QUASARS PROBING QUASARS. III. NEW CLUES TO FEEDBACK, QUENCHING, AND THE PHYSICS OF MASSIVE GALAXY FORMATION

Before delving into detailed photoionization models, one can build intuition by making qualitative inspection of the ions detected. Examining subsystem A in Figure 3, one notes strong absorption from a series of low ions, e.g., O⁰, Si⁺, N⁰, Fe⁺. This is characteristic of Lyman limit systems where the large H i opacity self-shields gas from local or background UV sources. Elements therefore occupy the first ionization state (termed the low ion) with an IP greater than 1 Ryd. One also identifies strong N ii absorption that traces the observed N i profile in subsystem A. The measured ratio of these ionization states is large, log [N(N⁺)/N(N⁰)] = +1.8 dex, revealing that the gas is partially ionized. On the other hand, there is only weak Si iv and C iv absorption at these velocities indicating the ionization state of the gas is not extreme. Furthermore, the absence of strong N v and O vi absorption at these velocities limits the flux of photons with energies hν ≳ 4 Ryd and also rules out a collisionally ionized gas with T ≈ 10⁵ K (see Section 4.4). Qualitatively, the data suggest a partially ionized gas with T < 10⁵ K.

There are two main mechanisms that produce a partially ionized gas: collisional ionization and photoionization. Under the assumption of collisional ionization equilibrium (CIE; Sutherland & Dopita 1993), the detection of low ions like O⁰ and N⁰ requires the electron temperature to be T_e < 30, 000 K. This constraint is supported by the small b-values measured for the N⁰ gas at v ≈ +130 km s⁻¹: b(N⁰) = 4.5 ± 0.3 km s⁻¹ (Table 1). If we assume the gas is broadened by purely thermal motions, we can set a 2σ upper limit to the temperature T_e< 25,000 K. We achieve a similar limit by fitting the N gas and Si gas independently at the same redshift and use the difference in Doppler parameters to estimate T. Nevertheless, a CIE model with T_e≈ 25,000 K does roughly reproduce the observed ionic ratios of Si⁺/Si⁺³, Al⁺/Al⁺⁺, and Fe⁺/Fe⁺⁺ with N⁺/N⁰ discrepant (the model underpredicts this ratio). Therefore, one cannot rule out a model where collisional ionization is the primary mechanism producing the observed ionic ratios, although to invoke this scenario one must introduce a heat source to maintain the gas at this temperature because the cooling time is short (t_cool ≲ 10⁴ yr) for any reasonable density. In the following photoionization modeling, we will, however, assume that photoionization is dominant and thereby set an upper limit to the intensity of the ionizing radiation field. Finally, because the gas is partially ionized one presumes that T_e > 10,000 K. In the following and throughout the remainder of the paper we will adopt an electron temperature T_e = 20,000 K.

To explore photoionization, we have used the Cloudy software package (Ferland et al. 1998) to calculate the ionization state of plane-parallel slabs with total column density log N_H i = 18.6, density n_H = 0.1 cm⁻³, and metallicity [M/H] = −0.5, while varying the ionization parameter U ≡ Φ/n_Hc where Φ is the flux of ionizing photons having hν ⩾ 1 Ryd. The results are largely insensitive to this choice of volume density (they are nearly homologous with U), but they do vary with metallicity because this affects the cooling rate of the gas and the electron density. We will demonstrate that the assumed metallicity is consistent with the [O/H] value inferred from the observed O⁰/H⁰ ratio. For the calculations, we assume a power-law spectrum f_ν ∝ ν^−1.57 which is representative of z ∼ 2 quasars (Telfer et al. 2002). The results are nearly identical if we instead use the extragalactic UV background (EUVB) field computed by Haardt & Madau (1996) because the radiation fields have very similar slopes at the energies that span the IPs of the observed ions (hν = 1 − 3 Ryd). When the input U parameter is varied, the algorithm varies the number of gas slabs to maintain a constant N_H i value. Because subsystem A is optically thick, the results are sensitive to the assumed N_H i value; unfortunately, this quantity is not well constrained by the observations (Section 2). Larger N_H i values imply more self-shielding of the inner regions which, in turn, demand a more intense radiation field to explain the observed ionization states. The various ions respond differently to the shielding effects and pose an independent constraint on the N_H i value under the assumptions of this photoionization model. For example, we cannot reproduce the observed Fe⁺/Fe⁺⁺, Si⁺/Si⁺³, and N⁰/N⁺ ratios when N_H i > 10¹⁹ cm⁻²; the N⁰/N⁺ ratios require log U = −2 while the other two ratios set an upper limit log U < −3. Under the assumption of a single-phase photoionization model with f_ν ∝ ν^−1.57, the data require N_H i < 10^18.75 cm⁻² with a preferred value of N_H i ≈ 10^18.6 cm⁻². This central value is consistent with the line-profile analysis of Lyα and Lyβ for subsystem A (Figure 2).

Figure 4 presents the results of the Cloudy calculations for a series of ionic ratios for a wide range of ionization parameters assuming N_H i = 10^18.6 cm⁻². As noted above, we examine multiple ionization states of the same element (e.g., N⁰/N⁺) to provide constraints that are independent of intrinsic abundances. The observational constraints (Table 2) on the ionic ratios are indicated by vertical error intervals (or lower and upper limits) and the corresponding horizontal error intervals (or lower and upper limits) on log U are indicated. One notes that even with this lower N_H i value, the constraints are not fully consistent with a single U value; in particular the observed N⁰/N⁺ ratio indicates log U ≳ −3 whereas the other ratios imply log U < −3. Although this inconsistency may suggest the low and intermediate ions arise in a multiphase or nonequilibrium medium, we caution that the systematic uncertainties inherent to photoionization modeling of optically thick absorbers are large (e.g., the assumed spectral shape, cloud geometry, and uncertain atomic data). In the following we will adopt an ionization parameter log U = −3.0 dex with an uncertainty of 0.3 dex. This U value is similar to the results derived for other LLS at these redshifts (e.g., Prochaska 1999). It implies an ionization fraction x ≡ H⁺/H = 0.96 and a total hydrogen column density N_H ≡ N_H i/(1 − x) = 10^20.0 cm⁻²(N_H i/10^18.6 cm⁻²). Note that the error in 1 − x is roughly linear with the uncertainty in U for log U > − 4 dex.

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At low ionization parameters (log U < −2.5; Figure 5), the O⁰/H⁰ ratio is a good estimator of the oxygen abundance¹³ because the two atoms have very similar IPs and also because charge-exchange reactions mediate their ionization fractions. We calculate [O/H] ≡log(O/H) − log(O/H)_☉ = −0.65 − log₁₀(N_H i/10^18.6 cm⁻²), assuming a solar oxygen abundance log(O/H)_☉ = −3.34 dex. The uncertainty in this measurement (and any other chemical abundance measurements of subsystem A) is dominated by the poor constraint on the N_H i value. The Lyα and Lyβ profiles indicate N_H i < 10¹⁹ cm⁻² which sets a lower limit to the metallicity of 1/10 solar abundance.

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Relative abundance ratios (e.g., O/Fe) are less sensitive to the H i column density but are not strictly independent of N_H i because it dominates the opacity in our ionization models. Adopting log U = −3 and log N_H i = 10^18.6 cm⁻², we find the following relative abundance values: [O/Fe] = +0.6 ± 0.1, [O/C] <+0.75, and [N/O] = −0.1 ± 0.2 dex (Table 3). The reported errors are dominated by uncertainty in the U parameter. We interpret these chemical abundance measurements in Section 4.2.

Independent of photoionization modeling, the data yield a measurement of the electron density from the observed populations of the fine-structure levels of Si⁺ and/or C⁺. The J = 1/2 ground state of these ions has a corresponding J = 3/2 fine-structure level which can be populated by collisions with ions and atoms, via indirect UV pumping, and also via a magnetic-dipole transition. For a partially ionized gas (demanded by the observed N⁺/N⁰ ratio), collisions with free electrons should dominate excitation to the J = 3/2 upper level. Indirect UV pumping could also contribute, but the quasars (foreground and background) are too distant and we assume that there are no important local sources (e.g., OB stars). In any case, contributions from UV pumping would only tighten the following upper limit on n_e. Unfortunately, the transitions from the J = 3/2 excited level of C⁺ are blended with the resonant C ii transitions of subsystem B. Therefore, only the Si⁺ levels (which have a wider energy separation) are available for analysis. We set an upper limit to the relative populations based on the nondetection of the Si ii* 1264 transition, log [N(Si⁺_{J = 3/2})]/[N(Si⁺_{J = 1/2})] < −2.2 dex. For a gas with T_e ≫ 413 K, the level populations for excitation dominated by electron collisions is given by:

$$\begin{equation} \frac{{N\big({\rm Si^+_{J=1/2}}\big)}}{{N\big({\rm Si^+_{J=3/2}}\big)}} = \frac{1}{2} + \frac{640 T_4^{1/2}}{n_{\rm e}} \;\;\; (T \gg 413\, {\rm K}) \;\;\;. \end{equation} \tag{ 1 }$$

Adopting T_e = 20, 000 K, the observations place an upper limit on the electron density, n_e < 6 cm⁻³.

One can use this constraint on the electron density to constrain the hydrogen volume density n_H by assuming the ionization fraction from our photoionization model, i.e., x = 0.96. We calculate

$$\begin{equation} n_{\rm H} = n_{\rm e}/x < 6.2 \, {\rm cm^{-3}} \;\;\;. \end{equation} \tag{ 2 }$$

One can also estimate a lower limit for the characteristic size of the system,

$$\begin{equation} \ell \equiv \frac{x}{1-x} \frac{N_{{\rm H}\, {*navin* i*navin*}}}{n_{\rm e}} \;\;\;. \end{equation} \tag{ 3 }$$

We derive ℓ>5.2(N_H i/10^18.6 cm⁻²) pc.

In comparison with subsystem A, we find similar results for the ionization state of subsystem C. These include strong N ii absorption relative to N i which indicates a partially ionized gas. Again, a CIE model with T_e ≈ 20, 000 K yields ionic ratios consistent with the majority of observed ionic ratios, but we will focus on photoionization models of the gas. Like subsystem A, we also find that models with N_H i < 10¹⁹ cm⁻² are preferred and the observed ionic ratios (Fe⁺/Fe⁺⁺, N⁰/N⁺, Si⁺/Si⁺³) imply N_H i ≈ 10^18.6 cm⁻² and log U ≲ −3. Using the same Cloudy model assumed for subsystem A, we derive the chemical abundances listed in Table 3.

In contrast to subsystem A, we measure larger metal column densities and a correspondingly higher oxygen abundance, [O/H] = +0.2 − log₁₀(N_H i/10^18.6 cm⁻²), if the subsystems have comparable N_H i values. Even if we have underestimated the H i column density of subsystem C by a factor of 0.5 dex (the maximum value allowed by the observed Lyα profile; Figure 2), the gas metallicity would be roughly solar. This lower limit ([O/H] > − 0.25) matches the highest values observed for DLA systems (Prochaska et al. 2007) and all but a few super-LLS studied to date (Péroux et al. 2006; Prochaska et al. 2006). The data also suggest variations between the oxygen abundances of subsystems A and C (and also B, see below). Abundance variations like these are rarely studied in optically thick absorption-line systems because it is difficult to resolve the H i Lyman series (G. Prochter et al. 2008, in preparation).

The relative chemical abundances of O/Fe and N/O are also significantly higher in subsystem C than subsystem A: [O/Fe] = +1.3 ± 0.1 dex, [N/O]= +0.3 ± 0.2 dex. Although these values include ionization corrections (IC; Figure 5), the gas is indisputably α-enhanced and the N/O ratio must be greater than one half solar. This N/O value is unique for optically thick absorbers and the large α-enhancement also exceeds most measurements of O/Fe in extragalactic environments. We interpret these results further in Section 4.2.

We derive a constraint on the electron density of subsystem C from observations of fine-structure levels of C⁺ and Si⁺. Assuming that excitation of the upper level is dominated by electron collisions, the populations of the excited state to the ground state for C⁺ are related to the gas temperature and electron density, e.g.,

$$\begin{equation} \frac{{N\big({\rm C^+_{J=1/2}}\big)}}{{N\big({\rm C^+_{J=3/2}}\big)}} = \frac{1}{2} + \frac{37 T_4^{1/2}}{n_{\rm e}} \;\;\; (T \gg 92\, {\rm K}) \;\;. \end{equation} \tag{ 4 }$$

As for subsystem A, we assume T_e = 20,000 K, and obtain

$$\begin{equation} n_{\rm e} = \frac{106}{2 \frac{{N({\rm C^+_{J=1/2}})}}{{N({\rm C^+_{J=3/2}})}} - 1} \;\;\;. \end{equation} \tag{ 5 }$$

Although the column density of the C⁺_{J = 3/2} excited state is well constrained by the spectra, the resonance C ii 1036 and C ii 1334 transitions are heavily saturated. A conservative lower limit to N(C⁺_{J = 1/2}) is derived by integrating the optical depth profile assuming a normalized flux equal to the 1σ error estimate, N(C⁺_{J = 1/2})>10^14.8 cm⁻². Combined with our measurement of N(C⁺_{J = 3/2}), we set an upper limit to the electron density n_e < 3.5 cm⁻³. Similar to subsystem A, we also derive an upper limit to n_e from the nondetection of the Si⁺ excited level, n_e < 2.5 cm⁻³ for T_e = 20,000 K (Equation 1). Assuming the same photoionization model (log U = −3, x = 0.96) as for subsystem A, we infer a hydrogen volume density n_H < 2.6 cm⁻³ and a lower limit to the characteristic size, ℓ>15.5(N_H i/10^18.6 cm⁻²) pc.

