with Omer Blaes, Shigenobu Hirose Scott Noble, John Hawley, Kris Beckwith

1. Understanding Thermal Stability of Radiation-Dominated DisksandRadiative Efficiency of Global Relativistic Disks with Omer Blaes, Shigenobu Hirose Scott Noble, John Hawley, Kris Beckwith

2. Understanding Thermal Stability of Radiation-Dominated Disks

3. = = 1 6 2 1 2 2 1 = ( = ) ( = ) L L M M 1 7 0 < r r E ¯ g Radiation-Dominance Is the Natural State of the Interesting Portions of Bright Disks Radiation pressure exceeds gas pressure for That is, for the most interesting parts of all bright accretion disks around black holes

4. h k & S S 1 9 7 6 a u r a u n y a e v Z Z Z Z Z Z ( = ) ( = ) h d Q Q Q t d d T d d Q ­ T p c ¿ ¿ c z » » » l z z p z z » Á h d » F Q Á r c o o r r / z = h l b l T I i i t t e r m a n s a y Yet a – Model Predicts Thermal Instability When pr > pg $\int dz Q \propto p_r h$$ Energy conservation gives The a model asserts When radiation pressure dominates, And

5. Dissipation and Pressure Are Correlated So why doesn’t the thermal instability take place ?

6. What Does Dimensional Analysis Really Imply? Pressure and stress are comparable, but does that mean pressure controls stress? 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!

7. Evidence from Simulation Data Magnetic leads Radiation leads Magnetic Energy vs. Radiation Energy

8. n µ ¶ d E E E E B B R B 0 ( ) R t ¡ = d E d E t t t B h d R i 0 t g r o w s s ( ) n R E E t ¡ = B R d ¿ d E E E R B R ¡ = d t t t d l i d s s c o o E E R B 0 1 ¡ ¡ ¢ s E E ¡ = B R d E ¿ R 0 Explore with Toy Model In dimensionless form,

9. Results Strongly Resemble Simulations Without any intrinsic pressure-stress correlation: n=s=0

10. 1 ¡ s E E / B R Including a Pressure/Magnetic Energy Correlation --- After the Fact Thermal balance means Independent of n

11. Which Variables Really Control the Stress? As suggested by the structure of shearing-box simulations, S and W 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.

12. Radiative Efficiency of Global Relativistic Disks

13. 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 h = ut(ISCO)

14. 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.

15. = 1 2 · ¸ ² ² j j L ­ 1 1 ¡ + ¡ ½ ² = ( ) ( ) 2 2 H ­ H ­ º r T L ¡ u = º ¹ ¹ 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

16. A First Result a/M = 0.9 H/r = 0.1 T = 15000 GM/c3

17. Surface Brightness in the Fluid Frame averaged over 10000—12000M

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