Math 2.0

Astronomy and astrophysics Definition

Parker instability

Builds on MagnetohydrodynamicsMagnetic fieldHydrostatic equilibrium

Definition

Consider a perfectly conducting gas in a uniform gravitational field −g ez-g \, e_z with g>0g > 0, governed by ideal magnetohydrodynamics. Let the gas be in a static equilibrium stratified in the height zz, with a horizontal magnetic field B(z)exB(z) e_x. In this equilibrium the gas pressure and the magnetic pressure together balance gravity, as in hydrostatic equilibrium. The Parker instability is the linear instability of this equilibrium to perturbations that bend the field lines in the vertical (x,z)(x, z) plane. In the growing perturbation, gas flows along the field lines from the crests into the troughs, and the crests rise by buoyancy.

Remarks

Example: in an isothermal layer with a constant ratio of magnetic to gas pressure, the equilibrium density falls off exponentially with height, and perturbations of long enough horizontal wavelength grow. Non-example: an isothermal layer with no magnetic field, supported by gas pressure alone, is convectively stable and shows no Parker instability. The instability needs the field to carry part of the weight. Perturbations that vary only across the field, without bending it, are called interchange modes; the Parker instability refers to the undular modes along the field. The cosmic rays of the galaxy add a pressure tied to the field and strengthen the instability.

Reading path

To understand this page from the ground up, read these 88 pages in order. The foundations come first.

  1. Derivative concept
  2. Differential equation concept
  3. Euclidean space object
  4. Euclidean vector concept
  5. Euler equations concept
  6. Function concept
  7. Interval concept
  8. Lane–Emden equation concept
  9. Limit point of a set definition
  10. Local maximum definition
  11. Magnetic field concept
  12. Magnetohydrodynamics concept
  13. Ordinary differential equation concept
  14. Partition of an interval definition
  15. Poisson's equation concept
  16. Sequence definition
  17. Velocity concept
  18. Fréchet derivative definition
  19. Cross product definition
  20. Ordinary differential equation definition
  21. Function of several variables concept
  22. Vector-valued function concept
  23. Lipschitz condition definition
  24. Classical mechanics concept
  25. Limit of a function definition
  26. Local minimum definition
  27. Mesh of a partition definition
  28. Riemann sum definition
  29. Real sequence definition
  30. Subsequence definition
  31. Limit of a function of several variables concept
  32. Momentum concept
  33. Partial derivative concept
  34. Solution of an ordinary differential equation definition
  35. Inertial frame of reference concept
  36. Continuity at a point definition
  37. Derivative definition
  38. Riemann integrable function definition
  39. Bounded sequence definition
  40. Limit of a sequence definition
  41. Monotone sequence definition
  42. Continuity in R^n definition
  43. Differentiable function of several variables definition
  44. Partial derivative definition
  45. Initial value problem definition
  46. Newton's laws of motion statement
  47. Continuous function definition
  48. Antiderivative definition
  49. Riemann integral definition
  50. Fermat's theorem on stationary points statement
  51. Convergent sequence definition
  52. Monotone convergence theorem for sequences statement
  53. Every sequence has a monotone subsequence statement
  54. Differentiable on an open set definition
  55. Gradient definition
  56. Higher partial derivatives definition
  57. Picard–Lindelöf hypotheses definition
  58. Intermediate value theorem statement
  59. Definite integral definition
  60. Bolzano–Weierstrass theorem statement
  61. Iterated derivative definition
  62. Picard operator definition
  63. Additivity of the integral over intervals statement
  64. Boundedness theorem statement
  65. Monotonicity of the integral statement
  66. C^k function characterised by continuous derivatives statement
  67. Integral equation form of an initial value problem statement
  68. An iterate of the Picard operator is a contraction statement
  69. Extreme value theorem statement
  70. Vector field definition
  71. Picard–Lindelöf theorem statement
  72. Mean value theorem for integrals statement
  73. Rolle's theorem statement
  74. Conservative vector field definition
  75. Mean value theorem statement
  76. First fundamental theorem of calculus statement
  77. Classical mechanics definition
  78. Potential energy definition
  79. Momentum definition
  80. Second fundamental theorem of calculus statement
  81. Kinetic energy definition
  82. Angular momentum definition
  83. Fundamental theorem of calculus statement
  84. Central force definition
  85. Virial theorem statement
  86. Newton's law of universal gravitation statement
  87. Hydrostatic equilibrium statement
  88. Parker instability definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Magnetic_buoyancy
About this page
TagT65B79VD3F
URIm2://T65B79VD3F
Kinddefinition
WritingW0 stub
MSC85A30, 76E25, 76W05
DefinesParker instability
UsesMagnetohydrodynamics, Magnetic field, Hydrostatic equilibrium
Changed3 November 2026

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