Understanding Thermal Stability of Radiation-Dominated Disks

and

Radiative Efficiency of Global Relativistic Disks

withOmer Blaes, Shigenobu Hirose

Scott Noble, John Hawley, Kris Beckwith

Understanding Thermal Stability of Radiation-Dominated Disks

Radiation-Dominance Is the Natural State of the Interesting Portions of Bright Disks

r=rg < 170(L=LE )16=21(M=M ¯ )2=21

Radiation pressure exceeds gas pressure for

That is, for the most interesting parts of all bright accretion disks around black holes

Yet – Model Predicts Thermal Instability When pr > pg

$\int dz Q \propto p_r h$$

Shakura & Sunyaev 1976

When radiation pressure dominates, h / F =

ZdzQ

And pr » Qtcool » Q(h=c)¿ » (¿=c)ZdzQ

Thermal Instability

Energy conservation gives

ZdzQ » ­

ZdzTrÁ

The model asserts

ZdzTr Á »

Zdzp

Dissipation and Pressure Are Correlated

So why doesn’t the thermal instability take place ?

What Does Dimensional Analysis Really Imply?

Orbital shear does work on magnetic field, magnetic field dissipates, heat becomes radiation----so magnetic energy and stress drive the pressure, not the other way around!

Pressure and stress are comparable, but does that mean pressure controls stress?

Evidence from Simulation Data

Magnetic Energy vs. Radiation Energy

Magnetic leads Radiation leads

Explore with Toy Model

In dimensionless form,

dEBd¿ = R(t)EnR ¡ EB

dERd¿ =

EB 0ER0

¡EB ¡ E1¡ sR

¢

dEBdt =R(t)

EB 0tgrowth

µERER0

¶n¡EBtdiss

dERdt =

EBtdiss

¡ERtcool

Results Strongly Resemble Simulations

Without any intrinsic pressure-stress correlation: n=s=0

Including a Pressure/Magnetic Energy Correlation --- After the Fact

EB / E1¡ sR

Thermal balance means

Independent of n

Which Variables Really Control the Stress?

As suggested by the structure of shearing-box simulations, and are the truly fundamental variables wherever the inflow time is the longest timescale.

Magnetic field intensity, and secondarily, the pressure, follow, with dissipation of magnetic energy driving the pressure, as regulated by the radiative loss rate.

Radiative Efficiency of Global Relativistic Disks

Origin of Traditional Efficiency Numbers:the Novikov-Thorne model

• Full GR• Time-steady, axisymmetric, vertically-integrated• Energy and angular momentum conservation• Boundary conditions—

energy: prompt radiation carries off dissipation

angular momentum: zero-stress at ISCO

= ut(ISCO)

MHD Stresses Don’t Know to Stop at the ISCO

(Thorne 1974): “In the words of my referee, James M. Bardeen (which echo verbal warnings that I have received from Ya. B. Zel’dovich and V.F. Schwartzman), ‘It seems quite possible that magnetic stresses could cause large deviations from circular orbits in the very inner part of the accretion disk….’”

It follows that the Novikov-Thorne radiative efficiency numbers may not be the last word when magnetic stresses are important.

Numerical Procedure

• Extend HARM (GR/MHD, total-energy, conservative) from 2-d axisymmetric to 3-d

• Introduce toy-model optically thin cooling function: (1) rapidly radiates (almost) all the heat generated (2) allows aspect ratio regulation

L = ­ ½²·

²(H ­ )2

¡ 1+ j²

(H ­ )2¡ 1j

¸1=2

r ºT º¹ = ¡ Lu¹

A First Result

a/M = 0.9

H/r = 0.1

T = 15000 GM/c3

Surface Brightness in the Fluid Frameaveraged over 10000—12000M

Preliminary Summary

• There is noticeable radiation beyond N-T• Dependence on H/r, a/M to be explored