A bit of (my) history My main PhD simulations were performed on COSMOS Mk I in ! My main PhD simulations were performed on COSMOS Mk I in ! 32 R10000, 8 GB of memory, $2,000, R10000, 8 GB of memory, $2,000, ×10 6 particles, only 4,000 timesteps 0.5×10 6 particles, only 4,000 timesteps Simulations Ill talk about today, 32 core servers, with 64 GB, $20,000 Simulations Ill talk about today, 32 core servers, with 64 GB, $20, ×10 6 particles, but ×10 timesteps 2.5×10 6 particles, but ×10 timesteps

AGN feedback modelling: a comparison of methods (a work in progress) Rob Thacker Associate Professor & Canada Research Chair Saint Marys University, Canada

Credit where a lot of credit is due This work is part of PhD student James Wursters thesis This work is part of PhD student James Wursters thesis

Outline Motivation Motivation Physics issues, obs vs theory Physics issues, obs vs theory Methods Methods Difficult choices to make, complicating factors Difficult choices to make, complicating factors Problem(s) and resolution(s) Problem(s) and resolution(s) Our results Our results Conclusions Conclusions

In a PhD thesis, far, far away….

Motivation Obs. evidence of AGN feedback has been noted for years Obs. evidence of AGN feedback has been noted for years Is the observational case compelling? Is the observational case compelling? Schawinski et al 2007, Fabian review (arXiv: ) Schawinski et al 2007, Fabian review (arXiv: ) Large ellipticals case is pretty good Large ellipticals case is pretty good Radio mode commonly observed Radio mode commonly observed Still need to understand situation in intermediate masses, plus redshifts Still need to understand situation in intermediate masses, plus redshifts

Feedback Terminology Radio mode Radio mode Accreting hot gas Accreting hot gas Sub-Eddington luminosity Sub-Eddington luminosity Radiatively inefficient accretion Radiatively inefficient accretion Radio jets provide heat source Radio jets provide heat source Quasar mode Quasar mode Accreting cold gas Accreting cold gas Up to Eddington luminosity Up to Eddington luminosity Radiatively efficient accretion disk Radiatively efficient accretion disk

Why compare? Comparison studies: Comparison studies: 1999 Santa Barbara cluster comparison 1999 Santa Barbara cluster comparison 2006 Radiative transfer comparison 2006 Radiative transfer comparison 2011 Aquila galaxy formation comparison 2011 Aquila galaxy formation comparison Dont give any real answers Dont give any real answers But do provide estimates of variation between methods But do provide estimates of variation between methods => Be careful about results until 3 groups agree on it => Be careful about results until 3 groups agree on it

Remember… The 9 orders of magnitude in physical scale means that all such simulations include subgrid assumptions and approximations. - Andy Fabian The Optimistic Numericists view: Can we be unwrong enough to give good insight?

Some thoughts to ponder… Timescale between onset of nuclear inflow and AGN activity ~ 10 8 yrs Timescale between onset of nuclear inflow and AGN activity ~ 10 8 yrs Many dynamical signatures evolve signifcantly on that time scale Many dynamical signatures evolve signifcantly on that time scale ALMA + JWST will be an enormous help ALMA + JWST will be an enormous help Simultaneous SFRs, mass inflow rates, understanding radiative behaviour Simultaneous SFRs, mass inflow rates, understanding radiative behaviour Good reasons to be optimistic Good reasons to be optimistic

Prototype merger

Merger movie

Four base models + one extra Springel, di Matteo, Hernquist 2005 (SDH05) Okamato, Nemmen & Bower 2008 (ONB08) Booth & Schaye 2009 (BS09, slightly odd one out) De Buhr, Quataret, & Ma 2011 (DQM11) +WT2012 But plenty of other work is related: High res simulations of individual BH evolution/small scale accretion e.g. Levine et al 2008, 2010 Alvarez, Wise & Abel 2009 Kim et al 2011 Hopkins & Quateart 2010 Other collision work e.g. Johansson, Naab & Burkert 2009 Halo evolution e.g. Sijacki et al 2009

Five key components Model for BH accretion rate (Feedback) energy return algorithm SPH particle accretion algorithm Black hole advection algorithm Black hole merger algorithm

Accretion physics Accretion of gas on to point in 1d: Bondi- Hoyle-Lyttleton (1939,1944,1952) Accretion of gas on to point in 1d: Bondi- Hoyle-Lyttleton (1939,1944,1952) - Gas density & sound speed at infinity - Velocity of BH wrt to (distant) gas

Accretion physics II Maximal symmetric accretion rate is limited by the Eddington rate Maximal symmetric accretion rate is limited by the Eddington rate - Proton mass and Thompson X-section - Efficiency of mass to energy conversion

Problems with BHL Physics: Physics: 2d problem is known to produce unstable flow 2d problem is known to produce unstable flow Material inflow not radial – what about angular momentum? Material inflow not radial – what about angular momentum? Radiative, magnetic effects etc Radiative, magnetic effects etc Numerics: Numerics: How to relate physical variables to simulation ones? How to relate physical variables to simulation ones? What additional variables to introduce for this? What additional variables to introduce for this?

What about angular momentum? Is the key physics actually how material reaches the black hole? Is the key physics actually how material reaches the black hole? Gravitational torques & viscosity keys? Gravitational torques & viscosity keys? Berkeley group (Hopkins et al) pursuing this aggressively Berkeley group (Hopkins et al) pursuing this aggressively

Accreting SPH particles on to the BH wiwi wiwi wiwi

Generic feedback physics E=mc 2 makes life easily parameterizable, ε r E=mc 2 makes life easily parameterizable, ε r Factor in efficiency of energy coupling, ε f Factor in efficiency of energy coupling, ε f But is the impact better modelled as heating or momentum? But is the impact better modelled as heating or momentum? +How to decide on sphere of influence?

