The bipolar, nonthermal, high-latitude lobes known as the Fermi bubbles (FBs) are thought to originate from a massive energy release near the Galactic centre (GC). We constrain the FB engine and the circumgalactic medium (CGM) by analytically and num
erically modeling the FB edges as strong forward shocks, as inferred from recent observations. A non-directed energy release produces shocks too spherical to account for observations even for a maximally massive Galactic disc, critical CGM rotation, or injection effectively offset from the GC. In contrast, collimated injection nearly perpendicular to the disc can account for observations in both ballistic (free expansion) and slowdown regimes, as we show using a simple stratified evolution model verified by hydrodynamic simulations. FBs still in their ballistic regime require injection (at $zsimeq100$ pc heights in our model) with a half-opening angle $thetasimeq4^circ$, a normalized velocity $beta_{-2}equiv v/(0.01c)gtrsim 0.4$, and an energy $Egtrsim2beta_{-2}^2times 10^{55}$ erg, launched $mathbb{T}simeq 3.3beta_{-2}^{-1}$ Myr ago, showing a distinctive low-pressure region behind the bubble head. Slowing-down (mass accumulated) FBs require a faster injection, a thinner jet, a smaller $E/(beta_{-2}theta)^{2}$, and a comparable $mathbb{T}$, and follow a ballistic stage that must reach a height $z_{s}gtrsim 5$ kpc.
We analyze the IceCube four-year neutrino data in search of a signal from the Fermi bubbles. No signal is found from the bubbles or from their dense shell, even when taking into account the softer background. This imposes a conservative $xi_i<8%$ upp
er limit on the cosmic-ray ion (CRI) acceleration efficiency, and an $etaequiv xi_e/xi_i gtrsim0.006$ lower limit on the electron-to-ion ratio of acceleration efficiencies (at the $2sigma$ confidence level). For typical $xi_i$, a signal should surface once the number of IceCube neutrinos increases by $sim$an order of magnitude, unless there is a $<$PeV cutoff on the CRI spectrum.
The nature of the bipolar, $gamma$-ray Fermi bubbles (FB) is still unclear, in part because their faint, high-latitude X-ray counterpart has until now eluded a clear detection. We stack ROSAT data at varying distances from the FB edges, thus boosting
the signal and identifying an expanding shell behind the southwest, southeast, and northwest edges, albeit not in the dusty northeast sector near Loop I. A Primakoff-like model for the underlying flow is invoked to show that the signals are consistent with halo gas heated by a strong, forward shock to $sim$keV temperatures. Assuming ion--electron thermal equilibrium then implies a $sim10^{56}$ erg event near the Galactic centre $sim7$ Myr ago. However, the reported high absorption-line velocities suggest a preferential shock-heating of ions, and thus more energetic ($sim 10^{57}$ erg), younger ($lesssim 3$ Myr) FBs.
Current measurements of the $gamma$-ray Fermi bubbles (FB) are based on model-dependent tracers, carry substantial systematic uncertainties, and are at some tension with each other. We show that gradient filters pick out the FB edges, which are found
to smoothly connect to the bipolar X-ray structure emanating from the Galactic center, thus supporting the interpretation of the FBs as a Galactic-scale phenomenon. The sharp edges facilitate a direct, model-free measurement of the peripheral FB spectrum. The result is strikingly similar to the full FB-integrated spectrum, softened by a power law of index $etasimeq (0.2mbox{--}0.3)$. This is naturally explained, in both hadronic and leptonic models, if cosmic rays are injected at the edge, and diffuse away preferentially at higher energies $E$. The inferred, averaged diffusion function in the (more plausible) leptonic model, $D(E)simeq 10^{29.5}(E/10mbox{ GeV})^{0.48pm0.02}mbox{ cm}^2mbox{ s}^{-1}$, is consistent with estimates for Kraichnan-like turbulence. Our results, in particular the minute spatial variations in $eta$, indicate that the FB edge is a strong, Mach $gtrsim5$, forward shock.
