Deciphering Lyman $\alpha$ blob 1 with deep MUSE observations^††thanks: Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 094.A-0605, programme ID 095.A-0570, and programme ID 097.A-0831.

For the reduction of the 17.6 h of MUSE observations into a science-ready datacube we used version 2.4.2 of the MUSE Instrument Pipeline (MUSE DRS – Weilbacher et al., 2016) provided by ESO⁷⁷7https://www.eso.org/sci/software/pipelines/muse/muse-pipe-recipes.html and version 3.0 of the MUSE Python Data Analysis Framework (MPDAF – Bacon et al., 2016; Piqueras et al., 2017) provided by the MUSE consortium⁸⁸8https://mpdaf.readthedocs.io/. The here MUSE DRS version used here incorporates the so-called self-calibration procedure to improve the flat-fielding accuracy for deep datasets (Conseil et al., 2016). For our data reduction we adopted a similar strategy as the one used for the reduction of the MUSE Hubble Ultra Deep Field (Bacon et al., 2017).

We first ran the MUSE DRS calibration recipes muse_bias, muse_flat, muse_wavecal, and muse_lsf on the calibration frames that are associated to each science and standard star exposure. We also used the muse_twilight recipe on the twilight frames. Next, we applied the resulting calibration data products to each science and standard star exposure using the recipe muse_scibasic. The resulting standard-star pixtables where then fed into muse_standard to create response curves. Those were the applied to each science exposure with the muse_scipost task, using its self-calibration feature, but not using its sky-subtraction capabilities. When running muse_scipost we used the associated astrometric calibrations provided from the ESO archive instead of the astrometric calibrations shipped with the pipeline. This approach was necessary, as the instrument underwent several interventions during the long period over which observations were taken. Not using the correct astrometric calibrations would result in uncorrected geometric distortions within the pixtables.

In order for self-calibration to work optimally, regions containing sources that are bright in the continuum needed to be masked. While in principle the DRS can automatically detect such regions, we manually masked out bright continuum objects a bit more conservatively compared to the DRS generated mask. Manual masking was performed by visual inspection of the datacubes with the ds9 software (Joye & Mandel, 2003) using polygon-shaped and circular regions. These regions where then converted into datacube masks using the pyregion python package⁹⁹9https://pyregion.readthedocs.io/. Additionally, four science exposures contained continuum bright linear trails from moving objects (likely satellite flares, meteors or aeroplanes – affected exposures are marked by a $\dagger$ in Table 2). These trails were also masked manually for the self-calibration.

We then removed night sky-emission with muse_create_sky and muse_subtract_sky. During this step we iteratively masked out regions that contained emission from the Ly$\alpha$ blob, so that the blob’s emission is not subtracted from the final data.

Next we resampled the individual sky-subtracted and flux-calibrated exposure tables to the final 3D grid with muse_scipost_make_cube. We defined this final grid via an initial run of muse_expcombine on a subset of pointings from each observing programme. Using MPDAF’s combine method we then produced an unweighted mean stack of those individual datacubes to produce the final science-ready datacube. Prior to this stack we masked out bright linear trails that were present in some observations (marked by a $\dagger$ in Table 2). We also ensured that remaining cosmic-ray residuals in the individual datacubes were filtered out in the final stack by using the $\kappa$-$\sigma$ clipping algorithm in the combine task (2 maximum iterations with $\sigma_{\mathrm{clip}}=5$).

The resulting final datacube has $456\times 378$ spatial elements (spaxels) that sample the sky parallel to right ascension and declination at 0.2″$\times$0.2″. Each spaxel consists of 3802 spectral elements that sample the spectral domain from 4599.6 Å to 9350.8 Å linearly with steps of 1.25 Å.

Throughout the above procedure a formal variance propagation is also carried out by each of the used routines, thus a second datacube containing the variance for each volume pixel (voxel) is also produced. However, the resampling procedure in muse_scipost_make_cube produces correlated noise between neighbouring voxels (see Figure 5 in Bacon et al., 2017). Since this co-variance term between neighbouring voxels can not easily be accounted for in the final reduction, the formal variance cube contains underestimates of the true variances. By processing artificial pixtables filled only with Gaussian noise, Bacon et al. (2017) demonstrate that the variance for a voxel in an individual exposure datacube must be corrected by a factor of $(1/0.6)^{2}$ (see Figure 6 in Bacon et al., 2017). Following Bacon et al. (2017) we apply this correction to our final variance cube.

We display a map of the integration time for each spaxel in the MUSE datacube of LAB1 in Figure 2. The maximum integration time of 61920 s (17.2h) is reached in a 32″$\times$48″ central region of our datacube. In this region all three ESO observing programmes overlap. This region completely encompassed the known extend of LAB 1 and LAB 8 prior to the here presented observations. Moreover, Figure 2 also illustrates the location of the masked out regions due to continuum-bright meteor trails or satellite tracks.

Lastly, we produce an emission line only datacube by subtracting a running median filter in spectral direction. This simple method for continuum removal has been proven effective in previous MUSE studies for isolating emission line signals (e.g. Borisova et al., 2016; Herenz & Wisotzki, 2017; Herenz et al., 2017a, b; Arrigoni Battaia et al., 2019). Here we set the width of the median filter conservatively to 301 spectral layers (376.25 Å).

We register the MUSE datacube to an absolute astrometric frame by using the 2MASS point-source catalogue (Skrutskie et al., 2006). Unfortunately, there are only two 2MASS sources within the limited FoV of the MUSE and STIS observations, with one of those sources actually being an extended galaxy. We therefore use the only real 2MASS point source (2MASS J22172397+0012359) to anchor our astrometric reference frame in both observational datasets.

By tying the astrometric reference frame only to one source there remain in principle still several degrees of freedom with respect to geometrical distortions and rotation. However, rotation geometrical distortion are corrected for MUSE data at the pipeline level, and the accuracy of this procedure is constantly monitored by ESO using astrometric calibration fields.

We verified our absolute astrometry against an archival HST/STIS 50CCD clear-filter image that is partially overlapping with our MUSE data (Proposal ID: 9174, presented and analysed in Chapman et al., 2001, 2004). We tied the absolute astrometry of this image also to the 2MASS point source. By visual inspection via blinking in ds9 we then ensured that no offsets exist between both datasets. We conservatively estimate that the absolute astrometric accuracy of our data to be on the order of one MUSE pixel (0.2″).

