OCR A-Level Physics: Astrophysics and Cosmology

A star with a mass roughly equal to that of the Sun forms within a cold cloud of gas and dust and eventually ends its life as a white dwarf.

Describe and explain the life cycle of such a star, from its origin in an interstellar cloud through to its final state as a white dwarf. In your answer you should refer to the gravitational collapse of the cloud, the onset of nuclear fusion, the equilibrium that holds the star stable on the main sequence, and the changes that occur once the core hydrogen is exhausted.

(6 marks)

A distant star behaves as a black body. Astronomers record its continuous spectrum and measure the wavelength at which the radiated power peaks. The star's radius has been estimated from other observations.

Quantity	Symbol	Value
Peak wavelength	$\lambda_{\max}$λmax​	$290 \ \text{nm}$290 nm
Stellar radius	$r$r	$1.20 \times 10^{9} \ \text{m}$1.20×109 m
Wien constant	—	$2.90 \times 10^{-3} \ \text{m K}$2.90×10−3 m K
Stefan-Boltzmann constant	$\sigma$σ	$5.67 \times 10^{-8} \ \text{W m}^{-2} \ \text{K}^{-4}$5.67×10−8 W m−2 K−4

(a) Use Wien's displacement law to calculate the surface temperature of the star. (2 marks)

(b) Hence use the Stefan-Boltzmann law to calculate the luminosity of the star. (3 marks)

(c) Suggest one reason why the temperature found in part (a) is best described as the star's surface (photosphere) temperature rather than its core temperature. (1 mark)

The stellar parallax of four nearby stars is measured. The parallax angle $p$p (in arcseconds) and the distance $d$d in parsecs are related by $d = \dfrac{1}{p}$d=p1​.

Star	Parallax angle, $p$p / arcsecond	Distance, $d$d / pc
A	0.760	to be found
B	0.025	to be found
C	0.012	to be found
D	0.380	2.63

(a) Calculate the distance to stars A, B and C in parsecs, and hence state which of the four stars is nearest to Earth. (3 marks)

(b) A fifth star is so distant that ground-based telescopes record a parallax angle of only $0.002$0.002 arcsecond, with an uncertainty of $\pm 0.002$±0.002 arcsecond. Use this to explain why the parallax method becomes unreliable for very distant stars. (2 marks)

A galaxy in a distant cluster is found to be receding from Earth at $2.1 \times 10^{4} \ \text{km s}^{-1}$2.1×104 km s−1. Its distance is estimated to be $295 \ \text{Mpc}$295 Mpc.

(Take $1 \ \text{Mpc} = 3.09 \times 10^{19} \ \text{km}$1 Mpc=3.09×1019 km.)

(a) Use Hubble's law to calculate a value for the Hubble constant $H_0$H0​ in $\text{km s}^{-1} \ \text{Mpc}^{-1}$km s−1 Mpc−1. (2 marks)

(b) Hence estimate the age of the Universe in seconds, and convert your answer to years. (3 marks)

(1 year $= 3.16 \times 10^{7} \ \text{s}$=3.16×107 s.)

In the laboratory a particular hydrogen spectral line is emitted at a wavelength of $434.0 \ \text{nm}$434.0 nm. When the same line is observed in the spectrum of a distant galaxy, it appears at $455.7 \ \text{nm}$455.7 nm.

(a) Calculate the redshift $z$z of the galaxy. (1 mark)

(b) Hence estimate the galaxy's recession speed, stating the approximation you use. (3 marks)

(Take $c = 3.00 \times 10^{8} \ \text{m s}^{-1}$c=3.00×108 m s−1.)

Astronomers use several defined quantities and laws to describe stars and the expanding Universe.

(a) State what is meant by the luminosity of a star, and give its SI unit. (1 mark)

(b) State Wien's displacement law, writing it as an equation and defining each symbol. (2 marks)