Precessing Black Hole Jets and Galactic Fossils

The Galactic Centre gamma-ray excess (GCE) - an anomalous ~ 2-5 GeV Fermi-LAT signal around SgrA$^{\star}$ - has remained without a consensus interpretation for more than fifteen years. Dark-matter annihilation and unresolved millisecond-pulsar populations remain the leading candidates, yet neither incorporates the past activity of SgrA$^{\star}$ recorded by the Fermi and eROSITA bubbles (FEB). We propose a unified scenario in which both the GCE and the FEB are fossil imprints of a single past episode of SgrA$^{\star}$ activity: a precessing parabolic Blandford-Znajek jet launched from a tilted, magnetically arrested disc during a ~7.5 Myr active phase ending ~ 2.6 Myr ago. The jet both inflated the kpc-scale FEB and injected hadronic cosmic rays contributing to the GCE flux. The model rests on three independently motivated inputs: the EHT-proposed ~ $35^{\circ}$ tilt of the SgrA$^{\star}$ spin axis from the Galactic rotation axis, Lense-Thirring precession of the disc through ~5 azimuthal cycles during the active phase, and a two-zone cosmic-ray transport prescription through the CMZ and bulge with standard inner-Galaxy diffusion coefficients. Internal consistency is verified by checking that the proton Larmor radius confines cosmic rays to the jet column and that the gamma-ray optical depth toward the Galactic Centre is negligible. Comparison with current GCE observations yields a spin-dependent hadronic contribution: for the EHT-favoured SgrA$^{\star}$ spin a$^{\star}$ = 0.9, we find an irreducible hadronic floor of ~ 3-14% of the observed GCE surface brightness across the inner ten degrees, highlighting a previously unexplored component relevant for comprehensive models of the GCE.