We present a spectral sequence of pseudo-narrowband images over the Ly$\alpha$ line in Figure 3. These images show that we can trace Ly$\alpha$ emission from LAB 1 over a bandwidth of $\approx 28$Å ($\pm 3000$km s^-1 around $z_{\mathrm{Ly}}=3.1$). As can be seen from Figure 3, the highest velocity gas emitting Ly$\alpha$ is located in vicinity of the central sources LAB1-ALMA1, LAB1-ALMA2, and VLA-LAB1a. However, numerous other features with narrower spectral width appear only in a few velocity slices. Overall the velocity slices reveal a complex spectral and morphological structure of Ly$\alpha$ emission throughout different parts of the blob. We labelled notable features in Figure 3, where we point at:

1. 1.

   A circular structure devoid of strong Ly$\alpha$ emission towards the north of the sub-mm sources. This feature is labelled as “bubble” in Figure 3. It is most clearly seen in the slice around 4979 Å, where we indicate this feature with an arrow. In subsequent redder slices this “bubble” appears with less contrast. It appears as if its radius increases from $\sim 20$ kpc at 4979 Å to up to $\sim 40$ kpc towards redder wavelengths.

2. 2.

   A filamentary narrow bridge connecting LAB 1 to LAB 8 in the north. This bridge becomes visible in the slice at 4979 Å and can be clearly followed until the 4989 Å slice. For LAB 8 the flux shears from the north-west to the south-east with increasing wavelength and the filament shows the same velocity shearing. We indicate this by labelling it as “LAB1-8 bridge (blue arm)” and “LAB1-8 bridge (red arm)” of the bridge in the panel displaying the 4979 Å slice and 4989 Å slice, respectively.

3. 3.

   A compact emission knot towards the north of LAB 8, that connects to LAB 8 via a faint low-surface brightness filament. This feature is seen in the slices at 4981.5 Å and 4984 Å, and we label it as “LAE with filament” in the 4984 Å slice. This newly discovered LAE and filament is close to the edge of the field of view of the observations, and thus only exposed at 8 h to 12 h, thus the noise in this part of the datacube is significantly larger. Nevertheless, as we will discuss in the following Sect. 5.4, the compact emitter and the filament are significant detections.

4. 4.

   A faint extended, slightly curved, shell-like region towards the south-west of LAB 1. Along the major axis the extent of the shell is $\sim 120$ kpc, and its projected thickness is $\sim 30$ kpc. This low-surface brightness emission is visible in the slices from 4976.5 Å to 4981.5 Å where we label it simply as “shell”. The indicated previously undetected Ly$\alpha$ emitting region appears to be connected to the main area of LAB 1 via a low-surface brightness filament trailing from the north-east to the south-west. The filament is most prominently visible in the 4981.5Å slice where we label it “shell connecting filament”. In the northern part of this shell-like region a compact high-surface brightness knot is visible. This knot is accompanied by another slightly more diffuse knot. These two knots in the northern part of the shell can be traced in the velocity slices from 4974Å to 4981.5Å, and we label both features as “2 knots” in the 4974Å slice.

5. 5.

   Another compact isolated Ly$\alpha$ line emitter towards the south-east of LAB 1 seen in the slices from 4984 Å to 4989 Å. We will show in the following Sect. 5.2, that this emitter is one of four newly detected Ly$\alpha$ emitters in the proximity of the LAB 1/LAB 8. We label this emitter “LAE” in the 4984Å slice.

A closer inspection of the velocity slices reveals that there appears to be an overall velocity shear. The bluer $v<0$ km s^-1 slices show predominantly emission towards the west, while the redder $v>0$ km s^-1 slices are dominated by emission from the east. This structure of the velocity shear becomes more clear in our moment based analysis of the Ly$\alpha$ line profiles (Sect. 5.3).

By visually inspecting the Ly$\alpha$ spectral profile as a function of position with the QFitsView software¹⁴¹⁴14The QFitsView software is publicly available via the Astrophysics Source Code Library: http://ascl.net/1210.019. (Davies et al., 2010; Ott, 2012), we find that the line profile complexity varies strongly throughout the blob. We illustrate this by showing a selection of representative profiles in Figure 6. As can be seen, in some region the profiles appear very broad and with a dominating peak (e.g. panel 12 in Figure 6), while other regions are characterised by clearly double- (e.g. panel 3) or even multi-component profiles (e.g. panel 5 or panel 9). The isolated LAEs in the outskirts (example in panel 4, see also Figure 9), or in the shell-like region (panel 7) show narrower Ly$\alpha$ profiles.

The varying complexity of the Ly$\alpha$ profiles as a function of position prohibit parametric fits of a simple model to the spaxels of the datacube in order to create maps of, e.g., the velocity centroid ($v_{r}$) or line-width ($\sigma_{v}$). Such an analysis was presented for the much shallower SAURON data of LAB 1 (Bower et al., 2004; Weijmans et al., 2010), but the increased sensitivity and resolution of our MUSE data warrant a different approach. We thus resort on a moment-based non-parametric analysis. Our method is rooted in descriptive statistics (e.g. Ivezić et al., 2014), but we need to account for two differences when describing spectroscopic line profiles instead of statistical data with such an ansatz. First, formal validity of the summarising parameters is only given when positive values are considered in the calculations. Second, the presence of noise and the usage of small sets of input values can lead to non-trivial biases in moment-based quantities, especially if the analysed profiles are of low S/N. To ensure positive values and in order to minimise low-S/N biases we first applied three preprocessing steps to the continuum-subtracted datacube:

1. 1.

   We used the 3D mask that was already used for the creation of the adaptive narrow band image in Sect. 5.2.2. We recall that this 3D mask was constructed by thresholding the matched-filtered datacube with $\mathrm{S/N>4}$. Voxels that do not fulfil this criterion will be set to 0 in the analysis.

2. 2.

   We smoothed each layer of the flux datacube with a circular 2D Gaussian ($\sigma$ 0.8″). This is done to reduce the spaxel-to-spaxel noise in the final maps, especially in low surface-brightness regions. This value significantly improved the S/N ratio of the Ly$\alpha$ profiles in the filaments and low surface-brightness regions of the blob.

3. 3.

   We used a 2D mask by thresholding the maximum S/N map shown in Figure 4 to exclude spaxels were only a very small number of spectral bins would contribute to the resulting moments. After visual inspection we set this “display threshold” to $\mathrm{S/N}_{\mathrm{max}}=6$, i.e.  the analysed regions are exactly the regions that we regarded as confident detections in Sect. 5.2.2.

After these preparatory steps we created a 2D array of the central flux-weighted moment (first moment) from the processed datacube voxels $F_{xyz}$,

as well as 2D arrays $m_{k}^{xy}$ of the $k$-th flux-weighted moments,

for $k=2$, $k=3$ and $k=4$. In Eqs. (5) and (6), as well as in the following equations below, $x$ and $y$ denote the indices of spatial axes of the flux datacube $F$, while $z$ indexes the spectral direction.

