AST-13

Chandrasekhar mass

M_Ch ≈ 1.456 (2/μ_e)² M_⊙. White-dwarf mass limit.

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StarsChandrasekhar

Governing equation

M_{\mathrm{Ch}}\approx 1.456\,(2/\mu_e)^2 M_\odot

$\mu_e \in \left[1.5, 2.2\right]$

where

\mu_e: Mean e per nucleon (—)
M_{Ch}: Chandrasekhar mass (M_\odot)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

M_{\mathrm{Ch}}\approx 1.456\,(2/\mu_e)^2 M_\odot

$\mu_e \in \left[1.5, 2.2\right]$

$\mu_e = 1.5$ $M_{Ch} = 2.588$

Along the curve

②

Domain of the variable — blue

\mu_e_{\min} = 1.5,\quad \mu_e_{\max} = 2.2

$\mu_e \in \left[1.5, 2.2\right]$

$\mu_e = 1.5$ $\mu_e = 1.5$

Along the curve

③

Response curve — green

M_{\mathrm{Ch}}\approx 1.456\,(2/\mu_e)^2 M_\odot

$\mu_e \in \left[1.5, 2.2\right]$

$\mu_e = 1.5$ $M_{Ch} = 2.588$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}M_{Ch}}{\mathrm{d}\mu_e}

$\mu_e \in \left[1.5, 2.2\right]$

$\mu_e = 1.504$ $M_{Ch}^{\prime} = -3.421$

Along the curve

Lecture brief

Historical brief

Hubble expansion, Jeans collapse, Eddington luminosity, Bondi accretion and Stefan–Boltzmann stars are the first astrophysical budgets. The sheets scale a star, a cloud and a horizon. This sheet (AST-13 — Chandrasekhar mass) is the form associated with Chandrasekhar. Working symbols: $\mu_e$ $\rightarrow$ $M_{Ch}$ . Electron degeneracy versus gravity. Type Ia supernovae sit at this edge.

Purpose

Purpose: compute

M_{Ch}

from

\mu_e

in Astrophysics via

M_{\mathrm{Ch}}\approx 1.456\,(2/\mu_e)^2 M_\odot

M_Ch ≈ 1.456 (2/μ_e)² M_⊙. White-dwarf mass limit. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mu_e = 2.000\,\mathrm{—}

, the governing relation

M_{\mathrm{Ch}}\approx 1.456\,(2/\mu_e)^2 M_\odot

yields

M_{Ch} = 1.456\,\mathrm{M_odot}

. A dwarf, a mass bar hitting a ceiling. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mean e per nucleon \mu_e2 —

Outputs

Chandrasekhar mass M_{Ch}1.456 M_\odot

Reading speed

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Narration of this film

A dwarf, a mass bar hitting a ceiling.

Electron degeneracy versus gravity. Type Ia supernovae sit at this edge.

Reading speed

Watch on YouTube