Physics › Astrophysics › Quasars and exoplanets
Quasars and exoplanets
Quasars are the most luminous objects known, outshining whole galaxies from billions of parsecs away, and exoplanets are among the faintest things detected at all. Both are found indirectly, from changes in the light received: a large red shift and a strong radio output for one, a periodic dip in brightness or a wobble in a spectrum for the other.
Pick your board and the few notes written for the other boards quietly fold away, here and in the practice players. Nothing is deleted: every folded piece reopens on a tap.
Builds on The Doppler effect and Hubble's law and The HR diagram and stellar evolution.
IN THIS TOPIC
- Describe the discovery and nature of quasars, and estimate their distances and power outputs from red shift.
- Explain why direct exoplanet detection fails, and interpret the radial velocity method and the transit light curve.
COMMON MISCONCEPTION
We find planets around other stars by photographing them beside their suns.
Quasars: small, distant, absurdly bright
In the 1950s radio surveys turned up strong sources that matched nothing obvious in the visible sky. When optical counterparts were finally pinned down they looked like faint blue stars, hence the name quasar, from quasi-stellar radio source. Then their spectra came in and the puzzle deepened, because the lines showed enormous red shifts, far beyond any star's.
Take the red shift at face value and Hubble's law puts quasars billions of parsecs away. That has a striking consequence. To appear even faintly visible from there, a quasar must outshine an entire galaxy of stars. Yet their brightness flickers over days, and nothing can coordinate a flicker faster than light can cross the source, so quasars are roughly solar-system sized. A galaxy's power, from a light-day of space.
The specification calls quasars the most distant measurable objects, and for the 1960s that was fair. It is no longer true. Ordinary galaxies have since been found at red shifts far beyond any quasar's, and gamma-ray bursts have been measured further still. Quasars remain among the most distant objects bright enough to study in detail, and that is the defensible version. Write the spec's phrase if a question wants it, but know what it now means.
Only one mechanism fits. An active supermassive black hole of millions to billions of solar masses sits at the centre of a young galaxy, and matter spiralling in heats by friction to millions of kelvin, blazing across the spectrum before it crosses the horizon. The supermassive black holes met with the HR diagram are the quiet survivors of that era. A quasar is one still feeding.
WORKED EXAMPLE
Distance and power from a spectrum
A quasar's 656.3 nm hydrogen line arrives at 984.5 nm. Use the low red shift approximations to estimate its distance (H = 65 km s−1 Mpc−1), and its absolute magnitude given an apparent magnitude of +17.0.
z = (984.5 − 656.3) / 656.3 = 0.50. The specification's route is v = zc = 1.5 × 108 m s−1, then d = v/H = 150 000 / 65 ≈ 2300 Mpc.
Now say plainly what that is. Both v = zc and d = v/H are low red shift approximations, comfortable below about z = 0.1 and badly stretched at z = 0.50. At red shifts this large the shift is cosmological, space stretching while the light travels, rather than a source rushing through space, so no single corrected speed replaces zc; a modern distance needs a specified cosmological model and a named distance measure, and different measures legitimately give different figures at the same z. The exam's route stays v = zc then d = v/H, so give its answer and call it the estimate it is. Two significant figures is generous, and the word estimate belongs in the answer.
M = m − 5 log(d/10 pc) = 17.0 − 5 log(2.3 × 108) ≈ −25. The distance fed in came from the low-red-shift approximations, and reading d as an ordinary Euclidean distance is itself approximate out here, so the figure carries an error of its own at this red shift; the modulus relation stays exact only when d is the luminosity distance cosmologists use. Feed in 3000 Mpc instead and it still rounds to −25, so the conclusion below survives the wobble.
The conclusion holds despite the approximations, which is the point of doing it at all. Against a bright galaxy at M ≈ −21 the quasar is about four magnitudes brighter, a factor of a few tens, and it manages that from a source the size of the solar system. One measured wavelength did all of that, through speed and then distance and then power.
Exoplanets: why looking fails
A planet orbiting another star emits almost nothing of its own and reflects only a scrap of its star's light. Two problems follow, and an exam answer needs both. The star typically outshines the planet by a factor of a billion, and at interstellar distances the angular separation between them falls below what any telescope's diffraction limit can cleanly resolve. Photographing an exoplanet is like spotting a moth beside a lighthouse from across a sea. Direct images therefore remain rare, managed only for a few giant, young, widely separated planets, and nearly everything we know comes from two indirect methods.
