A DEEP NARROWBAND IMAGING SEARCH FOR C iv AND He ii EMISSION FROM Lyα BLOBS^*

We obtained deep C iv and He ii narrowband images of 13 LABs in the SSA22 proto-cluster field, including the two largest LABs that were originally discovered by Steidel et al. (2000). Data were taken in service-mode using the FORS2 instrument on the VLT 8.2 m telescope Antu (UT1) on 2010 August, September, October and 2011 September over 25 nights. We used two narrowband filters, Oi/2500+57 and Sii+62 matching the redshifted C iv λ1549 and He ii λ1640 at z = 3.1, respectively. The Oi/2500+57 filter has a central wavelength of λ_c ≈ 6354 Å and has an FWHM of Δλ_FWHM ≈ 59 Å, while the Sii+62 filter has ${{\lambda }_{c}}\;\approx \;6714$ Å and ${\Delta }{{\lambda }_{{\rm FWHM}}}\;\approx \;69$ Å (Figure 1). These bandwidths provide a line-of-sight depth of Δz ≃ 0.038 and Δz ≃ 0.042, respectively for the Oi/2500+57 and Sii+62 filter. Thus, given the typical uncertainties in the redshift measurements for the LABs (e.g., z_LAB1 = 3.097 ± 0.002, Ohyama et al. 2003; z_LAB2 = 3.103 ± 0.002, Matsuda et al. 2005) and the good agreement between the central wavelengths of the three narrowband filters used in this work (see Figure 1), we are confident that, if present, the C iv and He ii lines would fall within the targeted wavelength ranges. Note that very large velocity offsets (>2000 km s⁻¹) with respect to the Lyα line would thus be required to bring the C iv or He ii line outside our set of narrowband filters. Such large kinematic offsets are not expected in these systems (e.g., Prescott et al. 2015).

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The FORS2 has a pixel scale of 0 25 pixel⁻¹ and a field of view (FOV) of 7' × 7' that allow us to observe a total of 13 LABs in a single pointing. The pointing was chosen to maximize the number of LABs while including the two brightest LABs, LAB1 and LAB2 (Steidel et al. 2000). We show the spatial distribution of ∼300 LAEs and 35 LABs in the SSA22 region and mark the LABs within FORS2 narrowband images in Figure 2.

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The total exposure time was 19.9 and 19.0 hr for C iv and He ii lines, respectively. These exposures consist of 71 and 68 individual exposures of ∼17 minutes, taken with a dither pattern to fill in a gap between the two chips, and to facilitate the removal of cosmic rays. Because our targets are extended over 5''–17'' diameter and our primary goal is to detect the extended features rather than compact embedded galaxies, we carried out our observations under any seeing conditions (program ID: 085.A-0989, 087.A-0297). Figure 3 shows the distribution of FWHMs measured from stars in individual exposures. Although the observations were carried out under poor or variable seeing condition, the seeing ranges from 0 5 to 1 4 depending on the nights, and the median seeing is ∼0 8 in both filters. In Table 1, we summarize our VLT/FORS2 narrowband observations.

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Table 1.  VLT FORS2 Observations and Subaru Data

Telescope	Instrument	Filter (Target Line)	${{\lambda }_{{\rm Central}}}$ a	${\Delta }{{\lambda }_{{\rm FWHM}}}$ b	Seeingc	Exp. Time	Depthd	Pixel Scale
			(Å)	(Å)	(arcseconds)	(hours)	(mag)	(arcseconds)
VLT	FORS2	Oi/2500+57 (C iv)	6354	59	0.8	19.9	25.9	0.25
VLT	FORS2	Sii+62 (He ii)	6714	69	0.8	19.0	26.5	0.25
Subarue	S-Cam	NB 497 (Lyα)	4977	77	1.0	7.2	26.2	0.20
Subarue	S-Cam	R	6460	1177	1.0	2.9	26.7	0.20

^aCentral wavelength of the filter. ^bFWHM of the filter. ^cMedian seeing of our FORS2 observations and average seeing of the Subaru data (Matsuda et al. 2004). ^d5σ detection limit for 2''-diameter aperture. ^eImages from Hayashino et al. (2004) and Matsuda et al. (2004).

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The data were reduced with standard routines using IRAF.¹² The images were bias-subtracted and flat-fielded using twilight flats. To improve the flat-fielding essential for detecting faint extended emission across the fields, we further correct for the illumination patterns using night-sky flats. The night-sky flats were produced by combining the unregistered science frames with an average sigma-clipping algorithm after masking out all the objects. Satellite trails, CCD edges, bad pixels, and saturated pixels are masked. Each individual frame is cleaned from cosmic rays using the L.A.Cosmic algorithm (van Dokkum 2001). The astrometry was calibrated with the SDSS-DR7 r-band catalog using SExtractor and SCAMP (Bertin 2006). The rms uncertainties in our astrometric calibration are ∼0 2 for both C iv and He ii images.

The final stacks for each filter (C iv and He ii) were obtained using SWarp (Bertin et al. 2002): the individual frames were sky-subtracted using a background mesh size of 256 pixels (≈64''), then projected onto a common WCS using a Lanczos3 interpolation kernel, and average-combined with weights proportional to flat and night-sky flat images. Note that we choose the mesh size to be large enough to ensure that we do not mistakenly subtract any extended emission as sky background. For flux calibration, we use four spectrophotometric standard stars (Feige 110, EG 274, LDS 749B, and G158-100) that were repeatedly observed during our observations. Typical uncertainties in the derived zero points are ≈0.03 mag.

