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

Figure credit: Read & Trentham 2005

Baryonic mass function of galaxies (data points) compared to CDM mass spectrumLines 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 wellHigh mass end of spectrum

- AGN feedback ???

For AGN feedback need to know how supermassive BHs accrete gas...AGN feeding problem!

Figure credit: MPA Garching, Volker Springel

1) Introduction & motivation

Growth of SMBHs closely related to formation of

hostCo-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)

Mbh - Mbh - Mbulge

Observations of high redshift quasars (z 6, 1047 erg s-1) suggest SMBH masses 109 Msun (Kurk et al. 2007)

BHs start out as seeds in early universe (z 14) with masses 103 Msun

Require BHs to grow close to Eddington limit for 1 Gyr!

Figure credit: MPA Garching, Volker Springel

1) Introduction & motivation

Growth of SMBHs closely related to formation of

hostCo-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)

Mbh - Mbh - Mbulge

Observations of high redshift quasars (z 6, 1047 erg s-1) suggest SMBH masses 109 Msun (Kurk et al. 2007)

BHs start out as seeds in early universe (z 14) with masses 103 Msun

Require BHs to grow close to Eddington limit for 1 Gyr!

Figure credit: MPA Garching, Volker Springel

1) Introduction & motivation

Growth of SMBHs closely related to formation of

hostCo-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)

Mbh - Mbh - Mbulge

Observations of high redshift quasars (z 6, 1047 erg s-1) suggest SMBH masses 109 Msun (Kurk et al. 2007)

BHs start out as seeds in early universe (z 14) with masses 103 Msun

Require BHs to grow close to Eddington limit for 1 Gyr!

Figure credit: MPA Garching, Volker Springel

1) Introduction & motivation

Growth of SMBHs closely related to formation of

hostCo-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)

Mbh - Mbh - Mbulge

Observations of high redshift quasars (z 6, 1047 erg s-1) suggest SMBH masses 109 Msun (Kurk et al. 2007)

BHs start out as seeds in early universe (z 14) with masses 103 Msun

Require BHs to grow close to Eddington limit for 1 Gyr!

*poetic license*

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

Large-scale (hydro + DM) simulationsLimited 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 SMBHRequire 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

Can supersonic turbulence feed AGN?

2) Numerical modelRan 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 MsunMass enclosed within radius r:

One-dimensional velocity dispersion:

2) Numerical modelInitial 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

3/112 ~||)( kvkP kv

Velocity field: net rotation + turbulent spectrumRotation 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

“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

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 s-1 (pink dotted), vturb = 400 km s-1 (blue dashed)

Mass accreted by SMBH strongly correlates with strength of imposed turbulence

3) Results - turbulence and accretion

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 s-1 (pink dotted), vturb = 400 km s-1 (blue dashed)

Mass accreted increases rapidly with increasing vturb while vturb << vrot but saturates when vturb vrot

Mass accreted by SMBH strongly correlates with strength of imposed turbulence

3) Results - turbulence and accretion

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 s-1 (pink dotted), vturb = 400 km s-1 (blue dashed)

L

Mass accreted by SMBH strongly correlates with strength of imposed turbulenceMass 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

Movie – laminar setup

Movie – turbulent setup

3) Results - accretion rate trend

Accretion rate trend: i) with rotation

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)

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

Accretion rate trend: ii) with turbulence

Accreted mass by t = 106 yrs vs. mean turbulent velocity for runs with varying strengths of vrot.

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)

Accretion onto SMBH increases significantly with increasing turbulenceTrend saturates once vturb > vrot, 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

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

tAnalyse 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

vturb >> vrot

vturb vrot

vturb << vrot

actual max

min

Key:

Trend with accretion radius at t = 5 x 105 yrs Error bars t/3

...agrees with results

Accreted mass trend with rotation velocity

...agrees with results

when vturb vrot max

Accreted mass trend with rotation velocity

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 vturb vrot

- 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)

Future work

Take input from cosmological/galactic merger simulations as outer boundary conditionCouple accretion model to a physically-motivated feedback prescription (w. Chris Power)

Goal:

embed SMBH feeding and feedback model into large-scale simulation