Because we have a positive detection for the C ii* 1335 transition, we may further constrain the volume density by estimating the total C⁺ column density from a proxy ion. A good choice is Si⁺ because our Cloudy calculations indicate Si⁺/Si ≈ C⁺/C for log U ≈ −3 dex. This requires, however, that one adopt a value for the intrinsic Si/C ratio. If we assume solar relative abundances [Si/C] = 0, which is consistent with the C/Si ratio deduced from the ratio of C iv to Si iv assuming the IC of our best-fit photoionization model, we estimate log N(C⁺) = 15.2 dex. From Equation (4) we estimate n_e = 1.7 cm⁻³, which nearly matches the upper limit we have derived above. A more conservative estimate is to assume [Si/C] > − 1 and report a lower limit to the electron density, n_e > 0.2 cm⁻³.

As noted in Section 2, the velocity profiles of subsystem B are complex and preclude a well constrained solution using line-profile fitting techniques. Our expectation is that the velocity profiles comprised a series of overlapping components each with a line-profile similar to the components observed in subsystems A and C. With higher S/N data, one might be able to discern such structure. For now, we use the AODM to measure ionic column densities for this subsystem. This approach is problematic, however, for constraining the ionization state because the ionic ratios vary across the velocity profiles (e.g., N⁺/N⁰ is significantly larger at δv = +470 km s⁻¹ than δv = +350 km s⁻¹). Therefore, we cautiously report constraints on the ionization state and chemical abundances. We examine the integrated ionic column densities (and their ratios) which give optical depth weighted averages.

The integrated ionic column density ratios (e.g., N⁰/N⁺, Fe⁺/Fe⁺⁺) in subsystem B are consistent with those observed for subsystems A and C. This suggests that the average ionization state of subsystem B is similar to that of subsystems A and C. Empirically, the low observed Fe⁺/Fe⁺⁺ and Al⁺/Al⁺⁺ ratios imply a modestly ionized gas with log U < −2.5 dex, and the oxygen abundance should follow the O⁰/H⁰ ratio: [O/H] = −0.64 ± 0.15 dex. This value is lower than the O/H abundance derived for subsystem C and suggests modest abundance variations exist between the subsystems. We also note that the observed O⁰/Fe⁺ ratio for subsystem B requires at least a modest α-enhancement, [O/Fe] > + 0.4 dex and that the observed N⁰/O⁰ ratio implies [N/O] > − 0.7 dex. These values are similar to the results derived for subsystem A. For the remainder of the paper, we will adopt log U = −3.0 for this subsystem. Because this subsystem has a significantly higher N_H i value, this implies a higher neutral fraction (1 − x = 0.2) compared to subsystems A and C.

Finally, the nondetection of Si ii* 1264 absorption sets an upper limit to the electron density n_e < 2.5 cm⁻³ under the assumption that electron collisions dominate the excitation rate and that T_e = 20, 000 K (Equation 1). If we assume the gas has an ionization fraction near unity, we set a similar upper limit for the hydrogen volume density and a size estimate ℓ>21 pc.

The most robust measurements for SLLS/SDSSJ1204 +0221BG from our high-resolution spectrum of SDSSJ1204 +0221BG are on the velocity field of the gas. Both the absolute (i.e., redshift) and relative velocities constrain the origin of the gas and its relation to the foreground quasar SDSSJ1204+0221FG. The redshift of SDSSJ1204+0221FG was measured from our observations of the rest-frame optical [O iii] λ5007 emission line using the GNIRS spectrometer on the Gemini-S telescope (Section 2; Figure 1). We achieved a velocity precision of ≈40 km s⁻¹ giving z_fg = 2.4360 ± 0.0005. Figures 2 and 3, which present the velocity profiles of SLLS/SDSSJ1204+0221BG relative to z_fg, show strong H i and metal-line absorption from δv ≈ +70 to +700 km s⁻¹. These absorption profiles have two notable characteristics. First, the gas along the SDSSJ1204+0221BG sightline is asymmetrically distributed relative to z_fg, i.e., within a 2000 km s⁻¹ window centered on z = z_fg, there is significant absorption only at z > z_fg. The nearest "cloud" with τ_Lyα > 1 and δv < 0 km s⁻¹ lies off of Figure 2 at δv ≈ −1500 km s⁻¹, which corresponds to ≈6 h⁻¹ Mpc (proper) under the assumption of Hubble expansion. Second, the total velocity width is very large, Δv ≈ 650 km s⁻¹. One may compare this value against the velocity widths measured for systems with comparable H i surface density, i.e., the DLA and SLLSs. Regarding the former, the velocity width of SLLS/SDSSJ1204+0221BG exceeds greater than 99% of the Δv values for randomly selected DLAs at z > 2 (Prochaska & Wolfe 1997, 2001). Regarding the SLLS population (Péroux et al. 2003), none have as large a velocity width. The equivalent width of the metal-line transitions (a proxy for velocity width) is also large compared with systems selected on the basis of metal-line absorption (e.g., the Mg ii systems; Prochter et al. 2006). In these respects, the velocity field of the gas near SDSSJ1204+0221FG is extreme.

Several factors lead us to conclude that the distance between the gas in SLLS/SDSSJ1204+0221BG and SDSSJ1204 +0221FG is comparable to the impact parameter. Recall that SLLS/SDSSJ1204+0221BG exhibits a multicomponent kinematic structure with unusually large velocity width between the components. If the relative motions of the clouds and the quasar are to be interpreted as Hubble flow, their implied line-of-sight separation would be ≈2.8 Mpc (for Δv ≈ 700 km s⁻¹). The chance alignment of several galaxies across this large distance is unlikely, however, which we can quantify with clustering arguments. Quasars arise in highly biased regions of the universe. They are observed to cluster strongly on ∼10 h⁻¹ Mpc scales (Croom et al. 2001; Porciani et al. 2004; Croom et al. 2005; Myers et al. 2007a; Shen et al. 2008b) and the correlation function steepens considerably on smaller scales ∼100 h⁻¹ kpc (Hennawi 2004; Hennawi et al. 2006b; Myers et al. 2007b, 2008). High-redshift quasars also exhibit a large cross-correlation amplitude with star-forming galaxies (Adelberger & Steidel 2005; Coil et al. 2007), and it is possible that galaxies clustered around the quasar are giving rise to the Lyα and metal-line absorption seen in SLLS/SDSSJ1204+0221BG. Another possibility is that the absorption in SLLS/SDSSJ1204+0221BG is not due to a nearby galaxy, but is rather halo gas distributed around the quasar with some density profile. Either scenario results in a clustering pattern around the quasar, which we measured in Hennawi & Prochaska (2007). The probability P(<r|R_⊥, v_max) that the total distance between the quasar and the absorber is less than r, given a fixed impact parameter R_⊥ and the knowledge that absorption occurs within a velocity interval ±v_max, is simply an integral over this quasar–absorber correlation function.

Figure 6 shows this cumulative probability for v_max = 700 km s⁻¹ and the impact parameter of R_⊥ = 108 kpc, from which we deduce that the probability for the gas in SLLS/SDSSJ1204+0221BG lying within 500 kpc of SDSSJ1204+0221FG is ≈70%. Perhaps an even stronger argument that the gas in SLLS/SDSSJ1204+0221BG lies at a distance comparable to the impact parameter is that the physical characteristics (ionization state, H i surface density, chemical abundances) of the subsystems comprising SLLS/SDSSJ1204+0221BG show only modest variations. Several of these same properties—specifically the metallicity, relative abundance pattern, and the velocity field—are highly anomalous compared with the population of intervening optically thick absorbers. In particular, the only place that such large N/O ratios are observed is in quasar environments. Finally, it is worth emphasizing that the very small sizes deduced for the subsystems of SLLS/SDSSJ1204+0221BG (d ≲ 100 pc) imply that their relative separations are also comparable to the impact parameter. The alternative, which would be for the subsystems to be part of a single structure with size d ≲ 100 pc, would imply an unphysically large velocity shear across this small distance.

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Clues to the origin of SLLS/SDSSJ1204+0221BG are encoded in the enrichment pattern of its gas. In particular, the relative abundances constrain the timescales and intensity of star formation of the galaxy (or galaxies) that produced the observed metals. Because the gas is partially ionized and we do not observe transitions from all ionization states, we proceed cautiously to interpret the observed ionic ratios. One robust conclusion from our abundance analysis (Section 3; Table 4) is that the gas is highly enriched. The observed O⁰/H⁰ ratio indicates [O/H] > − 1 across the ≈650 km s⁻¹ velocity interval spanning the entire system and we derive an integrated average abundance: [O/H]_TOT > − 0.5 dex. This metallicity is expressed as a lower limit for several reasons. First, IC to the observed O⁰/H⁰ ratios will give larger [O/H] values (Figure 5). Second, the lower limit assumes the nearly maximal N_H i values permitted by the data for the three subsystems. If we adopt a modest IC and lower N_H i values, the oxygen metallicity for SLLS/SDSSJ1204+0221BG approaches the solar abundance. Finally, a proper derivation of the oxygen metallicity for the SLLS is to take an N_H-weighted average of each subsystem. This is especially important for predominantly ionized gas. Using our fiducial values, we find <[O/H]> = −0.23 dex assuming no IC. We emphasize that even a 1/3 solar metallicity ([O/H] = −0.5 dex) represents a very high enrichment level. It exceeds the metallicity of nearly all optically thick absorbers at these redshifts: 98% of sightlines randomly intersecting galaxies (DLAs; Prochaska et al. 2003) and 95% of the super-LLS population (Péroux et al. 2007). Such high enrichment levels are generally observed only in gas within and around starburst galaxies (Pettini et al. 2002; Simcoe et al. 2006) and in quasar environments (Dietrich et al. 2003; D'Odorico et al. 2004; Arav et al. 2007).

The observations also constrain the relative abundances of O, Fe, and N, e.g., the O/Fe and N/O ratios. These diagnostics are valuable for constraining the star formation history for SLLS/SDSSJ1204+0221BG because each element is associated with a unique nucleosynthetic site and has a unique production timescale. Oxygen is made in massive stars and one predicts minimal delay (t < 100 Myr) for its nucleosynthesis and release to the ISM following the onset of star formation. The production of nitrogen and iron, however, is expected to be delayed by several 100 Myr to ≈1 Gyr because these elements are made in intermediate-mass stars and Type Ia Supernova (SN), respectively. By examining the relative abundances of O, N, and Fe, therefore, one may constrain the duration of the star formation episode that produced the metals.

Unfortunately, the relative abundance ratios of O, N, and Fe are more sensitive to the ionization state of the gas. The most conservative treatment is to report lower limits to O/Fe and N/O from the observed ionic column density ratios of O⁰/Fe⁺ and N⁰/O⁰. As with O⁰/H⁰, corrections to these ionic ratios are positive definite (Figure 5). We measure lower limits to [O/Fe] of +0.1, + 0.5, + 0.8 dex for subsystems A, B, C, respectively, and conclude the gas has a super-solar α/Fe ratio. For even a modest IC, the integrated average α/Fe ratio approaches 10 times the solar ratio and exceeds the value measured for nearly all intervening absorption-line systems. In Figure 7, we present an estimate for these values for the various subsystems and also for the N_H-weighted averages against measurements for a set of high-z galactic observations.

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In the local universe, large α/Fe ratios are observed in metal-poor stars (e.g., McWilliam 1997), massive early-type galaxies (Trager et al. 2000), and highly depleted ISM gas (e.g., Savage & Sembach 1996). The first two examples reflect nucleosynthetic enhancements and are attributed to the Type II supernovae (SNe) of massive stars. The latter example, however, results from the highly refractory nature of Fe relative to O, i.e., one observes enhanced O/Fe gas-phase abundances in the ISM because Fe is preferentially depleted into dust grains. The observed α/Fe enhancement in SLLS/SDSSJ1204+0221BG could be due to one or both of these effects, but our expectation is that differential depletion is not dominant. A high depletion level would be unusual for gas with modest surface and volume densities that is predominantly ionized with a temperature of T ≈ 20, 000 K. It is more likely that the super-solar α/Fe ratios reflect an intrinsic, nucleosynthetic enhancement. Granted the high metallicity of SLLS/SDSSJ1204+0221BG, the α/Fe enhancement suggests a star formation history representative of bright spheroids (e.g., bulges, elliptical galaxies Graves et al. 2007). Chemical evolution modeling suggests these stellar systems underwent a short period of intense star formation where the gas was rapidly enriched by SNe from massive stars before Type Ia SN could contribute (e.g., Matteucci 1994). We conclude that the metals for SLLS/SDSSJ1204+0221BG were produced in a starburst lasting less than ∼1 Gyr.

