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Recently the first detections of highly ionised gas associated with twoWarm-Hot Intergalactic Medium (WHIM) filaments have been reported. The evidenceis based on X-ray absorption lines due to O VII and other ions observed byChandra towards the bright blazar Mrk 421. We investigate the robustness ofthis detection by a re-analysis of the original Chandra LETGS spectra, theanalysis of a large set of XMM-Newton RGS spectra of Mrk 421, and additionalChandra observations. We address the reliability of individual spectralfeatures belonging to the absorption components, and assess the significance ofthe detection of these components. We also use Monte Carlo simulations ofspectra. We confirm the apparent strength of several features in the Chandraspectra, but demonstrate that they are statistically not significant. Thisdecreased significance is due to the number of redshift trials that are madeand that are not taken into account in the original discovery paper. Thereforethese features must be attributed to statistical fluctuations. This isconfirmed by the RGS spectra, which have a higher signal to noise ratio thanthe Chandra spectra, but do not show features at the same wavelengths. Finally,we show that the possible association with a Ly-alpha absorption system alsolacks sufficient statistical evidence. We conclude that there is insufficientobservational proof for the existence of the two proposed WHIM filamentstowards Mrk 421, the brightest X-ray blazar on the sky. Therefore, the highlyionised component of the WHIM still remains to be discovered.Comment: 13 pages, 4 figures, submitted to the Astrophysical Journa

The OviiX‐Ray Forest toward Markarian 421: Consistency betweenXMM‐NewtonandChandra