withincreasing accretion rate is less clear at both redshifts. At 𝑧 ≈ 𝑀 (cid:12) , pre-processed accretion rates, onaverage, exceed first-infall accretion rates (see Figure 1). The pre-processed mode averages pre-accretion metallicities of ≈ − . 𝑍 (cid:12) in this mass range (see Figure 5), which corresponds very closely tothe measured metallicity of the CGM in this mass range. This meansthat in this mass range, the effect of CGM dilution by gas accretionmay not necessarily be expected - and is indeed not observed.At 𝑧 ≈
2, above ≈ 𝑀 (cid:12) , we find that accreting metallicitiesare typically below the metallicity of the CGM (with first-infall stilldominating, see Figure 1), suggesting that we may expect to see anet CGM dilution effect at higher masses for this redshift. At thisredshift, however, we find the spread in CGM metallicities for haloeswith mass (cid:38) 𝑀 (cid:12) is very low, and in the same mass range thatthe spread in Δ (cid:164) 𝑀 gas | 𝑀 halo is also extremely small ( (cid:46) . 𝑧 ≈
0, the gradientin excess CGM metallicity is steepest in the regime where excessgas accretion is below the median; i.e. the lack of gas accretion tothe halo appears to drive CGM metallicities up, and a surplus ofgas accretion decreases CGM metallicities comparatively modestly.
MNRAS , 1–23 (2020) R. J. Wright et al.
In this regime, haloes with the lowest accretion rates are thosebeing most significantly influenced by stellar feedback (compareL25-NOFB and L50-NOAGN in Figure 1 and Wright et al. 2020).In such haloes, there is likely a dual effect occurring: there beingless CGM metal dilution due to lack of inflow, but also enhancedmetal-rich outflows from feedback - both acting simultaneously toincrease the CGM’s bulk metal fraction.We also remark that we do not see the same trend for low-massCGM dilution when using the L25-NOFB run. While accretion ratesstill correlate with the scatter in the ISM MZR in this run, this is notthe case for the CGM, where we find that the circum-galactic gas isminimally enriched at low halo mass ( 𝑍 CGM < − 𝑍 (cid:12) ). The lackof CGM metal content is a result of the lack of enriching stellar-feedback driven outflows in this run, with the enriched gas beingmostly confined to the central galaxy. Thus, on average, accretinggas is of similar metallicity to the CGM even at dwarf halo masses,and gas inflow cannot act to dilute its bulk metal content.Our results in §5.1 indicate that halo-scale accretion acts tomodulate the ISM MZR (by altering galaxy-scale accretion rates)and influences, arguably even more strongly, the metal content ofthe CGM in low-mass haloes. This highlights the fact that the CGMis a very dynamic reservoir, particularly in low-mass systems. In this section, we investigate the dependence central galaxy SFRson halo-scale gas accretion rates in EAGLE. We focus specificallyon the sSFR ≡ (cid:164) 𝑀 ★ / 𝑀 ★ - stellar mass plane (Figure 10) to explorethis dependence.Figure 10 shows the stellar mass - sSFR plane in L50-REFat 𝑧 ≈ 𝑧 ≈
2, coloured by Δ (cid:164) 𝑀 gas | 𝑀 ★ , which includes thecontribution from all modes of inflow. To generate our sSFR mainsequence (SFMS), we use all central galaxies in haloes with mass 𝑀 halo (cid:38) 𝑀 (cid:12) and non-zero SFRs. We remark that the normal-isation and shape of our SFMS is consistent with that originallypresented in Schaye et al. (2015) using the public subfind cata-logues. At 𝑧 ≈
0, sSFRs are relatively flat with stellar mass (at ≈ − Gyr − ) up to 𝑀 ★ ≈ 𝑀 (cid:12) , above which there is a down-turn due to the growing passive population.At 𝑧 ≈ 𝑧 ≈
2, where thespread in sSFRs and gas accretion rates are smaller.The bottom panels of Figure 10 show the standard deviationin the SFMS ( 𝜎 sSFR ) as a function of stellar mass, together witha selection of observational datasets (Santini et al. 2017; Davieset al. 2019a). Recent observational work has highlighted that 𝜎 sSFR against 𝑀 ★ has a distinct ’U’ shape, with a minimum spread inter-mediate stellar mass, 𝑀 ★ ≈ . 𝑀 (cid:12) (see Figure 7 in Davies et al.2019a). This has been supported qualitatively with the EAGLE sim-ulations in Katsianis et al. 2019 and the Shark semi-analytic model(Lagos et al. 2018) - who find enhanced diversity in the SFRs oflow- and high-mass systems (driven by stellar and AGN feedback,respectively), with a minimum 𝜎 sSFR at intermediate stellar mass.Our results agree with Katsianis et al. (2019), and demonstrate aminimum in 𝜎 sSFR at intermediate stellar mass, between 10 𝑀 (cid:12) and 10 𝑀 (cid:12) , for both 𝑧 ≈ 𝑧 ≈ Δ (cid:164) 𝑀 gas | 𝑀 ★ (grey), to draw attention to its behaviour relative to 𝜎 sSFR over stellar mass. While we expect a different normalisation, we find that 𝜎 Δ (cid:164) 𝑀 gas decreases monotonically with stellar mass at bothredshifts and does not display the same ’U’ shape over stellar massas 𝜎 sSFR does. We explore this further in Figure 11, which showsgalaxy excess sSFR ( Δ sSFR | 𝑀 ★ ) as a function of excess halo gasaccretion rates (at fixed stellar mass, Δ (cid:164) 𝑀 gas | 𝑀 ★ ) in two bins of stellarmass. We choose these bins to capture the physics behind the flaringof 𝜎 sSFR , which is most significant at low, log ( 𝑀 ★ / 𝑀 (cid:12) ) ∈ [ , ) ,and high, [ , . ) stellar masses.Concentrating on 𝑧 ≈
