Describe how some white dwarf stars become type Ia supernovae.

Hence, explain why a type Ia supernova is used as a standard candle.

Explain how the observation of type Ia supernovae led to the hypothesis that dark energy exists.

white dwarf must have companion «in binary system»

white dwarf gains material «from companion»

when dwarf reaches and exceeds the Chandrasekhar limit/1.4 M_SUN supernova can occur

a standard candle represents a «stellar object» with a known luminosity

this supernova occurs at an certain/known/exact mass so luminosity/energy released is also known

OWTTE

MP1 for indication of known luminosity, MP2 for any relevant supportive argument.

distant supernovae were dimmer/further away than expected

hence universe is accelerating

dark energy «is a hypothesis to» explain this

Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is 5.0 × 10^–21 kg m^–3.

Explain why the rotation curves are evidence for the existence of dark matter.

v = «$\sqrt{\frac{4\pi G\rho }{3}}r$» $=\sqrt{\frac{4}{3}\times \pi \times 6.67\times {10}^{-11}\times 5.0\times {10}^{-21}}\times \left(4000\times 3.1\times {10}^{16}\right)$

v is about 146000 «m s^–1» or 146 «km s^–1»
Accept answer in the range of 140000 to 160000 «m s^–1».

rotation curves/velocity of stars were expected to decrease outside core of galaxy

flat curve suggests existence of matter/mass that cannot be seen – now called dark matter

Outline, with reference to star formation, what is meant by the Jeans criterion.

In the proton–proton cycle, four hydrogen nuclei fuse to produce one nucleus of helium releasing a total of 4.3 × 10^–12 J of energy. The Sun will spend 10¹⁰ years on the main sequence. It may be assumed that during this time the Sun maintains a constant luminosity of 3.8 × 10²⁶ W.

Show that the total mass of hydrogen that is converted into helium while the Sun is on the main sequence is 2 × 10²⁹ kg.

Massive stars that have left the main sequence have a layered structure with different chemical elements in different layers. Discuss this structure by reference to the nuclear reactions taking place in such stars.

a star will form out of a cloud of gas

when the gravitational potential energy of the cloud exceeds the total random kinetic energy of the particles of the cloud
OR
the mass exceeds a critical mass for a particular radius and temperature

[2 marks]

number of reactions is $\frac{{10}^{10}\times 365\times 24\times 3600\times 3.8\times {10}^{26}}{4.3\times {10}^{-12}}=2.79\times {10}^{55}$

H mass used is $2.79\times {10}^{55}\times 4\times 1.67\times {10}^{-27}=1.86\times {10}^{29}$ «kg»

[2 marks]

nuclear fusion reactions produce ever heavier elements depending on the mass of the star / temperature of the core

the elements / nuclear reactions arrange themselves in layers, heaviest at the core lightest in the envelope

[2 marks]

In 2017, two neutron stars were observed to merge, forming a black hole. The material released included chemical elements produced by the r process of neutron capture. Describe two characteristics of the elements produced by the r process.

higher atomic number than iron ✓

excess of neutrons ✓

radioactive/undergoing beta decay ✓

Allow heavier than iron for MP1

The rapid process proved to be known by many although fewer candidates were able to provide two characteristics.

Derive, using the concept of the cosmological origin of redshift, the relation

T $\propto \frac{1}{R}$

between the temperature T of the cosmic microwave background (CMB) radiation and the cosmic scale factor R.

The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of 1100. Estimate the temperature of the CMB at the time of its emission.

State how the anisotropies in the CMB distribution are interpreted.

the cosmological origin of redshift implies that the wavelength is proportional to the scale factor: $\lambda$ $\propto$ R

combining this with Wien’s law $\lambda$ $\propto$ $\frac{1}{T}$

OR

use of kT $\propto \frac{hc}{\lambda }$

«gives the result»

Evidence of correct algebra is needed as relationship T = $\frac{k}{R}$ is given.

