TRACING THE COSMIC METAL EVOLUTION IN THE LOW-REDSHIFT INTERGALACTIC MEDIUM^*

We express the mass density of a metal ion, ρ_ion = Ω_ionρ_cr, relative to ρ_cr, the cosmological closure density. For Hubble constant H₀ = (70 km s⁻¹Mpc⁻¹)h₇₀, we can write $\rho _{\rm cr} = (3 H_0^2/8 \pi G) = 9.205 \times 10^{-30} h_{70}^2 \,{\rm g \,cm}^{-3}$, or in more convenient galactic units, $1.36 \times 10^{11} h_{70}^2 \, M_{\odot } \,{\rm Mpc}^{-3}$. The mean comoving baryon overdensity (at z = 0) is written $\bar{\rho }_b = [\Omega _b \rho _{\rm cr} (1-Y_p)/m_H] \approx 1.90 \times 10^{-7}$ cm⁻³, appropriate for Ω_b = 0.0461 (Hinshaw et al. 2013) and primordial helium abundance Y_p = 0.2485 (Aver et al. 2013). The ion mass density is found by integrating over its observed column-density distribution function (CDDF) of absorbers, $f(N,z) \equiv (\partial ^2 {\cal N} / \partial N \, \partial z)$, as described in Tilton et al. (2012),

$$\begin{eqnarray} \Omega _{\rm ion} &=& \frac{ H_0 \, m_{\rm ion}}{c \, \rho _{\rm cr}} \int _{\rm N_{\rm min}}^{\rm N_{\rm max}} f(N,z) \, N \, dN \nonumber \\ &=& (1.365 \times 10^{23} {\rm cm}^2) \, h_{70}^{-1} \left(\frac{m_{\rm ion}}{{\rm amu}} \right) \int _{\rm N_{\rm min}}^{\rm N_{\rm max}} f(N,z) \, N \, dN \;. \nonumber\\ \end{eqnarray} \tag{ 1 }$$

The integral is performed as a sum over logarithmic bins of size Δlog N ≈ 0.2. The range of integration is set at the lower end (N_min) by our 30 m Å equivalent width threshold and at the upper end (N_max) by the column density where absorber statistics become uncertain. Depending on the slope of the distribution, f(N, z)∝N^−β, we can make corrections for absorption systems outside this range. Appendix A describes our formalism for fitting these distributions and integrating power-law fits to f (N, z). This technique provides a check on the numerical integration and allows us to assess the fiducial metal content, extrapolated to column densities above and below the observed range.

Table 2 gives the Ω_ion values for all six ions, measured in low-z surveys with HST/STIS (Tilton et al. 2012) and HST/COS (Danforth et al. 2014). Although our metal absorber list is large, there is considerable overlap with prior studies (Danforth & Shull 2008; Cooksey et al. 2011; Tilton et al. 2012). We express values of Ω_ion in units of $10^{-8} h_{70}^{-1}$. All values from our previous STIS survey were recalculated from the Tilton et al. (2012) absorber lists to match the column density ranges in Table 2. We then compare the low-z measurements to values from previous surveys, including Songaila (2001, 2005), Becker et al. (2009), Simcoe (2006), Simcoe et al. (2011), and Ryan-Weber et al. (2006). All values of Ω_ion were revised to agree with our adopted (ΛCDM) cosmological parameters, h = 0.7, Ω_m = 0.275, and Ω_Λ = 0.725.

Table 2. Summary of Metal–Ion Densities^a

Iona	Nabsa	Range in (log N)a	Ωion(STIS)a	Ωion(COS)a
		(N in cm−2)	(in $10^{-8} h_{70}^{-1}$)	(in $10^{-8} h_{70}^{-1}$)
C iii	77	12.67–14.19	$4.6^{+1.8}_{-0.8}$	$7.1^{+1.9}_{-1.2}$
C iv	49	12.87–14.87	$8.1^{+4.6}_{-1.7}$	$10.1 ^{+5.6}_{-2.4}$
N v	37	13.15–14.01	$0.9^{+1.3}_{-0.5}$	$1.9^{+0.6}_{-0.4}$
O vi	212	13.38–14.83	$33.9^{+9.3}_{-4.1}$	$38.6^{+4.8}_{-3.2}$
Si iii	87	12.15–13.44	$1.1^{+0.8}_{-0.3}$	$1.4^{+0.3}_{-0.2}$
Si iv	31	12.53–13.94	$4.5^{+3.0}_{-1.2}$	$2.1^{+1.0}_{-0.5}$

Notes. ^aColumns (1)–(3) list the observed ions and the number of absorbers in the COS survey in the stated range of ion column densities (log N). Minimum column density (N_min) corresponds to 30 m Å equivalent width in primary diagnostic line (Table 1). Maximum (N_max) corresponds to the last measured absorber at which survey statistics are reliable. Columns (4) and (5) list IGM mass density (at low z) of six ions, quoted as the fractional contribution (Ω_ion = ρ_ion/ρ_cr) to closure density. These values are derived from the HST/STIS survey (Tilton et al. 2012, revised as noted in text) and the HST/COS survey (Danforth et al. 2014).

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The distributions in column density were shown in Danforth et al. (2014) plotted versus column density, N_ion, for C iv, Si iv, C iii, Si iii, and O vi. These distributions illustrate the systematic uncertainties inherent in computing values of Ω_ion from Equation (1) over the measured range of column densities (log N_min < log N < log N_max). For several ions, the discrete sums are sensitive to the small number of absorbers at the high end, as well as the reduced pathlength Δz for absorbers at the low end. As was done by previous authors (Cooksey et al. 2010, 2013; D'Odorico et al. 2013), we fit power laws to the CDDF and extrapolate to a standard range of column densities as discussed in Appendix A and Table 3. These distributions are often more useful to observers than the single parameter Ω_ion, and they convey information about the sparse statistics for metal absorbers at both low and high column densities.

