DEEP HE ii AND C iv SPECTROSCOPY OF A GIANT LYα NEBULA: DENSE COMPACT GAS CLUMPS IN THE CIRCUMGALACTIC MEDIUM OF A z ∼ 2 QUASAR^*

In the modern astrophysical lexicon, the intergalactic medium (IGM) is the diffuse medium tracing the large-scale structure in the universe, while the so-called circumgalactic medium (CGM) is the material on smaller scales within galactic halos (r ≲ 200 kpc), for which nonlinear processes and the complex interplay between all mechanisms that lead to galaxy formation take place.

Whether one is studying the IGM or the CGM, for decades the preferred technique for characterizing such gas has been the analysis of absorption features along background sightlines (e.g., Croft et al. 2002; Bergeron et al. 2004; Hennawi et al. 2006; Hennawi & Prochaska 2007, 2013; Prochaska & Hennawi 2009; Rudie et al. 2012; Farina et al. 2013; Prochaska et al. 2013a, 2013b; Lee et al. 2014). However, as the absorption studies are limited by the rarity of suitably bright background sources near galaxies, and to the one-dimensional information that they provide, they need to be complemented by the direct observation of the medium in emission.

In particular, it has been shown that UV background radiation could be reprocessed by these media and be detectable as fluorescent Lyα emission (Hogan & Weymann 1987; Binette et al. 1993; Gould & Weinberg 1996; Cantalupo et al. 2005). However, current facilities are still not capable of revealing such low radiation levels, e.g., an expected surface brightness (SB) of the order of SB_Lyα ∼ 10⁻²⁰ erg s⁻¹ cm⁻² arcsec⁻² (see, e.g., Rauch et al. 2008). Nonetheless, this signal can be boosted to observable levels by the intense ionizing flux of a nearby quasar which, like a flashlight, illuminates the gas in its surroundings (Rees 1988; Haiman & Rees 2001; Alam & Miralda-Escudé 2002; Cantalupo et al. 2012), shedding light on its physical nature.

Detecting this fluorescence signal has been a subject of significant interest, and several studies which specifically searched for emission from the IGM in the proximity to a quasar (e.g., Fynbo et al. 1999; Francis & Bland-Hawthorn 2004; Cantalupo et al. 2007; Rauch et al. 2008; Hennawi & Prochaska 2013) thus far do not have a straightforward interpretation. However, recently Cantalupo et al. (2012) identified a population of compact Lyα emitters with rest-frame equivalent widths exceeding the maximum value expected from star-formation, ${\mathrm{EW}}_{0}^{\mathrm{Ly}\alpha }\gt 240$ Å (e.g., Charlot & Fall 1993), which are the best candidates to date for fluorescent emission powered by a proximate quasar.

Besides illuminating nearby clouds in the IGM, a quasar may irradiate gas in its own host galaxy or CGM. A number of studies have reported the detection of extended Lyα emission in the vicinity of z ∼ 2–4 quasars (e.g., Hu & Cowie 1987; Heckman et al. 1991a, 1991b; Christensen et al. 2006; Hennawi et al. 2009; North et al. 2012), but detailed comparison is hampered by the different methodologies of these studies. Although extended Lyα nebulae on scales of ∼100 kpc (up to 250 kpc) have been observed around high-redshift radio galaxies (HzRGs; e.g., McCarthy 1993; van Ojik et al. 1997; Reuland et al. 2003, 2007; Villar-Martín et al. 2003a, 2003b; Miley & De Breuck 2008), these objects have the additional complication of the interaction between the powerful radio jets and the ambient medium, complicating the interpretation of the observations. Nebulae of comparable size and luminosity have similarly been observed in a distinct population of objects known as "Lyα blobs" (LABs; e.g., Steidel et al. 2000; Matsuda et al. 2004; Dey et al. 2005; Geach et al. 2007; Smith & Jarvis 2007; Prescott et al. 2009; Yang et al. 2011, 2012, 2014; Arrigoni Battaia et al. 2015), which do not show direct evidence for an active galactic nucleus (AGN). Despite increasing evidence that the LABs are also frequently associated with obscured AGNs (Geach et al. 2009; Overzier et al. 2013; Prescott et al. 2015b; although lacking powerful radio jets), the mechanism powering their emission remains controversial with at least four proposed which may even act together: (i) photoionization by a central obscured AGN (Geach et al. 2009; Overzier et al. 2013), (ii) shock-heated gas by galactic superwinds (Taniguchi et al. 2001), (iii) cooling radiation from cold-mode accretion (e.g., Fardal et al. 2001; Yang et al. 2006; Faucher-Giguère et al. 2010; Rosdahl & Blaizot 2012), and (iv) resonant scattering of Lyα from star-forming galaxies (Dijkstra & Loeb 2008; Hayes et al. 2011; Cen & Zheng 2013).

The largest and most luminous Lyα nebula known is that around the quasar UM287 (i-mag = 17.28) at z = 2.279, recently discovered by Cantalupo et al. (2014) in a narrow-band imaging survey of hyper-luminous quasars (Arrigoni Battaia et al. 2014). Its size of 460 kpc and average Lyα SB of ${\mathrm{SB}}_{\mathrm{Ly}\alpha }=6.0\times {10}^{-18}$ erg s⁻¹ cm⁻² arcsec⁻² (from the 2σ isophote), which corresponds to a total luminosity of L_Lyα = (2.2 ± 0.2) × 10⁴⁴ erg s⁻¹, make it the largest reservoir (M_c ∼ 10¹² M_⊙) of cool (T ∼ 10⁴ K) gas ever observed around a QSO. The emission has been explained as recombination and/or scattering emission from the central quasar and has been regarded as the first direct detection of a cosmic web filament (Cantalupo et al. 2014).

However, as discussed in Cantalupo et al. (2014), Lyα emission alone does not allow us to break the degeneracy between the clumpiness or density of the gas and the total gas mass. Indeed, in the scenario where the nebula is ionized by the quasar radiation, the total cool gas mass scales as ${M}_{{\rm{c}}}\sim {10}^{12}{C}^{-1/2}$ M_⊙, where $C=\langle {n}_{{\rm{H}}}^{2}\rangle /\langle {n}_{{\rm{H}}}{\rangle }^{2}$ is a clumping factor introduced by Cantalupo et al. (2014) to account for the possibility of higher density gas unresolved by the cosmological simulation used to model the emission. Thus, if one assumes C = 1, the implied cool gas mass in the extended nebula is exceptionally high for the expected dark matter halo inhabited by a z ∼ 2−3 quasar, i.e., ${M}_{\mathrm{DM}}={10}^{12.5}$ M_⊙ (White et al. 2012). This is further aggravated by the fact that current cosmological simulations show that only a small fraction (∼15%, Cantalupo et al. 2014; Faucher-Giguere et al. 2015; Fumagalli et al. 2014) of the total baryons reside in a phase ($T\lt 5\times {10}^{4}$ K) sufficiently cool to emit in the Lyα line. A possible solution to this discrepancy would be to assume a very high clumping factor up to C ≃ 1000, which would then imply a large population of cool, dense clouds in the CGM and extending into the IGM, which are unresolved by current cosmological simulations (Cantalupo et al. 2014).

Both of these scenarios, whether it be too much cool gas or a large population of dense clumps, are reminiscent of a similar problem that has emerged from absorption line studies of the quasar CGM (Hennawi et al. 2006; Hennawi & Prochaska 2007; Prochaska & Hennawi 2009; Prochaska et al. 2013a, 2013b, 2014). This work reveals substantial reservoirs of cool gas $\gtrsim {10}^{10}$ M_⊙, manifest as a high covering factor ≃50% of optically thick absorption, several times larger than predicted by hydrodynamical simulations (Faucher-Giguere et al. 2015; Fumagalli et al. 2014). This conflict most likely indicates that current simulations fail to capture essential aspects of the hydrodynamics in massive halos at z ∼ 2 (Prochaska et al. 2013b; Fumagalli et al. 2014), perhaps failing to resolve the formation of clumpy structure in cool gas, which in the most extreme cases give rise to giant nebulae like UM287.

In an effort to better understand the mechanism powering the emission in UM287, and further constrain the physical properties of the emitting gas, this paper presents the result of a sensitive search for emission in two additional diagnostics, namely He iiλ1640 Å⁶ and C iv λ1549 Å. The detection of either of these high-ionization emission lines in the extended nebula would indicate that the nebula is "illuminated" by an intense source of hard ionizing photons E ≳ 4 Ryd, and would thus establish that photoionization by the quasar is the primary mechanism powering the giant Lyα nebula. As we will show in this work, in a photoionization scenario where He ii emission results from recombinations, the strength of this line is sensitive to the density of the gas in the nebula, which can thus break the degeneracy between gas density and gas mass described above. In addition, because He ii is not a resonant line, a comparison of its morphology and kinematics to the Lyα line can be used to test whether Lyα photons are resonantly scattered. On the other hand, a detection of extended emission in the C iv line can provide us information on the metallicity of the gas in the CGM, and simultaneously constrain the size at which the halo is metal-enriched. To interpret our observational results, we exploit the models presented by Hennawi & Prochaska (2013) and already used in the context of extended Lyα nebulae (i.e., LABs) in Arrigoni Battaia et al. (2015), and show how a sensitive search for diffuse emission in Lyα and additional diagnostic lines can be used to constrain the physical properties of the quasar CGM.

This paper is organized as follows. In Section 2, we describe our deep spectroscopic observations, the data reduction procedures, and the SB limits of our data. In Section 3, we present our constraints on emission in the C iv and He ii lines, and our analysis of the kinematics of the Lyα line. In Section 4, we present the photoionization models for UM287 and in Section 5 we compare them with our observational results and with absorption spectroscopic studies (Sections 5.1 and 5.2). In Section 6, we discuss which other lines might be observable with current facilities. In Section 7, we further discuss some of the assumptions made in our modeling. Finally, Section 8 summarizes our conclusions.

Throughout this paper, we adopt the cosmological parameters H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_M = 0.3, and Ω_Λ = 0.7. In this cosmology, 1'' corresponds to 8.2 physical kpc at z = 2.279. All magnitudes are in the AB system (Oke 1974).

Two moderate resolution (FWHM ∼ 300 km s⁻¹) spectra of the UM287 nebula were obtained using the Low Resolution Imaging Spectrograph (LRIS; Oke et al. 1995) on the Keck I telescope on UT 2013 August 4, in multi-slit mode with custom-designed slitmasks. We used the 600 lines mm⁻¹ grism blazed at 4000 Å on the blue side, resulting in wavelength coverage of ≈3300−5880 Å, which allows us to cover the location of the C iv and He ii lines. The dispersion of this grism is ∼4 Å per pixel and our 1'' slit give a resolution of FWHM ≃ 300 km s⁻¹. We observed each mask for a total of ∼2 hr in a series of four exposures.

Figure 1 shows the position of the two 1''-slits (red and blue) on top of the narrow-band image (matching the Lyα line at the redshift of UM287) presented by Cantalupo et al. (2014). We remind the reader that Cantalupo et al. (2014) found an optically faint (V = 21.54 ± 0.06) radio-loud quasar ("QSO b") at the same redshift and at a projected distant of 24.3 arcsec (∼200 kpc) from the bright UM287 quasar ("QSO a"). The first slit orientations was chosen to simultaneously cover the extended Lyα emission and the UM287 quasar (blue slit), whereas the second (red slit) was chosen to cover the companion quasar "b" together with the diffuse nebula. By covering one of the quasars with each slit orientation we are thus able to cleanly subtract the point-spread function (PSF) of the quasars from our data (see Section 3).

