25.1 Standard candles
- Syllabus
- 9702–2028–2029
- Topic
- 25.1
- Level
- A2
Learning objectives
25.1.1The term luminosity as the total power of radiation emitted by a star• understand the term luminosity as the total power of radiation emitted by a star25.1.2The inverse square law for radiant flux intensity F• recall and use the inverse square law for radiant flux intensity F in terms of the luminosity L of the source F = L / (4πd 2)25.1.3An object of known luminosity is called a standard candle• understand that an object of known luminosity is called a standard candle25.1.4The use of standard candles to determine distances to galaxies• understand the use of standard candles to determine distances to galaxies
Luminosity is a star's total emitted radiation power
Luminosity L is the total power of electromagnetic radiation emitted by a star in all directions. Its SI unit is the watt (W).
Luminosity is an intrinsic property of the source: moving the observer does not change L, provided the star itself is unchanged.
Radiant flux intensity F is power received per unit area at a location, in W m⁻². It decreases with distance even though the source luminosity remains the same.
Do not define luminosity as apparent brightness or power received by a telescope. Include total, radiation and power in the definition.
Radiant flux falls as luminosity spreads over a sphere
For an isotropic source, total power L crosses a sphere of radius d and area 4πd². Power per unit area is therefore the inverse-square radiant flux intensity.
F=L/(4πd2)L=4πd2F;d=√[L/(4πF)]
L is in W, d in m and F in W m⁻². Doubling d makes F one quarter; multiplying d by k divides F by k².
For the Sun L=3.85×10²⁶ W at d=1.50×10¹¹ m, F=3.85×10²⁶/[4π(1.50×10¹¹)²]=1.36×10³ W m⁻².
Square the entire distance and retain 4π. This law assumes approximately isotropic emission and no additional absorption between source and observer.
A standard candle is an astronomical object with known luminosity
A standard candle is an astronomical object whose luminosity L is known from its identified class or an independent calibration.
Because L is known, measuring its radiant flux intensity F supplies the two quantities needed to infer distance from the inverse-square law.
The object must be correctly identified as belonging to the calibrated class; 'standard' means known intrinsic luminosity, not equal apparent brightness wherever observed.
A bright object is not automatically a standard candle. Its luminosity must be known independently of the distance being inferred.
Use a standard candle's known luminosity and measured flux to find galaxy distance
- Identify a standard candle in the galaxy. 2. Use its calibrated luminosity L. 3. Measure its radiant flux intensity F at Earth. 4. Calculate the distance.
d=√[L/(4πF)]
For L=1.90×10³⁶ W and F=8.42×10⁻¹⁶ W m⁻², d=√[1.90×10³⁶/(4π×8.42×10⁻¹⁶)]=1.34×10²⁵ m.
A star or event inside a distant galaxy is effectively at the galaxy's distance because the galaxy's size is small compared with its distance from Earth.
Uncorrected absorption by dust makes F too small and therefore makes the inferred d too large. The method assumes the calibrated L applies and propagation losses are corrected or negligible.