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(Abridged) The quiet M2.5 star GJ 436 hosts a warm Neptune that displays anextended atmosphere that dwarfs its own host star. Predictions of atmosphericescape in such planets state that H atoms escape from the upper atmosphere in acollisional regime and that the flow can drag heavier atoms to the upperatmosphere. It is unclear, however, what astrophysical mechanisms drive theprocess. Our objective is to leverage the extensive coverage of HST/COSobservations of the far-ultraviolet (FUV) spectrum of GJ 436 to search forsignals of metallic ions in the upper atmosphere of GJ 436 b. We analyzed fluxtime-series of species present in the FUV spectrum of GJ 436, as well as theLyman-$\alpha$ line. GJ 436 displays FUV flaring events with a rate of $\sim$10d$^{-1}$. There is evidence for a possibly long-lived active region orlongitude that modulates the FUV metallic lines of the star with amplitudes upto 20%. Despite the strong geocoronal contamination in the COS spectra, wedetected in-transit excess absorption signals of $\sim$50% and $\sim$30% in theblue and red wings, respectively, of the Lyman-$\alpha$ line. We rule out awide range of excess absorption levels in the metallic lines of the star duringthe transit. The large atmospheric loss of GJ 436 b observed in Lyman-$\alpha$transmission spectra is stable over the timescale of a few years, and the redwing signal supports the presence of a variable hydrogen absorption sourcebesides the stable exosphere. The previously claimed in-transit absorption inthe Si III line is likely an artifact resulting from the stellar magneticcycle. The non-detection of metallic ions in absorption could indicate that theescape is not hydrodynamic or that the atmospheric mixing is not efficient indragging metals high enough for sublimation to produce a detectable escape rateof ions to the exosphere.

The Hubble PanCET program: An extensive search for metallic ions in the exosphere of GJ 436 b