[2 marks]

use of T $\propto$$\frac{1}{R}$

= 2.8 x 1100 x 3080 ≈ 3100 «K»

[2 marks]

CMB anisotropies are related to fluctuations in density which are the cause for the formation of structures/nebulae/stars/galaxies

OWTTE

[1 mark]

The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

Show that the critical density of the universe is

$$\frac{3H^2}{8\pi G}$$

where H is the Hubble parameter and G is the gravitational constant.

interstellar gas/dust «from earlier supernova»

gravitational attraction between particles

if the mass is greater than the Jean’s mass/M_j the interstellar gas coalesces

as gas collapses temperature increases leading to nuclear fusion

MP3 can be expressed in terms of potential and kinetic energy

fluctuations in CMB due to differences in temperature/mass/density

during the inflationary period/epoch/early universe

leading to the formation of galaxies/stars/structures

gravitational interaction between galaxies can lead to collision

[Max 3 Marks]

ALTERNATIVE 1

kinetic energy of galaxy $\frac{1}{2}$mv² = $\frac{1}{2}$mH²r² «uses Hubble’s law»

potential energy = $\frac{GMm}{r}$ = G$\frac{4}{3}$$\pi$r³$\rho \frac{m}{r}$ «introduces density»

KE=PE to get expression for critical $\rho$

ALTERNATIVE 2

escape velocity of distant galaxy v = $\sqrt{\frac{2GM}{r}}$

where H₀r = $\sqrt{\frac{2GM}{r}}$

substitutes M =  $\frac{4}{3}$$\pi$r³$\rho$ to get result

The graph shows the variation with time t of the cosmic scale factor R in the flat model of the universe in which dark energy is ignored.

On the axes above draw a graph to show the variation of R with time, when dark energy is present.

The density of the observable matter in the universe is only 0.05 ρ_c. Suggest how the remaining 0.27 ρ_c is accounted for.

The density of dark energy is ρ_Λc² where ρ_Λ = ρ_c – ρ_m. Calculate the amount of dark energy in 1 m³ of space.

curve starting earlier, touching at now and going off to infinity

[1 mark]

there is dark matter that does not radiate / cannot be observed

Unexplained mention of "dark matter" is not sufficient for the mark.

[1 mark]

ρ_Λ = 0.68ρ_c = 0.68 × 10⁻²⁶ «kgm⁻³»

energy in 1 m³ is therefore 0.68 × 10⁻²⁶ × 9 × 10¹⁶ ≈ 6 × 10⁻¹⁰ «J»

[2 marks]

The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt{\frac{GM}{r}}$.

Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.

Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R₀.

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$ and correct rearranging

[1 mark]

linear / rising until R₀ 

then «almost» constant

[2 marks]

for v to stay constant for r greater than R₀, M has to be proportional to r

but this contradicts the information from the M-r graph

OR

if M is constant for r greater than R₀, then we would expect v $\propto r^{\frac{-1}{2}}$

but this contradicts the information from the v-r graph

[2 marks]

The light from a distant galaxy shows that $z=0.11$.

Calculate the ratio $\frac{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{when} \mathrm{the} \mathrm{light} \mathrm{was} \mathrm{emitted}}{\mathrm{size} \mathrm{of} \mathrm{the} \mathrm{universe} \mathrm{at} \mathrm{present}}$.

Outline how Hubble’s law is related to $z$.

Hubble originally linked galactic redshift to a Doppler effect arising from galactic recession. Hubble’s law is now regarded as being due to cosmological redshift, not the Doppler effect. Explain the observed galactic redshift in cosmological terms.

