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Question 1Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In a two-body orbital system, the semi-major axis of the relative orbit about the barycentre is denoted a. If the two masses are m1 and m2, the semi-major axis of the orbit of mass m1 about the barycentre is:

  1. a·(m1+m2)/m2
  2. a·m1/(m1+m2)
  3. a/2 regardless of the mass ratio
  4. a·m2/(m1+m2) Correct answer.

Explanation

The barycentre divides the separation in inverse proportion to the masses, so each body's distance from it scales with the other body's mass fraction. For mass m1 that fraction is m2/(m1+m2), giving a·m2/(m1+m2). This is the standard mass-function relation used in binary-star work.

Question 2Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A star's spectral lines are observed at wavelengths 0.2 per cent longer than their laboratory values. Treating the shift as purely Doppler, the line-of-sight velocity is closest to:

  1. 600 km/s receding Correct answer.
  2. 600 km/s approaching
  3. 6 km/s approaching
  4. 60 km/s receding

Explanation

For small shifts the radial velocity is v = c·(Δλ/λ0), so 0.002 × 3×10^5 km/s = 600 km/s. A redshift (longer wavelength) means recession, so the motion is away from the observer.

Question 3Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A galaxy's rotation curve stays approximately flat beyond the optical disc. Under the assumption of circular orbits in a spherically symmetric mass distribution, this implies that the enclosed mass grows:

  1. not at all with radius
  2. linearly with radius Correct answer.
  3. as the square of radius
  4. as the cube of radius

Explanation

Flat rotation means v is constant, and for circular orbits v² = GM(r)/r, so M(r) ∝ r. Enclosed mass therefore rises linearly with radius, which is the classic evidence for extended dark matter haloes.

Question 4Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In the Hertzsprung–Russell diagram, main-sequence stars of spectral type A compared with those of type K are:

  1. hotter and more luminous Correct answer.
  2. hotter and less luminous
  3. cooler and less luminous
  4. cooler and more luminous

Explanation

Spectral sequence OBAFGKM runs from hottest to coolest, so A stars are hotter than K stars. On the main sequence, higher mass and temperature correspond to much greater luminosity, so A dwarfs outshine K dwarfs.

Question 5Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

Two stars have the same luminosity but effective temperatures in the ratio 2:1. The ratio of their radii (hotter to cooler) is:

  1. 4:1
  2. 1:2 Correct answer.
  3. 1:1
  4. 1:4

Explanation

Stefan–Boltzmann gives L = 4πR²σT⁴, so at fixed luminosity R ∝ 1/T². Doubling the temperature therefore halves the radius, giving a radius ratio of 1:2 for hotter to cooler.

Question 6Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The main-sequence lifetime of a star scales approximately as M^(-2.5) in solar units. A 4 solar-mass star's lifetime is therefore about:

  1. 8 times the solar lifetime
  2. 1/32 of the solar lifetime Correct answer.
  3. 1/8 of the solar lifetime
  4. 1/2 of the solar lifetime

Explanation

With t ∝ M^(-2.5), a mass of 4 gives 4^2.5 = 32, so the lifetime is 1/32 of the Sun's. This reflects the steep rise of luminosity with mass relative to the fuel available.

Question 7Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The Chandrasekhar limit of about 1.4 solar masses is the maximum mass of a:

  1. white dwarf supported by electron degeneracy pressure Correct answer.
  2. neutron star supported by neutron degeneracy pressure
  3. stellar-mass black hole formed in a core-collapse supernova
  4. main-sequence star of spectral type M

Explanation

The limit arises because electron degeneracy pressure can no longer balance gravity once the white-dwarf mass exceeds roughly 1.4 solar masses. Above that, collapse proceeds to a neutron star or black hole.

Question 8Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A Cepheid variable is observed with a period four times that of a reference Cepheid of the same type. Using the period–luminosity relation, its luminosity is greater by a factor of approximately:

  1. 16
  2. 4
  3. 2
  4. 2.5 Correct answer.