The first moment map resulting from Eq. (5) directly translates into a line-of-sight velocity map

where $c$ is the speed of light, $\lambda_{\mathrm{vac}}(m_{1}^{xy})$ is the non-linear translation between MUSE spectral pixel coordinate and vacuum wavelength¹⁵¹⁵15We use the air-to-vacuum wavelength conversion that has been adopted in the Vienna Atomic Line Database (Ryabchikova et al., 2015): https://www.astro.uu.se/valdwiki/Air-to-vacuum\%20conversion. and $z_{\mathrm{LAB1}}$ is the systemic redshift of LAB 1. For this translation we fix the systemic redshift of LAB 1 to $z_{\mathrm{LAB1}}=3.1$, in agreement with known redshifts of the galaxies within the blob. The so created $v_{1}^{xy}$ map is shown in the left panel of Figure 7. There we also show the photometric centre and the principal axis that were computed from the adaptive narrow band image as described in the previous section. We point out that the principal axis is oriented orthogonal to the direction of the apparent large scale velocity gradient. This feature will be further discussed in Sect. 6.3.

By taking the square root of second moment map (Eq. 6, with $k=2$) we compute a map that provides a measure of the width of the spectral profiles:

This $\sigma_{v}$ map is shown in the right panel of Figure 7. We express the width of the profiles $\sigma_{v}$ in km s^-1, but caution that this measurement can not be directly interpreted as velocity dispersion as it is often done for non-resonant emission lines. For example, double- or multiple peaked profiles generally have larger second moments than single peaked profiles. Moreover, radiative transfer effects are also known to broaden the single-peaked Ly$\alpha$ line profiles when compared to non-resonant emission lines (see also Sect. 5.5). We thus call the second moment based measure “apparent velocity dispersion”. Lastly, the spectral resolution of MUSE also has an effect on the apparent velocity dispersion. Given the complexity of the profiles and the non-parametric nature of our measurement the effect of broadening the profiles via convolution with the spectrograph’s line spread function is not easily quantifiable. The measured instrumental width for MUSE at 4980Å is $\sigma_{\mathrm{inst}}\approx 75$ km s^-1 (Bacon et al., 2017). As a figure of merit estimate, this translates into resolution corrections $\sigma_{\mathrm{corr}}$ of -34 km s^-1, -20 km s^-1, -15 km s^-1, and -10 km s^-1 for apparent velocity dispersions of 100 km s^-1, 150 km s^-1, 200 km s^-1, and 300 km s^-1, respectively, if the observed line profiles and the line spread function are well approximated by a Gaussian profile i.e.

Creating such moment-based maps of line-of-sight velocity and apparent velocity dispersion is common in the analysis of synthesised datacubes from radio-interferometric 21 cm observations of galaxies (e.g. Thompson et al., 2017, Section 10.5.4). It now is also routinely used in the analyses of extended Ly$\alpha$ nebulae surrounding quasars (e.g. Borisova et al., 2016; Arrigoni Battaia et al., 2018, 2019; Drake et al., 2019). Moreover, recent theoretical work by Remolina-Gutiérrez & Forero-Romero (2019) and Smith et al. (2019) resort on a moment-based analysis in the analysis of Ly$\alpha$ profiles from Ly$\alpha$ radiative transfer simulations. However, in order to create maps that characterise the varying complexity of the Ly$\alpha$ profile as a function of position in the blob, we use measurements involving higher-moments. Remolina-Gutiérrez & Forero-Romero (2019) suggest to use the skewness $s$, the kurtosis $\kappa$, and the bimodality $b$. These measurements will be detailed in the following. To provide a visual guide on how to interpret these quantities we also display their values next to the example profiles from the blob shown in Figure 6.

We calculate a map of the Ly$\alpha$ profile skewness $s$ via

The so defined skewness ($-1\leq s\leq 1$) quantifies the asymmetry of the spectral profile with respect to $m_{1}$. If $s\simeq 0$ the profile is symmetric around $m_{1}$ (panel 1 in Figure 6), while for $s>0$ a tail is found redwards of $m_{1}$ (e.g. panels 4 and 11 in Figure 6) and for $s<0$ a tail is bluewards of $m_{1}$ (e.g. panels 6, 8, and 10 Figure 6). We show our computed map for $s^{xy}$ in the left panel of Figure 8.

We note that other definitions than Eq. (10) have been used in the literature to quantify the asymmetric Ly$\alpha$ line-profile morphology of LAEs. For example, Shimasaku et al. (2006) quantified the observed skewness in spectral profiles from Lyman $\alpha$ emitting galaxies by multiplying the definition given in Eq. (10) with a measure of the width of the line, however, we prefer to not entangle those two quantities. Other authors (Mallery et al., 2012; U et al., 2015) quantified skewness $s$ by fitting a skewed Gaussian profile. But this approach does not capture the complex Ly$\alpha$ spectral profiles seen here in LAB 1. Additionally, Childs & Stanway (2018) showed recently that the skewness values derived from fitting an asymmetric Gaussian do not accurately capture the true skewness of Ly$\alpha$ profiles in the presence of finite spectral resolution and background noise. Two other alternative definitions have been put forward by Dawson et al. (2007). These authors quantify asymmetry either via the ratio of flux blue- and redwards of the peak or via the ratio of the widths than encompass 90% of the flux blue- and redwards of the peak. However, given that the profiles in LAB 1 sometimes show multiple peaks at substantial spectral distance (e.g. panel 1 and 3 in Figure 6), quantifying asymmetry around the higher peak would exaggerate the skew measure compared to the visual perception of symmetry in those profiles.

We obtain a map of the kurtosis of the Ly$\alpha$ profiles via

Kurtosis quantifies how much flux is in the wings of the profiles in comparison to the wings of Gaussian profile (i.e. their tail extremity). For $\kappa=3$ the tails are comparable to the Gaussian profile, while profiles with $\kappa>3$ show more pronounced tails (e.g. panels 6 and 11 in Figure 6), while $\kappa<3$ indicates the absence of pronounced tails (e.g. panels 1, 5, and 9 in Figure 6). Of course, only wings that are significantly above the noise can contribute to this statistic. As a corollary, regions of low S/N are biased towards to low kurtosis values. We avoid these biases by increasing the display threshold to $\mathrm{S/N}_{\mathrm{max}}=13$. We show the resulting map for $\kappa^{xy}$ in the centre panel of Figure 8.