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The two-dimensional (2D) spectroscopic data reduction is performed exactly as described in Hennawi & Prochaska (2013) and we refer the reader to that work for additional details. In what follows, we briefly summarize the key elements of the data reduction procedure. All data were reduced using the LowRedux pipeline,⁷ which is a publicly available collection of custom codes written in the IDL for reducing slit spectroscopy. Individual exposures are processed using standard techniques, namely they are overscan and bias subtracted and flat fielded. Cosmic rays and bad pixels are identified and masked in multiple steps. Wavelength solutions are determined from low order polynomial fits to arc lamp spectra, and then a wavelength map is obtained by tracing the spatial trajectory of arc lines across each slit.

We then perform the sky- and PSF-subtraction as a coupled problem, using a novel custom algorithm that we briefly summarize here (see Hennawi & Prochaska 2013 for additional details). We adopt an iterative procedure, which allows us to obtain the sky background, the 2D spectrum of each object, and the noise, as follows. First, we identify objects in an initial sky-subtracted image⁸  and trace their trajectories across the detector. We then extract a one-dimensional (1D) spectrum, normalize these sky-subtracted images by the total extracted flux, and fit a B-spline profile to the normalized spatial light profile of each object relative to the position of its trace. Given this set of 2D basis functions, i.e., the flat sky and the object model profiles, we then minimize chi-squared for the best set of spectral B-spline coefficients which are the spectral amplitudes of each basis component of the 2D model. The results of this procedure are then full 2D models of the sky background, all object spectra, and the noise (σ²). We then use this model sky to update the sky-subtraction, the individual object profiles are re-fit and the basis functions updated, and chi-square fitting is repeated. We iterate this procedure of object profile fitting and subsequent chi-squared modeling four times until we arrived at our final models.

For each slit, each exposure is modeled according to the above procedure, allowing us to subtract both the sky and the PSF of the quasars. These images are registered to a common frame by applying integer pixel shifts (to avoid correlating errors), and are then combined to form final 2D stacked sky-subtracted and sky-and-PSF-subtracted images. The individual 2D frames are optimally weighted by the ${({\rm{S}}/{\rm{N}})}^{2}$ of their extracted 1D spectra. The final results of our data analysis are three images: (1) an optimally weighted average sky-subtracted image, (2) an optimally weighted average sky-and-PSF-subtracted image, and (3) the noise model for these images σ². The final noise map is propagated from the individual noise model images taking into account weighting and pixel masking entirely self-consistently.

Finally, we flux-calibrate our data following the procedure in Hennawi & Prochaska (2013). As standard star spectra were not typically taken immediately before/after our observations, we apply an archived sensitivity function for the LRIS B600/4000 grism to the 1D extracted quasar spectrum for each slit, and then integrate the flux-calibrated spectrum against the SDSS g-band filter curve. The sensitivity function is then rescaled to yield the correct SDSS g-band photometry. Since the faint quasar is not clearly detected in SDSS, we only used the g-band magnitude of the UM287 quasar to calculate this correction. Note that this procedure is effective for point-source flux-calibration because it allows us to account for the typical slit-losses that affect a point source. However, this procedure will tend to underestimate our sensitivity to extended emission, which is not affected by these slit-losses. Hence, our procedure is to apply the rescaled sensitivity functions (based on point source photometry) to our 2D images, but reduce them by a geometric slit-loss factor so that we properly treat extended emission. To compute the slit-losses, we use the measured spatial FWHM to determine the fraction of light going through our 10 slits, but we do not model centering errors (see Section 3 for a test of our calibration, and see Hennawi & Prochaska 2013 for more details).

Given this flux calibration, the 1σ SB limit of our observations are SB_1σ = 1.3 × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² and SB_1σ = 1.5 × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻² for C iv and He ii, respectively. This limits are obtained by averaging over a 3000 km s⁻¹ velocity interval, i.e., ±1500 km s⁻¹ on either side of the systemic redshift of the UM287 quasar, i.e., z = 2.279 ± 0.001 (McIntosh et al. 1999), at the C iv and He ii locations, and a 1'' × 1'' aperture.⁹ This limits (approximately independent of wavelength) are about 3× the 1σ limit in 1 arcsec² quoted by Cantalupo et al. (2014) for their ∼10 hr narrow-band exposure targeting the Lyα line, i.e., 5 × 10⁻¹⁹ erg s⁻¹ cm⁻² arcsec⁻².¹⁰ Note that we choose this velocity range to enclose all the extended Lyα emission, even after smoothing (see Section 3), and because the narrow-band image of Cantalupo et al. (2014) covers approximately this width, i.e., ${\rm{\Delta }}v\sim 2400$ km s⁻¹.

Further, it is important to stress here that the line ratios we use in this work are only from the spectroscopic data (we do not use the NB data for the Lyα line), and hence they are independent of any errors in the absolute calibration. Although we do not use the NB data in our analysis, we show in the next section that our results are consistent with the NB imaging and are thus robustly calibrated.

Following Hennawi & Prochaska (2013), we search for extended Lyα, C iv, and He ii emission by constructing a χ image

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}^{{N}_{\mathrm{pix}}}\;\displaystyle \frac{{({\mathrm{DATA}}_{i}-{\mathrm{MODEL}}_{i})}^{2}}{{\sigma }_{i}^{2}}\end{eqnarray} \tag{ 1 }$$

where the sum is taken over all N_pix pixels in the image, "DATA" is the image, "MODEL" is a linear combination of 2D basis functions multiplied by B-spline spectral amplitudes, and σ is a model of the noise in the spectrum, i.e., ${\sigma }^{2}=\mathrm{SKY}+\mathrm{OBJECTS}+\mathrm{READNOISE}$. The "MODEL" and the σ² are obtained during our data reduction procedure (see Section 2 and Hennawi & Prochaska 2013 for details).

Figures 2 and 3 show the 2D spectra for the slits in Figure 1 plotted as χ-maps. Note that if our noise model is an accurate description of the data, the distribution of pixel values in the χ-maps should be a Gaussian with unit variance. In these images, emission will be manifest as residual flux, inconsistent with being Gaussian-distributed noise. The bottom row of each figure shows the χ_sky map (only sky-subtracted) at the location of the Lyα, C iv, and He ii, respectively. Even in these unsmoothed data the extended Lyα emission is clearly visible up to ∼200 kpc (∼24'') from "QSO b" along the "red" slit (Figure 2). This emission has SB_Lyα = (6.3 ± 0.4) × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻², calculated in a 1'' × 20'' aperture¹¹ and over a 3000 km s⁻¹ velocity interval (blue box in Figure 2). This value is in agreement with the emission detected in the continuum-subtracted image presented in Cantalupo et al. (2014) within a 1'' × 20'' aperture at the same position within the slit, i.e., SB_Lyα = (7.0 ± 0.1) × 10⁻¹⁸ erg s⁻¹ cm⁻² arcsec⁻². Along the "blue" slit, the extended emission is inevitably mixed with the PSF of the hyper-luminous UM287 QSO, making PSF subtraction much more challenging. Nevertheless, we compute the emission in the extended Lyα line in an aperture of about 1'' × 13'' aperture (from 40 to 150 kpc) and within 3000 km s⁻¹, after subtracting the PSF of the quasar (see Figure 3). Again, we find that SB measured from spectroscopy (SB${}_{\mathrm{Ly}\alpha }=1.4\times {10}^{-17}$ erg s⁻¹ cm⁻² arcsec⁻²), and from narrow-band imaging (SB_Lyα = 1.7 × 10⁻¹⁷ erg s⁻¹ cm⁻² arcsec⁻²) agree within the uncertainties.¹² The agreement between the Lyα spectroscopic and narrow-band imaging SBs for both slit orientations confirm that our spectroscopic calibration procedure is robust.

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We do not detect any extended emission in either the C iv or the He ii lines for either of the slit orientations. To better visualize the presence of extended emission, we first subtract the PSF of the QSOs for each position angle (see the middle rows in Figures 2 and 3), and finally we show in the upper rows the smoothed ${\chi }_{\mathrm{smth}}$ maps. These smoothed maps are of great assistance in identifying faint extended emission (see Hennawi & Prochaska 2013 for more details on the PSF-subtraction and the calculation of the smoothed χ-maps). The lack of compelling emission features in the PSF-subtracted smoothed maps confirm the absence of extended C iv and He ii at our sensitivity limits in both slit orientations.

As our goal is to measure line ratios between the Lyα emission and the C iv and He ii lines, we compute the SB limits within the same aperture in which we calculated the Lyα emission along the "red" slit, i.e., 1'' × 20'' and ${\rm{\Delta }}v=3000$ km s⁻¹. Because the companion quasar is much fainter than the UM287 quasar, the PSF-subtraction along the "red" slit does not suffer from systematics, whereas the large residuals in the left panel of Figure 3 indicate that there are significant PSF-subtraction systematics for the Lyα emission in the "blue" slit covering the UM287 quasar. We have thus decided to focus on the line ratios obtained from the "red" slit, although the constraints we obtain from the "blue" slit are comparable. We find ${\mathrm{SB}}_{1\sigma ,{\rm{C}}\;{\rm{IV}}}^{A=20}=3.3\times {10}^{-19}$ erg s⁻¹ cm⁻² arcsec⁻² and ${\mathrm{SB}}_{1\sigma ,\mathrm{He}\;{\rm{II}}}^{A=20}=3.7\times {10}^{-19}$ erg s⁻¹ cm⁻² arcsec⁻², respectively, at the C iv and He ii locations.

To better understand how well we can recover emission in the He ii and C iv lines in comparison to the Lyα, we visually estimate the detectability of extended emission in these lines by inserting fake sources as follows. First, we select the Lyα emission above its local 1σ limit along the "red" slit, we smooth it, and scale it to be 1, 2, 3, and 5 × ${\mathrm{SB}}_{1\sigma }^{A=20}$ at the location of the He ii and C iv lines. Finally, we add Poisson realizations of these scaled models into our 2D PSF- and sky-subtracted images. In Figure 4, we show the χ-maps for this test at the location of He ii. This test suggests that we should be able to clearly detect extended emission on the same scale as the Lyα line if the source is ≳3 × ${\mathrm{SB}}_{1\sigma }^{A=20}$. Thus, in the remainder of the paper we use 3σ (σ ≡ SB${}_{1\sigma }^{A=20}$) upper limits on the He ii/Lyα and C iv/Lyα ratios. Given the values for the ${\mathrm{SB}}_{\mathrm{Ly}\alpha }$ and the SB limits at the location of the C iv and He ii lines (within the 1'' × 20'' aperture and 3000 km s⁻¹ velocity window for the red slit), we get (He ii/Lyα)${}_{3\sigma }\lesssim 0.18$ and (C iv/Lyα)${}_{3\sigma }\lesssim 0.16$. Note that given the brighter Lyα emission at the location of the "blue" slit, the limits implied are about two times lower than these quoted limits for the "red" slit.

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It is important to note that we detect extended C iv emission around the faint companion quasar "b" (see the smoothed maps in Figure 2). As this line is physically distinct from the UM287 nebula and essentially follows the extended Lyα emission around the faint quasar (compare the smoothed maps for Lyα and C iv), this suggests that we have detected the extended narrow emission line region (EELR) of this source. This kind of emission, produced by the gas excited by an AGN on scales of tens of kiloparsecs, is usually observed around low redshift z < 0.5 type I (e.g., Stockton et al. 2006; Husemann et al. 2013) and type II quasars (e.g., Greene et al. 2011), traced by [O iii] and Balmer lines. We do not quote a value for the emission because, given the much smaller scales in play here, its accuracy depends on the PSF-subtraction. However note that this detection, near the limit of our sensitivity, clearly demonstrates that we could have detected faint extended emission in the C iv and He ii lines within the Lyα nebula itself if this emission were characterized by higher line ratios.