Table 3. Column-Density Distribution Fits^a

Ion	C0(weak)	β(weak)	C0(strong)	β(strong)	log Nb	log Nmin	log Nmax	Ωionb
								($10^{-8}\,h_{70}^{-1}$)
C iv	2.7 ± 1.6	1.5 ± 0.2	1.6 ± 0.3	2.0 ± 0.2	13.546	12.87	15.0	10.2
Si iv	0.2 ± 0.1	1.8 ± 0.1	...	...	...	12.53	15.0	3.2
O vi	9.6 ± 0.9	1.6 ± 0.1	11 ± 2	3.9 ± 0.6	14.026	13.38	15.0	46.4
N v	0.4 ± 0.1	2.1 ± 0.2	...	...	...	13.15	15.0	3.5

Notes. ^aPower-law fits to the cumulative column density distribution, $d{\cal N}(>N)/dz$, of the form C₀(N/N₀)^−β, with fiducial column N₀ = 10¹⁴ cm⁻². Ions Si iv and N v are fitted with a single power law, whereas C iv and O vi are fitted with a double power law (for weak and strong absorbers) matched at a break column density log N_b. ^bValue of ion density parameter, Ω_ion, integrating power-law distribution from N_min to N_max, using Equations (A4), (A5), or (A6) in Appendix A.

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Figure 1 shows the evolution of $\Omega _{\rm C\,\scriptsize{IV}}$ with redshift. The C iv data include high-redshift measurements (z ≈ 4.5–6) by Pettini et al. (2003), Becker et al. (2009), Ryan-Weber et al. (2009), Simcoe et al. 2011), and D'Odorico et al. (2013). We corrected the Pettini results for our values of H₀ and Ω_m using the scaling $\Omega _{\rm ion} \propto \Omega _m^{1/2} h^{-1}$. Values at intermediate redshifts (z ≈ 1.6–4.5) are taken from surveys by Boksenberg et al. (2003), D'Odorico et al. (2010), and Boksenberg & Sargent (2014). The latter paper includes updated values for $\Omega _{\rm C\,\scriptsize{IV}}$ provided by A. Boksenberg (2014, private communication). The data at z < 1 come from the HST survey by Cooksey et al. (2010) reported in two redshift bins: $\Omega _{\rm C\,\scriptsize{IV}} = 6.24^{+2.88}_{-2.14}$ ($10^{-8} h_{70}^{-1}$) from 17 C iv absorbers at 〈z〉 = 0.383 and $\Omega _{\rm C\,\scriptsize{IV}} = 6.35^{+2.52}_{-1.99}$($10^{-8} h_{70}^{-1}$) from 19 C iv absorbers at 〈z〉 = 0.786. For the entire redshift sample, they found $\Omega _{\rm C\,\scriptsize{IV}} = 6.20^{+1.82}_{-1.52}$ ($10^{-8} h_{70}^{-1}$) from 36 C iv absorbers at 〈z〉 = 0.654. The lowest-redshift points at 〈z〉 < 0.1 come from the Colorado group's surveys: $\Omega _{\rm C\,\scriptsize{IV}} = 7.7 \pm 1.5$ ($10^{-8} h_{70}^{-1}$) from 24 C iv absorbers (Danforth & Shull 2008), $\Omega _{\rm C\,\scriptsize{IV}} = 8.1^{+4.6}_{-1.7}$ ($10^{-8} h_{70}^{-1}$) from 29 C iv absorbers (Tilton et al. 2012), and $\Omega _{\rm C\,\scriptsize{IV}} = 10.1^{+5.6}_{-2.4}$ ($10^{-8} h_{70}^{-1}$) from 49 C iv absorbers (Danforth et al. 2014).

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Figure 2 shows the evolution of $\Omega _{\rm Si\,\scriptsize{IV}}$ with redshift, including high-redshift measurements (z ≈ 2–5) by Songaila (2001, 2005) converted to our parameters (H₀ and Ω_m). We also show data at z ≈ 2.4 (Scannapieco et al. 2006), at z ≈ 3.3 (Aguirre et al. 2004), and at z = 1.9–4.5 (Boksenberg & Sargent 2014). The latter paper includes new values for $\Omega _{\rm Si\,\scriptsize{IV}}$ provided by A. Boksenberg (2014, private communication.) The low-redshift data come from the HST survey by Cooksey et al. (2011) at z < 1. The lowest-redshift points at 〈z〉 < 0.1 are based on the Colorado group's recent surveys: $\Omega _{\rm Si\,\scriptsize{IV}} = 4.5^{+3.0}_{-1.2}$ ($10^{-8} h_{70}^{-1}$) from 30 Si iv absorbers (Tilton et al. 2012) and $\Omega _{\rm Si\,\scriptsize{IV}} = 2.1^{+1.0}_{-0.5}$ ($10^{-8} h_{70}^{-1}$) from 31 Si iv absorbers (Danforth et al. 2014). Evidently, the Si iv measurements still have some uncertainty arising from the column density distribution function.

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In Section 3.3 we will analyze the ionization states of C, Si, and O probed by the observed ions. This analysis requires photoionization modeling using estimates of the metagalactic flux of ionizing photons. Through analytic formulae, we can relate the hydrogen photoionization rate Γ_H for optically thin absorbers to the specific intensity I_ν and its value I₀ at the Lyman limit (912 Å), as well as to Φ₀, the one-sided (unidirectional) flux of ionizing photons. Because there has been some debate in the modeling literature over the strength of the metagalactic ionizing radiation field, we begin with clear definitions of flux and intensity. Part of the confusion arises from geometric differences between an isotropic radiation field, appropriate for intergalactic space far from individual sources, and a unidirectional radiation field arising from a single nearby source. In models for the local-source case, all photons enter the absorber at normal incidence from one side. In the isotropic case, half of the photons are directed into the forward hemisphere, and half are directed backward. One must also account for the angular dependence of the radiation, with 〈cos θ〉 = 1/2 averaged over the forward hemisphere. Thus, for an isotropic radiation field, the unidirectional flux Φ₀ = n_γ(c/4), and for the local source, Φ₀ = n_γc, where n_γ is the number density of ionizing photons. Geometric factors are less critical for optically thin absorber models, but one must be careful when using flux or intensity parameters to derive n_γ, the photoionization parameter U = n_γ/n_H, and the ionization fractions of H, He, and heavy elements.

The ionizing radiation background remains somewhat uncertain, despite two decades of estimating its strength and spectrum (Haardt & Madau 1996, 2001, 2012; Shull et al. 1999; Faucher-Giguère et al. 2009). Figure 3 shows several estimates of the ionizing background in the extreme ultraviolet (EUV) and soft X-ray. The labels (HM01, HM05, HM12, and FG11) refer to published or unpublished tabulations based on earlier publications. The HM05 spectrum refers to the 2005 August update to the Haardt & Madau (2001) radiation field², and the FG11 spectrum refers to the 2011 December update³ to the spectrum in Faucher-Giguère et al. (2009). The PL spectrum refers to our constructed broken power-law distribution consistent with recent HST/COS composite spectrum (Shull et al. 2012) in the EUV (500–912 Å) and connected to soft X-ray observations in the Lockman Hole (Hasinger 1994). The hard X-ray background (Churazov et al. 2007) from 10–100 keV has been included in some backgrounds (HM01, HM05, and HM12); these energetic photons have little effect on the ionization state of H, He, and heavy elements.

