We present measurements of the spin-orbit alignment angle, lambda, for the hot Jupiter systems WASP-32, WASP-38, and HAT-P-27/WASP-40, based on data obtained using the HARPS spectrograph. We analyse the Rossiter-McLaughlin effect for all three systems, and also carry out Doppler tomography for WASP-32 and WASP-38. We find that WASP-32 (T_eff = 6140 +90 -100 K) is aligned, with an alignment angle of lambda = 10.5 +6.4 -6.5 degrees obtained through tomography, and that WASP-38 (T_eff = 6180 +40 -60 K) is also aligned, with tomographic analysis yielding lambda = 7.5 +4.7 -6.1 degrees. This latter result provides an order of magnitude improvement in the uncertainty in lambda compared to the previous analysis of Simpson et al. (2011). We are only able to loosely constrain the angle for HAT-P-27/WASP-40 (T_eff = 5190 +160 -170 K) to lambda = 24.2 +76.0 -44.5 degrees, owing to the poor signal-to-noise of our data. We consider this result a non-detection under a slightly updated version of the alignment test of Brown et al. (2012). We place our results in the context of the full sample of spin-orbit alignment measurements, finding that they provide further support for previously established trends.
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