Co-Evolution of Halos, Galaxies & SMBHs in IllustrisTNG – Phase Framework & Observational Signposts

Abstract and Central Aims

  • IllustrisTNG (TNG100-1) is used to dissect co-evolution of dark-matter halos (DMHs), central galaxies, and super-massive black holes (SMBHs).

  • Individual MBH–M★ tracks decompose into four time-ordered phases, each separated by a transition point that can be quantitatively linked to physical criteria.

  • Overarching goal: derive necessary & sufficient conditions for phase changes, expose governing processes, and map them onto observable scaling relations that can test sub-grid physics.

ΛCDM Structure Formation Primer

  • Growth is hierarchical: small structures merge to make larger objects, gas cools, forms stars, occasionally produces central BHs.

  • Feedback is bidirectional: small-scale (stellar/AGN) energy input reshapes halo-scale gas; conversely halo accretion regulates what baryons are available.

  • Key observational constraints: M★{-}Mh, M{BH}{-}M★, M{BH}{-}Mh, galaxy/AGN luminosity & mass functions, clustering, CGM thermodynamics.

Simulation & Sample

  • IllustrisTNG100-1

    • Box \approx 110.7\,\mathrm{cMpc}; 2\times1820^3 elements; m{b}=1.4\times10^{6}\,M\odot.

    • Cosmology: h=0.6774,\;\Omegam=0.3089,\;\Omegab=0.0486,\;\Omega_\Lambda=0.6911 (Planck-2015).

  • Group finding: FoF (b=0.2); Subfind for sub-halos; central = most massive subhalo.

  • Merger trees: baryonic SubLink.

  • Derived quantities

    • Mh inside R{200\bar\rho}; V{h}=\sqrt{GMh/R_h}.

    • M★ within 2R{★,1/2}.

    • M_{BH} = sum of BH particles in subhalo.

    • Specific rates \dot M / M → sHAR, sSFR, sBHAR.

    • Quenching criterion: \mathrm{sSFR}<10^{-11}\,\mathrm{yr^{-1}} for ≥3 consecutive snapshots.

  • Final analysis sample (1425 galaxies)

    1. Central at z=0(no backsplash);

    2. Mh≥5\times10^{11}M\odot,\;M★≥10^{9}M\odot and host an SMBH;

    3. Quenched at z=0;

    4. Tree traced to z≈7.

Phenomenological Fit & Phase Boundaries

  • Fit each MBH–M★ history with piece-wise function:

    y(x)=\begin{cases}
    \frac{(a+b)^3}{2}\left[\frac{1}{(x-x0-a)^2}-\frac{1}{a^2}\right]+y0,&x<x0\[4pt] k(x-x0)+y0,&x\ge x0\end{cases}

    where y\equiv\log M{BH},\;x\equiv\log M★.

  • Three transition abscissae

    • x{12}=x0-b (slope becomes 1).

    • x{23}=x0 (end of rapid BH growth).

    • t{34}=tq (quenching; linear piece ends).

  • Phases: 1-SF dominated, 2-Rapid BH accretion, 3-Self-regulated, 4-Merger dominated.

Phase-1: Star-Formation Dominated

  • SMBH seed: M{seed}=1.18\times10^{6}M\odot planted once Mh>7.38\times10^{10}M\odot.

  • Bondi accretion \dot M{BH}=As M{BH}^2 with As=\frac{4\pi G^2\rho{gas}}{cs^3} constant because star-forming gas follows effective EOS.

  • Analytical growth: M{BH}(t)=\frac{M{seed}}{1-AsM{seed}(t-t{seed})} ⇒ blow-up at \tau1^{max}=(AsM{seed})^{-1}\approx1\text{–}2\,\mathrm{Gyr}.

  • Transition when \mathrm{sBHAR}=\mathrm{sSFR} (feedback energy ratio E{AGN}/E{SF}≈3000\,\dot M{BH}/\dot M★ reaches unity around M{BH}/M★\sim10^{-3}).

Phase-2: SMBH-Accretion Dominated

  • Exponential BH growth (Bondi) until AGN thermal feedback unbinds galactic gas.

  • Condition: E{AGN}^{therm}\gtrsim\eta{eff}^{-1}E{bind} where \eta{eff}\approx0.1.

    • E{AGN}=\eta{therm}M{BH}c^2,\;\eta{therm}=0.02.

    • E{bind}\approx\tfrac12\sum m{gas}\phi{gas} within 2R{★,1/2}.

  • Duration \tau2\lesssim1\,\mathrm{Gyr}; inside-out gas depletion: cold gas drops within 0.2R{★,1/2}, halo gas unchanged.