Heating approach (example) wiwi wiwi Note ONB08 apply heating to halo gas directly!

Momentum approach Sphere of influence 4sft

Black hole advection Black hole advection is trickier than you might think Black hole advection is trickier than you might think Very important for accretion calculation Very important for accretion calculation N-body integrators subject to 2-body effects N-body integrators subject to 2-body effects Want smooth advection Want smooth advection Ideally toward potential well bottom Ideally toward potential well bottom

Black hole advection – SDH05 For low mass BH (<10M gas ) For low mass BH (<10M gas ) Find gas part. with lowest PE Find gas part. with lowest PE Relocate to that position if v rel <0.25 c s Relocate to that position if v rel <0.25 c s If BH starts to carve void – can get problems If BH starts to carve void – can get problems

Black hole advection – ONB08 Calculate local stellar density Calculate local stellar density Follows local potential well Follows local potential well Move toward density maximum Move toward density maximum Step distance determined by both velocity and softening limit Step distance determined by both velocity and softening limit Avoids significant 2-body issues Avoids significant 2-body issues

Black hole merger algorithm Can give BH its own smoothing length Can give BH its own smoothing length Or use grav softening Or use grav softening Merge when within certain distance + Merge when within certain distance + When grav bound (e.g. ONB08) When grav bound (e.g. ONB08) Or, when relative velocity less than circ (e.g. BS09) Or, when relative velocity less than circ (e.g. BS09)

Summary of implemented models ModelAccretion model SPH accretion Feedback model BH advection BH merger SDH05BHLClassic probability HeatingLowest local PE Sound speed criterion BS09BHL+alpha mod Prob based on mass HeatingLowest local PE Circular vel criterion DQM11Viscous timescale Prob based on mass limit WindMassive tracer Distance only ONB08Drag basedProb based on mass Halo heatingToward max density Grav bound WT12BHLLocal particles first HeatingToward max density Sound speed criterion

Numerical issues Some of these processes involve very small cross-sections => numerically sensitive Some of these processes involve very small cross-sections => numerically sensitive Non-associativity of floating point has an impact Non-associativity of floating point has an impact Worse in parallel comps – accumulations come in different orders Worse in parallel comps – accumulations come in different orders Were still quantifying the impact Were still quantifying the impact

Difficult decisions To vary star formation model or not to vary? To vary star formation model or not to vary? Weve kept things the same – classical model thats pseudo-multiphase Weve kept things the same – classical model thats pseudo-multiphase Modified cooling based upon pressure eqlb between phases Modified cooling based upon pressure eqlb between phases Heated regions obvious in plots/movies Heated regions obvious in plots/movies Can introduce some differences compared to other researchers models (ask me at end) Can introduce some differences compared to other researchers models (ask me at end)

Simulation models Classic two spiral merger (very close to Springel et al 2005 model) Classic two spiral merger (very close to Springel et al 2005 model) End state: red & dead elliptical End state: red & dead elliptical Low (~200k particles per galaxy) and mid (~1m) resolution models Low (~200k particles per galaxy) and mid (~1m) resolution models

Movie 2

SFRs can be numerically sensitive SFRs are very numerically sensitive, from Springel et al 2005: SFRs are very numerically sensitive, from Springel et al 2005: Multiphase models suppress passage peak Multiphase models suppress passage peak If the star formation rate is tied to gas density, the amplitudes of merger-induced starbursts depend on the compressibility of the gas, which is influenced by both the stiffness of the EOS, as well as dynamic range in resolution of the numerical algorithm.

Results – SFRs Initial peak from disc response SDH05 BS09 DQMe DQM ONB08 WT12 Mid res Low res

Notice bar mode less strong Disk morphology at apoapsis

Movie 3

Results – black hole mass growth

M- σ for mid res final states ONB08 BS09 DQMe DQM, SDH05, WT12

Densities & temps similar

Results – time step SDH05 BS09 ONB08 WT12 DQM DQMe

Conclusions Very different behaviours – model assumptions have enormous range Very different behaviours – model assumptions have enormous range Interaction with SF very important Interaction with SF very important Need to quantify degeneracies between model parameters! Need to quantify degeneracies between model parameters! BH tracking is also quite resolution dependent BH tracking is also quite resolution dependent AGN impact is far harder to model than SF AGN impact is far harder to model than SF

Thanks for the invite! Acknowledgements: Acknowledgements: NSERC NSERC Canada Research Chairs Program Canada Research Chairs Program Canada Foundation for Innovation Canada Foundation for Innovation Nova Scotia Research & Innovation Trust Nova Scotia Research & Innovation Trust

Observational hope Duty cycle of AGN activity remains big unknown Duty cycle of AGN activity remains big unknown Transverse proximity effect (TPE) can measure it Transverse proximity effect (TPE) can measure it Problems Problems finding enough background sources finding enough background sources 30m class problem? 30m class problem? Foreground AGN Background sources

SF & AGN interaction Starburst-AGN connection well known Starburst-AGN connection well known Obs -> AGN peak activity about 0.5 Gyr after starburst Obs -> AGN peak activity about 0.5 Gyr after starburst SF impacts ISM around BH significantly SF impacts ISM around BH significantly Impacts temperature & accretion rates Impacts temperature & accretion rates How do these factors interplay? How do these factors interplay? Not that well studied in simulations Not that well studied in simulations Likely degeneracies between models Likely degeneracies between models