Questions on quasars

Question 1

Explain the origin of the name “quasar”, and how the first quasars were discovered.

Accepted Answer

Quasi-stellar radio source (1): they were identified in the early 1960s as strong radio sources whose optical counterparts looked like faint star-like points, not galaxies (1).

Question 2

Give two reasons why an exoplanet is extremely difficult to photograph directly.

Accepted Answer

Its star outshines it by a factor of order a billion (1), and at interstellar distances the angular separation between planet and star is below the diffraction-limited resolving power of telescopes (1).

Question 3

In the transit method, state what the depth of the dip in the light curve measures, and what its repeat interval gives.

Accepted Answer

The fractional dip equals (r_p/r_s)², the squared ratio of planet radius to star radius, so it measures the planet's relative size (1). The interval between dips is the planet's orbital period (1).

Question 4

State the type of object now believed to power a quasar, and where quasars are found.

Accepted Answer

An active supermassive black hole, of millions to billions of solar masses, fed by infalling matter (1). At the centres of galaxies in the early universe, at very large distances (1).

Question 5

Explain why the first exoplanets discovered by the radial velocity method were massive planets orbiting close to their stars.

Accepted Answer

A more massive planet drags its star through a faster counter-orbit about their common centre of mass, so the Doppler shift is larger (1); a close orbit makes the star's speed higher still and the period short, so the wobble is easiest to detect (1).

Question 6

State why only a small fraction of planetary systems can be detected by the transit method.

Accepted Answer

A transit is seen only when the orbit lies edge-on to us, so that the planet crosses the star's disc along our line of sight (1).

Question 7

A quasar shows a red shift of z = 0.40. Estimate its recession speed and its distance, taking H = 65 km s⁻¹ Mpc⁻¹, and state why both figures are only estimates.

Accepted Answer

v = zc = 0.40 × 3.0 × 10⁸ = 1.2 × 10⁸ m s⁻¹ (1). d = v/H = 120 000/65 ≈ 1800 Mpc (1). Both v = zc and d = v/H are low red shift approximations, valid for v much less than c (1); at z = 0.40 the relativistic Doppler speed is 0.32c, so v = zc runs about 23 per cent high, and the distance should not be quoted to more than two figures (1).

Question 8

A quasar's brightness varies noticeably over about three days. Estimate the maximum size of the emitting region, and comment on the scale.

Accepted Answer

An object cannot brighten as a whole faster than light crosses it (1)
size ≤ ct = 3.0 × 10⁸ × 3 × 86 400 ≈ 7.8 × 10¹³ m (1)
Comparable with the size of the solar system despite a galaxy-scale power output (1)

Question 9

During each transit of an exoplanet, its star (radius 6.96 × 10⁸ m) dims by a fraction 2.5 × 10⁻³. Calculate the planet's radius.

Accepted Answer

The fractional dip equals (r_p/r_s)² (1) r_p/r_s = √(2.5 × 10⁻³) = 0.050 (1) r_p = 0.050 × 6.96 × 10⁸ = 3.5 × 10⁷ m (1)

Question 10

An orbiting planet makes its star move along our line of sight at up to 55 m s⁻¹. Calculate the maximum shift this produces in the star's 656.3 nm line.

Accepted Answer

Δλ = λv/c (1) Δλ = 656.3 × 55/(3.0 × 10⁸) (1) Δλ = 1.2 × 10⁻⁴ nm (1)

Question 11

A space survey can detect any transit that dims a star by more than 1.0 × 10⁻⁴ of its brightness. A star of radius 6.96 × 10⁸ m is orbited by a gas giant of radius 7.0 × 10⁷ m and by a rocky planet of radius 6.37 × 10⁶ m, and both planets transit. Deduce which of the two planets the survey will detect.

Accepted Answer

Fractional dip = (r_p/r_s)² (1). Giant: (7.0 × 10⁷/(6.96 × 10⁸))² = 1.0 × 10⁻², well above the threshold (1). Rocky planet: (6.37 × 10⁶/(6.96 × 10⁸))² = 8.4 × 10⁻⁵, below 1.0 × 10⁻⁴ (1). Only the gas giant is detected (1).

