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AST-22

Mass–luminosity relation

L/L_⊙ ≈ (M/M_⊙)^{3.5} on the upper main sequence. A power-law sketch.

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StarsMass–luminosity

Governing equation

L/L⊙≈(M/M⊙)3.5L/L_\odot\approx(M/M_\odot)^{3.5}

where

M
Mass (M_\odot)
L
Luminosity (L_\odot)

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-22 — Mass–luminosity relation) is the form associated with Mass–luminosity. Working symbols: MM →\rightarrow LL. Eddington argued L ∝ M³ for radiative opacity. Massive stars live fast.

Purpose

Purpose: compute LL from MM in Astrophysics via L/L⊙≈(M/M⊙)3.5L/L_\odot\approx(M/M_\odot)^{3.5} L/L_⊙ ≈ (M/M_⊙)^{3.5} on the upper main sequence. A power-law sketch. Use it when a real astrophysics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given M=2.000 ModotM = 2.000\,\mathrm{M_odot}, the governing relation L/L⊙≈(M/M⊙)3.5L/L_\odot\approx(M/M_\odot)^{3.5} yields L=11.31 LodotL = 11.31\,\mathrm{L_odot}. A mass slider, a soaring L. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • Luminosity L11.31 L_\odot
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AST-22 · star
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Narration of this film

A mass slider, a soaring L.

Eddington argued L ∝ M³ for radiative opacity. Massive stars live fast.

Reading speed

Watch on YouTube