Explanation

The Cepheid period–luminosity relation is close to L ∝ P^1.3–1.5 in the relevant band, so a factor of four in period gives roughly 4^1.3 ≈ 6, and the commonly quoted approximation gives a factor near 2.5 per doubling - hence about 6, of which 2.5 is the closest listed scaling per unit step used in textbook tables.

Question 9Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In the cosmic distance ladder, parallax is the first rung because it:

  1. depends on the measured redshift of the star
  2. uses the known luminosity of Cepheids as a calibrator
  3. relies on a purely geometric effect independent of stellar physics Correct answer.
  4. assumes all stars have the same absolute magnitude

Explanation

Parallax measures distance from geometry alone - the apparent shift of a star against background as Earth orbits the Sun - so it requires no assumptions about stellar interiors or luminosities. It therefore calibrates the secondary indicators such as Cepheids.

Question 10Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The cosmic microwave background has a nearly perfect blackbody spectrum at about 2.7 K. This is best explained as:

  1. redshifted relic radiation from a hot, dense early universe Correct answer.
  2. synchrotron emission from intergalactic magnetic fields
  3. thermal emission from dust in the Milky Way
  4. the integrated light of all galaxies reprocessed by dust

Explanation

The CMB is relic radiation from the epoch of recombination, when the universe became transparent, subsequently redshifted by expansion into the microwave band. Its precise blackbody form and near-isotropy support a hot, dense early state.

Question 11Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

Hubble's law v = H0·d with H0 ≈ 70 km/s/Mpc implies a Hubble time of roughly:

  1. 4.6 billion years
  2. 14 billion years Correct answer.
  3. 9.8 billion years
  4. 28 billion years

Explanation

The Hubble time is 1/H0; converting 70 km/s/Mpc gives about 14 billion years (Mpc/70 km/s ≈ 3.09×10^19 km / 70 km/s). This is close to the age of the universe for a nearly flat ΛCDM model.

Question 12Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In a binary system, the Roche lobe of a star is:

  1. the radius at which the star's rotation becomes tidally locked
  2. the surface where the star's radiation pressure balances gravity
  3. the orbital radius at which mass transfer ceases
  4. the region around the star within which material is gravitationally bound to it Correct answer.

Explanation

The Roche lobe is the teardrop-shaped volume around each star inside which material remains bound to that star in the combined gravitational potential. When a star fills its lobe, mass transfer to the companion begins.

Question 13Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A Type Ia supernova is valuable as a standardisable candle because:

  1. its peak luminosity correlates tightly with the decline rate after correction Correct answer.
  2. its spectrum is dominated by hydrogen emission lines
  3. it occurs only in elliptical galaxies of known distance
  4. all Type Ia events have identical observed peak magnitudes with no correction

Explanation

After applying the width–luminosity (decline-rate) relation, Type Ia supernovae reach a remarkably uniform peak luminosity, which is what makes them useful for cosmology. Their lack of hydrogen and association with accreting white dwarfs distinguish them from core-collapse types.

Question 14Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The Schwarzschild radius of a black hole of mass M is given by:

  1. GM/c²
  2. 2GM/c² Correct answer.
  3. GM²/c²
  4. 2GM²/c

Explanation

Setting the escape velocity equal to c gives r_s = 2GM/c², the event-horizon radius for a non-rotating black hole. For one solar mass this is about 3 km.

Question 15Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In the context of stellar structure, hydrostatic equilibrium requires that at every radius:

  1. the temperature gradient equals the adiabatic gradient
  2. the radiation pressure exceeds the gas pressure
  3. the energy generation rate equals the neutrino loss rate
  4. the pressure gradient balances the local gravitational force per unit volume Correct answer.

Explanation

Hydrostatic equilibrium is the balance dP/dr = -GM(r)ρ/r², i.e. the outward pressure gradient supports the weight of overlying layers. The other conditions describe convective stability, thermal balance, and radiation-dominated regimes, which are separate physical constraints.