To subtract continuum from our narrowband images and compare the C iv and He ii line fluxes with those of Lyα, we rely on previous Subaru observations. The SSA22 field has been extensively observed in B, V, R, i', and NB 497 bands (Hayashino et al. 2004; Matsuda et al. 2004) with the Subaru Suprime-Cam (Miyazaki et al. 2002). These images have a pixel scale of 0 20 and an FOV of 34' × 27'. The NB 497 narrowband filter, tuned to the Lyα line at z ∼ 3.1, has a central wavelength of 4977 Å and an FWHM of 77 Å. The total exposure time for the Lyα narrowband image was 7.2 hr, with a 5σ sensitivity of 5.5 × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² per 1 arcsec² aperture, which is roughly 1.5–2.5 times shallower than those of FORS2 He ii and C iv images. In Table 1, we summarize the Subaru broadband and narrowband images that were used in this work.

Using these deep Subaru data, Matsuda et al. (2004) found 35 LABs, defined to be Lyα emitters with the observed EW(Lyα) > 80 Å and an isophotal area larger than 16 arcsec², which corresponds to a spatial extent of 30 kpc at z = 3. The isophotal area was measured above the 2σ SB limit (2.2 × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻²). In Table 2, we list the properties (e.g., Lyα luminosity and isophotal area) of the 13 LABs that were observed with VLT/FORS2. We refer readers to Matsuda et al. (2004) for more details of this LAB sample.

To identify the emission in the C iv λ1549 and He ii λ1640 lines, we subtract the continuum emission underlying the Oi/2500+57 and Sii+62 filter. We estimate the continuum using the deep Subaru R-band image. Because the Subaru and FORS2 images have different pixel scales, we resample the R-band images to the FORS2 pixel scale and register them to our WCS in order to compare all the images pixel by pixel. We do not match the point-spread functions (PSFs) given that FORS2 images were obtained with a wide range of seeing, and we are mostly interested in the extended emission. We produce the continuum-subtracted image for each filter (C iv and He ii) using the following relations (Yang et al. 2009):

$$\begin{eqnarray}&&f_{\lambda ,{\rm cont}}^{{\rm B}{\rm B}}=\frac{{{F}_{{\rm B}{\rm B}}}-{{F}_{{\rm N}{\rm B}}}}{{\Delta }{{\lambda }_{{\rm B}{\rm B}}}-{\Delta }{{\lambda }_{{\rm N}{\rm B}}}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{{F}_{{\rm line}}}={{F}_{{\rm N}{\rm B}}}-f_{\lambda ,{\rm cont}}^{{\rm B}{\rm B}}{\Delta }{{\lambda }_{{\rm N}{\rm B}}},\end{eqnarray} \tag{ 2 }$$

where F_BB is the flux in the R band and F_NB is the flux in one of the narrowband filters. Δλ_BB and Δλ_NB represent the FWHM of the R and narrowband filters, respectively. f_λ, cont^BB is the flux density of the continuum within the R band, and F_line is the line flux (C iv or He ii).

Note that the R-band image includes both the C iv and He ii lines, but here we adopt a simple approximation assuming that one emission line within the R band (e.g., He ii) is negligible in estimating the flux of the other emission line (e.g., C iv). For example, we would underestimate the line flux of C iv by >10% if the flux in He ii were F_line ≳ 2 × 10⁻¹⁷ erg s⁻¹ cm⁻², which is easily detectable in our deep images. We are using these simple equations because we aim to minimize the systemic effects such as poor PSF matching and imperfect sky subtraction. Note that we have also tried the continuum subtraction with two off-band images (V and i), as explained in Section 2.4.

We compute a global SB limit for detecting He ii and C iv lines using a global rms of the images. To calculate the global rms per pixel, we first mask out the sources, in particular the scattered light and halos of bright foreground stars, and compute the standard deviation of sky regions using a sigma-clipping algorithm. We convert these rms values into the SB limits per 1 arcsec² aperture. We find that the 1σ detection limit per 1 arcsec² aperture (SB₁) is 4.2 × 10⁻¹⁹ and 6.8 × 10⁻¹⁹ erg s⁻¹ cm⁻² arcsec⁻² for He ii and C iv, respectively. These represent the deepest He ii λ1640 and C iv λ1549 narrowband images ever taken.

The sensitivity required to detect an extended source depends on its size because one can reach lower SB levels by spatially averaging. In an ideal case of perfect sky and continuum subtraction, the 1σ SB limit for an extended source is given by ${\rm S}{{{\rm B}}_{1}}/\sqrt{{{A}_{{\rm src}}}}$, where A_src is the isophotal area in arcsec² and SB₁ is the SB limit per 1 arcsec² aperture. However, in practice the actual detection limits are limited by systematics resulting from imperfect sky and continuum subtraction. Therefore, we empirically determine the detection limits for extended sources with different sizes as follows.

