Magneto-acoustic waves in an asymmetric magnetic slab Progress in - PowerPoint PPT Presentation

Magneto-acoustic waves in an asymmetric magnetic slab Progress in spatial magneto-seismology Matthew Allcock and Robertus Erd´ elyi

Solar magneto-seismology Observations

Solar magneto-seismology Wave parameters Observations Equilibrium parameters

Solar magneto-seismology Wave Temporal parameters parameters Spatial Observations parameters Equilibrium parameters

Solar magneto-seismology Wave Temporal parameters parameters Spatial Observations parameters Equilibrium parameters Physical understanding

Solar magneto-seismology Wave Temporal parameters parameters Spatial Observations parameters Equilibrium parameters Physical Equilibrium understanding models

Solar magneto-seismology Wave Temporal parameters parameters Spatial Observations parameters Equilibrium parameters Physical Equilibrium Eigenmodes understanding models

Solar magneto-seismology Wave Temporal parameters parameters Spatial Temporal Observations parameters magneto-seismology Equilibrium Spatial parameters magneto-seismology Physical Equilibrium Eigenmodes understanding models

Solar magneto-seismology Wave Temporal parameters parameters Spatial Temporal Observations parameters magneto-seismology Equilibrium Spatial parameters magneto-seismology Physical Equilibrium Eigenmodes understanding models

Solar magneto-seismology Wave Temporal parameters parameters Spatial Temporal Observations parameters magneto-seismology Equilibrium Spatial parameters magneto-seismology Physical Equilibrium Eigenmodes understanding models

Solar magneto-seismology Wave Temporal parameters parameters Spatial Temporal Observations parameters magneto-seismology Equilibrium Spatial parameters magneto-seismology Physical Equilibrium Eigenmodes understanding models

Motivation Max Planck Institute for Solar System Research BBSO/NJIT

Equilibrium conditions ρ 1 , p 1 , T 1 ρ 2 , p 2 , T 2 ρ 0 , p 0 , T 0 z y x 0 x − x 0 Uniform magnetic field in the slab. Field-free plasma outside. Different density and pressure on each side.

Governing equations Ideal MHD equations: Conservation of: ρ D ✈ D t = −∇ p − 1 µ ❇ × ( ∇ × ❇ ) , momentum ∂ρ ∂ t + ∇ · ( ρ ✈ ) = 0 , mass � p � D = 0 , energy D t ρ γ ∂ ❇ ∂ t = ∇ × ( ✈ × ❇ ) , magnetic flux ✈ = plasma velocity, ❇ = magnetic field strength, ρ = density, p = pressure, µ = magnetic permeability, γ = adiabatic index.

Asymmetric slab modes Dispersion relation: ω 4 m 02 k 2 v A 2 − ω 2 + ρ 0 ρ 0 m 2 ( k 2 v A 2 − ω 2 ) m 1 ρ 1 ρ 2 � ρ 0 � − 1 m 1 + ρ 0 2 m 0 ω 2 m 2 (tanh m 0 x 0 + coth m 0 x 0 ) = 0 , ρ 1 ρ 2 m 02 = ( k 2 v A 2 − ω 2 )( k 2 c 2 0 − ω 2 ) ω 2 m 1 , 22 = k 2 − 0 + v A 2 )( k 2 c T 2 − ω 2 ) , c 1 , 22 , ( c 2 c 2 0 v A 2 B 0 c T 2 = v A = 0 + v A 2 , , c 2 √ µρ 0 See Allcock and Erd´ elyi, 2017.

Asymmetric slab modes

Asymmetric slab modes

Asymmetric slab modes

Amplitude ratio ˆ ˆ ξ x ( − x 0 ) ξ x ( x 0 ) x x 0 − x 0 Amplitude ratio ˆ ξ x ( x 0 ) Top = quasi-kink R A := ( Bottom = quasi-sausage ) ˆ ξ x ( − x 0 ) � tanh � ( k 2 v A 2 − ω 2 ) m 1 ρ 1 − ω 2 m 0 ρ 0 ( m 0 x 0 ) � + � ρ 1 m 2 coth � tanh � = ( k 2 v A 2 − ω 2 ) m 2 ρ 2 − ω 2 m 0 − ρ 2 m 1 ρ 0 ( m 0 x 0 ) coth

Minimum perturbation shift x x x 0 x 0 − x 0 − x 0 � � ξ x ξ x ∆ min ∆ min x 0 x x 0 x − x 0 − x 0

Minimum perturbation shift x x x 0 x 0 − x 0 − x 0 Quasi-kink: Quasi-sausage: � 1 � ∆ min = 1 ∆ min = 1 tanh − 1 ( D ) tanh − 1 m 0 m 0 D ( k 2 v A 2 − ω 2 ) m 2 ρ 2 tanh( m 0 x 0 ) − ω 2 m 0 ρ 0 where D = ( k 2 v A 2 − ω 2 ) m 2 ρ 2 − ω 2 m 0 tanh( m 0 x 0 ) ρ 0

Solar magneto-seismology Parameter inversion Observe : ω , k , x 0 , T i , and R A or ∆ min . Solve to find: v A and hence B 0 .

Further work Generalise the model to a variety of structures: ρ 1 , p 1 , T 1 ρ 2 , p 2 , T 2 ρ 0 , p 0 , T 0 z y x 0 x − x 0

Further work Generalise the model to a variety of structures: Add magnetic field outside the slab - coronal structures. See Zs´ amberger and Erd´ elyi , published soon. ρ 1 , p 1 , T 1 ρ 2 , p 2 , T 2 ρ 0 , p 0 , T 0 z y x 0 x − x 0

Further work Generalise the model to a variety of structures: Add magnetic field outside the slab - coronal structures. See Zs´ amberger and Erd´ elyi , published soon. Add steady flow - dynamic structures e.g. solar wind. See Mihai Barbulescu ’s poster. U 0 ρ 1 , p 1 , T 1 ρ 2 , p 2 , T 2 ρ 0 , p 0 , T 0 z y x 0 x − x 0

Future work Apply to observations of MHD waves in, for example: Elongated magnetic bright points , Adaptation of Liu et al., 2017, by N. Zs´ amberger

Future work Apply to observations of MHD waves in, for example: Elongated magnetic bright points , Prominences , NASA

Future work Apply to observations of MHD waves in, for example: Elongated magnetic bright points , Prominences , Sunspot light walls . Max Planck Institute for Solar System Research

”a day without the Sun is, you know, night” matthew allcock