Question 12

A quasar radiates a total power of 4.0 × 10³⁹ W. The Sun radiates 3.8 × 10²⁶ W. Calculate the number of Sun-like stars that would be needed to match the quasar, and comment on the result, given that a large galaxy contains about 10¹¹ stars.

Accepted Answer

N = 4.0 × 10³⁹/(3.8 × 10²⁶) (1) = 1.1 × 10¹³ (1). That is around a hundred times the star count of a large galaxy: the quasar alone outshines its entire host galaxy (1).

Question 13

The 656.3 nm line of a star is observed to swing by up to 2.6 × 10⁻⁴ nm either side of its laboratory wavelength. Calculate the maximum line-of-sight speed of the star, and state what the periodic swing reveals.

Accepted Answer

v = cΔλ/λ = 3.0 × 10⁸ × 2.6 × 10⁻⁴/656.3 (1) = 119 m s⁻¹ (1). The star is being swung round the centre of mass it shares with an unseen orbiting companion, a planet (1).

Question 14

A quasar of apparent magnitude 16.1 has an estimated distance of 1800 Mpc, obtained from its red shift through v = zc and d = v/H. Calculate its absolute magnitude, compare its output with a bright galaxy of absolute magnitude −21, and state one reason the absolute magnitude is approximate.

Accepted Answer

M = m − 5 log(d/10 pc) = 16.1 − 5 log(1.8 × 10⁸) (1) = −25.2 (1). That is 4.2 magnitudes brighter than the galaxy: a factor of 2.51^4.2 ≈ 48 (1). The distance itself came from low red shift approximations that are already strained at z = 0.40, and m − M = 5 log(d/10) assumes flat Euclidean space with no expansion between source and observer, so treat M as good to a few tenths of a magnitude at best (1).

Question 15

Explain how an active supermassive black hole accounts for both defining properties of a quasar: enormous power output and small size.

Accepted Answer

Matter spiralling towards the black hole heats by friction to millions of kelvin (1) and radiates fiercely before crossing the event horizon, releasing energy far more efficiently than fusion (1), so a galaxy's worth of power is possible (1). The engine is only as big as the hole and its inner disc, a solar-system-scale region, consistent with the rapid brightness variation (1).

Question 16

A star's light curve shows periodic dips, and its spectrum shows a periodic Doppler wobble with the same period. Explain what each measurement contributes to the picture of the orbiting planet.

Accepted Answer

The transit dip gives the planet's size, through (r_p/r_s)², and its interval gives the orbital period (1). The radial velocity wobble confirms the period (1) and its size reflects the planet's mass, since a heavier planet drags its star through a faster counter-orbit (1).

Question 17

A transit survey finds that a star of radius 6.5 × 10⁸ m dims by a fraction 1.1 × 10⁻⁴ during each transit. Radial velocity measurements give the orbiting planet's mass as 7.3 × 10²⁴ kg. The Earth's mean density is 5.5 × 10³ kg m⁻³. Determine the planet's density, and suggest whether the planet is rocky or gaseous.

Accepted Answer

r_p = r_s√(1.1 × 10⁻⁴) (1) = 6.82 × 10⁶ m (1). V = (4/3)πr_p³ = 1.33 × 10²¹ m³ (1). ρ = M/V = 7.3 × 10²⁴/(1.33 × 10²¹) = 5.5 × 10³ kg m⁻³ (1). This matches the Earth's mean density, so the planet is rocky rather than gaseous (1).

Question 18

Stars V and W are similar stars, each orbited by a single planet in a similar orbit, and both systems are observed in the plane of the orbit. Star V's 550 nm line swings by up to 3.2 × 10⁻⁴ nm; star W's swings by up to 8.0 × 10⁻⁵ nm. Deduce which planet is the more massive.

Accepted Answer

V: v = 3.0 × 10⁸ × 3.2 × 10⁻⁴/550 = 175 m s⁻¹ (1). W: v = 44 m s⁻¹ (1). With similar stars and orbits, a faster stellar counter-orbit about the centre of mass means a heavier planet dragging it (1). Star V moves about four times faster, so V's planet is the more massive (1).