AGN feeding: the
intermediate scale
Alexander Hobbs
Collaborators: Sergei Nayakshin, Chris Power, Andrew King
Talk outline
1) Introduction & motivation
2) Outline of numerical model
3) Results of the model (inc. movies)
4) Analytical interpretation
5) Conclusions
1) Introduction & motivation
1) Introduction & motivation
Baryonic mass function of galaxies
(data points) compared to CDM
mass spectrum
Missing
satellites
problem!
Lines are fits by Hubble type
Data from SDSS and Subaru 8m
deep wide-angle survey
Missing satellites problem
- Explained via SNe feedback in
shallow potential well
AGN feedback?
High mass end of spectrum
- AGN feedback ???
For AGN feedback need to know
how supermassive BHs accrete
gas...AGN feeding problem!
Figure credit: Read & Trentham 2005
1) Introduction & motivation
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)
Mbh - 
Mbh - Mbulge
Growth of SMBHs closely related
to formation of host
Co-evolution of SMBHs and galaxy
populations requires understanding of
how AGN are fed
Figure credit: MPA Garching, Volker
Springel
BHs start out as seeds in early universe (z  14) with masses  103 Msun
Observations of high redshift quasars (z  6, 1047 erg s-1) suggest SMBH masses  109 Msun
(Kurk et al. 2007)
Require BHs to grow close to Eddington limit for  1 Gyr!
1) Introduction & motivation
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)
Mbh - 
Mbh - Mbulge
Growth of SMBHs closely related
to formation of host
Co-evolution of SMBHs and galaxy
populations requires understanding of
how AGN are fed
Figure credit: MPA Garching, Volker
Springel
BHs start out as seeds in early universe (z  14) with masses  103 Msun
Observations of high redshift quasars (z  6, 1047 erg s-1) suggest SMBH masses  109 Msun
(Kurk et al. 2007)
Require BHs to grow close to Eddington limit for  1 Gyr!
1) Introduction & motivation
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)
Mbh - 
Mbh - Mbulge
Growth of SMBHs closely related
to formation of host
Co-evolution of SMBHs and galaxy
populations requires understanding of
how AGN are fed
Figure credit: MPA Garching, Volker
Springel
BHs start out as seeds in early universe (z  14) with masses  103 Msun
Observations of high redshift quasars (z  6, 1047 erg s-1) suggest SMBH masses  109 Msun
(Kurk et al. 2007)
Require BHs to grow close to Eddington limit for  1 Gyr!
1) Introduction & motivation
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)
Mbh - 
Mbh - Mbulge
Growth of SMBHs closely related
to formation of host
Co-evolution of SMBHs and galaxy
populations requires understanding of
how AGN are fed
Figure credit: MPA Garching, Volker
Springel
BHs start out as seeds in early universe (z  14) with masses  103 Msun
*poetic license*
Observations of high redshift quasars (z  6, 1047 erg s-1) suggest SMBH masses  109 Msun
(Kurk et al. 2007)
Require BHs to grow close to Eddington limit for  1 Gyr!
Large-scale (hydro + DM) simulations
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
Figure credit: Cornell Theory Center, Princeton
Figure credit: Tiziana Di Matteo, Carnegie
Mellon University
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)
Large-scale (hydro + DM) simulations
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!
estimate physically wrong
ii) Density under-resolved in simulations
estimate numerically wrong
- 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...
Can supersonic turbulence
feed AGN?
2) Numerical model
Ran simulations using SPH code GADGET-3 (Springel 2005)
- Nsph = 4 x 106 particles
- Computational domain 0.1 pc – 100 pc
- Adaptive smoothing lengths down to hmin = 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 Mbh = 108 Msun
- Isothermal potential   r-2 with scale radius a = 1 kpc, Ma = 1010 Msun
- Constant density core within r < 20 pc, Mcore = 2 x 108 Msun
Mass enclosed within radius r:
One-dimensional velocity dispersion:
2) Numerical model
Initial conditions for simulations
- Uniform density, spherically-symmetric thick gaseous shell
- Mshell = 5.1 x 107 Msun
- rin = 30 pc, rout = 100 pc
- Cut from relaxed glass-like particle configuration
- Isothermal T = 103 K
- Accretion (capture) radius racc = 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
Pv (k )  | vk |2 ~ k 11/ 3
“Laminar” initial conditions
Angular momentum conservation
and symmetry
Formation of geometrically thin
disc in xy-plane
“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
Turbulent initial conditions
Turbulent flow creates long dense
filaments
Flow exhibits strong density
contrasts of up to three orders of
magnitude
Turbulent initial conditions
Some signatures of net
rotation retained but far more
isotropic than laminar case
3) Results - turbulence and accretion
Mass accreted by SMBH strongly correlates
with strength of imposed turbulence
Accreted mass vs. time for simulations with vrot = 100
km s-1 and varying strengths of vturb.
