The Decoupled Kinematics of high-z QSO Host Galaxies and their Lya halos

We present a comparison of the interstellar medium traced by [CII] (ALMA), and ionised halo gas traced by Lya (MUSE), in and around QSO host galaxies at z~6. To date, 18 QSOs at this redshift have been studied with both MUSE and high-resolution ALMA imaging; of these, 8 objects display a Lya halo. Using datacubes matched in velocity resolution, we compare and contrast the spatial and kinematic information of the Lya halos and the host galaxies' [CII] (and dust-continuum) emission. We find that the Lya halos extend typically 3-30 times beyond the interstellar medium of the host galaxies. The majority of the Lya halos do not show ordered motion in their velocity fields, whereas most of the [CII] velocity fields do. In those cases where a velocity gradient can be measured in Lya, the kinematics do not align with those derived from the [CII] emission. This implies that the Lya emission is not tracing the outskirts of a large rotating disk that is a simple extension of the central galaxy seen in [CII] emission. It rather suggests that the kinematics of the halo gas are decoupled from those of the central galaxy. Given the scattering nature of Lya, these results need to be confirmed with JWST IFU observations that can constrain the halo kinematics further using the non-resonant Ha line.


INTRODUCTION
High-redshift quasars (QSOs) present a unique opportunity to study some of the most extreme objects in the Universe, back to < 1 Gyr after the Big Bang. In these objects vast amounts of material are funnelled onto galaxies' central supermassive black holes. This leads to accretion disks that shine with sufficiently high luminosities to allow their detection well into the epoch of reionisation (e.g. Mortlock et al. 2011, Bañados et al. 2018, Yang et al. 2020. At z ∼ 6, several hundred QSOs have now been detected (e.g. Bañados et al. 2016, Jiang et al. 2016, Mazzucchelli et al. 2017 and it was recently discovered that some of these QSOs are surrounded by giant Lyα halos. Drake et al. (2019) for instance presented deep muse observations of 5 QSOs at z ∼ 6, and revealed that 4 of these objects displayed Lyα halos comparable in extent and luminosity to their lower redshift counterparts at 2 ≤ z ≤ 3 (e.g. Borisova et al. 2016). This confirmed earlier evidence of Lyα halos at z ∼ 6 based on long-slit spectroscopy and/or narrow-band imaging for both the radio-loud QSO J2228+0110 at z = 5.903 (Roche et al. 2014, Zeimann et al. 2011, and J2329−0301 at z = 6.43 (Goto et al. 2009, Willott et al. 2011, Goto et al. 2012 and Momose et al. 2018) and was later followed-up by Farina et al. (2019) who presented additional Lyα halos as part of the muse snapshot survey "requiem".
Contemporaneously, observations from alma have revealed the far-infrared (FIR) dust-continuum and [Cii] emission from the interstellar medium (ISM) in ≥ 27 z ∼ 6 quasar host galaxies ). These observations confirmed earlier studies in that these objects are rich in gas and dust. Higher spatial-resolution observations from alma reaching resolution of ∼ 1 pkpc, have been analysed in a series of papers: These ob- The area corresponding to complex residuals following PSF-subtraction is shown by the hatched circle. In addition, grey contours show the region from which [Cii] emission is mapped. The lower panels zoom-in to a box of 4 a side (grey dashed boxes in the top row), and display the [Cii] moment maps together with a grey contour that traces the edge of the Lyα halo shown above). The left-hand column shows the flux images (moment 0), the central column shows the velocity offset relative to systemic z (moment 1; note that the colourbar for the lower panels is a zoom-in to the range shown by two black bars on the colourbar in the upper panels) and the right-hand column shows the velocity dispersion (σ, moment 2) of the gas. Moment maps for the full sample can be found in the figure set available in the online journal (or in the Appendix on arXiv). servations revealed centrally-concentrated dust emission around the supermassive black holes (traced by FIR continuum emission; Venemans et al. 2020), and a diverse set of kinematics traced by [Cii] emission (Neeleman et al. 2021) broadly split into three categories of equal number; disturbed, dispersion-dominated, or smoothly rotating. The third paper, Novak et al. (2020), determined that both [Cii] and dust continuum morphologies can be described with a two-component model consisting of a central steep component and an extended component of shallower gradient. While for the compact components the FIR continuum emission is more compact than the [Cii], the extended components of both tracers extend over similar scales.
