Standard candles
| English | Chinese | Pinyin |
|---|---|---|
| standard candle | 标准烛光 | biāo zhǔn zhú guāng |
| luminosity | 光度 | guāng dù |
| flux | 流量 | liú liàng |
| Cepheid variable | 造父变星 | zào fù biàn xīng |
| parallax | 视差 | shìchā |
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 标准烛光 — an object whose true brightness we already know.
- Compare known brightness with how bright it looks, and the distance follows.
Standard candle distance lab
brightness proportional to 1 / distance^2
Move distance and see why brightness falls quickly.
Luminosity 光度 and flux 流量
- 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 $\dfrac{1}{d^{2}}$.
For Cepheid variables 造父变星 the pulsation period sets the luminosity, making them standard candles
The luminosity of a star is:
Luminosity $L$ is the energy radiated per second in all directions (watts).
The flux received from a star falls as 1 over the distance ____.
$F = \dfrac{L}{4\pi d^{2}}$ — the inverse-square law.
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 $d$.
The Andromeda Galaxy, our nearest large galaxy, about 2.5 million light-years away
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 视差.
The four units of ESO's Very Large Telescope in Chile, used to measure the flux from distant stars
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.
A Cepheid variable's pulsation period tells you its luminosity.
The period–luminosity relation makes Cepheids excellent standard candles.
You've got it
- 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