1. AGN feeding: the intermediate scale Alexander Hobbs Collaborators: Sergei Nayakshin, Chris Power, Andrew King

2. Talk outline 1) Introduction & motivation 2) Outline of numerical model 3) Results of the model (inc. movies) 4) Analytical interpretation 5) Conclusions

3. 1) Introduction & motivation

4. Figure credit: Read & Trentham 2005 Baryonic mass function of galaxies (data points) compared to CDM mass spectrum Lines are fits by Hubble type Data from SDSS and Subaru 8m deep wide-angle survey Missing satellites problem! AGN feedback? Missing satellites problem - Explained via SNe feedback in shallow potential well High mass end of spectrum - AGN feedback ??? For AGN feedback need to know how supermassive BHs accrete gas...AGN feeding problem!

5. Figure credit: MPA Garching, Volker Springel 1) Introduction & motivation Growth of SMBHs closely related to formation of host Co-evolution of SMBHs and galaxy populations requires understanding of how AGN are fed Supermassive black holes (SMBHs) lurk at centres of galaxies with bulges/spheroids (Kormendy & Richstone 1995) Tight correlation between SMBH properties and bulge properties (Ferrarese & Merritt 2000, Magorrian et al. 1998) M bh -  M bh - M bulge Observations of high redshift quasars (z  6, 10 47 erg s -1 ) suggest SMBH masses  10 9 M sun (Kurk et al. 2007) BHs start out as seeds in early universe (z  14) with masses  10 3 M sun Require BHs to grow close to Eddington limit for  1 Gyr!

6. Figure credit: MPA Garching, Volker Springel 1) Introduction & motivation Growth of SMBHs closely related to formation of host Co-evolution of SMBHs and galaxy populations requires understanding of how AGN are fed Supermassive black holes (SMBHs) lurk at centres of galaxies with bulges/spheroids (Kormendy & Richstone 1995) Tight correlation between SMBH properties and bulge properties (Ferrarese & Merritt 2000, Magorrian et al. 1998) M bh -  M bh - M bulge Observations of high redshift quasars (z  6, 10 47 erg s -1 ) suggest SMBH masses  10 9 M sun (Kurk et al. 2007) BHs start out as seeds in early universe (z  14) with masses  10 3 M sun Require BHs to grow close to Eddington limit for  1 Gyr!

7. Figure credit: MPA Garching, Volker Springel 1) Introduction & motivation Growth of SMBHs closely related to formation of host Co-evolution of SMBHs and galaxy populations requires understanding of how AGN are fed Supermassive black holes (SMBHs) lurk at centres of galaxies with bulges/spheroids (Kormendy & Richstone 1995) Tight correlation between SMBH properties and bulge properties (Ferrarese & Merritt 2000, Magorrian et al. 1998) M bh -  M bh - M bulge Observations of high redshift quasars (z  6, 10 47 erg s -1 ) suggest SMBH masses  10 9 M sun (Kurk et al. 2007) BHs start out as seeds in early universe (z  14) with masses  10 3 M sun Require BHs to grow close to Eddington limit for  1 Gyr!

8. Figure credit: MPA Garching, Volker Springel 1) Introduction & motivation Growth of SMBHs closely related to formation of host Co-evolution of SMBHs and galaxy populations requires understanding of how AGN are fed Supermassive black holes (SMBHs) lurk at centres of galaxies with bulges/spheroids (Kormendy & Richstone 1995) Tight correlation between SMBH properties and bulge properties (Ferrarese & Merritt 2000, Magorrian et al. 1998) M bh -  M bh - M bulge Observations of high redshift quasars (z  6, 10 47 erg s -1 ) suggest SMBH masses  10 9 M sun (Kurk et al. 2007) BHs start out as seeds in early universe (z  14) with masses  10 3 M sun Require BHs to grow close to Eddington limit for  1 Gyr! *poetic license*

9. Figure credit: Tiziana Di Matteo, Carnegie Mellon University Quarter of a billion gas and dark matter particles Cubic box 100 million light years across 2000 CPUs (Pittsburgh Supercomputing Centre) Gas density increasing with brightness, yellow circles indicate BHs 134 million gas particles, 17 million dark matter particles Projected density of slab 8 Mpc deep Colors show increasing density on logarithmic scale: black (least dense), blue, green, yellow, red, white (most dense) Figure credit: Cornell Theory Center, Princeton Large-scale (hydro + DM) simulations