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The hydrogen-ionizing background Φ₀ and photoionization rate Γ_H of HM12 have been questioned (Kollmeier et al. 2014) as inconsistent with the column density distribution of low-redshift Lyα (H i) absorbers (Danforth et al. 2014). The numerical simulations in the Kollmeier et al. (2014) analysis were based on the HM12 background, which was deemed too low by a factor of five. However, they noted better agreement when the HM01 background was used. A similar comparison (Egan et al. 2014) also obtained agreement with the Lyα distribution, based on the HM01 ionizing background used in our group's grid-code (Enzo) simulations (Smith et al. 2011). The primary difference between HM01 and HM12 radiation fields comes from different assumptions about the escape fraction (f_esc) of Lyman continuum (LyC) radiation from galaxies (Shull et al. 1999). In the HM12 formulation, the ionizing background is dominated by AGN, the escape fraction is parameterized as f_esc(z) ≈ (1.8 × 10⁻⁴)(1 + z)^3.4, and galaxies make almost no contribution to the photoionization rate at z < 2. Such low values of f_esc are probably unrealistic, because the usual observational constraints (direct LyC detection, diffuse Hα emission, and metal-ion ratios) depend on small-number statistics and geometric uncertainties. If the LyC photons escape through vertical cones above star-forming regions in galactic disks (Dove & Shull 1994), the observational constraints require large samples to deal with inclination bias. High-redshift surveys (Shapley et al. 2006) find either large transmitted LyC fluxes or none at all. As a consequence, if f_esc were only 5%, one would need to survey well over 20 galaxies to obtain a statistically accurate escape fraction.

Systematic uncertainties also affect indirect limits on the metagalactic background from diffuse Hα emission (Stocke et al. 1991; Donahue et al. 1995; Vogel et al. 1995; Weymann et al. 2001). Translating Hα surface brightnesses into limits on Φ₀ or Γ_H requires assumptions about emitting geometries and radiative transfer of LyC. Adams et al. (2011) used integral-field spectroscopy to set deep limits on Hα emission from the outskirts of two low-surface-brightness, edge-on Sd galaxies, UGC 7321 and UGC 1281. They constrained the H i photoionization rate to be Γ_H < 2.3 × 10⁻¹⁴ s⁻¹ (UGC 7321) and Γ_H < 14 × 10⁻¹⁴ s⁻¹ (UGC 1281). The UGC 7321 limit comes from a (5σ) absence of Hα, and it lies well below previous observational limits and theoretical predictions. However, we are reluctant to adopt such a low value of Γ_H or Φ₀ from a single object⁴. Their method of inferring the metagalactic flux Φ₀ and ionization rate Γ_H relies on a large and uncertain geometric correction for the gas cloud aspect ratio, A_tot/A_proj, of total exposed area to projected area. As noted by Stocke et al. (1991), this ratio is 4 for a sphere and π for a cylinder viewed transversely. The value $\langle A_{\rm tot} / A_{\rm proj} \rangle = 24.8^{+3.4}_{-1.5}$ adopted by Adams et al. (2011) is based on the projection of a homogeneous thin disk viewed nearly edge-on, whereas the Hα emission likely arises in smaller clumps of gas, whose geometries are probably closer to spheres or cylinders. With the inferred ionizing flux scaling as Φ₀∝(A_tot/A_proj)⁻¹, their lower limit arises from a six to eight times larger aspect ratio compared to values for spherical or cylindrical clouds.

In view of the extensive experimental and theoretical literature on metagalactic fluxes, hydrogen ionization rates, and IGM ionization conditions, the limits on low-redshift ionizing radiation remain uncertain. In Section 3.3, we use ratios of adjacent ion stages (C iii/C iv and Si iii/Si iv) from IGM absorption-line spectroscopy to constrain ionizing flux Φ₀ ≈ 10⁴ cm⁻² s⁻¹. A similar technique (Tumlinson et al. 1999), based on the ions Fe i/Fe ii and Mg i/Mg ii in the low-redshift absorption system around NGC 3067 probed by the background QSO 3C 232, gave a lower limit of Φ₀ > 2600 cm⁻² s⁻¹. Our models in Section 3.3 are scaled to Φ₀ ≈ 10⁴ cm⁻² s⁻¹, Γ_H ≈ (8 ± 2) × 10⁻¹⁴ s⁻¹, and I₀ ≈ (3 ± 1) × 10⁻²³erg cm⁻² s⁻¹ Hz⁻¹ sr⁻¹. These parameters are in reasonable agreement with past calculations, observational estimates (other than the single galaxy probed by Adams et al. 2011), and our low-redshift absorber data on C iii, C iv, Si iii, and Si iv. We now explore this issue quantitatively.

For an isotropic radiation field of specific intensity I_ν, the normally incident photon flux per frequency is (πI_ν/hν) into an angle-averaged, forward directed effective solid angle of π steradians. The isotropic photon flux striking an atom or ion is 4π(I_ν/hν). The hydrogen photoionization rate follows by integrating this photon flux times the photoionization cross section over the frequency from the threshold (ν₀) to ∞.

$$\begin{eqnarray} \Gamma _{\rm H} &=& \int _{\nu _0}^{\infty } \frac{4 \pi \, I_{\nu }}{h \nu } \sigma _{\nu } \, d \nu \approx \left(\frac{ 4 \pi I_0 \sigma _0}{h} \right) \int _{1}^{\infty } x^{-\alpha -\beta -1} \, dx \nonumber\\ &=& \frac{ 4 \pi I_0 \sigma _0}{h (\alpha +\beta) } \;. \end{eqnarray} \tag{ 2 }$$

