Quasars: Supermassive Black Holes and Energy Output Revision Notes | A Level AQA Physics

1. The Mystery at the Edge of the Observable Universe

In the early 1960s, radio astronomers pinpointed tiny, star-like objects that turned out to be billions of light-years away — yet shining with the power of hundreds of entire galaxies. Nothing in classical astrophysics could explain it. These objects are quasars, and understanding them requires pushing every concept you have met in astrophysics to its limit.

Two things define quasars in the AQA specification: their large optical redshifts, which allow us to estimate their distance and power output, and their origin as active supermassive black holes. Both threads run through everything that follows.

2. What a Quasar Looks Like — and Why That Is Strange

Through an optical telescope, a quasar looks like a faint star — a point of light with no visible disc or spiral arms. The name itself comes from quasi-stellar object. The strangeness emerges when you measure the spectrum: the emission lines are shifted dramatically towards the red end, indicating enormous recession velocities.

Recall from your study of stellar spectra that a redshift arises when a source moves away from the observer — the wavelengths of emitted photons are stretched. For quasars, the redshift parameter $z$ can exceed 1, meaning the observed wavelength is more than double the emitted wavelength. No ordinary star in our galaxy has a redshift anywhere near this value.

For recession speeds much less than the speed of light, Hubble's law connects redshift to distance: $v = H_0 d$, and since $v \approx cz$ for small $z$, we get $d \approx \frac{cz}{H_0}$. AQA expects you to use this relationship to estimate quasar distances — the word estimate is deliberate, because at cosmological distances the simple Hubble formula is an approximation.

With $H_0 \approx 2.2 \times 10^{-18}$ s$^{-1}$ and $c = 3.0 \times 10^8$ m/s, a quasar with $z = 0.5$ sits at a distance of roughly $6.8 \times 10^{25}$ m — over two billion parsecs. That distance alone tells you the light left the quasar when the universe was far younger than it is today.

3. Estimating Distance and Power Output — The Calculation Chain

Once you have the distance, you can estimate the power output (luminosity) of a quasar from its observed flux — the energy received per unit area per second at Earth. The relationship is the inverse-square law for radiation: $F = \frac{L}{4\pi d^2}$, rearranged to give $L = 4\pi d^2 F$.

This is the same inverse-square law you used for stars. The difference is the scale: quasar luminosities come out in the range $10^{38}$ to $10^{41}$ W, compared with roughly $3.8 \times 10^{26}$ W for the Sun and around $10^{37}$ W for an entire ordinary galaxy. A single quasar can outshine its host galaxy by a factor of up to tens of thousands ($10^4$).

Worked example: Estimating Quasar Distance and Luminosity from Redshift and Flux

A quasar has a redshift of $z = 0.20$. Its observed flux at Earth is $F = 1.5 \times 10^{-16}$ W m$^{-2}$. Estimate (a) the distance to the quasar and (b) its luminosity. Use $H_0 = 2.2 \times 10^{-18}$ s$^{-1}$ and $c = 3.0 \times 10^8$ m/s.

1. $d \approx \frac{cz}{H_0}$ — [M1] Correct formula linking redshift to distance via Hubble's law.
2. $d \approx \frac{(3.0 \times 10^8) \times 0.20}{2.2 \times 10^{-18}}$ — [M1] Substituting $c$, $z$, and $H_0$ with correct units.
3. $3.0 \times 10^8 \times 0.20 = 6.0 \times 10^7$ m/s — Multiply $c$ by $z$ first to keep the arithmetic clean.
4. $d \approx \frac{6.0 \times 10^7}{2.2 \times 10^{-18}} = \frac{6.0}{2.2} \times 10^{7-(-18)} = 2.727\ldots \times 10^{25}$ m — [A1] $6.0 \div 2.2 \approx 2.73$; exponent: $10^{7+18} = 10^{25}$. Distance $\approx 2.7 \times 10^{25}$ m.
5. $L = 4\pi d^2 F$ — [M1] Inverse-square law rearranged for luminosity.
6. $d^2 = (2.7 \times 10^{25})^2 = 2.7 \times 2.7 \times 10^{25 \times 2} = 7.29 \times 10^{50}$ m$^2$ — Expand the square explicitly: $2.7 \times 2.7 = 7.29$; $10^{25} \times 10^{25} = 10^{50}$.
7. $L = 4 \times \pi \times 7.29 \times 10^{50} \times 1.5 \times 10^{-16}$ — Collect numerical and power-of-ten parts separately.
8. $4 \times 3.1416 \times 7.29 \times 1.5 = 4 \times 3.1416 \times 10.935 \approx 137.4$\n$10^{50} \times 10^{-16} = 10^{34}$\n$L \approx 1.37 \times 10^{36}$ W — [A1] Numerical part: $4 \times 3.1416 \approx 12.566$; $12.566 \times 10.935 \approx 137.4$; so $L \approx 1.4 \times 10^{36}$ W. This is roughly $4 \times 10^{9}$ times the Sun's luminosity ($3.8 \times 10^{26}$ W).

