Radial Velocity Signal or Stellar Rotation?
A G-type main-sequence star (mass 1.0 M_sun, radius 1.0 R_sun, v sin i = 4.5 km/s, rotation period 24 d) is monitored with a high-resolution spectrograph for 120 nights. The team reports a periodic radial-velocity signal with P = 24.0 d and semi-amplitude K = 8 m/s. The photometric light curve shows a 12.0 d modulation with amplitude 0.4 mmag, and the bisector span of the cross-correlation function varies in phase with the 24 d RV signal. The instrumental long-term stability is 1 m/s, and the star has log R'_HK = -4.9. The team claims a planet with m sin i = 12 M_earth in a 24 d orbit.
1. Assess whether the 24 d RV signal is planetary. Use the period relationships, activity indicators, and amplitude consistency to justify your conclusion.
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The photometric period is 12.0 d, exactly half the RV period. This is the classic signature of spots: two antipodal active regions produce a light-curve modulation at half the true rotation period, while the RV signal traces the full rotation. The RV period therefore matches the rotation period, not a Keplerian orbit. The bisector span varies in phase with the RV signal, which means the line profile is changing shape - a planetary Doppler shift moves the whole profile without changing its shape. log R'_HK = -4.9 is modestly active, consistent with spots. The amplitude is also consistent with activity: a 4.5 km/s projected rotation with 0.4 mmag photometric amplitude implies a spot covering fraction of order a percent, which can produce several m/s of RV jitter. The claimed m sin i = 12 M_earth in 24 d around a 1 M_sun star would produce K = 8 m/s only if the orbit is nearly edge-on; the signal is better explained by rotation. Conclusion: the signal is not securely planetary; it is most likely stellar activity (spots) at the rotation period.
2. The team argues that the 1 m/s instrumental stability rules out activity. Explain why instrumental precision does not establish astrophysical origin, and propose two observations that would discriminate.
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Instrumental stability limits only the noise floor of the measurement; it says nothing about astrophysical signals from the star itself. A 1 m/s spectrograph can measure a 8 m/s stellar jitter perfectly well - the jitter is signal, not noise. To discriminate, first obtain a longer baseline: if the 24 d signal is rotation, it will drift in phase and amplitude as spots evolve, whereas a planet remains phase-stable over many cycles. Second, use line-by-line or chromatic RV analysis: spot-induced signals are wavelength-dependent because the spot contrast changes with wavelength, while a Keplerian signal is achromatic. A third option is to check the phase of the bisector and photometry jointly; a planet should not produce photometric modulation at half the RV period.