Despite the growing wealth of information now available for these objects, we have few constraints on the flow of gas into-and around QSO host galaxies, and also the mechanisms governing the supply of pristine gas available to their rapidly-accreting supermassive black holes. Indeed it is a long-standing question for simulations how the cold gas which is funnelled along filaments connects to-and feeds galaxies. Some numerical simulations have suggested that large Lyα halos will trace high angular-momentum gas as it is accreted (e.g Stewart et al. 2011 andStewart et al. 2013) -obser-vational evidence for this scenario is found in Prescott et al. (2015), where the authors report large-scale rotation of a collapsing gas structure. To date, no further rotation of gas in emission on this scale has been presented in the literature. It is prudent then, to compare and contrast available datasets, to gain insights on the relationship between the kinematics of the ISM inside QSO host galaxies and extended Lyα halos tracing ionised gas around them (likely to be connected to the circumgalactic medium; CGM e.g. Drake et al. 2019. In this work we examine z ∼ 6 QSOs observed with high-resolution alma configurations to compare and contrast the bright, central emission from the host galaxies (the core-like component reported in Novak et al. 2020 andexamined in Venemans et al. 2020) to observations of the same QSOs with muse as part of the requiem survey ) which have reported the presence/absence of Lyα halos (tracing gaseous reservoirs) down to 5σ surface-brightness limits of 0.1 − 1.1 × 10 −17 erg s −1 cm −2 arcsec −2 over a 1 arcsec 2 aperture. This paper proceeds as follows: in Section 2 we describe the observations and datasets compiled for this work; in Section 3 we present [Cii] and Lyα channel maps and moment maps of our targets. In Table 1. Quasars at z ∼ 6 observed with both alma and muse. We list here: object names (column 1), coordinates (columns 2 & 3), systemic redshift from [Cii] (z [CII] ; column 4), three luminosities L [CII] (column 5) and LFIR (column 6) from Venemans et al. (2020), LLyα (column 7) from Farina et al. (2019). In the final three columns we list the diameter d of the [Cii], FIR and Lyα halo components reported in Venemans et al. (2020) and Farina et al. (2019). d [CII] (column 8) and dFIR (column 9) are the geometric averages of a 2D Gaussian fit, and dLyα (column 10) is the diameter at which the surface-brightness-dimming-corrected light profile drops below 3 ×10 −18 erg s −1 cm −2 arcsec −2 } Section 4 we discuss our findings and comment on our targets individually. Finally, in Section 5 we summarise our findings. Throughout this work we assume a ΛCDM cosmology with Ω m = 0.3, Ω Λ = 0.7 and H 0 = 70 km s −1 Mpc −1 . In this cosmology, 1 = 5.71 pkpc at z ≈ 6. All velocities, wavelengths and frequencies refer to vacuum values.

Sample Selection
We draw our sample from a total of 18 sources that represent the overlap between the high-resolution alma [Cii] imaging survey published in Venemans et al. (2020) and the muse requiem survey . We list the full sample in Table 1, before defining a subset where a Lyα halo detection has been made in Drake et al. (2019) or Farina et al. (2019). The sample with robust detections in both datasets amounts to 8 objects.

MUSE Data
muse data cubes are taken from the requiem survey , in order to homogenise the reduction process across all objects. Farina et al. (2019) define the Lyα halo as a 3D structure of connected voxels of significance > 2 σ after smoothing the PSF-subtracted datacube in the spatial and spectral directions with kernels of σ spat = 0.2 and σ spec = 2.5Å. The study also provide moment maps for the Lyα halos, with a velocity zero point that refers to the flux-weighted centroid of the voxels included in the mask. For the purpose of this work, we require moment maps centred on systemic velocity, and so we utilise additional data products released with requiem to construct our own maps as described in Section 3.1.  2020). The data have been re-imaged with natural weighting to maximise sensitivity to any extended emission, and sampled with a velocity width of 30MHz per channel to match the velocity width of a single layer of the (slightly oversampled) muse datacube (∼ 40 km s −1 ). All data cubes were observed in the local standard of rest (LSRK) velocity frame.