Finally, we briefly comment on the nature of two other sources which fall within the "red" slit, i.e., a Lyman alpha emitter (LAE; i.e., ${\mathrm{EW}}_{\mathrm{Ly}\alpha }^{\mathrm{rest}}\gt 20$ Å) and a continuum source (see Figure 2). Indeed, this slit orientation was also chosen to confirm the presence of a LAE at about 350 kpc northward of "QSO b", clearly visible in the narrow-band image in Figure 2 of Cantalupo et al. (2014) and in our Figure 1. Our LRIS data confirm the presence of a line emission from a LAE at a redshift z = 2.280 ± 0.002, which is consistent with the redshift of the UM287 quasar, within our uncertainties. We ascribe this emission to the Lyα line, and we compute a flux of F_Lyα = (9.2 ± 0.9) × 10⁻¹⁸ erg s⁻¹ cm⁻² (in an aperture of ${\rm{\Delta }}v=1400$ km s⁻¹ and 4 arcsec²), in agreement with F_Lyα = (8.4 ± 0.4) × 10⁻¹⁸ erg s⁻¹ cm⁻² computed in an aperture of 4 arcsec² in the map of Cantalupo et al. (2014). We also serendipitously obtained a spectrum of a source at ∼230 kpc from quasar "b", which coincides with a continuum sources in our deep V-band image (Cantalupo et al. 2014). In our 2D spectrum, we detect a faint continuum associated with this source and an emission line at a wavelength of 5123 Å, which appears at a velocity ∼2750 km s⁻¹ from the C iv line in the right panel of Figure 2. However, given the low signal-to-noise ratio (S/N) of the continuum and the detection of a single emission line, we are unable to determine the redshift of this source.

3.1. Kinematics of the Nebula

As shown by Cantalupo et al. (2014), the extended Lyα emission nebula around UM287 can be explained by photoionization from the central quasar, implying a large amount of cool (T ∼ 10⁴ K) gas, i.e., ${M}_{{\rm{c}}}\simeq {10}^{12}\;{C}^{-1/2}$ M_⊙. To further constrain the properties of the gas in this huge nebula, in this section we exploit the simple model for cool clouds in a quasar halo introduced by Hennawi & Prochaska (2013) and the consequent photoionization modeling procedure introduced by Arrigoni Battaia et al. (2015). Our main goal is to show how our line ratio constraints on C iv/Lyα and He ii/Lyα can be used to constrain the physical properties of the gas in the UM287 nebula, such as the volume density (n_H), column density (${N}_{{\rm{H}}}$), and gas metallicity (Z).

As in our previous work (Cantalupo et al. 2014), we reiterate that modeling the Lyα emission alone cannot break the degeneracy between the clumpiness or density of the gas and the total gas mass. In the next sections, we show how information on additional lines (in particular He ii) can constrain the density of the emitting gas and thus break this degeneracy.

4.1. Photoionization Modeling

In the following, we briefly outline the simple model for cool halo gas introduced by Hennawi & Prochaska (2013) for the case of UM287. We assume a simple picture where UM287 has a spherical halo populated with spherical clouds of cool gas (T ∼ 10⁴ K) at a single uniform hydrogen volume density ${n}_{{\rm{H}}}$, and uniformly distributed throughout the halo. We model a scale length of R = 160 kpc from the central quasar, which approximately corresponds to the distance probed by the "red" slit, and represents the expected virial radius for a dark matter halo hosting a quasar at this redshift. In this configuration, the spatial distribution of the gas is completely specified by n_H, R, the hydrogen column density N_H, and the cloud covering factor f_C.

Note that the total mass of cool gas in our simple model can be written as (Hennawi & Prochaska 2013):

$$\begin{eqnarray}{M}_{{\rm{c}}} & = & \pi {R}^{2}{f}_{{\rm{C}}}{N}_{{\rm{H}}}\displaystyle \frac{{m}_{{\rm{p}}}}{X}\\ & = & 2.7\times {10}^{10}{(\displaystyle \frac{R}{160\;\mathrm{kpc}})}^{2}(\displaystyle \frac{{N}_{{\rm{H}}}}{{10}^{19.5}\;{\mathrm{cm}}^{-2}})(\displaystyle \frac{{f}_{{\rm{C}}}}{1.0})\;{M}_{\odot }\end{eqnarray} \tag{ 2 }$$

where m_p is the mass of the proton and X is the hydrogen mass fraction.

In this simple model, the Lyα SB is determined by simple relations which depend only on n_H, N_H, f_C, and the luminosity of the QSO at the Lyman limit (${L}_{{\nu }_{\mathrm{LL}}}$; see Hennawi & Prochaska 2013 for details). To build intuition, it is useful to consider two limiting regimes for the recombination emission, for which the clouds are optically thin (${N}_{\mathrm{HI}}\ll {10}^{17.2}$ cm⁻²) and optically thick (${N}_{\mathrm{HI}}\gg {10}^{17.2}$ cm⁻²) to the Lyman continuum photons, where N_HI is the neutral column density of a single spherical cloud. We argue below that given the luminosity of the UM287 quasar, the optically thick case is however unrealistic.

• 1.  
  Optically thin to the ionizing radiation:

  $$\begin{eqnarray}&&{\mathrm{SB}}_{\mathrm{Ly}\alpha }^{\mathrm{thin}}=\displaystyle \frac{{\eta }_{\mathrm{thin}}h{\nu }_{\mathrm{Ly}\alpha }}{4\pi {(1+z)}^{4}}{\alpha }_{{\rm{A}}}(1+\displaystyle \frac{Y}{2X}){n}_{{\rm{H}}}{f}_{{\rm{C}}}{N}_{{\rm{H}}},\end{eqnarray} \tag{ 3 }$$

  where ${\eta }_{\mathrm{thin}}=0.42$ is the fraction of recombinations which result in a Lyα photon in the optically thin limit (Osterbrock & Ferland 2006), h is the Planck constant, ${\nu }_{\mathrm{Ly}\alpha }$ is the frequency of the Lyα line, ${\alpha }_{{\rm{A}}}=4.18\times {10}^{-13}\;{\mathrm{cm}}^{-3}\;{{\rm{s}}}^{-1}$ is the case A recombination coefficient at T = 10,000 K (Osterbrock & Ferland 2006),¹³ and X = 0.76 and Y = 0.24 are the respective hydrogen and helium mass fractions implied by Big Bang Nucleosynthesis (Boesgaard & Steigman 1985; Izotov et al. 1999; Iocco et al. 2009; Planck Collaboration et al. 2014).
• 2.  
  Optically thick to the ionizing radiation

  $$\begin{eqnarray}&&{\mathrm{SB}}_{\mathrm{Ly}\alpha }^{\mathrm{thick}}=\displaystyle \frac{{\eta }_{\mathrm{thick}}h{\nu }_{\mathrm{Ly}\alpha }}{4\pi {(1+z)}^{4}}{f}_{{\rm{C}}}{{\rm{\Phi }}}_{\mathrm{LL}}(R/\sqrt{3}),\end{eqnarray} \tag{ 4 }$$

  where ${\eta }_{\mathrm{thick}}=0.66$ is the fraction of ionizing photons converted into Lyα photons, and where ${{\rm{\Phi }}}_{\mathrm{LL}}([\mathrm{phot}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2}])$ is the ionizing photon number flux,

  $$\begin{eqnarray}&&{{\rm{\Phi }}}_{\mathrm{LL}}={\displaystyle \int }_{{\nu }_{\mathrm{LL}}}^{\infty }\displaystyle \frac{{F}_{\nu }}{h\nu }d\nu =\displaystyle \frac{1}{4\pi {r}^{2}}{\displaystyle \int }_{{\nu }_{\mathrm{LL}}}^{\infty }\displaystyle \frac{{L}_{\nu }}{h\nu }d\nu .\end{eqnarray} \tag{ 5 }$$

Thus, in the optically thick case the Lyα SB scales with the luminosity of the central source, ${\mathrm{SB}}_{\mathrm{Ly}\alpha }^{\mathrm{thick}}\propto {f}_{C}{L}_{{\nu }_{\mathrm{LL}}}$, while in the optically thin regime the SB does not depend on ${L}_{{\nu }_{\mathrm{LL}}}$, ${\mathrm{SB}}_{\mathrm{Ly}\alpha }^{\mathrm{thin}}\propto {f}_{{\rm{C}}}{n}_{{\rm{H}}}{N}_{{\rm{H}}}$, provided the AGN is bright enough to keep the gas in the halo ionized enough to be optically thin.

We now argue that the Lyα emitting gas is unlikely to be optically thick N_HI ≳ 10^17.2 cm⁻². Equations (4) and (5) can be combined to express the SB in terms of ${L}_{{\nu }_{\mathrm{LL}}}$, the luminosity at the Lyman edge. To compute this luminosity, we assume that the quasar spectral energy distribution (SED) obeys the power-law form ${L}_{\nu }={L}_{{\nu }_{\mathrm{LL}}}{(\nu /{\nu }_{\mathrm{LL}})}^{{\alpha }_{\mathrm{UV}}}$, blueward of ${\nu }_{\mathrm{LL}}$ and adopt a slope of α_UV = −1.7 consistent with the measurements of Lusso et al. (2015). The quasar ionizing luminosity is then parameterized by ${L}_{{\nu }_{\mathrm{LL}}}$, the specific luminosity at the Lyman edge.¹⁴ We determine the normalization ${L}_{{\nu }_{\mathrm{LL}}}$ by integrating the Lusso et al. (2015) composite spectrum against the SDSS filter curve, and choosing the amplitude to give the correct i-band magnitude of the UM287 quasar (i-mag = 17.28), which gives a value of ${L}_{{\nu }_{\mathrm{LL}}}=5.4\times {10}^{31}$ erg s⁻¹ Hz⁻¹.

Substituting this value of ${L}_{{\nu }_{\mathrm{LL}}}$ for UM287 into Equation (4), we thus obtain

$$\begin{eqnarray}{\mathrm{SB}}_{\mathrm{Ly}\alpha }^{\mathrm{thick}} & = & 8.8\times {10}^{-16}{(\displaystyle \frac{1+z}{3.279})}^{-4}(\displaystyle \frac{{f}_{{\rm{C}}}}{1.0}){(\displaystyle \frac{R}{160\;\mathrm{kpc}})}^{-2}\\ & & \times (\displaystyle \frac{{L}_{{\nu }_{\mathrm{LL}}}}{{10}^{31.73}\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{Hz}}^{-1}})\;\mathrm{erg}\;{{\rm{s}}}^{-1}\;{\mathrm{cm}}^{-2}\;{\mathrm{arcsec}}^{-2}.\end{eqnarray} \tag{ 6 }$$

This value is over two orders of magnitude larger than the observed SB value of the Lyα emission at 160 kpc from UM287. Even if we consider a larger radius, R = 250 kpc, in order to get the observed ${\mathrm{SB}}_{\mathrm{Ly}\alpha }$, we would need a very low covering factor, i.e., ${f}_{{\rm{C}}}\sim 0.02$. Such a small covering factor would be strictly at odds with the observed smooth morphology of the diffuse nebula as seen in Figure 1. We directly test this assumption as follows. We randomly populate an area comparable to the extent of the Lyα nebula with point sources such that f_C = 0.1–1.0, and we convolve the images with a Gaussian kernel with a FWHM equal to our seeing value in order to mimic the effect of seeing in the observations. We find that the smooth morphology observed cannot be reproduced by images with ${f}_{{\rm{C}}}\lt 0.5$, as they appear too clumpy. Thus, the smooth morphology of the emission in the Lyα nebula implies a covering factor of f_C ≳ 0.5.