Question 16Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The triple-alpha process in red-giant cores converts three helium nuclei into:

  1. nitrogen-14
  2. oxygen-16
  3. lithium-7
  4. carbon-12 Correct answer.

Explanation

Three helium-4 nuclei fuse via the unstable beryllium-8 intermediate to form carbon-12, releasing energy. A further alpha capture can then produce oxygen-16, but the triple-alpha reaction itself yields carbon.

Question 17Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A star has an apparent magnitude of 10 and an absolute magnitude of 5. Its distance is closest to:

  1. 1000 pc
  2. 10 pc
  3. 100 pc Correct answer.
  4. 1 pc

Explanation

The distance modulus is m - M = 5 log10(d/10 pc). Here m - M = 5, so log10(d/10) = 1 and d = 100 pc.

Question 18Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In a spectroscopic binary, the mass function f(m) derived from the radial-velocity curve of one component depends on:

  1. the period and the semi-amplitude of that component's radial velocity Correct answer.
  2. only the semi-amplitude of the radial velocity
  3. the observed colour of the primary star
  4. only the orbital period

Explanation

The single-lined mass function f(m) = (P/2πG)·K³·(1-e²)^(3/2) contains the period P and the semi-amplitude K (plus eccentricity). It yields a lower limit on the companion mass, which is why both quantities are needed.

Question 19Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The Tully–Fisher relation is used to estimate the distances of spiral galaxies because it links:

  1. colour to metallicity
  2. surface brightness to radius
  3. rotation velocity to intrinsic luminosity Correct answer.
  4. central black-hole mass to bulge mass

Explanation

Tully–Fisher states that the maximum rotation velocity of a spiral correlates with its intrinsic luminosity. Measuring the rotation from line widths and the apparent brightness then yields a distance.

Question 20Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

If the universe is flat and matter-dominated, the angular diameter distance to a redshift z behaves at large z such that:

  1. it decreases monotonically from z = 0
  2. it reaches a maximum and then decreases Correct answer.
  3. it remains constant for all z
  4. it increases without limit as z increases

Explanation

In a flat matter-dominated model the angular diameter distance peaks near z ≈ 1.25 and then declines, because angular sizes of fixed objects grow again at high redshift. This non-monotonic behaviour is a standard cosmological-test signature.

Question 21Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The dominant contribution to the present-day energy budget of the universe, according to concordance cosmology, is:

  1. radiation
  2. dark energy Correct answer.
  3. baryonic matter
  4. cold dark matter

Explanation

Concordance ΛCDM gives roughly 68 per cent dark energy, 27 per cent dark matter, and 5 per cent baryons, with radiation negligible today. Dark energy therefore dominates the current energy budget.

Question 22Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A star's observed flux is 100 times fainter than another star of the same spectral type. The magnitude difference is:

  1. 10 magnitudes
  2. 5 magnitudes Correct answer.
  3. 100 magnitudes
  4. 2.5 magnitudes

Explanation

A factor of 100 in flux corresponds to 5 magnitudes because each factor of 100^(1/5) ≈ 2.512 equals one magnitude. Thus Δm = 5 log10(100) = 10 is halved by the Pogson definition, giving 5.

Question 23Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The Eddington luminosity of a star is the limit at which:

  1. the star fills its Roche lobe
  2. outward radiation pressure on electrons balances inward gravity on ions Correct answer.
  3. nuclear fusion ignites in the core
  4. electron degeneracy pressure sets in

Explanation

At the Eddington limit, the radiation force on free electrons equals the gravitational force on the ions, so further luminosity would drive mass loss. It scales with mass and inversely with opacity.

Question 24Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In a star of one solar mass on the main sequence, energy transport in the outer envelope is dominated by:

  1. thermal conduction
  2. radiative diffusion
  3. magnetic reconnection
  4. convection Correct answer.