Moment Maps
As we require the velocity fields (moment 1) to describe ionised gas motion relative to the systemic velocity of the host galaxy (defined as the [Cii] redshift), we utilise two data-products released with the requiem survey; the PSF-subtracted datacubes, and the 3D mask cubes to reconstruct the 3D Lyα halo as defined in Farina et al. (2019). With these cubes we then re-compute moment maps relative to systemic velocity, using the method applied in Drake et al. (2020).
In Figure 1 we show an example of the Lyα and [Cii] moment maps, for P308−21. Maps for the full sample can be found in the figure set available in the online journal. The three columns of panels present the zeroth moment (total flux), the first moment (velocity field) and the second moment (a measure of the velocity dispersion), respectively. The upper row of panels focuses on the Lyα halo in cutouts of 10 a side, while the lower panels present [Cii] emission originating in the quasar host galaxy in panels which zoom-in to 4 a side.
An immediate take-away from this comparison is the relative sizes of the extended halo gas traced by Lyα, and the more compact [Cii] emission which traces the host galaxy. Typically, the extent of the [Cii] emission is encompassed within the region of ∼ 1 diameter, which corresponds to the region of the Lyα emission that is subject to complex residuals due to the PSF-subtraction (here, this region is masked on the Lyα images). We will return to size comparison in Section 4.1 where measurements for the full sample will be considered.
The central columns of Figure 1 depicting the velocity fields of the emission demonstrate a general feature of the data: There is no obvious coherence between the velocity field of the host galaxy, and that of the extended ionised gas for any of the 8 objects. We will discuss this further in Section 4.2. We also note that a comparison of the general velocity shifts is presented in section 5.1.1. and figure 5 of Farina et al. (2019).

Channel Maps
In addition to the moment analysis of gas kinematics for each object, we include in the Appendix a series of channel maps comparing Lyα and [Cii] emission for each QSO. In every case, the Lyα extends over a much greater velocity range than the more compact [Cii] emission, and the maps emphasise again the extent of the gaseous ionised halo gas compared to the cold gas in the host galaxy.

Size Comparison
In Figure 2 we compare the sizes of the [Cii] and FIR continuum emission to that of the Lyα halo. The adopted size measurements are listed in Table 1 (2020), where sizes from the casa task imfit are provided using a 2D fit. In this work we take the geometric average of these two measurements as the effective [Cii] or FIR extent.
The two panels show on the x-axes the [Cii] size (lefthand side) and FIR dust continuum (right-hand size) against the Lyα extend on the y-axes. As was evident from Figure 1 the Lyα halos are significantly more extended than the [Cii] (and also dust continuum) emission. This is because the [Cii] emission primarily traces photo-dominated regions within the host galaxy, meanwhile, the extended Lyα emission traces the extended ionized gas surrounding the central host galaxy.
Lyα halo sizes fall anywhere between ∼ 2 and ∼ 30 times larger than the [Cii] sizes. P009−10, at z = 6.00 shows the smallest Lyα halo, 4 times larger than its extended [Cii] which stretches ∼ 4 pkpc. At the other end of the scale, P231−20, at z = 6.59 has a Lyα halo extending ≈ 30 times further than its compact [Cii] emission which is measured at 1 pkpc. In the right-hand panel we confirm that the FIR (tracing the dust continuum) is smaller than the [Cii] size (e.g. see Novak et al. (2020) for a detailed analysis of [Cii] and FIR dust continuum sizes). The Lyα halos range between ∼ 3 and > 50 times larger than the dust continuum. Much as for the [Cii] comparison, P009−10 exhibits the lowest size ratio of d Lyα /d FIR = 5, and again, P231−20 exhibits the largest size ratio of d Lyα /d FIR = 67. Interestingly, in the FIR, P323+12, moves up the ranking, and exhibits the second largest size ratio d Lyα /d FIR = 61. Additional information is encoded in the figure, using QSO redshift to colour the data points, and scaling the size of each point by the QSO's SMBH mass (taken from Schindler et al. 2020). No correlation is seen between M BH and any of the size measures (Lyα, [Cii], or FIR), nor with the ratio of Lyα halo size to host-galaxy tracer size. A Kendall's rank correlation test (accounting for upper limits) shows that there is no evidence for a correlation between the [CII]/FIR and Lyα halo sizes.
In Figure 3 we consider the ratio of sizes between the Lyα halo and the two tracers of the galaxy's ISM as a function of redshift. Neither the Lyα/[Cii] size, nor the Lyα/FIR size shows any correlation with redshift (τ = 0.067 with p = 0.42, and τ = 0.04 with p = 0.40 respectively) -this implies no evolution of the size ratio across our redshift range.