0, we see that each mass bin exhibitsa positive correlation between Δ sSFR | M ★ and Δ M gas | 𝑀 ★ , with thedynamic range in Δ M gas | 𝑀 ★ being greatest for the low-mass sample.In the low-mass central sample, we find that a factor of 10 increasein gas accretion excess on average leads to an increase in excesssSFR of ≈ . ≈ . 𝑧 ≈
0, 10 𝑀 (cid:12) ≤ 𝑀 ★ < . 𝑀 (cid:12) , weobserve a steeper slope at sub-median gas accretion excess values,with a 0 . ≈ Δ M gas | 𝑀 ★ .Interestingly, we remark that the same relation in the L50-NOAGN run (not shown) does not show the same steep gradient atlow accretion rates for the high stellar mass bin, suggesting that thespread in sSFR is physically linked to reduced gas accretion ontothe galaxy in this mass regime due to AGN activity. Wright et al.(2020) showed that the inclusion of AGN feedback in EAGLE leadsto an average decrease in gas accretion rates onto haloes of ≈ 𝑀 halo ≈ 𝑀 (cid:12) and 10 . 𝑀 (cid:12) , reducing the capabilityof galaxies to replenish their ISM and continue star formation.In massive EAGLE haloes, AGN feedback acts as a maintenancemode, preventing cooling flows onto galaxies (Bower et al. 2017).This means that even though accretion onto haloes can still takeplace in the L50-REF run, much of the accreting gas simply willnot enter the central galaxy. This is shown explicitly in Correaet al. (2018b), where galaxy-scale accretion rates are reduced by ≈ . ≈ 𝑀 halo ≈ . 𝑀 (cid:12) , compared to the relatively modest reduction inhalo-scale accretion rates. This leads to the significant reduction in Δ sSFR | 𝑀 ★ in the high stellar mass bin when Δ (cid:164) 𝑀 gas | 𝑀 ★ < 𝑧 ≈
2, the modulating effect of Δ (cid:164) 𝑀 gas | 𝑀 ★ on Δ sSFR | 𝑀 ★ isstill present, but less clear (as also noted in Figure 10). In general,variation about the SFMS is lower at 𝑧 ≈ 𝑧 ≈
0, witha minimum in 𝜎 sSFR of ≈ .
15 dex and ≈ . ≈
100 galaxiesat 𝑧 ≈
2, providing limited statistical power. We observe a positivetrend between Δ (cid:164) 𝑀 gas | 𝑀 ★ and Δ sSFR | 𝑀 ★ for the low-mass sample,and a similar steepening for the high-mass sample at sub-medianaccretion rates.Our work provides context for the result presented by Katsianiset al. (2019), which demonstrated that stellar and AGN feedback areresponsible for the increase in 𝜎 sSFR at low and high stellar massesrespectively. While we don’t observe a flaring of halo-scale 𝜎 (cid:164) 𝑀 gas at high stellar masses like 𝜎 sSFR , we note that the effect of AGNis to primarily suppress gas accretion to the central galaxy, ratherthan the halo itself (Correa et al. 2018b). We expect that in theirrespective mass regimes, stellar and AGN feedback play a dual rolein modulating galaxy-scale SFRs by (i) removing gas eligible forstar formation (e.g. see Mitchell et al. 2020b; Davies et al. 2019b),and (ii) preventing further gas inflow onto haloes (Wright et al.2020). The galaxies associated with low accretion rates are those MNRAS , 1–23 (2020) he nature of gas accretion to haloes Figure 10.
Top panels: The specific star formation rate (sSFR; (cid:164) 𝑀 ★ / 𝑀 ★ ) - stellar mass plane, coloured by excess gas accretion efficiency ( Δ (cid:164) 𝑀 gas ). The binsin sSFR are spaced in increments of 0 . 𝑧 ≈ 𝑧 ≈
0. In the bottom panels, we also include the standard deviation in excess gasaccretion rate at fixed stellar mass (grey). Left panels correspond to a selection at 𝑧 ≈
0, while right panels correspond to a selection at 𝑧 ≈
2. Error bars showthe 16 th − th percentile range in sSFR. In the top panels, hatched regions show the bootstrap-generated 95% confidence interval error on the sSFR median,while in the bottom panels, the hatched regions show the bootstrap-generated 95% confidence interval error on the sSFR standard deviation ( 𝜎 ). Similarly, thegrey shaded regions in the bottom panels show the bootstrap-generated 95% confidence interval error on 𝜎 Δ (cid:164) 𝑀 gas as a function of stellar mass. Figure 11.
The relationship between excess gas accretion rate ( Δ (cid:164) 𝑀 gas | 𝑀 ★ ) and excess specific star formation rate ( Δ sSFR | 𝑀 ★ ) in L50-REF for 2 bins ofcentral galaxy stellar mass: log ( 𝑀 ★ / 𝑀 (cid:12) ) ∈ [ , ) , and [ , . ) . The left panel shows the relations at 𝑧 ≈
0, while right panel shows the relations at 𝑧 ≈
2. Error bars correspond to 16 th − th percentile ranges, and shaded regions show the bootstrap-generated 95% confidence interval error on the median.MNRAS , 1–23 (2020) R. J. Wright et al. being most strongly influenced by feedback, and thus subject toboth of these modulating processes. Our halo-scale accretion ratemeasurements indicate that feedback-induced modulation of gasaccretion is one of the physical driving forces that regulate galaxySFRs.