Following Remolina-Gutiérrez & Forero-Romero (2019) we calculate a map of the bi-modality of the Ly$\alpha$ line profiles using

Remolina-Gutiérrez & Forero-Romero (2019) introduced this quantity to discriminate whether their Ly$\alpha$ radiative transfer models result in single- or double component profiles. We point out that this measure is not a formal statistical test for bi-modality, but it can capture the visual appearance of the Ly$\alpha$ profile morphologies. We find that for $b\lesssim 2.6$ profiles appear mostly to have clearly distinct double component structures (e.g. panels 1 and 4 in Figure 6, but see panel 5 and 9), while profiles with $b\gtrsim 3$ appear single peaked (e.g. panel 2, 6, and 7 in Figure 6). However, some $b\gtrsim 3$ profiles may also have a subdominant second component, that is mainly contributing to the kurtosis (e.g. panel 11 in Figure 6). In the range $2.6\lesssim b\lesssim 3$, however, the discriminatory power of $b$ appears not strong, and visual inspection of those profiles indicates a high complexity with possible multiple components or peaks (see e.g. panels 3 and 10 in Figure 6). Despite its potential lack of accuracy, qualitatively $b$ captures the visual complexity of the profiles, with higher values indicating simple single component profiles and lower values indicating more complex profiles, and with the lowest values often corresponding to the presence of double component profiles. Moreover, since the $\kappa$ is biased towards low values in regions of low S/N, also $b$ will be biased low in those regions. Thus, we hide the biased regions by setting the display threshold to $\mathrm{S/N}_{\mathrm{max}}=13$. We show our computed map for $b^{xy}$ in the right panel of Figure 8.

It can be seen that most of the blob shows low values of $b$ indicative of double component Ly$\alpha$ profiles. This impression is also on par with our visual inspection of the line profile variations throughout the blob. Moreover, in the central high surface-brightness region of LAB, where also the broadest profiles are observed, we obtain $b$ values in the intermediate range – these profiles often appear to exhibit a high-degree of complexity. Lastly, only a few small island regions can be characterised by high values of $b$. These regions show clearly distinct single peaked profiles, often with very pronounced tails. We will describe and discuss the here derived and presented maps from the moment based analysis further in Sect. 6.3.

As mentioned in Section 5.2, our S/N map revealed four detections that are not embedded in the extended Ly$\alpha$ radiation from the blob. We labelled those sources 1 – 4 in Figure 4. These sources are detected with S/N$>6$ in the LSDCat cross-correlated datacube. Formally there exists one more detection with S/N$>6$ at $z=3.1$ close to the eastern border of Figure 4, however this detection turned out to be an artefact near the edge of our field of view.

The coordinates, Kron-radii, and fluxes of the newly detected LAEs are listed in Table 16. These measurements have been obtained with the LSDCat software (Herenz & Wisotzki, 2017). In Figure 9 we show the spectral profiles of the detections. These 1D spectra have been extracted within a circular aperture of radius $R_{\mathrm{kron}}$. No other lines are detected at these positions and thus we are confident that the sources are LAEs in physical proximity to the blob. Additionally, two of the line-profiles (LAE 3 & LAE 4) are reminiscent of the characteristic red-asymmetric line-profiles seen typically in LAEs (e.g. Dawson et al., 2007; Yamada et al., 2012). At $z=3.1$ the range of the measured fluxes is $\log F_{\mathrm{Ly\alpha}}[\mathrm{erg}\,\mathrm{s}^{-1}\mathrm{cm}^{-2}]=-17.2\dots-16.6$, which corresponds to Ly$\alpha$ luminosities $\log L_{\mathrm{Ly\alpha}}[\mathrm{erg}\,\mathrm{s}^{-1}]=41.7\dots 42.3$. Hence those galaxies occupy the faint-end ($L_{\mathrm{Ly\alpha}}<L_{\mathrm{Ly\alpha}}^{*}$) of the LAE luminosity function (Drake et al., 2017a, b; Herenz et al., 2019) and are thus below the detection limit of classical narrow-band imaging surveys.

From the spectral profiles we measure the LAEs redshifts using the first flux-weighted moment (Eq. 5). These redshifts are indicated as a vertical dotted lines in Figure 9. We list the velocity difference $\Delta v$ with respect to $z=3.1$ in Table 16. The two galaxies 1 and 3 south-east of the blob show large positive $\Delta v$. In fact, their redshifts appear to be a continuation of the overall west-to-east line-of-sight velocity gradient seen in the blob. For such large values of $\Delta v$ radiative transfer effects are unlikely the main cause for the redshift offsets. We speculate, that the peculiar motion of those galaxies are driven by the gravitation potential of LAB 1’s dark matter halo. The peculiar motion of the compact sources embedded in the northern part of the south-western shell-like structure (labelled as “knots” in Figure 4) could also be explained by this scenario. Moreover, the small blue-shift of our LAE 4 to the north of LAB 8 appears consistent with a smooth continuation of the overall blob velocity field. However, the base of the blob’s filament which points towards the LAE 3 shows blue-shifts and thus deviates from a smooth velocity-field continuation. As we will discuss in more detail in Sect. 6, such small scale modulations of a velocity field could be interpreted as peculiar motions of individual galaxies or filamentary cooling flows. Lastly, the eastern-most galaxy (2) is significantly blue-shifted and does not follow any trend. This galaxy might thus be at a larger distance from LAB 1’s halo and thus not subject to its gravitational potential.

We quantify the line widths of the LAEs from the square root of the second flux-weighted moment (Eq. 8). As already discussed in Sect. 5.3, the moment-based $\sigma_{v}$ measurement is not readily corrected for the instrumental resolution. Nevertheless, compared to the complexity of the line profiles seen in the blob, the profiles of the isolated LAEs appear relatively simple, hence the prescription for the figure-of-merit estimate in Eq. (9) provides a valid approximation here. The so corrected Ly$\alpha$ line-widths are 102 km s^-1, 57 km s^-1, 208 km s^-1, and 73 km s^-1 for our LAEs 1, 2, 3, and 4, respectively. These line-widths are within the range of typical $\sigma_{v}$ values obtained for a sample of brighter LAEs in the SSA22 field (Yamada et al., 2012, mean$=108$ km s^-1, median$=84$ km s^-1). Moreover, Yamada et al. (2012) also found that the line-widths for some less extreme LABs in SSA22 are significantly broader than those of the isolated LAEs. We thus may consider these faint LAEs as an extension of the known SSA22 LAE population that exists below the detection limits of narrow-band selected samples.

