The role of magnetic fields in shaping $γ$-ray emission from the Fermi bubbles

TL;DR

The paper addresses the origin of the Fermi bubbles by testing whether a magnetized, subsonic Galactic breeze can yield the observed bilobed, sharp-edged $\gamma$-ray emission. It couples a 2.5D MHD Galactic breeze simulated with PLUTO to a cosmic-ray transport model that includes anisotropic diffusion along the magnetic field and advection by the outflow, with CRs injected in a collimated cone of half-angle $\theta_{1/2}=20^{\circ}$ and a spectrum $\propto p^{-2}$. Using a fiducial CR luminosity $L_{\rm CR}=1.3\times10^{40}$ erg s$^{-1}$, the model reproduces a $1$–$3$ GeV gamma-ray luminosity of $L_{\gamma}=2.7\times10^{37}$ erg s$^{-1}$ and a calorimetric fraction of $\sim 6\times10^{-3}$, indicating the bubbles are non-calorimetric. The results show that diffusion anisotropy, guided by the evolving magnetic field, combined with a collimated injection, naturally produces bilobed emission with sharp edges, in good agreement with Fermi-LAT observations and improving on isotropic-diffusion or uncollimated-hydrodynamic models. This framework provides a physically motivated mechanism for the Fermi bubbles and a basis for future spectral comparisons and extensions to larger halo scales and other galaxies.

Abstract

Despite their discovery fifteen years ago, the nature and origin of the Fermi bubbles remain unclear. We here investigate the effect a magnetic field can have on a subsonic breeze outflow emanating from the Galactic centre region. The presence of this magnetic field allows anisotropic diffusion of cosmic rays within the outflow, shaping the resultant cosmic ray distribution obtained out at large distances within the Galactic halo. We show that our magnetohydrodynamic Galactic breeze model, in combination with an opening angle for the injection of cosmic rays, leads to $γ$-ray emission from the Fermi bubble region with relatively sharp edges.

Figures (11)

• Figure 1: Gas density distribution of the hot Galactic halo as a function of Galactic height for R = 0.3 kpc. The dashed red line represents the hydrostatic density distribution for the Galactic halo (Eq. \ref{['eq:rho']}). The solid blue line represents the steady-state density distribution for the numerical simulation. The red shaded region represents a fitting range provided by observations of the O VII spectrum and ram pressure stripping Martynenko_2022.
• Figure 2: Spatial distribution of the steady-state (a) velocity and (b) magnetic field strength, both for a 2D map with cylindrical coordinates. The white arrows represent the direction of the respective vector field. The continuous colour bar indicates the logarithm in base 10 for each quantity. For Fig. \ref{['fig:_a']} the black contour lines represent the velocity distribution for two specific values of 100 km s$^{-1}$ and 30 km s$^{-1}$. For Fig. \ref{['fig:_b']} the black contour lines represent magnetic field strengths of 0.1 $\mu$G and 0.03 $\mu$G. Fig. \ref{['fig:_c']} shows the distribution of the velocity as a function of Galactic height, $z$, for $R=300$ pc. The solid orange line represents the velocity profile from the MHD simulation, and the dashed blue line represents the velocity profile for the hydrodynamic solution. The dotted red line represents the thermal velocity. Fig. \ref{['fig:_d']} shows the distribution of both magnetic field components, $B_r$ and $B_{\phi}$, along the cylindrical radius, $R$, for $z=300$ pc. The solid blue and orange lines represent the distribution of $B_r$ and $B_{\phi}$. For comparison, the dashed green line represents the analytic solution for the distribution of $B_{\phi}$.
• Figure 3: Spatial distribution of (a) the diffusion scattering length and (b) the ratio of the diffusion time to the advection time. The continuous colour bar indicates the logarithm in base 10. (a) The dashed contour lines represent the diffusion scattering length, $3D_{\parallel}(30~{\rm GeV})/c$, for three different values, 0.3 pc , 0.42 pc and 0.9 pc. (b) The solid contour line represents the position where the ratio of the diffusion time is equal to the advection time.
• Figure 4: Spatial CR density distribution in the Galactic halo for an energy range of $E_{\mathrm{CR}} = 10~-~30$ GeV with the colour bar showing the logarithm in base 10. The black dashed black lines are contours representing different density distributions, i.e., $n_{\mathrm{CR}} = 0.3, 1$ and $3\times 10^{-11}$ cm$^{-3}$, respectively.
• Figure 5: The 1-3 GeV $\gamma$-ray emission map produced through the energy losses of 10-30 GeV CR. The map uses a Mollweide projection. The colour bar is linear, and the Galactic plane is masked with $E_{\gamma}F_{\gamma} = 0$ at $|b| < 10^{\circ}$. Both colours and mask provide a setup similar to the observational paper Ackermann_2012. The resulting emission produces a bubble shape, broadly consistent with observations (i.e. a height of $\sim 50^{\circ}$ and a width of $\sim 40^{\circ}$).