Standard candles
How far is that galaxy?
- We can't lay a tape measure to a galaxy millions of light-years away.
- Instead we use a standard candle — an object whose true brightness we already know.
- Compare known brightness with how bright it looks, and the distance follows.
Luminosity and flux
- Luminosity $L$ is the total power a star radiates.
- At distance $d$ the power spreads over a sphere, so the flux is $F = \dfrac{L}{4\pi d^{2}}$ — it falls as $\dfrac{1}{d^{2}}$.
Practice
The luminosity of a star is:
Luminosity $L$ is the energy radiated per second in all directions (watts).
Practice
The flux received from a star falls as 1 over the distance ____.
$F = \dfrac{L}{4\pi d^{2}}$ — the inverse-square law.
Practice
A star gives a flux of $100\ \dfrac{\text{W}}{\text{m}^2}$ at distance $d$. What is the flux at $3d$?
Inverse-square: $\dfrac{100}{3^{2}} = \dfrac{100}{9} \approx 11\ \dfrac{\text{W}}{\text{m}^2}$.
Finding the distance
- Rearrange: $d = \sqrt{\dfrac{L}{4\pi F}}$.
- Measure the flux $F$ with a telescope, know $L$ from the object's type, and you have $d$.
Standard candles
- Cepheid variables: the pulsation period sets the luminosity.
- Type Ia supernovae: all explode at about the same peak luminosity.
- Both give $L$ without first knowing the distance — reaching far beyond parallax.
Practice
A standard candle is an object whose ____ is known from its type.
Knowing $L$ (without first knowing distance) lets you get the distance from the measured flux.
Practice
A Cepheid variable's pulsation period tells you its luminosity.
The period–luminosity relation makes Cepheids excellent standard candles.
You've got it
Key idea
- luminosity $L$ = total power; flux $F = \dfrac{L}{4\pi d^{2}}$ (inverse-square)
- distance $d = \sqrt{\dfrac{L}{4\pi F}}$ once $L$ is known
- standard candles (Cepheids, Type Ia supernovae) give $L$ from the object's type