tokens: consuming and may suffer from a low S/N (Grier et al. 2013 ) caused by the combination of weak absorption lines, surface brightness dimming, instrument sensitivity and atmospheric transmission. In the rest-frame optical regime, the QSO and host galaxy contribution can be separated in high S/N single-aperture spectra by directly modelling them with template spectra for each component (Shen et al. 2008a , 2015 ). While a large sample can be studied with this technique, the fixed aperture size prevents such studies from measuring σ * at a physical size matched to the spheroid component. Furthermore, the reliability of the measurements decreases with increasing AGN luminosity and contrast ratio, thus limiting this technique to AGN with L 5100 ≲ 10 45 erg s −1 . To probe more luminous AGN, deep off-axis spectroscopy a few arcsec away from the QSO has been obtained to reduce the contrast between QSO and host galaxy emission (Wolf Sheinis 2008 ; Hughes et al. 2000 ; Wold et al. 2010 ). While σ * can be reliably derived from these off-axis spectra (Wolf Sheinis 2008 ), an uncertain aperture correction needs to be applied to infer comparable measurements representative for the spheroidal component. A direct decomposition the stellar continuum of the host galaxy underneath very luminous QSOs with deep optical integral-field unit observations was previously attempted with VIMOS for HE 1029−1401 (Husemann et al. 2010 ). Although HE 1029−1401 is much closer with a redshift of z = 0.086 but has a similar luminosity as PG 1307+085, the achieved S/N in the host spectrum was significantly lower than what we obtained with MUSE for PG 1307+085. This can be clearly attributed to the superior sensitivity, spatial resolution/sampling, and image quality of MUSE compared to VIMOS. These capabilities allow direct measurements of σ * with MUSE even in a high contrast regime that has not been accessible to any other techniques so far. 4.2 The nature of the large extended emission line region 4.2.1 Ionized gas shells driven by AGN outflows? A number of recent studies report kpc-scale high-velocity outflows to be common around luminous AGN with line widths of about 1000 km s −1 (e.g. Cano-Díaz et al. 2012 ; Liu et al. 2013 ; Harrison et al. 2014 ; Liu, Zakamska Greene 2014 ). Those outflows have been interpreted as spherically symmetric radiation pressure-dominated winds (Liu et al. 2013 ) and are possibly common for AGN with L bol > 2 × 10 45 erg s −1 (Zakamska Greene 2014 ). However, not all QSOs above this luminosity threshold exhibit such powerful superbubble-like outflows (e.g. Husemann et al. 2010 , 2013 ). The ionized gas kinematics of the ENLR around PG 1307+085 exhibits only small line widths with a velocity dispersion of 50 km s −1 in all the bright extended knots without any asymmetric component. This confidently rules out the AGN-driven superbubble scenario at least for this particular QSO. Although PG 1307+085 is classified as radio-quiet QSO with R 0.1
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