The N/O ratio of the gas offers additional constraints on the star formation history. Similar to O/Fe, IC may be important and the conservative approach is to adopt the N⁰/O⁰ ratio as a lower limit to N/O. We find [N/O] > − 0.7 dex for subsystems A and B and [N/O] > − 0.2 dex for subsystem C (Table 4). The observations, specifically the large N⁺/N⁰ ratio, indicate nonzero IC. We estimate the correction from photoionization modeling to be +0.25 to +0.5 dex for log U = −4 to −3 dex and conclude that N/O is at least 1/3 of the solar ratio in each subsystem and may be super-solar in subsystem C. These values are larger than N/O values observed for quasar absorption-line systems (Figure 7; e.g., Henry & Prochaska 2007). Indeed, solar N/O ratios are commonly observed only in quasar environments (Hamann & Ferland 1999; Dietrich et al. 2003; D'Odorico et al. 2004; Arav et al. 2007). This further reflects the high metallicity of SLLS/SDSSJ1204+0221BG because N behaves as a "secondary element" with its yield scaling as the square of the enrichment level (M/H)². Therefore, one expects near-solar or even super-solar N/O abundances in high-metallicity environments. The exception to this expectation is if the system is too young for many intermediate-mass stars to have cycled through the asymptotic giant branch phase. The observation of nearly solar N/O in SLLS/SDSSJ1204+0221BG, therefore, implies the gas was enriched over an episode of at least a few 100 Myr (Matteucci & Padovani 1993; Romano et al. 2002).

As noted above, the high metallicity and solar or super-solar N/O and α/Fe ratios for SLLS/SDSSJ1204+0221BG describe a chemical abundance pattern that matches the abundances commonly measured for gas near quasars. This includes the high metallicities inferred from emission lines from the quasar broad-line region and the relative abundances derived for NAALs (Dietrich et al. 2003; D'Odorico et al. 2004). We are inclined, therefore, to causally connect the enrichment pattern of SLLS/SDSSJ1204+0221BG with SDSSJ1204+0221FG. A key question that follows is whether the metals were produced by the quasar's host galaxy or whether they originated in a neighboring galaxy or galaxies. The latter hypothesis would imply that galaxies near quasars have enrichment histories similar to that inferred for the quasar environment, which could be tenable considering that early-type galaxies near the centers of modern clusters have very uniform colors and spectra indicating a common age of formation and star formation history (e.g., Bower et al. 1992). Alternatively, as we discuss further in the next section, the metals may have been generated during an early episode of star formation in the host galaxy of SDSSJ1204+0221FG, and then transported to large radii R_⊥ ≈ 100 kpc via a large-scale outflow in ≈100 Myr time. To achieve a high N/O ratio while maintaining a super-solar α/Fe ratio, the data suggest a starburst lasting several 100 Myr but less than ≈1 Gyr. It is intriguing that the implied sequence of early, intense star formation followed by an optically bright quasar phase and possibly a large-scale outflow follows the general prescription for quasar activity proposed by Hopkins and collaborators (Springel et al. 2005a; Cox et al. 2006; Hopkins et al. 2008a).

The current paradigm of baryons within galactic halos envisions a hot, diffuse medium that has been heated by shocks during virialization and/or feedback from SNe within the galaxy. Embedded within this diffuse medium may be cooler, dense clouds that may be photoionized by the local or background UV radiation field. In the Galaxy, this simple picture is supported by the observations of the high-velocity clouds (cool, dense clumps, e.g.; Wakker & van Woerden 1997; Putman et al. 2002) and the widespread detection of O vi absorption which traces a hotter, diffuse medium (Sembach et al. 2003). This model is also supported by quasar absorption line surveys, i.e., the association of Mg ii, C iv, and O vi gas with galactic halos (e.g., Steidel 1993; Chen et al. 2001; Fox et al. 2007). On theoretical grounds, it has been argued that a hot diffuse component pressure confines a population of cold clouds, which are unlikely to be massive enough to be self-gravitating (Mo & Miralda-Escude 1996; Maller & Bullock 2004).

With these scenarios in mind, we are motivated to search for absorption from a diffuse, hot component that could be associated with the halo of SDSSJ1204+0221FG. The sightline to SDSSJ1204+0221BG intersects the presumed galactic halo of SDSSJ1204+0221FG at an impact parameter R_⊥ = 108 kpc. As we will see in Section 5.1, the virial radius of the dark matter halo expected to host SDSSJ1204+0221FG is r_vir ≃ 250 kpc, so that our background sightline easily resolves the virial radius. In Section 3, we discussed the detection and analysis of low and intermediate ion transitions observed in SLLS/SDSSJ1204+0221BG. We also commented on the general absence of strong absorption by high ions like O⁺⁵, C⁺³, and N⁺⁴. These ions trace gas either with a large ionization parameter (log U > − 2) or with a high temperature (T > 10⁵ K). Their observed column densities, therefore, constrain the nature of a diffuse and/or hotter phase within the halo of SDSSJ1204+0221FG.

In Figure 8, we present the apparent column densities, Nⁱ_a ≡ 10^14.5761ln(1/Iⁱ)/(fλ), of the C iv, N v, and O vi profiles (smoothed by 5 pixels) for the velocity interval spanning the quasar redshift and the three subsystems of SLLS/SDSSJ1204+0221BG. The C⁺³ and O⁺⁵ ions exhibit multiple transitions which allow one to identify line blending by visual inspection, i.e., regions where the two profiles diverge significantly. The C iv 1548 and 1550 profiles track each other closely for δv > + 200 km s⁻¹ indicating a positive detection without blending at these velocities. At δv < +200 km s⁻¹, the profiles diverge because the C iv 1548 profile of component C blends into the C iv 1550 profile of component A (see also Figure 3). Therefore, the C iv 1548 profile sets an upper limit to the column density of C⁺³ at these velocities. At δv ⩽ 0 km s⁻¹, there is no statistically significant detection of C iv.

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The N v and O vi doublets lie within the Lyα forest and therefore are more likely to suffer from line blending. Examining the O vi transitions, the two profiles diverge at nearly all velocities. This indicates that the line profiles are severely affected by blends, most likely Lyα and Lyβ absorption from gas at lower redshift. The only interval where the O vi profiles roughly coincide is at 400 km s⁻¹ < δv < 550 km s⁻¹. One may optimistically interpret the absorption as a positive detection of O⁺⁵ ions, but the more conservative approach is to report even this absorption as an upper limit. Turning to N v, we present only the N v 1242 transition because the N v 1238 profile is heavily blended with a strong Lyα system at z = 2.502. We also expect that the broad absorption at δv < 200 km s⁻¹ is associated with coincident Lyα absorption; meanwhile, the optical depth in subsystem C (δv < 600 km s⁻¹) is not statistically significant. The only plausible N v absorption, therefore, is within subsystem B where one notes the optical depth profile of N v 1242 resembles that of C iv in the interval 300 km s⁻¹ < δv < 500 km s⁻¹. We caution, however, that the O vi profiles do not track N v in this velocity interval. This draws into question a positive detection of N v absorption because the O⁺⁵ and N⁺⁴ ions trace gas with similar physical properties and one generally expects coincident N v and O vi absorption. It is possible, therefore, that the apparent N v profile instead tracks an unidentified blend and we report the measured optical depth as an upper limit to N(N⁺⁴) in subsystem B.

Table 5 summarizes the column densities of the high ions in subsystems A, B, and C and in the velocity interval containing z = z_fg. For C⁺³ and N⁺⁴, the column densities are lower than 10¹⁴ cm⁻² and fall below 10¹³ cm⁻² in several regions. For O⁺⁵, the upper limits are a factor of 10 higher owing to noisier data and a higher frequency of line blending. All of these values lie below the ≳10¹⁴ cm⁻² column densities measured for the low ions of CNO in SLLS/SDSSJ1204+0221BG (Table 2). This has significant implications for the physical conditions of diffuse gas associated with the galactic halo of SDSSJ1204+0221FG.

A direct conclusion from these observations is that the sightline does not intersect a large column density of an optically thin, photoionized material. In the lower panel of Figure 9, we present the predicted column densities of C⁺³, N⁺⁴, and O⁺⁵ ions for a wide range of physical density assuming an absorber with total hydrogen column density N_H = 10^20.5 cm⁻² and metallicity [M/H] = −0.5 dex. For these calculations, we assume the gas is illuminated by the SDSSJ1204+0221FG at a distance of r = R_⊥. Focusing on the parameter space where the gas is optically thin (n_H < 0.3 cm⁻³), one predicts column densities exceeding 10^14.5 cm⁻² for all of the ions. Even if we assume a 10× lower metallicity, we can rule out such a phase of gas along the sightline.

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The absence of photoionized high ions like O⁺⁵ is not particularly surprising, however, because the ambient medium in the outer galactic halo surrounding a high-z quasar almost certainly is at a temperature so high that collisional ionization dominates over photoionization. This material may be observed independently of the gas contributing to SLLS/SDSSJ1204+0221BG. A galaxy with mass M > 10¹²M_☉, for example, has an implied virial temperature in excess of 10⁶ K and the dark matter halo expected to host SDSSJ1204+0221FG would have a virial temperature T_vir ∼ 10⁷ K (see Section 5.1). In Figure 10 we present predicted column densities for C⁺³, N⁺⁴, and O⁺⁵ ions assuming CIE (Sutherland & Dopita 1993), N_H = 10^21.8 cm⁻², and [M/H] = −0.5 dex. This H column density is the predicted value at R_⊥ = 108 kpc in a M = 10^13.3M_☉ halo with a Navorro–Frank–White (NFW) profile (concentration c = 4) and assuming a gas fraction f_g = 0.17 equal to the cosmic baryon fraction (Dunkley et al. 2008, see Section 5.1). The figure demonstrates that the gas must have T > 10⁶ K to be consistent with the observed upper limits to N(O⁺⁵). The dependence of N(O⁺⁵) on T is so strong that even if we assume considerably lower N_H and [M/H] values for the diffuse component, the gas must have T > 10⁶ K. A cooler phase is only allowed if log N_H + [M/H] < 17.7.

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The principal conclusion of this section is that a diffuse medium in the halo of SDSSJ1204+0221FGmust have a temperature exceeding 10⁶ K. This is consistent with the virial temperature T_vir ∼ 10⁷ K for the gas in the M ≳ 10¹³M_☉ dark matter halo that is expected to host the f/g quasar (see Section 5.1). Note, however, that the absence of strong high ion transitions associated with SDSSJ1204+0221FG contrasts with similar observations (using a b/g quasar sightline) of z ∼ 2.3 star-forming galaxies where strong O vi and N v absorption is detected at similar impact parameters (Simcoe et al. 2006). In addition, the damped Lyα systems (DLAs) also frequently exhibit O vi absorption which reflects a highly ionized, diffuse medium in the halos of these galaxies (Fox et al. 2007). The average N(O⁺⁵) for the DLAs exceeds 10¹⁴ cm⁻². The DLA sightlines presumably intersect galactic halos at much smaller impact parameters than R_⊥ = 108 kpc. Nevertheless, the high ion material in DLAs is undoubtedly associated with the galactic halo (Wolfe & Prochaska 2000; Maller et al. 2003; Prochaska et al. 2008a) and may extend to many tens kpc. The fundamental difference is that DLA sightlines will rarely penetrate the galaxies hosting high-z quasars and likely trace lower mass halos with significantly lower virial temperatures.

Of considerable interest to studies of quasars and the buildup of supermassive black holes in the universe (e.g., Yu & Tremaine 2002; Hopkins et al. 2007b; Shankar et al. 2007) is whether their optical–UV emission is isotropic and/or intermittent. Evidence that quasars emit anisotropically or intermittently comes from the null detections of the transverse proximity effect in the Lyα forests of projected quasar pairs (Crotts 1989; Dobrzycki & Bechtold 1991; Fernandez-Soto et al. 1995; Liske & Williger 2001; Schirber et al. 2004; Croft 2004, but see Jakobsen et al. 2003), the anisotropic clustering of optically thick absorbers near quasars (Hennawi & Prochaska 2007; Prochaska et al. 2008b), and the absence of fluorescence detections in optically thick gas proximate to quasars (J. F. Hennawi & J. Prochaska 2009, in preparation; but see Adelberger et al. 2006). Together, these studies provide a statistical case that quasars emit anisotropically or intermittently.

For an individual quasar, one can use a background sightline to observe nearby gas in absorption, and test whether it is illuminated by studying its ionization state. The general approach is to (1) derive the ionization parameter U of the gas near the quasar using ionic metal-line transitions, (2) estimate the volume density of the gas, and (3) compare the inferred intensity of the impingent radiation field with that estimated for the nearby quasar. Worseck et al. (2007) and Goncalves et al. (2008) have conducted this test for highly ionized gas near several z ∼ 2 quasars. The Worseck et al. (2007) study was deemed inconclusive. Goncalves et al. (2008), meanwhile, identified several absorbers proximate to quasars with high ionization parameters and estimated an ionizing radiation field that exceeds the EUVB. Instead, the estimated fluxes roughly match the values calculated for the nearby quasars under the assumption that they emit isotropically. These authors, however, did not place empirical constraints on the gas density, did not consider the effects of collisional ionization, and did not explore the effects of nonsolar relative abundances. In these respects, we consider their results to be suggestive but inconclusive.