In this paper, we present measurements of the diverse properties ofgas accreting to haloes (namely its spatial distribution, metallicity,density and temperature) in the EAGLE simulations, based on themethods outlined in 2 and Wright et al. (2020). We decompose theaccreting gas into a number of contributing channels based on (a)the history of inflow particles (rows 2-4 of Table 2): (i) first-infallmode - inflow particles which have never been identified as partof a halo in the past; (ii) pre-processed mode - particles whichhad been processed in a halo beforehand, but were most recentlyaccreted from the field; and (iii) merger-mode - particles which wereaccreted onto a halo which, at the previous snapshot, were part ofanother halo. In addition to these 3 history-based accretion modes,we also decompose the same (non-merger/smooth) accreting gasinto (b) a hot- and cold-mode, based on a post-accretion (post-shock) temperature cut of 10 . K (rows 5-6 of Table 2).In § 3.1, we focus on the temperature of gas accreting to haloes,specifically the correspondence between the history-based classifi-cation of inflow channels and the hot- and cold- modes of gasaccretion. With L50-REF (reference physics), we find that the hotfraction of first-infall gas is lower than the pre-processed mode forhaloes in the mass range between 10 . 𝑀 (cid:12) and 10 𝑀 (cid:12) at 𝑧 ≈ 𝑧 ≈ 𝑓 cov , defined in §2.4) to quantify how isotropic ( 𝑓 cov →
1) or filamentary ( 𝑓 cov → 𝑧 ≈ 𝑓 cov values of approximately 80% and60% respectively. We also find that hot-mode inflow is similarlymore isotropic than cold-mode inflow, with 𝑧 ≈ 𝑓 cov values ofapproximately 80% and 50% respectively – the temperature-basedinflow channels showing a slightly stronger separation in 𝑓 cov thanthe history-based channels. The disparity in covering fractions iseven greater in the L50-NOAGN run ( ≈ 𝑧 ≈ 𝑍 FI / 𝑍 (cid:12) ≈ − . 𝑍 PP / 𝑍 (cid:12) ≈ − . 𝑀 halo ≈ 𝑀 (cid:12) (Figure 5).We also find that gas accreting to haloes in the L25-NOFB run islower in metal content than accreting gas in L50-REF, which ap-pears to be the result of reduced feedback-driven enrichment. Inhaloes between 10 𝑀 (cid:12) and 10 . 𝑀 (cid:12) (MW-like mass), the metalcontent of pre-processed accreting gas and existing CGM reservoirsare very similar, and grow very closely over cosmic time (within0 . − . 𝑍 / 𝑍 (cid:12) ≈ − . − .
5, see Figure6). This highlights the degeneracy between accreting and outgoing gas when their enrichment is considered in isolation. ISM metallici-ties are systematically enhanced compared to CGM metallicities by ≈ . − . 𝑍 / 𝑍 (cid:12) ≈ − . − . ≈ 𝑛 H (cid:46) − cm − ), with a small coolingtail extending towards the EAGLE imposed equation of state. High-metallicity gas tends to occupy the outskirts of the phase spacedistribution, with a particularly prominent hot and dense ( 𝑇 ≈ K, 𝑛 H ≈ − − cm − ) population at 𝑧 ≈
2. We find that thispopulation corresponds primarily to recycling or merging gas thatwas recently subject to stellar feedback induced heating.In general, we find that the history-based classification of ac-creting gas (specifically, whether the gas has been processed in ahalo previously) is a very good predictor of its metallicity; whilethe classification of accreting gas based on post-shock temperaturebetter predicts the gases’ spatial properties.In § 5, we investigate the influence of halo-scale gas accretionon the properties of halo circum-galactic media, and the ISM oftheir central galaxies. In § 5.1, we show that the gas inflow rates tolow mass haloes ( 𝑀 halo (cid:46) 𝑀 (cid:12) ) play a role in determining themetallicity of a halo’s CGM. This is analogous to the driving forceof galaxy-scale inflow, which is shown to regulate the scatter inthe galaxy-scale stellar mass - ISM metallicity relation (previouslyexplored in the context of EAGLE by Collacchioni et al. 2020and van Loon et al. 2021). The modulation of CGM metallicityis strongest in this mass regime for several reasons: (i) accretingmetallicities are lower, enhancing the metal “dilution” effect; (ii) theaccreted gas constitutes a larger percentage of the gas reservoir ( ≈
50% of CGM gas in 10 𝑀 (cid:12) haloes has been accreted within the lastdynamical timescale, compared to ≈
25% in 10 𝑀 (cid:12) haloes); and(iii) there is less scatter in CGM metallicities in higher mass haloes.This highlights the dynamic nature of the CGM as a reservoir,particularly below masses of 10 𝑀 (cid:12) .Finally, in § 5.2, we explore the influence of halo-scale gas ac-cretion on the scatter of the star-forming main sequence in EAGLE.The characteristic ’U’ shape in 𝜎 sSFR over stellar mass, describedin observations in Davies et al. (2019b) and explored in EAGLE inKatsianis et al. (2019), has previously been explained by stellar feed-back and AGN feedback in the low and high stellar mass regimesrespectively. We show that the central galaxies in haloes experienc-ing low gas accretion rates (driven by stellar and AGN feedback, seeWright et al. 2020) preferentially sit below the star-forming mainsequence. Thus, we find that the preventative influence of thesefeedback mechanisms may offer a natural explanation for variationin central galaxy SFRs, and the consequent flaring of 𝜎 sSFR at bothstellar mass extremes.We remind the reader that the sub-grid models included inEAGLE have been calibrated to match 𝑧 = MNRAS , 1–23 (2020) he nature of gas accretion to haloes represents a field seldom explored directly in observational andtheoretical literature, and we hence remark that it is difficult toascertain the dependence of our quantitative results on the modelused.Our findings repeatedly highlight the dynamic nature of theCGM: its properties set by the continuous interplay of inter-galacticgas inflow and galaxy-driven baryonic feedback processes. Thismakes the CGM of galaxies a particularly pertinent location to studyand constrain different aspects of the baryon cycle, sitting at theinterface between cosmological and galactic scales. Mitchell et al.