Here, we define the dimensionless variable x = ν/ν₀ and approximate the frequency dependence of specific intensity and photoionization cross section by power laws, I_ν = I₀(ν/ν₀)^−α and σ_ν = σ₀(ν/ν₀)^−β, where σ₀ = 6.30 × 10⁻¹⁸ cm² and β ≈ 3. The integrated unidirectional flux of ionizing photons is

$$\begin{equation} \Phi _0 = \int _{\nu _0}^{\infty } \frac{ \pi I_{\nu } }{h \nu } \; d \nu = \left(\frac{ \pi I_0 }{h} \right) \int _{1}^{\infty } x^{-\alpha - 1} \, dx = \frac{\pi I_0}{h \alpha } \; \;, \end{equation} \tag{ 3 }$$

which can be related to the density of hydrogen-ionizing photons by Φ₀ = n_γ(c/4). We note that this definition differs by a factor of one-fourth from that given in Cloudy, which adopts the convention that Φ₀ = n_γc, appropriate for all photons arriving at normal incidence from one direction. We then use I₀ = (hα/π)Φ₀ to relate Γ_H to the flux and spectrum parameters:

$$\begin{eqnarray} \Gamma _{\rm H} &=& 4 \sigma _0 \Phi _0 \left(\frac{\alpha }{ \alpha + \beta } \right) = (8.06 \times 10^{-14} \,{\rm s}^{-1}) \Phi _4 \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} \Gamma _{\rm H} &=& \left(\frac{ 4 \pi I_0 \sigma _0 }{ \alpha + \beta } \right) = (2.71\times 10^{-14} \,{\rm s}^{-1}) I_{-23} \; \;. \end{eqnarray} \tag{ 5 }$$

We will see that Φ₄ ≈ 1 and I₋₂₃ ≈ 3 give reasonable fits to the ionization ratios, where we scale the incident flux of ionizing photons and specific intensity to characteristic values, Φ₀ = (10⁴ cm⁻² s⁻¹)Φ₄ and I₀ = (10⁻²³ erg cm⁻² s⁻¹ Hz⁻¹ sr⁻¹)I₋₂₃ at the hydrogen Lyman limit (hν₀ = 13.60 eV). We adopt β ≈ 3 for hydrogen and an AGN composite spectrum (Shull et al. 2012) with mean spectral index α ≈ 1.41 between 1.0–1.5 ryd. For these parameters, we can write the photoionization parameter U = n_γ/n_H as

$$\begin{equation} U \equiv \left(\frac{4 \Phi _0}{n_H c} \right) = (7.02 \times 10^{-2}) \Phi _4 \Delta _{100}^{-1} \; \;, \end{equation} \tag{ 6 }$$

where the absorber hydrogen density is n_H = (1.90 × 10⁻⁷ cm⁻³)Δ_b at z = 0 with baryon overdensity scaled to Δ_b ≡ 100Δ₁₀₀. Because U∝Φ₀/Δ_b, one can rescale the baryon density to lower values of ionizing flux, if so desired.

Recent calculations of the metagalactic ionizing background (Haardt & Madau 2012) yield a hydrogen photoionization rate, which can be fitted to Γ_H = (2.28 × 10⁻¹⁴ s⁻¹)(1 + z)^4.4 over the range 0 ⩽ z ⩽ 0.7. This HM12 ionization rate at z = 0 would correspond to Φ₀ = [Γ_H(α + β)/4σ₀ α] ≈ 2630 cm⁻² s⁻¹ and I₋₂₃ ≈ 0.823 for the radio-quiet AGN spectral index (α = 1.57) assumed by HM12. These fluxes are lower by a factor of three compared to the z = 0 metagalactic radiation fields from AGN and galaxies calculated by Shull et al. (1999), $I_{\rm AGN} = 1.3^{+0.8}_{-0.5} \times 10^{-23}$ and $I_{\rm Gal} = 1.1^{+1.5}_{-0.7} \times 10^{-23}$, respectively. Adding these two values with propagated errors gives a total intensity and hydrogen ionization rate of $I_{\rm tot} = 2.4^{+1.7}_{-0.9} \times 10^{-23} \; {\rm erg \,cm}^{-2} \,{\rm s}^{-1} \,{\rm Hz}^{-1} \,{\rm sr}^{-1}$ and $\Gamma _{\rm H} = 6.0^{+4.2}_{-2.1} \times 10^{-14} \; {\rm s}^{-1}$. These backgrounds are consistent with those that we estimate below from the C and Si ionization states. The difference between these radiation fields appears to be the small contribution of galaxies assumed in the HM12 background compared to that of Shull et al. (1999), HM01, and HM05. For these reasons, as well as the issues raised by Kollmeier et al. (2014), we normalize our modeled spectral energy distributions (SEDs) to unidirectional, normally incident fluxes Φ₀ = 10⁴ cm⁻² s⁻¹, corresponding to specific intensity I₀ ≈ 3 × 10⁻²³ erg cm⁻² s⁻¹ Hz⁻¹ sr⁻¹ and hydrogen photoionization rate Γ_H ≈ 8 × 10⁻¹⁴ s⁻¹.

The IGM metal density traced by these six ion species can be estimated by correcting for unseen ionization states and scaling to total metal abundances. For the latter, we initially adopted solar abundances to compute the fractional contributions of C, Si, or O to the total metal abundances by mass. However, after comparing the C and Si abundances, we prefer an abundance pattern in which alpha-process elements (e.g., Si and O) are enhanced relative to C owing to early nucleosynthesis sources by massive stars. In high-redshift spectra, observers usually measure C iv and Si iv, and sometimes C ii and Si ii, but they often lack the important intermediate ion states C iii and Si iii, whose absorption lines at 977.0 Å and 1206.5 Å can be confused by the Lyα forest. Here, in our low-z survey, we measure C iii and C iv as well as Si iii and Si iv. We use the mean (statistical) values of the ratios of adjacent ion states, C iii/C iv and Si iii/Si iv, to constrain the IGM density and the strength and shape of the ionizing radiation background. We then use the ionization corrections for C and Si to estimate consistent individual metallicities. By comparing these metallicities to their expected abundance ratios, we derive additional constraints on Si/C abundance enhancement, radiation field, and IGM density.