We can similarly test for illumination of SLLS/SDSSJ1204 +0221BG by SDSSJ1204+0221FG. In Section 3, we compared the observed ratios of N, Si, Al, Fe, and C atoms and ions against photoionization models assuming a single phase, plane-parallel slab of gas illuminated by a quasar spectrum (f_ν ∝ ν^−1.57). For subsystems A+C of SLLS/SDSSJ1204+0221BG, the majority of the observational constraints imply log U < −3.25. The only exception is the large N⁺/N⁰ ratio which indicates log U ≈ −3 for subsystem A, and log U > − 4 for subsystem C. Under the constraints of a single-phase model and a plane-parallel geometry, one cannot identify an equilibrium photoionization model that reproduces all of the observed ionic ratios. By the same token, the observations are inconsistent with any CIE model. We do not know if these inconsistencies highlight errors in the atomic data (e.g., dielectronic recombination rates), the oversimplification of a single-phase, plane-parallel geometry, an erroneous shape for the radiation field, and/or the presumption of equilibrium models. We will proceed under the relatively conservative assumption that the ionization parameter log U < −3 and we will comment on the implications for significantly smaller values. We also remind the reader that the observed ionic ratios are roughly consistent with a T ≈ 20, 000 K CIE model. Any contribution of collisional ionization processes to the observations would lower the estimated flux of ionizing radiation.

The other key physical constraint is the volume density of the gas n_H. For a predominantly ionized gas, this can be estimated from the electron density n_e. Our analysis of the fine-structure levels of the C⁺ and Si⁺ ions indicates n_e less than approximately 5 cm⁻³ for each of the subsystems. These upper limits could be improved by obtaining higher S/N observations of the undetected Si ii* 1264 transition at λ ≈ 4350 Å. In any case, we will adopt this conservative limit to the electron density and assume n_H ≈ n_e, which is appropriate for a predominantly ionized medium.

Adopting log U < −3 and n_H < 5 cm⁻³, we infer an upper limit to the ionizing photon flux,

$$\begin{equation} \Phi _{\rm obs} = U n_{\rm H} c \; < \; 1.5{\; \times \; 10^{8}} \;{\rm photons \; s^{-1} \; cm^{-2}}. \end{equation} \tag{ 6 }$$

We may compare this value with the ionizing flux of SDSSJ1204+0221FG under the assumptions that the gas lies at a distance equal to the impact parameter and that the quasar emits isotropically. Combining the SDSS optical photometry of SDSSJ1204+0221FG with an assumed power-law spectral shape (f_ν ∝ ν^−1.57), we derive an AB magnitude m₉₁₂ = 21.42 at 1 Ryd. At z_fg = 2.436, this gives a specific luminosity L₉₁₂ = 1.16 × 10³⁰ erg s⁻¹ cm⁻² Hz⁻¹ and we estimate an ionizing photon flux at r = R_⊥ = 108 kpc of

$$\begin{equation} \Phi _{\rm QSO} = 9{\; \times \; 10^{7}} \; {\rm photons \; s^{-1} \; cm^{-2}}, \end{equation} \tag{ 7 }$$

assuming the quasar emits isotropically. Therefore, the conservative upper limit to Φ_obs roughly matches the predicted photon flux from SDSSJ1204+0221FG at the observed impact parameter. In this conservative observational limit, we do not have strong evidence for anisotropic emission.

If we adopt less conservative but more realistic constraints on the ionization parameter and volume density (log U < −4; n_H < 1 cm⁻³), we set an upper limit to the observed photon flux Φ'_obs < 3 × 10⁶  photons s⁻¹ cm⁻². To maintain the null hypothesis that SLLS/SDSSJ1204+0221BG is illuminated, we would require the gas to be located at r > 500 kpc. This large distance is disfavored by other arguments. The extreme velocity field, high metallicity, and quasar-like relative abundances suggest the gas is local to the quasar host galaxy. At r = 500 kpc, one could associate SLLS/SDSSJ1204+0221BG with a protocluster containing SDSSJ1204+0221FG, but not its galactic halo. Furthermore, the strong clustering of optically thick absorbers around quasars at z ∼ 2.5 implies a high probability that r ≈ R_⊥ (Hennawi & Prochaska 2007). In Figure 6, we show the probability of the absorber lying at a distance less than r from the f/g quasar, given the knowledge that it is within a velocity interval v_vmax = ±700 km s⁻¹ and has an impact parameter R_⊥ = 108 kpc. The upper x-axis of the figure shows the corresponding cumulative probability of the ionizing flux ϕ_QSO, assuming that SDSSJ1204+0221FG emits isotropically. We calculate a 70% probability that SLLS/SDSSJ1204+0221BG is located within 500 kpc of the quasar.

We independently test whether the transverse direction is illuminated by searching for Lyα fluorescence from the optically thick gas near the b/g quasar sightline. By coadding a series of longslit exposures of SDSSJ1204+0221 using Gemini/GMOS, amounting to a 7200 s total integration, we have not detected any extended emission (J. F. Hennawi & J. Prochaska 2009, in preparation; but see Adelberger et al. 2006) at the f/g quasar redshift near the impact parameter of the b/g quasar sightline. The gas clouds comprising SLLS/SDSSJ1204+0221BG have estimated sizes of ∼ 10–100 pc, making them so small that it would be impossible (with current sensitivity) to detect Lyα emission from the actual clouds we see in absorption in SLLS/SDSSJ1204+0221BG. However, the high covering factor of optically thick gas near foreground quasars with R_⊥ ≲ 100 kpc characterized statistically by Hennawi et al. (2006a), together with the detection of three such optically thick subsystems in SLLS/SDSSJ1204+0221BG, argues that the covering factor of optically thick gas is indeed roughly unity at R_⊥ near SDSSJ1204+0221FG. If this gas is illuminated, it should be emitting detectable Lyα photons. The fluorescent surface brightness of clouds illuminated by SDSSJ1204+0221FG at a distance of R_⊥ = 108 kpc would be SB_Lyα < 4.8 × 10⁻¹⁷erg s⁻¹  cm⁻² arcsec⁻². From a preliminary analysis, we conservatively estimate that we could have detected extended emission of a factor of 10 fainter than this expectation, implying that the distance to the clouds would have to be $r > \sqrt{10}\,R_\perp$ to render them undetectable if the foreground quasar emits isotropically. Thus, isotropic emission from SDSSJ1204+0221FG is ruled out unless all of the optically thick gas lies beyond r > 340 kpc.

Hennawi & Prochaska (2007) have demonstrated that high-z quasars exhibit a high covering fraction to optically thick absorbers at impact parameters R_⊥ ≲ 200 kpc, and argued that the incidence of such transverse absorption exceeds the incidence along the line of sight to bright high-z quasars. Prochaska et al. (2008b) similarly concluded that there are fewer DLAs near z > 2 quasars than expected from clustering arguments, and Wild et al. (2008) have recently reported a similar deficit of strong Mg ii absorbers along the line of sight compared to the transverse direction. Together, these observations argue that quasars emit ionizing radiation anisotropically or intermittently. Hence, a paucity of optically thick absorbers is detected along the line of sight because this gas, which is by construction illuminated, is photoionized by the quasar. One test of this hypothesis is to search for an enhancement of highly ionized material along the sightline, e.g., Si iv, C iv, N v, O vi. Indeed, Wild et al. (2008) report a higher incidence of C iv absorption along the same sightlines where the lower IP transition, Mg ii, is deficient. There is also a high incidence of highly ionized absorbers within several thousand km s⁻¹ of the quasar redshift commonly termed NAAL systems (D'Odorico et al. 2004). We now explore the physical conditions required for SDSSJ1204+0221FG to photoionize/photoevaporate SLLS/SDSSJ1204+0221BG and also the expected properties of SLLS/SDSSJ1204+0221BG if it were illuminated by the quasar, and thus exposed to a more intense radiation field. These calculations are similar to those performed by Chelouche et al. (2008) and we refer the reader to their work for additional analysis.

In Figure 9 we present a series of calculations from the Cloudy software package for constant density gas slabs placed 100 kpc from SDSSJ1204+0221FG along the sightline to Earth. The quasar's specific luminosity was assumed to be a power law (L_ν ∝ ν^−1.57) and was normalized to SDSS photometry: L_ν = L₉₁₂(ν/ν₉₁₂)^−1.57 with L₉₁₂ = 1.16 × 10³⁰ erg s⁻¹ Hz⁻¹. In all of the calculations we assume a gas metallicity [M/H] = −0.5 dex with solar relative abundances. In the upper panel of the figure, we show the H i column densities for slabs with a series of total H column densities¹⁴ log N_H = 19, 19.5, ..., 21 as a function of the gas density n_H. For slabs with N_H = 10¹⁹ cm⁻², the gas has N_H i < 10^17.2 and is hence optically thin to ionizing photons, provided n_H < 10 cm⁻³; while slabs with N_H = 10²¹ cm⁻² are optically thin only if n_H < 0.1 cm⁻³.

In Section 3, we estimated N_H ≈ 10²⁰ cm⁻² and n_H ≈ 1 cm⁻³ for subsystems A and C based on the relative column densities of several ion pairs, our estimate of the H i column density (uncertain by ±0.4 dex), and an analysis of C ii and Si ii fine-structure transitions. According to the calculations presented in Figure 9, this gas would have N_H i ≈ 10¹⁷ cm⁻² if it were at 100 kpc from SDSSJ1204+0221FG along our sightline. If the volume density is just a little lower (permitted by the fine-structure analysis), the gas would be optically thin. We conclude that subsystems A and C of SLLS/SDSSJ1204+0221BG would be photoionized by SDSSJ1204+0221FG if it were placed along our sightline. Subsystem B, however, exhibits a larger N_H i value and has a larger implied N_H ≈ 10^20.3 cm⁻² value. Assuming n_H = 1 cm⁻³, this system would have N_H i ≈ 10^17.3 cm⁻² if illuminated by the SDSSJ1204+0221FG at a distance of 100 kpc. To be optically thin and illuminated at this distance requires n_H < 1 cm⁻³. It is important to note that SDSSJ1204+0221FG is relatively faint compared to the brighter quasars studied to establish the low incidence of optically thick absorbers near quasars (e.g., Russell et al. 2006; Prochaska et al. 2008b; Wild et al. 2008). These quasars are a factor of ∼ 5–10 brighter and the resulting ionization parameters are higher by the same factor. Thus, clouds with properties similar to SLLS/SDSSJ1204+0221BG could still appear optically thin if illuminated, resulting in no conflict with previous observations. Similarly, it would be very fruitful to characterize the incidence of proximate optically thick absorbers as a function of quasar luminosity.

If an absorber like SLLS/SDSSJ1204+0221BG is photoionized by a nearby quasar, the system may still give rise to several discernible features. If the H i column density exceeds 10¹⁴ cm⁻², it would exhibit a strong Lyα absorption feature. This would be difficult to distinguish from the ambient Lyα forest, however. If this gas has even a modest metallicity, it may show unique metal-line signatures. The lower panel of Figure 9 presents the predicted column densities of several high ions assuming N_H = 10^20.5 cm⁻², [M/H] = −0.5 dex, and that the cloud is at a distance of 100 kpc from SDSSJ1204+0221FG along our sightline. Once the cloud becomes optically thin (at n_H ≲ 0.5 cm⁻³), large column densities of C⁺³, N⁺⁴, and O⁺⁵ ions are expected. The alkali doublets associated with these ions saturate at column densities of ≈10¹⁴ cm⁻² and, therefore, would yield absorption lines that could be detected at even the modest resolution of the SDSS spectroscopic survey. These column densities scale directly with the assumed metallicity and are also sensitive to the N_H value. Combining the high incidence of optically thick gas observed in the transverse direction with the high ionization parameter along the sightline, and using our knowledge of the physical properties of the (unilluminated) absorbing clouds from SLLS/SDSSJ1204+0221BG, we conclude that a large fraction of bright quasars should exhibit strong C iv, N v, and O vi absorption at z ≈ z_em along their sightlines.

Absorption systems with strong high ion absorption near quasars with z_abs ≈ z_em or small velocity intervals (Δv < 1000 km s⁻¹) have been detected in quasar spectra, and are referred to as NAAL systems (e.g., Wampler et al. 1993; Srianand & Petitjean 2000). The most comprehensive survey of these NAALs using high-resolution spectra was performed by D'Odorico et al. (2004) who analyzed the UVES key project of z ≈ 2 quasars. Of the 22 quasars in the sample, D'Odorico et al. (2004) report that 16 exhibit significant C iv absorption within ±5000 km s⁻¹ of z_em for a total of 34 C iv systems, 15 of which also exhibit N v absorption. D'Odorico et al. (2004) studied the properties of a subset which allowed for detailed photoionization modeling. The characteristics of this subset are similar in metallicity, density, and relative abundances to SLLS/SDSSJ1204+0221BG (see also Section 4.2). Furthermore, the authors used observed limits on the volume density of the gas (from fine-structure analysis) and estimates of partial coverage to infer distances of 10 to 200 kpc from the quasar. We conclude, therefore, that if SLLS/SDSSJ1204+0221BG experienced an ≈10 times higher ionization parameter, it would show characteristics common to NAAL systems. Indeed, SDSSJ1204+0221FG is approximately 2.5 mag (10×) fainter than the quasars of the D'Odorico et al. (2004) sample. We speculate that an absorption line survey of intrinsically faint quasars will show a high incidence of absorbers with properties similar to SLLS/SDSSJ1204+0221BG and a correspondingly lower incidence of NAAL systems. One could perform such a survey with current and future echellette spectrometers on 10 m class telescopes.