In the continuum-subtracted line images, we mask all the artifacts (e.g., CCD edges and scattered light from bright stars) and also the locations of the LABs. For each LAB that we consider, we randomly place circular apertures with the same area of the LAB and extract the fluxes (F_src) within these apertures. If the images have uniform noise properties in the absence of systematics, the fluxes (F_src) from many random apertures should follow a Gaussian distribution with a width of σ_src ≡ ${\rm S}{{{\rm B}}_{1}}\sqrt{{{A}_{{\rm src}}}}.$ We find that the actual Gaussian width ($\sigma _{{\rm src}}^{\prime }$) of the distribution is much broader than σ_src (Figures 4 and 5). We adopt ${{F}_{{\rm limit}}}$ ≡ $\sigma _{{\rm src}}^{\prime }$ as a 1σ upper limit on the total line flux of each LAB. The corresponding upper limit for the SB is given by SB_limit ≡ ${{F}_{{\rm limit}}}$/A_src.

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Figures 4 and 5 show the distribution of ${{F}_{{\rm src}}}$/σ_src for He ii and C iv images, respectively. Note that we normalize the extracted fluxes to the σ_src in order to show the distributions for LABs with similar sizes in one plot. As the size of the LABs in our sample spans a large range, we show the distributions for two sub-samples: one for LAB1 and LAB2 with A_src > 100 arcsec² and the other for the remaining LABs with A_src < 40 arcsec². As previously stated, in the ideal case of no systematics, σ_src characterizes the noise in F_src, and thus the distribution of the quantity F_src/σ_src should be a Gaussian with unit variance. For both sub-samples, we find that F_src/σ_src histograms show a variance greater than unity, suggesting that imperfect sky and continuum subtraction dominates our error budget. The normalized histograms have a standard deviation of ≈3 on the scale of the bigger LABs (LAB1 and LAB2) and ≈2 on the scale of the smaller LABs. Thus, as our 1σ limit on the total line flux of the largest LABs in our sample (LAB1 and LAB2), we adopt ${{F}_{{\rm limit}}}\equiv \sigma _{{\rm src}}^{\prime }=3{{\sigma }_{{\rm src}}}$, where σ_src ≡ ${\rm S}{{{\rm B}}_{1}}\sqrt{{{A}_{{\rm src}}}}$ is computed using the area of the blob. For all of the other blobs in our sample, we follow the same approach but use a value F_limit ≡ $\sigma _{{\rm src}}^{\prime }=2{{\sigma }_{{\rm src}}}$. We conservatively define our detection threshold to be $5\sigma _{{\rm src}}^{\prime },$ which formally means 15σ_src for LAB1 and LAB2 and 10σ_src for all the other blobs. In each histogram, we show the values extracted inside the isophotal contours of each LAB (black arrows). These values are well within the distribution of F_src/σ_src determined from random apertures (see Table 3).

To test if our derived detection limits are reasonable, we visually confirm the detectability as a function of size by placing artificial model sources in He ii and C iv narrowband images. We adopt circular top-hat sources with a uniform SB corresponding to 1, 2, 3, 4, 5, 8, 10, 20 SB_limit and an area of 200, 100, 40 and 20 arcsec², comparable to the size of the LABs in our sample (see Table 2). After placing the simulated sources in the narrowband images, we subtract the continuum in the same way as explained in Section 2.3. Because the detectability strongly depends on the residual structure of the continuum subtraction, we place the model sources at different locations in the narrowband images after masking all the bad regions as explained above. Following Hennawi & Prochaska (2013), we construct a χ image by dividing the continuum-subtracted image by a "sigma" image. Here, the sigma image (or the square root of the variance image) is calculated by taking into account our stacking procedure, e.g., bad pixels, satellite trails, and sky subtraction. In other words, this variance image is the theoretical photon counting noise variance, taking into account all the bad-behaving pixels. In this calculation, we do not include the variance due to R-band continuum, i.e., we ignore the photon counting noise from R-band image; thus, it is likely that our sigma image might slightly underestimate the noise. Note, however, that the shallower NB images are very likely dominating the noise; thus, the R-band contribution to the variance is a small correction.

To test the detectability of extended emission, we compute a smoothed χ image following the technique in Hennawi & Prochaska (2013). First, we smooth an image:

$$\begin{eqnarray}&&{{I}_{{\rm smth}}}={\rm CONVOL}[{\rm NB}-{\rm CONTINUUM}],\end{eqnarray} \tag{ 3 }$$

where the CONVOL operation denotes convolution of the stacked images with a Gaussian kernel with FWHM = 2 35. Then, we calculate the sigma image (σ_smth) for the smoothed image (I_smth) by propagating the variance image of the unsmoothed data:

$$\begin{eqnarray}&&{{\sigma }_{{\rm smth}}}=\sqrt{{\rm CONVO}{{{\rm L}}^{2}}[\sigma _{{\rm unsmth}}^{2}]},\end{eqnarray} \tag{ 4 }$$

where the CONVOL² operation denotes the convolution of variance image with the square of the Gaussian kernel. Thus, the smoothed χ image is defined by

$$\begin{eqnarray}&&{{\chi }_{{\rm smth}}}=\frac{{{I}_{{\rm smth}}}}{{{\sigma }_{{\rm smth}}}}.\end{eqnarray} \tag{ 5 }$$

This χ_smth is more effective in visualizing the presence of extended emission.

