A bit of (my) history

1. A bit of (my) history • My main PhD simulations were performed on COSMOS Mk I in 1998-99! • 32 R10000, 8 GB of memory, $2,000,000 • 0.5×106 particles, only 4,000 timesteps • Simulations I’ll talk about today, 32 core servers, with 64 GB, $20,000 • 2.5×106particles, but ×10 timesteps

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

3. Credit where a lot of credit is due • This work is part of PhD student James Wurster’s thesis

4. Outline • Motivation • Physics issues, obsvs theory • Methods • Difficult choices to make, complicating factors • Problem(s) and resolution(s) • Our results • Conclusions

5. In a PhD thesis, far, far away….

6. Motivation • Obs. evidence of AGN feedback has been noted for years • Is the observational case compelling? • Schawinski et al 2007, Fabian review (arXiv:1204.4114) • Large ellipticals case is pretty good • Radio mode commonly observed • Still need to understand situation in intermediate masses, plus redshifts

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

8. Why compare? • Comparison studies: • 1999 Santa Barbara cluster comparison • 2006 Radiative transfer comparison • 2011 Aquila galaxy formation comparison • Don’t give any real “answers” • But do provide estimates of variation between methods • => “Be careful” about results until 3 groups agree on it 

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

10. Some thoughts to ponder… • Timescale between onset of nuclear inflow and AGN activity ~ 108yrs • Many dynamical signatures evolve signifcantly on that time scale • ALMA + JWST will be an enormous help • Simultaneous SFRs, mass inflow rates, understanding radiativebehaviour • Good reasons to be optimistic

11. Prototype merger

12. Merger movie

13. Four base models + one extra 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 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

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

15. Accretion physics • 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

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

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

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

19. Accreting SPH particles on to the BH wi wi wi

20. Generic feedback physics • E=mc2 makes life easily parameterizable, εr • Factor in efficiency of energy coupling, εf • But is the impact better modelled as heating or momentum? +How to decide on sphere of influence?

21. Heating approach (example) wi wi Note ONB08 apply heating to halo gas directly!

22. Momentum approach Sphere of influence 4sft

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

24. Black hole advection – SDH05 • For low mass BH (<10Mgas) • Find gas part. with lowest PE • Relocate to that position if vrel<0.25 cs • If BH starts to carve void – can get problems

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

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

27. Summary of implemented models

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

29. Difficult decisions • To vary star formation model or not to vary? • We’ve kept things the same – “classical” model that’s pseudo-multiphase • Modified cooling based upon pressure eqlb between phases • Heated regions obvious in plots/movies • Can introduce some differences compared to other researcher’s models (ask me at end)

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

31. Movie 2

32. SFRs can be numerically sensitive • SFRs are very numerically sensitive, from Springel et al 2005: • 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.

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

34. Disk morphology at apoapsis Notice bar mode less strong

35. Movie 3

36. Results – black hole mass growth

37. M-σfor mid res final states DQMe DQM, SDH05, WT12 BS09 ONB08

38. Densities & temps “similar”

39. Results – time step SDH05 BS09 ONB08 WT12 DQM DQMe

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

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

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

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