Porciani et al. (2004) measured the clustering of quasars in the redshift range 0.8 < z < 2.1, which allowed them to estimate that quasars are hosted by dark matter halos with mass M ∼ 10¹³M_☉. As they found strong evolution of the clustering with redshift, which continues to even higher redshift (z > 3.0; see Shen et al. 2008b), we henceforth assume that SDSSJ1204+0221FG resides in a dark matter halo M = 10^13.3M_☉, but we caution that this mass is uncertain by a factor of ∼0.5 dex, due to both the measurement error and the intrinsic distribution of quasar host halo masses.

For a dark matter halo of this mass with an NFW profile (Navarro et al. 1997), the virial radius is

$$\begin{equation} r_{\rm vir} = 251\left(\frac{M}{10^{13.3}\, M_\odot }\right)^{1/3} {\rm kpc}. \end{equation} \tag{ 8 }$$

Thus, if SDSSJ1204+0221FG resides at the center of its host dark matter halo, the SDSSJ1204+0221BG sightline probes it at ≲50% of the virial radius. If we assume a concentration parameter c = 4 (characteristic of high-redshift halos), the peak circular velocity of the dark matter halo is

$$\begin{equation} v_{\rm circ} = 604\left(\frac{M}{10^{13.3} M_\odot }\right)^{1/3}\,{\rm \; km\;s^{-1}}, \end{equation} \tag{ 9 }$$

which implies a dynamical time at the impact parameter R_⊥ of the background sightline of

$$\begin{equation} t_{\rm dyn} \sim R_\perp /v_{\rm circ} = 1.7{\; \times \; 10^{8}}\left(\frac{M}{10^{13.3}\, M_\odot }\right)^{-1/3}\,{\rm yr}. \end{equation} \tag{ 10 }$$

The circular velocity we deduce is comparable to the extreme kinematics observed in the subsystems of SLLS/SDSSJ1204+0221BG. It is thus conceivable that the motions in SLLS/SDSSJ1204+0221BG represent gravitational infall or virial motion of "cold gas clouds" orbiting in the dark matter halo potential, just as galaxies would. To make this more precise we note that the maximum extent spanned by the three components of SLLS/SDSSJ1204+0221BG is Δv ≈ 650 km s⁻¹. For a Gaussian distribution, we find that the maximum extent measured from three samples is related to the dispersion by Δv = 1.69σ, so we estimate that the dark matter halo hosting SDSSJ1204+0221FG and SLLS/SDSSJ1204+0221BG has a line-of-sight velocity dispersion σ ≃ 380 km s⁻¹. Tormen (1997) found that the maximum circular velocity of an NFW halo is a factor of ≈1.4 times larger than the maximum of the one-dimensional velocity dispersion, so our kinematics suggest v_circ = 540 km s⁻¹. The velocity width of SLLS/SDSSJ1204+0221BG is consistent with the characteristic velocity for the dark matter halos hosting z ∼ 2.5 quasars (Equation (9)), thus gravitational dynamics in the halo surrounding SDSSJ1204+0221FG could explain the observed kinematics.

One challenge to this scenario is that the velocities of the clouds comprising SLLS/SDSSJ1204+0221BG are systematically offset to positive values relative to SDSSJ1204+0221FG. Such an offset is characteristic of organized motions (e.g., rotation, infall along a filament) rather than a random velocity field and we question whether a highly organized velocity field with large velocity width can occur in the outer halo. It is worth noting, however, that the offset resembles a similar trend observed for optically thick absorbers (Mg ii systems) at z ∼ 1. For these absorbers, Steidel et al. (2002) and Kacprzak et al. (2007) report a systematic velocity offset between the gas and the systemic velocity of its host galaxy. The origin of this asymmetry is not understood. Another explanation for the observed kinematics is that SLLS/SDSSJ1204+0221BG represents cold material swept up in large-scale outflow, which we consider in more detail in Section 5.4.

In the standard structure formation picture, gas falling into a massive dark matter halo will be shock-heated to near the virial temperature of the dark halo, converting its gravitational kinetic energy into thermal energy. The virial temperature is defined as

$$\begin{equation} T_{\rm vir} = \frac{\mu m_{\rm p} v_{\rm circ}}{2k_{\rm B}} = 1.3{\; \times \; 10^{7}}\left(\frac{M}{10^{13.3} M_\odot }\right)^{2/3}\,{\rm K}, \end{equation} \tag{ 11 }$$

where μ is the mean atomic weight, which we take as μ = 0.59 for a fully ionized primordial gas. Gas at these high temperatures will be collisionally ionized and should result in negligible H i absorption.

As we detect a large column of enriched and cold photoionized gas at T≃ 20,000 K in the background sightline, it is of interest to calculate the time that it would take gas shock-heated to the virial temperature to cool at the distance of our impact parameter. The cooling time of a gas is conventionally taken to be the ratio of its specific thermal energy to the volumetric cooling rate, or t_cool = [3(n_e + n)kT]/[2n_enΛ], where Λ is the cooling function (e.g., Sutherland & Dopita 1993) and n is the total ion density. We can estimate the ion density of the quasar host halo assuming that the total mass (dark matter + gas) distribution follows an NFW density profile ρ(r), with the gas density being a fraction f_g of the total density ρ_g(r) = f_gρ(r). We then have n = ρ_g/μm_p, or

$$\begin{equation} n(r\,{=}\,108\,{\rm kpc}) \,{\approx}\, 7.5{\, \times \, 10^{-3}}\left(\frac{f_{\rm g}}{0.17}\right) \left(\frac{M}{10^{13.3}\, M_\odot }\right)^{0.73}\,{\rm cm}^{-3}, \end{equation} \tag{ 12 }$$

where we took f_g = Ω_b/Ω_m = 0.17 to be the cosmic baryon fraction from Dunkley et al. (2008). We finally find for the cooling time at r = 108 kpc, t_cool ≈ 3.2 × 10⁹(M/10^13.3M_☉)^−0.22 yr. Note that at the high virial temperatures T ∼ 10⁷ K characteristic of our dark matter halo, cooling is dominated by thermal bremsstrahlung radiation and hence does not depend strongly on metallicity. According to the current structure formation paradigm, the bulk of the gas interior to the virial radius should have been shock-heated to T_vir, and the cooling time of this hot phase at R ≃ 100 kpc is comparable to the age of the universe at z = 2.4360, t_H = 2.6 × 10⁹ yr. Thus, the impact parameter R_⊥ = 108 kpc for SDSSJ1204+0221BG probes SDSSJ1204+0221FG at approximately the cooling radius (where t_cool = t_H, which is r_cool = 99 kpc). Furthermore, because the dynamical time (Equation (10)) is a factor of ∼20 shorter than the cooling time, the dark matter halo we consider satisfies the condition for stable shock formation (Dekel & Birnboim 2006) and is in the pressure-supported "hot-halo" regime.

From the foregoing discussion, we expect the bulk of the gas near SDSSJ1204+0221FG to have been shock-heated to the virial temperature of its hot-halo (see Equation (11)). However, our analysis of SLLS/SDSSJ1204+0221BG indicates a column density N_H i = 10^19.65 cm⁻², and hence a substantial amount of "cold" gas at R_⊥ ≃ 108 kpc. Similarly, a high covering factor of high column density (N_H i > 10¹⁹cm⁻²) cold gas was seen statistically by Hennawi et al. (2006a) and Hennawi & Prochaska (2007). In what follows we combine the Hennawi & Prochaska (2007) measurement of the clustering of cold gas around quasars, with our measurements of the properties of SLLS/SDSSJ1204+0221BG (see Table 4), to estimate the covering factor, density, and volume filling factor of cold gas in the halos surrounding high-z massive galaxies.

At a transverse separation R_⊥ from a foreground quasar, the covering factor of absorbers can be written (Hennawi & Prochaska 2007) as

$$\begin{equation} C(R_\perp) = \left\langle \frac{dN}{dD}\right\rangle \left[1 + \chi _{\perp }(R_\perp,\Delta D)\right] \Delta D, \end{equation} \tag{ 13 }$$

where we search over a radial (comoving) distance interval ΔD corresponding to a redshift interval Δz in the background quasar spectrum. Here $\left\langle \frac{dN}{dD}\right\rangle = n_{\rm abs}A$ is the incidence of absorption line systems per unit comoving distance, which is simply the product of the comoving number density of the clouds which give rise to absorption line systems and their absorption cross-section A (in comoving units). The transverse correlation function χ_⊥(R, ΔD) accounts for the enhancement due to clustering and can be written as an integral of the three-dimensional quasar–absorber correlation function, ξ_QA(r), over the search window (see Hennawi & Prochaska 2007 for details). Assuming a power-law shape for the quasar–absorber cross-correlation function, Hennawi & Prochaska (2007) measured r₀ = 9.2^+1.5_−1.7 h⁻¹ Mpc for γ = 1.6, or r₀ = 5.8^+1.0_−0.6 h⁻¹ Mpc for γ = 2. These fits imply covering factors of C(R_⊥ = 108 kpc) = 0.29 ± 0.08 and 0.35^+0.13_−0.07, respectively. For this calculation we chose a projection distance ΔD = 19.2 Mpc along the line of sight, which corresponds to a velocity interval ±700 km s⁻¹, motivated by the 650 km s⁻¹ extent of the absorption components in SLLS/SDSSJ1204+0221BG.

For the simplified case of identical clouds of mass M_c, the mass density of cold gas (in proper units) is

$$\begin{eqnarray} \nonumber \rho _{\rm cold}(r) &=& \frac{1}{a^3}n_{\rm abs}[1 + \xi _{\rm QA}(r)]M_{\rm c}\\ &=& \frac{1}{a}\left\langle \frac{dN}{dD}\right\rangle [1 + \xi _{\rm QA}(r)]N_{\rm H}\frac{1}{X}, \end{eqnarray} \tag{ 14 }$$

where a is the scale factor, M_c is the mass of the clouds, X = 0.76 is the hydrogen mass fraction, and μ_c = 0.61 is the mean atomic weight of the cold gas.¹⁵ Plugging in numbers using the parameters of SLLS/SDSSJ1204+0221BG we find

$$\begin{eqnarray} &&\nonumber \rho _{\rm cold}(r=108\,{\rm kpc})\approx 3.0{\; \times \; 10^{-6}}\, \left[\frac{\left(108\,{\rm kpc}\slash r_0\right)^{-\gamma }}{472}\right]\\ &&\qquad\times \left(\frac{N_{\rm H}}{10^{20.6}\,{\rm cm^{-2}}}\right) \,M_\odot \,{\rm pc^{-3}}. \end{eqnarray} \tag{ 15 }$$

We can compare this to our expectation for the baryon density in an NFW halo at this distance (see Equation (12)), and thus compute the cold gas fraction

$$\begin{eqnarray} &&\nonumber \frac{\rho _{\rm cold}}{\rho _{\rm g}}(r=108\,{\rm kpc})\approx 0.03 \left(\frac{f_{\rm g}}{0.17}\right)^{-1} \left[\frac{\left(108\,{\rm kpc}\slash r_0\right)^{-\gamma }}{472}\right]\\ &&\qquad\times \left(\frac{N_{\rm H}}{10^{20.6}\,{\rm cm^{-2}}}\right) \left(\frac{M}{10^{13.3}\,M_\odot }\right)^{-0.73} \;. \end{eqnarray} \tag{ 16 }$$

Unfortunately, this estimate suffers from a large uncertainty. Besides the ∼0.5 dex in the dark halo mass, the quasar–absorber correlation function has significant errors and an uncertain slope. Also we assumed a single cloud population with a total hydrogen column density N_H = 10^20.6 cm⁻² equal to the total in SLLS/SDSSJ1204+0221BG. This value may not be representative of the cloud population near quasars as a whole, although the neutral column of SLLS/SDSSJ1204+0221BG N_H i = 10^19.65 cm⁻² is lower than the average 〈N_H i〉 ≈ 10^20.1 cm⁻² of the four absorbers with R ≲ 200 kpc in the Hennawi & Prochaska (2007) clustering analysis. Finally, it is important to note that we have assumed a maximal value for the gas fraction, f_g = Ω_b/Ω_m = 0.17, equal to the universal baryon fraction. While in principle the gas fraction can be this large, it is probably smaller because of gas loss from outflows. In this regard the cold gas fraction in Equation (15) could easily be a factor of ∼2 higher.

Despite the uncertainties, Equation (15) illustrates how measurements of the covering factor and column density distribution of optically thick absorbers combined with photoionization modeling, can be used to measure the cold gas density as a function of radius from massive dark halos. This new observable¹⁶ thus provides a direct test of ideas which are currently popular in structure formation models, such as the cooling radius, cold accretion, the formation of pressure-supported hot halos, and multiphase media (see below). Furthermore, although the current estimate crudely assumed that all gas clouds are the same as those in SLLS/SDSSJ1204+0221BG, a larger statistical analysis could use the distribution of cloud column densities measured from high-resolution spectra and photoionization modeling.

