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The final lesson of this astrophysics option draws together the most spectacular and rapidly developing objects in modern observational astronomy: exoplanets orbiting other stars, active galactic nuclei including quasars, supernovae (and Type Ia supernovae as the cosmological standard candle), and black holes from stellar-mass examples to the supermassive monsters at the centres of galaxies. Each of these phenomena was either unknown or unrecognised a century ago. Today they are routinely catalogued, monitored, and used as probes of fundamental physics. This lesson develops the detection methods, the underlying physics, and the role of each class of object in the broader narrative of cosmic structure and evolution.
Spec mapping. This lesson covers AQA 7408 section 3.9.3, specifically: exoplanet detection by radial velocity and transit photometry; the recognition of light curves; quasars and active galactic nuclei as compact, luminous, high-redshift sources powered by supermassive black holes; supernova classification — Type Ia (thermonuclear, standard candles) and Type II (core-collapse); stellar-mass and supermassive black holes; event horizon and Schwarzschild radius r_s = 2GM/c². (Refer to the official AQA specification document for exact wording.)
Synoptic links. Exoplanet detection by radial velocity uses the Doppler effect of Lesson 5. Type Ia supernovae sit on the cosmic distance ladder (Lesson 2) and were the standard candles that revealed cosmic acceleration. Black-hole formation follows directly from the stellar-evolution sequence of Lesson 4 (Chandrasekhar / TOV limits). The Schwarzschild radius is an application of escape velocity (AQA gravitational fields, section 3.7) taken to its relativistic limit.
The first exoplanet around a Sun-like star was confirmed in 1995 (Michel Mayor and Didier Queloz, 51 Pegasi b — Nobel Prize 2019). Since then over 5000 exoplanets have been catalogued. The two dominant detection methods are the radial-velocity (Doppler) technique and the transit photometry technique. A third method, direct imaging, is increasingly important for young, wide-orbit, massive planets.
A planet orbiting a star produces a wobble in the star — the two bodies orbit their common centre of mass. The wobble velocity is
K_⋆ = (m_p / M_⋆) × v_p
where K_⋆ is the star's wobble speed, m_p is the planet mass, M_⋆ is the stellar mass, and v_p is the planet's orbital speed.
The wobble produces a periodic Doppler shift in the stellar spectral lines:
Δλ / λ = K_⋆ / c
Modern stabilised spectrographs (HARPS, ESPRESSO) routinely achieve 1 m s⁻¹ precision; future instruments aim for 10 cm s⁻¹ — enough to detect Earth analogues. The radial-velocity method has been the workhorse of exoplanet detection and is biased towards massive planets in close orbits (both increase K_⋆).
If the orbit of the exoplanet happens to be edge-on (as seen from Earth), the planet passes in front of its star once per orbit. During the transit, the planet blocks a small fraction of the star's light:
ΔF / F = (R_p / R_⋆)²
where R_p is the planet radius and R_⋆ the star's radius. For a Jupiter-sized planet (~10⁻¹ R_⋆), the dip is ~1%; for an Earth-sized planet, ~10⁻⁴. The transit duration gives the orbital geometry, and repeated transits confirm the period.
Transit photometry is the method behind Kepler (2009–2018, 2700 confirmed planets) and TESS (2018– ). It is biased towards edge-on orbits (geometric probability ~R_⋆/a) and large planets.
The light curve drops by ΔF/F during the transit, recovers to baseline, and repeats once per orbital period.
Combining transit photometry (giving R_p) with radial velocity (giving m_p sin i, and i ≈ 90° from the transit geometry) yields density ρ_p = m_p / (4πR_p³/3). Density discriminates between rocky and gaseous planets — a key step on the road to characterising potentially habitable worlds.
A transit signal shows a flux drop of 1.0 × 10⁻², a transit duration of 3.0 hours, and a 3.5-day orbital period. Spectroscopy gives a radial-velocity semi-amplitude K_⋆ = 170 m s⁻¹. The host star has M_⋆ = 1.0 M_⊙ and R_⋆ = 1.0 R_⊙. Estimate the planet's mass and radius.
Solution.
So this is a Jupiter-mass, Jupiter-sized planet in a 3.5-day orbit — a classic hot Jupiter.
In 1963 Maarten Schmidt, analysing the spectrum of a starlike radio source called 3C 273, realised that its prominent emission lines were the familiar hydrogen Balmer lines — but redshifted by z = 0.158. For a starlike object that redshift corresponds to a distance of ~750 Mpc, and for 3C 273's apparent magnitude (~13) it implied a luminosity of ~10¹² L_⊙ — more than a hundred times the entire Milky Way, but emerging from a region so small (variability on timescales of days implied a size of light-days, ~10¹⁵ m) that it could not possibly contain that many stars.
These objects were called quasi-stellar radio sources — quasars — and are now understood as the most luminous class of active galactic nuclei (AGN): galaxies whose central regions emit far more power than the rest of the galaxy combined.
