A comparative study of AGN feedback algorithms

MNRAS 431, 2513–2534 (2013) doi:10.1093/mnras/stt346 Advance Access publication 2013 March 21 A comparative study of AGN feedback algorithms J. Wurster‹ and R. J. Thacker Department of Astronomy and Physics, St Mary’s University, Halifax B3H 3C3, Canada Accepted 2013 February 21. Received 2013 February 20; in original form 2013 January 14 ABSTRACT Key words: black hole physics – methods: numerical – galaxies: active – galaxies: interactions. 1 I N T RO D U C T I O N In the hierarchical model of galaxy formation, the largest galaxies are formed last. Naively, we would expect the highest star formation rates (SFRs) and the activity from active galactic nuclei (AGNs) to occur in these most massive galaxies. However, observational evidence contradicts this, showing that in massive galaxies, the peak SFRs and peak AGN activity occurred at redshifts 1–2 (e.g. Madau et al. 1996; Shaver et al. 1996), and not today. This reduction in activity from z ∼ 2 to today was termed ‘downsizing’ by Cowie  E-mail: et al. (1996). One favoured explanation of downsizing is that during mergers, gas from the merger fuels both star formation and AGN activity (e.g. Sanders et al. 1988; Scannapieco, Silk & Bouwens 2005); the feedback from the increased AGN activity then blows away all the gas, leading to a red and dead galaxy (e.g. Springel, Di Matteo & Hernquist 2005). The observational motivation for this picture is the evidence that a supermassive black hole resides at the centre of all galaxies with stellar spheroids (e.g. Kormendy & Richstone 1995; Ferrarese & Merritt 2000), and that they did not evolve independently of one another. The two strongest correlations are the relationship between the black hole mass and the stellar velocity dispersion (MBH −σ ; e.g. Silk & Rees 1998; Ferrarese & Merritt 2000; Gebhardt et al. 2000;  C 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Modelling active galactic nuclei (AGN) feedback in numerical simulations is both technically and theoretically challenging, with numerous approaches having been published in the literature. We present a study of five distinct approaches to modelling AGN feedback within gravitohydrodynamic simulations of major mergers of Milky Way-sized galaxies. To constrain differences to only be between AGN feedback models, all simulations start from the same initial conditions and use the same star formation algorithm. Most AGN feedback algorithms have five key aspects: the black hole accretion rate, energy feedback rate and method, particle accretion algorithm, black hole advection algorithm and black hole merger algorithm. All models follow different accretion histories, and in some cases, accretion rates differ by up to three orders of magnitude at any given time. We consider models with either thermal or kinetic feedback, with the associated energy deposited locally around the black hole. Each feedback algorithm modifies the region around the black hole to different extents, yielding gas densities and temperatures within r ∼ 200 pc that differ by up to six orders of magnitude at any given time. The particle accretion algorithms usually maintain good agreement between the total mass accreted by Ṁdt and the total mass of gas particles removed from the simulation, although not all algorithms guarantee this to be true. The black hole advection algorithms dampen inappropriate dragging of the black holes by two-body interactions. Advecting the black hole a limited distance based upon local mass distributions has many desirably properties, such as avoiding large artificial jumps and allowing the possibility of the black hole remaining in a gas void. Lastly, two black holes instantly merge when given criteria are met, and we find a range of merger times for different criteria. This is important since the AGN feedback rate changes across the merger in a way that is dependent on the specific accretion algorithm used. Using the MBH –σ relation as a diagnostic of the remnants yields three models that lie within the one-sigma scatter of the observed relation and two that fall below the expected relation. The wide variation in accretion behaviours of the models reinforces the fact that there remains much to be learnt about the evolution of galactic nuclei. 2514 J. Wurster and R. J. Thacker rS = 2GMBH , c2 (1) where MBH is the mass of the black hole, G is Newton’s gravitational constant and c is the speed of light; typical values range rS ≈ 3 × 106−8 km. On the next larger scale is the Bondi radius (Bondi 1952), rBondi = GMBH , 2 c∞ (2) where c∞ is the sound speed of gas at infinity. The value of the Bondi radius is dependent on the black hole’s environment and can range from a few parsecs to tens of parsecs (e.g. Springel et al. 2005; Kurosawa et al. 2009). This radius, also known as the capture radius, divides a gas flow into two regimes (Frank, King & Raine 2002). Consider a spherically symmetric gas cloud centred on a black hole, where the gas is initially at rest at infinity. The only forces acting on the gas are the gravitational force from the central black hole and the pressure forces within the gas (assuming that we neglect the self-gravity of the gas). Beyond the Bondi radius, the gas is comparatively uninfluenced by the black hole and flows subsonically. Within rBondi , the gas density begins to increase, and the gas flow inward eventually reaches a sonic point. At the sonic point, the gas plunges at a free-fall rate into the black hole (Hobbs et al. 2012). Thus, the Bondi radius can be viewed as the black hole’s gravitational radius of influence. The last spatial scale of interest is that of an entire galaxy (or a galaxy cluster), which can span dozens of kiloparsecs (or a few megaparsecs). When considering all of these scales, comparing the size of a black hole to its massive host galaxy is similar to comparing a coin to the Earth (Fabian 2012). To complement the range of spatial scales, studying AGN feedback also requires a large range of temporal scales. At short intervals, observations show that the luminosity of the central engines of AGN varies on time-scales ranging from days to years (e.g. Webb & Malkan 2000 and references therein; Sarajedini et al. 2011); moreover, there are short-term differences in variability amongst the different classes of AGN, making the variable luminosity challenging to understand and constrain. Large-scale observations have detected large (∼10 kpc radius) X-ray cavities in the gas around the AGN. To inflate these cavities, an outburst of 1058 –1061 erg of energy would be required (Bı̂rzan et al. 2004; McNamara et al. 2005) every few ∼108 yr, or a time-averaged output of ∼1043 –1045 erg s−1 (Churazov et al. 2002). Thus, the next inherent difficulty in modelling AGN becomes obvious: AGN luminosity varies on time-scales as short as days, yet they are expected to produce major outbursts every few ∼108 yr. Numerically, we can (...truncated)