Figures 6 and 7 show the χ_smth for the simulated sources for He ii and C iv images, respectively. For each detection significance and source size, the simulated sources are shown for two different positions within the He ii or the C iv images. To guide the eye, these positions are highlighted by a black circle. These simulated χ_smth images confirm that we should be able to detect extended emission down to a level of 5SB_limit, justifying our choice for this detection threshold. Note again that SB_limit includes the correction we made to take into account the systematics.

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In addition to the previous analysis, in order to further test our continuum subtraction, we also performed the continuum subtraction using two off-band images (V and i'; Hayashino et al. 2004), finding that the results remain unchanged. Note, however, that due to the differences in the telescope PSFs and seeing of the observations, the use of two bands increases the noise. Thus, we prefer to estimate the continuum using only the R-band image.

It is well established that the ionizing radiation from a central AGN can power giant Lyα nebulae, with sizes up to ∼200 kpc, around HzRGs (e.g., Reuland et al. 2003; Villar-Martín et al. 2003b; Venemans et al. 2007) and quasars (e.g., Heckman et al. 1991b; Christensen et al. 2006; Smith et al. 2009), together with extended He ii and C iv emission (Villar-Martín et al. 2003a). Although HzRGs are more rare ($n\sim {{10}^{-8}}$ Mpc⁻³; Miley & De Breuck 2008), the similarity between the volume density of LABs (n ∼ 10⁻⁵ Mpc⁻³; Yang et al. 2010) and luminous QSOs (n ∼ 10⁻⁵ Mpc⁻³; Hopkins et al. 2007) suggests that the LABs could represent the same photoionization process around obscured QSOs. Unified models of AGNs invoke an obscuring medium that could extinguish a bright source of ionizing photons along our line of sight (e.g., Urry & Padovani 1995). Indeed, evidence for obscured AGNs has been reported for several LABs (e.g., Basu-Zych & Scharf 2004; Dey et al. 2005; Geach et al. 2007; Barrio et al. 2008; Geach et al. 2009; Overzier et al. 2013; Yang et al. 2014a), lending credibility to a photoionization scenario; however, this is not always the case (Nilsson et al. 2006; Smith & Jarvis 2007; Ouchi et al. 2009).

Despite these circumstantial evidences in favor of the photoionization scenario, detailed modeling for He ii and C iv lines due to AGN photoionization in the context of large Lyα nebulae has not been carried out in the literature, with the exceptions of some studies focusing on the modeling of emission lines in the case of extended emission line regions (EELRs) of HzRGs (e.g., Humphrey et al. 2008). Although many authors have modeled the NLR of AGNs (e.g., Groves et al. 2004, Nagao et al. 2006, Stern et al. 2014), the physical conditions (i.e., gas density, ionization parameter) on these small scales ≳1 kpc (e.g., Bennert et al. 2006; Hainline et al. 2014) are expected to be very different from the ∼100 kpc scale emission of interest to us here. As such, we model the photoionization of gas on scales of 100 kpc from a central AGN to predict the resulting level of the He ii and C iv lines, relative to the Lyα emission.

To select the parameters of the models in order to recover the Lyα SB of LABs, we follow the simple picture described by Hennawi & Prochaska (2013) and assume an LAB to be powered by an obscured QSO with a certain luminosity at the Lyman limit (${{L}_{{{\nu }_{{\rm LL}}}}}$). In this picture, the QSO halo is populated with spherical clouds of cool gas (T ∼ 10⁴ K) at a single uniform hydrogen volume density ${{n}_{{\rm H}}}$ and with an average column density N_H, and uniformly distributed throughout a halo of radius R, such as they have a cloud covering factor f_C (see Hennawi & Prochaska 2013 for details). We consider two limiting regimes for recombination: the optically thin (N_Hi < 10^17.2 cm⁻²) and thick (${{N}_{{\rm HI}}}\gt {{10}^{17.2}}$ cm⁻²) to the Lyman continuum photons, where N_Hi is the neutral column density of a single spherical cloud. In this scenario, once the size of the halo is fixed, in the optically thick case the Lyα SB scales with the luminosity at the Lyman limit of the central source, $SB_{{\rm Ly}\alpha }^{{\rm thick}}\propto {{f}_{C}}{{L}_{{{\nu }_{{\rm LL}}}}}$, while in the optically thin regime (N_Hi < 10^17.2 cm⁻²) the SB does not depend on ${{L}_{{{\nu }_{{\rm LL}}}}},$ $SB_{{\rm Ly}\alpha }^{{\rm thin}}\propto {{f}_{C}}{{n}_{{\rm H}}}{{N}_{{\rm H}}},$ provided that the AGN is bright enough to keep the gas in the halo ionized.

To cover the full range of possibilities, we thus construct a grid of ∼5000 Cloudy models with parameters in the following range (see Appendix B for additional information on how the parameters were chosen):

• n_H = 0.01–100 cm⁻³ (steps of 0.2 dex);
• ${\rm log} {{N}_{{\rm H}}}=18$–22 (steps of 0.2 dex);
• ${\rm log} {{L}_{{{\nu }_{{\rm LL}}}}}=29.3$–32.2 (steps of 0.4 dex).

