Detection of exoplanets (A-level only) — AQA A-Level Physics

This topic covers the methods used by astronomers to detect planets orbiting stars other than our Sun. You will study the transit method, which measures the small dip in a star's brightness as a planet passes in front of it, and the radial velocity method, which detects the star's tiny wobble due to the gravitational pull of an orbiting planet. These techniques allow determination of planetary radius, orbital period, and minimum mass.

Understanding exoplanet detection is crucial because it connects fundamental physics - gravitation, light, and spectra - to real-world astronomy and the search for habitable worlds. It builds on your knowledge of circular motion, gravitational fields, and the Doppler effect, and is an A-level only topic that often appears in exam questions involving calculations and data analysis.

• →Transit method: A planet passing in front of its star causes a periodic dip in the star's light curve. The depth of the dip gives the ratio of planet radius to star radius: depth = (R_planet / R_star)^2.
• →Radial velocity method: The star and planet orbit a common centre of mass. The star's motion causes a periodic Doppler shift in its spectral lines. The maximum radial velocity gives a minimum mass for the planet: m_planet sin i = (M_star v_star / v_planet) but often derived from Kepler's laws.
• →Kepler's third law: For a planet orbiting a star, T^2 = (4 pi^2 / G M_star) r^3, where T is orbital period, r is orbital radius, and M_star is the star's mass. This allows calculation of orbital radius or period.
• →Doppler shift: The observed wavelength change Δλ/λ = v/c, where v is the radial velocity of the star. This is used to measure the star's wobble.
• →Limitations: Transits require alignment of orbit with line of sight; radial velocity gives only minimum mass because inclination is unknown. Both methods are biased towards large, close-orbiting planets.

• The host star greatly outshines the planet, so the planet's reflected or emitted light is difficult to isolate.
• The angular separation between star and planet is very small, requiring high angular resolution.
• Earth's atmosphere blurs images, so ground-based direct detection needs adaptive optics or space-based observation.
• Scattered starlight and instrumental glare add background that can hide the planet's faint signal.
• Small, close-in planets are especially hard to image directly because their contrast and separation are both unfavourable.
• Techniques such as coronagraphy, adaptive optics and infrared space telescopes improve but do not remove these difficulties.
• The radial velocity method detects the periodic Doppler shift of the star's spectral lines as the star moves towards and away from the observer.
• The observed wavelength change Δλ is related to radial speed v by Δλ/λ ≈ v/c for speeds much less than c, so a measured shift gives the star's radial velocity.
• A repeating pattern in the radial velocity curve gives the orbital period, and the amplitude gives information about the planet's mass and orbit.
• The transit method detects a small, regular decrease in the star's apparent brightness when the planet passes across the stellar disc.
• Transit depth relates approximately to the square of the ratio of planet radius to star radius, so a deeper transit indicates a larger planet relative to its star.
• Transit timing gives the orbital period, and the duration and shape of the dip give information about orbital speed and geometry.
• Both methods require repeated, precise observations over at least one orbital period to confirm a periodic signal rather than random variability.
• The two methods are complementary: radial velocity gives mass-related information, while transits give radius-related information, and a planet seen by both allows density to be estimated.
• The vertical axis represents relative flux or apparent brightness, often normalised to 1.0 outside transit, and the horizontal axis represents time.
• The baseline is the unobscured stellar flux, and a transit appears as a temporary decrease below this baseline.
• Ingress and egress are the sloping parts of the curve where the planet's disc partially overlaps the star's disc.
• The flat bottom occurs while the planet is fully within the stellar disc, and its depth gives the fraction of starlight blocked.
• The depth is approximately equal to the square of the ratio of planet radius to star radius, so a larger or deeper transit indicates a larger planet relative to its star.
• The interval between repeated dips is the orbital period, and the width of the dip depends on the orbital speed and the path the planet takes across the stellar disc.
• A real light curve contains noise and may show slight variations, so a planet detection requires a periodic, repeatable signal rather than one isolated dip.