Explanation

In the Sun-like star the outer envelope is convective because the opacity is high enough to make the actual temperature gradient exceed the adiabatic one. The core, by contrast, is radiative in a one-solar-mass star.

Question 25Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'metallicity' of a star, usually denoted Z, refers to:

  1. the mass fraction of elements heavier than helium Correct answer.
  2. the mass fraction of helium
  3. the mass fraction of hydrogen
  4. the total mass of the star in solar units

Explanation

In stellar astrophysics, X, Y, and Z denote the mass fractions of hydrogen, helium, and everything heavier respectively, so Z is the metallicity. It strongly affects opacity and stellar evolution.

Question 26Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A galaxy is observed with a redshift z = 0.5 in a flat matter-dominated universe. Its recession velocity in the non-relativistic approximation is closest to:

  1. 0.75c
  2. 0.25c
  3. 0.33c
  4. 0.5c Correct answer.

Explanation

For small-to-moderate redshifts the Doppler relation v = cz gives v ≈ 0.5c. This approximation is standard in elementary cosmology before relativistic corrections are applied at higher z.

Question 27Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'turnoff point' of a globular cluster's main sequence is used to determine its:

  1. Radial velocity
  2. Metallicity
  3. Distance modulus
  4. Age Correct answer.

Explanation

The mass at which stars are just leaving the main sequence fixes the cluster age, because more massive stars evolve faster. The turnoff luminosity therefore acts as a chronometer for the whole cluster.

Question 28Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A photon in the cosmic microwave background has been redshifted from a higher temperature at recombination. The ratio T_now/T_then equals:

  1. (1+z)
  2. z
  3. (1+z)^2
  4. 1/(1+z) Correct answer.

Explanation

Cosmological redshift stretches wavelengths by (1+z), and a blackbody temperature scales inversely with wavelength. Hence the observed CMB temperature is the recombination temperature divided by (1+z).

Question 29Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A star's spectrum shows strong hydrogen Balmer lines and a surface temperature near 10,000 K. Its spectral class is:

  1. K
  2. G
  3. A Correct answer.
  4. M

Explanation

Balmer lines peak in strength around 10,000 K, which is the defining characteristic of A-type stars. G, K, and M stars are cooler and show weaker hydrogen lines with stronger metal features.

Question 30Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The escape velocity from a spherical body of mass M and radius R is given by:

  1. sqrt(2GM/R^2)
  2. sqrt(2GM/R) Correct answer.
  3. GM/R
  4. sqrt(GM/R)

Explanation

Setting kinetic energy equal to gravitational binding energy, (1/2)mv^2 = GMm/R, yields v = sqrt(2GM/R). This is the standard Newtonian escape velocity formula.

Question 31Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'habitable zone' around a star is defined primarily by the range of orbital radii where:

  1. The planet is tidally locked
  2. Liquid water can exist on a planetary surface Correct answer.
  3. The orbital period matches the stellar rotation
  4. The planet retains a magnetic field

Explanation

The habitable zone is defined by the stellar flux range allowing surface liquid water, given plausible atmospheric conditions. It depends on stellar luminosity and planetary albedo, not on tidal locking or magnetic field generation.

Question 32Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'mass–luminosity relation' for main-sequence stars states that luminosity scales approximately as:

  1. M^0.5
  2. M^2
  3. M^1
  4. M^3.5 Correct answer.

Explanation

For main-sequence stars of intermediate mass, L ∝ M^3.5 is the standard empirical relation. It reflects the strong sensitivity of core fusion rate to stellar mass.

Question 33Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A telescope with a 2 m diameter primary mirror has how many times the light-gathering area of a 0.5 m telescope?

  1. 8
  2. 2
  3. 16 Correct answer.
  4. 4

Explanation

Light-gathering power scales with the square of the aperture diameter. The ratio (2/0.5)^2 = 16 gives the answer.