Kinematic Comparison
We now compare the overall kinematics of the ISM in the host galaxy, traced by [Cii], with the larger-scale kinematics as traced by the Lyα line. The underlying question is whether the bulk motion between the two tracers is the same, i.e. if they trace the same gravitationally bound structure. We acknowledge that the gas kinematics traced by Lyα are difficult to interpret due to the complex radiative transfer of Lyα photons that may prevent a clear kinematic signature.
By comparing the [Cii] velocity fields to those of the Lyα line we find, to first order, no evidence for coherent rotation between these two tracers. In many cases this is due to the fact that the Lyα velocity field does not show a clear velocity gradient. The [Cii], on the other hand, does indeed show such a velocity gradient in the majority of sources (Neeleman et al. 2021). There are three cases, discussed in detail below, where we see a clear gradient in the velocity field of the Lyα halos, these are P359 − 06, P036 + 03, and P231 − 20. In the notes below, we use the commonly-adopted definition of the position angle (P.A.) -the angle measured from North, counter-clockwise, to the receding part of the emission.

P009−10
Given the asymmetric extended [Cii] emission, Venemans et al. (2020) speculate that P009−10 may be in the process of merging with another source. Examining the moment maps in Figure 1, P009 − 10's elongation in [Cii] aligns with the orientation of the Lyα halo. In terms of kinematics, a velocity gradient is seen along the [Cii] emission, meanwhile an obvious gradient in the Lyα halo is absent.

P359−06
The [Cii] emission from P359−06 is surrounded by a Lyα halo. The kinematics of P359−06 in [Cii] show a velocity gradient approximately from east to west (P.A. of 315.7 ± 2.6 • , Neeleman et al. (2021)), meanwhile the kinematic structure of the surrounding Lyα halo does not appear to be aligned, with a mild gradient from north to south and additional blue-shifted emission in the southern outskirts.

P065−26
Venemans et al. (2020) note that the [Cii] morphology of P065−26 is extended and disturbed. The Lyα halo surrounds the [Cii], with a marginal extension towards the north. The kinematics show no obvious velocity gradient across the structure, but simply patches of mildly blue-and red-shifted emission. In contrast, the entirety of the Lyα halo appears to be blue-shifted by a few hundred km s −1 .

P308−21
P308−21 is extended in both [Cii] and Lyα emission. The [Cii] emission has been extensively studied in Decarli et al. (2019) with high resolution imaging. The authors argue that the extended tails of [Cii] emission are due to the tidal stripping of a satellite galaxy. In the moment maps, we see that the Lyα halo is much larger still than the extended [Cii]. The peak of the Lyα emission is north-easterly from the peak in [Cii] which is centred on the QSO position. The [Cii] emission from the QSO host galaxy shows a velocity gradient in the south-north direction. The Lyα halo meanwhile is red-shifted across almost the entirety of the structure, except for the very outskirts of the halo in the east.