(2020b) show that there is still considerable uncertainty betweenmodels regarding the spatial scale of outflows and recycling withinand beyond the CGM. EAGLE suggests that outflows due to stellarfeedback are driven to large radii ( (cid:38) 𝑅 ), in the process entrailinga significant amount of CGM gas. Comparatively, the Illustris-TNGand fire models suggest a scenario where outflows are not drivenas far, with lower baryon ejection rates at the halo-scale than atthe galaxy-scale (ultimately leading to higher halo-scale baryonfractions in TNG compared to EAGLE, e.g. Davies et al. 2019b).While the models may disagree on the scale of recycling,Péroux et al. (2020) show at 𝑀 ★ ≈ . 𝑀 (cid:12) and an impact pa-rameter of 𝑏 ≈
100 kpc (slightly shy of 𝑅 ) that EAGLE andTNG produce similar mass flow rates as function of azimuthal an-gle; with inflows and outflows dominating the major and minor axesof galaxies respectively. The same study showed that metal-poor(rich) gas preferentially exists on the major (minor) axis of galaxiesat 𝑏 ≈
100 kpc in EAGLE and Illustris-TNG, however given thedifferent recycling scenarios, the agreement between models willlikely be a function of impact parameter. As mentioned above, weshow that pre-processed gas accretion to haloes in EAGLE closelymimics the integrated metallicity of the CGM. Observations, how-ever, have shown that sight-line measurements of CGM metallicitycan vary greatly in the same halo (up to ≈ and radial variations would manifest in discretesight-line observations, could constitute a promising test of modelaccuracy. Upcoming absorption observations of the CGM (usingstate-of-the-art facilities such as VLT/MUSE and Keck/KCWI) willform an ideal statistical test-bed for such predictions, as well asthose that we present in this paper. ACKNOWLEDGEMENTS
The authors thank Dr. Peter Mitchell for his helpful input and sug-gestions. RW is funded by a Postgraduate Research Scholarshipfrom the University of Western Australia (UWA). CL is funded bythe ARC Centre of Excellence for All Sky Astrophysics in 3 Dimen-sions (ASTRO 3D), through project number CE170100013. CL alsothanks the MERAC Foundation for a Postdoctoral Research Award.CP acknowledges the support ASTRO 3D. This work made use ofthe supercomputer OzSTAR, which is managed through the Centrefor Astrophysics and Supercomputing at Swinburne University ofTechnology. This super-computing facility is supported by Astron-omy Australia Limited and the Australian Commonwealth Govern-ment through the National Collaborative Research InfrastructureStrategy (NCRIS). The EAGLE simulations were performed usingthe DiRAC-2 facility at Durham, managed by the ICC, and thePRACE facility Curie based in France at TGCC, CEA, Bruyeres-le-Chatel. The authors used the following software tools for the dataanalysis and visualisation in the paper: • python3 (van Rossum & Drake Jr 1995) • numpy (Harris et al. 2020) • matplotlib (Hunter 2007) • yt (Turk et al. 2011) DATA AVAILABILITY
Particle data from a subset of the EAGLE runs used for our analy-sis is publicly available at http://dataweb.cosma.dur.ac.uk:8080/eagle-snapshots/ - specifically the L25-REF, L50-REF,L50-NOAGN, and L25N752-RECAL runs. All VELOCIraptor-generated halo catalogues, and TreeFrog merger trees, are avail-able upon request from the corresponding author (RW). The codewe used to generate accretion rates to haloes is available at https://github.com/RJWright25/CHUMM . REFERENCES
Adelberger K. L., Steidel C. C., Shapley A. E., Pettini M., 2003, ApJ, 584,45Afruni A., Fraternali F., Pezzulli G., 2019, A&A, 625, A11Afruni A., Fraternali F., Pezzulli G., 2020, MNRAS,Agertz O., et al., 2007, MNRAS, 380, 963Anglés-Alcázar D., Faucher-Giguère C.-A., Kereš D., Hopkins P. F.,Quataert E., Murray N., 2017, MNRAS, 470, 4698Augustin R., et al., 2019, MNRAS, 489, 2417Berta S., et al., 2020, arXiv e-prints, p. arXiv:2012.01448Binney J., 1977, ApJ, 215, 483Birnboim Y., Dekel A., 2003, MNRAS, 345, 349Bish H. V., Werk J. K., Prochaska J. X., Rubin K. H. R., Zheng Y., O’MearaJ. M., Deason A. J., 2019, ApJ, 882, 76Bordoloi R., et al., 2011, ApJ, 743, 10Borthakur S., et al., 2015, ApJ, 813, 46Bothwell M. S., Maiolino R., Cicone C., Peng Y., Wagg J., 2016, A&A, 595,A48Bouché N., Murphy M. T., Kacprzak G. G., Péroux C., Contini T., MartinC. L., Dessauges-Zavadsky M., 2013, Science, 341, 50Bouché N., et al., 2016, ApJ, 820, 121Bower R. G., Schaye J., Frenk C. S., Theuns T., Schaller M., Crain R. A.,McAlpine S., 2017, MNRAS, 465, 32Brown T., Cortese L., Catinella B., Kilborn V., 2018, MNRAS, 473, 1868Cañas R., Elahi P. J., Welker C., del P Lagos C., Power C., Dubois Y., PichonC., 2019, MNRAS, 482, 2039Chabrier G., 2003, PASP, 115, 763Chowdhury A., Kanekar N., Chengalur J. N., Sethi S., Dwarakanath K. S.,2020, Nature, 586, 369Collacchioni F., Cora S. A., Lagos C. D. P., Vega-Martínez C. A., 2018,MNRAS, 481, 954Collacchioni F., Lagos C. D. P., Mitchell P. D., Schaye J., Wisnioski E., CoraS. A., Correa C. A., 2020, MNRAS, 495, 2827Correa C. A., Schaye J., Wyithe J. S. B., Duffy A. R., Theuns T., Crain R. A.,Bower R. G., 2018a, MNRAS, 473, 538Correa C. A., Schaye J., van de Voort F., Duffy A. R., Wyithe J. S. B., 2018b,MNRAS, 478, 255Crain R. A., et al., 2015, MNRAS, 450, 1937Dalla Vecchia C., Schaye J., 2012, MNRAS, 426, 140Davé R., Finlator K., Oppenheimer B. D., 2012, MNRAS, 421, 98Davies L. J. M., et al., 2019a, MNRAS, 483, 1881Davies J. J., Crain R. A., McCarthy I. G., Oppenheimer B. D., Schaye J.,Schaller M., McAlpine S., 2019b, MNRAS, 485, 3783Davis M., Efstathiou G., Frenk C. S., White S. D. M., 1985, ApJ, 292, 371MNRAS , 1–23 (2020) R. J. Wright et al.