Next, we use our measurement of the electron density (see Section 3 and Table 4) and hence size of the absorbing clouds to determine their volume filling factor. The filling factor can be written as

$$\begin{equation} C_{\rm v}(r)=\frac{1}{a^3}n_{\rm abs}[1 + \xi _{\rm QA}(r)]V_{\rm c} = \frac{1}{a}\left\langle \frac{dN}{dD}\right\rangle [1 + \xi _{\rm QA}(r)] \frac{N_{\rm H}}{n_{\rm H}}, \end{equation} \tag{ 17 }$$

where we used the fact that the ratio of the cloud volume to cloud area is the absorption path length V_c/(a²A) = ℓ = N_H/n_H. Plugging in numbers we find

$$\begin{eqnarray} &&\nonumber C_{\rm v}(r=108\,{\rm kpc})\approx 2.2{\; \times \; 10^{-5}} \left[\frac{\left(108\,{\rm kpc}\slash r_0\right)^{-\gamma }}{472}\right] \\ &&\quad\times \left(\frac{N_{{\rm H}\, {*navin* i*navin*}}}{10^{20}\,{\rm cm^{-2}}}\right) \left(\frac{n_{\rm e}}{1.7\,{\rm cm^{-3}}}\right)^{-1}, \end{eqnarray} \tag{ 18 }$$

where we have used the H i column and electron density measurements for component C (see Section 3). The mass of the clouds $M_{\rm c}\sim \frac{4\pi }{3}n_{\rm c}\mu _{\rm c} m_{\rm p}(\ell / 2)^3$, where n_c is the cold gas ion density and R_c is the cloud radius. For a hard sphere the cloud radius is related to the average absorption path by $R_{\rm c} = \frac{3}{4} \ell$. Again, plugging in numbers for component C, we find

$$\begin{equation} M_{\rm c} = 720\left(\frac{N_{\rm H}}{10^{20}\,{\rm cm^{-2}}}\right)^{3} \left(\frac{n_{\rm e}}{1.7\,{\rm cm^{-3}}}\right)^{-2}M_\odot, \end{equation} \tag{ 19 }$$

however, we caution that this estimate is highly uncertain because of its dependence on large powers of quantities with significant errors.

Our conclusion from Equation (16) that a few percent of the total baryon supply is in a "cold" gas phase at T≃ 20,000 K implies that SDSSJ1204+0221FG has intercepted a multiphase medium. This is of particular interest in light of considerable theoretical work which indicates that the hot gas associated with massive galaxies should be thermally unstable and prone to fragmentation instabilities (Field 1965; Fall & Rees 1985; Murray & Lin 1990; Mo & Miralda-Escude 1996; Maller & Bullock 2004, but see Malagoli et al. 1990). The expected result of these instabilities is a fragmented distribution of cooled material at T ∼ 10⁴ K, in pressure equilibrium with a hot gas background (Mo & Miralda-Escude 1996; Maller & Bullock 2004; Dekel & Birnboim 2006). These instabilities have not yet been seen in hydrodynamical simulations of galaxy formation (Katz 1992; Thoul & Weinberg 1995; Springel et al. 2001; Yoshida et al. 2002; Helly et al. 2003), which lack the mass resolution necessary to resolve them (Kaufmann et al. 2006). Some have suggested that the formation of this multiphase medium can dramatically influence galaxy formation, resulting in a maximum galaxy mass in massive halos (Maller & Bullock 2004), or providing an important source of feedback energy (Dekel & Birnboim 2008).

To this end we compute the pressure P_c = n_cT_c of the cold clouds that we detect in absorption as SLLS/SDSSJ1204+0221BG to be

$$\begin{equation} P_{\rm c}=7.1{\; \times \; 10^{4}}\left(\frac{n_{\rm e}}{1.7\,{\rm cm}^{-3}}\right) \left(\frac{T}{20{,}000\ {\rm K}}\right)\,{\rm K\, cm^{-3}}. \end{equation} \tag{ 20 }$$

This value can be compared to our estimate of the pressure in the NFW halo at r = 108 kpc thought to be hosting SDSSJ1204+0221FG, by combining equations (11) and (12),

$$\begin{equation} P_{\rm h}\approx 9.8{\; \times \; 10^{4}}\left(\frac{f_{\rm g}}{0.17}\right) \left(\frac{M}{10^{13.3} M_\odot }\right)^{1.4}{\rm K\, cm^{-3}}. \end{equation} \tag{ 21 }$$

It is compelling that these pressures are comparable. Our determination of the pressure of the absorbing gas in SLLS/SDSSJ1204+0221BG indicates that the gas clouds could very well be pressure confined by the hot T ∼ 10⁷ K gas which is expected to permeate the dark matter halo of SDSSJ1204+0221FG.

We can calculate the number density of the absorbing clouds from Equation (13) if we have knowledge of the absorption cross-section A,

$$\begin{equation} n(r) = n_{\rm abs}[1 + \xi _{\rm QA}(r)] = \frac{C(R_\perp)}{A \Delta D} \frac{1 + \xi _{\rm QA}(r)}{1 + \chi _{\perp }(R_\perp,\Delta D)}. \end{equation} \tag{ 22 }$$

We use our estimate for the radius of the absorber from component C, r_abs = 15 pc (see Section 3), to determine A = πr²_abs. Combined with C(R_⊥ = 108 kpc) = 0.35 from Hennawi & Prochaska (2007), Equation (22) gives for the number density

$$\begin{eqnarray} &&\nonumber n(r = 108\,{\rm kpc}) = 3.7{\; \times \; 10^{7}}\,{\rm Mpc}^{-3}\left(\frac{C}{0.35}\right) \left(\frac{r_{\rm abs}}{15\,{\rm pc}}\right)^{-2}\\ &&\qquad\times \left(\frac{1+\xi _{\rm QA}}{473}\right) \left(\frac{1 + \chi _\perp }{28}\right)^{-1}. \end{eqnarray} \tag{ 23 }$$

This extremely high number density of clouds leads us to consider an alternative scenario where the small clouds we observe with characteristic size r_abs = 15 pc are organized in larger galactic structures (with characteristic size r_gal) which are clustered around the quasar. This scenario would still give rise to the small absorption path length of r_abs ∼ 15 pc, but since the clouds are associated with galaxies the macroscopic absorption cross-section would be Aπr²_gal, and hence the implied number density of galactic hosts n_abs would be significantly smaller than determined from Equation (23). This scenario could also help explain why the metallicities deduced for SLLS/SDSSJ1204+0221BG are so high in spite of the large impact parameter R_⊥ = 108 kpc from the quasar. If the absorbers are associated with nearby galaxies, then the characteristic size of these enriched regions would be r_gal, obviating the need for the quasar to have transported the metals to large distances, perhaps via a large-scale outflow (see Section 5.4).

First, we assume the absorbers are as numerous as the faintest most abundant star-forming galaxies which have been studied to date and determine the corresponding size of the enriched regions. Reddy et al. (2008) calculated the luminosity function for a combined sample of brighter spectroscopic Lyman break galaxies (LBGs) and the fainter photometric LBGs from the Hubble Deep Field-North studied by Steidel et al. (1999). The comoving number density of the faintest star-forming galaxies at z ∼ 3 is n_LBG = 6.9 × 10⁻³ Mpc⁻³ for a flux limit of M_AB(1700 Å) <−18.2, corresponding to ${\cal R} < 26.9$ or L > 0.09 L_*. Adelberger & Steidel (2005) measured the clustering of LBGs around luminous quasars in the redshift range (2 ≲ z ≲ 3.5), and found a best-fit correlation length of r₀ = 4.7 h⁻¹ Mpc for a slope of γ = 1.6, which should be considered an upper limit for the much fainter galaxies we consider, which are likely to cluster less strongly. If we use the Adelberger & Steidel (2005) correlation function to calculate the factor of χ_⊥ in Equation (13), then we find that the size of the absorber galaxies has to be

$$\begin{eqnarray} &&\nonumber r_{\rm gal} = 91\,{\rm kpc}\left(\frac{C}{0.35}\right)^{1/2} \left(\frac{n_{\rm LBG}}{6.9{\; \times \; 10^{-3}}\,{\rm cm}^{-3}}\right)^{-1/2}\\ &&\qquad\times \left(\frac{1 + \chi _\perp }{9}\right)^{-1/2}. \end{eqnarray} \tag{ 24 }$$

Since this value for r_gal is very similar to R_perp there is little point in distinguishing between the star-forming galaxy halo and the quasar halo, or stated in a different way, the average number of LBGs in the cylindrical volume set by R_perp and ΔD is, including the effects of clustering, about one (N_LBG = 0.8). Thus, associating the high-metallicity absorbing clouds with faint LBGs does not help explain the high covering factor of enriched material at large impact parameter.

If the absorption is to be associated with galaxies near the quasar, they must arise from a population much more abundant than L ∼ 0.1 L_* galaxies. These dwarf systems will be significantly fainter and smaller. If we arbitrarily choose a value of r_abs = 20 kpc for their absorption cross-section radius, then Equation (13) implies a comoving number density of n_dwarf = 0.14 Mpc⁻³. Hence, if galaxies clustered around the quasar have r_abs = 20 kpc then they must be 20 times more abundant than the faintest photometric LBGs studied to date. Extrapolating the Reddy et al. (2008) luminosity function fit to achieve this number density implies L ∼ 10⁻³L_*, or an apparent magnitude limit of ${\cal R} < 31.7$. The challenge to this scenario, however, is achieving a nearly solar metallicity in these extremely faint, high-z dwarf galaxies. Indeed, the DLAs are thought to arise from a population of faint galaxies and are likely to have an absorption size r_abs comparable to what we assume, but their metallicities are much lower (see Figure 7) and similarly low metallicities are seen locally in dwarf galaxies.

How do we explain the presence of such a large gas mass of highly enriched material with a broad-line-region-like enrichment pattern at such a large distance from the quasar (r ∼ 100 kpc)? It is tempting to associate the absorbing material with a large-scale outflow or galactic wind from SDSSJ1204+0221FG and/or its host galaxy. Indeed, quasars exhibit fast outflows in the form of BAL systems on small scales (within 100 pc of the engine) and on large scales as radio jets extending to tens of kpc. Furthermore, high-z quasars are believed to reside in actively star-forming galaxies perhaps with highly elevated star formation rates. Such galaxies may drive fast outflows that, in principal, could extend to tens or even hundreds of kpc.

Therefore, in terms of an outflow, there are two extreme scenarios to consider: (1) a highly collimated outflow such as a radio jet associated with the quasar and (2) a large-scale, expanding "bubble" of cold swept up material driven by star formation feedback and/or the quasar accretion power. The first "jet" scenario naturally yields an asymmetric velocity field and may accelerate gas to very high speeds. However, it has at least two serious drawbacks. First, the cross-section of a highly collimated outflow is, by definition, small. This is not a viable model for reproducing the high incidence of optically thick absorbers near quasars (Hennawi et al. 2006a; Hennawi & Prochaska 2007), although it might explain the single example presented here. Second, the large relative velocities among the subsystems of SLLS/SDSSJ1204+0221BG contradict the notion of a collimated flow—in order for an outflow to remain collimated out to ∼100 kpc, it must have a very small velocity shear.

For the case of a large-scale outflow driven by intense star formation or accretion onto the AGN, there are three issues to consider: (1) is there a viable physical mechanism present to drive a wind to the observed speed? (2) will the outflow propagate to a distance exceeding the observed impact parameter, that is ≳100 kpc? and (3) will the outflow yield an asymmetric velocity field relative to z_fg? The last point requires an asymmetric outflow which might be achieved by an irregular gas distribution in the halo of SDSSJ1204+0221FG (e.g., variable inertia in different directions) or if the gas has been asymmetrically photoionized by the quasar. The required outflow speed, meanwhile, is a very challenging constraint. Allowing for viewing angle, portions of the outflow would need speed of greater than 1000 km s⁻¹. This surpasses the speed of outflows generally observed in star-forming galaxies (Pettini et al. 2001; Martin 2005). Finally, theoretical treatments of galactic outflows suggest these will not extend to this large distance in halos with masses characteristics of z > 2 quasar host galaxies (Furlanetto & Loeb 2001; Aguirre et al. 2001), but of course this depends on the assumed energetics of the flow.

In what follows we will use the observed properties of SLLS/SDSSJ1204+0221BG to estimate, in an order of magnitude sense, the energetics of the presumed outflow, under the assumption that we have detected cold swept up material. We then consider if an outflow with these energetics could be plausibly produced by a starburst or AGN.

The mass of a shell of material at radius r_w, with column density N_w, and covering solid angle Ω, is M_w = m_pN_HΩr²_w. If this shell is outflowing at velocity v_w in a wind, the mass outflow rate is ${\dot{M}_{\rm w}} \sim M_{\rm w} v_{\rm w}/ r_{\rm w}$. For our fiducial values and Ω = 2π, we derive M_w ∼ 3 × 10¹¹M_☉ and $\dot{M}_{\rm w} \sim 3000\, M_\odot\, \rm yr^{-1}$. Note that we have taken the outflow velocity to be v_w = 1000 km s⁻¹ because SLLS/SDSSJ1204+0221BG shows velocity separations as large as ≃700 km s⁻¹ from the f/g quasar, but this represents only the radial component of the velocity vector. The corresponding energy, power, and momentum deposition rate of the wind are E_w ∼ 1/2 M_wv²_w, ${\dot{E}_{\rm w}} \sim 1/ 2\, {\dot{M}_{\rm w}} v_w^2$, and ${\dot{P}_{\rm w}}\sim {\dot{M}_{\rm w}}v_{\rm w}$, respectively. With our fiducial values, these are E_w ∼ 3 × 10⁶⁰ erg, ${\dot{E}_{\rm w}} \sim 9{\; \times \; 10^{44}} \, \rm erg \, s^{-1}$, and ${\dot{P}_{\rm w}} \sim 2{\; \times \; 10^{37}} \, \rm g \, cm \, s^{-2}$.

