AST-02

Eddington luminosity

Thomson electron scattering.

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AstroEddington

Governing equation

L_{\mathrm{Edd}}=4\pi G M c/\kappa

$M \in \left[0.5, 1\times 10^{8}\right]$

where

M: Mass (M_\odot)
L: L (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_{\mathrm{Edd}}=4\pi G M c/\kappa

$M \in \left[0.5, 1\times 10^{8}\right]$

$M = 0.5$ $L = 16000$

Along the curve

②

Domain of the variable — blue

M_{\min} = 0.5,\quad M_{\max} = 1\times 10^{8}

$M \in \left[0.5, 1\times 10^{8}\right]$

$M = 0.5$ $M = 0.5$

Along the curve

③

Response curve — green

L_{\mathrm{Edd}}=4\pi G M c/\kappa

$M \in \left[0.5, 1\times 10^{8}\right]$

$M = 0.5$ $L = 16000$

Along the curve

④

Rate of change — amber

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

$M \in \left[0.5, 1\times 10^{8}\right]$

$M = 6.29\times 10^{5}$ $L^{\prime} = 32000$

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-02 — Eddington luminosity) is the form associated with Eddington. Working symbols: $M$ $\rightarrow$ $L$ . Thomson electron scattering.

Purpose

Purpose: compute

L

from

M

in Astrophysics via

L_{\mathrm{Edd}}=4\pi G M c/\kappa

Thomson electron scattering. 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 = 10.000\,\mathrm{M_odot}

, the governing relation

L_{\mathrm{Edd}}=4\pi G M c/\kappa

yields

L = 320000.00\,\mathrm{L_odot}

. Thomson electron scattering. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass M10 M_\odot

Outputs

L L320000.00 L_\odot

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Narration of this film

Thomson electron scattering.

Reading speed

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