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The Spin Effect on Planetary Radial Velocimetry of Exoplanets

We consider the effect of planetary spin on the planetary radial velocity (PRV) in dayside spectra of exoplanets. To understand the spin effect qualitatively, we derive an analytic formula of the intensity-weighted radial velocity from planetary surface on the following assumptions: 1) constant and solid rotation without precession, 2) stable and uniform distribution of molecules/atoms, 3) emission models from dayside hemisphere, and 4) a circular orbit. On these assumptions, we find that the curve of the PRV is distorted by the planetary spin and this anomaly is characterized by spin radial velocity at equator and a projected angle on a celestial plane between the spin axis and the axis of orbital motion λ_p in a manner analogous to the Rossiter-McLaughlin effect. The latter can constrain the planetary obliquity. Creating mock PRV data with 3 km/s accuracy, we demonstrate how λ_p and the spin radial velocity at equator are estimated. We find that the stringent constraint of eccentricity is crucial to detect the spin effect. Though our formula is still qualitative, we conclude that the PRV in the dayside spectra will be a powerful means for constraining the planetary spin.