In view of both the size of its gap and the previously reported asymmetries and near-infrared spiral arms, the transition disk of the Herbig Fe star HD 142527 constitutes a remarkable case study. This paper focuses on the morphology of the outer disk through ALMA observations of $^{12}$CO J=2-1, $^{12}$CO J=3-2 and $^{13}$CO J=2-1. Both $^{12}$CO J=2-1 and $^{12}$CO J=3-2 show spiral features of different sizes. The innermost spiral arm (S1) is a radio counterpart of the first near-infrared spiral observed by Fukagawa et al. (2006), but it is shifted radially outward. However, the most conspicuous CO spiral arm (S2) lies at the outskirts of the disk and had not been detected before. It corresponds to a cold density structure, with both brightness and excitation temperatures of order 13$pm$2 K and conspicuous in the $^{12}$CO J=2-1 peak-intensity map, but faint in $^{12}$CO J=3-2. There is also a faint counterarm (S3), point-symmetrical of S2 with respect to the star. These three spirals are modelled separately with two different formulae that approximate the loci of density maxima in acoustic waves due to embedded planets. S1 could be fit relatively well with these formulae, compared to S2 and S3. Alternative scenarios such as gravitational instability or external tidal interaction are discussed. The impact of channelization on spectrally and spatially resolved peak intensity maps is also briefly addressed.
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