The radial velocity method is the binary-star method of the last lesson, pushed to extremes. The planet does not orbit a stationary star. Both bodies orbit their common centre of mass, so the star performs a miniature mirror-orbit and its spectral lines swing to and fro with the planet's period. The period of the wobble gives the planet's year. The size of the wobble hints at its mass, since heavier planets drag their stars through faster counter-orbits.
The transit method looks for the small regular eclipse of a star whose planetary system happens to lie edge-on to us. Each orbit, the planet's disc blocks a fraction of the starlight equal to the ratio of the two discs' areas, so the fractional dip equals (rp/rs)2. The light curve's depth measures the planet's size and its repeat interval gives the orbital period. A Jupiter crossing a Sun dims it by about one per cent. An Earth manages one part in ten thousand.
GUIDED PRACTICE
Sizing a planet from a dip
A star of radius 6.96 × 108 m dims by a fraction 4.0 × 10−4 during each transit. Find the planet's radius, and compare it with the Earth's 6.37 × 106 m.
Show the working
(rp/rs)2 = 4.0 × 10−4, so rp/rs = 0.020 and rp = 0.020 × 6.96 × 108 = 1.4 × 107 m.
That is about 2.2 Earth radii, a super-Earth. The square root is a required step. The dip compares areas, and the answer wants a radius.
INDEPENDENT PRACTICE
Why the wobble is hard
Jupiter makes the Sun orbit their shared centre of mass at about 13 m s−1. Find the fractional Doppler shift this produces, and the wavelength shift on a 550 nm line.
Show the working
Δλ/λ = v/c = 13 / (3.0 × 108) = 4.3 × 10−8.
Δλ = 4.3 × 10−8 × 550 nm = 2.4 × 10−5 nm, a shift a hundred-thousandth of a nanometre wide. Exoplanet spectrographs are consequently among the most stable instruments ever built, and the first planets found this way were heavy ones huddled close to their stars.
ASSESSMENT FOCUS
- The quasar story scores in sequence, so tell it in order. Strong radio source, star-like optical appearance, very large red shift, therefore very distant by Hubble's law, therefore galaxy-scale power from a solar-system-sized region, powered by an active supermassive black hole.
- Quasar distance estimates run z, then v = zc, then d = v/H. Flag that a large z strains the approximation. A complete answer states that caveat. Both formulas hold for v much less than c, so past z of about 0.1 every figure that follows is an estimate, and at z = 0.5 the speed is out by around thirty per cent.
- The specification's phrase is that quasars are the most distant measurable objects. It is a historical statement. Galaxies and gamma-ray bursts are now measured at greater red shifts, so if a question invites comment, say that quasars are among the most distant objects bright enough to study.
- Direct detection fails for two stated reasons, and one alone will not do. The star's overwhelming brightness, and an angular separation below the resolving limit.
- Transit questions live on the light curve, so sketch it. Flat, dip, flat, with depth (rp/rs)2 and the repeat time giving the orbital period. Radial velocity answers must mention the centre of mass, because the star wobbles only since both bodies orbit it.
CHECK YOURSELF
A quasar's brightness varies noticeably over about two days. Explain what this says about its size, and why that observation, combined with its red shift, forces an extraordinary power source.
Show a hint
Nothing can synchronise a change faster than light can cross the object.
Show the answer
A source cannot brighten as a whole faster than light can cross it, so its diameter is at most about two light-days, roughly 5 × 1013 m. Solar-system sized, not galaxy sized.
The large red shift places the quasar billions of parsecs away by Hubble's law, and to be visible at all from there it must radiate more power than a whole galaxy.
Ordinary starlight cannot deliver galaxy-scale power from a solar-system-scale volume. Only matter heating violently as it falls towards a supermassive black hole fits both facts at once.
A quasar is an active supermassive black hole, giving galaxy power from a solar-system volume.
Its flicker time caps its size, and its red shift estimates its distance.
Exoplanets are found indirectly, by the star's Doppler wobble or by a transit dip of (rp/rs) squared.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the quasars and exoplanets questions page.
WHERE TO GO NEXT
- Standard form and prefixes is the maths this lesson leans on, worked through from GCSE.
CHECK YOUR PROGRESS
Rate how confident you feel with each objective for this lesson. Ratings are saved in this browser, on this device, unless you sign in.
- Describe the discovery and nature of quasars, and estimate their distances and power outputs from red shift.
- Explain why direct exoplanet detection fails, and interpret the radial velocity method and the transit light curve.
Open the full revision checklist to track your progress across the whole unit.