We detect low-SB He ii emission from three distinct regions within the Ly$\alpha$ blob. We visualise this detection in Figure 10, where we show the resulting maximum S/N map from the LSDCat 3D cross-correlated datacube (Sect. 5.2.2). Here we evaluated the S/N datacube between $\lambda_{\mathrm{min}}=6719$Å and $\lambda_{\mathrm{max}}=6729$Å (i.e. $\pm 5$Å around He ii at $z=3.1$). We also show in Figure 10 an adaptive narrow-band image for He ii constructed similarly as the adaptive Ly$\alpha$ image in Sect. 5.2.3. Due to the faintness of the emission we lowered the extraction threshold a bit, i.e. here the image was extracted by using voxels with $\mathrm{S/N}>3$ from the S/N datacube. We provide a visual representation of the noise level in regions not containing any detected signal in the same manner as we did for the adaptive Ly$\alpha$ image, i.e. we sum $\mathrm{S/N}<3$ spaxels by $\pm 2.5$Å (4 spectral bins) around 6724 Å.

We label the three regions where He ii is detected with $\mathrm{S/N}>6$ “south”, “north”, and “LAB8” in Figure 10. The “south” region is located south-west in proximity the ALMA continuum sources LAB1-ALMA1 and LAB1-ALMA2 while being slightly north-east of the Lyman break galaxy SSA22a-C11. The “north” He ii region can not be associated with any known source in LAB 1. This region is co-spatial with the feature labelled “northern high SB region” in Fig. 4. It is also co-spatial with the region labelled R2 in Weijmans et al. (2010) and McLinden et al. (2013). Lastly, the “LAB8” region appears in proximity to the Lyman break galaxy SSA22a-C15. We report in Table 4 positions of those regions. These positions are S/N-weighted, i.e. calculated according to Eq. (1) with $I_{xy}$ replaced by the pixel values of the maximum S/N map $\mathrm{SN}_{xy}$ and only considering pixels satisfying $\mathrm{SN}_{xy}\geq 6$ for each region. All He ii peaks are within regions of Ly$\alpha$ surface-brightness above $5\times 10^{-18}$erg s^-1cm^-2arcsec^-2. But the morphological features seen in He ii are considerably different compared to the morphology of Ly$\alpha$ above this surface brightness limit.

In order to extract 1D spectra from those regions we created apertures consisting of contiguous regions with $\mathrm{S/N}>5.5$ in the maximum S/N image. The corresponding areas of these He ii morphology-matched apertures are also listed in Table 4. The in those regions extracted spectral profiles of the He ii emission are shown in the bottom panels of Figure 10. We furthermore compare in this figure the He ii spectral profiles to the Ly$\alpha$ profiles extracted in the same regions.

We measured the He ii fluxes in those regions by summing the spectral profiles shown in Figure 10 over their full width at zero intensity. The error on the fluxes was obtained from $10^{4}$ Monte-Carlo (MC) realisations of the profile, where we used the propagated variances as input for adding noise to each spectral bin. The so obtained flux measurements are listed in Table 4. Given the areas of the extraction apertures, the measured fluxes correspond to He ii surface-brightness values of 7.6$\times 10^{-19}$erg s^-1cm^-2arcsec^-2, 5.7$\times 10^{-19}$erg s^-1cm^-2arcsec^-2, and 7.6$\times 10^{-19}$ erg s^-1cm^-2arcsec^-2 for region “south”, “north”, and “LAB8”, respectively. The measured He ii surface-brightness is $\sim 4-5$ times fainter than the upper limits reported for a previous attempt to detect He ii emission in LAB 1 using narrow-band imaging (Arrigoni Battaia et al., 2015).

To quantify the He ii/Ly$\alpha$ flux ratios we measured the Ly$\alpha$ fluxes over their full width at zero intensity within the three He ii emitting regions. We obtained $F_{\mathrm{Ly\alpha}}=1.7\times 10^{-16}$erg s^-1cm^-2, $1\times 10^{-16}$erg s^-1cm^-2, and $6.1\times 10^{-17}$erg s^-1cm^-2, corresponding to He ii/Ly$\alpha$ $0.06\pm 0.01$, $0.07\pm 0.01$, and $0.10\pm 0.02$, for region “south”, “north”, and “LAB8”, respectively (see also Table 4). The errors on those ratios have also been computed from $10^{4}$ MC simulations for the individual He ii and Ly$\alpha$ flux measurements. From the previous non-detection of He ii Arrigoni Battaia et al. (2015) determined upper limits He ii/Ly$\alpha$$<0.11$ for LAB 1 and He ii/Ly$\alpha$$<0.22$ for LAB8, thus the measured He ii/Ly$\alpha$ ratios are a factor of two lower.

Using the first flux-weighted moment (Eq. 5) on the extracted profiles, we determined the relative redshift offset between He ii and the Ly$\alpha$ $\Delta v(z_{\mathrm{Ly\alpha}})=c\times(z_{\mathrm{Ly\alpha}}-z_{\mathrm{HeII}})/(1+z_{\mathrm{HeII}})$. Again, the errors have been computed from $10^{4}$ MC realisations.

A significant offset between Ly$\alpha$ and He ii is only detected for the LAB 8 region, where Ly$\alpha$ appears modestly blue-shifted. Blue-shifted Ly$\alpha$ emission with respect to non-resonant nebular lines is atypical for normal Ly$\alpha$ emitting galaxies, that show often $\Delta v(z_{\mathrm{Ly\alpha}})\gtrsim 200$ km s^-1 (e.g. Rakic et al., 2011; Song et al., 2014), although few exceptions exist (e.g. Trainor et al., 2015). Interestingly, our non-detections of velocity offsets between Ly$\alpha$ and He ii around C11 and LAB 8 is consistent with the non-detection of offsets between Ly$\alpha$ and [O iii] for those systems by McLinden et al. (2013). Moreover, Prescott et al. (2015a) also report similar low velocity offsets between He ii and Ly$\alpha$ in a He ii detected LAB at $z=1.67$. These authors also compile data from the literature to show that LABs exhibit generally lower kinematic offsets between Ly$\alpha$ and optically thin lines and the here presented measurements on He ii emitting regions in LAB1 corroborate this fact.

Lastly, it is visible in Figure 10 that in all three regions the Ly$\alpha$ profile appears broader compared to He ii. To quantify this we measured the width of the He ii and Ly$\alpha$ lines, $\sigma_{v}^{\mathrm{HeII}}$ and $\sigma_{v}^{\mathrm{Ly\alpha}}$, using the second flux-weighted moment (Eq. 6, with $k=2$). The measurements obtained are reported in Table 4. We find that Ly$\alpha$ is 1.6$\times$, 2.4$\times$, and 1.4$\times$ broader than He ii in the “south”, “north” and “LAB8” region, respectively. These values are in agreement with the broadening for Ly$\alpha$ with respect to He ii observed in a $z=1.67$ LAB by Prescott et al. (2015a). As pointed out by these authors, the absence of significant velocity offsets between Ly$\alpha$ and He ii and the presence of line broadening in Ly$\alpha$ with respect to He ii are consistent with a scenario where a significant fraction of the extended Ly$\alpha$ emission is produced in situ. We will discuss this physical interpretation further in Sect. 6.4.

