Supernovae, neutron stars & black holes

The galaxy M87 is at a distance of 5.3 × 10⁷ ly from the Earth.

Determine, in m s⁻¹, the recessional velocity of M87 relative to the Earth.

Astronomers believe that M87 has an active supermassive black hole at its centre.

Suggest one observation that leads to this conclusion.

Which provides evidence for the existence of dark energy?

Tick (✓) one box.

The Earth is in the galaxy known as the Milky Way. The Andromeda Galaxy is one of the closest galaxies to the Milky Way.

The Andromeda Galaxy approaches the Milky Way at a speed of 110 km s⁻¹. The distance between the galaxies is 770 kpc.

Discuss whether these data can be used to estimate an age for the Universe.

There is a supermassive black hole at the centre of the Andromeda Galaxy. The mass of this black hole is 1.60 × 10⁸ solar masses.

Calculate the radius of the event horizon of this black hole. State an appropriate unit for your answer.

Scientists predict that a quasar will be produced as the Milky Way and the Andromeda Galaxy merge.

Explain what is meant by a quasar. Go on to suggest why a quasar may be produced as galaxies merge.

In your answer you should:

• describe the typical properties of a quasar

• explain how observations of quasars provide evidence for these properties

• suggest the process of quasar formation that is likely when two galaxies merge.

Draw a labelled diagram to define the parsec (pc).

Table 1 shows data for two stars: Rigel and the Sun.

State the spectral class of Rigel.

The apparent magnitude of Rigel is 0.11

Calculate, in pc, the distance from Rigel to the Earth.

Figure 1 shows a Hertzsprung–Russell (HR) diagram.

Draw a line on Figure 1 to show the evolution of the Sun from formation to white dwarf.

One stage in the evolution of Rigel includes the emission of a gamma ray burst.

Outline the circumstances during which a gamma ray burst will be emitted by Rigel.

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.

Figure 2 shows, for some galaxies, how their recession speed v varies with distance d from the Earth.

Estimate, using Figure 2, the age in seconds of the Universe.

The estimate in Question 05.1 assumes that the Universe has expanded at a constant rate. Measurements involving type 1a supernovae that are at large distances from Earth caused astronomers to make a modification to this assumption.

State:

• the modification

• the explanation that was proposed to account for this modification.

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.

C 273 was the first quasar to be discovered. IC 1101 is one of the largest galaxies known. Table 2 shows some information about these objects.

State the property of the quasar that led to its discovery.

Show that the absolute magnitude X of quasar 3 C 273 is about −27

Assume that the quasar and the galaxy are both viewed from the same distance.

Explain which would be the brighter object.

The black hole at the centre of IC 1101 has a mass of 7.1 × 10¹¹ M_S

Calculate the average density within the event horizon of the black hole.

Which graph shows the light curve for a typical type 1 a supernova?

Tick () one box.

The Andromeda galaxy is approximately 7.7 × 10⁵ pc from Earth.

Deduce whether a type 1 a supernova which occurred in Andromeda can be observed from Earth with the naked eye.

Table 1 summarises some information about four stars in the constellation Cassiopeia.

Which star has the highest surface temperature? Tick () one box.

Figure 1 shows the intensity received at Earth from two of the stars, plotted against wavelength. The effect of absorption by the Earth’s atmosphere is not shown.

Discuss what information can be found from Figure 1 about the temperature and colour of these stars. Support your answer with suitable calculations.

State which star in Table 1 is dimmest on the absolute magnitude scale.

Calculate the absolute magnitude of Schedar.

Tsih has a mass over 15 times the mass of the Sun. Tsih may eventually collapse to form a black hole.

Calculate the radius of the event horizon for a black hole with a mass 15 times that of the Sun.

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.

Table 2 gives data about the supergiant star Melnick 34 and the Sun.

Discuss why the evolution of a supergiant star in the local part of our galaxy could be dangerous for life on Earth.

Figure 2 is a Hertzsprung-Russell (HR) diagram.

Label the absolute magnitude axis with a suitable scale.

Label with an S the position of the Sun on the HR diagram.

Draw a line on the HR diagram to show the evolution of a star similar to the Sun from formation to white dwarf.

Label with a P the position on the HR diagram of a star much redder, and with a greater power output, than the Sun.

A star much more massive than the Sun may become a supernova and then a black hole.

Discuss whether supernovae and black holes can be placed on the HR diagram in Figure 2.

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.

Sketch, on the axes in Figure 1, the light curve for a typical type 1a supernova. Label the axes with suitable scales.

Type 1a supernovae can be used as standard candles.

Explain what is meant by a standard candle.

Measurements of type 1a supernovae in 1999 led to a controversy concerning the behaviour of the Universe.

Describe this controversy and how the measurements led to it.