An analytic model of angular momentum transport by gravitational torques: from galaxies to massive black holes

By P. Hopkins, E. Quataert. 2010

188 citations recorded by the source corpus.

We present analytic calculations of angular momentum transport and gas inflow in galaxies, from scales of ∼ kpc to deep inside the potential of a central massive black hole (BH). We compare these analytic calculations to numerical simulations and use them to develop a sub-grid model of BH growth that can be incorporated into semi-analytic calculations or cosmological simulations. Motivated by both analytic calculations and simulations of gas inflow in galactic nuclei, we argue that the strongest torque on gas arises when non-axisymmetric perturbations to the stellar gravitational potential produce orbit crossings and shocks in the gas. This is true both at large radii ∼0.01―1 kpc, where bar-like stellar modes dominate the non-axisymmetric potential, and at smaller radii ≲10 pc, where a lopsided/eccentric stellar disc dominates. The traditional orbit-crossing criterion is not always adequate to predict the locations of, and inflow due to, shocks in gas+stellar discs with finite sound speeds. We derive a modified criterion that predicts the presence of shocks in stellar-dominated systems even absent formal orbit crossing. We then derive analytic expressions for the loss of angular momentum and the resulting gas inflow rates in the presence of such shocks. We test our analytic predictions using hydrodynamic simulations at a range of galactic scales, and show that they successfully predict the mass inflow rates and quasi-steady gas surface densities with a small scatter ≃0.3 dex. We use our analytic results to construct a new estimate of the BH accretion rate given galaxy properties at larger radii, for use in galaxy and cosmological simulations and semi-analytic models. While highly simplified, this accretion rate predictor captures the key scalings in the numerical simulations. By contrast, alternate estimates such as the local viscous accretion rate or the spherical Bondi rate fail systematically to reproduce the simulations and have significantly larger scatter.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/1215cc15a500a0eec36d7799e528a303a9b4492b

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Citations in the corpus

Gravitational torque-driven black hole growth and feedback in cosmological simulations (2016, methodology): “…factor T is intended to capture processes that affect the radial transport of gas on unresolved scales,3 such as star formation, feedback from stars and the central black hole, and mass-loss in winds from the accretion disc, which were not modelled explicitly in Hopkins & Quataert (2011).”
The Romulus cosmological simulations: a physical approach to the formation, dynamics and accretion models of SMBHs (2016, background): “However, even with a well motivated (but often poorly constrained) density boost, Bondi-Hoyle accretion is unable to account for angular momentum support, which often dominates the dynamics of cold gas at resolved scales, as in the disks of star forming galaxies (Hopkins & Quataert 2010, 2011).”
Stellar and Quasar Feedback in Concert: Effects on AGN Accretion, Obscuration, and Outflows (2015, methodology): “This agrees well with the analytic (Hopkins & Quataert 2011) predictions for “gravitational torque”-driven accretion.”
FEEDBACK FROM CENTRAL BLACK HOLES IN ELLIPTICAL GALAXIES: TWO-DIMENSIONAL MODELS COMPARED TO ONE-DIMENSIONAL MODELS (2010, methodology): “In future work, we will expand our treatment to include angular momentum transport via the standard α prescription (Shakura & Sunyaev 1973) and more recent models based on gravitational torques (Hopkins & Quataert 2010a).”
Morphologies of z ∼ 0.7 AGN host galaxies in CANDELS: no trend of merger incidence with AGN luminosity (2014, background): “Some theoretical models suggest that torques on galaxy wide scales (Hopkins & Quataert 2011; Anglés-Alcázar et al. 2013) or violent disc instabilities driven by cold flows or other processes (e.g. Dekel et al. 2009) could be drivers for AGN activity.”
Simulating galaxy formation with black hole driven thermal and kinetic feedback (2016, background): “First, the detailed physical mechanisms of both accretion on to SMBHs (Hopkins & Quataert 2010, 2011; Anglés-Alcázar et al. 2013; Gaspari et al. 2013; Anglés-Alcázar et al. 2015, 2016; Curtis & Sijacki 2015, 2016; Emsellem et al. 2015; Rosas-Guevara et al. 2015) and the AGN-gas interaction…”
The impact of angular momentum on black hole accretion rates in simulations of galaxy formation (2013, background): “On the scales relevant to our simulations, the appropriate transport mechanism is likely to be gravitational instability (Hopkins & Quataert 2010, 2011) rather than the magnetorotational instability.”
Physical Models of Galaxy Formation in a Cosmological Framework (2014, background): “…analytic work into zooms and cosmological runs, Anglés-Alcázar et al. (2013a) and Anglés-Alcázar et al. (2013b) showed that this torque-limited accretion behaves qualitatively differently than Bondi accretion, since in the Hopkins & Quataert (2011) model, the exponent of BH growth is p = 1 6 .”
Theoretical Challenges in Galaxy Formation (2016, background): “Hopkins & Quataert (2011) argue that ’torque limited’ accretion behaves qualitatively different to other accretion models and produces reasonable scaling relations with a smaller scatter.”
The Coevolution of Galaxies and Supermassive Black Holes: Insights from Surveys of the Contemporary Universe (2014, background): “There are three main features that we need to consider when examining the fueling of AGN: the origin of the fueling gas, the mechanism by which it is transported to the vicinity of the black hole (e.g. Hopkins & Quataert 2011), and the nature of the accretion flow onto the black hole.”
Star formation in galaxy mergers with realistic models of stellar feedback and the interstellar medium (2012, background): “The slope of the central mass profile is set by equilibrium between gravitationally driven inflow and star formation (Hopkins & Quataert 2011b).”
HOW EMPTY ARE DISK GAPS OPENED BY GIANT PLANETS (2013, background): “…and found results forΣgap that matched those with our standard accreting boundaries to better than 1%. non-linear at launch, the torque exerted on the disk by the planet scales asq1(h/r)0 (e.g., Hopkins and Quataert 2011, their section 2.3).8 Then the same arguments in§1.1 yield Σgap ∝ q−1(h/r)2.”
simba: Cosmological simulations with black hole growth and feedback (2019, methodology): “The normalization factor T ≡ m×αT encapsulates processes that affect the radial transport of gas on unresolved scales (e.g. nuclear star formation and stellar feedback and mass loss in winds from the accretion disk), where αT = 5 is the original normalization of ÛMTorque in Hopkins & Quataert (2011)”
Black holes on FIRE: stellar feedback limits early feeding of galactic nuclei (2017, methodology): “We model accretion as ṀBH = (1 − η) ṀTorque, where η = 0.1, ṀTorque ∝ T f 5/2d Md R−3/20 M1/6BH (Hopkins & Quataert 2011, equation 65), and fd and Md are the mass fraction and total mass of the disc (stars and gas) within a radial aperture R0 enclosing 256 gas elements.”