We detect no significant signal from the C iv doublet (1548.203 Å and 1550.777 Å) in the MUSE data of LAB 1. This can be seen in Figure 11 where we show the maximum S/N map for C iv from evaluation of the 3D cross-correlated S/N datacube (see Sect. 5.2). Here the S/N cube was evaluated between $\lambda_{\mathrm{min}}=6345$Å and $\lambda_{\mathrm{max}}=6360$Å. While there are a few patches within the blob that indicate possible signal at $\mathrm{S/N}\approx 5$, this spectral region of the datacube is highly contaminated by sky-subtraction residuals. As these systematic residuals are not accounted for in the variance datacube, our S/N estimates are biased high. These sky-subtraction residuals appear especially pronounced at the edges of the individual observational datasets (see exposure map in Figure 2). These edge-residuals are apparent as a patchy horizontal stripe of $\mathrm{S/N}\approx 4$ values slightly south of the photometric centre of LAB 8, as well as a vertical stripe on the western edge of the displayed region. A few pixels in the maximum S/N map show values above 5 in regions within the blob, but the extracted spectra in those regions do not show signal. We show in Figure 11 the spectral region of interest around C iv for the spectra extracted within the three He ii emitting regions (Sect. 5.5). In order to suppress the high-frequency sky-noise and residuals we also smoothed those spectra with a $\sigma=3.6$ Å wide Gaussian. Interestingly, the smoothed spectrum – shown as a blue line in Figure 11 – indeed appears to exhibit a small bump at the position of the $\lambda 1549$ line in all three regions. However, from the noise in those three regions (shown as a grey line in Figure 11), it is obvious that these features are not significant and can be only considered as a hint of C iv emission.

To provide upper limits on C iv emission we perform a source insertion and recovery experiment. For this experiment we assume that the C iv emission would be co-spatial with the He ii emitting regions. As noted in Sect. 5.5, each of the three He ii emitting region is defined by a cluster of connected spaxels that have $\mathrm{S/N}>5.5$. For simplicity we assume constant surface brightness within each region. Furthermore, we model the spectral profile of the $\lambda\lambda 1548,1550$ doublet by two Gaussians, where the dispersion is set to the average width measured from the He ii line: $\langle\sigma_{v}^{\mathrm{HeII}}\rangle=215$ km s^-1 and we fix the ratio to 1.7 between $\lambda 1548$ and $\lambda 1550$. We implant the so generated C iv emitting regions at surface-brightness levels from $10^{-19}$erg s^-1cm^-2arcsec^-2 to $9\times 10^{-19}$erg s^-1cm^-2arcsec^-2 in steps of $10^{-19}$erg s^-1cm^-2arcsec^-2 prior to median-filter subtracting the fully reduced datacube. After median-filter subtracting each datacube with artificial C IV sources we ran the 3D cross-correlation procedure from LSDCat. From this experiment we found that we would detect the C iv emission significantly in all three regions at surface-brightness levels $\geq 8\times 10^{-19}$erg s^-1cm^-2arcsec^-2. Given the areas of the three He ii emitting regions, our surface-brightness limit corresponds upper limits in C iv flux of $1.1\times 10^{-16}$erg s^-1cm^-2, $1.0\times 10^{-16}$erg s^-1cm^-2, and $6.1\times 10^{-16}$erg s^-1cm^-2 for region “south”, “north”, and “LAB 8”, respectively. Given the measured Ly$\alpha$ fluxes in those regions (see Sect. 5.5), this corresponds to upper limits in C iv/Ly$\alpha$ ratios of 0.06, 0.1, and 0.11 for region “south”, “north”, and “LAB 8”, respectively. Our upper limits on C iv translate into upper limits of $<1$, $<1.4$, $<1$ of C IV / He ii in region “south”, “north”, and “LAB 8”, respectively.

Our upper limit for C iv emission within the He ii emitting zones appears, at first sight, less constraining than the previous upper limit of 7.4$\times 10^{-19}$erg s^-1cm^-2arcsec^-2 from narrow-band observations Arrigoni Battaia et al. (2015). However, the comparison has to be treated with caution, as the previous estimate assumed constant C iv emission over the whole area of the blob ($\sim$200 arcsec²). But, we assumed here that C IV emission is confined to the three He ii emitting regions ($\lesssim$10 arcsec²). The assumption of overlapping C IV and He ii emission appears a good first-order approximation in scenario where C IV and He ii act as a coolant of shock heated gas, as for both lines the maximum emissivity is obtained in a similar gas phase of $T\sim 10^{5}$K (Cabot et al., 2016), where C iv is driven through collisional excitations of C³⁺ (ionisation potential 47.9 eV) while He ii is originating from the recombination cascade of collisionally ionised He²⁺ (ionisation potential 54.4 eV). Nevertheless, the C iv emissivity also peaks in a region of slightly lower density ($n_{\mathrm{H}}\sim 2-5$ cm^-3) compared to He ii ($n_{\mathrm{H}}\sim 5-20$ cm^-3), thus C iv could potentially also be more extended (Cabot et al., 2016). This effect could be further enhanced by the resonant nature of C iv (see also Berg et al., 2019). On the other hand, if photo-ionisation from a AGN produces C⁴⁺ (ionisation potential 64.4 eV) that emits C iv as a result of recombinations, the C⁴⁺ zone would be confined within the He²⁺ zone. Lastly, we will show below (Sect. 6.4) that under certain conditions C IV might be even brighter than He ii. For this reason some detections of extended C IV without corresponding He II around quasars have been reported (Borisova et al., 2016; Travascio et al., 2020).

Before interpreting flux-weighted moment maps from Ly$\alpha$ as a tracer of gaseous motions, we need to asses how Ly$\alpha$ radiative transfer effects may have influenced these measurements. Ly$\alpha$ velocity fields found to exhibit coherent large-scale kinematics have been observed around known (e.g. Arrigoni Battaia et al., 2018; Martin et al., 2019) or suspected (Prescott et al., 2015a) quasars. Details on the density distribution of the gas within those systems are still not settled, but it has been asserted that the strong ionisation field from the quasar produces a large fraction of Ly$\alpha$ photons in situ throughout the nebula via recombinations (e.g. Martin et al., 2014, 2019; Cantalupo et al., 2014, 2019). Nevertheless, even small residual neutral H i fractions ($\lesssim 10^{-4}$) within the ionised halo will result in high Ly$\alpha$ optical depths. Still, we suspect that the radiative transfer modulation of the Ly$\alpha$ profile for an extended intrinsic Ly$\alpha$ radiation field is less dramatic compared to the effect of an integrated spectrum within a compact Ly$\alpha$ emitting source. The reason is that the profile measured at each position in the nebula only reflects small local velocity offsets between point of emission and surface of last scattering (Prescott et al., 2015a). At typical spectral resolving powers then only a broadening of the Ly$\alpha$ line may be observed. This expectation appears consistent with our results for the He ii emitting regions in LAB 1. Moreover, systemic literature redshifts of the galaxies associated with LAB 1 do not show significant offsets with respect to those determined from Ly$\alpha$ (McLinden et al., 2013; Kubo et al., 2016; Umehata et al., 2017). From this we conclude that the first-moment map traces the gas-kinematics close to the embedded sources. For those galaxy near zones we then can assume that significant amounts of Ly$\alpha$ photons must be produced in situ.