In the following sections, we construct photoionization models for a grid of parameters governing the physical properties of the gas to estimate the expected He ii and C iv emission. Following the discussion here, we shall see that the models that reproduce the observed Lyα SB will be optically thin because, given the high covering factor, optically thick models would be too bright.

4.2. The Impact of Resonant Scattering

4.3. Modeling the UM287 Quasar SED

We assume that the SED of UM287 has the form shown in Figure 5. As we do not have complete coverage of the spectrum of this quasar, we adopt the following assumptions to model the full SED. 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 47.9 eV for C iv, we have decided to stick to power-law approximations above 1 Ryd. However, note that the UV range of the SED is so far not well constrained (see Lusso et al. 2015 and references therein). In particular, we model the quasar SED using a composite quasar spectrum which has been corrected for IGM absorption (Lusso et al. 2015). This IGM-corrected composite is important because it allows us to relate the i-band magnitude of the UM287 quasar to the specific luminosity at the Lyman limit ${L}_{{\nu }_{\mathrm{LL}}}$. For energies greater than 1 Rydberg, we assume a power-law form ${L}_{\nu }={L}_{{\nu }_{\mathrm{LL}}}{(\nu /{\nu }_{\mathrm{LL}})}^{{\alpha }_{\mathrm{UV}}}$ and adopt a slope of ${\alpha }_{\mathrm{UV}}=-1.7$, consistent with the measurements of Lusso et al. (2015). In the appendix we test also the cases for α_EUV = −1.1 and $-2.3$. We determine the normalization ${L}_{{\nu }_{\mathrm{LL}}}$ by integrating the Lusso et al. (2015) composite spectrum against the SDSS filter curve and choosing the amplitude to give the correct i-band magnitude of the UM287 quasar (i.e., i = 17.28), which gives a value of ${L}_{{\nu }_{\mathrm{LL}}}=5.4\times {10}^{31}$ erg s⁻¹ Hz⁻¹. We extend this UV power law to an energy of 30 Rydberg, 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 ${L}_{\nu }(2\;\mathrm{keV})$ implied by measurements of ${\alpha }_{\mathrm{OX}}$, defined to be ${L}_{\nu }{(2\;\mathrm{keV})/{L}_{\nu }(2500\;\mathring{\rm{A}} )\equiv ({\nu }_{2\;\mathrm{keV}}/{\nu }_{2500\;\mathring{\rm{A}} })}^{{\alpha }_{\mathrm{OX}}}$. We adopt the value ${\alpha }_{\mathrm{OX}}=-1.5$ measured by Strateva et al. (2005) for SDSS quasars. An X-ray slope of ${\alpha }_{{\rm{X}}}=-1$, which is flat in $\nu {f}_{\nu }$, 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. (2015), 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). In summary, given the lack of information, for energies greater than 1 Rydberg we parametrized the SED of the UM287 quasar with a series of power laws as

$$\begin{eqnarray}{f}_{\nu }\propto \{\begin{array}{ll}{\nu }^{{\alpha }_{\mathrm{EUV}}}, & \mathrm{if}\ h\nu \geqslant 1\;\mathrm{Ryd}\\ {\nu }^{\alpha }, & \mathrm{if}\ 30\;\mathrm{Ryd}\leqslant h\nu \lt 2\;\mathrm{keV}\\ {\nu }^{{\alpha }_{{\rm{X}}}}, & \mathrm{if}\ 2\;\mathrm{keV}\leqslant h\nu \lt 100\;\mathrm{keV}\\ {\nu }^{{\alpha }_{\mathrm{HX}}}, & \mathrm{if}\ h\nu \geqslant 100\;\mathrm{keV}.\end{array}\end{eqnarray} \tag{ 7 }$$

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4.4. Input Parameters to Cloudy

As we discuss in Section 3, our LRIS observations provide upper limits on the C iv/Lyα and He ii/Lyα ratios, i.e., (C iv/Lyα)${}_{3\sigma }\lesssim 0.16$ and (He ii/Lyα)${}_{3\sigma }\lesssim 0.18$. On the other hand, each photoionization model in our grid predicts these line ratios, and Figure 6 shows the trajectory of these models in the He ii/Lyα versus C iv/Lyα plane. The region allowed given our observational constraints on the line ratios is indicated by the green shaded area. We remind the reader that we select only the models which produce the observed Lyα emission of ${\mathrm{SB}}_{\mathrm{Ly}\alpha }\sim 7\times {10}^{-18}$ erg s⁻¹ cm⁻² arcsec⁻², which, to the lowest order, requires a combination of N_H and n_H as shown by Equation (3). Since the luminosity of the central source is known, these models can be thought to be parametrized by either n_H or the ionization parameter U, as shown by the color coding on the color bar. In the same plot we show trajectories for different metallicities $Z=1,$ 0.1, 0.01, 10⁻³ Z_⊙.

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We now reconsider the covering factor. We argued in Section 4.1 that based on the morphology of the nebula, the covering factor need to be ${f}_{{\rm{C}}}\gtrsim 0.5$, and that optically thick gas clouds would tend to overproduce the Lyα SB for such high covering factors. Our models provide a confirmation of this behavior. For a covering factor of ${f}_{{\rm{C}}}=1.0$ a large number of models are available, whereas if we lower the covering factor to f_C = 0.3, we find that only two models in our extensive model grid can satisfy the Lyα SB of the nebula. This results because as we decrease ${f}_{{\rm{C}}}$, assuming the gas is optically thin, Equation (3) indicates we must correspondingly increase the product ${N}_{{\rm{H}}}{n}_{{\rm{H}}}$ by $1/{f}_{{\rm{C}}}$ in order to match the observed Lyα SB. However, note that the neutral fraction also scales with this product ${x}_{\mathrm{HI}}\propto {N}_{{\rm{H}}}{n}_{{\rm{H}}}$ such that for low enough values of f_C increasing ${N}_{{\rm{H}}}{n}_{{\rm{H}}}$ would result in self-shielding clouds that are optically thick. We already argued in Section 4.1 that if the clouds are optically thick the covering factor must be much lower f_C ≃ 0.02, which is ruled out by the diffuse morphology of the nebula. Hence, our constraint on the covering factor ${f}_{{\rm{C}}}\gtrsim 0.5$ can also be motivated by the simple fact that gas distributions with lower covering factors would overproduce the Lyα SB. Henceforth, for simplicity, we assume a covering factor of f_C = 1.0 throughout this work, but in Section 7 we test the sensitivity of our results to this assumption.

The gray symbols in Figure 6 also show a compilation of measurements of the He ii/Lyα and C iv/Lyα line ratios from the literature for other giant Lyα nebulae from the compilation in Arrigoni Battaia et al. (2014b). Specifically, we show measurements or upper limits for the two line ratios for seven Lyα blobs (Dey et al. 2005; Prescott et al. 2009, 2013; Arrigoni Battaia et al. 2015),¹⁷ and Lyα nebulae associated with 53 HzRG (Humphrey et al. 2006; Villar-Martín et al. 2007). Note that we show measurements from the literature in Figure 6 for reference, but these measurements cannot be directly compared to our observations or our models for several reasons. First, the emission arising from the NLR of the central obscured AGN is typically included for the HzRGs, contaminating the line ratios for the nebulae. In addition, the central source UV luminosities are unknown for both LABs and HzRGs, and thus they cannot be directly compared to our models, which assume a central source luminosity. See Arrigoni Battaia et al. (2015) and references therein for a discussion on this dataset and its caveats.

The trajectory of our optically thin models through the He ii/Lyα and C iv/Lyα diagram can be understood as follows. We first focus on the curve for Z = Z_⊙ and follow it from low to high U (i.e., from high to low volume density n_H). 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 the fraction of Helium that is doubly ionized. For this reason, the He ii/Lyα ratio is increasing from $\mathrm{log}\;U\sim -3$ and "saturates", reaching a peak at a value of ∼0.34 which is set by atomic physics and in particular by the ratio of the recombination coefficients of Lyα and He ii. Indeed, if we neglect the contribution of collisional excitation to the Lyα line emission, which is a reasonable assumption near solar metallicity, then both the He ii and Lyα are produced primarily by recombination and the recombination emissivity can be written as

$$\begin{eqnarray}&&{j}_{\mathrm{line}}={f}_{{\rm{V}}}^{\mathrm{elem}}\displaystyle \frac{h{\nu }_{\mathrm{line}}}{4\pi }{n}_{{\rm{e}}}{n}_{\mathrm{ion}}{\alpha }_{\mathrm{line}}^{\mathrm{eff}}(T),\end{eqnarray} \tag{ 8 }$$

where n_ion is the volume density of ${\mathrm{He}}^{++}$ and H⁺ for the case of He ii and Lyα, respectively. Here ${\alpha }_{\mathrm{line}}^{\mathrm{eff}}(T)$ is the temperature-dependent recombination coefficient for He ii or Lyα, and the factor ${f}_{{\rm{V}}}^{\mathrm{elem}}=3{f}_{{\rm{C}}}{N}_{\mathrm{elem}}/(4{{Rn}}_{\mathrm{elem}})$ takes into account that the emitting clouds fill only a fraction of the volume (see Hennawi & Prochaska 2013). Thus, once the Helium is completely doubly ionized, i.e., ${n}_{{\rm{p}}}\sim {n}_{{\rm{H}}}$ and ${n}_{{\mathrm{He}}^{++}}\sim (Y/2X){n}_{{\rm{H}}}$, the ratio between the two lines is given by the relation

$$\begin{eqnarray}\displaystyle \frac{{j}_{\mathrm{He}\;{\rm{II}}}}{{j}_{\mathrm{Ly}\alpha }} & = & 0.34(\displaystyle \frac{{\alpha }_{\mathrm{He}\;{\rm{II}}}^{\mathrm{eff}}(20,000\;{\rm{K}})}{1.15\times {10}^{-12}\;{\mathrm{cm}}^{3}\;{{\rm{s}}}^{-1}})\\ & & \times {(\displaystyle \frac{{\alpha }_{\mathrm{Ly}\alpha }^{\mathrm{eff}}(\mathrm{20,000}\;{\rm{K}})}{2.51\times {10}^{-13}\;{\mathrm{cm}}^{3}\;{{\rm{s}}}^{-1}})}^{-1}.\end{eqnarray} \tag{ 9 }$$

Note that Equation (9) depends slightly on temperature, with a decrease of the ratio at higher temperatures. Before reaching this maximum line ratio, He ii/Lyα is lower because helium is not completely ionized, and is roughly given by $\mathrm{He}\;{\rm{II}}/\mathrm{Ly}\alpha \sim {x}_{{\mathrm{He}}^{++}}\times {({j}_{\mathrm{He}\;{\rm{II}}}/{j}_{\mathrm{Ly}\alpha })}_{\mathrm{max}}$, where ${x}_{{\mathrm{He}}^{++}}$ is the fraction of doubly ionized helium. As stated above, this simple argument does not take into account collisional excitation of Lyα. In particular, at lower metallicities when metal line coolants are lacking, the temperature of the nebula is increased and collisionally excited Lyα, which is extremely sensitive to temperature, becomes an important coolant, boosting the Lyα emission over the pure recombination value. Thus, metallicity variations result in a change of the level of the asymptotic He ii/Lya ratio, as seen in Figure 6.

