Global Compton heating/cooling in hot accretion flows

Feng Yuan

with:

F. G. Xie (谢富国； Shanghai Astronomical Observatory) J. P. Ostriker (Princeton University)

Two effects of Compton scattering Two effects of Compton scattering in accretion flowsin accretion flows

Consider collision between photons and electrons in Consider collision between photons and electrons in hot accretion flow, two effects:hot accretion flow, two effects:

Momentum Momentum – Radiation force: Radiation force: – Balance with grav. force Balance with grav. force Eddington luminosity Eddington luminosity

Energy Energy – For For photons: Compton up-scattering or Comptonization, : Compton up-scattering or Comptonization,

which is the mechanism of producing X-ray emission in BH systemswhich is the mechanism of producing X-ray emission in BH systems

– For For electronselectrons: they can obtain or loss energy due to the : they can obtain or loss energy due to the scattering with photons (e.g., Compton radiative cooling)scattering with photons (e.g., Compton radiative cooling)

Tcc

U

ADAF

Assume the electrons have Te and the photon energy is Є, after each scattering on average the electron will obtain energy:

We will focus on electrons and We will focus on electrons and “non-local”“non-local” scattering scattering (because hot accretion flow is optically thin (because hot accretion flow is optically thin in radial directionin radial direction))

Thompson limit:

The spectrum received at radius rThe spectrum received at radius r

It is difficult to directly calculate the radiative transfer when scattering is important.

So we use two-stream approximation, calculate the vertical radiative transfer in a zone around r’.

The spectrum before Comptonization is:

The spectrum after Comptonization is calculated based on Coppi & Blandford (1990)

The spectrum received at radius rThe spectrum received at radius r

When calculating the radiative transfer from dr’ to r, we neglect for simplicity the scattering.

Then from the region inside of r:

From the region outside of r:

The Compton heating/cooling rateThe Compton heating/cooling rate

The number of scattering at The number of scattering at

radius r with unit length andradius r with unit length and

optical depth is :optical depth is :

So the heating/cooling rate (per unit volume of the So the heating/cooling rate (per unit volume of the accretion flow) at radius r is:accretion flow) at radius r is:

es

unit length in r

When Compton heating/cooling is important?When Compton heating/cooling is important?

Result: Cooling is important when dotM>0.01 Heating is important when dotM>0.2 (function of r!)

We compare Compton heating/cooling with viscous heating (why?)

Getting the self-consistent solutionsGetting the self-consistent solutions

ieii

ieee

k

s

out

out

qqdr

dp

dr

dv

qqqdr

dp

dr

dv

prjrv

dr

dpr

dr

dvv

R

RMvRHM

)1(

)(

1

4

2

2

2

22

..

compq

δ~0.5 (from the modeling to Sgr A*)

The new Compton heating/cooling term

Get the self-consistent solutions Get the self-consistent solutions using the iteration methodusing the iteration method

procedure: procedure: – guess the value of Compton heating/cooling guess the value of Compton heating/cooling

at each radius, at each radius, – solve the global solution,solve the global solution,– compare the obtained Compton compare the obtained Compton

heating/cooling with the guessed value to see heating/cooling with the guessed value to see whether they are identical. whether they are identical.

– If not, use the new value of Compton heating If not, use the new value of Compton heating and get the new solution until they are and get the new solution until they are identical.identical.

Electron temperature Compton heating/cooling rate

The self-consistent solutions (I): dynamics

Self-consistent solution

The self-consistent solutions (II): spectrum

For a given dotM, L should be larger, but Ecutoff smaller

Consequence of strong Compton Consequence of strong Compton heating at large radiiheating at large radii

Compton heating is important at large radii when Compton heating is important at large radii when accretion rate is largeaccretion rate is large

As a result, As a result, no steadyno steady hot solution exists when hot solution exists when Mdot is largeMdot is large

This will result in “oscillation” of the activity of BH:This will result in “oscillation” of the activity of BH:strong Compton heating strong Compton heating drive the gas outside of a certain drive the gas outside of a certain

radius out and only matter within this radius accreted radius out and only matter within this radius accreted all matter all matter

is used up is used up the central luminosity stops the central luminosity stops inflow resumes on inflow resumes on

a cooling timescale a cooling timescale the cycle repeats. the cycle repeats.

Two-dimensional caseTwo-dimensional case

The above conclusion holds for 1-DThe above conclusion holds for 1-D

For a 2-D accretion flow, when Mdot is high, For a 2-D accretion flow, when Mdot is high, scattering is important. Then, much of the scattering is important. Then, much of the luminosity will "leak out" perpendicular to the discluminosity will "leak out" perpendicular to the disc

In this caseIn this case– we may obtain we may obtain steadysteady solution up to a higher luminosity solution up to a higher luminosity– Strong outflow will be driven (force & energy) in the Strong outflow will be driven (force & energy) in the

vertical directionvertical direction– These outflow may be fragmented due to thermal These outflow may be fragmented due to thermal

instability instability explain the origin of BLR in AGNs? explain the origin of BLR in AGNs?– radiation-hydrodynamic simulation is required to checkradiation-hydrodynamic simulation is required to check