10. Limited computational resources – necessary to use “sub-grid” prescriptions - Feedback (from AGN, supernovae) - SMBH growth Currently treated with Bondi-Hoyle accretion (Bondi 1952) i) Gas has angular momentum! ii) Density under-resolved in simulations - arbitrary numerical factors used to enhance accretion rate Need a physically motivated sub-grid prescription for accretion onto an SMBH Require an understanding of the flow on scales of a galactic bulge (  hundreds of pc) - currently under-represented! Need to bridge gap between pc and kpc scales... estimate physically wrong estimate numerically wrong

11. Can supersonic turbulence feed AGN?

12. 2) Numerical model Ran simulations using SPH code GADGET-3 (Springel 2005) - N sph = 4 x 10 6 particles - Computational domain 0.1 pc – 100 pc - Adaptive smoothing lengths down to h min = 2.8 x 10 -2 pc - Fixed artificial viscosity (Monaghan-Balsara form with  = 1) Gravitational forces implemented via background potential (no gas self-gravity) - Central SMBH of M bh = 10 8 M sun - Isothermal potential   r -2 with scale radius a = 1 kpc, M a = 10 10 M sun - Constant density core within r < 20 pc, M core = 2 x 10 8 M sun Mass enclosed within radius r: One-dimensional velocity dispersion:

13. 2) Numerical model Initial conditions for simulations - Uniform density, spherically-symmetric thick gaseous shell - M shell = 5.1 x 10 7 M sun - r in = 30 pc, r out = 100 pc - Cut from relaxed glass-like particle configuration - Isothermal T = 10 3 K - Accretion (capture) radius r acc = 1 pc Velocity field: net rotation + turbulent spectrum Rotation about z-axis with constant v - varying between 0 and 100 km s Turbulence seeded as a Gaussian random field in velocity, with a Kolmogorov spectrum - varying between 0 and 400 km s-1 - divergence-free - max  60 pc

14. “Laminar” initial conditions Angular momentum conservation and symmetry Formation of geometrically thin disc in xy-plane

15. “Laminar” initial conditions Majority of gas stays uniform as it falls in Radial shocks in disc plane lead to mixing of gas with different angular momenta

16. Turbulent initial conditions Turbulent flow creates long dense filaments Flow exhibits strong density contrasts of up to three orders of magnitude

17. Turbulent initial conditions Some signatures of net rotation retained but far more isotropic than laminar case

18. 3) Results - turbulence and accretion Accreted mass vs. time for simulations with v rot = 100 km s -1 and varying strengths of v turb. Key: no turbulence (solid black), v turb = 20 km s -1 (black dotted), v turb = 40 km s -1 (black dashed), v turb = 60 km s -1 (black dot-dashed), v turb = 100 km s -1 (brown dot-dot-dash), v turb = 200 km s -1 (red dashed), v turb = 300 km s - 1 (pink dotted), v turb = 400 km s -1 (blue dashed) Mass accreted by SMBH strongly correlates with strength of imposed turbulence

19. 3) Results - turbulence and accretion Accreted mass vs. time for simulations with v rot = 100 km s -1 and varying strengths of v turb. Key: no turbulence (solid black), v turb = 20 km s -1 (black dotted), v turb = 40 km s -1 (black dashed), v turb = 60 km s -1 (black dot-dashed), v turb = 100 km s -1 (brown dot-dot-dash), v turb = 200 km s -1 (red dashed), v turb = 300 km s - 1 (pink dotted), v turb = 400 km s -1 (blue dashed) Mass accreted increases rapidly with increasing v turb while v turb << v rot but saturates when v turb  v rot Mass accreted by SMBH strongly correlates with strength of imposed turbulence