Answer: (a) $d \approx 2.7 \times 10^{25}$ m; (b) $L \approx 1.4 \times 10^{36}$ W

Notice the two-stage structure of that calculation: redshift gives distance, distance feeds into the inverse-square law to give luminosity. Examiners frequently split this into two separate parts, awarding method marks at each stage independently — so even if your distance is slightly off, you can still earn the luminosity marks by carrying your value forward correctly.

4. Formation of Quasars — Active Supermassive Black Holes

To explain a luminosity of $10^{38}$–$10^{41}$ W from a region smaller than our solar system, you need the most efficient energy-release mechanism in nature. Nuclear fusion — the process powering stars — converts only about 0.7% of rest-mass energy into radiation. Gravitational accretion onto a black hole can convert up to ~10% of infalling rest-mass energy into radiation. That is why a supermassive black hole is the only plausible engine.

A supermassive black hole has a mass of $10^6$ to $10^{10}$ solar masses. Every large galaxy is now thought to harbour one at its centre. When the black hole is actively accreting — drawing in surrounding gas and dust — it becomes an active galactic nucleus (AGN). A quasar is the most luminous class of AGN, observed when the accretion rate is very high.

Picture the process in stages. Gas from the surrounding galaxy — or from a merging companion galaxy — falls towards the central black hole. Angular momentum causes it to settle into a disc rather than plunging directly inward. Viscous friction within the disc transfers angular momentum outward and allows material to spiral inward, releasing gravitational potential energy as heat and radiation. The inner regions of the disc reach temperatures of millions of kelvin, producing intense ultraviolet and X-ray emission.

The black hole itself emits nothing — it is the accretion disc and associated jets of plasma that produce the observed radiation. This distinction matters for exam answers: the energy source is the gravitational potential energy of infalling matter, not the black hole radiating directly.

5. Why Quasars Are Seen Only at Large Distances

Here is a striking observational fact: quasars are found almost exclusively at large redshifts. Very few are found nearby. This is not a selection effect — it tells us something profound about cosmic history. Because light takes time to travel, observing a quasar at $z = 2$ means we are seeing it as it was roughly ten billion years ago, when the universe was much younger and denser.

In the early universe, galaxies were still forming and merging frequently. These mergers funnelled large quantities of gas into galactic centres, feeding supermassive black holes at high accretion rates and switching on quasar activity. As the universe aged and gas supplies were depleted, accretion rates dropped and quasars faded. The supermassive black holes remain — including the one at the centre of our own Milky Way, Sagittarius A* — but they are now largely dormant, accreting at far lower rates.

This evolutionary picture means that quasars are not a different type of object from ordinary galaxies — they are ordinary galaxies caught at an active phase in their early history. The large redshifts of quasars are therefore both a distance indicator and a window into the early universe.

6. Comparing Quasar Power Output with Ordinary Galaxies

One of the most striking aspects of quasars is the sheer scale of their energy output relative to anything else in the universe. Placing the numbers side by side makes the comparison concrete.

The region producing this output is extraordinarily compact. The luminosity of a quasar can vary on timescales of days to weeks, which places an upper limit on the size of the emitting region: if the luminosity changes coherently over one day, the emitting region can be no larger than one light-day across; if it varies over one week, the limit is one light-week across (roughly $1.8 \times 10^{14}$ m). An entire galaxy's worth of power from a volume smaller than our solar system — that is the observational puzzle that the accretion disc model resolves.

7. Exam Technique — Getting Full Marks on Quasar Questions

Quasar questions on AQA papers tend to fall into three categories: calculation chains (redshift to distance to luminosity), descriptive/explanatory questions about formation, and evaluative questions about what the observations tell us. Each type rewards a slightly different approach.

For calculation questions, the two-step chain is almost always present. Write the formula first, substitute with units, and carry forward your answer even if you are unsure — method marks are available at each stage independently. Always quote your distance to two or three significant figures before using it in the luminosity calculation; rounding too early introduces unnecessary error.

For extended-response questions asking you to evaluate what quasar observations tell us about the early universe, structure your answer as: observation (large redshifts) → inference (large distances, large look-back times) → implication (quasars were more common when the universe was young) → conclusion (quasars represent an early active phase of galaxy evolution). A conclusion that explicitly weighs the evidence earns the top-band mark.