The mean observed ionization fractions of the ensemble of metal-line absorbers are

$$\begin{equation} \frac{\Omega _{{\rm C\,\scriptsize{III}}} }{ \Omega _{\rm C\,\scriptsize{IV}} } = 0.70^{+0.43}_{-0.20} \quad {\rm and} \; \; \; \frac{\Omega _{\rm Si\,\scriptsize{III}} }{ \Omega _{\rm Si\,\scriptsize{IV}} } = 0.67^{+0.35}_{-0.19} \; \;. \end{equation} \tag{ 7 }$$

We will show that, for a range of ionizing background shapes, these ratios are consistent with the photoionization parameter log U ≈ −1.5 ± 0.4. As noted earlier, U = n_γ/n_H expresses the density ratio of ionizing photons to hydrogen, where n_H = (1.90 × 10⁻⁷ cm⁻³)Δ_b(1 + z)³, with baryon overdensity Δ_b. Because the absorption lines of C iii λ977 and C iv λ1548 redshift in and out of the COS G130M and G160M bands at z ≈ 0.16, our COS survey does not observe C iii and C iv in the same absorbers. Thus, there may be some concern that these ions are experiencing different radiation fields, in which the ionization parameter U(z)∝(1 + z)^1.4 for an ionization rate Γ_H∝(1 + z)^4.4 and hydrogen density n_H∝(1 + z)³. In the COS sample (Danforth et al. 2014) the mean redshifts of the carbon absorbers are $\langle z_{{\rm C\,\scriptsize{III}}} \rangle = 0.35$ and $\langle z_{\rm C\,\scriptsize{IV}} \rangle = 0.06$, so we might expect a 0.15 dex offset in U between those absorbers. However, we have also examined low-redshift data from our FUSE and STIS survey (Tilton et al. 2012), in which both ions are seen in the same absorbers. In those 28 absorbers, with $\langle z_{{\rm C\,\scriptsize{III}}} \rangle = 0.15$ and $\langle z_{\rm C\,\scriptsize{IV}} \rangle = 0.056$, the C iii/C iv ratios are essentially the same as in the COS data. Therefore, we choose to make no correction for possible small offsets in the radiation field.

We explore the ionizing spectra and their effects on the observed ion densities through a series of photoionization calculations with version 13.03 of Cloudy, last described by Ferland et al. (2013). All spectra were flux-normalized to Φ₀ = 10⁴ cm⁻² s⁻¹. The hydrogen density was related to the baryon overdensity Δ_b, and the metallicity in the simulations was taken as 0.1 solar, consistent with inferences for the mean in the low-z IGM (Shull et al. 2012). The input spectra consisted of a variety of SEDs of ionizing photons, reflecting the uncertain intensities in the EUV and soft X-ray (Shull et al. 2012; Haardt & Madau 2012; Faucher-Giguère et al. 2009). We constrain the SED from the observed abundance ratios of adjacent ionization states, C iii/C iv and Si iii/Si iv, and then estimate the total mass densities of C and Si,

$$\begin{eqnarray} \Omega _{\rm C} &=& \left(\Omega _{{\rm C\,\scriptsize{III}}} + \Omega _{\rm C\,\scriptsize{IV}} \right) \left(\frac{ {\rm C_{\rm tot}} }{{\rm C\,\scriptsize{III}} + {\rm C\,\scriptsize{IV}} } \right) \end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray} \Omega _{\rm Si} &=& \left(\Omega _{\rm Si\,\scriptsize{III}} + \Omega _{\rm Si\,\scriptsize{IV}} \right) \left(\frac{{\rm Si_{\rm tot}} }{ {\rm Si\,\scriptsize{III}} + {\rm Si\,\scriptsize{IV}} } \right) \; \;. \end{eqnarray} \tag{ 9 }$$

The second parenthetical terms in these relations are the ionization correction factors, abbreviated CF_C and CF_Si, which quantify the amount of C and Si in higher ion states. As discussed more fully in Appendix B, ionizing EUV photons can produce helium-like carbon (C v) by ionizing C iv at energies E ⩾ 64.49 eV. The EUV photons also make Si v, Si vi, and Si vii with production threshold energies 33.49 eV (from Si iii), 45.14 eV (from Si iv), and 166.77 eV (from Si v), respectively. These ions can also be produced by inner-shell ionization by soft X-rays (E ⩾ 1.9 keV) followed by Auger electron emission, which boosts the ionization by two or more stages. Further discussion and analytic estimates of the abundances of higher ion states of C and Si are provided in Appendix B.

Figure 4 shows the ratios, C iii/C iv and Si iii/Si iv, as functions of Δ_b, and Figure 5 shows the ionization correction factors CF_C and CF_Si versus Δ_b for various SEDs. Our Cloudy photoionization models of the observed C and Si ion ratios, together with their uncertainties, suggest that Δ_b ≈ 70–230 for the HM12 and PL spectral distributions. The agreement is not as good with the FG11 and HM05 background, with HM12 and PL models providing better agreement. The correction factors corresponding to the two observed stages of C and Si are ${\rm CF}_{\rm C} = \Omega _{\rm C} / \left[ \Omega _{{\rm C\,\scriptsize{III}}} + \Omega _{\rm C\,\scriptsize{IV}} \right] = 2.0^{+1.0}_{-0.5}$ and ${\rm CF}_{\rm Si} = \Omega _{\rm Si} / \left[ \Omega _{\rm Si\,\scriptsize{III}} + \Omega _{\rm Si\,\scriptsize{IV}} \right] = 6^{+4}_{-3}$.

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An additional constraint comes from the C and Si metallicities inferred from our ionization corrections, which must be consistent with their relative abundances by mass. For solar abundances, the Si/C ratio is ρ_Si/ρ_C = 0.238 by mass, but our survey suggests that Si must be enhanced by a factor of three (Figure 6), probably owing to "alpha-process" nucleosynthesis. Using the observed mass densities in Table 2, $(\Omega _{{\rm C\,\scriptsize{III}}} + \Omega _{\rm C\,\scriptsize{IV}}) = 17.2^{+5.9}_{-2.7}$ $(10^{-8} h_{70}^{-1})$ and $(\Omega _{\rm Si\,\scriptsize{III}} + \Omega _{\rm Si\,\scriptsize{IV}}) = 3.5^{+1.0}_{-0.5}$ $(10^{-8} h_{70}^{-1})$, we can relate the Si/C abundance ratio to the ion correction factors:

$$\begin{equation} \frac{ {\rm CF}_{\rm Si} }{ {\rm CF}_{\rm C} } = (1.17^{+0.52}_{-0.25}) \left[ \frac{\rho _{\rm Si} / \rho _{\rm C} }{0.238} \right] \; \;. \end{equation} \tag{ 10 }$$