For interpreting the entire first-moment map as a tracer of the underlying gas kinematics, especially in regions far from known galaxies in LAB 1, we can not resort to the argument above. The detection of polarised Ly$\alpha$ emission, both in imaging polarimetry (Hayes et al., 2011) and spectro-polarimetry (Beck et al., 2016), shows that significant fractions of the observed Ly$\alpha$ photons must have scattered into the line of sight after being emitted from a central source. According to radiative transfer theory the observed polarisation signal in Ly$\alpha$ stems from scattered photons within the wing of the absorption profile (e.g. Dijkstra & Loeb, 2008; Eide et al., 2018). Hence, while these photons preserve information regarding the kinematics of the surface of last scattering, they appear red- or blue-shifted (depending on the kinematics of the scattering medium) with respect to the overall kinematics of the gas. Therefore, in a scenario where only scattered Ly$\alpha$ photons are observed at large distance to the embedded sources, the measured first-moments would be biased towards higher or lower velocities compared to the true gas kinematics. This could potentially increase the observed amplitude of the observed velocity gradient.

However, the above scenario also requires that significant amounts of Ly$\alpha$ photons are released by the dust-rich ALMA 850$\mu$m detected galaxies in LAB 1 (see also Geach et al., 2016). The possibility of this process is indicated by the detection of Ly$\alpha$ emission from nearby ultra-luminous infrared galaxies (Martin et al., 2015a). Feedback driven outflows powered by star-formation is believed to create the required Ly$\alpha$ escape channels. Evidence for the required feedback effects at the positions of the galaxies comes from our higher-moment analysis discussed below (Sect. 6.3), but also from the spectro-polarimetry measurements by Beck et al. (2016). These authors find that the polarisation signal is increased in the wings of the Ly$\alpha$ profile, especially near the embedded galaxies. According to recent Ly$\alpha$ radiative transfer models of Eide et al. (2018) this is an expected polarisation signature in the presence of outflowing gas. Moreover, the Ly$\alpha$ escape channels produced by gaseous outflows can potentially also act as escape channels for ionising photons from the embedded systems, thus a significant fraction of those photons might indeed be available to power the emission from the blob via recombination. Empirical evidence for such a process have also been observed in the nearby universe (Herenz et al., 2017a; Bik et al., 2018; Menacho et al., 2019). Thus, in addition to Ly$\alpha$ scattering far from the embedded galaxies, we also expect that also in LAB 1 a significant fraction of Ly$\alpha$ radiation is produced in-situ at larger distances from the known embedded sources. Hence, the observed emission from the galaxy far-zones is likely superposition of scattered and in-situ produced Ly$\alpha$ emission. This potentially mitigates biases in the first moment maps that would result from pure Ly$\alpha$ scattering.

To summarise, we presented qualitative arguments in favour of interpreting large-scale coherent features in the first-moment map from Ly$\alpha$ as tracers of the gaseous motion in the system. These qualitative arguments are, as of yet, not tested for Ly$\alpha$ radiative transfer simulations in realistic Ly$\alpha$ blob environments. As we will also discuss further below, radiative transfer effects are, however, expected to strongly influence the Ly$\alpha$ line-width and the derived moments of higher order. We suggest that the here presented non-parametric moment-based measurements of the line profiles present a starting point to summarise the complexity of the encountered profiles in LAB environments. Guided by radiative transfer simulations then these measurements may help to disentangle scattering processes from in-situ Ly$\alpha$ photon production.

Hayes et al. (2011) studied LAB1 using the FORS2 polarimeter at VLT in order to spatially map the polarimetric properties of the Ly$\alpha$ emission, including the Stokes vectors ($Q$ and $U$), the polarised light fraction ($P$) and angle of the linear polarisation vector ($\chi$). The resulting maps of $P$ and $\chi$ were qualitatively consistent with theoretical predictions by Lee & Ahn (1998), Rybicki & Loeb (1999), and Dijkstra & Loeb (2008), and implied a geometry in which Ly$\alpha$ is produced inside, or close to the central regions of the highest Ly$\alpha$ surface brightness (at the positions of the later-discovered ALMA sources 1 and 2) and scattered at large impact parameters, from vectors in the plane of the sky to the sightline of the observer. However the narrowband imaging polarimetry data contained no information regarding the kinematic properties of the Ly$\alpha$ emission, and we could not study where in the Ly$\alpha$ line profile the polarisation signal is imparted. To remedy this Beck et al. (2016) conducted spectroscopic polarisation observations with the same instrument, to study $P$ and $\chi$ as a function of frequency. Those observations showed that the wavelength dependence of $P$ is small near line centre, but rises towards the line wings. This is again qualitatively consistent with the numerical predictions of Dijkstra & Loeb (2008). Those slit data contained the necessary frequency information, but only at eight positions identified along the 1″ wide slit. Moreover, those studies were limited to the regions of highest surface brightness (Beck et al. 2016, their Figure 3).

In this Section we use the 3D spectroscopy provided by MUSE to shed further light on the origin of the polarisation pattern. We perform a hybrid study, and contrast the spatially known (but spectrally-unknown) measurements of $P$ and $\chi$ with the Ly$\alpha$ kinematics using 3D spectroscopy. Hayes et al. (2011) used Voronoi tessellation to locally enhance the SNR in the images taken in individual beams (‘ordinary & extraordinary’), and we apply the same binning patterns to the MUSE data: we aligned the FORS2 Ly$\alpha$ intensity images with the MUSE data, and propagate the recovered astrometric information into the maps of $P$ and $\chi$. For every Voronoi tessellated cell we then extract the corresponding spaxels from the MUSE datacube, and compute the moments described in Section 5.3.