Phase-3: Self-Regulation Dominated

  • Thermal-mode feedback keeps galaxy in quasi-equilibrium:
    \eta{eff}\eta{therm}M{BH}\sim f{gas}f{★}^{-5/3}M★^{5/3} → predicts M{BH}\propto M★^{5/3} near Mh\sim10^{12}M\odot.

  • Observed in simulation: slope k≈1.35 anti-correlates with initial BH-to-stellar mass ratio (self-correcting).

  • Eddington ratio threshold for kinetic mode: \chi{th}=\min\bigl[0.02\bigl(\frac{M{BH}}{10^8M_\odot}\bigr)^2,0.1\bigr].

    • Low-mass halos: transition coincides with halo entering slow-accretion phase (peak V_{max} time).

    • Massive halos: fixed \chi_{th}=0.1 ⇒ transition at z\approx2 irrespective of halo growth.

Phase-3 → Phase-4 & Quenching Criterion

  • Kinetic feedback must balance cooling of all non-SF gas in subhalo:
    \dot E{kin}=\eta{kin}\dot M{BH}c^2\approx\dot E{cool,sub}.

  • Quenching lag tq-t{kin}\lesssim1\,\mathrm{Gyr} for Mh<10^{12.3}M\odot; extended lags at higher masses due to merger-induced gas supply.

  • After quenching the balance \dot E{kin}\simeq\dot E{cool} persists.

Phase-4: Merger Dominated Growth

  • In-situ SFR and BHAR nearly zero; mass assembly via:

    • Ex-situ stars: fraction f{★,ex}^{[tq,0]} rises with halo mass; can exceed 80\% for Mh>10^{12.6}M\odot.

    • BH-BH mergers dominate BH mass growth in quenched centrals.

  • Mergers drive (M{BH},M★) toward 1:1 vector, steepening high-mass end of scaling relations.

Evolution of Scaling Relations

  • At t{23}: M{BH}\propto M_★^{\gamma} with \gamma\approx5/3 (thermal feedback threshold).

  • At t_q: shallower (\gamma<1) because kinetic feedback triggered earlier for massive BHs.

  • At z=0: near-linear (\gamma\approx1) at high masses; low-mass end linear in TNG due to late seeding.

  • MBH–Mh relation bends; peak correlation near Mh\approx10^{12}M\odot where f_{gas} maximal.

Observable Diagnostics & Tests

  • Edges/Slices: scaling relations at successive $z$ provide time slices of flow; compare to predicted phase edges.

  • Derivatives: combining BHAR + SFR observations yields motion vectors in MBH–M★ plane → phase identification.

  • High-z probes: JWST ‘Little Red Dots’ likely Phase-2 systems; Pop-III star clusters could reveal seeding stage.

  • Low-z dissection: IFU kinematics (in-situ vs ex-situ stars) + lensing BH mass can isolate post-quench merger growth.

Key Numerical/Physical Parameters (TNG)

  • SMBH seed mass 1.18\times10^6M\odot @ Mh>7.38\times10^{10}M_\odot.

  • Bondi accretion cap = Eddington.

  • Thermal-mode efficiency \eta{therm}=0.02; kinetic-mode coupling \eta{kin}=\min(\rho/0.05\rho_{SF},0.2).

  • Quenching sSFR threshold 10^{-11}\,\mathrm{yr^{-1}}.

Limitations & Sensitivities

  • Phase-1 duration and low-mass scaling depend on seed choice & gas EOS.

  • Phase-2 length responds to star-forming threshold density and Bondi kernel.

  • \chi{th}(M{BH}) curve shapes t{kin} distribution and M{BH}{-}M_★ slope at quenching.

  • Efficiencies \eta{therm},\eta{kin},\eta_{eff} dictate normalisations of all scaling laws.

Comparison Across Simulations

  • EAGLE: stronger SN winds → prolonged Phase-1, non-linear low-mass MBH–M★ at all z.

  • SIMBA: delayed seeding ⇒ non-linear relation persists to z=0.

  • Horizon-AGN: weak SN feedback → Phase-1 absent, early linearity.

Study-Guide Take-Aways

  • Memorise four phases, their governing physics & duration hierarchy \tau1<\tau2\ll\tau3,\tau4.

  • Master transition criteria:

    1. \mathrm{sBHAR}=\mathrm{sSFR} (start rapid BH growth).

    2. E{AGN}^{therm}\gtrsim\eta{eff}^{-1}E_{bind} (end rapid growth).

    3. \chi<\chi_{th} (switch to kinetic mode).

    4. \dot E{kin}\approx\dot E{cool} (quenching).

  • Be able to derive M{BH}\propto M★^{5/3} from energy balance.

  • Recognise observational proxies (e.g., entropy, Pop-III clusters, merger signatures) for each phase.

  • Understand how sub-grid choices (seeding, feedback efficiencies) propagate into macroscopic observables.

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