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Date	November 2017	Marks available	3	Reference code	17N.3.HL.TZ0.20
Level	Higher level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show that	Question number	20	Adapted from	N/A

Question

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.

[4]

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

[3]

Show that the critical density of the universe is

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

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

[3]

Markscheme

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

Examiners report

[N/A]

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Additional higher level option topics) » D.5 – Further cosmology (HL only)

Show 34 related questions

17M.3.HL.TZ1.17a:
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.
16N.3.HL.TZ0.25b: Explain why the rotation curves are evidence for the existence of dark matter.
19M.3.HL.TZ2.22c: The accepted value for the Hubble constant is 2.3 × 10−18 s−1. Estimate the critical density...
17N.3.HL.TZ0.20b:
Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.
19M.3.HL.TZ2.22b:
At critical density there is zero total energy. Show that the critical density of the universe is: ${{\text{r}}_c} = \frac{{3H_0^2}}{{8\pi G}}$ .
18N.3.HL.TZ0.20a: Outline what is meant by dark energy.
18N.3.HL.TZ0.21a:
Show that the temperature of the universe is inversely proportional to the cosmic scale factor.
18N.3.HL.TZ0.20b: State two candidates for dark matter.
19N.3.HL.TZ0.16b(iii): It is estimated that less than 20 % of the matter in the universe is observable. Discuss how...
17M.3.HL.TZ2.20c:
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.
18M.3.HL.TZ1.19a:
The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt {\frac{{GM}}{r}}$ .
17M.3.HL.TZ2.20a:
Describe what is meant by dark matter.
17M.3.HL.TZ1.17b.i:
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.
19M.3.HL.TZ1.20b.ii:
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.
18M.3.HL.TZ2.19a:
Explain the evidence that indicates the location of dark matter in galaxies.
17M.3.HL.TZ1.17b.ii:
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.
19N.3.HL.TZ0.16b(i): State what is meant by the critical density.
16N.3.HL.TZ0.25a:
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.
18N.3.HL.TZ0.21b:
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.
20N.3.HL.TZ0.21c: Hubble originally linked galactic redshift to a Doppler effect arising from galactic...
20N.3.HL.TZ0.24a: State the nature of the anisotropies observed in the CMB radiation.
19N.3.HL.TZ0.16b(ii):
Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.
17M.3.HL.TZ2.19b:
State how the anisotropies in the CMB distribution are interpreted.
20N.3.HL.TZ0.24b:
Identify two possible causes of the anisotropies in (a).
18M.3.HL.TZ1.19b:
Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.
17M.3.HL.TZ2.19a.i:
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.
17M.3.HL.TZ2.19a.ii:
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.
19M.3.HL.TZ2.22a:
Justify that the total energy of this particle is $E = \frac{1}{2}m{v^2} - \frac{4}{3}\pi G{\text{r}}{r^2}m$ .
19M.3.HL.TZ1.20b.i: Draw, on the axes, a graph to show the variation with time of the cosmic scale factor R for...
19M.3.HL.TZ1.20a: Light from distant galaxies is redshifted. Explain the cosmological origin of this redshift.
18M.3.HL.TZ2.19b:
Outline why a hypothesis of dark energy has been developed.
17M.3.HL.TZ2.20b:
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.
18M.3.HL.TZ1.19c:
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.
21N.1.SL.TZ0.30: Which is correct for a black-body radiator? A. The power it emits from a unit surface area...

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Option D: Astrophysics » Option D: Astrophysics (Additional higher level option topics)

Option D: Astrophysics

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