Our photoionization models indicate that the C iv emission line is an important coolant and is powered primarily by collisional excitation. The efficiency of C iv as a coolant depends on the amount of carbon in the ${{\rm{C}}}^{+3}$ ionic state. For this reason, the C iv/Lyα ratio is increasing from $\mathrm{log}\;U\sim -3$, reaches a peak due to a maximum in the C⁺³ fraction, and lowers again at higher U where carbon is excited to yet higher ionization states, e.g., C v. For example, for the $Z=0.1\ {Z}_{\odot }$ models, the C iv/Lyα ratio peaks at log U = −1.4 and then decreases at higher U. Given that C iv is a coolant, the strength of its emission depends on the metallicity of the gas. Indeed, for metallicities lower than solar, C iv becomes a sub-dominant coolant with respect to collisionally excited Lyα (and for very low metallicity, e.g., Z = 10⁻³ Z_⊙, also to He Lyα), and its emission becomes metallicity-dependent, as can be seen in Figure 6.

At lower metallicities the Lyα line becomes an important coolant. For the $Z=0.001{Z}_{\odot }$ grid, the collisional contribution to Lyα has an average value of ∼40%, while it decreases to ∼37%, ∼25%, and ∼1% for the Z = 0.01, 0.1, 1 Z_⊙ cases, respectively. Given that the strength of the collisionally excited Lyα emission increases with density along each model trajectory, this slightly dilutes the aforementioned trends in the He ii and C iv line emission. Specifically, the density dependence of collisionally excited Lyα emission moves the line ratios to lower values for $\mathrm{log}\;U\gtrsim -1.5$, which would otherwise asymptote at the expected He ii/Lyα ratio in Equation (9). Thus, the effect of collisionally excited Lyα emission tend to mask the "saturation" of the He ii/Lyα ratio due to recombination effects alone, and results in a continuous increase of He ii/Lyα with U.

Overall, Figure 6 illustrates that our simple photoionization models can accommodate the constraints implied by our observed upper limits on the He ii/Lyα and C iv/Lyα ratios of UM287. In particular, our non-detections are satisfied (green shaded region) for models with high volume densities, n_H, and low metallicities, Z. These constraints can be more easily visualized in Figure 7, where we show the allowed regions in the ${n}_{{\rm{H}}}$–Z plane implied by our limits on the He ii/Lyα (panel (a)) and C iv/Lyα ratios (panel (b)). Specifically, in these panels the solid black lines indicate the upper limits in the case of the UM287 nebula, i.e., He ii/Lyα < 0.18 (or log(He ii/Lyα) < −0.74), and C iv/Lyα = 0.16 (or log(C iv/Lyα) < −0.79), while the arrows indicate the region of the parameter space that is allowed. It is evident that our limits on the extended emission in the He ii/Lyα ratio give us stronger constraints than those from the C iv/Lyα ratio. The He ii/Lyα ratio provides a constraint on the volume density which is metallicity-dependent; however, even if we assume a ${\mathrm{log}}_{10}\;Z\simeq -2-3$, which are the lowest possible values comparable to the background metallicity of the IGM (e.g., Schaye et al. 2003), we obtain a conservative lower limit on the volume density of n_H ≳ 3 cm⁻³.

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Given this constraint on n_H, and the fact that we know the Lyα emission level, which in turn approximately scales as ${n}_{{\rm{H}}}{N}_{{\rm{H}}}$ (see Equation (3)), we can use our lower limit on n_H to place an upper limit on ${N}_{{\rm{H}}}$ or equivalently on the total cool gas mass because it scales as ${f}_{{\rm{C}}}\;{N}_{{\rm{H}}}$ once the radius is fixed (see Equation (2)). Panel (c) of Figure 7 shows that our limit on the He ii/Lyα ratio combined with the total ${\mathrm{SB}}_{\mathrm{Ly}\alpha }$ implies the emitting clouds have column densities ${N}_{{\rm{H}}}\lesssim {10}^{20}$ cm⁻². Thus, if we assume that the physical properties of the slab modeled at 160 kpc are representative of the whole nebula, we can compute a rough estimate for the total cool gas mass. With this strong assumption that n_H ≳ 3 cm⁻³ is valid over the entire area of the nebula, i.e., 911 arcsec² (from the 2σ isophote of the Lyα map; Cantalupo et al. 2014), we then deduce that N_H ≲ 10²⁰ cm⁻² over this same area, and hence the total cool gas mass is M_c ≲ 6.4 × 10¹⁰ M_⊙.

Further, by combining the lower limit on volume density n_H and upper limit on column density N_H, we can also obtain an upper limit on the sizes of the emitting clouds defined as $R\equiv {N}_{{\rm{H}}}/{n}_{{\rm{H}}}$. Panel (d) in Figure 7 shows that this upper limit is constrained to be R ≲ 20 pc. Assuming a unit covering factor f_C = 1.0, this constraint on cloud sizes implies $\gtrsim 53,500$ clouds per square arcsec on the sky, and each cloud should have a cool gas mass ${M}_{{\rm{c}}}\;\lesssim \;1.3\times {10}^{3}$ M_⊙. Assuming these clouds have the same properties throughout the whole nebula, we find that $\gtrsim 4.9\times {10}^{7}$ clouds are needed to cover the extent of the Lyα emission (∼911 arcsec²).¹⁸

The foregoing discussion indicates that we are able to break the degeneracy between the volume density of the gas n_H and the total cool gas mass presented in Cantalupo et al. (2014). As a reminder, this degeneracy arises because the Lyα SB scales as ${\mathrm{SB}}_{\mathrm{Ly}}\alpha \propto {n}_{{\rm{H}}}{N}_{{\rm{H}}}$, whereas the total cool gas mass is given by ${M}_{{\rm{c}}}\propto {N}_{{\rm{H}}}$. Thus, observations of the Lyα alone cannot independently determine the cool gas mass. Cantalupo et al. (2014) modeled the Lyα emission in the UM287 nebula in a way that differs from our simple model of cool clouds in the quasar CGM. Specifically, they used the gas distribution in a massive dark matter halo M = 10^12.5 M_⊙ meant to represent the quasar host, and carried out ionizing and Lyα radiative transfer simulations under the assumption the gas is highly ionized by a quasar with the same luminosity as UM287, and the extended Lyα emission is dominated by recombinations, similarly to our simpler Cloudy models.¹⁹ Under these assumptions, they are not able to reproduce the observed Lyα SB of the nebula. This arises because only ∼15% of the total gas in the simulated halo is cool enough to emit Lyα recombination radiation (T < 5 × 10⁴ K), because the vast majority of the baryons in the halo have been shock-heated to the virial temperature of the halo, i.e., $T\sim {10}^{7}$ K. Even if they assume all of the gas in the simulated halo can produce the Lyα line (${M}_{\mathrm{gas}}\approx {10}^{11.3}$ M_⊙ for the dark matter halo; Cantalupo et al. 2014), the SB of the resulting nebula is still too faint. As a result, Cantalupo et al. (2014) postulated that the emission in the simulated halo must be boosted by a clumping factor $C=\langle {n}_{{\rm{H}}}^{2}\rangle /\langle {n}_{{\rm{H}}}{\rangle }^{2}$, which represents the impact of clumps of cool gas which are not resolved by the simulation. They then determined the scaling relation between the simulated Lyα emission and the column density of the simulated gas distribution, i.e., ${N}_{{\rm{H}}}\propto {\mathrm{SB}}_{\mathrm{Ly}}{\alpha }^{1/2}\;{C}^{-1/2}$ ²⁰ (Cantalupo et al. 2014), as expected for recombination radiation. Note that accordingly ${\mathrm{SB}}_{\mathrm{Ly}}{\alpha }^{1/2}\propto {N}_{{\rm{H}}}\;{C}^{1/2}\propto {M}_{{\rm{c}}}\;{C}^{1/2}$ and one sees that this is identical to the scaling implied by Equation (3), ${\mathrm{SB}}_{\mathrm{Ly}}\alpha \propto {N}_{{\rm{H}}}{n}_{{\rm{H}}}$, if one identifies n_H with ${C}^{1/2}\langle {n}_{{\rm{H}}}\rangle$. Our simple cloud model adopts a single density for all the clouds n_H, whereas in the clumping picture there could be a range of densities present, but the emission is dominated by gas with ${n}_{{\rm{H}}}\simeq {C}^{1/2}\;\langle {n}_{{\rm{H}}}\rangle$. In this context, Cantalupo et al. (2014) inferred that if C = 1, the high observed ${\mathrm{SB}}_{\mathrm{Ly}\alpha }$, implies very high column densities up to N_H ≈ 10²² cm⁻² corresponding to cool gas masses M_c = 10¹² M_⊙, in excess of the baryon budget of the simulation. More generally, in the presence of clumping this constraint becomes ${M}_{{\rm{c}}}={10}^{12}\;{C}^{-1/2}$ ${M}_{\odot }$.

By introducing the constraint on the volume density ${n}_{{\rm{H}}}\gtrsim 3$ cm⁻³ using the He ii/Lyα ratio, our work (i) breaks the degeneracy between density ${n}_{{\rm{H}}}$ (or equivalently C) and total column density ${N}_{{\rm{H}}}$ (or equivalently ${M}_{{\rm{c}}}$), (ii) allows us to then constrain the total cool gas mass ${M}_{{\rm{c}}}\lesssim 6.4\times {10}^{10}$ ${M}_{\odot }$ without making any assumptions about the quasar host halo mass, and (iii) demands the existence of a population of extremely compact ($R\lesssim 20$ pc) dense clouds in the CGM/IGM. The ISM-like densities and extremely small sizes of these clouds clearly indicate that they would be unresolved by current cosmological hydrodynamical simulations, given their resolution on galactic scales (Faucher-Giguere et al. 2015; Fumagalli et al. 2014; Crighton et al. 2015; Nelson et al. 2015). Indeed, our measurements would imply a clumping factor $C\gtrsim 200$ for the simulation of Cantalupo et al. (2014), in agreement with the value they required in order to reproduce the observed Lyα from their simulated halo.

5.1. Constraints from Absorption Lines

A source lying in the background of the UM287 nebula that pierces the gas at an impact parameter of ≃160 kpc may also exhibit absorption from high-ion UV transitions like C iv and N v, which can be constrained from absorption spectroscopy. In Figure 8 we show a map for the column density of the C iv and N v ionic states (${N}_{{\rm{C}}\;{\rm{IV}}}$, ${N}_{\mathrm{NV}}$) for our model grid that reproduces the observed ${\mathrm{SB}}_{\mathrm{Ly}\alpha }\sim 7\times {10}^{-18}$ erg s⁻¹ cm⁻² arcsec⁻². Given our non-detection of He ii emission, our upper limits on the He ii/Lyα ratios (indicated by the black solid line in both panels) imply ${N}_{{\rm{C}}\;{\rm{IV}}}\lesssim {10}^{13.8}$ cm⁻² and ${N}_{\mathrm{NV}}\lesssim {10}^{13.0}$ cm⁻², respectively. The quasar UM287 resides at the center of the nebula, and our narrow-band image indicates it is surrounded by Lyα emitting gas. It is thus natural to assume that the UM287 quasar pierces the nebular gas over a range of radial distances.²¹ Thus, a non-detection of absorption in these transitions places further constraints on the physical state of the absorbing gas in the nebula.