Key: no turbulence (solid black), vturb = 20 km s-1 (black dotted), vturb = 40
km s-1 (black dashed), vturb = 60 km s-1 (black dot-dashed), vturb = 100 km
s-1 (brown dot-dot-dash), vturb = 200 km s-1 (red dashed), vturb = 300 km s1 (pink dotted), v
-1
turb = 400 km s (blue dashed)
3) Results - turbulence and accretion
Mass accreted by SMBH strongly correlates
with strength of imposed turbulence
Mass accreted increases rapidly with
increasing vturb while vturb << vrot but
saturates when vturb  vrot
Accreted mass vs. time for simulations with vrot = 100
km s-1 and varying strengths of vturb.
Key: no turbulence (solid black), vturb = 20 km s-1 (black dotted), vturb = 40
km s-1 (black dashed), vturb = 60 km s-1 (black dot-dashed), vturb = 100 km
s-1 (brown dot-dot-dash), vturb = 200 km s-1 (red dashed), vturb = 300 km s1 (pink dotted), v
-1
turb = 400 km s (blue dashed)
3) Results - turbulence and accretion
Mass accreted by SMBH strongly correlates
with strength of imposed turbulence
Mass accreted increases rapidly with
increasing vturb while vturb << vrot but
saturates when vturb  vrot
Turbulence broadens angular
momentum distribution, putting
some gas on low L orbits
Accreted mass vs. time for simulations with vrot = 100
km s-1 and varying strengths of vturb.
L
Key: no turbulence (solid black), vturb = 20 km s-1 (black dotted), vturb = 40
km s-1 (black dashed), vturb = 60 km s-1 (black dot-dashed), vturb = 100 km
s-1 (brown dot-dot-dash), vturb = 200 km s-1 (red dashed), vturb = 300 km s1 (pink dotted), v
-1
turb = 400 km s (blue dashed)
Movie – laminar setup
Movie – turbulent setup
3) Results - accretion rate trend
Accretion rate trend: i) with rotation
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
Accreted mass by t = 106 yrs vs. rotation velocity for
simulations with varying strengths of vturb.
Key: no turbulence (solid black), vturb = 20 km s-1 (black dotted), vturb =
40 km s-1 (black dashed), vturb = 60 km s-1 (black dot-dashed), vturb =
100 km s-1 (brown dot-dot-dash), vturb = 200 km s-1 (red dashed), vturb =
300 km s-1 (pink dotted), vturb = 400 km s-1 (blue dashed)
Accretion rate trend: ii) with turbulence
Accretion onto SMBH increases
significantly with increasing turbulence
Trend saturates once vturb > vrot, and
begins to slowly decrease as turbulence
increased further
Weak turbulence
- Broadens angular momentum distribution
Strong turbulence
- Strong density enhancements
- Dense regions propagate unaffected by
hydrodynamical drag
- ‘Ballistic’ motion of high density gas?
Accreted mass by t = 106 yrs vs. mean turbulent
velocity for runs with varying strengths of vrot.
...loss-cone argument
Key: no rotation (solid), vrot = 20 km s-1 (dotted), vrot = 40 km s-1 (dashed),
vrot = 60 km s-1 (dot-dashed), vrot = 80 km s-1 (dot-dot-dash), vrot = 100 km
s-1 (long dashes)
4) Analytical interpretation: ‘ballistic’ mode
4) Analytical interpretation: f(v) spectrum
vrot
Analyse result of this integral in three extremes:
4) Analytical interpretation: f(v) spectrum
vrot
Analyse result of this integral in three extremes:
i) when vturb >> vrot
actual
4) Analytical interpretation: f(v) spectrum
vrot
Analyse result of this integral in three extremes:
i) when vturb  vrot
max
4) Analytical interpretation: f(v) spectrum
vro
t
Analyse result of this integral in three extremes:
i) when vturb << vrot
min
...agrees with results
Trend with size of shell at t = 5 x 105 yrs
Error bars  t/3
Key:
vturb << vrot
min
vturb >> vrot
actual
vturb  vrot
max
Trend with accretion radius at t = 5 x 105 yrs
Error bars  t/3
...agrees with results
Accreted
velocity
mass
trend
with
rotation
...agrees with results
Accreted mass trend with rotation velocity
when vturb  vrot
max
5) Conclusions
- In the presence of net rotation, turbulence can enhance accretion (for a given rotation velocity)
...by up to 3-4 orders of magnitude!
- 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 vturb  vrot
- Weak turbulence trend
- Strong turbulence trend
broadening of angular momentum distribution
ballistic trajectories of high density gas
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)
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