«$\frac{R_0}{R}=$»

$\frac{1}{1.11}$  OR  $0.90$  OR  $90\%$ ✓

«Hubble’s » measure of v/recessional speed uses redshift which is $z$
OR
redshift ($z$) of galaxies is proportional to distance «from earth»
OR
combines $v=Hd$  AND  $z=\frac{v}{c}$ into one expression, e.g. $z=\frac{Hd}{c}$ ✓

OWTTE

reference to «redshift due to» expansion of the universe, «not recessional speed» ✓

expansion of universe stretches spacetime / increases distance between objects ✓

«so» wavelength stretches / increases leading to observed redshift ✓

Many candidates got the ratio upside down and ended up with R/R₀ as 1.11.

This was not accepted as it would have required an identification of the variables. Perhaps candidates need to look more carefully at which R is which here. R is the current value of the scale factor in the data book, so R₀/R = 0.9 was required.

To show the link between z and Hubble's law many rearranged formulae to obtain zc = Hd or similar. Others stated that Hubble used redshift z to determine that v was proportional to distance. Either approach was allowed.

The galactic redshift was successfully explained by many in terms of the stretching of spacetime.

Show by calculation that Eta Aquilae A is not on the main sequence.

Estimate, in $\mathrm{pc}$, the distance to Eta Aquilae A using the parallax angle in the table.

Estimate, in $\text{pc}$, the distance to Eta Aquilae A using the luminosity in the table, given that $L_{\odot }=3.83\times {10}^{26} \mathrm{W}$.

Suggest why your answers to (b)(i) and (b)(ii) are different.

Eta Aquilae A is a Cepheid variable. Explain why the brightness of Eta Aquilae A varies.

Eta Aquilae A was on the main sequence before it became a variable star. Compare, without calculation, the time Eta Aquilae A spent on the main sequence to the total time the Sun is likely to spend on the main sequence.

$«\frac{L}{L_{\odot }}=\frac{M^{3.5}}{{M_{\odot }}^{3.5}}=5.{70}^{3.5}=» 442$ ✓

the luminosity of Eta (2630$L_{\odot }$) is very different «so it is not main sequence» ✓

Allow calculation of $L^{\frac{1}{3.5}}$ to give $M=9.5$ $M_{\odot }$ so not main sequence

OWTTE

$d«=\frac{1}{2.36\times {10}^{-3}}»=424 «\mathrm{pc}»$ ✓

Use of $d=\sqrt{\frac{L}{4\mathrm{\pi }b}}$ ✓

$=\sqrt{\frac{2630\times 3.83\times {10}^{26}}{4\mathrm{\pi }\times 7.20\times {10}^{-10}}}$ ✓

$«=\frac{1.055\times {10}^{19}}{3.26\times 9.46\times {10}^{15}}»=342 «\mathrm{pc}»$ ✓

Award [3] marks for a bald correct answer between $\mathit{340}$ and $\mathit{344}\mathit{ }«\mathrm{pc}»$

parallax angle in milliarc seconds/very small/at the limits of measurement ✓

uncertainties/error in measuring $L$ οr $b$ or $\theta$ ✓

values same order of magnitude, so not significantly different ✓

Accept answers where MP1 and MP2 both refer to parallax angle

OWTTE

reference to change in size ✓
reference to change in temperature ✓
reference to periodicity of the process ✓
reference to transparency / opaqueness ✓

shorter time ✓

star more massive and mass related to luminosity
OR
star more massive and mass related to time in main sequence
OR
position on HR diagram to the left and above shows that will reach red giant region sooner ✓

Most candidates were successful in using the mass luminosity relationship.

The conversion to parsecs proved to be a very well known skill.

Very well answered by most candidates.

Candidates related the difference in the two methods for finding d to the large uncertainty in finding parallax angle at this distance (>400pc). Fewer also spotted that the luminosity of the star is also error prone unless its distance is already known.

Candidates were clearly familiar with Cepheids and the process leading to its variability in brightness.

Candidates showed clear ideas and were able to explain successfully why Eta Aquilae A lifetime as a main sequence star is much shorter than the one expected for the Sun.

State the nature of the anisotropies observed in the CMB radiation.