De Lucia G., Xie L., Fontanot F., Hirschmann M., 2020, MNRAS, 498,3215De Rossi M. E., Bower R. G., Font A. S., Schaye J., Theuns T., 2017,MNRAS, 472, 3354Dekel A., Birnboim Y., 2006, MNRAS, 368, 2Dekel A., et al., 2009, Nature, 457, 451Elahi P. J., Thacker R. J., Widrow L. M., 2011, MNRAS, 418, 320Elahi P. J., Cañas R., Poulton R. J. J., Tobar R. J., Willis J. S., Lagos C. d. P.,Power C., Robotham A. S. G., 2019a, Publ. Astron. Soc. Australia, 36,e021Elahi P. J., Poulton R. J. J., Tobar R. J., Cañas R., Lagos C. d. P., Power C.,Robotham A. S. G., 2019b, Publ. Astron. Soc. Australia, 36, e028Fielding D. B., et al., 2020, ApJ, 903, 32Fox A. J., et al., 2014, ApJ, 787, 147Fraternali F., Marasco A., Armillotta L., Marinacci F., 2015, MNRAS, 447,L70Haardt F., Madau P., 2001, in Neumann D. M., Tran J. T. V., eds, Clustersof Galaxies and the High Redshift Universe Observed in X-rays. p. 64( arXiv:astro-ph/0106018 )Hafen Z., et al., 2019, MNRAS, 488, 1248Harris C. R., et al., 2020, Nature, 585, 357Hayes M., Melinder J., Östlin G., Scarlata C., Lehnert M. D., Mannerström-Jansson G., 2016, ApJ, 828, 49Heckman T., Borthakur S., Wild V., Schiminovich D., Bordoloi R., 2017,ApJ, 846, 151Herrera-Camus R., et al., 2020, A&A, 633, L4Hughes T. M., Cortese L., Boselli A., Gavazzi G., Davies J. I., 2013, A&A,550, A115Hunter J. D., 2007, Computing in Science and Engineering, 9, 90Jenkins A., 2013, MNRAS, 434, 2094Kacprzak G. G., Churchill C. W., Steidel C. C., Spitler L. R., HoltzmanJ. A., 2012, MNRAS, 427, 3029Kacprzak G. G., Muzahid S., Churchill C. W., Nielsen N. M., Charlton J. C.,2015, ApJ, 815, 22Kacprzak G. G., et al., 2016, ApJ, 826, L11Kacprzak G. G., Pointon S. K., Nielsen N. M., Churchill C. W., Muzahid S.,Charlton J. C., 2019, ApJ, 886, 91Katsianis A., et al., 2019, ApJ, 879, 11Katz N., Keres D., Dave R., Weinberg D. H., 2003, in Rosenberg J. L.,Putman M. E., eds, Astrophysics and Space Science Library Vol. 281,The IGM/Galaxy Connection. The Distribution of Baryons at z=0. p. 185( arXiv:astro-ph/0209279 ), doi:10.1007/978-94-010-0115-1_34Kennicutt R. C. J., 1983, ApJ, 272, 54Kennicutt Jr. R. C., 1998, ApJ, 498, 541Kereš D., Katz N., Weinberg D. H., Davé R., 2005, MNRAS, 363, 2Kereš D., Katz N., Davé R., Fardal M., Weinberg D. H., 2009, MNRAS,396, 2332Lagos C. D. P., Baugh C. M., Zwaan M. A., Lacey C. G., Gonzalez-PerezV., Power C., Swinbank A. M., van Kampen E., 2014, MNRAS, 440,920Lagos C. d. P., et al., 2016, MNRAS, 459, 2632Lagos C. d. P., Tobar R. J., Robotham A. S. G., Obreschkow D., MitchellP. D., Power C., Elahi P. J., 2018, MNRAS, 481, 3573Lara-López M. A., et al., 2010, A&A, 521, L53Lehner N., Howk J. C., 2011, Science, 334, 955Lehner N., et al., 2013, ApJ, 770, 138Lehner N., O’Meara J. M., Howk J. C., Prochaska J. X., Fumagalli M., 2016,ApJ, 833, 283Lilly S. J., Carollo C. M., Pipino A., Renzini A., Peng Y., 2013, ApJ, 772,119Lokhorst D., Abraham R., van Dokkum P., Wijers N., Schaye J., 2019, ApJ,877, 4Macquart J. P., et al., 2020, Nature, 581, 391Madau P., Dickinson M., 2014, ARA&A, 52, 415Maiolino R., et al., 2008, A&A, 488, 463Mannucci F., Cresci G., Maiolino R., Marconi A., Gnerucci A., 2010, MN-RAS, 408, 2115Marasco A., Fraternali F., Binney J. J., 2012, MNRAS, 419, 1107 McAlpine S., et al., 2016, Astronomy and Computing, 15, 72Mitchell P. D., Schaye J., Bower R. G., 2020a, arXiv e-prints, p.arXiv:2005.10262Mitchell P. D., Schaye J., Bower R. G., Crain R. A., 2020b, MNRAS, 494,3971Nelson D., Vogelsberger M., Genel S., Sijacki D., Kereš D., Springel V.,Hernquist L., 2013, MNRAS, 429, 3353Nelson D., Genel S., Vogelsberger M., Springel V., Sijacki D., Torrey P.,Hernquist L., 2015, MNRAS, 448, 59Nelson D., et al., 2020, MNRAS, 498, 2391Nielsen N. M., Kacprzak G. G., Pointon S. K., Murphy M. T., ChurchillC. W., Davé R., 2020, arXiv e-prints, p. arXiv:2002.08516Ocvirk P., Pichon C., Teyssier R., 2008, MNRAS, 390, 1326Oppenheimer B. D., Schaye J., Crain R. A., Werk J. K., Richings A. J., 2018,MNRAS, 481, 835Oppenheimer B. D., et al., 2020, MNRAS, 491, 2939Péroux C., et al., 2016, MNRAS, 457, 903Péroux C., Nelson D., van de Voort F., Pillepich A., Marinacci F., Vogels-berger M., Hernquist L., 2020, MNRAS, 499, 2462Planck Collaboration et al., 2014, A&A, 571, A16Pointon S. K., Kacprzak G. G., Nielsen N. M., Muzahid S., Murphy M. T.,Churchill C. W., Charlton J. C., 2019, ApJ, 883, 78Prochaska J. X., Hennawi J. F., Simcoe R. A., 2013, ApJ, 762, L19Prochaska J. X., et al., 2017, ApJ, 837, 169Rees M. J., Ostriker J. P., 1977, MNRAS, 179, 541Roberts-Borsani G. W., Saintonge A., 2019, MNRAS, 482, 4111Rubin K. H. R., 2017, Gas Accretion Traced in Absorption in Galaxy Spec-troscopy. p. 95, doi:10.1007/978-3-319-52512-9_5Rubin