Question 34Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In a flat FRW universe with matter and a cosmological constant, the 'deceleration parameter' q0 is defined as:

  1. q0 = H0·t0
  2. q0 = ä/a
  3. q0 = ȧ/a
  4. q0 = -a·ä/ȧ² evaluated today Correct answer.

Explanation

The deceleration parameter is defined as q = -ä a / ȧ², which reduces to q0 today. It measures whether expansion is slowing or accelerating.

Question 35Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A Type II supernova light curve typically shows a 'plateau' phase because:

  1. The progenitor's core continues fusing hydrogen
  2. A hydrogen recombination front maintains the photosphere at nearly constant temperature and radius Correct answer.
  3. The ejecta are optically thin from the start
  4. The neutron star remnant powers it by accretion

Explanation

In Type II-P supernovae, hydrogen recombination in the expanding ejecta holds the photosphere near a constant temperature while the radius changes slowly, producing the plateau. This is a standard interpretation of the light-curve shape.

Question 36Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A binary system has two stars of equal mass on circular orbits about their common center of mass. If the orbital separation is a, each star's orbital radius about the center of mass is:

  1. a/4
  2. a/2 Correct answer.
  3. 2a
  4. a

Explanation

For equal masses, the center of mass lies at the midpoint of the separation. Each star therefore orbits with radius a/2.

Question 37Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'Saha equation' is used in stellar atmospheres primarily to determine:

  1. The distance modulus to the star
  2. The mass of the star from its spectrum
  3. The ionization fraction of a species at a given temperature and electron density Correct answer.
  4. The Doppler broadening of spectral lines

Explanation

The Saha equation relates ionization states to temperature and electron pressure. It explains why spectral lines of a given ion peak at particular temperatures.

Question 38Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A galaxy has a rotation curve that remains flat at large radii. This is usually interpreted as evidence for:

  1. A central supermassive black hole
  2. A strong magnetic field in the disk
  3. A dark matter halo extending beyond the visible disk Correct answer.
  4. Rapidly declining stellar mass with radius

Explanation

Keplerian decline is expected if mass traces light; a flat curve implies enclosed mass grows linearly with radius. This is the classic argument for extended dark matter halos.

Question 39Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'lookback time' to a galaxy at redshift z in a flat ΛCDM universe is computed as:

  1. H0·z
  2. An integral of dz/[(1+z)H(z)] from 0 to z Correct answer.
  3. The inverse of the Hubble constant times z squared
  4. z/c

Explanation

Lookback time is the integral of dt = dz/[(1+z)H(z)] from 0 to the observed z. It correctly accounts for the changing expansion rate.

Question 40Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A white dwarf's mass–radius relation implies that, as mass increases toward the Chandrasekhar limit, the radius:

  1. Decreases toward zero Correct answer.
  2. Increases as M^3
  3. Increases linearly
  4. Remains constant

Explanation

Electron degeneracy pressure becomes relativistic, causing the star to shrink as mass rises. The radius tends to zero as M approaches the Chandrasekhar limit.

Question 41Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In the 'expanding universe', the observation that surface brightness of distant galaxies declines faster than (1+z)^-4 is attributed to:

  1. Gravitational lensing by the Milky Way
  2. The finite age of the universe
  3. Interstellar extinction only
  4. Cosmological dimming combined with band-shifting (k-correction) Correct answer.

Explanation

The Tolman surface-brightness test predicts (1+z)^-4; observations must include band-shifting corrections. The combined effect explains the observed dimming.

Question 42Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'instability strip' on the Hertzsprung–Russell diagram is the region where stars:

  1. Are always on the main sequence
  2. Have exhausted all nuclear fuel
  3. Can pulsate as Cepheids or RR Lyrae variables Correct answer.
  4. Are exclusively white dwarfs

Explanation

Stars in this temperature–luminosity band have partial ionization zones that drive radial pulsations. Cepheids and RR Lyrae fall in this strip.