Identify two possible causes of the anisotropies in (a).

the temperature/«peak» wavelength/intensity «of the CMBR» varies «slightly» / is not constant in different directions ✓

quantum fluctuations «that have expanded» ✓

density perturbations «that resulted in galaxies and clusters of galaxies» ✓

dipole distortion «due to the motion of the Earth» ✓

This was not the best answered question in the Option. Candidates oscillated between correct identification of characteristics of the CMB radiation and more generic explanations about the Big Bang.

Those who correctly identified specific characteristics of the CMB radiation were able to quote causes for this during the early Big Bang.

Explain the evidence that indicates the location of dark matter in galaxies.

Outline why a hypothesis of dark energy has been developed.

«rotational» velocity of stars are expected to decrease as distance from centre of galaxy increases

the observed velocity of outer stars is constant/greater than predicted

implying large mass on the edge «which is dark matter»

OWTTE

1st and 2nd marking points can be awarded from an annotated sketch with similar shape as the one below

[3 marks]

data from type 1a supernovae shows universe expanding at an accelerated rate

gravity was expected to slow down the expansion of the universe

OR

this did not fit the hypotheses at that time

dark energy counteracts/opposes gravity

OR

dark energy causes the acceleration

OWTTE

[3 marks]

Distinguish between a constellation and an open cluster.

The parallax angle of Mintaka measured from Earth is 3.64 × 10^–3 arc-second. Calculate, in parsec, the approximate distance of Mintaka from Earth.

State why there is a maximum distance that astronomers can measure using stellar parallax.

The Great Nebula is located in Orion. Describe, using the Jeans criterion, the necessary condition for a nebula to form a star.

In cluster, stars are gravitationally bound OR constellation not ✔

In cluster, stars are the same/similar age OR in constellation not ✔

Stars in cluster are close in space/the same distance OR in constellation not ✔

Cluster stars appear closer in night sky than constellation ✔

Clusters originate from same gas cloud OR constellation does not ✔

d = 275 «pc» ✔

because of the difficulty of measuring very small angles ✔

mass of gas cloud > Jeans mass ✔

«magnitude of» gravitational potential energy > E_k of particles ✔

cloud collapses/coalesces «to form a protostar» ✔

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

Using the axis, draw the variation with wavelength of the intensity of the radiation emitted by Epsilon Indi.

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = $L_{\odot }$

Mass                          = $M_{\odot }$

Radius                       = $R_{\odot }$

Epsilon Indi has a radius of 0.73 $R_{\odot }$. Show that the luminosity of Epsilon Indi is 0.2 $L_{\odot }$.

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 $M_{\odot }$.

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

Describe the stages in the evolution of Epsilon Indi from the point when it leaves the main sequence until its final stable state.

λ = «$\frac{2.9\times {10}^{-3}}{4600}$ =» 630 «nm» ✔

black body curve shape ✔

peaked at a value from range 600 to 660 nm ✔

$\frac{L}{L_{\odot }}={\left(\frac{0.73R_{\odot }}{R_{\odot }}\right)}^2\times {\left(\frac{4600}{5800}\right)}^4$ ✔

L = 0.211 $L_{\odot }$ ✔

M = «${0.21}^{\frac{1}{3.5}}{M}_{\odot }$ =» 0.640 $M_{\odot }$ ✔

$\frac{T_E}{T_{\odot }}=$ «$\frac{\frac{M_E}{L_E}}{\frac{M_{\odot }}{L_{\odot }}}=\frac{0.64}{0.21}=$» 3.0  ✔

T ≈ 27 billion years ✔

red giant ✔

planetary nebula ✔

white dwarf ✔

do NOT accept supernova, red supergiant, neutron star or black hole as stages

Outline how Hubble measured the recessional velocities of galaxies.