Finally, we decide to fix the covering factor to unity f_C = 1.0. The assumption of a high or unit covering factor is driven by the observed diffuse morphology of the Lyα nebulae, which do not show evidence for clumpiness arising from the presence of a population of small unresolved clouds. We directly test this assumption as follows. We randomly populate an area of 200 arcsec² (area of LAB1) with point sources such that f_C = 0.1–1.0, and we convolve the images with a Gaussian kernel with an FWHM equal to our median seeing value, in order to mimic the effect of seeing in the observations. We find that the smooth morphology observed for LABs cannot be reproduced by images with f_C < 0.5, as they appear too clumpy.

We perform photoionization calculations using the Cloudy photoionization code (v10.01), last described by Ferland et al. (2013). As the LABs are extended over ∼100 kpc, whereas the radius of the emitting clouds is expected to be much smaller, we assume a standard plane-parallel geometry for the emitting clouds illuminated by the distant central source. Note that we evaluate the ionizing flux at a single location for input into Cloudy, specifically at $R/\sqrt{3}$ (where R = 100 kpc). Capturing the variation of the physical properties of the nebula with radius is beyond the purpose of this work. Indeed, given that for the objects in the literature radial trends for the C iv/Lyα and He ii/Lyα ratios are not reported, and given that we have non-detections, modeling the emission as coming from a single radius is an acceptable first-order approximation. Further, given the ionization energies for the species of interest to us in this work, i.e., 1 Ryd = 13.6 eV for hydrogen, 4 Ryd = 54.4 eV for He ii, and 64.5 eV for C iv, we have decided to stick to standard parameterizations above 1 Ryd. However, note that the UV range of the SED is so far not well constrained (see Lusso et al. 2014 and reference therein). In particular, we model the quasar SED using a composite quasar spectrum that has been corrected for IGM absorption (Lusso et al. 2014). This IGM-corrected composite is important because it allows us to relate the i-band magnitude of the central source to the specific luminosity at the Lyman limit ${{L}_{{{\nu }_{{\rm LL}}}}}.$ For energies greater than 1 Ryd, we assume a power-law form ${{L}_{\nu }}={{L}_{{{\nu }_{{\rm LL}}}}}{{(\nu /{{\nu }_{{\rm LL}}})}^{{{\alpha }_{{\rm UV}}}}}$ and adopt a slope of α_UV = −1.7, consistent with the measurements of Lusso et al. (2014). We determine the normalization ${{L}_{{{\nu }_{{\rm LL}}}}}$ by integrating the Lusso et al. (2014) composite spectrum against the SDSS filter curve and choosing the amplitude to give i-band apparent magnitudes of i = 16–23, in steps of unity. We extend this UV power law to an energy of 30 Ryd, at which point a slightly different power law is chosen, α = −1.65, such that we obtain the correct value for the specific luminosity at 2 keV L_ν(2 keV) implied by measurements of α_OX, defined to be ${{L}_{\nu }}(2\;{\rm keV})/{{L}_{\nu }}(2500\;\overset{\circ}{\rm A} )\equiv {{({{\nu }_{2\,{\rm keV}}}/{{\nu }_{2500\,\overset{\circ}{\rm A} }})}^{{{\alpha }_{{\rm OX}}}}}.$ We adopt the value α_OX = −1.5 measured by Strateva et al. (2005) for SDSS quasars. An X-ray slope of ${{\alpha }_{{\rm X}}}=-1$, which is flat in ν f_ν, is adopted in the interval of 2–100 keV, and above 100 keV, we adopt a hard X-ray slope of α_HX = −2. For the rest-frame optical to mid-IR part of the SED, we splice together the composite spectra of Lusso et al. (2014), Vanden Berk et al. (2001), and Richards et al. (2006). These assumptions about the SED are essentially the standard ones used in photoionization modeling of AGNs (e.g., Baskin et al. 2014). See also Arrigoni Battaia et al. (2015) for further details on the SED.

Finally, we consider only models with solar metallicity, and from our model grid, we select only models with SB$_{{\rm Ly}\alpha }$ = (1–9) × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻², comparable to LABs.

It is important to stress here that we neglect the contribution due to the resonant scattering of Lyα photons produced by the quasar itself. Indeed, radiative transfer simulations of radiation from a bright quasar (i = 17.28) through a simulated gas distribution have shown that the scattered Lyα line photons from the quasar do not contribute significantly to the Lyα SB of the nebula on large scales, i.e., ≳100 kpc (Cantalupo et al. 2014). This is due to the great efficiency of the resonant scattering in diffusing the photons both spatially and in the velocity space.

In Figure 12 we compare our photoionization model predictions in the He ii/Lyα versus C iv/Lyα diagram to our LAB limits and the data points from the literature. The left panel and right panels show the optically thin and optically thick regimes, respectively. Note that this division into optically thin and thick models corresponds to a division in the ionizing luminosity of the central source (which in the case of LABs and HzRGs is obscured from our vantage point and is thus unknown). Specifically, in the optically thin regime we find that for the range of ${\rm S}{{{\rm B}}_{{\rm Ly}\alpha }}$ considered, the central source must have ${{L}_{{{\nu }_{{\rm LL}}}}}\gtrsim {{10}^{30.5}}$ erg s⁻¹ Hz⁻¹ or i ≲ 20.¹⁵ On the other hand, because in the optically thick limit ${\rm S}{{{\rm B}}_{{\rm Ly}\alpha }}\propto {{L}_{{{\nu }_{{\rm LL}}}}},$ the ionizing luminosity is fixed to be in a relatively narrow range ${{L}_{{{\nu }_{{\rm LL}}}}}\simeq {{10}^{29.7}}-{{10}^{29.3}}$ erg s⁻¹ Hz⁻¹ (i ≃ 22–23).