K. H. R., Prochaska J. X., Koo D. C., Phillips A. C., 2012, ApJ, 747,L26Sánchez Almeida J., 2017, Gas Accretion and Star Formation Rates. p. 67,doi:10.1007/978-3-319-52512-9_4Sancisi R., Fraternali F., Oosterloo T., van der Hulst T., 2008, A&ARv, 15,189Santini P., et al., 2017, ApJ, 847, 76Schaller M., Dalla Vecchia C., Schaye J., Bower R. G., Theuns T., CrainR. A., Furlong M., McCarthy I. G., 2015, MNRAS, 454, 2277Schaye J., Dalla Vecchia C., 2008, MNRAS, 383, 1210Schaye J., et al., 2015, MNRAS, 446, 521Schroetter I., et al., 2016, ApJ, 833, 39Shen S., Madau P., Aguirre A., Guedes J., Mayer L., Wadsley J., 2012, ApJ,760, 50Springel V., 2005, MNRAS, 364, 1105Springel V., Di Matteo T., Hernquist L., 2005, ApJ, 620, L79Steidel C. C., Bogosavljević M., Shapley A. E., Kollmeier J. A., ReddyN. A., Erb D. K., Pettini M., 2011, ApJ, 736, 160Stern J., Fielding D., Faucher-Giguère C.-A., Quataert E., 2020, MNRAS,492, 6042Stewart K. R., Kaufmann T., Bullock J. S., Barton E. J., Maller A. H.,Diemand J., Wadsley J., 2011, ApJ, 738, 39Stocke J. T., Penton S. V., Danforth C. W., Shull J. M., Tumlinson J., McLinK. M., 2006, ApJ, 641, 217The LUVOIR Team 2019, arXiv e-prints, p. arXiv:1912.06219Tumlinson J., et al., 2011, Science, 334, 948Turk M. J., Smith B. D., Oishi J. S., Skory S., Skillman S. W., Abel T.,Norman M. L., 2011, ApJS, 192, 9Turner M. L., Schaye J., Crain R. A., Rudie G., Steidel C. C., Strom A.,Theuns T., 2017, MNRAS, 471, 690Voit G. M., 2018, ApJ, 868, 102Werk J. K., et al., 2014, ApJ, 792, 8White S. D. M., Frenk C. S., 1991, ApJ, 379, 52White S. D. M., Rees M. J., 1978, MNRAS, 183, 341Wiersma R. P. C., Schaye J., Theuns T., Dalla Vecchia C., Tornatore L.,2009, MNRAS, 399, 574Williams C. C., et al., 2020, arXiv e-prints, p. arXiv:2012.01433Wisotzki L., et al., 2018, Nature, 562, 229Wright R. J., Lagos C. d. P., Power C., Mitchell P. D., 2020, MNRAS,Zabl J., et al., 2019, MNRAS, 485, 1961 MNRAS000
De Lucia G., Xie L., Fontanot F., Hirschmann M., 2020, MNRAS, 498,3215De Rossi M. E., Bower R. G., Font A. S., Schaye J., Theuns T., 2017,MNRAS, 472, 3354Dekel A., Birnboim Y., 2006, MNRAS, 368, 2Dekel A., et al., 2009, Nature, 457, 451Elahi P. J., Thacker R. J., Widrow L. M., 2011, MNRAS, 418, 320Elahi P. J., Cañas R., Poulton R. J. J., Tobar R. J., Willis J. S., Lagos C. d. P.,Power C., Robotham A. S. G., 2019a, Publ. Astron. Soc. Australia, 36,e021Elahi P. J., Poulton R. J. J., Tobar R. J., Cañas R., Lagos C. d. P., Power C.,Robotham A. S. G., 2019b, Publ. Astron. Soc. Australia, 36, e028Fielding D. B., et al., 2020, ApJ, 903, 32Fox A. J., et al., 2014, ApJ, 787, 147Fraternali F., Marasco A., Armillotta L., Marinacci F., 2015, MNRAS, 447,L70Haardt F., Madau P., 2001, in Neumann D. M., Tran J. T. V., eds, Clustersof Galaxies and the High Redshift Universe Observed in X-rays. p. 64( arXiv:astro-ph/0106018 )Hafen Z., et al., 2019, MNRAS, 488, 1248Harris C. R., et al., 2020, Nature, 585, 357Hayes M., Melinder J., Östlin G., Scarlata C., Lehnert M. D., Mannerström-Jansson G., 2016, ApJ, 828, 49Heckman T., Borthakur S., Wild V., Schiminovich D., Bordoloi R., 2017,ApJ, 846, 151Herrera-Camus R., et al., 2020, A&A, 633, L4Hughes T. M., Cortese L., Boselli A., Gavazzi G., Davies J. I., 2013, A&A,550, A115Hunter J. D., 2007, Computing in Science and Engineering, 9, 90Jenkins A., 2013, MNRAS, 434, 2094Kacprzak G. G., Churchill C. W., Steidel C. C., Spitler L. R., HoltzmanJ. A., 2012, MNRAS, 427, 3029Kacprzak G. G., Muzahid S., Churchill C. W., Nielsen N. M., Charlton J. C.,2015, ApJ, 815, 22Kacprzak G. G., et al., 2016, ApJ, 826, L11Kacprzak G. G., Pointon S. K., Nielsen N. M., Churchill C. W., Muzahid S.,Charlton J. C., 2019, ApJ, 886, 91Katsianis A., et al., 2019, ApJ, 879, 11Katz N., Keres D., Dave R., Weinberg D. H., 2003, in Rosenberg J. L.,Putman M. E., eds, Astrophysics and Space Science Library Vol. 281,The IGM/Galaxy Connection. The Distribution of Baryons at z=0. p. 185( arXiv:astro-ph/0209279 ), doi:10.1007/978-94-010-0115-1_34Kennicutt R. C. J., 1983, ApJ, 272, 54Kennicutt Jr. R. C., 1998, ApJ, 498, 541Kereš D., Katz N., Weinberg D. H., Davé R., 2005, MNRAS, 363, 2Kereš D., Katz N., Davé R., Fardal M., Weinberg D. H., 2009, MNRAS,396, 2332Lagos C. D. P., Baugh C. M., Zwaan M. A., Lacey C. G., Gonzalez-PerezV., Power C., Swinbank A. M., van Kampen E., 2014, MNRAS, 440,920Lagos C. d. P., et al., 2016, MNRAS, 459, 2632Lagos C. d. P., Tobar R. J., Robotham A. S. G., Obreschkow D., MitchellP. D., Power C., Elahi P. J., 2018, MNRAS, 481, 3573Lara-López M. A., et al., 2010, A&A, 521, L53Lehner N., Howk J. C., 2011, Science, 334, 955Lehner N., et al., 2013, ApJ, 770, 138Lehner N., O’Meara J. M., Howk J. C., Prochaska J. X., Fumagalli