Simulating AGN feedback

Arnau Quera-Bofarull

Supervised by: Cedric Lacey, Chris Done & Richard Bower

A study of AGN line-driven winds

What is AGN feedback?

Energy coupling between the central black hole and its host galaxy.

 

\frac{\text{size of BH}}{\text{size of Galaxy}} \approx

Joint evolution of BH and Galaxy

  • This energy coupling implies a joint evolution between the black hole and the host galaxy.

  • BH mass is correlated with bulge luminosity and velocity dispersion across a wide range.

Kormendy and Ho (2013)

Black Hole Mass

Bulge velocity dispersion

Kormendy & Ho (2013)

Effects on galaxy population.

Image credit: Mutch et al (2013)

Mass

Mass Function

(log) Mass Number Count

Stellar Mass

Schaye et al (2014)

AGN ( and supernova) feedback are needed to match observations.

The origin of the coupling: Accretion

E = \eta m c^2
\text{ BH accretion } \rightarrow \eta \approx 0.1

Credit: NASA/Goddard Space Flight Center

  • Matter falls in gaining kinetic energy.
  • Part of this energy released as radiation.

Fun fact: throwing 50kg down to a black hole powers the UK electric grid for a year!

Is that enough to alter the galaxy?

E_\text{outflow} \approx 0.1 M_{BH} c^2 \approx 10^{61} \text{erg}
\text{Consider a BH grown through accretion to } M = 10^8 M_\odot
\text{Consider a galaxy bulge with } M=10^{11} M_\odot \text{ and } \sigma_v = 200 \text{km}/\text{s}
E_\text{binding} \approx M_\text{bulge} \sigma_v^2 \approx 10^{58} \text{erg}

More than enough energy...

Can this radiation be (minimally) coupled with the surrounding material?

Eagle AGN feedback

In EAGLE, a fraction of the radiated energy from accretion is coupled thermally to the surrounding gas.

\dot E_\text{inj} = \epsilon_f \dot E_\text{acc.}

Calibrated to match observations (ϵ = 0.15).

Since final BH masses depend on it, they are not a prediction of the simulation.

Ideally, ϵ should be derived from first principles.

\epsilon_f = \epsilon_f ( M_\text{BH}, \dot M, a)

Feedback mechanisms

Radiative mode

Kinetic mode

Winds

Credit: ESA/ATG medialab

Credit: NRAO/AUI

\text{Unlikely to directly cause } M - \sigma \text{ relation.}

Jets

Radiation vs Gravity

The Eddington Limit

g_\text{rad} = g_\text{rad}\left( \kappa , L\right)

Luminosity

Opacity

g_\text{grav} = g_\text{grav}\left(M_\text{BH}\right)
\text{Assuming } \kappa = \kappa_{e.s.} \text{, both quantities are equal at }
L_\text{Edd} = \frac{4 \pi G M_\text{BH} c}{\kappa_\text{es}}

How do we create a wind?

L>L_\text{Edd} \longrightarrow \text{ Super Eddington winds}
\kappa > \kappa_\text{e.s.} \longrightarrow \text{Line-driven winds}

Radiation vs Gravity

The line-driving mechanism

Opacities can be much larger than free electron scattering.

\frac{\kappa_\text{lines + e.s.}}{\kappa_\text{e.s}} = M\left( \frac{dv}{dr}, \xi \right)
v
\xi \propto L_\text{X-Rays}

Ionisation parameter

Castor, Abbot & Klein (1975)

Force Multiplier

The setup

Need to shield against X-Rays

How to drive a wind

X-Rays vs UV

  • Need a shielding mechanism that sets ξ < 100 at ~ 100-400 Rg.
  • Most of the work so far, e.g.,
    • Proga & Kallman (2000, 2004)
    • Risaliti & Elvis (2010)
    • Nomura et al ( 2013, 2016, 2017, 2018)
\sigma_\text{X} = \begin{cases} \sigma_\text{e.s.} & \text{ if } \xi > 10^5 \\ 100\sigma_\text{e.s.} & \text{ if } \xi < 10^5 \end{cases}

assumes X-Ray opacities to be

Simulating line-driven winds

Different approaches

Disc radius [Rs]

Height [Rs]

Density

Nomura et al (2018)

Hydro

Disc radius [Rs]

Height [Rs]

Qwind model, Risaliti & Elvis (2010)

Non-hydro

  • Accounts for gas pressure and heating/cooling.
  • Slow
  • Neglects gas pressure forces.
  • Lots of independent input parameters
  • Very fast.

Shielding

Our goal: improve Qwind (non-hydro)

Following the same non-hydro approach, we are working on a new code with major improvements:

  • Fully written in Python while keeping performance, and open source.
  • Sensitive treatment of the radiation field, motivated by Cloudy runs.
  • Reduced number of input parameters.
  • Self-consistent with the disc structure, i.e, mass loss due to wind should change accretion rate, and thus luminosity.

X-Ray opacities with Cloudy

Current simulations overestimate X-Ray obscuration.

\sigma_\text{X} = \begin{cases} \sigma_\text{e.s.} & \text{ if } \xi > 10^5 \\ 100\sigma_\text{e.s.} & \text{ if } \xi < 10^5 \end{cases}

How bad is it?

Qwind code, old Opacities

New opacities,

with no UV obscuration

Conclusions

  • AGN Feedback is one of the cornerstones of cosmological simulations.
  • Line-driven winds are a strong candidate for setting M-σ relationship, as well as the feedback efficiency.
  • We need to improve our line-driven winds models, making them more physically motivated and self consistent.

TO-DO

  • Improve numerical code for line-driven winds.
  • Scan parameter range to deduce feedback efficiency.
  • Implement new feedback scheme in cosmological simulations.
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