1 M09/4/PHYSI/SP3/ENG/TZ1/XX+ Option E — Astrophysics E1. This question is about stars. (a) Distinguish between apparent magnitude and absolute magnitude. [2] ● apparent magnitude is a measure of how bright a star appears from Earth; ● absolute magnitude is a measure of how bright a star would appear from a distance of 10 pc; (b) The table gives information on three stars, Achernar, EG 129 and Mira. (i) State which one of the three stars appears brightest from Earth. [1] ● Achernar; (ii) Estimate the ratio where LA is the luminosity of Achernar and LE is the luminosity of EG 129. [3] ● stars differ by ΔM = 16; ● for ΔM = 1 we have a ratio of luminosities by a factor ≈ 2.51 6 ● so ( ) ≈ 2.5 x 10 (iii) Show that the distance of the star Achernar from Earth is approximately 50 pc. [2] ● m – M = 5 log ( ) (c) The surface temperature of Mira is 5 times lower than that of Achernar. Estimate the ratio where RM is the radius of Mira and RA is the radius of Achernar. [3] ● = 1 ( ) (d) State and explain which of the stars in the table in (b) is a white dwarf. [3] ● it has to be hot star/ a B star ● with low luminosity/ high absolute magnitude ● hence EG129 2 E2. This question is about cosmic microwave background radiation. The graph shows the spectrum of the cosmic microwave background radiation. The shape of the graph suggests a black body spectrum i.e. a spectrum to which the Wien displacement law applies. (a) Use the graph to estimate the black body temperature. [2] ● T = 2.7 K ● Accept wavelengths in the range 1.05 to 1.10 for a temperature range 2.64 to 2.76 K. (b) Explain how your answer to (a) is evidence in support of the Big Bang model. [2] ● according to the Big Bang model the temperature of the universe (and the radiation it contained) in the distant past was very high; ● the temperature falls as the universe expands and so does the temperature of the radiation in the universe; (c) State and explain another piece of experimental evidence in support of the Big Bang model. [2] ● (Hubble’s law shows that) the universe is expanding; ● therefore in the distant past the universe must have been a very small/hot/dense point-like object; or ● Doppler shift of spectral lines; ● indicates galaxies moving away so in the past they were close to each other; 3 M09/4/PHYSI/SP3/ENG/TZ2/XX+ Option E — Astrophysics E1. This question is about the star Antares. The star Antares is a red supergiant star in the constellation Scorpius. (a) Describe three characteristics of a red supergiant star and state what is meant by a constellation.[4] Red supergiant star: [3 max] ● appears red in colour; ● (has a very) large luminosity; ● (relatively) low (surface) temperature; ● (very) large mass; ● (very) large surface area; Constellation: ● a group of stars that form a recognizable pattern (as viewed from Earth) / OWTTE; [1 max] (b) The apparent magnitude of Antares is + 1.1 and its absolute magnitude is – 5.3. (i) Distinguish between apparent magnitude and absolute magnitude. [2] ● apparent magnitude is a measure of how bright a star appears from Earth/observer; ● absolute magnitude is the apparent magnitude of a star at a distance of 10 pc from Earth / how bright a star would appear if it were at a distance of 10 pc from Earth; 7 (ii) Show that the distance of Antares from Earth is 3.9x10 AU. [3] ● m – M = 5 log ( ) ( ) 5 log ( ) ● ● (iii) State the name of the method that is used to measure the distance of Antares from Earth. [1] ● stellar / spectroscopic parallax (c) The apparent brightness of Antares is 4.3 x10-11 times the apparent brightness of the Sun. (i) Define apparent brightness. [1] ● the power per square meter received at the surface of Earth / observer 4 (ii) Using the answer to (b)(ii), show that Antares is 6.5 x10 times more luminous than the Sun. [3] 4 ( )( ) E2. This question is about models of the universe. Observations of the night sky indicate that there are many regions of the universe that do not contain any stars. (a) Explain why this observation contradicts Newton’s model of the universe. [3] ● Newton’s model states that the universe is infinite (static) and uniform; ● this means that stars are uniformly spaced; ● and that if it is infinite there must be a star at every point in space / a star along every line of sight; ● since there are regions without stars, Newton’s model must be inadequate; [3 max] (b) Outline how the Big Bang model of the universe is consistent with this observation. [3] ● both space and time