• 💡Quantify the contrast between star and planet to show why the planet's light is hard to see.
• 💡Use the idea of angular resolution to explain why close-in planets are difficult to separate from their star.
• 💡Mention at least one practical technique, such as a coronagraph or adaptive optics, and state what limitation it reduces.
• 💡Sketch or describe a labelled radial velocity curve and a transit light curve, labelling period, amplitude or depth, and explain what each feature represents.
• 💡Use the approximation Δλ/λ ≈ v/c only when v is much less than c, and state that the shift is measured relative to the star's rest wavelength.
• 💡When comparing methods, refer explicitly to what each measures and to the need for periodic confirmation rather than claiming one method is always better.
• 💡Define symbols clearly in calculations, for example Δλ for wavelength shift, λ for rest wavelength, v for radial speed and c for the speed of light.
• 💡Label the axes, baseline, ingress, flat bottom, egress and period when sketching a typical light curve.
• 💡Use the depth to compare planet sizes only when comparing transits of the same star, and explain that depth is a ratio of areas.
• 💡Explain that repeated dips at regular intervals provide stronger evidence than a single dip because they confirm a periodic orbit.
• 💡Keep descriptions of the curve consistent with the physics: the planet blocks a fraction of the star's light, so the flux falls and then recovers.
• 💡Always define the symbols in equations (e.g., R_star, R_planet) and state the formula you are using before substituting numbers. This secures method marks even if arithmetic slips.
• 💡When describing the radial velocity method, explicitly mention the Doppler shift of spectral lines and that the star's motion is due to the planet's gravitational pull. Use the term 'minimum mass' and explain why it is a minimum.
• 💡For graph questions, ensure you can interpret light curves (transit depth, duration, period) and radial velocity curves (amplitude, period). Label axes correctly and use the graph to extract values.

• Confusing direct detection with indirect methods such as transit or radial-velocity measurements: correct this by stating that direct detection requires light from the planet itself.
• Assuming the main problem is simply distance: correct this by explaining that contrast and angular separation are the dominant difficulties even for relatively nearby systems.
• Believing that a larger telescope alone solves the problem: correct this by noting that atmospheric blurring, scattered starlight and glare also limit detection.
• Thinking the Doppler shift is caused by the planet's light rather than the star's motion; correct this by stating that the star's spectral lines shift as the star orbits the common centre of mass.
• Confusing a transit dip with an eclipse of one star by another or with stellar variability; correct this by requiring a regular, repeating, shallow dip consistent with an orbiting planet.
• Assuming the radial velocity method gives the planet's exact mass directly; correct this by explaining that it gives a minimum mass because the orbital inclination is usually unknown.
• Treating the transit method as measuring mass directly; correct this by stating that transit depth primarily indicates the planet's radius relative to the star's radius.
• Reading the depth as the planet's diameter rather than a ratio of areas; correct this by relating depth to the square of the radius ratio.
• Assuming the dip is perfectly rectangular; correct this by including gradual ingress and egress as the planet's disc partially overlaps the star.
• Treating a single dip as conclusive; correct this by requiring a regular, repeating pattern consistent with an orbiting planet.
• Confusing the time between dips with the duration of one dip; correct this by distinguishing orbital period from transit duration.
• Students often think the transit method directly gives the planet's mass. In fact, it gives radius; mass requires radial velocity or other methods.
• Many believe the star remains stationary while the planet orbits. Actually, both orbit their common centre of mass, causing the star to wobble.
• Students sometimes forget that the radial velocity method only provides a minimum mass (m sin i) unless the inclination is known from transits.

1. 1Day 1-2: Learn the theory of the transit method. Understand the light curve, depth, and how to calculate planet radius. Practice rearranging depth = (R_planet/R_star)^2.
2. 2Day 3-4: Study the radial velocity method. Revise the Doppler effect and learn how to derive the star's velocity from spectral shifts. Understand why it gives minimum mass.
3. 3Day 5-6: Master Kepler's third law for exoplanets. Practice calculations converting units and solving for orbital radius or period.
4. 4Day 7-8: Work through past paper questions on exoplanet detection. Focus on graph interpretation and multi-step calculations.
5. 5Day 9-10: Create a summary sheet comparing the two methods, including advantages, limitations, and typical exam question styles. Test yourself with active recall.

• 📋Calculation of planet radius from transit depth: Given the stellar radius and depth, use depth = (R_planet/R_star)^2. Advice: ensure you square root the depth and keep units consistent.
• 📋Calculation of orbital radius or period using Kepler's third law: Often requires converting days to seconds and using the star's mass. Advice: write down the formula, rearrange, then substitute.
• 📋Explanation of the radial velocity method: Describe how the star's spectral lines shift due to its orbital motion and how this leads to a minimum mass. Advice: use key terms like 'Doppler shift', 'centre of mass', and 'minimum mass'.
• 📋Data analysis from light curves or radial velocity graphs: Identify period, depth, or amplitude and calculate quantities. Advice: read axes carefully and show all working.