From the constraints in Figures 4–6, we find that Δ_b ≈ 200  ±  50 for ionizing flux Φ₀ = 10⁴ cm⁻² s⁻¹. If one were to lower the ionizing background flux to Φ₀ = (3000–5000) cm⁻² s⁻¹, our ionization models for the C and Si ion ratios would require rescaling the baryon overdensity to Δ_b = 50–100 to keep U constant. As can be seen in Figures 4 and 5, the ionization correction factors become unrealistically large, particularly for the silicon ions, ${\rm Si_{\rm tot}} / ({\rm Si\,\scriptsize{III}} + {\rm Si\,\scriptsize{IV}})$. Thus, the observed metal-line systems probably reside in higher-density regions than the Lyα-forest systems at lower column densities. The observed ionization ratios of C iii/C iv and Si iii/Si iv provide additional evidence for a higher metagalactic radiation field, Φ₀ ≈ 10⁴ cm⁻² s⁻¹ and ionization rate Γ_H ≈ 8 × 10⁻¹⁴ s⁻¹. These values, while still uncertain, are consistent with theoretical calculations (Haardt & Madau 2001; Shull et al. 1999) and inferences from the Lyα column-density distribution (Kollmeier et al. 2014; Egan et al. 2014).

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Thus, the enhanced Si/C abundances are consistent with the PL, FG11, and HM05 radiation fields, but not with HM12. However, the constraints are not always in full agreement. Our choice of Δ_b is guided primarily by the need for sensible (finite and consistent) ionization correction factors for C and Si (Figures 5 and 6). Our inference of enhanced Si/C and softer radiation fields was also based on these consistency arguments. High radiation fields in the EUV and soft X-ray produce far too many high ions (C v, Si v, Si vi, and Si vii) to be consistent with the expected metallicities. Because the high ionization states of Si are sensitive to hard EUV and soft X-ray photons, the Si ionization correction curves in Figure 5 are too high for the HM12 radiation field, which has elevated fluxes between 3 and 300 Å. The bottom panel of Figure 5 shows that CF_Si > 10 for Δ_b ⩽ 300, inconsistent with the values of CF_C unless the Si/C abundance is enhanced above solar ratios. Figure 4 shows that the adjacent ion ratios for C iii/C iv and Si iii/Si iv are somewhat inconsistent with the softer radiation backgrounds (FG11 and HM05), preferring the HM12 and PL distributions. Clearly, there is a need for additional work to infer the uncertain metagalactic background between 2 and 20 ryd, particularly between the He ii edge (54.4 eV) and the soft X-ray band (0.3–3 keV) responsible for inner-shell ionization of many metal ions.

The total metal abundance, Ω_Z, can be estimated by dividing Ω_C, Ω_Si, and Ω_O by the individual mass fractions of these elements relative to all heavy elements. From the recent solar abundance calculations of Caffau et al. (2011), the relevant fractions are 18.2% (C), 4.34% (Si), and 44.0% (O). Using our corrections for ionization state and metal fractions of C and Si, we find mean mass densities of Ω_C = 3.4 × 10⁻⁷ and Ω_Si = 2.1 × 10⁻⁷. If we divide these parameters by the solar mass fractions of C (18.2%) and Si (4.34%), the photoionized Lyα-forest absorbers at low redshift traced by C iii, C iv, Si iii, and Si iv would correspond to total metal mass densities Ω_Z = 1.9 × 10⁻⁶ from carbon or Ω_Z = 4.8 × 10⁻⁶ from silicon. To make these two metallicity estimates consistent, we require Si/C to be enhanced by a factor of three relative to solar abundances. Such enhancements of alpha-process elements, [O/Fe] ≈+0.5, have also been seen in metal-poor halo stars (Akerman et al. 2004) and in low-metallicity DLAs (Pettini et al. 2008). For example, in a survey of 20 metal-poor DLAs, Cooke et al. (2011) found a mean value [O/Fe] = +0.39 ± 0.12.

We then recalculate the metal fractions, enhancing the abundances by a factor of three for all alpha-process elements: even-Z nuclei from atomic number Z = 8 to 20 (O through Ca). The mass fractions become 7.95% (C), 5.70% (Si), and 58.0% (O), and the inferred metal abundances are Ω_Z = 4.3 × 10⁻⁶ from carbon and Ω_Z = 3.7 × 10⁻⁶ from silicon. With the Si/C enhancement, we infer a consistent value Ω_Z = (4.0 ± 0.5) × 10⁻⁶ in the photoionized gas, or a mass density (5.4 ± 0.7) × 10⁵ M_☉ Mpc⁻³. We can perform a similar estimate of metal abundance from O vi, the single observed ion stage of oxygen. Numerous observations and models suggest that O vi can be formed from both photoionization and collisional ionization. As shown in Figure 7, the fraction of O vi from photoionization is expected to be small in the photoionized absorbers at Δ_b = 200 ± 50. In the hot gas, reflecting the fragility of its Li-like ionization state, the maximum O vi abundance fraction in collisional ionization equilibrium is $f_{\rm O\,\scriptsize{VI}} \approx 0.2$. Cosmological N-body hydrodynamic simulations (Smith et al. 2011; Shull et al. 2012) of the low-redshift IGM, accounting for both photoionization and collisional ionization, show that O vi exists in multiphase gas, with inhomogeneous distributions of metallicity (Z/Z_☉) and ionization fraction $f_{\rm O\,\scriptsize{VI}}$. In these calculations, the IGM-averaged product is $\langle (Z/Z_{\odot }) f_{\rm O\,\scriptsize{VI}} \rangle = 0.01$, a factor of two lower than the frequently assumed values of Z/Z_☉ = 0.1 and $f_{\rm O\,\scriptsize{VI}} = 0.2$. Here, we assume an ionization fraction $f_{\rm O\,\scriptsize{VI}} = \Omega _{\rm O\,\scriptsize{VI}} / \Omega _{\rm O} = 0.1$ and an oxygen-to-metals fraction Ω_O/Ω_Z = 0.58, appropriate for all alpha-process elements enhanced by a factor of three. The observed value in Table 2, $\Omega _{\rm O\,\scriptsize{VI}} = 38.6^{+4.8}_{-3.2}$ ($10^{-8} h_{70}^{-1}$) corresponds to Ω_O = (3.9 ± 0.5) × 10⁻⁶ and total metal abundance Ω_Z = (6.7 ± 0.8) × 10⁻⁶. The metal density in the O vi-traced gas is ρ_Z = (9.1 ± 0.6) × 10⁵ M_☉ Mpc⁻³.