These crude estimates can be compared with the momentum and energy-driven winds of a starburst and/or AGN. Following the formalism presented in Murray et al. (2005), the SN deposition rate for a starburst galaxy with star formation rate ${\dot{M}_{\ast }}$ is ${\dot{P}_{\rm SN}} \sim 2{\; \times \; 10^{33}} {\dot{M}_{\ast }}/(M_\odot \,{\rm yr^{-1}}) \, \rm g \, cm \, s^{-2}$. A similar deposition rate is inferred from radiation pressure from assuming the gas is optically thick to absorption by dust grains. We conclude that if the absorption in SLLS/SDSSJ1204+0221BG is from material swept up in a large-scale wind, the star formation rate required to power the momentum flow is extremely large ${\dot{M}_{\ast }}\sim 10^4\,M_\odot \,{\rm yr^{-1}}$. Furthermore, this estimate should be considered a lower limit because it assumes all momenta deposited into the galaxy are assumed to add coherently which can significantly overestimate the deposition (Socrates et al. 2008).

The rest-frame near-UV luminosity from such a high star formation rate can be estimated (Kennicutt 1998), and it is L_UV ∼ 10⁴⁷erg s⁻¹; this would outshine the quasar bolometric luminosity L_QSO ≃ 1.4 × 10⁴⁶ erg s⁻¹ by an order of magnitude, which can easily be ruled out since a starburst spectrum is not observed in SDSSJ1204+0221FG or detected in the SDSS imaging. While the starburst could be significantly extincted by dust (this is in fact an implicit assumption), the fact that we observe the f/g quasar unextincted along our line of sight implies that we should have been able to see some evidence for a starburst 10 times brighter. Finally, we note that radiation pressure from the quasar radiation is also unable to drive the presumed outflow,¹⁷ since ${\dot{P}_{\rm QSO}} = L_{\rm QSO}/ c \sim 5{\; \times \; 10^{35}} {\rm g\,cm\,s^{-2}}$, which is a factor of 40 lower than our estimate.

Next, we consider the wind power, again following the formalism in Murray et al. (2005). For SNe, assuming a rate of one per 100 yr per 1 M_☉ yr⁻¹, the SNe energy can only power the outflow for an extremely large star formation rate: ${\dot{M}_{\ast }}\sim 3{\; \times \; 10^{4}}\,M_\odot \,{\rm yr^{-1}}$. We conclude that the kinematics of SLLS/SDSSJ1204+0221BG are not driven by SN winds and consider, instead, the energy from the AGN. The absolute B-band magnitude¹⁸ of SDSSJ1204+0221FG is M_B = −24.8, which corresponds to a bolometric luminosity of L_QSO = 1.4 × 10⁴⁶ erg s⁻¹, where we used the McLure & Dunlop (2004) fit to the Elvis et al. (1994) bolometric correction to determine L_QSO from M_B. The ratio of the outflow power to the accretion power is then

$$\begin{eqnarray} &&\nonumber {\dot{E}_{\rm w}}\slash L_{\rm QSO} \sim 0.06 \left(\frac{\Omega }{2\pi }\right) \left(\frac{N_{\rm H}}{10^{20.6}\,{\rm cm^{-2}}}\right) \left(\frac{R_\perp }{108\,{\rm kpc}}\right) \\ &&\qquad\times\left(\frac{v_{\rm w}}{1000{\rm \; km\;s^{-1}}}\right)^3\,{\rm erg}. \end{eqnarray} \tag{ 25 }$$

If indeed the AGN is powering an outflow, then ∼6% of the accretion power has been coupled to the host via a large-scale wind. A similar comparison can be made between the energy of the outflow, which is E_w ∼ 4 × 10⁶⁰ erg and the rest-mass energy liberated to grow the supermassive black hole E_BH = _radM_BHc². Assuming an Eddington ratio of f_Edd ≡ L_QSO/L_Edd = 0.1, consistent with recent estimates for a quasar at z ∼ 2.5 near the luminosity of SDSSJ1204+0221FG (Kollmeier et al. 2006; Shen et al. 2008a), we deduce a black hole mass of $M_{\rm BH} = 1.1{\; \times \; 10^{9}}\big(\frac{f_{\rm Edd}}{0.1}\big)^{-1}\,M_\odot$. Thus, we can write

$$\begin{equation} E_{\rm w}\slash E_{\rm BH} \sim 0.01\left(\frac{f_{\rm Edd}}{0.1}\right) \left(\frac{\epsilon _{\rm rad}}{0.1}\right)^{-1}. \end{equation} \tag{ 26 }$$

To summarize, if the H i and metal-line absorption in SLLS/SDSSJ1204+0221BG are from material swept up in a large-scale outflow, then the energetics are extreme. Starburst feedback is highly unlikely unless we are willing to consider unprecedented star formation rates ${\dot{M}_{\ast }}\gtrsim 10^4\,M_\odot \,{\rm yr^{-1}}$. Radiation pressure feedback from the quasar cannot drive the outflow even if all of the bolometric luminosity were absorbed by dust grains. Although large, the implied power of the presumed outflow is only a few percent of the bolometric luminosity of the f/g quasar, or similarly, its energy is of the order a percent of the radiated rest-mass energy required to grow an ∼10⁹M_☉ black hole. It is intriguing that we are led to deduce a few percent coupling between the black hole accretion and the host galaxy. This is very similar to the coupling factors used in simulations of quasar feedback. For instance, Springel et al. (2005a) must inject a fraction η = 0.05 of the accreted energy into the host galaxy to reproduce the observed M_BH–σ correlation, where η is defined by E_feedback = η_radM_BHc² (see also Granto et al. 2004). However, if such a large amount of energy is being deposited in the host galaxy, radiative losses from the wind could be significant, which we have not considered. Thus, in effect, our estimate of the coupling factor is a lower limit.

Finally, it is worth noting that high speed outflows of cold gas have been identified in a small sample of post-starburst galaxies at z ∼ 0.5 (Tremonti et al. 2007). In several cases the wind speeds exceed 1000 km s⁻¹ and the authors also argue that the energetics may require prior quasar activity. Similarly, the high speeds of NAALs detected in quasars are also suggestive of fast outflows (D'Odorico et al. 2004; Wild et al. 2008). However, the mass and energetics of these outflows, detected along the line of sight to background sources, cannot be reliably estimated because of the highly uncertain column density of the absorbers and the unknown distance to the absorbing gas.

In our Keck/HIRES of SDSSJ1204+0221BG, we identify an SLLS with an redshift z = 2.44. A Voigt-profile fit to the Lyα and Lyβ profiles implies a total H i column density N_H i = 10^{19.65 ± 0.15} cm⁻². The H i absorption occurs redward of z_fg, spanning from δv = +50 to +780 km s⁻¹. There is no H i absorption detected (N_H i < 10^13.5 cm⁻²) in the velocity interval δv = −1500 to 0 km s⁻¹. We identify a series of metal lines coincident in velocity with the H i absorption (distributed in three primary components) that includes transitions from a range of ionization states of C, O, Fe, Si, Al, and N. We observe an integrated O⁰/H⁰ ratio of log [N(O⁰)/N(H⁰)] = −3.9 dex which indicates a highly enriched gas. Ignoring IC to this ratio, which should be negligible, the average gas metallicity is [O/H] = −0.5 dex. Both the extreme kinematics and high metallicity of this system are highly uncommon for intervening SLLSs.

The Doppler parameters of the low and intermediate ions are small (b ≲ 5 km s⁻¹) indicating a gas temperature T ≃ 20, 000 K. At all velocities we observe an ionic ratio N⁺/N⁰ > 1 which implies the gas is predominantly ionized. We observe weak, (if any) C iv, N v, and O vi absorption indicating a modest (or negligible) quantity of metal-enriched gas with T ≈ 10⁵ to 10⁶ K in the halo surrounding SDSSJ1204+0221FG.

Under the assumption that the gas is photoionized by a hard radiation field (e.g., the nearby quasar or the EUVB), we estimate an ionization parameter log U = −3.0 ± 0.3 for the gas. This implies an ionization fraction x = 0.96 for the two lower column density components, and x = 0.2 for the component with the largest column. The total implied hydrogen column density of the system is N_H = 10^20.6 cm⁻². Applying IC to the observed N⁰/O⁰ ratio, we infer solar to super-solar N/O abundances. At high z, such large N/O values are only found in gas associated with quasar environments. At δv ≈ +700 km s⁻¹, we detect absorption from the excited fine-structure level of C⁺, C ii* 1335. Under the assumptions that electron collisions dominate the C⁺ excitation and that N(C⁺) = N(Si⁺) + log(C/Si)_☉, we estimate an electron density n_e = 0.2 to 10 cm⁻³. By comparing this volume density to the ionization corrected column density, we determine characteristic sizes ℓ ∼ 10 to 100 pc for the absorbing "clouds."

The properties of the SLLS toward SDSSJ1204+0221BG—z ≈ z_fg, extreme kinematics, high metallicity, and a solar N/O ratio—argue that this gas is located within the halo of SDSSJ1204+0221FG. There is an additional statistical argument: the strong clustering of optically thick absorbers around z ∼ 2 quasars (Hennawi & Prochaska 2007) implies the SLLS is likely to lie at a distance near the observed transverse distance (see Figure 6). We summarize in the next subsection several interpretations drawn from associating SLLS/SDSSJ1204+0221BG with the galactic halo of SDSSJ1204+0221FG.

We tested the hypothesis that the SLLS/SDSSJ1204+0221BG is illuminated by ionizing radiation from f/g quasar by comparing the radiation field intensity inferred from the analysis of the SLLS against the value expected from SDSSJ1204+0221FG. Adopting the most conservative parameters for the SLLS (log U = −3 and n_H = 5 cm⁻³), illumination of the SLLS cannot be ruled out if it is located at r = R_⊥ = 108 kpc from SDSSJ1204+0221FG. Adopting more realistic values (log U = −4 and n_H < 1 cm⁻³), we conclude that SLLS/SDSSJ1204+0221BG is not illuminated by SDSSJ1204+0221FG, unless the SLLS is located at an unlikely distance of greater than 500 kpc. We further demonstrated that if a system like SLLS/SDSSJ1204+0221BG were located along the sightline to a bright quasar at r < 100 kpc, and hence illuminated, then it would exhibit properties characteristic of the NAAL systems. This would include strong absorption by high ion transitions of O vi, N v, and C iv, optically thin H i absorption, and solar chemical abundances. The absence of strong high-ion absorption in this SLLS further suggests it is not illuminated by SDSSJ1204+0221FG and it also indicates that there is not a large reservoir of warm (T ≈ 10⁵ to 10⁶ K) gas in the halo surrounding the quasar. We suggest that there may still be a diffuse shock-heated medium but that it has a high temperature (T > 10⁶ K), characteristic of the virial temperature of the massive dark matter halo M ≳ 10¹³M_☉ expected to be hosting the f/g quasar. If it exists, this material remains undetectable in absorption with the transitions accessible with our b/g quasar spectrum.

The covering factor of cold T ∼ 10⁴ K, neutral, optically thick gas is nearly unity for transverse sightlines to z ∼ 2 quasars with R_⊥ ≲ 100 kpc (Hennawi et al. 2006a), although this high column density absorbing gas is rarely observed along the line of sight to individual quasars (Russell et al. 2006; Prochaska et al. 2008b). The explanation for this anisotropic absorption is that the transverse direction is much less likely to be illuminated by the f/g quasar ionizing flux, because of either obscuration or intermittent emission (Hennawi et al. 2006a; Hennawi & Prochaska 2007; Prochaska et al. 2008b). Besides this anisotropic absorption pattern, several independent lines of evidence corroborate this picture for the case of SDSSJ1204+0221. First, we modeled the ionization state of SLLS/SDSSJ1204+0221BG which indicates that the gas is unlikely illuminated by SDSSJ1204+0221FG (see Section 4.4). Second, we failed to detect high ion transitions like N v or O vi that should have been seen if the gas were highly ionized by a hard radiation field (see Section 4.3). Third, we showed that if gas clouds similar to those in SLLS/SDSSJ1204+0221BG were at a similar distance along the line of sight (and hence illuminated), they would explain the population of much more highly ionized associated NAALs, commonly detected in quasar spectra (see Section 4.5). Fourth, fluorescent Lyα emission is not observed near R_⊥ in SDSSJ1204+0221 (J. F. Hennawi & J. X. Prochaska 2009, in preparation), whereas the clouds responsible for the high covering factor of optically thick gas (Hennawi et al. 2006a) near quasars (three such clouds were detected in SLLS/SDSSJ1204+0221BG) would be emitting detectable Lyα photons if illuminated (J. F. Hennawi & J. X. Prochaska 2009, in preparation). The upshot of this anisotropic illumination picture is that the b/g quasar sightline probes the physical state of gas near SDSSJ1204+0221FG which is shadowed and hence unaltered by the intense ionizing radiation emitted by the f/g quasar.