Use the graph to determine the age of the universe in s.

measured redshift «z» of star ✔

use of Doppler formula OR z∼v/c OR v = $\frac{c\mathrm{\Delta }\lambda }{\lambda }$ to find v ✔

OWTTE

use of gradient or any point on the line to obtain any expression for either $\text{H}=\frac{\text{v}}{\text{d}}$ or $\text{t}=\frac{\text{d}}{\text{v}}$ ✔

correct conversion of d to m and v to m/s ✔

= 4.6 × 10¹⁷ «s» ✔

Outline what is meant by dark energy.

State two candidates for dark matter.

energy filling all space ✔

resulting in a repulsive force/force opposing gravity ✔

accounts for the accelerating universe ✔

makes up about 70% of «the energy» of universe ✔

black hole ✔

brown dwarf ✔

massive compact halo object /MACHO✔

neutrinos ✔

weakly interacting massive particle /WIMP ✔

Light from distant galaxies is redshifted. Explain the cosmological origin of this redshift.

Draw, on the axes, a graph to show the variation with time of the cosmic scale factor R for the flat model of the universe with dark energy.

Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.

«according to general relativity» space expands stretching distances between far away objects ✔

wavelengths of photons «received a long time after they were emitted» are thus longer leading to the observed redshift ✔

Do not accept references to the Doppler effect.

 ✔

«since T ∝ $\frac{1}{R}$ » the temperature drops for both models ✔

but in the accelerating model R increases faster and so the temperature drops faster ✔

Cosmological origin of redshift. The cosmological redshift and variation with time of the cosmic scale factor proved to be a well-mastered concept by many students.

Cosmological origin of redshift. The cosmological redshift and variation with time of the cosmic scale factor proved to be a well-mastered concept by many students.

In (ii) however, many candidates did not directly answer the question, making little to no reference of temperature.

Describe what is meant by dark matter.

The distribution of mass in a spherical system is such that the density ρ varies with distance r from the centre as

ρ = $\frac{k}{r^2}$

where k is a constant.

Show that the rotation curve of this system is described by

v = constant.

Curve A shows the actual rotation curve of a nearby galaxy. Curve B shows the predicted rotation curve based on the visible stars in the galaxy.

Explain how curve A provides evidence for dark matter.

dark matter is invisible/cannot be seen directly
OR
does not interact with EM force/radiate light/reflect light

interacts with gravitational force
OR
accounts for galactic rotation curves
OR
accounts for some of the “missing” mass/energy of galaxies/the universe

OWTTE

[6 marks]

«from data booklet formula» $v=\sqrt{\frac{4\pi G\rho }{3}}r$ substitute to get $v=\sqrt{\frac{4\pi Gk}{3}}$

Substitution of ρ must be seen.

[1 mark]

curve A shows that the outer regions of the galaxy are rotating faster than predicted

this suggests that there is more mass in the outer regions that is not visible
OR
more mass in the form of dark matter

OWTTE

[2 marks]

Outline how the light spectra of distant galaxies are used to confirm hypotheses about the expansion of the universe.

Light from a hydrogen source in a laboratory on Earth contains a spectral line of wavelength 122 nm. Light from the same spectral line reaching Earth from a distant galaxy has a wavelength of 392 nm. Determine the ratio of the present size of the universe to the size of the universe when the light was emitted by the galaxy.

State what is meant by the critical density.

Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.

It is estimated that less than 20 % of the matter in the universe is observable. Discuss how scientists use galactic rotation curves to explain this.

spectra of galaxies are redshifted «compared to spectra on Earth» ✔

redshift/longer wavelength implies galaxies recede/ move away from us
OR
redshift is interpreted as cosmological expansion of space ✔

«hence universe expands»

NOTE: Universe expansion is given, so no mark for repeating this.
Do not accept answers based on CMB radiation.

