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Astronomy & space · lesson 2 of 4

Flux, luminosity and stellar magnitudes

Luminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).

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Learn the ideas

Prerequisites: Logarithms and inverse-square relationships.

Luminosity and flux

Luminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).

Magnitude

Magnitude differences use a logarithmic scale: m2−m1=−2.5 log10(F2/F1). A smaller magnitude denotes a brighter source in the same band.

Absolute magnitude

Absolute magnitude compares sources at the conventional distance of 10 pc. Bandpass and extinction assumptions must be specified.

Distance modulus

Ignoring extinction, m−M=5 log10(d/10 pc). Dust can dim and redden a source, so uncorrected brightness is not purely a distance indicator.

Worked examples

Example 1

For equal luminosity and negligible absorption, one source is twice as far away. Find its flux divided by the nearer source's flux.

The inverse-square law gives 1/2².

0.25

Example 2

A source becomes 100 times brighter in the same band. Find mnew−mold.

−2.5 log10(100)=−5.

-5

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

1 For equal luminosity and negligible absorption, one source is twice as far away. Find its flux divided by the nearer source's flux.

Show answer and explanation

0.25

The inverse-square law gives 1/2².

2 A source becomes 100 times brighter in the same band. Find mnew−mold.

Show answer and explanation

-5

−2.5 log10(100)=−5.

3 Which quantity describes emitted power rather than received power per area?

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Luminosity

Luminosity is intrinsic emitted power under the model.

4 Ignoring extinction, find m−M for d=100 pc.

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5

5 log10(100/10)=5.

5 At which conventional distance is absolute magnitude defined?

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10 pc

Absolute magnitude standardizes the distance at 10 parsecs.

6 Why can two equally bright-looking stars have different luminosities?

Sample answer and marking guidance

Their distances and intervening extinction can differ. The received flux alone does not uniquely determine luminosity.

Credit distance and at least the possibility of absorption.

7 If two sources have the same flux but one has distance 3 times the other, find the luminosity ratio for the farther source.

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9

At equal flux, L scales as d².

8 Why must a magnitude comparison specify the bandpass?

Sample answer and marking guidance

Different spectral energy distributions yield different relative brightness in different bands. A magnitude without a consistent band can mislead.

Credit wavelength-dependent measurement.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.