Qwind

Simulating UV line-driven winds in AGNs

 

Arnau Quera-Bofarull

Supervised by:

Ken Ohsuga  -  Tsukuba University

Cedric Lacey, Chris Done - Durham University                                              

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 host Galaxy

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 300kg down to a black hole powers all Japan 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

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

X-Rays vs UV

The setup

Need to shield against X-Rays

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

Revisiting Qwind

Key general assumptions

  • Wind modeled as a set of streamlines
  • Gas parcels are launched from the disc, and evolved according to their equation of motion
  • Gas pressure is neglected (supersonic wind)

Revisiting Qwind

Radiation treatment assumptions

  • Simple X-Ray opacity law

     
  • Optical depths are calculated from the center of the grid
\sigma_X = \begin{cases} 100\sigma_T & \mathrm{ if } &\xi &< 10^5\\ \sigma_T & \mathrm{ if } &\xi &\geq 10^5 \end{cases}

Revisiting Qwind

  • Code release with significant techincal improvements
    (Quera-Bofarull et al. (2020)): arXiv:2001.04720
    github.com/arnauqb/qwind

"Qwind 1"

"Qwind 2"

A case study

M=10^8\; M_\odot \;,\; \dot m = 0.5
  • Free input parameters:
    •  
    • T
  • Example
\dot M_\mathrm{wind} = 8 \times 10^{-3} M_\odot / \mathrm{yr} \approx 0.4 \% \,\dot M \\ L_\mathrm{kin} \approx 0.03 \% L_\text{Eddington}

Too low for feedback...

n_0, \, v_0, \, z_0
n_0 = 2 \times 10^8\; \text{ cm}^{-3} \\ v_0 = 10^7\; \text{ cm s}^{-1} \\ z_0 = 1 \;R_g \\ T = 2.5 \times 10^4 \; \text{K}

A case study

M=10^8\; M_\odot \;,\; \dot m = 0.5

... but Qwind strongly depends on the initial density and velocity of the streamlines

Need physical model for initial conditions

TO DO LIST

A case study, comparison with hydro

M=10^8\; M_\odot \;,\; \dot m = 0.5
  • We can compare the results our model with a hydrodynamic simulation (Proga et al 2004), setting the same parameter values.
\text{Qwind}\\ \dot{M}_\text{wind} = 0.3 \; \text{M}_\odot / \text{yr} \\ v_\text{terminal} \in (0.016-0.18) c
\text{P04}\\ \dot{M}_\text{wind} \in (0.16 - 0.3) \; \text{M}_\odot / \text{yr} \\ v_\text{terminal} \in (0.006-0.06) c

Future work

Text

  • We are currently improving the Phyiscs of Qwind

Realistic optical depths...

... with physically motivated SEDs

\dot m = 0.05
\dot m = 0.5

Kubota & Done (2016)

Future work

Text

Self-consistent accretion rate

\dot M
\dot M_\text{wind}

We can easily identify where the wind is coming from, and subtract it to the local accretion rate

Future work

Text

Physically motivated initial conditions

  • Model disc annuli as O-stars (Nomura 2012)
    • Use 1D analytical solution locally at the disc surface
       
  • Another option: "Solve" vertical disc structure.

Stay tuned for updates!

Conclusions

Text

  1. Subgrid models of AGN feedback in cosmological simulations need to be more physically motivated.
     
  2. Qwind model able to mimic results of hydrodynamic simulations at a much lower cost.
     
  3. Realistic radiation transfer and physical initial conditions, most important improvements to do.

Thank you! Questions?

Quera-Bofarull et al. (2020) : arXiv:2001.04720

Try the code at github.com/arnauqb/qwind

Qwind Hokkaido

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