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To this end, we examined the high S/N ${\rm{S}}/{\rm{N}}\;\simeq$ 70 pixel⁻¹ SDSS spectrum of the UM287 quasar, which has a resolution of $R\simeq 2000$. We find no evidence for any metal line absorption within a ∼2000 km s⁻¹ window of the quasar systemic redshift coincident with the velocity of the Lyα emitting nebula (see Figures 2 and 3), implying ${N}_{{\rm{C}}\;{\rm{IV}}}\;\lt {10}^{13.2}$ cm⁻² (EW${}_{{\rm{C}}\;{\rm{IV}}}\lt 15$ mÅ) and ${N}_{\mathrm{NV}}\lt {10}^{13.4}$ cm⁻². These limits constrain the amount of gas in these ionic states intercepted by the quasar at all distances, but in particular at ≃160 kpc, where we conducted our detailed modeling of the emission. As such, directly analogous to our constraints from the emission line ratios, we can similarly determine the constraints in the ${n}_{{\rm{H}}}$–Z plane from the non-detections of C iv and N v absorption, which are shown as the gray dashed lines in Figure 8. As expected, these metal absorption constraints depend sensitively on the enrichment of the gas, but the region of the ${n}_{{\rm{H}}}$–Z plane required by our non-detections are consistent with that required by our He ii/Lyα emission constraint. Specifically, for log $Z\gt -2.3$, the absence of absorption provides a comparable lower limit on the density as the non-detection of emission, whereas at lower metallicities the absorption constraint allows lower volume densities ${n}_{{\rm{H}}}\gt 0.1$ cm⁻³ (Figure 8), which are already ruled out by He ii/Lyα. To conclude, in the context of our simple model, both high-ion metal line absorption and He ii and C iv emission paint a consistent picture of the physical state of the gas.

For completeness, we also searched for metal line absorption along the companion quasar "QSO b" sightline in our Keck/LRIS spectrum (resolution $R\simeq 1000$ and ${\rm{S}}/{\rm{N}}\simeq 60$ pixel⁻¹). We do detect strong, saturated C iv absorption with ${N}_{{\rm{C}}\;{\rm{IV}}}\gt {10}^{14.4}$ cm⁻² and $z=2.2601$. This implies, however, a velocity offset of $\approx -1700$ km s⁻¹ with respect to the systemic redshift of the UM287 quasar and thus from the extended Lyα emission detected in the slit spectrum of Figure 2. Given this large kinematic displacement from the nebular Lyα emission, we argue that this absorption is probably not associated with the UM287 nebulae and is likely to be a narrow-associated absorption line system associated with the companion quasar. This is further supported by the strong detection of the rarely observed N v doublet. The large negative velocity offset $-1370$ km s⁻¹ between the absorption and our best estimate for the redshift of QSOb $z=2.275$ (from the Si iv emission line) suggests that this is outflowing gas, but given the large error $\sim 800\;\mathrm{km}\;{{\rm{s}}}^{-1}$ on the latter and the unknown distance of this absorbing gas along the line of sight, we do not speculate further on its nature.

Finally, note that at the time of writing, there is no existing echelle spectrum of UM287 available, although given that this quasar is hyper-luminous $r\simeq 17$, a high S/N, high-resolution spectrum could be obtained in a modest integration. Such a spectrum would allow us to obtain much more sensitive constraints on the high-ion states C iv and N v, corresponding to ${N}_{{\rm{C}}\;{\rm{IV}}}\lt {10}^{12}$ cm⁻² and ${N}_{{\rm{N}}\;{\rm{V}}}\lt {10}^{12.5}$ cm⁻², respectively, and additionally search for O vi absorption down to ${N}_{{\rm{O}}\;{\rm{VI}}}\lt {10}^{13}$ cm⁻². If, for example, C iv were still not detected at these low column densities, this would raise our current constraint on ${n}_{{\rm{H}}}$ by 0.5 dex to ${n}_{{\rm{H}}}\gtrsim 10\;{\mathrm{cm}}^{-3}$ as shown in Figure 8. Furthermore, the detection of metal line absorption (at a velocity consistent with the nebular Lyα emission) would determine the metallicity of the gas in the nebula, and Figure 8 suggests we would be sensitive down to metallicities as low as $Z\simeq -3$, i.e., as low as the background metallicity of the IGM (e.g., Schaye et al. 2003).

5.2. Comparison to Absorption Line Studies

In order to assess the feasibility of detecting other emission lines besides Lyα from the UM287 nebula and other similar extended Lyα nebulae, e.g., around other quasars, HzRGS, or LABs, we construct model spectra using the output continuum and line emission data from Cloudy. In Figure 9 we show the predicted median spectrum for the nebula at 160 kpc from UM287, resulting from our modeling. Specifically, the solid black curve represents the median of all the models in our parameter grid which simultaneously satisfy the conditions $5.5\times {10}^{-18}$ erg s⁻¹ cm⁻² arcsec⁻² $\lt \;{\mathrm{SB}}_{\mathrm{Ly}\alpha }\lt 8.5\times {10}^{-18}$ erg s⁻¹ cm⁻² arcsec⁻², such that they produce the right Lyα emission level, as well as the emission line constraints He ii/Lyα $\lt \;0.18$ and C iv/Lyα $\lt \;0.16$ implied by our spectroscopic limits. Following our discussion in the appendix, this grid also includes models with a harder (softer) ${\alpha }_{\mathrm{EUV}}=-1.1$ (${\alpha }_{\mathrm{EUV}}=-2.3$) quasar ionizing continuum, in addition to our fiducial value of ${\alpha }_{\mathrm{EUV}}=-1.7$. The gray shaded area indicates the maximum and the minimum possible values for the selected models at each wavelength.

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For comparison, we show our Keck/LRIS 3σ sensitivity limits from Section 2 calculated by averaging over a 1 arcsec² aperture and over a 3000 km s⁻¹ velocity interval (solid red line), together with the 3σ sensitivity limits for 10 hr of integration with the Multi Unit Spectroscopic Explorer (MUSE; Bacon et al. 2010; solid blue line), and with the K-band Multi Object Spectrograph (KMOS; Sharples et al. 2006; gold, orange, and dark-red solid lines), on the VLT, computed for the same spatial and spectral aperture. Note that these sensitivity limits can be lowered by assuming a certain amount of spatial averaging, following the relation ${\mathrm{SB}}_{\mathrm{limit}}={\mathrm{SB}}_{1\sigma }/\sqrt{A}$, where A is the area in arcsec² over which the data are averaged. Indeed, we employed this approach in Section 3, and averaged over an area of 20 arcsec² to obtain a more sensitive constraint on the He ii/Lyα and C iv/Lyα line ratios. This lower SB level is indicated by the red dashed line in Figure 9. In contrast with a long-slit, integral field units like MUSE and KMOS, as well as the upcoming Keck Cosmic Web Imager (KCWI; Morrissey et al. 2012), provide near continuous spatial sampling over wide areas, and are thus the ideal instruments for trying to detect extended line emission from the CGM. Thus, for MUSE and KMOS, we have assumed that we can average over an area as large as 300 arcsec², as shown by the colored dashed lines, and indeed this approach has already been used with the Cosmic Web Imager (Martin et al. 2014a) to study lower SB Lyα emission (Martin et al. 2014b).

Given these expected sensitivities, in Figure 9 we indicate the principal emission lines that may be detectable (vertical green dashed lines), whose observation would provide additional constraints on the properties of the emitting gas. The large range of metallicities in our grid $Z={10}^{-3}\;{Z}_{\odot }$ to ${Z}_{\odot }$ results in a correspondingly large range of metal emission line strengths, whereas the Hydrogen Balmer lines and He ii are much less sensitive to metallicity and thus show very little variation across our model grid.

Focusing first on the primordial elements, we see that He ii is the strongest line, and in particular it is stronger than Hα. Indeed, if the helium is completely doubly ionized then He ii/H $\alpha \sim 3$, and although it decreases to lower values for lower ionization parameters (higher densities), it always remains higher than unity. As we have argued in Section 5, a detection of He ii can be used to measure the volume density ${n}_{{\rm{H}}}$ of the emitting gas. Further, by comparing the morphology, size, and kinematics of the non-resonant extended He ii emission to that of Lyα, one can test whether resonant scattering of Lyα plays an important role in the structure of the nebula (Prescott et al. 2015a). Naively, one might have thought that Hα would be ideal for this purpose given that it is the strongest hydrogen recombination line after Lyα. However, our models indicate that for photoionization by a hard source, the He ii line is always stronger than Hα, and given that He ii is in the optical whereas Hα is in the near-IR, it is also much easier to detect.

Figure 9 shows that deep integrations in the near-IR with KMOS will consistently detect the Hydrogen Balmer lines Hα and Hβ. When compared to the Lyα emission, these lines would allows one to determine the extinction due to dust (Osterbrock & Ferland 2006). Further, at the low densities we consider (${n}_{{\rm{H}}}\ll {10}^{4}$ cm⁻³), any departure of the ratios Hα/Hβ and Lyα/Hβ from their case B values provide information on the importance of collisional excitation of Lyα, which is exponentially sensitive to the gas temperature (Ferland & Osterbrock 1985). In other words, the amount of collisional excitation is set by the equilibrium temperature of the gas, which is set by the balance of heating and cooling. Photoionization by a hard source will result in a characteristic temperature and hence ratio of Lyα/Hβ set by the ionizing continuum slope, whereas an additional source of heat, as has been postulated in gravitational cooling radiation scenarios for Lyα nebulae (e.g., Rosdahl & Blaizot 2012), would increase the amount of collisionally excited Lyα and hence the ratio of Lyα/Hβ.

Figure 9 shows also that one could probably detect metal emission lines depending on the physical conditions in the gas, which are parameterized by ${n}_{{\rm{H}}}$ and Z. In particular, if the gas has metallicity $Z\gt 0.1{Z}_{\odot }$, a deep integration with MUSE would detect C iv, [C iii], and, for metallicity close to solar, also [Si iii] $\lambda 1883$. In the near-IR, we see that a deep integration with KMOS would detect [O iii] for $Z\gt 0.1{Z}_{\odot }$ and [O ii] for metallicity close to solar. Note that for similar bright nebulae at different redshifts, it would be possible to detect other lines in extended emission for particular ${n}_{{\rm{H}}}$ and Z combinations, e.g., Si iv $\lambda 1394$, and [N iv] $\lambda 1480$.

According to Figure 9, a good observational strategy is thus to look for the He ii line, which appears to be the strongest and easiest line to detect, and our analysis in Section 5 indicates that its detection constrains the gas properties to lie on a line in the ${n}_{{\rm{H}}}$–Z plane (see panel (a) in Figure 7). Following our discussion of C iv (panel (b) of Figure 7), the detection of any metal line would define another line in the ${n}_{{\rm{H}}}$–Z plane, and the intersection of these curves would determine the ${n}_{{\rm{H}}}$ and Z of the gas. These conclusions will be somewhat sensitive to the assumed spectral slope in the UV (see the Appendix), but, given the different ionization thresholds to ionized carbon to C iv (47.9 eV), and Oxygen to O iii (35.1 eV) or O ii (13.6 eV), it is clear that detections or limits on multiple metal lines from high- and low-ionization states would also constrain the slope ${\alpha }_{\mathrm{EUV}}$ of the ionizing continuum.

To summarize, our photoionization modeling and analysis provide a compelling motivation to find more bright nebulae by surveying large samples of quasars and HzRGs, and conducting NB emission line surveys of LABs over large areas. Armed with the brightest and largest giant nebulae like UM287, one can conduct deep observations with IFUs, and combined with suitable spatial averaging, this will uncover a rich emission line spectrum from the CGM and its interface with the IGM, which can be used to constrain the physical properties of the emitting gas, and shed light on physical mechanism powering giant nebulae.

In section Section 5, under the assumption of photoionization by the central QSO, and in the context of a simple model for the gas distribution, we showed how our upper limits on the He ii/Lyα and C iv/Lyα ratios can set constraints on the physical properties of the cool gas observed in emission. However, this simple modeling is just a zeroth-order approximation to a more complicated problem which is beyond the scope of the present work. In what follows, we highlight some issues which should be examined further.