20. 3) Results - turbulence and accretion Accreted mass vs. time for simulations with v rot = 100 km s -1 and varying strengths of v turb. Key: no turbulence (solid black), v turb = 20 km s -1 (black dotted), v turb = 40 km s -1 (black dashed), v turb = 60 km s -1 (black dot-dashed), v turb = 100 km s -1 (brown dot-dot-dash), v turb = 200 km s -1 (red dashed), v turb = 300 km s - 1 (pink dotted), v turb = 400 km s -1 (blue dashed) L Mass accreted by SMBH strongly correlates with strength of imposed turbulence Mass accreted increases rapidly with increasing v turb while v turb << v rot but saturates when v turb  v rot Turbulence broadens angular momentum distribution, putting some gas on low L orbits

21. Movie – laminar setup

22. Movie – turbulent setup

23. 3) Results - accretion rate trend

24. Accretion rate trend: i) with rotation Accreted mass by t = 10 6 yrs vs. rotation velocity for simulations with varying strengths of v turb. Key: no turbulence (solid black), v turb = 20 km s -1 (black dotted), v turb = 40 km s -1 (black dashed), v turb = 60 km s -1 (black dot-dashed), v turb = 100 km s -1 (brown dot-dot-dash), v turb = 200 km s -1 (red dashed), v turb = 300 km s -1 (pink dotted), v turb = 400 km s -1 (blue dashed) Increased net rotation acts to decrease accreted mass in all cases With no turbulence, large decrease in accretion when small amount of angular momentum added High turbulence flattens slope of trend, preventing such a high reduction in accretion Turbulence significantly lessens importance of net rotation in reducing accretion rate For a given (finite) rotation velocity, turbulence enhances accretion

25. Accretion rate trend: ii) with turbulence Accreted mass by t = 10 6 yrs vs. mean turbulent velocity for runs with varying strengths of v rot. Key: no rotation (solid), v rot = 20 km s -1 (dotted), v rot = 40 km s -1 (dashed), v rot = 60 km s -1 (dot-dashed), v rot = 80 km s -1 (dot-dot-dash), v rot = 100 km s -1 (long dashes) Accretion onto SMBH increases significantly with increasing turbulence Trend saturates once v turb > v rot, and begins to slowly decrease as turbulence increased further Weak turbulence Strong turbulence - Broadens angular momentum distribution - Strong density enhancements - Dense regions propagate unaffected by hydrodynamical drag - ‘ Ballistic’ motion of high density gas?...loss-cone argument

26. 4) Analytical interpretation: ‘ballistic’ mode

27. 4) Analytical interpretation: f(v) spectrum v rot Analyse result of this integral in three extremes:

28. 4) Analytical interpretation: f(v) spectrum v rot Analyse result of this integral in three extremes: i) when v turb >> v rot actual

29. 4) Analytical interpretation: f(v) spectrum v rot Analyse result of this integral in three extremes: i) when v turb  v rot max

30. 4) Analytical interpretation: f(v) spectrum v ro t Analyse result of this integral in three extremes: i) when v turb << v rot min

31. ...agrees with results Trend with size of shell at t = 5 x 10 5 yrs Error bars  t/3 v turb >> v rot v turb  v rot v turb << v rot actual max min Key: Trend with accretion radius at t = 5 x 10 5 yrs Error bars  t/3

32. ...agrees with results Accreted mass trend with rotation velocity

33. ...agrees with results when v turb  v rot max Accreted mass trend with rotation velocity

34. 5) Conclusions - In the presence of net rotation, turbulence can enhance accretion (for a given rotation velocity) - For our particular initial condition, runs without turbulence form rings rather than discs...whereas runs with high turbulence form discs - Accretion trend with turbulence saturates at v turb  v rot - Weak turbulence trend broadening of angular momentum distribution - Strong turbulence trend ballistic trajectories of high density gas...by up to 3-4 orders of magnitude! Key points: - Taken one of the first steps in modelling the intermediate-scale flow in a galactic potential - Identified a possible ‘ballistic’ mode of AGN feeding - If supernovae-driven turbulence can enhance accretion rate onto SMBH then this speaks to a starburst-AGN connection such as is observed (e.g. Farrah et al. 2003)

35. Future work Take input from cosmological/galactic merger simulations as outer boundary condition Couple accretion model to a physically-motivated feedback prescription (w. Chris Power) Goal: embed SMBH feeding and feedback model into large-scale simulation