M., 2016,ApJ, 833, 283Lilly S. J., Carollo C. M., Pipino A., Renzini A., Peng Y., 2013, ApJ, 772,119Lokhorst D., Abraham R., van Dokkum P., Wijers N., Schaye J., 2019, ApJ,877, 4Macquart J. P., et al., 2020, Nature, 581, 391Madau P., Dickinson M., 2014, ARA&A, 52, 415Maiolino R., et al., 2008, A&A, 488, 463Mannucci F., Cresci G., Maiolino R., Marconi A., Gnerucci A., 2010, MN-RAS, 408, 2115Marasco A., Fraternali F., Binney J. J., 2012, MNRAS, 419, 1107 McAlpine S., et al., 2016, Astronomy and Computing, 15, 72Mitchell P. D., Schaye J., Bower R. G., 2020a, arXiv e-prints, p.arXiv:2005.10262Mitchell P. D., Schaye J., Bower R. G., Crain R. A., 2020b, MNRAS, 494,3971Nelson D., Vogelsberger M., Genel S., Sijacki D., Kereš D., Springel V.,Hernquist L., 2013, MNRAS, 429, 3353Nelson D., Genel S., Vogelsberger M., Springel V., Sijacki D., Torrey P.,Hernquist L., 2015, MNRAS, 448, 59Nelson D., et al., 2020, MNRAS, 498, 2391Nielsen N. M., Kacprzak G. G., Pointon S. K., Murphy M. T., ChurchillC. W., Davé R., 2020, arXiv e-prints, p. arXiv:2002.08516Ocvirk P., Pichon C., Teyssier R., 2008, MNRAS, 390, 1326Oppenheimer B. D., Schaye J., Crain R. A., Werk J. K., Richings A. J., 2018,MNRAS, 481, 835Oppenheimer B. D., et al., 2020, MNRAS, 491, 2939Péroux C., et al., 2016, MNRAS, 457, 903Péroux C., Nelson D., van de Voort F., Pillepich A., Marinacci F., Vogels-berger M., Hernquist L., 2020, MNRAS, 499, 2462Planck Collaboration et al., 2014, A&A, 571, A16Pointon S. K., Kacprzak G. G., Nielsen N. M., Muzahid S., Murphy M. T.,Churchill C. W., Charlton J. C., 2019, ApJ, 883, 78Prochaska J. X., Hennawi J. F., Simcoe R. A., 2013, ApJ, 762, L19Prochaska J. X., et al., 2017, ApJ, 837, 169Rees M. J., Ostriker J. P., 1977, MNRAS, 179, 541Roberts-Borsani G. W., Saintonge A., 2019, MNRAS, 482, 4111Rubin K. H. R., 2017, Gas Accretion Traced in Absorption in Galaxy Spec-troscopy. p. 95, doi:10.1007/978-3-319-52512-9_5Rubin K. H. R., Prochaska J. X., Koo D. C., Phillips A. C., 2012, ApJ, 747,L26Sánchez Almeida J., 2017, Gas Accretion and Star Formation Rates. p. 67,doi:10.1007/978-3-319-52512-9_4Sancisi R., Fraternali F., Oosterloo T., van der Hulst T., 2008, A&ARv, 15,189Santini P., et al., 2017, ApJ, 847, 76Schaller M., Dalla Vecchia C., Schaye J., Bower R. G., Theuns T., CrainR. A., Furlong M., McCarthy I. G., 2015, MNRAS, 454, 2277Schaye J., Dalla Vecchia C., 2008, MNRAS, 383, 1210Schaye J., et al., 2015, MNRAS, 446, 521Schroetter I., et al., 2016, ApJ, 833, 39Shen S., Madau P., Aguirre A., Guedes J., Mayer L., Wadsley J., 2012, ApJ,760, 50Springel V., 2005, MNRAS, 364, 1105Springel V., Di Matteo T., Hernquist L., 2005, ApJ, 620, L79Steidel C. C., Bogosavljević M., Shapley A. E., Kollmeier J. A., ReddyN. A., Erb D. K., Pettini M., 2011, ApJ, 736, 160Stern J., Fielding D., Faucher-Giguère C.-A., Quataert E., 2020, MNRAS,492, 6042Stewart K. R., Kaufmann T., Bullock J. S., Barton E. J., Maller A. H.,Diemand J., Wadsley J., 2011, ApJ, 738, 39Stocke J. T., Penton S. V., Danforth C. W., Shull J. M., Tumlinson J., McLinK. M., 2006, ApJ, 641, 217The LUVOIR Team 2019, arXiv e-prints, p. arXiv:1912.06219Tumlinson J., et al., 2011, Science, 334, 948Turk M. J., Smith B. D., Oishi J. S., Skory S., Skillman S. W., Abel T.,Norman M. L., 2011, ApJS, 192, 9Turner M. L., Schaye J., Crain R. A., Rudie G., Steidel C. C., Strom A.,Theuns T., 2017, MNRAS, 471, 690Voit G. M., 2018, ApJ, 868, 102Werk J. K., et al., 2014, ApJ, 792, 8White S. D. M., Frenk C. S., 1991, ApJ, 379, 52White S. D. M., Rees M. J., 1978, MNRAS, 183, 341Wiersma R. P. C., Schaye J., Theuns T., Dalla Vecchia C., Tornatore L.,2009, MNRAS, 399, 574Williams C. C., et al., 2020, arXiv e-prints, p. arXiv:2012.01433Wisotzki L., et al., 2018, Nature, 562, 229Wright R. J., Lagos C. d. P., Power C., Mitchell P. D., 2020, MNRAS,Zabl J., et al., 2019, MNRAS, 485, 1961 MNRAS000 , 1–23 (2020) he nature of gas accretion to haloes Zahedy F. S., Chen H.-W., Johnson S. D., Pierce R. M., Rauch M., HuangY.-H., Weiner B. J., Gauthier J.-R., 2019, MNRAS, 484, 2257Zhu G., et al., 2014, MNRAS, 439, 3139van Loon M. L., Mitchell P. D., Schaye J., 2021, arXiv e-prints, p.arXiv:2101.11021van Rossum G., Drake Jr F. L., 1995, Python reference manual. Centrumvoor Wiskunde en Informatica Amsterdamvan de Voort F., Schaye J., 2012, MNRAS, 423, 2991van de Voort F., Schaye J., Booth C. M., Haas M. R., Dalla Vecchia C.,2011, MNRAS, 414, 2458van de Voort F., Bahé Y. M., Bower R. G., Correa C. A., Crain R. A., SchayeJ., Theuns T., 2017, MNRAS, 466, 3460
APPENDIX A: MAXIMUM TEMPERATURE OFACCRETING GAS PARTICLES
