UV line-driven winds:

Dependence on black hole Properties

PhD supervisors: Chris Done, Cedric Lacey

Collaborators: Mariko Nomura, Ken Ohsuga

Arnau Quera-Bofarull

Institute for Computational Cosmology, Durham (UK)

KEy Findings

1. UV line-driven winds are more polar than equatorial

(as opposed to other models)

As opposed to Proga 04, Risaliti & Elvis 10, Nomura 16

2. UV line-driven winds get v ~ (0.05 - 0.5) c, with relativistic corrections

As opposed to Luminari 21

3. UV line-driven winds kinetic luminosity scales as the (3-4)th power of Eddington ratio.

As opposed to cosmological simulations AGN feedback models Schaye 15 (Eagle), Weinberger 18 (IllustrisTNG), Dave 19 (Simba)

*Not peer-reviewed, T&C apply.

METHODs

Simulating line-driven winds

Different approaches

Nomura et al (2018)

Hydro

Non-hydro (QWIND)

Solves hydrodynamics
Slow

No gas pressure.
Very fast
Steady-state solutions

Risaliti & Elvis 2010, Quera-Bofarull (2020)

The Qwind code

Simulate gas blob trajectories

\vec{a} =

\vec{a}_\mathrm{es} +

\vec{a}_\mathrm{grav}

\vec{a}_\mathrm{lines}

UV vs X-rays

Need to shield against X-Rays

\vec{a}_\mathrm{lines}

X-Rays

The Qwind code

Original model limitations include:

Initial conditions as free parameter
Simplified radiation transfer (constant density atmosphere, UV optical depth from centre, "colorless" SED...)
No relativistic corrections to the radiation flux (wind velocity > c in some cases)

The Qwind ROADMAP

Original model

Risaliti & Elvis 2010

Code release

Quera-Bofarull 2020

Qwind3

Quera-Bofarull 2021

Numerical improvements
Port to Python

Self-consistent initial conditions
Realistic SED and Radiation Transfer
Relativistic Corrections
Port to Julia

Improvements to qwind

INITIAL coNDITIONS

Density and velocity at the base of the wind

Model very sensitive to these values:

How much mass is lifted from the disc
How much obscuration in the wind

INITIAL coNDITIONS

Idea: Use a 1D solution to approximate them

Close to the disc surface:

a_R \sim 0

INITIAL coNDITIONS

Think the accretion disc as a collection of O-stars at different temperatures

INITIAL coNDITIONS

1D solution -> O star winds

a_\mathrm{grav}

a_\mathrm{rad}

O stars

Solution is well studied

CAK formalism

Castor, Abbott & Klein (1975)

INITIAL coNDITIONS

We apply the CAK formalism to accretion discs

Pereyra et al. (04, 06)

\rho \frac{dV}{dt} = - \rho \,(a_\mathrm{grav} + a_\mathrm{rad}) - \frac{\partial P}{\partial z}

Compute mass loss at the "critical point"

Get density at the sonic point

INITIAL coNDITIONS

Initial density

Initial velocity

Initial radius

M_\mathrm{BH} = 10^8 M_\odot \\ \dot m = 0.5

INITIAL coNDITIONS

Initial Density [cm^-3]

Radiation Transfer

Two main sources of radiation:

Accretion disc (UV)

Vicinity of the BH (X-ray)

Radiation Transfer

UV source (disc) treatment limitations

UV power fraction per annulus = const.

UV Fraction with radius

\dot m = 0.5

Interesting physics: this breaks wind properties symmetry on

M_\mathrm{BH}

Radiation Transfer

UV source (disc) treatment limitations

2. Ray tracing through the wind

Original model:

\tau_\mathrm{UV}

\tau_\mathrm{X}

Radiation Transfer

UV source (disc) treatment limitations

2. Ray tracing through the wind

Updated model:

\tau_\mathrm{UV}

\tau_\mathrm{X}

\tau_\mathrm{UV}

See Christian Knigge talk for X-ray treatment limitations

Relativistic correction also takes into account the full velocity field

Radiation Transfer

We integrate the disc radiation force mitigating each individual light ray.

Radiation Transfer

Wind Dynamics

Radiation Transfer

Density field

an iterative approach

1st iteration: Assume vacuum atmosphere.

Wind fails because ionisation (no shielding against X-Rays)

an iterative approach

It converges!

ONE Free parameter left

We know initial density and velocity

At what radius do we start launching the wind?

R_\mathrm{in}

DEPENDENCE ON INITIAL RADIUS

Initial radius (Rg)

Highest UV emission

M_\mathrm{BH} = 10^8 M_\odot \;\; \dot m = 0.5

P04

Wind Geometry

Polar or equatorial?

R_\mathrm{in} = 20 \; R_g

R_\mathrm{in} = 100 \; R_g

DEPENDENCE on MASS AND MASS ACCRETION RATE

Mass LOss rate

R_\mathrm{in} = 20 R_g

Mass invariant if fuv = constant

R_\mathrm{in} = 20 R_g

DEPENDENCE on MASS AND MASS ACCRETION RATE

KINETIC LUMINOSITY

R_\mathrm{in} = 20 R_g

\frac{L_\mathrm{kin}}{L_\mathrm{Edd}} \sim \dot m^{3-4}

Can uv line-driven winds be ufos?

R_\mathrm{in} = 20 R_g

Can uv line-driven winds be ufos?

v ~ (0.1 - 0.5) c

even when including relativistic corrections

We do not "need" magnetic winds to generate UFOs.

Different than Luminari 2021

Summary

Slides: www.arnau.space/diskwinds

1. Wind properties heavily dependent on Eddington fraction, weakly dependent on BH mass.

3. Wind can reach up to 0.5c with relativistic corrections

2. Line-driving "natural" range

10^7 - 10^9 M_\odot

BACKUP SLIDES

INITIAL coNDITIONS

Idea: Stable solution passes through the critical point

Critical point defined as the minimum of the nozzle function

INITIAL coNDITIONS

Critical point

~ Mass loss rate at critical point

INITIAL coNDITIONS

Critical point position

Disc radius

INITIAL coNDITIONS

Critical point position

Mass loss rate (at critical point)

Density and velocity at the sonic point

Use it as our initial state

UV vs X-rays

\vec{a}_\mathrm{lines}

Shielding by failed wind.

Czerny 21

(yesterday's talk)

Qwind