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For the total IGM metal density, we combine the values for photoionized gas (traced by the C and Si ions) with the hot gas (traced by O vi). The total metal density in both phases of the low-z IGM is ρ_Z = (1.4 ± 0.9) × 10⁶ M_☉ Mpc⁻³ or Ω_Z ≈ 10⁻⁵. As we discuss in the next section, this corresponds to ∼10% of the expected heavy elements produced by cosmic star formation, integrated from z ≈ 8 down to z = 0. The resulting metal density, (1.5 ± 0.8) × 10⁷ M_☉ Mpc⁻³, is estimated from the integrated SFR density, ρ_* = (6 ± 2) × 10⁸ M_☉ Mpc⁻³, assuming a mean metal yield y_m = 0.025 ± 0.010.

We now estimate the global metal-production, based on cosmological parameters and observations of the cosmic SFR history. Several groups have integrated the metal-production density. Pettini (1999) suggested that ρ_Z ≈ 4.5 × 10⁶ M_☉ Mpc⁻³ of metals were produced by z = 2.5, with a metal-production yield y_m = 1/42 from star formation between 11–13 Gyr. In a follow-up analysis, Pettini (2006) revised this to 3.4 × 10⁶ M_☉ Mpc⁻³ now assuming y_m = 1/64. Bouché et al. (2007) integrated the parameterized SFR history from Cole et al. (2001) with y_m = 1/42 to find 4 × 10⁶ M_☉ Mpc⁻³ down to z = 2 and 2.13 × 10⁷ M_☉ Mpc⁻³ down to z = 0.

In our current low-redshift IGM survey, we are interested in the star formation and metal production down to z = 0. We adopt somewhat larger error bars on ρ_* and ρ_Z that reflect systematic uncertainties in measuring the SFR history and computing the metal yield. These include a large (typically factor of five) dust correction to the SFR history applied between 1 < z < 4 (Bouwens et al. 2011). Translating galactic luminosity density into mass density also requires assumptions about the stellar IMF, including its mass range, slope, and low-mass turnover. Similar assumptions affect the metal yield (Madau & Dickinson 2014), which can range from y_m = 0.016 to 0.032 for a Salpeter or Chabrier IMF counting the metals produced by massive stars between 10 and 40 M_☉. Metal contributions from higher-mass stars are cut off by core collapse into black holes. The range increases to y_m = 0.023–0.048 if the black hole cutoff is raised to 60 M_☉. Studies of the dependence of metal production on cutoff (Brown & Woosley 2013) suggest a range 25 M_☉ < M_BH < 60 M_☉. Some of the uncertainty in metal production is offset with the conversion from UV light to mass because the same massive stars produce both UV photons and metals (Madau & Shull 1996).

Adding appropriate uncertainties in the SFR measurements and dust corrections, we adopt an integrated stellar mass density ρ_* ≈ (6 ± 2) × 10⁸ M_☉ Mpc⁻³. In their review, Madau & Dickinson (2014) quote ρ_* = 5.8 × 10⁸ M_☉ Mpc⁻³ from their model SFR history, in good agreement with the value (6.0 ± 1.0) × 10⁸ M_☉ Mpc⁻³ found by Gallazzi et al. (2008). As a final check, we integrated the SFR history (Bouwens et al. 2011) from z = 8 to the present. Over the past 10 Gyr, the SFR density, expressed in units M_☉ yr⁻¹Mpc⁻³, falls dramatically, from $\dot{\rho }_* \approx 0.1$ at t = 10 Gyr (z = 1.76) to $\dot{\rho }_* \approx 0.01$ (z ≈ 0). The SFR density is well-fitted in look-back time (t) over the range 0 < t < 10 Gyr by $\log \dot{\rho }_* = -2.0 + (t / 10 \, {\rm Gyr})$, equivalent to the exponential form:

$$\begin{equation} \dot{\rho }_* = (0.01 \,M_{\odot } {\rm yr}^{-1} {\rm Mpc}^{-3}) \, \exp \, [ 2.3026 \,(t / {\rm 10\, Gyr})] \;. \end{equation} \tag{ 11 }$$

Integrated back to 10 Gyr (0 < z < 1.76), this gives a total density of star formation, ρ_* = (0.01)(10¹⁰yr)(9/2.3026) = 3.9 × 10⁸ M_☉ Mpc⁻³. From t = 10–11 Gyr (1.76 < z < 2.4) the SFR density is near its peak value (0.1 M_☉ yr⁻¹Mpc⁻³) and contributes ∼1 × 10⁸ M_☉ Mpc⁻³. The declining star formation from z = 2.4 to z ≈ 8 (Bouwens et al. 2011) adds a similar metal density, for an integrated total of 6 × 10⁸ M_☉ Mpc⁻³.

Taking into account uncertainties in IMF and metal production, we adopt a metal yield y_m = 0.025 ± 0.010 and predict an integrated metal density ρ_Z = (1.5 ± 0.8) × 10⁷ M_☉ Mpc⁻³. This corresponds to a fractional metal density Ω_Z = (1.1 ± 0.7) × 10⁻⁴ with combined uncertainties in integrated SFR and metal yield. Some of these metals stay locked into stellar remnants, others remain within the galactic interstellar medium, and some are blown into the CGM and IGM. Estimates of the metal fractions in these components range from 60%–70% (Bouché et al. 2007; Peeples et al. 2014). For the CGM and IGM surveys, the primary issues are (1) How many metals were expelled by galactic winds? (2) In what thermal phase and ionization state do they reside? (3) How many metals are undetected owing to their existence in higher ionization states?

A considerable mass of metals resides in the halos of galaxies, in the CGM, and probably in gas expelled to the IGM. We estimate the galactic-halo contribution from the luminosity function of the Millennium Survey (Driver et al. 2005) with their Schechter-function parameters (ϕ* = 0.0177h³Mpc⁻³, α = −1.13). We compute a galactic space density $3.8\times 10^{-3} \, h_{70}^3\, {\rm Mpc}^{-3}$, converting from h to h₇₀ and integrating between 0.5 and 1.5L* (effective bandwidth of 0.63L*). We multiply by an estimated fraction, f_SF ≈ 0.3, of active star-forming galaxies and the mean mass of metals per halo, 2.65 × 10⁷ M_☉, found in O vi absorbers from the COS–Halos study (Tumlinson et al. 2011, 2013) and scaled to total metals using the likely range of oxygen mass fractions (50 ± 10%). We obtain a metal density ρ_Z ≈ 3 × 10⁴ M_☉ Mpc⁻³ corresponding to Ω_Z ≈ 2 × 10⁻⁷. This is only a small fraction of the cosmic metal production, but there are large uncertainties in these estimates. The star-forming fraction f_SF depends on which stellar mass M* one chooses (Ilbert et al. 2013; Baldry et al. 2012), whereas the integrated SFR, with its dust correction, is probably uncertain by a factor of two (Karim et al. 2011; Madau & Dickinson 2014).

