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We present skeleton studies of non‐Gaussianity in the cosmic microwave background temperature anisotropy observed in the 5‐yr  Wilkinson Microwave Anisotropy Probe  ( WMAP ) data. The local skeleton is traced on the 2D sphere by cubic spline interpolation which leads to more accurate estimation of the intersection positions between the skeleton and the secondary pixels than conventional linear interpolation. We demonstrate that the skeleton‐based estimator of non‐Gaussianity of the local type (  f  local  NL  ) – the departure of the length distribution from the corresponding Gaussian expectation – yields an unbiased and sufficiently converged likelihood function for   f  local  NL  .  We analyse the skeleton statistics in the  WMAP  5‐yr combined  V ‐ and  W ‐band data outside the Galactic base‐mask determined from the KQ75 sky coverage. The results are consistent with Gaussian simulations of the best‐fitting cosmological model, but deviate from the previous results determined using the  WMAP  1‐yr data. We show that it is unlikely that the improved skeleton tracing method, the omission of  Q ‐band data, the modification of the foreground‐template fitting method or the absence of six extended regions in the new mask contribute to such a deviation. However, the application of the Kp0 base‐mask in data processing does improve the consistency with the  WMAP 1 results.  The   f  local  NL  ‐likelihood functions of the data are estimated at nine different smoothing levels. It is unexpected that the best‐fitting values show positive correlation with the smoothing scales. Further investigation argues against a point source or goodness‐of‐fit explanation but finds that about 30 per cent of either Gaussian or  f  NL  samples having better goodness‐of‐fit than the  WMAP  5‐yr data show a similar correlation. We present the estimate   f  local  NL = 47.3 ± 34.9  (1σ error) determined from the first four smoothing angles and   f  local  NL = 76.8 ± 43.1  for the combination of all nine. The former result may be overestimated at the 0.21σ level because of point sources.

The primordial non‐Gaussianity of local type ( f local NL ) in the WMAP 5‐year data: the length distribution of CMB skeleton