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Whithin the framework of the Planck satellite polarisation calibration, wepresent a study of the Crab Nebula spectral energy distribution (SED) over morethan 6 decades in frequency ranging from 1 to $\rm 10^6 GHz$. The Plancksatellite mission observes the sky from 30 to 857 GHz and therefore we focus onthe millimetre region. We use radio and submillimetre data from the WMAPsatellite between 23 and 94 GHz (from 13 to 3.18 mm) and from the Archeopsballoon experiment between 143 (2.1 mm) and 545 GHz (0.55 mm), and a compendiumof other Crab Nebula observations. The Crab SED is compared to models includingthree main components : synchrotron which is responsible for the emission atlow and at high frequencies, dust which explains the excess of flux observed bythe IRAS satellite and an extra component on the millimetre regime. From thisanalysis we conclude that the unpolarised emission of the Crab Nebula atmicrowave and millimetre wavelengths is the same synchrotron emission that theone observed in the radio domain. Therefore, we expect the millimetre emissionof the Crab nebula to be polarised with the same degree of polarisation andorientation than the radio emission. We set upper limits on the possible errorsinduced by any millimetre extra component on the reconstruction of the degreeand angle of polarisation at the percent level as a maximum. This resultstrongly supports the choice by the Planck collaboration of the Crab nebulaemission for performing polarisation cross-checks in the range 30 (299 mm) to353 GHz (0.849 mm).

Global spectral energy distribution of the Crab Nebula in the prospect of the Planck satellite polarisation calibration