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For clarity, in Figure 12 we show only the models with N_H = 10¹⁸, 10¹⁹, 10²⁰, 10²¹, 10²² cm⁻². The model grids are color coded according to the ionization parameter U, which is defined to be the ratio of the number density of ionizing photons to hydrogen atoms ($U\equiv {{{\Phi }}_{{\rm LL}}}/c{{n}_{{\rm H}}}\propto {{L}_{{{\nu }_{{\rm LL}}}}}/{{n}_{{\rm H}}}$) and provides a useful characterization of the ionization state of the nebulae. Because photoionization models are self-similar in this parameter (Ferland 2003), our models will exhibit a degeneracy between n_H and ${{L}_{{{\nu }_{{\rm LL}}}}}.$ Nevertheless, we decided to construct our model grid in terms of n_H and ${{L}_{{{\nu }_{{\rm LL}}}}},$ in order to explore the possible ranges of both parameters.

Figure 12 illustrates that, overall, our photoionization models can cover the full range of He ii/Lyα and C iv/Lyα line ratios that are observed in the data. Note that previous studies of EELRs around HzRGs favored models with logU ∼ −1.46 (e.g., Humphrey et al. 2008), which are consistent with our results. Note, however, that two HzRGs with He ii/Lyα ≈ 1 and C iv/Lyα ≈ 1 are not covered by our models. For both of these data, emission from the central source has not been excluded, and thus we speculate that these very high line ratios arise because of contamination from the narrow-line region of the obscured AGN, where Lyα photons have been destroyed by dust. Indeed, both of these objects, MG1019+0535 and TXS0211–122, have a C iv/He ii ratio similar to the bulk of the HzRG population, but they exhibit unusually weak Lyα lines (Dey et al. 1995; van Ojik et al. 1994). Note, however, that while destruction of Lyα by dust grains can have a large impact on these line ratios for emission emerging from the much smaller scale narrow-line region, dust is not expected to significantly attenuate the Lyα  emission in the extended nebulae around QSOs (see discussion in Appendix A of Hennawi & Prochaska 2013) given the physical conditions characteristic of the CGM, and thus we neglect destruction of Lyα photons by dust in our modeling.

The optically thin regime (see left panel) seems to better reproduce the range of high He ii/Lyα and C iv/Lyα ratios and seems to have difficulties in reproducing the low ratios implied by our observations (see below). To understand why the optically thin models do not cover low He ii/Lyα ratios, we describe here the trajectory of the optically thin models through the He ii/Lyα and C iv/Lyα diagram. We follow the curves from low to high U. Recall that in the optically thin regime $S{{B}_{{\rm Ly}\alpha }}\propto {{n}_{{\rm H}}}{{N}_{{\rm H}}},$ but is roughly independent of the source luminosity ${{L}_{{{\nu }_{{\rm LL}}}}}.$ ¹⁶ Thus, by fixing N_H and requiring that $S{{B}_{{\rm Ly}\alpha }}\;=\;$(1–9) × 10⁻¹⁸ erg s⁻¹ cm⁻², we also fix n_H. Thus, U increases along this track because the central source luminosity ${{L}_{{{\nu }_{{\rm LL}}}}}$ is increasing, which hardly changes the Lyα emission but results in significant variation in both He ii and C iv.

First consider the trend of the He ii/Lyα  ratio. He ii is a recombination line, and thus, once the density is fixed, its emission depends basically on what fraction of helium is doubly ionized. For this reason, the He ii/Lyα  ratio is increasing from logU = −3.3 and reaches a peak at log $U\sim -2.0,$ corresponding to an increase in the fraction of the He⁺⁺ phase from about 20% to 90% of the total helium. Further increases U result in only modest changes to the He⁺⁺ fraction but result in an increase in gas temperature. These higher temperatures change the value at which the He ii/Lyα ratio saturates. In particular, at higher temperatures, if both hydrogen and helium are completely ionized, the He ii/Lyα saturation value decreases (see Arrigoni Battaia et al. 2015).

Our photoionization models indicate that the C iv emission line is an important coolant and is powered primarily by collisional excitation. Figure 12 shows that our models span a much wider range in the C iv/Lyα (∼3 dex) ratio than in He ii/Lyα (≲2 dex). The strong evolution in C iv/Lyα results from a combination of two effects. First, increasing U increases the temperature of the gas, and the C iv collisional excitation rate coefficient has a strong temperature dependence (Groves et al. 2004). Second, the efficacy of C iv as a coolant depends on the amount of carbon in the C⁺³ ionic state. As logU increases from ≃−3.3 to ≃−2, the C⁺³ fraction increases from 1% to 37%. These two effects conspire to give rise to nearly three orders of magnitude of variation in the C iv emission.

From the left panel of Figure 12, it is clear that our optically thin models with solar metallicities populate the region below our most stringent upper limits (LAB1 and LAB2) only for very low U (logU ∼ −3.0), i.e., which means at very high density n_H ≳ 6 cm⁻³.¹⁷ These are models for which helium is not completely ionized, and thus low He ii/Lyα ratios are allowed. This result agrees with Cantalupo et al. (2014) and Arrigoni Battaia et al. (2015), who invoke the presence of dense clouds to explain the Lyα emission around the UM287 quasar in the optically thin regime. In a next paper we explore this scenario and understand the dependence of this density threshold on metallicity and on the luminosity of the central source.