originated with the Big Bang; ● the universe is expanding (and not infinite); ● due to the expansion, light from the Big Bang is red-shifted to the microwave region so regions between stars will not appear bright; ● light from very distant stars will not have reached us yet; ● the universe has not existed for all time; [3 max] N09/4/PHYSI/SP3/ENG/TZ0/XX+ Option E — Astrophysics E1. This question is about the star Becrux and Cepheid variables. (a) Describe what is meant by (i) the apparent magnitude scale. [2] ● gives the relative (visual) brightness of stars as seen from Earth; ● e.g. a magnitude 1 star is 100 times brighter than a magnitude 6 star; To award [2] the idea of a relative scale must be clear. (ii) absolute magnitude. [1] ● the apparent magnitude a star would have if it were 10 pc from Earth; (b) Becrux is a main sequence star and is one of the stars that make up the Southern Cross. 5 The following data are available for Becrux. Apparent magnitude 1.25 Absolute magnitude –3.92 -12 Apparent brightness 7.00 x 10 bSun bSun is the apparent brightness of the Sun. Use the data to deduce that the (i) distance of Becrux from Earth is 108 pc. [3] ● m – M = 5 log ( ) log ( ) = 1.03 1.03 ● d = 10 x 10 = 108 pc 3 (ii) luminosity of Becrux is 3.43 x 10 LSun where LSun is the luminosity of the Sun. 5 (1 pc 2.05 x10 AU) [3] 2 ● L = 4π d b ( )( ) (c) Becrux is a spectral class B star. On the axes of the Hertzsprung–Russell diagram label with the letter B the approximate position of Becrux. [1] ● in the region [30 50, – 2.55 – 5.0] 6 (d) On the axes of the Hertzsprung–Russell diagram above, draw the approximate region in which Cepheid variable stars are located. [1] ● Cepheid as shown; ● Judge by eye for reasonable range of magnitude and temperature. (e) State the reason for the periodic variation in luminosity of a Cepheid variable. [1] ● the outer layers undergo a periodic expansion and contraction/periodic fluctuations in temperature; (f) State the two quantities that need to be measured in order to use a Cepheid variable as a “standard candle” to determine the distance to the galaxy in which the Cepheid is located. [2] 1. ● period/frequency with which luminosity varies 2. ● apparent brightness / apparent magnitude; E2. This question is about cosmology. (a) The diagram below represents a spherical region of space based on Newton’s model of the universe. Earth is at the centre of the region. The dark line represents a very thin spherical shell of space distance R from Earth. With reference to the diagram and Newton’s model of the universe explain quantitatively Olbers’ paradox. [4] 7 ● Newton’s model assumed a uniform infinite (and static) universe; 2 ● therefore number of stars in shell is proportional to R 2 ● intensity of radiation/light from shell reaching Earth is proportional to 1/R ● since according to Newton’s model such shells stretch to infinity / the sky can never be dark/willalways be light / OWTTE; (b) Outline how the Big Bang theory provides a resolution to Olbers’ paradox. [2] ● the universe is expanding; ● the universe has a beginning; ● the stars (and galaxies) are not uniformly distributed; [2 max] M10/4/PHYSI/SP3/ENG/TZ1/XX+ Option E — Astrophysics E1. This question is about determining some properties of the star Wolf 359. (a) The star Wolf 359 has a parallax angle of 0.419 arcseconds. (i) Describe how this parallax angle is measured. [4] ● angular position of star measured; ● relative to the background of fixed stars; ● in two positions six months apart; ● p is ½ of the angle of separation / p indicated on diagram; (ii) Calculate the distance in light-years from Earth to Wolf 359. [2] ● ● = 2.3866 x 3.26 ly = 7.78 ly (iii) State why the method of parallax can only be used for stars at a distance of less than a few hundred parsecs from Earth. [1] ● beyond this distance the parallax angle is too small to be measured (accurately)/ OWTTE 8 (b) The ratio Show that the ratio ( ) 2 ● L = 4 π d b 4 5 ● dS =1 AU dW = 7.78x 6.3 x 10 = 4.9 x 10 AU 5 2 -15 -4 = [4.9 x 10 ] x 3.7 x 10 = 8.9 x 10 (c) The surface temperature of Wolf 359 is 2800 K and its luminosity is 3.51023 W. Calculate the radius of Wolf 359. [2] √ √ (d) By reference to the data in (c), suggest why Wolf 359 is neither a white dwarf nor a red giant. [2] ● temperature too low to be white dwarf; ● luminosity too low to be red giant; ● radius too small to be a red giant; [2 max] Answer must be consistent with answer in (c) for third marking point.