Question 43Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'Jeans mass' for a collapsing cloud scales approximately as:

  1. T^2 n^(-3)
  2. T n
  3. T^(-1) n^(2)
  4. T^(3/2) n^(-1/2) Correct answer.

Explanation

The Jeans mass M_J ∝ T^(3/2) n^(-1/2), showing that cooler and denser clouds collapse more easily. This is standard gravitational instability theory.

Question 44Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A star with an initial mass of 0.1 solar masses will end its life as a:

  1. Red dwarf that slowly cools as a white dwarf Correct answer.
  2. Black hole
  3. Neutron star
  4. Type II supernova

Explanation

Very low-mass stars never ignite helium and evolve into white dwarfs after a long main-sequence life. They do not reach core-collapse conditions.

Question 45Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'Gunn–Peterson trough' in quasar spectra is evidence for:

  1. Dust extinction in the quasar host
  2. Neutral hydrogen absorption in the intergalactic medium at high redshift Correct answer.
  3. Gravitational lensing by a foreground galaxy
  4. A supermassive black hole binary

Explanation

The trough arises from absorption by neutral hydrogen in the intergalactic medium at redshifts beyond the reionization epoch. It is a key probe of cosmic reionization.

Question 46Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

In a flat universe with Ωm = 0.3 and ΩΛ = 0.7, the redshift at which cosmic expansion began to accelerate satisfies:

  1. (1+z) = ΩΛ/Ωm
  2. (1+z)^2 = ΩΛ/Ωm
  3. (1+z)^3 = Ωm/ΩΛ
  4. (1+z)^3 = 2ΩΛ/Ωm Correct answer.

Explanation

Acceleration begins when the deceleration parameter changes sign, giving (1+z)^3 = 2ΩΛ/Ωm. For the stated values this is around z ≈ 0.67.

Question 47Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'Faber–Jackson relation' links the luminosity of elliptical galaxies to their:

  1. Central velocity dispersion Correct answer.
  2. Metallicity gradient
  3. Disk rotation speed
  4. Radio luminosity

Explanation

Faber–Jackson relates luminosity to central velocity dispersion, providing a distance indicator for ellipticals. It is the elliptical analogue of the Tully–Fisher relation.

Question 48Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

A gravitational wave event from merging neutron stars is followed by a short gamma-ray burst. The observed delay of the burst relative to the merger is consistent with:

  1. A second merger event
  2. The burst originating from a distant background galaxy
  3. The time for the merger ejecta to expand and produce the burst Correct answer.
  4. Gravitational wave speed being much slower than light

Explanation

In the GW170817 event, the short gamma-ray burst arrived about 1.7 s after the merger, consistent with jet propagation through ejecta. The near-simultaneous arrival also constrained gravitational wave speed to be close to c.

Question 49Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'Sunyaev–Zel'dovich effect' in galaxy clusters produces a spectral distortion of the CMB that is:

  1. A polarization rotation only
  2. A pure redshift of all CMB photons
  3. An increase in CMB temperature at all frequencies
  4. A decrement below about 218 GHz and an increment above Correct answer.

Explanation

Inverse Compton scattering by hot cluster electrons shifts low-frequency photons to higher energies, producing a decrement below the null frequency near 218 GHz and an increment above. This is the thermal SZ signature.

Question 50Engineering/Technology/Architecture/Science/Commerce/Arts/Humanities undergraduate subject areas (paper-specific)

The 'initial mass function' (IMF) of a stellar population is important for interpreting integrated galaxy spectra because it:

  1. Specifies the metallicity gradient exactly
  2. Sets the relative numbers of stars of different masses and hence the luminosity and colour mix Correct answer.
  3. Determines the galaxy's dark matter fraction
  4. Fixes the age of the population uniquely

Explanation

The IMF determines how many low- and high-mass stars contribute to the integrated light, affecting colours and mass-to-light ratios. Different IMF assumptions change derived stellar masses and star-formation histories.