Radial Dependence: for simplicity we have evaluated the ionizing flux at a single radial location for input into Cloudy. We have tested the impact of this assumption, by decreasing R from 160 to 100 kpc, and find that our lower limit on the density increases by 0.4 dex. This results from the fact that the He ii/Lyα ratio varies with ionization parameter U, and our upper limit on the line ratio sets a particular value of U. By decreasing R, the density ${n}_{{\rm{H}}}$ corresponding to this specific value of U thus increases by a factor R². The variation of the ionizing flux with radius should be taken into account in a more detailed calculation.

Slope of the Ionizing Continuum: we have assumed ${\alpha }_{\mathrm{EUV}}=-1.7$ (Lusso et al. 2015). However, estimates for ${\alpha }_{\mathrm{EUV}}$ in the literature vary widely (Zheng et al. 1997; Scott et al. 2004; Shull et al. 2012), most likely because of uncertainties introduced when correcting for absorption due to the IGM or because of the heterogeneity of the samples considered. Furthermore, the shape of the ionizing continuum near the He ii edge of 4 Rydberg is not well constrained. For a detailed analysis on the sensitivity of our results to the ionizing continuum slope, see the appendix, where we consider two different ionizing slopes, i.e., ${\alpha }_{\mathrm{EUV}}=-1.1$ and $-2.3$. We find that a harder ionizing slope ${\alpha }_{\mathrm{EUV}}=-1.1$ moves our lower limit on the density from ${n}_{{\rm{H}}}\gtrsim 3$ cm⁻³ to ${n}_{{\rm{H}}}\gtrsim 1$ cm⁻³. Thus, the uncertainty on the ionizing slope has an order of unity impact on our constraints of the volume density. As discussed at the end of Section 6, the detection of additional metal lines with a range of ionization thresholds would further constrain ${\alpha }_{\mathrm{EUV}}$.

Covering Factor: based on the morphology of the emission we argued ${f}_{{\rm{C}}}\gtrsim 0.5$, but assumed the value of ${f}_{{\rm{C}}}=1.0$ for simplicity. The ${f}_{{\rm{C}}}$ drops out of the line ratios (see Equations (3) and (8)); however, our model depends on f_C since we were selecting only models able to reproduce the observed Lyα SB, which varies linearly with covering factor. We estimate that lowering the covering factor to ${f}_{{\rm{C}}}=0.4$ will only change our lower limit on the density at the 15% level. As discussed in Section 5, lowering ${f}_{{\rm{C}}}$ results in a reduction of the number of models that are able to reproduce the observed Lyα SB because models with high ${n}_{{\rm{H}}}{N}_{{\rm{H}}}$ values become optically thick and thus overestimate the Lyα emission. In particular, there are no models that reproduce the observed Lyα SB for low covering factors (${f}_{{\rm{C}}}\lt 0.3$). Thus, our conclusions are largely insensitive to the covering factor we assumed.

Geometry: we have assumed the emitting clouds are spatially distributed uniformly throughout a spherical halo. This simple representation would need geometric corrections to take into account more complicated gas distributions, such as variation of the covering factor with radius or filamentary structures. However, these corrections should be of the order of  unity and are thus likely sub-dominant compared to other effects. In addition, to explain the morphology and extent of the Lyα emission, a complete modeling needs to take into account (i) the effects of the opening angle of the ionizing cones, (ii) the orientation of the ionizing cones of the QSO with respect to the observer line of sight, and to the gas distribution surrounding the QSO (Weidinger et al. 2004, 2005), and (iii) light-travel and finite light-speed effects (Cantalupo et al. 2014). Note that all these effects have been taken into account in the previous analysis by Cantalupo et al. (2014). Indeed, high-resolution simulations of high massive halos randomly illuminated by a central QSO are needed to simultaneously address all these effects and will be fundamental to better constrain future observations of giant Lyα nebulae.

Single Uniform Cloud Population: our simple model assumes a single population of clouds which all have the same constant physical parameters ${N}_{{\rm{H}}}$, ${n}_{{\rm{H}}}$, and Z, following a uniform spatial distribution throughout the halo. In reality, one expects a distribution of cloud properties and a radial dependence. Indeed, Binette et al. (1996) argued that a single population of clouds is not able to simultaneously explain both the high- and low-ionization lines in the EELRs of HzRGs, and instead invoked a mixed population of completely ionized clouds and partially ionized clouds. While for the case of EELRs around quasars, which are on a scale smaller $R\lt 50\;\mathrm{kpc}$ than studied here, detailed photoionization modeling of spectroscopic data has demonstrated that at least two density phases are likely required: a diffuse abundant cloud population with ${n}_{{\rm{H}}}\sim 1$ cm⁻³, and much rarer dense clouds with ${n}_{{\rm{H}}}\sim 500$ cm⁻³ (Stockton et al. 2002; Fu & Stockton 2007; Hennawi et al. 2009). Further, these clouds may be in pressure equilibrium with the ionizing radiation (Dopita et al. 2002; Stern et al. 2014), as has been invoked in modeling the narrow-line regions of AGNs. Future detailed modeling of multiple emission lines from giant nebulae, analogous to previous work on the smaller scale of EELRs (Stockton et al. 2002; Fu & Stockton 2007), might provide information on multiple density phases.

In order to properly address the aforementioned issues, the ideal approach would be to conduct a full radiative transfer calculation on a three-dimensional gas distribution, possibly taken from a cosmological hydrodynamical simulation. Cantalupo et al. (2014) carried out exactly this kind of calculation treating both ionizing and resonant radiative transfer; however, this analysis was restricted to only the Lyα line. Full radiative transfer coupled to detailed photoionization modeling as executed by Cloudy would clearly be too computationally challenging. However, it would be interesting to introduce the solutions of 1D Cloudy slab models into a realistic gas distribution drawn from a cosmological simulation. This would be relatively straightforward for the case of optically thin nebulae (e.g., van de Voort & Schaye 2013).

To study the kinematics of the extended Lyα line and to search for extended He ii $\lambda 1640$ and C iv $\lambda 1549$ emission, we obtained deep spectroscopy of the UM287 nebula (Cantalupo et al. 2014) with the Keck/LRIS spectrograph. Our spectrum of the nebula provides evidence for large motions suggested by the Lyα line of ${\mathrm{FWHM}}_{\mathrm{Gauss}}\sim 500$ km s⁻¹ which are spatially coherent on scales of ∼150 kpc. There is no evidence for a "double-peaked" line along either of the slits, as might be expected in a scenario where resonant scattering determines the Lyα kinematic structure.

Although our observations achieve an unprecedented sensitivity in the He ii and C iv line (${\mathrm{SB}}_{3\sigma }\simeq {10}^{-18}$ erg s⁻¹ cm⁻² arcsec⁻², average over 1'' × 20'' and ${\rm{\Delta }}v=3000$ km s⁻¹) for giant Lyα nebulae, we do not detect extended emission in either line for both of our slit orientations. We constrain the He ii/Lyα and C iv/Lyα ratios to be $\lt 0.18$ (3σ), and $\lt 0.16$ (3σ), respectively.

To interpret these non-detections, we constructed models of the emission line ratios, assuming photoionization by the central quasar and a simple spatial distribution of cool gas in the quasar halo. We find the following.

• 1.  
  If the gas clouds emitting Lyα are optically thick to ionizing radiation, then the nebula would be ∼120 × brighter than observed, unless we assume an unrealistically low covering factor, i.e., ${f}_{{\rm{C}}}\lesssim 0.02$, which is in conflict with the smooth morphology of the nebula. Thus, we conclude that the covering factor of cool gas clouds in the nebula is high ${f}_{{\rm{C}}}\gtrsim 0.5$ and that the gas in the nebula is highly ionized, resulting in gas clouds optically thin (${N}_{\mathrm{HI}}\lt 17.2$) to ionizing radiation.
• 2.  
  The He ii line is a recombination line and thus once the density is fixed, its emission depends primarily on the fraction of helium that is doubly ionized. On the other hand, the C iv emission line is an important coolant and is powered primarily by collisional excitation, and thus its emission depends on the amount of carbon in the ${{\rm{C}}}^{+3}$ ionic state. As we know the ionizing luminosity of the central quasar and the Lyα SB of the nebula, constraints on the He ii/Lyα and C iv/Lyα ratios determine where the gas lives in the ${n}_{{\rm{H}}}-Z$ diagram.
• 3.  
  Photoionization from the central quasar is consistent with the Lyα emission and the He ii and C iv upper limits, provided that the gas distribution satisfies the following constraints:

  • (a)  
    ${n}_{{\rm{H}}}\gtrsim 3$ cm⁻³,
  • (b)  
    ${N}_{{\rm{H}}}\lesssim {10}^{20}$ cm⁻²,
  • (c)  
    $R\lesssim 20$ pc.

  If these properties hold through the entire nebula, it then follows that the total cool gas ($T\sim {10}^{4}$ K) mass is ${M}_{{\rm{c}}}\lesssim 6.4\times {10}^{10}$ ${M}_{\odot }$.

Because the Lyα SB scales as ${\mathrm{SB}}_{\mathrm{Ly}\alpha }\propto {n}_{{\rm{H}}}{N}_{{\rm{H}}}$, whereas the total cool gas mass as ${M}_{{\rm{c}}}\propto {N}_{{\rm{H}}}$, observations of Lyα emission cannot independently determine the cool gas mass and ${n}_{{\rm{H}}}$ (or the gas clumping factor C), which limited the previous modeling by Cantalupo et al. (2014). Our non-detection of He ii/Lyα combined with photoionization modeling allows us to break this degeneracy and independently constrain both ${n}_{{\rm{H}}}$ and ${M}_{{\rm{c}}}$.

Our results point to the presence of a population of compact ($R\lesssim 20$ pc) cool gas clouds in the CGM at ISM-like densities of ${n}_{{\rm{H}}}\gtrsim 3\;{\mathrm{cm}}^{-3}$ moving through the quasar halo at velocities $\simeq 500\;\mathrm{km}\;{{\rm{s}}}^{-1}$. It is well known that even by $z\sim 2$, the gas in the massive $M\sim {10}^{12.5}$ ${M}_{\odot }$ halos hosting quasars is expected to be dominated by a hot shock-heated plasma at the virial temperature $T\sim {10}^{7}\;{\rm{K}}$. Cool clouds moving rapidly through a hot plasma will be disrupted by hydrodynamic instabilities on the cloud-crushing timescale (e.g., Jones et al. 1994; Agertz et al. 2007; Schaye et al. 2007; Crighton et al. 2015; Scannapieco & Brüggen 2015)

$$\begin{eqnarray}{t}_{\mathrm{cc}} & \approx & 1.3\;\mathrm{Myr}(\displaystyle \frac{R}{20\;\mathrm{pc}}){(\displaystyle \frac{v}{500\;\mathrm{km}\;{{\rm{s}}}^{-1}})}^{-1}\\ & & \times {(\displaystyle \frac{{n}_{\mathrm{cl}}/{n}_{\mathrm{halo}}}{1000})}^{1/2},\end{eqnarray} \tag{ 10 }$$

where we assume that the Lyα line trace the kinematics of the cool clouds, and that the cloud-halo density contrast is of the order of 1000 (${n}_{\mathrm{halo}}\sim {10}^{-3}$ cm⁻³). If there is hot plasma present in the halo, these clouds are thus very short-lived and can only be transported $\sim 0.7\;\mathrm{kpc}$ before being disrupted. These very short disruption timescales thus require a mechanism that makes the clumps resistant to hydrodynamic instabilities, such as confinement by magnetic fields (e.g., McClure-Griffiths et al. 2010; McCourt et al. 2015), otherwise the population of cool dense clouds must be constantly replenished. In the latter scenario, the short-lived clouds might be formed in situ, via cooling and fragmentation instabilities. If the hot plasma pressure confines the clouds, this might compresses them to high enough densities (Mo & Miralda-Escude 1996; Maller & Bullock 2004) to explain our results. Emission line nebulae from cool dense gas has also been observed at the centers of present-day cooling flow clusters (Heckman et al. 1989; McDonald et al. 2010), albeit on much smaller scales $\lesssim 50\;\mathrm{kpc}$. The giant Lyα nebula in UM287 might be a manifestation of the same phenomenon, but with much larger sizes and luminosities, reflecting different physical conditions at high redshift. Detailed study of the hydrodynamics of cool dense gas clouds, with properties consistent with our constraints, moving through hot plasma are clearly required (Scannapieco & Brüggen 2015).

