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We report the measurement of the spin-orbit angle of the extra-solar planets HAT-P-8 b, HAT-P-9 b, HAT-P-16 b and HAT-P-23 b, thanks to spectroscopic observations performed at the Observatoire de Haute-Provence with the SOPHIE spectrograph on the 1.9 3-m telescope. Radial velocity measurements of the Rossiter-McLaughlin effect show the detection of an apparent prograde, aligned orbit for all systems. The projected spin-orbit angles are found to be lambda=-17 deg (+9.2,-11.5), -16 deg (8), -10 deg (16), +15 deg (22) for HAT-P-8, HAT-P-9, HAT-P-16 and HAT-P-23 respectively, with corresponding projected rotational velocities of 14.5 (0.8), 12.5 (1.8), 3.9 (0.8), and 7.8 (1.6) km/s. These new results increase to 37 the number of accurately measured spin-orbit angles in transiting extrasolar systems. We conclude by drawing a tentative picture of the global behaviour of orbital alignement, involving the complexity and diversity of possible mechanisms.
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