Math 2.0

Astronomy and astrophysics Definition

Hayashi track

Builds on Stellar structureSchwarzschild criterion for convectionEffective temperature

Definition

Fix a stellar mass MM and a chemical composition. Consider the stellar structure models of mass MM that are convective from the centre to the photosphere. Here convective is meant in the sense of the Schwarzschild criterion, and the interior gradient is taken adiabatic. Let LL be the luminosity and TeffT_{\mathrm{eff}} the effective temperature. The Hayashi track of mass MM is the curve traced by these models, as their radius varies, in the plane of log⁡Teff\log T_{\mathrm{eff}} and log⁡L\log L.

Remarks

Matching an adiabatic interior to a photosphere whose opacity is dominated by negative hydrogen ions makes TeffT_{\mathrm{eff}} depend only weakly on LL, so the track is nearly vertical. Example: a newly formed star of one solar mass contracts down its Hayashi track, with TeffT_{\mathrm{eff}} around 4000 K4000 \, \mathrm{K}, until a radiative core appears. Non-example: the Sun today is not on its Hayashi track, since its core is radiative; only its outer envelope is convective. Models to the right of the track, at lower TeffT_{\mathrm{eff}}, would need a temperature gradient steeper than adiabatic, which convection removes at once, so such equilibria do not exist.

Reading path

To understand this page from the ground up, read these 90 pages in order. The foundations come first.

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

Further reading

  1. Web https://en.wikipedia.org/wiki/Hayashi_track
About this page
TagFNY22W16F8
URIm2://FNY22W16F8
Kinddefinition
WritingW0 stub
MSC85A15
DefinesHayashi track
UsesStellar structure, Schwarzschild criterion for convection, Effective temperature
Changed3 November 2026

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