As we showed in Section 6, deep observations ($\sim 10\;\mathrm{hr}$) of UM287 and other giant nebulae with the new integral field units such as MUSE (Bacon et al. 2010), KCWI (Morrissey et al. 2012), and KMOS (Sharples et al. 2006), combined with spatial averaging, will be able to detect extended emission from other lines besides Lyα (see Figure 9). In particular, the strongest line will be He ii,  which should be routinely detectable and, following our analysis, will enable measurements of the volume density ${n}_{{\rm{H}}}$ of the gas. Specifically, a 10 hr MUSE integration would correspond to a sensitivity in He ii/Lyα of ∼0.01 ($3\sigma$ in 300 arcsec²), which would allow us to probe gas densities as high as ${n}_{{\rm{H}}}=1000$ cm⁻³. Although we have argued that the UM287 is powered by photoionization, which is compelling given the presence of a hyper-luminous quasar, a non-detection of He ii in a 10 hr MUSE integration would imply such extreme gas densities in the CGM, i.e., ${n}_{{\rm{H}}}\gt 1000$ cm⁻³, that one might need to reconsider other potential physical mechanisms for powering the Lyα nebula which do not produce He ii, such as cold-accretion (e.g., Haiman et al. 2000; Furlanetto et al. 2005; Dijkstra et al. 2006a; Faucher-Giguère et al. 2010; Rosdahl & Blaizot 2012), star-formation (e.g., Cen & Zheng 2013), or superwinds (e.g., Taniguchi & Shioya 2000; Taniguchi et al. 2001; Wilman et al. 2005). Furthermore, comparison of the morphology and kinematics of the nebula in He ii and Lyα can be used to test whether resonant scattering of Lyα photons is important. Although Hα could also be used to test the impact of resonant scattering, it is always fainter than He ii and redshifted into the near-IR, where a detection of extended emission is much more challenging.

In a photoionization scenario, a 10 hr observation of UM287 or a comparable nebula with MUSE (or KCWI) and KMOS would result in a rich emission line spectrum of the CGM, which, depending on the properties of the gas (i.e., ${n}_{{\rm{H}}}$ and Z), could yield detections of Lyα, [N iv], Si iv, [Ne iv], C iv, [C iii], [Si iii], [O iii], [O ii], Hβ, and Hα. This would enable modeling of the CGM at a comparable level of detail as models of H ii regions and the narrow and broad-line regions of AGNs, resulting in comparably detailed constraints on the physical properties of the gas.

Current estimates suggest that ∼10%–20% of quasars exhibit bright giant nebulae (Hennawi et al. 2015) like UM287, and our results provide a compelling motivation to expand current samples by surveying large numbers of quasars with instruments like MUSE and KCWI. At the same time, this same survey data would enable one to compute a stacked composite CGM spectrum of quasars which do not exhibit bright nebulae, constraining the gas properties around typical quasars.

Further, the observations of more peculiar systems, such as binary or multiple quasar systems, could enhance the probability of detecting large-scale Lyα emission. Indeed, in Section 7 we have stressed that the orientation of the ionizing cones with respect to the observer line of sight and the large-scale structures can play an important role in the observation of such giant nebulosities (Weidinger et al. 2004; Cantalupo et al. 2014). Thus, naively, the presence of multiple randomly oriented ionization cones would result in a higher detection probability of the circumgalactic gas in emission, which might also be boosted by the presence of an overdensity (Hennawi et al. 2015). To our knowledge, except for the system studied here (Cantalupo et al. 2014), only few multiple systems has been observed in the Lyα line (Zafar et al. 2011; Hennawi et al. 2015), leading to promising results, with the detection of extended Lyα emission. In order to verify this simple picture, more work in this direction is needed and ongoing (E.P. Farina et al. 2015, in preparation).

We are grateful to the anonymous referee for the punctual and useful comments. We thank the members of the ENIGMA group²² at the Max Planck Institute for Astronomy (MPIA) for helpful discussions. J.F.H. acknowledges generous support from the Alexander von Humboldt foundation in the context of the Sofja Kovalevskaja Award. The Humboldt foundation is funded by the German Federal Ministry for Education and Research. J.X.P. is supported by NSF grants AST-1010004 and AST-1412981. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

We test the robustness of our results to the change of the slope of the EUV as mentioned in Section 4.3. In particular, we model the extremes of the range allowed by the recent estimates of Lusso et al. (2015), i.e., ${\alpha }_{\mathrm{EUV}}=-1.7\pm 0.6$. To fulfill the ${\alpha }_{\mathrm{OX}}$ requirement of Strateva et al. (2005) as explained in Section 4.3, the value ${\alpha }_{\mathrm{EUV}}=-2.3$ and −1.1 imply at higher energies ($30\;\mathrm{Ryd}\lt h\nu \lt 2\;\mathrm{keV}$) slopes of $\alpha =-0.36$ and −2.93, respectively. In our fiducial input spectrum (${\alpha }_{\mathrm{EUV}}=-1.7$), the photoionization rate at the Lyman limit is

$$\begin{eqnarray}&&{\rm{\Gamma }}=\displaystyle \frac{1}{4\pi {r}^{2}}{\displaystyle \int }_{{\nu }_{\mathrm{LL}}}^{\infty }\displaystyle \frac{{L}_{\nu }}{h\nu }{\sigma }_{\nu }d\nu =6.7\times {10}^{-9}\;{{\rm{s}}}^{-1},\end{eqnarray} \tag{ 11 }$$

while at 4 Ryd, i.e., at the ionization energy of He ii, the photoionization rate is ${{\rm{\Gamma }}}_{4\;\mathrm{Ryd}}\sim 1.0\times {10}^{-11}$ s⁻¹. By changing the slope in the extreme ultraviolet from ${\alpha }_{\mathrm{EUV}}=-1.7$ to −1.1 and to −2.3, we increase the photoionization rate by ∼15% and decrease it by ∼13%, respectively. Instead, for the same change, the ${{\rm{\Gamma }}}_{4\;\mathrm{Ryd}}$ is increased/decreased by a factor of 2.6, respectively. As it is clear from the small changes in Γ, the Hydrogen ionization state is not affected by the change in slope, and the models are always optically thin. Conversely, as expected, the changes in ${{\rm{\Gamma }}}_{4\;\mathrm{Ryd}}$ affect He ii and C iv. The general trend is that a softer slope, e.g., ${\alpha }_{\mathrm{EUV}}=-2.3$, produces fewer He ii ionizing photons, and thus at fixed density the He iii fraction will be lower, resulting in lower He ii recombination emission. This thus leads to a lower He ii/Lyα ratio. Similarly, a softer slope is less effective at ionizing carbon. In particular, at fixed ionization parameter U, the amount of carbon in the ${{\rm{C}}}^{+3}$ phase is lower for a softer slope.

In Figure 10 we compare our grids of models with different EUV slopes at two different metallicities, i.e., $Z={Z}_{\odot }$ and $0.01{Z}_{\odot }$, in the He ii/Lyα versus C iv/Lyα plot. The dependencies outlined above are better visible in the plot for solar metallicity (upper panel) because the Lyα line is mainly produced by recombinations and its behavior is not influencing the general trends. From the figure, it is clear that a grid with a softer slope (see grid with ${\alpha }_{\mathrm{EUV}}=-2.3$) can reach lower He ii/Lyα ratios because the fraction of doubly ionized helium is lower at high densities. In the same upper panel of Figure 10 it is also evident that the simulation grids for different UV slopes all asymptote to a fixed He ii/Lyα ratio when helium is completely doubly ionized, which occurs at slightly different ${n}_{{\rm{H}}}$ (or equivalently U) for each slope. Note that the value of the asymptotic He ii/Lyα ratio varies slightly with slope. Indeed, as mentioned in Section 5, since this asymptotic value is proportional to the ratio of the recombination coefficients of He ii and Lyα, the value depends on temperature (Equation (9)). Higher temperatures, which arise for a harder slope, lead to a lower asymptotic He ii/Lyα ratio.

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In the bottom panel of Figure 10, we show the same comparison at $Z=0.01{Z}_{\odot }$. In this case, the trends are masked by the Lyα line, which is powered also by collisions. Indeed, the saturation in the He ii/Lyα ratio is not appreciable because, given the dependence on density of the collisional contribution to the Lyα line, the ratio is progressively lowered at higher density. However, it is still appreciable that the C iv/Lyα ratio is moved to lower ratios for higher slopes above $\mathrm{log}U\sim -1.5$. This is mainly due to the fact that Carbon goes to higher ionization state, lowering the fraction of Carbon in the ${{\rm{C}}}^{+3}$ species. Thus, in our case study, where the input spectrum is not well known, the dependence of the amount of ${{\rm{C}}}^{+3}$ on the slope of the EUV makes the C iv line a weak metallicity indicator.

Changes in the slope ${\alpha }_{\mathrm{EUV}}$ only slightly modifies the constraints on ${n}_{{\rm{H}}}$ that we previously obtained. In particular, since the He ii/Lyα ratio gives the stronger constraints, in Figure 11 we show how a variation in the EUV slope affects the selection of ${n}_{{\rm{H}}}$ (compare Figures 10 and 11). This figure highlights in green the parameter space favored by our upper limits (the lines show the location of the upper limit He ii/Lyα $=\;0.18$). The mild change in the location of the line is explained by the dependencies outlined above. At a fixed low metallicity, where the Lyα line is an important coolant, i.e., log $Z\lt {-1.5Z}_{\odot }$, a harder slope moves the lower limit boundary implied by our measurement on the He ii/Lyα ratio to lower densities. Indeed, the expected increase of the He ii line due to a harder slope is washed out by the increase in the emission in the Lyα line due to collisions. Thus, our constraint on the density that we quote in the main text is weakened from ${n}_{{\rm{H}}}\gtrsim 3$ cm ${}^{-3}$ to ${n}_{{\rm{H}}}\gtrsim 1$ cm ${}^{-3}$. On the other hand, at higher metallicities, a harder UV slope will doubly ionize helium at higher density, moving the lower limit boundary implied by our measurement to higher densities. For example, at solar metallicity, the limit is moved to $\gtrsim 100$ cm ${}^{-3}$ from $\gtrsim 40$ cm ${}^{-3}$.

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Thus, in conclusion, our ignorance on the slope of the EUV has a small effect on our density constraints and makes the C iv line a weak metallicity indicator. However, as discussed at the end of Section 6, the detection of multiple metal lines with a range of ionization energies would indirectly constrain ${\alpha }_{\mathrm{EUV}}$ and simultaneously constrain the metallicity of the gas.