The only known mechanism that can liberate ~10¹² L_⊙ from a region a few light-days across is accretion onto a supermassive black hole. As gas spirals inward through an accretion disc towards a black hole of mass 10⁶ – 10¹⁰ M_⊙, it heats up (through viscous dissipation) to ~10⁵ K in the inner disc and radiates a substantial fraction of its rest-mass energy — typically 10% of mc², far higher than any nuclear fusion process (~0.7% of mc² for hydrogen burning).
Accretion luminosity: L = η Ṁ c² where η ≈ 0.1 for a thin disc around a non-spinning black hole; up to 0.42 for a maximally-spinning Kerr black hole.
Different types of AGN (Seyfert galaxies, radio galaxies, blazars, BL Lac objects) are now understood as the same kind of object seen from different angles. The unifying picture is a central supermassive black hole, an accretion disc, a dusty molecular torus surrounding it, and bipolar jets perpendicular to the disc plane. Whether you see broad emission lines, narrow lines, or relativistic beaming depends only on the viewing angle.
Quasars at z > 6 — observed less than 1 Gyr after the Big Bang — pose a puzzle: how did 10⁹ M_⊙ black holes form so quickly? Direct collapse of primordial gas clouds, and runaway mergers of stellar-mass black holes in dense early clusters, are the leading candidates.
A supernova is a stellar explosion in which a star briefly outshines an entire galaxy. Two distinct physical mechanisms produce supernovae, and the resulting spectra and light curves allow astronomers to classify them.
| Type | H lines present? | Si II 6150 Å? | Mechanism |
|---|---|---|---|
| Ia | No | Yes | Thermonuclear detonation of a white dwarf |
| Ib | No | No (He lines present) | Core collapse, hydrogen envelope stripped |
| Ic | No | No (no He either) | Core collapse, H and He envelopes stripped |
| II | Yes | No | Core collapse of a red supergiant |
The historic Type I / II split was based purely on the presence (II) or absence (I) of hydrogen lines in the spectrum. Modern classification distinguishes Type Ia (thermonuclear) from the core-collapse types (Ib, Ic, II), which have very different physics despite the spectroscopic similarities.
A Type Ia supernova is the thermonuclear detonation of a carbon-oxygen white dwarf that has been pushed to or near the Chandrasekhar limit by accretion from a companion star (or, in some models, by merger with another white dwarf). When the dwarf's mass approaches 1.4 M_⊙, runaway carbon fusion ignites, releasing ~10⁴⁴ J of energy and completely disrupting the star. Because the trigger mass is essentially fixed at the Chandrasekhar limit, the peak luminosity is approximately uniform: M_V ≈ −19.3 with intrinsic scatter ~0.3 magnitudes.
This near-uniformity makes Type Ia supernovae the workhorse standard candles for the cosmic distance ladder. By the late 1990s two competing groups (Saul Perlmutter's Supernova Cosmology Project and Brian Schmidt and Adam Riess's High-Z Supernova Search Team) had charted enough distant Type Ia supernovae to discover, in 1998, that the expansion of the universe is accelerating. The acceleration is attributed to dark energy — currently estimated at ~68% of the energy content of the universe. The discovery was awarded the 2011 Nobel Prize.
A Type II supernova is the death of a massive star (initially > 8 M_⊙) that has built up an iron core. When the iron core exceeds the Chandrasekhar limit, electron degeneracy fails and the core collapses on the dynamical timescale of milliseconds, reaching nuclear density. The infall releases ~10⁴⁶ J of gravitational binding energy, of which 99% goes into neutrinos, ~1% into kinetic energy of the ejecta, and ~0.01% into electromagnetic radiation. The ejected envelope, still rich in hydrogen, produces strong Balmer absorption and emission lines that distinguish Type II spectra.
The most famous recent example is SN 1987A, observed in the Large Magellanic Cloud in February 1987 — a Type II event from a 20 M_⊙ blue supergiant progenitor. Crucially, neutrino detectors in Japan, the US and Russia recorded a burst of ~20 neutrinos arriving 2–3 hours before the optical brightening — direct confirmation that ~99% of the supernova's energy is in neutrinos.
For Type Ia supernovae, the procedure is:
The 1998 result — that distant Type Ia supernovae are fainter than would be expected for a decelerating universe — established cosmic acceleration.
A black hole is a region of spacetime so curved that no signal — not even light — can escape from inside its event horizon. Black holes form in three known mass ranges:
In 1916, Karl Schwarzschild found the first exact solution of Einstein's field equations of general relativity, describing the gravitational field around a non-rotating spherical mass M. The solution has a characteristic radius — the Schwarzschild radius — at which the event horizon sits:
r_s = 2GM / c²
where G = 6.67 × 10⁻¹¹ N m² kg⁻², M is the black-hole mass, and c is the speed of light. For any mass smaller than its own r_s, no signal can escape.
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