Our best estimate is that the low-z IGM contains 10% ± 5% of the cosmic metals, which agrees with estimates for the metal abundance in various thermal phases of the IGM. For example, we can combine the mean IGM metallicity, Z_IGM, to the solar metallicity, Z_☉ ≈ 0.0153, by mass (Caffau et al. 2011) with the cosmological baryon density, Ω_b ≈ 0.0461, measured by microwave background experiments (Hinshaw et al. 2013). Our recent baryon census (Shull et al. 2012) found that the low-z Lyα forest contains 28 ± 11% of the baryons, with the shock-heated WHIM traced by O vi and broad Lyα absorbers containing 25% ± 8%. The expected metal densities in the Lyα forest and O vi-traced WHIM would then be

$$\begin{eqnarray} \Omega _{Z}^{(\rm Lya)} & \approx & 0.28 \, \Omega _b \, Z_{\rm IGM} \approx (2.0 \times 10^{-6}) \left(\frac{Z_{\rm IGM}}{0.01 Z_{\odot }} \right) \nonumber \\ \Omega _{Z}^{(\rm WHIM)} & \approx & 0.25 \, \Omega _b \, Z_{\rm IGM} \approx (1.8 \times 10^{-6}) \left(\frac{Z_{\rm IGM}}{0.01 Z_{\odot }} \right) \;. \quad\quad \end{eqnarray} \tag{ 12 }$$

In our survey, the observed ion states (C iii, C iv, Si iii, and Si iv) with ionization corrections suggested that 4% of the cosmic metals reside in the photoionized IGM, with an additional 6% in hotter gas traced by O vi. The inferred metal densities were (5.4 ± 0.7) × 10⁵ M_☉ Mpc⁻³ or Ω_Z = (4 ± 0.5) × 10⁻⁶ for the Lyα absorbers and (9.1 ± 0.6) × 10⁵ M_☉ Mpc⁻³ or Ω_Z = (6.7 ± 0.5) × 10⁻⁶ for the O vi-traced WHIM. These densities correspond to mean metallicities of 2% solar (Lyα forest) and 4% solar (WHIM), both with substantial uncertainty from the ionization corrections. One expects large variations in the IGM metallicity owing to incomplete metal transport and mixing.

Finally, it is appropriate to ask whether the ions in this survey can be described, in either photoionization or collisional ionization equilibrium, with the alpha-enhanced abundance pattern as discussed above. Most observations and cosmological simulations suggest that the low-z IGM absorbers are multiphase gas, with contributions from photoionization at T ≈ 10⁴ K (for H i, C iii, C iv, Si iii, and Si iv) and hotter, shock-heated gas at T ≈ 10^{5.5 ± 0.5} K containing much of the O vi. The oxygen ionization correction is less certain than those of C and Si; some of the O vi may be photoionized and double-counted in the Lyα forest traced by C and Si ions. Below, we compare ratios of the observed ion states for the elements (O/C), (O/Si), (C/Si), (N/C), and (N/O) to their values assuming relative solar abundances:

$$\begin{eqnarray} ({\rm O/C)} &=& \Omega _{\rm O\,\scriptsize{VI}} / (\Omega _{{\rm C\,\scriptsize{III}}} + \Omega _{\rm C\,\scriptsize{IV}}) \approx 2.24^{+0.80}_{-0.40} \nonumber \\ ({\rm O/Si)} &=& \Omega _{\rm O\,\scriptsize{VI}} / (\Omega _{\rm Si\,\scriptsize{III}} + \Omega _{\rm Si\,\scriptsize{IV}}) \approx 11.0^{+3.5}_{-1.9} \nonumber \\ ({\rm C/Si)} &=& (\Omega _{{\rm C\,\scriptsize{III}}} + \Omega _{\rm C\,\scriptsize{IV}}) / (\Omega _{\rm Si\,\scriptsize{III}} + \Omega _{\rm Si\,\scriptsize{IV}}) \approx 4.9^{+2.2}_{-1.1} \nonumber \\ ({\rm N/C)} &=& \Omega _{\rm N\,\scriptsize{V}} / (\Omega _{{\rm C\,\scriptsize{III}}} + \Omega _{\rm C\,\scriptsize{IV}}) \approx 0.11^{+0.05}_{-0.03} \nonumber \\ ({\rm N/O)} &=& \Omega _{\rm N\,\scriptsize{V}} / \Omega _{\rm O\,\scriptsize{VI}} \approx 0.049^{+0.017}_{-0.011}. \end{eqnarray} \tag{ 13 }$$

For reference, the solar mass-abundance ratios can be derived from the abundances by number (Caffau et al. 2011): ρ_O/ρ_C = (16/12)(n_O/n_C) = 2.43, ρ_O/ρ_Si = (16/28)(n_O/n_Si) = 8.65, ρ_C/ρ_Si = (12/28)(n_C/n_Si) = 4.18, ρ_N/ρ_C = (14/12)(n_N/n_C) = 0.25, and ρ_N/ρ_O = (14/16)(n_N/n_O) = 0.12. From photoionization modeling of the C and Si ions⁵ we only obtain a consistent metallicity if Si/C is enhanced by a factor of three over solar values. The (O/C) and (C/Si) ratios are comparable to the solar abundances (Asplund et al. 2009; Caffau et al. 2011), whereas the (O/Si) ratio is somewhat larger. As often is the case, N is underabundant relative to both C and O, although with just a single measured ion state (N v and O vi) these ratios are not necessarily accurate indicators of total abundances. However, the observed mass–density ratio, $\Omega _{\rm N\,\scriptsize{V}} / \Omega _{\rm O\,\scriptsize{VI}} \approx 0.049$ may indicate that (N/O) ≈ 40% of the solar ratio. From an analysis (Pettini & Cooke 2012) of the nitrogen metallicity dependence on primary and secondary nucleosynthesis, this ratio suggests that the sources of this gas likely had metallicity well above the metal-poor floor at log (N/O) = −2.3.