Astrophysics Chandrasekhar Limit Rs

The Chandrasekhar limit

The Chandrasekhar limit is the maximum mass a white dwarf star can have before electron degeneracy pressure can no longer hold it up against gravity. Above roughly 1.4 solar masses, the star must collapse further, becoming a neutron star or a black hole. Subrahmanyan Chandrasekhar derived this threshold in 1930 using quantum mechanics and special relativity; it is one of the best-known numbers in astrophysics.

The limit follows from balancing the inward pull of gravity against the outward pressure of electrons packed so tightly that quantum effects dominate. In the standard derivation, the maximum mass depends only on fundamental constants and the mean molecular weight per electron, not on the star's temperature or composition. The result is usually written as about 1.4 M☉, where M☉ is one solar mass.

In Recognition Science, the framework models recognition costs with a forced cost function J(x) = (x + 1/x)/2 - 1. The module domainCost, a cost function defined on a ratio of two masses, is set to J(m/e). The formal library proves three general facts about this cost: it is zero when the two masses are equal, it is nonnegative for positive masses, and the quantity phi - 3/2 is positive. Those are the only proved results; the module contains no theorem specific to stars.

The research note in the module suggests a match: phi^(-1) * 2.26 M☉ equals 1.40 M☉, the standard Chandrasekhar value. That identification is a hypothesis, not a derivation. The module does not define m and e in astrophysical terms, so the framework cannot yet claim to prove the limit.

What the module does establish is a small, clean set of properties any such cost function must satisfy. A reader can see that the framework's cost vanishes at equality, stays nonnegative, and has a positive threshold. The astrophysical punchline, the 1.4 solar mass value, remains a target for future work.

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

What this page does not claim

The framework proves the Chandrasekhar limit is 1.4 solar masses. The match phi^(-1) * 2.26 M☉ = 1.40 M☉ is a derived result. The module defines m and e in astrophysical terms.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Astrophysics/Chandrasekhar_Limit_RS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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