On the other hand, the optically thick models (see right panel of Figure 12) can also populate the area below the upper limits for LAB1 and LAB2, namely, the lower part of the observed He ii/Lyα–C iv/Lyα diagram. Note that given the range of ${{L}_{{{\nu }_{{\rm LL}}}}}$ and n_H in our parameter grid, models with ${{N}_{{\rm H}}}={{10}^{18}}-{{10}^{19}}$ cm⁻² are never optically thick,¹⁸ which explains why we only show optically thick models with ${{N}_{{\rm H}}}={{10}^{20}},{{10}^{21}},{{10}^{22}}$ cm⁻². The bulk of these models reside on a sequence with almost constant He ii/Lyα (around He ii/Lyα = 0.04–0.05) for a wide range of C iv/Lyα, which is driven by variation in U. The models departing from this sequence are characterized by N_Hi slightly greater than 10^17.2 cm⁻², and they can thus be seen as a transition between the optically thick case and the optically thin case.

It is worth to stress here that some of the HzRGs show lower Lyα emission, and thus higher ratios in these plots, because of intervening neutral hydrogen (e.g., Wilman et al. 2004). It has been shown that this absorption is mainly caused by strong absorbers, i.e., N_Hi > 10¹⁸ cm⁻². For example, van Ojik et al. (1997) show that strong Hi absorption (${{10}^{18}}\;{\rm c}{{{\rm m}}^{-2}}\lt {{N}_{{\rm HI}}}\lt {{10}^{20}}\;{\rm c}{{{\rm m}}^{-2}}$) is found in 11 out of 18 sources in their sample. As we are not taking into account the absorption in our modeling and as we do not have complete information to correct the data for absorption, one needs to be cautious, particularly when comparing our models with the data of HzRGs.

To summarize, the photoionization models produce line ratios that are consistent with our upper limits and that span the values observed in the literature. In the next section we consider the degree to which shock powered emission can explain line ratios in Lyα nebulae.

Taniguchi & Shioya (2000) and Mori & Umemura (2006) have speculated that intense star formation accompanied by successive supernova explosions could power a large-scale galactic superwind, and radiation generated by overlapping shock fronts could power the Lyα emission in the LABs. However, it is well known that it is difficult to distinguish between photoionization and fast shocks using line ratio diagnostic diagrams (e.g., Allen et al. 1998). Furthermore, for AGN narrow-line regions, the Lyα line is typically avoided in these diagrams because of its resonant nature and the fact that it may be more likely to be destroyed by dust, although we have argued that it is not an issue for CGM gas. It is thus interesting to study how shock models populate the He ii/Lyα versus C iv/Lyα diagram in comparison with photoionization models and our observational limits.

To build intuition about the line ratios expected in a shock scenario, we rely on the modeling of fast shocks by Allen et al. (2008). We thus imagine the Lyα emission as the sum of overlapping shock fronts with shock velocity v_s, moving into a medium with preshock density ${{n}_{{\rm H}}}$. In the case of such shocks, Allen et al. (2008) showed that the Lyα emission depends strongly on v_s, i.e., ${{F}_{{\rm Ly}\alpha }}\propto {{n}_{{\rm H}}}v_{s}^{3}$ (their Table 6). In order to test a realistic set of parameters in the case of LABs, we limit the grid of models presented by Allen et al. (2008) to:

• 1.  
  ${{n}_{{\rm H}}}=0.01,0.1,1.0,10,100$ cm⁻³,
• 2.  
  shock velocities, v_s, from 100 to 1000 km s⁻¹ in steps of 25 km s⁻¹.

We consider only models with solar metallicity.¹⁹ The magnetic parameter B/n^1/2, where B is the magnetic field in μG, determines the relative strength of the thermal and magnetic pressure. We adopt a magnetic parameter B/n^1/2 = 3.23 μG cm^3/2, which represents a value expected for ISM gas assuming equipartition of magnetic and thermal energy. However, note that, given the very strong dependence of the ionizing flux on the shock velocity ${{F}_{{\rm UV}}}\propto v_{{\rm s}}^{3},$ the line ratios do not vary so markedly with either the metallicity or the magnetic field (see Allen et al. 2008 for further details).

In Figure 13 we show two sets of shock models. On the left, we plot the models for which the emission is coming solely from the shocked region, where the gas, moving at about v_s, is ionized and excited to high temperatures by the shock. Temperatures ahead of the shock front are of the order of 10⁴ K, whereas temperatures as high as 10⁶ K can be reached in the post-shock gas (Allen et al. 2008). On the right, we plot a combination of the emission coming from the shocked gas and from the "static" precursor, i.e., the pre-shock region, which is photoionized by the radiation emitted upstream from the shocked region. The trends of the models can be explained as follows. The models for the shock component (left panel of Figure 13) show a rapid decrease in the C iv/Lyα ratio for increasing v_s. This is due to a rapid increase in the Lyα line due to the strong scaling of the ionizing flux with ${{v}_{{\rm s}}},$ and to a decrease in the C iv line due to the lack of carbon in the C³⁺ phase for high velocities (i.e., carbon is in higher ionization species; see Figure 9 of Allen et al. 2008). The He ii/Lyα ratio depends more strongly on the gas density because n_H sets the volume of the shocked region and thus the recombination luminosity of helium, i.e., at fixed ${{v}_{{\rm s}}}$, a higher density corresponds to a smaller shocked volume and less helium emission (see Figure 6 of Allen et al. 2008).

