Disc-halo gas outflows driven by stellar clusters as seen in multiwavelength tracers

We consider the dynamics of and emission from growing superbubbles in a stratified interstellar gaseous disc driven by energy release from supernovae explosions in stellar clusters with {masses $M_{cl}= 10^5-1.6\times 10^6~M_\odot$}. Supernovae are spread randomly within a sphere of $r_c=60$ pc, and inject energy episodically with a specific rate $1/130~M_\odot^{-1}$ proportional to the star formation rate (SFR) in the cluster. Models are run for several values of SFR in the range $0.01$ to $0.1~M_\odot$ yr$^{-1}$, with the corresponding average surface energy input rate $\sim 0.04-0.4$ erg cm$^{-2}$ s$^{-1}$. We find that the discrete energy injection by isolated SNe are more efficient in blowing superbubbles: asymptotically they reach heights of up to 3 to 16 kpc for $M_{cl}=10^5-1.6\times 10^5~M_\odot$, correspondingly, and stay filled with a hot and dilute plasma for at least 30 Myr. During this time they emit X-ray, H$\alpha$ and dust infrared emission. X-ray liminosities $L_X\propto {\rm SFR}^{3/5}$ that we derive here are consistent with observations in star-forming galaxies. Even though dust particles of small sizes $a\leq 0.03~\mu$m are sputtered in the interior of bubbles, larger grains still contribute considerably ensuring the bubble luminosity $L_{\rm IR}/{\rm SFR}\sim 5\times 10^7 L_\odot M_\odot^{-1} ~{\rm yr}$. It is shown that the origin of the North Polar Spur in the Milky Way can be connected with activity of a cluster with the stellar mass of $\sim 10^5~M_\odot$ and the ${\rm SFR}\sim 0.1~M_\odot$ yr$^{-1}$ some 25--30 Myr ago. Extended luminous haloes observed in edge-on galaxies (NGC 891 as an example) can be maintained by disc spread stellar clusters of smaller masses $M_\ast \simlt 10^5~M_\odot$.