Transit signal: planet, starspot or eclipsing binary?
A transiting planet candidate orbits a Sun-like star (1.0 solar mass, 1.0 solar radius). The light curve shows dips every 12.0 days. The dip depth is 1.0% of the star's brightness, and the dip lasts 3.0 hours. There is no detected secondary eclipse at the 0.02% level. Radial-velocity measurements show a periodic signal with semi-amplitude 12 m/s, consistent with the same 12.0-day period; the star's other activity indicators are stable. The star's effective temperature is 5800 K and luminosity is 1.0 solar luminosity. A team claims the object is 'an Earth-like planet in the habitable zone' because the dip is small. Another team suspects a starspot or an eclipsing binary. The telescope has only one filter (white light), and no high-resolution imaging has been done. The candidate is being considered for follow-up observing time.
1. Calculate the planet's radius in Earth radii and evaluate the claim that it is Earth-like.
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Transit depth = (Rp/Rs)^2 = 0.01, so Rp/Rs = 0.10. With Rs = 1.0 Rsun, Rp = 0.10 Rsun. Since 1 Rsun ≈ 109 Earth radii, Rp ≈ 10.9 Earth radii, about Jupiter's radius, not Earth's (1 Earth radius). The claim 'Earth-like' is therefore wrong on size alone. A 1% dip is small relative to a stellar eclipse but still large for a planet; Earth around a Sun-like star would give about 0.008% depth. The object could still be a planet, but it is a gas-giant-sized planet, not a rocky Earth analogue.
2. Assess whether the signal is most likely a planet, a starspot or an eclipsing binary. Use all the evidence.
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A starspot would produce a dip that changes with rotation, is wavelength-dependent, and may not be strictly periodic at 12 days unless the star rotates at that period; the stable 12-day period and lack of activity indicators argue against it. An eclipsing binary would likely show a secondary eclipse and a much larger radial-velocity amplitude; no secondary at 0.02% and 12 m/s are consistent with a planet. The 3-hour duration and 12-day period are plausible for a close-in giant planet. However, without high-resolution imaging or multi-colour data, a blended background eclipsing binary cannot be fully excluded; the radial-velocity signal helps but should be checked for line-shape variations. Most likely a planet, but confirmation requires more follow-up.
3. Use Kepler's third law to estimate the orbital distance and decide whether it is in the habitable zone.
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P = 12.0 days = 12/365.25 = 0.03285 yr. For a 1 solar-mass star, a^3 = P^2 in AU and yr, so a^3 = 0.001079 and a = 0.102 AU. The habitable zone for a Sun-like star is roughly 0.95–1.4 AU, so this planet is about ten times closer than the inner edge. Its stellar flux is about (1/0.102)^2 ≈ 96 times Earth's, so it is far too hot for liquid water on its surface. Even allowing for albedo, its equilibrium temperature is much higher than 273 K. It is not in the habitable zone; the claim is inconsistent with the data.