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The combination of shock and precursor models mainly alters the ratios for models with high v_s (see right panel of Figure 13). This is because the precursor component is adding the contribution of a photoionized gas at temperature of the order of 10⁴ K, and the ionizing flux scales strongly with shock velocity ${{F}_{{\rm UV}}}\propto v_{{\rm s}}^{3}.$ For velocities v_s ≳ 400 km s⁻¹, the resulting hard radiation field results in a large fraction of double ionized helium He⁺⁺ over a significant volume of the precursor, significantly increasing the He ii emission and the He ii/Lyα ratio. This photoionized precursor similarly increases the abundance of the C³⁺ phase, giving rise to a higher C iv/Lyα ratio. Thus, adding the precursor contribution to the shock models causes the models to fold over each other at high velocities.

Figure 13 illustrates that the shock models with v_s > 250 km s⁻¹ are capable of populating the line ratio diagram below our tightest upper limits (i.e., LAB1 and LAB2) (see Figure 13). However, the shock velocities above ∼250 km s⁻¹ could be in potential disagreement with recent observations of outflow velocities (Yang et al. 2011, 2014a, 2014b). Using the velocity offset between the Lyα and the non-resonant [O iii] or Hα line, the offset of stacked interstellar metal absorption lines, and the [O iii] line profile, Yang et al. (2011, 2014b) find that the kinematics of gas along the line of sight to galaxies in LABs are consistent with a simple picture in which the gas is stationary or slowly outflowing at velocities of a few hundred km s⁻¹ from the embedded galaxies. In addition, Prescott et al. (2009) showed that the He ii line detected in an LAB at z = 1.67 is narrow: FWHM ≲ 500 km s⁻¹. Therefore, these observations seem to rule out the shock-only models (left panel of Figure 13), where the gas velocities, i.e., the observed velocities, are expected to be similar to the shock velocity v_s.

In the case of a combination of shock and precursor (right panel of Figure 13), the interpretation is more complicated. As we explained above, the emission from the precursor dominates the line ratios at v_s ≳ 250 km s⁻¹, where the models lie below our upper limits. As the precursor is static, if we are preferentially seeing this state of the gas, we would measure velocities lower than v_s. In this case, as the shock is behaving as a photoionizing source, it would be difficult to disentangle the combination of shock and precursor from the photoionization case. Furthermore, it is important to note that we are not taking into account any deceleration of the shock. A detailed modeling of a superposition of blast waves that are slowing down with time is beyond the scope of this work.

It is worth stressing again here that these models suffer from uncertainty in the Lyα calculation. In particular, the additional contribution from scattering is not taken into account, thus making the Lyα line weaker. As a consequence, these grids may be shifted to lower values on both axes. Note also that we fix the metallicity to the solar value. However, a decrease in the C iv emission is expected for sub-solar metallicity, weakening the constraints on the shock velocities. The trends with metallicity are beyond the scope of this work, and we are going to address them in a subsequent paper (F. Arrigoni Battaia et al. 2015, in preparation). Another caveat is that the line ratios of HzRGs can be biased because the absorption of Lyα due to the intervening hydrogen was not taken into account.

Thus, even though our models can give us a rough idea of the line emission in the shock scenario, these plots should be treated with caution.

As stated in the previous sections, rigorous modeling of photoionization of large Lyα nebulae in the context of LABs has never been performed. However, Prescott et al. (2009) reported a detection of extended He ii and modeled simple, constant density gas clouds assuming illumination from an AGN, Pop III, and Pop II stars. They are not quoting all the parameters of their Cloudy models (e.g., N_H), and thus it is not possible to make a direct comparison. However, they found that the data are in agreement with photoionization from a hard ionizing source, due to either an AGN or a very low metallicity stellar population ($Z\lt {{10}^{-2}}{\rm to}{{10}^{-3}}{{Z}_{\odot }}$). They conclude that, in the case of an AGN, this source must be highly obscured along the line of sight. They also showed that their observed ratios are inconsistent with shock ionization in solar metallicity gas.

On smaller scales, photoionization has been modeled in the case of EELRs of HzRGs. In particular, Humphrey et al. (2008), using the code MAPPINGS Ic (Binette et al. 1985), shows that the data are best described by AGN photoionization with the ionization parameter U varying between objects, in a range comparable with our grid. However, they found that a single-slab photoionization model is unable to explain adequately the high-ionization (e.g., N v) and low-ionization (e.g., C ii], [N ii], [O ii]) lines simultaneously, with higher U favored by the higher ionization lines. They also demonstrated that shock models alone are overall worse than photoionization models in reproducing HzRGs data. In the shock scenario an additional source of ionizing photons is required, i.e., the obscured AGN, in order to match most of the line ratios studied by Humphrey et al. (2008). However, note that shocks with precursor models can explain some ratios, e.g., N v/N iv], which are hardly explained by a single-slab photoionization model (Humphrey et al. 2008).