ALTERNATIVE 1

$z=\frac{392-122}{122}=2.21$ ✔

$\frac{R}{R_0}=«2.21+1=» 3.21$ ✔

ALTERNATIVE 2

$\frac{R}{R_0}=\frac{{\displaystyle 392}}{122}$ ✔

= 3.21 ✔

density of flat/Euclidean universe
OR
density for which universe has zero curvature
OR
density resulting in universe expansion rate tending to zero ✔

$H=«\frac{70\times {10}^3}{\left({10}^6\times 3.26\times 9.46\times {10}^{15}\right)}=»2.27\times {10}^{-18}\hspace{0.17em}«{\mathrm{s}}^{-1}»$✔

$\rho =0.32\times \frac{3\times {\left(2.27\times {10}^{-18}\right)}^2}{8\mathrm{\pi }\times 6.67\times {10}^{-11}}$✔

$3.0\times {10}^{-27}\hspace{0.17em}«\mathrm{kg} {\mathrm{m}}^{-3}»$✔

NOTE: MP1 for conversion of H to base units.
Allow ECF from MP1, but NOT if H is left as 70.

rotation speed of galaxies is larger than expected away from the centre ✔

there must be more mass «at the edges» than is visually observable «indicating the presence of dark matter» ✔

Describe the formation of a type Ia supernova.

Show that the distance to the supernova is approximately 3.1 × 10¹⁸ m.

State one assumption made in your calculation.

a white dwarf accretes mass «from a binary partner»

when the mass becomes more than the Chandrasekhar limit (1.4M_s) «then asupernova explosion takes place»

[2 marks]

d = $\sqrt{\frac{\text{L}}{4\pi \text{b}}}=\sqrt{\frac{5\times {10}^5\times 3.8\times {10}^{26}}{4\pi \times 1.6\times {10}^{-6}}}$

d = 3.07 × 10¹⁸ «m»

At least 3 sig fig required for MP2.

[2 marks]

type Ia supernova can be used as standard candles

there is no dust absorbing light between Earth and supernova

their supernova is a typical type Ia

[1 mark]

Justify that the total energy of this particle is $E=\frac{1}{2}m{v}^2-\frac{4}{3}\pi G\text{r}{r}^{2}m$.

At critical density there is zero total energy. Show that the critical density of the universe is: ${\text{r}}_c=\frac{3H_0^2}{8\pi G}$.

The accepted value for the Hubble constant is 2.3 × 10⁻¹⁸ s⁻¹. Estimate the critical density of the universe.

total energy=kinetic energy+potential energy

OR

total energy= $\frac{1}{2}m{v}^2-\frac{GMm}{r}$ ✔

substitution of M = $\frac{4}{3}\pi r^3\rho$ ✔

«Hence answer given»

Answer given so for MP2 look for clear evidence that M_Universe$\left(\frac{4}{3}\pi r^3\rho \right)$ is stated and substituted.

substitutes H₀r for v ✔

«total energy = 0»

$\frac{1}{2}m{H}_0^2{r}^2=\frac{4}{3}\pi G\rho r^{2}m$  ✔

«hence ρ_c = $\frac{3H_0^2}{8\pi G}$ »

Answer given, check working carefully.

9.5 × 10⁻²⁷ « kgm^–3» ✔

The vast majority of the candidates could state that the total energy is equal to the sum of the kinetic and potential energies but quite a few did not use the correct formula for the gravitational potential energy. The formula for the mass of the sun was usually correctly substituted.

This was a relatively easy demonstration given the equation in 22a. However many candidates did not show the process followed in a coherent manner that could be understood by examiners.

The question was well answered by many candidates.

Describe the mechanism of formation of type I a supernovae.

Describe the mechanism of formation of type II supernovae.

Suggest why type I a supernovae were used in the study that led to the conclusion that the expansion of the universe is accelerating.

ALTERNATIVE 1
a white dwarf star in a binary system accretes mass from the companion star ✔

when the white dwarf star mass reaches the Chandrasekhar limit the star explodes «due to fusion reactions»✔

ALTERNATIVE 2
it can be formed in the collision of two white dwarf stars ✔

where shock waves from the collision rip both stars apart ✔

a red supergiant star explodes when its core collapses ✔

«it was necessary» to measure the distance «of very distant objects more accurately» ✔

type I a are standard candles/objects of known luminosity ✔

Supernova. The mechanism of the formation of supernovae Ia was well described by many candidates.

