A research group uses type Ia supernovae as standard candles. Each explosion is assumed to have a power output of 1.0 × 1036 W at maximum brightness. Table ...
Question 1 Report
A research group uses type Ia supernovae as standard candles. Each explosion is assumed to have a power output of 1.0 × 1036 W at maximum brightness. Table 1 gives measurements from four host galaxies. The redshift has been found from spectral lines, and intensity is the power received per square metre at Earth.
| supernova | redshift, z | peak intensity / W/m2 |
|---|---|---|
| A | 0.025 | 7.2 × 10-15 |
| B | 0.040 | 2.8 × 10-15 |
| C | 0.055 | 1.5 × 10-15 |
| D | 0.070 | 9.2 × 10-16 |
For these small redshifts, use v = zc, c = 3.0 × 105 km/s and H0 = 70 km s-1 Mpc-1. Also use I = P/(4πd2) and 1 Mpc = 3.09 × 1022 m.
(a) Calculate the recession speed of the host galaxy of supernova C. [2]
(b) Calculate the distance to the host galaxy of supernova C using Hubble’s law. [2]
(c) Calculate the distance to supernova B from its peak intensity. Give your answer in Mpc. [4]
(d) Describe the trend in Table 1 between redshift and the measured intensity. [2]
(e) Explain why a standard candle can be used to test the expansion of the universe. [3]
Answer Details
(a)
\[v=zc=0.055\times3.0\times10^5=16\,500\text{ km/s}\]
16 500 km/s. [2 marks]
(b) Use Hubble's law, \(d=v/H_0\):
\[d=\frac{16\,500}{70}=236\text{ Mpc}\]
236 Mpc, with 240 Mpc also acceptable. [2 marks]
(c) Rearrange the intensity equation:
\[d=\sqrt{\frac{P}{4\pi I}}\]
\[d=\sqrt{\frac{1.0\times10^{36}}{4\pi\times2.8\times10^{-15}}}=5.3\times10^{24}\text{ m}\]
Convert to megaparsecs:
\[d=\frac{5.3\times10^{24}}{3.09\times10^{22}}=172\text{ Mpc}\]
172 Mpc, with 170 Mpc also acceptable. [4 marks]
(d) As redshift increases from 0.025 to 0.070, the measured intensity decreases. Therefore more red-shifted supernovae appear dimmer. [2 marks]
(e) A standard candle has a known power output, or luminosity. Its measured intensity can therefore be used to calculate its distance. Comparing this distance with redshift or recession speed tests Hubble's relationship and hence the expansion of the universe. [3 marks]
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