Circumgalactic Ly$\alpha$ emission around submillimeter-bright galaxies with different quasar contributions

We present VLT/MUSE observations targeting the extended Lyman-$\alpha$ (Ly$\alpha$) emission of five high-redshift ($z\sim$3-4) submillimeter galaxies (SMGs) with increasing quasar (QSO) radiation: two SMGs, two SMGs hosting a QSO, and one SMG hosting a QSO with a SMG companion (QSO+SMG). These sources should be located in dark matter halos of comparable masses (average mass of $M_{\rm DM}\sim10^{12.2}\,{\rm M}_\odot$). We quantify the luminosity and extent of the Ly$\alpha$ emission, together with its kinematics, and examine four Ly$\alpha$ powering mechanisms: photoionization from QSOs/star formation, shocks by galactic/QSO outflows, gravitational cooling radiation, and Ly$\alpha$ photons resonant scattering. We find a variety of Ly$\alpha$ luminosities and extents, with the QSO+SMG system displaying the most extended and bright nebula, followed by the SMGs hosting a QSO, and finally the undetected circumgalactic medium (CGM) of SMGs. This diversity implies that gravitational cooling is unlikely to be the main powering mechanism. We show that photoionization from the QSO and QSO outflows can contribute to power the emission for average densities $n_{\rm H}>0.5\,$cm$^{-3}$. Moreover, the observed Ly$\alpha$ luminosities scale with the QSO's budget of Ly$\alpha$ photons modulo the dust content in each galaxy, highlighting a possible contribution from resonant scattering of QSO's radiation in powering the nebulae. We find larger Ly$\alpha$ linewidths (FWHM$\gtrsim 1200\,$km$\,$s$^{-1}$) than usually reported around radio-quiet systems, pointing to large-scale outflows. A statistical survey targeting similar high-redshift massive systems with known host properties is needed to confirm our findings.