In (ii), for the description of the mechanism of type II supernovae, many responses lacked detail and did not make mention of core collapse.

Part b) was well answered by most of the prepared candidates with a good understanding that these stars behave as “standard candles”.

Proxima Centauri is a main sequence star with a mass of 0.12 solar masses.

Estimate $\frac{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Proxima} \mathrm{Centauri}}{\mathrm{lifetime} \mathrm{on} \mathrm{main} \mathrm{sequence} \mathrm{of} \mathrm{Sun}}$.

Describe why iron is the heaviest element that can be produced by nuclear fusion processes inside stars.

Discuss one process by which elements heavier than iron are formed in stars.

realization that lifetime $T\propto \frac{\mathrm{mass}}{\mathrm{luminosity}}$ ✔

$\frac{T}{T_{\odot }}={\left(\frac{M}{M_{\odot }}\right)}^{-2.5}=0.{12}^{-2.5}=200$ ✔

the binding energy per nucleon is a maximum for iron ✔

formation of heavier elements than iron by fusion is not energetically possible ✔

NOTE: For MP2 some reference to energy is needed

ALTERNATIVE 1 — s-process
s-process involves «slow» neutron capture ✔
in s-process beta decay occurs before another neutron is captured ✔
s-process occurs in giant stars «AGB stars» ✔
s-process terminates at bismuth/lead/polonium ✔

ALTERNATIVE 2 — r-process
r-process involves «rapid» neutron capture ✔
in r-process further neutrons are captured before the beta decay occurs ✔
r-process occurs in type II supernovae ✔
r-process can lead to elements heavier than bismuth/lead/polonium ✔

NOTE: If the type of the process (r or s/rapid or slow) is not mentioned, award [2 max].

Show that the temperature of the universe is inversely proportional to the cosmic scale factor.

The present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.

«wavelength of light/CBR» λ ∝ R ✔

reference to Wien’s law showing that λ ∝ $\frac{1}{T}$ ✔

combine to get result ✔

OWTTE

$\frac{R_{\text{past}}}{R_{\text{now}}}=\frac{3}{300}=0.01$ ✔

Outline, with reference to the Jeans criterion, why a cold dense gas cloud is more likely to form new stars than a hot diffuse gas cloud.

Explain how neutron capture can produce elements with an atomic number greater than iron.

«For a star to form»: magnitude of PE of gas cloud > KE of gas cloud

OR

Mass of cloud > Jean's mass

OR

Jean’s criterion is the critical mass

hence a hot diffuse cloud could have KE which is too large/PE too small

OR

hence a cold dense cloud will have low KE/high PE

OR

a cold dense cloud is more likely to exceed Jeans mass

OR

a hot diffuse cloud is less likely to exceed the Jeans mass

Accept E_p + E_k < 0

[2 marks]

Neutron capture creates heavier isotopes / heavier nuclei / more unstable nucleus

β^– decay of heavy elements/iron increases atomic number «by 1»

OWTTE

[2 marks]

Explain the formation of a type I a supernova which enables the star to be used as a standard candle.

Describe the r process which occurs during type II supernovae nucleosynthesis.

white dwarf attracts mass from another star ✔

explodes/becomes supernova when mass equals/exceeds the Chandrasekhar limit / 1.4M_SUN ✔

hence luminosity of all type I a supernova is the same ✔

OWTTE

«successive» rapid neutron capture ✔

faster than «β» decay can occur ✔

results in formation of heavier/neutron rich isotopes ✔

OWTTE

The formation of Type 1a supernovae was well known by most candidates but few were able to explain how this process resulted in a standard candle.

Many candidates could describe the r process correctly but quite a large number of candidates seemed completely at a loss and could not relate the r process to neutron capture.