Accretion Disk Matt Coleman Institute for Advanced Study Boundary - - PowerPoint PPT Presentation
Accretion Disk Matt Coleman Institute for Advanced Study Boundary Layers mcoleman@ias.edu UNLV - Athena++ User Meeting - 3/20/19 The Boundary Layer P disk, ram > P , mag Where the disk meets the star MRI doesnt work How
UNLV - Athena++ User Meeting - 3/20/19
Matt Coleman Institute for Advanced Study mcoleman@ias.edu
Mach number
ℳ = ( 8π 3 G3σm4
u
k4
b
)
1/8
M3/2μ1/2 · M−1/8R−1/8τ−1/8 (CV hot) = 32 ( M 0.6M⊙ )
3/8
( μ 0.6)
1/2
( · M−9 R 9 Mm τ 104 )
−1/8
(CV cold) = 270 ( M 0.6M⊙ )
3/8
( μ 2 )
1/2
( · M−11 R 9 Mm τ 5 )
−1/8
(AM CVn hot) = 55 ( M 1.1M⊙ )
3/8
( μ 1.4)
1/2
( · M−9 R 4.7 Mm τ 5 × 104 )
−1/8
(AM CVn cold) = 330 ( M 1.1M⊙ )
3/8
( μ 4 )
1/2
( · M−12 R 4.7 Mm τ 2000 )
−1/8
(PPD) = 53 ( M M⊙ )
3/8
( μ 2 )
1/2
( · M−8 R 2R⊙ τ 75 )
−1/8
(FU Ori) = 5.3 ( M M⊙ )
3/8
( μ 0.6)
1/2
( · M−5 R 2R⊙ τ 6 × 105)
−1/8
Numeric considerations
h⋆ ∼ ℳ−2, dt ∼ h⋆ ℳ ∼ ℳ−3
Hydrodynamically Unstable
ϕ = ϕ0 − sign (r − rp) 2 R⋆ r + r R⋆ ( R⋆ rp )
3/2
− 3 R⋆ rp
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 −2 −1 CS ×10−5
CS 10 5 11 16 4 sum
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 −0.5 0.0 ×10−4
CL CA CS
m9-0.90 t/2π = 299.9 − 399.9
CS = Stress Transport CA = Advective Transport CL = CS + CA = Total Transport
Sim Class M Runs done Nr Nphi 2DM5 5 2 1024 1024 2DM6 6 4 1024 1024 2DM6HR 6 6 2048 2048 2DM7 7 1 2048 2048 2DM8 8 1 2048 2048 2DM9LR 9 7 2048 2048 2DM9 9 7 4096 4096 2DM9HR 9 1 8192 8192 2DM10 10 1 4096 4096 2DM11 11 1 4096 4096 2DM12 12 5 4096 4096 2DM13 13 1 8192 8192 2DM14 14 1 8192 8192 2DM15 15 1 8192 8192
Curves are single parameter fit.
5 10 15 20 25 30 m 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ωp
M=5, r0 =0.82 M=6, r0 =0.85 M=7, r0 =0.86 M=8, r0 =0.88 M=9, r0 =0.89
Ωp Ω (R⋆) = ℳ−2 + ( ℳR⋆ 2mr0 )
2
Accretion Disk Boundary Layers
Matt Coleman Institute for Advanced Study mcoleman@ias.edu