Figure A1 illustrates the mass-weighted PDF of the maximum tem-perature gas particles reached prior to accretion at 𝑧 ≈ 𝑧 ≈ 𝑀 (cid:12) and 10 . 𝑀 (cid:12) , and split the accreting particlesbased on their inflow channel. We quantify the amount of gas heatedby stellar feedback by identifying gas particles with 𝑇 max values ina band of 0 . Δ 𝑇 SNe value of 10 . K, and quote thisproportion as a fraction of mass in the legend.Encouragingly, we find that the first-infall mode has a verysmall proportion of contamination by stellar feedback at ≈ − .
5% for both redshift selections. In comparison, 12 −
13% of pre-processed accreting gas mass has been directly affected by stellarfeedback. We believe the slight contamination in the first-infallmode could be a result of the simulation cadence - if a particle wasaccreted onto a halo and swiftly ejected within the gap betweensimulation outputs, our algorithm would not identify the particle as“processed”.The significant proportion of pre-processed and merger gaswith 𝑇 max values near the Δ 𝑇 SNe value highlights the value in sep-arating inflow modes based on current temperature (as in Correaet al. 2018b) as opposed to their 𝑇 max value. Using a 𝑇 max cutoffwould not allow particles to cool and does not reflect the extent ofvirial shock-heating which we are attempting to quantify. APPENDIX B: CONVERGENCE OF COVERINGFRACTIONS
In Figure B1, we compare total covering fractions and accretionefficiencies of haloes (in the mass range 10 𝑀 (cid:12) − 𝑀 (cid:12) ) inthe L50-OLDSPH and L25-RECAL runs to the reference physicsrun (L50-REF). This allows us to measure the influence of SPHimplementation and mass resolution respectively on values of 𝑓 cov (defined in Equation 8) and total accretion rates.The L50-OLDSPH EAGLE run (see Schaller et al. 2015) usesan older density-SPH formulation, which is known for its weaknessat modelling discontinuities and mixing (e.g. Agertz et al. 2007).Given the established mixing problems and expectation for more“clumpy” structure formation in this run, we compare the coveringfraction of inflow between this run and the L50-REF run in thetop left panel of Figure B1. We find that across cosmic time, gasaccretion onto haloes is marginally (but significantly) more colli-mated than accreting gas in L50-REF by ≈ − 𝑧 = . with 2 × particles. These simulations havebetter mass and spatial resolution than the intermediate-resolutionof the L50-REF simulation by factors of 8 and 2, respectively.We check the weak convergence of our 𝑓 cov parameter by us-ing the L25N752-RECAL run (top right panel, Figure B1), with 4recalibrated parameters that were tuned to reproduce the 𝑧 = 𝑓 cov value over redshift, thecovering fraction of accreting gas in L25-RECAL and L50-REFare largely consistent. At high redshift, 𝑧 (cid:38)
1, covering fractionsin L25-RECAL may be marginally lower than we find in L50-REF,however it is difficult to ascertain the significance of this disparitywith the limited number of sufficiently sized haloes in L25-RECAL.We thus conclude that covering fractions appear to be consistentbetween L25-RECAL and L50-REF, indicating that there is weakconvergence in the 𝑓 cov parameter. This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS , 1–23 (2020) R. J. Wright et al.
Figure A1.
The mass-weighted PDF of pre-accretion gas 𝑇 max values in L50-REF, split by history-based accretion mode. The PDF is shown for 𝑧 ≈ 𝑧 ≈ 𝑀 (cid:12) < 𝑀 halo < . 𝑀 (cid:12) . These distributionsreflect the maximum temperatures that gas particles had reached prior to accretion. We also included the mass-weighted median 𝑇 max values as dashed lines.We quantify the amount of gas heated by stellar feedback by identifying gas particles with 𝑇 max values in a band of 0 . Δ 𝑇 SNe value of 10 . K,quoted in the legend.
Figure B1.
Top panels: The median covering fraction, 𝑓 cov , of gas accreting to selected EAGLE haloes as a function of the scale factor, 𝑎 = /( + 𝑧 ) ,comparing L50-REF with L50-OLDSPH in the left panel and L50-REF with L25-RECAL in the right panel. We note this 𝑓 cov in this plot is not broken downinto different modes of accretion, but is calculated for all accreting particles regardless of their history or temperature. Haloes are included at each snap ifthey are (i) within the mass range 10 𝑀 (cid:12) (cid:46) 𝑀 halo (cid:46) 𝑀 (cid:12) , and (ii) have accreted ≥ gas particles since the last snapshot. Bottom panels: the medianhalo-scale gas accretion efficiency (using the same halo selections as above) as a function of scale factor, comparing L50-REF with L50-OLDSPH in the leftpanel and L50-REF with L25-RECAL in the right panel. In each panel, we also include the bootstrap-generated 95% confidence interval on the median from100 resamples of the median, with half of the respective populations. MNRAS000