By combining the statistical covering factor measured by Hennawi & Prochaska (2007) with the total N_H column determined for SLLS/SDSSJ1204+0221BG, we argued in Section 5.2 that the amount of cold gas at r ∼ 100 kpc is significant, amounting to $\sim 3\% \big(\frac{f_{\rm g}}{\Omega _{\rm b}/ \Omega _{\rm m}}\big)^{-1}$ of the total expected gas density of the f/g quasar's dark matter halo, if the gas fraction f_g is equal to the cosmic baryon fraction Ω_b/Ω_m. Similarly, if one assumes the material is distributed in a thin shell of radius R_⊥ which subtends Ω = 2π, the implied gas mass is M ∼ 3 × 10¹¹M_☉. Although we have deduced much about the physical state of this cold gas (see Table 4), its origin is still unclear. The biggest clue could lie in its extreme enrichment patterns. The nearly solar metallicity of SLLS/SDSSJ1204+0221BG and its roughly solar N/O relative abundance make it anomalous relative to the population of intervening SLLS and DLAs (see Figure 7). Indeed, at z ∼ 2.5 such high metallicities have only been observed on kpc scales in starburst galaxies (Pettini et al. 2001; Steidel et al. 2003) and solar N/O has only been observed in the broad-line regions of quasars (Dietrich et al. 2003; Arav et al. 2007) or in the NAALs (D'Odorico et al. 2004).

How do we explain the presence of such a large cold gas mass of highly enriched material with a broad-line-region–like enrichment pattern at such a large distance from the quasar r ∼ 100 kpc? It is tempting (and fashionable) to associate the absorbing material with a large-scale outflow or galactic wind. If we are observing dense material swept up by an outflow, then the energetics are extreme ${\dot{E}_{\rm w}} \sim 10^{45}\,{\rm erg\,s^{-1}}$. A starburst cannot drive this wind unless we are willing to consider unprecedented star formation rates ${\dot{M}_{\ast }}\gtrsim 10^4\,M_\odot \,{\rm yr^{-1}}$. Radiation pressure feedback from the quasar cannot drive an outflow with this power even if its bolometric luminosity were completely absorbed by dust grains (along a different direction than our line of sight). However, the power of the flow is only a few percent of SDSSJ1204+0221FG's estimated bolometric luminosity, or similarly, its energy is of the order of a percent of the radiated rest-mass energy required to grow a ∼10⁹M_☉ black hole. So, the feedback hypothesis suggests a coupling between black hole accretion and outflow which is comparable to the value used by simulators to reproduce the supermassive black hole M_BH–σ correlation (e.g., Springel et al. 2005a). Furthermore, radiative losses from such an energetic flow could be significant, so our estimate of the coupling factor must be considered a lower limit. If we are in fact observing feedback in SLLS/SDSSJ1204+0221BG, then the kinematics, radial extent, and high metallicity of the emergent outflow bear intriguing similarities to the giant Lyα nebulae observed in HzRGs. However, it is difficult to explain why such an energetic outflow would result in so little material at intermediate temperature T ∼ 10^4.5–10⁶ K, which we would have easily detected (but did not; see Section 4.3).

But, we may not be observing an outflow at all. The observed kinematics in SLLS/SDSSJ1204+0221BG, although extreme relative to the intervening SLLS population, are consistent with the expected gravitational motions if the f/g quasar is indeed hosted by a massive dark matter halo M ≳ 10¹³ M_☉, as indicated by the strong clustering of z ∼ 2.5 quasars (Croom et al. 2001; Porciani et al. 2004; Croom et al. 2005). In this alternative scenario, the absorption is being caused by cold clouds, with sizes r_abs = 10–100 pc, unit covering factor and implied volume filling factor C_v ∼ 10⁻⁵ − 10⁻⁴, which are either infalling or virialized in the deep potential well of the massive dark matter halo. We estimated the pressure of these clouds to be P ∼ 10⁵ K cm⁻³, which intriguingly matches the pressure of the T_vir ∼ 10⁷ K shock-heated gas expected to permeate the massive dark matter halo hosting the f/g quasar. This pressure equilibrium is reminiscent of a large class of galaxy formation models that postulate cold T ∼ 10⁴ K clouds pressure confined by a hot shock-heated virialized medium (Mo & Miralda-Escude 1996; Maller & Bullock 2004; Dekel & Birnboim 2006), and these scenarios might explain the lack of significant intermediate temperature T ∼ 10^5–6 K gas near the f/g quasar. However, if we are indeed detecting pressure-confined cold clouds undergoing gravitational motions, why should these clouds have such a high metallicity? This question is all the more puzzling considering that the expected cooling time of the tenuous virialized hot gas would be comparable to the Hubble time at r ∼ 100 kpc. While it may be more plausible to associate the cold gas and metals with star-forming galaxies clustered around the quasar, they would need to be extremely abundant n ∼ 0.1 Mpc⁻³ to produce the near unit covering factor of cold gas and metals. These faint L ∼ 10⁻³L_* dwarf galaxies would need to enrich spheres of r_abs ∼ 20 kpc to solar metallicity, which seems implausible in light of the low metallicities observed in most DLAs (see Figure 7) and the similarly low values seen locally in dwarf galaxies.

With just a single sightline, we cannot distinguish between a quasar-powered outflow or cold clouds undergoing gravitational motions. However, similar observations of a statistical sample of projected quasar pairs stand to teach us a tremendous amount about the physics of massive galaxy formation. This is nicely illustrated by the preliminary comparison of the absorption-line properties of z ∼ 2.2 quasars to z ∼ 2.3 star-forming galaxies presented in Figure 11. The primary motivation for this comparison is that, across the two populations, we are afforded a mass baseline of more than an order of magnitude. The clustering of star-forming galaxies at z ∼ 2 indicates that they inhabit dark matter halos with M ≲ 10¹²M_☉, making them the likely progenitors of ∼L_* galaxies that inhabit the "blue-cloud" of the color–magnitude diagram today (Conroy et al. 2008); whereas, the stronger clustering of quasars at z ∼ 2 implies larger halo masses M ≳ 10¹³M_☉ (Croom et al. 2001; Porciani et al. 2004; Croom et al. 2005), making them progenitors of massive red-and-dead galaxies on the red sequence. Hence, in comparing quasars to star-forming galaxies at z ∼ 2, we are effectively comparing the progenitors of quenched galaxies to those of unquenched galaxies.

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The lower panel of Figure 11 plots the H i column density of absorbers at the f/g quasar (or galaxy) redshift versus the impact parameter to the b/g quasar sightline. The (red) circles are the 13 f/g quasars (〈z_fg〉 = 2.2) with a background quasar within R_⊥ < 350 kpc uncovered by Hennawi et al. (2006a), and (blue) squares are seven f/g star-forming galaxies (〈z_fg〉 = 2.3) studied in absorption against a bright b/g quasar by Simcoe et al. (2006). The vertical rectangles in the upper panel illustrate the range of metallicities encountered in the individual components of each system at each impact parameter. The only f/g quasar metallicity measured thus far is for SDSSJ1204+0221 (this work), whereas Simcoe et al. (2006) measured metallicities near six f/g galaxies.

Two notable features of Figure 11 warrant further discussion. First, at R_⊥ ≃ 100 kpc, one galaxy and one quasar metallicity have been measured, and both indicate abundances near solar. Simcoe et al. (2006) attributed the high metallicity of their smallest impact parameter system (MD103) to galaxy formation feedback, and we similarly cited the high metallicity of SDSSJ1204+0221 as the most compelling argument for an outflow powered by the quasar. By mapping out the run of abundance with impact parameter in this plot, one could characterize the size of the enriched regions around protogalaxies with a significant mass lever arm. If feedback is responsible for the metals at large impact parameters, measuring the abundance–impact parameter relation would constrain the energetics and transport processes characterizing the relevant feedback mechanism. Furthermore, this measurement would be fundamental to any discussion of the enrichment history of the IGM and the ICM.

The second noteworthy feature of Figure 11 is that on small scales the f/g quasars appear to have N_H i column densities significantly larger than the f/g galaxies. This comparison is complicated by the fact that the dark matter halos that host the quasars are expected to be larger and more massive than those hosting the galaxies. For reference, Conroy et al. (2008) estimated that the average halo mass of z ∼ 2 star-forming galaxies to be M = 10¹²M_☉, which implies a virial radius r_vir = 89 kpc; whereas, at z ∼ 2.4 we are using M = 10^13.3M_☉ implying r_vir = 250 kpc (Porciani et al. 2004). At an impact parameter of R_⊥ = 100 kpc, the ratio of the total hydrogen column densities of these dark matter halos is N^QSO_H/N^gal_H = 5, whereas the quasars in Figure 11 have H i column densities a factor of ≳100 times larger than the galaxies for R_⊥ ≲ 200 kpc. Although we caution that the statistics in the lower panel of Figure 11 are still very poor, it is nevertheless interesting to speculate about the implications of this tentative result. Why would the quasars have a much larger reservoir of cold gas at R_⊥ ∼ 100 kpc, of the order of a few percent of the total expected gas density (see Section 5.2), than star-forming galaxies? Can this difference be attributed to a distinct feedback mechanism operating in quasars that does not occur in star-forming galaxies? If instead the absorbers at R_⊥ ∼ 100 kpc arise from cold gas accretion rather than outflows, then the larger relative density of cold gas around quasars is particularly puzzling. Cosmological hydrodynamical simulations predict the opposite trend with dark halo mass: cold accretion accounts for a smaller fraction of the total accreted gas in higher mass halos where shocks become stable throughout the halo and the cold filamentary mode of accretion disappears (Kereš et al. 2005; Dekel & Birnboim 2006; Ocvirk et al. 2008). Whether the cold gas around quasars is ejected by feedback or accreted in gravitational collapse, what is the ultimate fate of this material? Does it eventually fall back onto the quasar host galaxy or do the gas and metals blend into the IGM? Do we expect to observe a similar cold halo of gas around nearby massive elliptical galaxies, since their progenitors are z ∼ 2 quasars like SDSSJ1204+0221FG?

Although preliminary, the putative trends in Figure 11 provoke fundamental questions about feedback, quenching, and the physics of massive galaxy formation. Yet, this discussion represents just two measurements (metallicity and N_H i) gleaned from our analysis of the spectrum of SDSSJ1204+0221BG. Other properties of the gas such as its kinematics, temperature, ionization structure, relative abundance patterns, the presence or absence of a hot collisionally ionized phase, and the volume density and size of the clouds have a similar potential to constrain the physics of massive galaxy formation if they can be mapped out for statistical samples. Such a statistical analysis is well within reach. To date, our pair confirmation program (Hennawi 2004; Hennawi et al. 2006a, 2006b) has confirmed about 90 pairs of quasars with impact parameter R < 300 kpc and z_fg > 1.6, and about a comparable number still remain to be discovered in the existing SDSS photometric data. Of the known pairs, only about five are bright enough r ≲ 19 for high-resolution (FHWM ∼10 km s⁻¹) echelle spectroscopy like the HIRES used to study SLLS/SDSSJ1204+0221BG. However, higher throughput but lower resolution echellette spectrographs, such as the Echellette Spectrograph and Imager (ESI; Sheinis et al. 2002) on Keck II, the Magellan Echellette (MagE) on the Magellan Clay Telescope, or the planned X-Shooter spectrograph (D'Odorico et al. 2006) for the VLT, can deliver spectra with FHWM ∼30 − 50 km s⁻¹ and the required S/N (∼10 per resolution element), in 1–2 hr for r ≲ 21.5, which would make all of the quasar pairs known observable. Although these instruments have lower spectral resolution, they roughly resolve the H i Lyman series affording precise estimates of N_H i. Furthermore, such data would yield metallicity and relative abundance estimates to a precision of 0.3 dex, and would allow for the construction of photoionization models with an accuracy comparable to that achieved in this work.

The most important aspect of the approach taken to understanding galaxy formation in this study and (Simcoe et al. 2006; see also Adelberger et al. 2003) is that they provide the first observational constraints on the physical state of the gas on scales ≳ kpc in high-z protogalaxies. Although the ideas behind quenching and feedback were introduced to explain the observed properties of local galaxy stellar populations, such as the bimodality in the color–magnitude diagram (Strateva et al. 2001; Baldry et al. 2004; Bell et al. 2004; Blanton et al. 2005; Faber et al. 2007), and the sharp cutoff in the luminosity function (Benson et al. 2003), these are fundamentally gas dynamics problems. Many of the relevant hydrodynamical and physical processes can be (or are nearly) resolved by simulation grids with current technology. Conversely, predicting how this gas physics manifest itself in the stellar populations of local or high-z galaxies requires that the uncertain "subgrid" physics of star formation be inserted by hand, or with the aid of semianalytical recipes. Thus, observational constraints on the gas provide especially fruitful comparisons to theory. If the techniques presented here for a single object can be expanded to statistical samples, that will constitute a significant step on the road toward understanding massive galaxy formation.