Figure 12 shows the results, where we display the absolute velocity offset from $z_{\mathrm{Ly\alpha}}=3.1$ (left panel) and the velocity dispersion (right panel). We show the absolute value of the first moment because the polarisation signal is imparted by wing scatterings, and scatterings in both the blue and red wings manifest in the same $P$ (the quantity measured in our polarimetry data Dijkstra & Loeb, 2008). We find a positive correlation between $P$ and the absolute line-of-sight velocity, and also an anti-correlation between $P$ and the velocity dispersion. The $p$-values of $10^{-5}-10^{-4}$ suggest that correlations of this magnitude or larger are very unlikely to have arisen by a random process. That Ly$\alpha$ should exhibit higher degrees of polarisation for narrow lines is a curious result, and may stem from several effects.

The polarisation data show a high $P$, and a pattern in $\chi$ that is close-to tangentially aligned with a central source, and follows contours of surface brightness at smaller scales (Hayes et al., 2011, Figure 2). To impart such a pattern, scattering in the wing of the redistribution profile needs to be promoted, so as to in turn enhance scattering through the $2P_{3/2}$ excited level (Dijkstra & Loeb, 2008; Eide et al., 2018). $P$ will instead decrease if too many core (resonance) scattering events occur (through the $2P_{1/2}$ level). Such an enhancement of wing events cannot be the case for a static medium, where the gas would absorb Ly$\alpha$ close to line-centre (core). Some velocity offset is needed, which implies that high $P$ should avoid $|\Delta v_{\mathrm{los}}|=0$ (the original motivation for the outflowing shell models of Dijkstra & Loeb 2008). Moreover, even if large bulk velocity offsets are present, the velocity dispersion cannot be significantly larger than the absolute $|v_{\mathrm{los}}|$: the consequence of a broad velocity range of absorbing material will always leave some high column density gas close to line-centre, and maintain significant core scattering. In a complicated, 3-dimensional environment with multiple sources of Ly$\alpha$ and many velocity components of scattering gas, highly polarised regions should favour larger velocity shifts and narrower lines, and we would expect $P$ to correlate with $|v_{\mathrm{los}}|$ and anti-correlate with the line width. This is precisely what Figure 12 shows and the combination of 2D polarimetric data and 3D spectroscopic data supports a scenario in which preferential scattering outside the Doppler core is enhanced by velocity differences.

In Sect. 5.5 we reported on the detection of three distinct extended He ii emitting zones with $\mathrm{SB}_{\mathrm{HeII}}\sim 6-7\times 10^{-19}$erg s^-1cm^-2arcsec^-2. Extended He II emission is commonly observed within the extended Ly$\alpha$ emitting regions surrounding high-$z$ radio galaxies (e.g., Maxfield et al., 2002; Villar-Martín et al., 2007a, b; Morais et al., 2017; Marques-Chaves et al., 2019). Broad line profiles and alignments with the radio-jet axes indicate that He ii is, at least partly, powered by jet-gas interactions in those objects. Detections of He ii emitting zones within the extended Ly$\alpha$ nebulae surrounding radio quiet quasars or in LABs not directly associated with an AGN appear less frequent and more difficult to interpret (Scarlata et al., 2009b; Prescott et al., 2009; Cai et al., 2017; Cantalupo et al., 2019; Humphrey et al., 2019). Different explanations have been put forward, e.g. with Scarlata et al. (2009b) favouring cooling-radiation in their system, Prescott et al. (2009) arguing for photo-ionisation by an AGN or an extremely metal poor stellar population in their object, while Cai et al. (2017) reason that their extended He ii zone is powered by shocks. We now try to constrain the physical mechanisms responsible for the extended He ii emission in the blob. To this aim we will also consider the upper limits on C IV emission from the He ii emitting zones (Sect. 5.6).

To place our result in context with previous observations (or upper limits) of He ii and C iv emission from high-$z$ sources with extended Ly$\alpha$ emission we compare in Figure 13 our measured He ii/Ly$\alpha$ ratios and our derived upper limits on C iv/Ly$\alpha$ to the literature. The majority of comparison objects in Figure 13 harbour a bright active galactic nucleus. We observe that that the ratios and upper limits in LAB 1 appear not unusual with respect to other extended Ly$\alpha$ objects, i.e, some objects exhibit significantly higher ratios both in He ii/Ly$\alpha$ and C iv/Ly$\alpha$, but also significantly lower ratios or upper-limits have been reported. The diversity in ratios observed for nebulae with known powering source imply that varying physical conditions (e.g. metallicity, temperature, and density) within the emitting gas significantly influences the observed ratios. Additionally, radiative transfer effects in both Ly$\alpha$ and C iv (Berg et al., 2019, their Sect. 2.3) can also bias conclusions drawn from this diagram (e.g. Caminha et al., 2016). This diagram has now been frequently used in the literature for attempting to understand the physical conditions of the ionised gas.

We show in Figure 13 the track of a photo-ionisation model from Villar-Martín et al. (2007a) that appears to be in good agreement with the He ii/Ly$\alpha$ ratios and C iv/Ly$\alpha$ ratios from our observations. This track was computed for gas of solar metallicity at a density of $n_{\mathrm{H}}=100$ cm^-3 as a function of varying (dimensionless) ionisation parameter

where $\dot{Q}$ denotes the rate of hydrogen ionising photons produced by the source and $r$ denotes the distance of the ionised gas cloud to the source. As spectral energy distribution of the ionising source Villar-Martín et al. (2007a) assumed an idealised quasar described by a $F_{\nu}\propto\nu^{\alpha}$ power-law continuum with slope $\alpha=-1.5$. Along the displayed track $\log U$ varies from -2.3 (start of the upper branch) to 0 (end of the lower branch); the inflection point in C iv/Ly$\alpha$ is at $\log U=-1$ (the model is adopted from Figure 1 of Villar-Martín et al., 2007a).

While the predicted line-ratios show some agreement with our observation, for region “north” the assumptions in this model require extremely high photo-ionisation rates: Region “north” is $\sim$ 50 kpc in projection towards LAB-ALMA1, LAB-ALMA2, and VLA-LAB1a. Thus, according to Eq. (13), even the smallest $\log U=-2.3$ in the Villar-Martín et al. (2007a) model corresponds $\dot{Q}\sim 10^{57}$s^-1 if we assume a galaxy at the position of LAB-ALMA1, LAB-ALMA2, or VLA-LAB1a as the ionising source. This value would be similar to the photo-ionisation rate inferred for the luminous quasar UM 287 that powers the “Slug” nebulae (Cantalupo et al., 2014) and two orders of magnitude higher than the $\dot{Q}\approx 10^{55}$s^-1 that would be required to power the whole blob via photo-ionisation (under case-B assumptions). While the photo-ionisation model might be more fitting for the zones “south” and “LAB 8”, as they are in close vicinity to known galaxies, existing deep multi-wavelength data does not find strong evidence in favour of such a luminous AGN (Ao et al., 2017). Thus, we also explore different mechanism that have been put forward to explain He ii in LABs.