The Doppler effect

Mintaka Aa1 and Mintaka Aa2 are two stars in a binary system. This means that they orbit their common centre of mass with the same period.

Table 2 gives information about the two stars.

Show that the data in Table 2 are consistent with the two stars being in a binary system.

State the most prominent absorption lines in the spectrum of Mintaka Aa2.

Explain which star in Table 2 has the greater temperature.

Figure 2 shows how the apparent magnitude of the binary system varies with time.

Explain the variation in apparent magnitude shown in Figure 2.

In your answer you should explain:

the changes in observed brightness at P and Q, as shown in Figure 2

why the observed brightness at P is different from the observed brightness at Q.

Determine the angular velocity of the binary system.

State the defining property of a black hole.

In 2019, astronomers linked several radio telescopes to produce a single telescope called the EHT. The resolution of the EHT is the same as the resolution that a telescope with an aperture equal to the diameter of the Earth could achieve.

Table 2 shows data about the EHT and the Hubble telescope.

Galaxy M87 is 5.3 × 10⁷ light years from Earth. The supermassive black hole at the centre of M87 has a mass 6.5 × 10⁹ times the mass of the Sun.

The radius of the event horizon is R.

The astronomers propose to use either the EHT or the Hubble telescope to observe stars whose distance from the centre of the black hole is less than 1000 R.

Discuss, with calculations, which telescope is more suitable for this observation.

A star is orbiting the black hole in M87. The star is observed in the plane of its orbit. The wavelength of a spectral line observed in the light emitted from the star varies between a maximum and a minimum value.

maximum value observed = 374.96 nm minimum value observed = 373.53 nm

Calculate the orbital speed of the star.

U Cephei is an eclipsing binary system consisting of two stars that orbit their common centre of mass. The primary star is class B; the secondary star is class G.

Figure 1 shows the variation of apparent magnitude of U Cephei with time as observed from Earth.

Explain the shape of the graph in Figure 1.

A particular spectral line has a wavelength of 486.136 nm when measured from a source in the laboratory. This line is also present in the absorption spectrum of the primary star of U Cephei. When observed from Earth, the wavelength of the primary star’s absorption line varies as shown in Table 1.

State why the average of the values in Table 1 is different from the laboratory value.

Show that the orbital speed of the primary star is about 250 km s⁻¹.

Calculate the orbital radius of the primary star.

Which absorption lines would be most prominent in the spectrum of the primary star? Tick () one box.

A different eclipsing binary star system is thought to consist of a white dwarf star and a neutron star.

Discuss how astronomers could confirm this.

IC 2497 is a galaxy that contained a quasar. It is believed that the quasar stopped emitting radiation several thousand years ago.

Suggest why the quasar stopped emitting radiation.

IC 2497 has a red shift of 0.0516

Determine the distance from the Earth to IC 2497. Give an appropriate unit for your answer.

Type 1 a supernovae can be used as standard candles.

State what is meant by a standard candle.

Sketch on Figure 2 the light curve for a type 1 a supernova. Annotate your graph with suitable scales and a unit for time.

Measurements of type 1 a supernovae are used to find a value for the Hubble constant.

The distance from Earth is known for many type 1 a supernovae.

Describe how these values of distance are used, with other data, to find the Hubble constant.

Your answer should include:

• the other data needed and how these data are used

• the graph plotted, including appropriate units for the axes

• how the Hubble constant is obtained and any limitations on the result.

Describe the links between galaxies, black holes and quasars.

At a distance of 5.81 × 10⁸ light year, Markarian-231 is the closest known quasar to the Earth. The red shift z of Markarian-231 is 0.0415

Use these data to estimate an age, in seconds, of the Universe.

A typical quasar is believed to be approximately the size of the solar system, with a power output similar to that of a thousand galaxies.

Estimate, with reference to the inverse-square law, how much further the most distant visible quasar is likely to be compared to the most distant visible galaxy.