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_\odot\approx(M/M_\odot)^{3.5}

$M \in \left[0.2, 40\right]$

where

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

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

$M \in \left[0.2, 40\right]$

$M = 0.2$ $L = 0.004$

Along the curve

②

Domain of the variable — blue

M_{\min} = 0.2,\quad M_{\max} = 40

$M \in \left[0.2, 40\right]$

$M = 0.2$ $M = 0.2$

Along the curve

③

Response curve — green

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

$M \in \left[0.2, 40\right]$

$M = 0.2$ $L = 0.004$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}L}{\mathrm{d}M}

$M \in \left[0.2, 40\right]$

$M = 0.45$ $L^{\prime} = 0.568$

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

Purpose

Purpose: compute

L

from

M

in Astrophysics via

L/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\,\mathrm{M_odot}

, the governing relation

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

yields

L = 11.31\,\mathrm{L_odot}

. A mass slider, a soaring L. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass M2 M_\odot

Outputs

Luminosity L11.31 L_\odot

Reading speed

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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