P036+03
P036+03 shows a relatively compact [Cii] morphology, and a Lyα halo extending towards the north. The [Cii] emission shows a gradient from north to south (P.A. 189.9 • +1.8 −2.0 , Neeleman et al. (2021)), meanwhile the Lyα halo shows a gradient that is approximately perpendicular to this (from east to west, with an approximate P.A. of ≈ 270 • ). P036+03 presents the most striking contrast between the halo and ISM velocity fields of the objects studied here.  (2016), and supplemented with very high resolution data in Venemans et al. (2020), resolving scales of ∼ 400 pc. The Lyα halo was the first z ∼ 6 halo reported with muse, presented in Farina et al. (2017). Neither the [Cii] emission, nor the Lyα halo are particularly luminous. In terms of kinematics, the [Cii] displays a clear gradient from the south west to the north east. The Lyα halo within which it is embedded is red-shifted in its entirety, extending mainly to the south.

SUMMARY
We have presented a comparison of Lyα and [Cii] emission of a sample of 8 QSOs at z ∼ 6, using muse and alma datacubes matched in velocity resolution. The [Cii] emission traces the extent and kinematics of the interstellar medium of the QSO host-galaxy, whereas the Lyα emission traces the extent and kinematics of the ionised gaseous halos that surround the quasar hosts.
We find that the Lyα halo sizes are typically 3 − 30 times larger than the extent of the [Cii] that is associated with the host galaxy (and 3 − 60 times larger than the host galaxy's dust continuum emission). A comparison of the kinematics has proven more difficult, as the majority of the Lyα halos do not show ordered motion in their velocity fields. In those three cases where a kinematic P.A. can be determined in the respective Lyα halos, their velocity fields are not aligned with that of the [CII] emission. In other words, we find not a single case where the rotational signature associated with the host galaxy extends to the Lyα halo. This suggests that the Lyα emission is not simply tracing the outskirts of a large rotating disk structure that is a simple extension of the central structure seen in [Cii] (and dust) emission. It rather suggests that the kinematics of the halo gas are decoupled from those of the interstellar medium in the host galaxies' disks.
Connecting the kinematics of [Cii] and Lyα remains a challenge, in particular in the presence of companions and/or asymmetries in the gas distribution. An additional caveat is that, given its highly scattering nature, the Lyα emission line is not an ideal tracer for gas kinematics. While we do not think this should affect our ability to detect rotational signatures at large galactocentric radii, a confirmation of our results will have to await observations of the sources with the NIRSpec IFU on-board the James Webb Space Telescope. Ideally, a large sample of isolated sources is required, to investigate the general case of cosmological accretion using the Hα emission line, allowing a direct and unambiguous comparison of the halo kinematics to those of the host galaxy in [Cii].

A. MOMENT MAPS
We include here the full series of moment maps continuing as in Figure 1.

B. CHANNEL MAPS OF LYα AND [Cii] EMISSION
We include here a series of channel maps depicting emission from [Cii] in the QSO host galaxies, and Lyα in the extended halos extracted at the same velocity. The [CII] emission in each panel is that arising in a single channel of 30MHz (∼ 40 km s −1 ), in comparison, the Lyα emission from the slightly over-sampled muse datacube is the sum across a 2Å wide window (∼ 66 km s −1 ). All panels are cutouts of 10 a-side, with the exception of the highest redshift object, J0305−3150 where the very high resolution observations from alma dictate that we zoom in to panels of 6 a-side, and remove the masking of PSF residuals in the Lyα image in order to see the host galaxy in [Cii] in these maps. Channel maps for the full sample can be found in the figure set available in the online journal (or in the Appendix on arXiv). emission at the same velocity. The lowest positive (solid) and negative (dashed) contour levels represent ±2σ (±4σ for J0305− 3150) in the [Cii] channel after smoothing with a Gaussian kernel of fwhm = 2.23 pixels. The [Cii] emission in each panel is that arising in a single channel of 30MHz (∼ 40 km s −1 ), in comparison, the Lyα emission from the slightly over-sampled muse datacube is the sum across a 2Å wide window (∼ 66 km s −1 ). The Lyα image is smoothed with a Gaussian kernel of fwhm = 3.30 pixels and contoured at ±1.5σ (solid, dashed lines). This demonstrates that an extended low-surface-brightness component is contiguous over multiple velocity channels. We present two pages of channel maps for each object in turn, beginning with the lowest redshift quasar, P009−10. Channel maps for the full sample can be found in the figure set available in the online journal or in the Appendix on arXiv.