Synthetic $^{26}$Al emission from galactic-scale superbubble simulations

Emission from the radioactive trace element $^{26}$Al has been observed throughout the Milky Way with the COMPTEL and INTEGRAL satellites. In particular the Doppler shifts measured with INTEGRAL connect $^{26}$Al with superbubbles, which may guide $^{26}$Al flows off spiral arms in the direction of Galactic rotation. In order to test this paradigm, we have performed galaxy-scale simulations of superbubbles with $^{26}$Al injection in a Milky Way-type galaxy. We produce all-sky synthetic $\gamma-$ray emission maps of the simulated galaxies. We find that the 1809keV emission from the radioactive decay of $^{26}$Al is highly variable with time and the observer's position. This allows us to estimate an additional systematic variability of 0.2dex for a star formation rate derived from $^{26}$Al for different times and measurement locations in Milky Way-type galaxies. High-latitude morphological features indicate nearby emission with correspondingly high integrated $\gamma-$ray intensities. We demonstrate that the $^{26}$Al scale height from our simulated galaxies depends on the assumed halo gas density. We present the first synthetic 1809keV longitude-velocity diagrams from 3D hydrodynamic simulations. The line-of-sight velocities for $^{26}$Al can be significantly different from the line-of-sight velocities associated with the cold gas. Over time, $^{26}$Al velocities consistent with the INTEGRAL observations, within uncertainties, appear at any given longitude, broadly supporting previous suggestions that $^{26}$Al injected into expanding superbubbles by massive stars may be responsible for the high velocities found in the INTEGRAL observations. We discuss the effect of systematically varying the location of the superbubbles relative to the spiral arms.