Cloud-by-cloud, multiphase, Bayesian modelling: application to four weak, low-ionization absorbers Free

ABSTRACT

1 INTRODUCTION

The circumgalactic medium (CGM) is the tenuous, multiphase medium in the environment of a galaxy. It plays an important role in steering the evolution of galaxies. The massive reservoir of gas in the CGM seeds the formation of stars which evolve and distribute their energy and content back into the galaxy. CGM gas of galaxies can be probed in intricate detail by using metal absorption lines (e.g. Bergeron 1986; Bergeron & Boissé 1991; Lanzetta & Bowen 1992; Steidel & Sargent 1992; Churchill, Steidel & Vogt 1996; Churchill et al. 2000, 2020; Adelberger et al. 2005; Kacprzak et al. 2008, 2015, 2019; Chen & Mulchaey 2009; Steidel et al. 2010; Nielsen et al. 2013a; Nielsen, Churchill & Kacprzak 2013b; Stocke et al. 2013; Werk et al. 2013; Bordoloi et al. 2014; Turner et al. 2014; Johnson, Chen & Mulchaey 2015; Richter et al. 2016; Keeney et al. 2017; Muzahid et al. 2018) observed in the spectra of background quasars. Absorption-line spectroscopic studies provide information about the metallicities, densities, temperatures, and kinematic structure of various parcels of gas along the lines of sight. These studies are important because they potentially allow us to learn about the processes that supply inflowing gas to the galaxy, enrich the surroundings with metal-rich outflows, minor and major mergers, and send enriched gas back to the galaxy as recycled accretion.

In this paper, we present a new Bayesian method for extracting the physical properties of the multiphase gaseous medium probed by quasar absorption-line systems. To demonstrate the method, we apply it to four, well-studied, weak, low ionization, systems, also known as weak Mg ii absorbers (Narayanan et al. 2005). These systems were chosen because they are relatively simple in the number of low-ionization components, but still have multiphase structure, and also because the origins of these tiny pockets of high metallicity, far from galaxy centres, are of particular interest.

Weak Mg ii-absorbers are defined by rest-frame equivalent width |$W_r^{2796}\lt $|0.3 Å. Unlike strong Mg ii absorbers, which are typically found within ∼60 kpc of a luminous galaxy (Nielsen et al. 2013b, 2018), the weak Mg ii absorbers are found to be associated with lower neutral hydrogen column densities, and are at larger impact parameters within the circumgalactic environment, typically >40 kpc (Nielsen et al. 2013b, 2018). Churchill et al. (1999) conducted the first systematic survey of weak Mg ii absorbers in the redshift range 0.4 < |$z$| < 1.4 using HIRES/Keck spectra, and found that the number of weak absorbers per unit redshift of |${\rm d}\mathcal {N}/{\rm d}z\approx 1.74\pm 0.10$| is ≈four times higher than that of the Lyman limit systems (LLSs) which have neutral hydrogen column density |$N({H \rm {\small {I}}})\gt 10^{17.2}$| cm⁻², indicating an origin of the weak absorbers in sub-LLSs (Churchill et al. 2000). A tantalizing aspect of the weak Mg ii-absorbers is that, generally, their low-ionization phases exhibit near-solar to supersolar metallicities (Rigby, Charlton & Churchill 2002; Lynch & Charlton 2007; Misawa, Charlton & Narayanan 2008; Narayanan et al. 2008) in spite of the fact that luminous galaxies are typically 50−200 kpc away. Detailed photoionization models of the intermediate redshift, weak Mg ii-absorbers show that they often have two phases, a high-density region/s that is 1–300 pc thick and produces narrow (a few km s⁻¹) low-ionization lines, and kiloparsec-scale, lower density region/s that produces broader, high-ionization lines (Charlton et al. 2003; Narayanan et al. 2007). By comparing the relative number of Mg ii and C iv absorbers, Milutinović et al. (2006) concluded that the low-ionization absorption must occur in flattened or filamentary structures that occupy more than half the solid angle subtended by structures that produce only C iv absorption.

Studies of weak absorbers at low-|$z$| offer the advantage of the ease of detection of host galaxies. At low redshift, 0 < |$z$| < 0.3, Narayanan et al. (2005) measured |${\rm d}\mathcal {N}/{\rm d}z = 1.00\pm 0.20$| for weak Mg ii absorbers (with |$W_r^{2796}\gt 0.02$| Å) using Si ii and C ii as proxies in HST/COS spectra. This is smaller than expected based on the evolution expected for the intermediate redshift population, given the decreasing extragalactic background radiation (EBR). This is because the low redshift population should consist both of 1–300 pc absorbers that gave rise to Mg ii absorption at intermediate redshift, and larger clouds that gave rise only to higher ionization (C iv) absorption at intermediate redshift. Understanding which of these types of absorbers dominate the population at low redshift is important to understanding the processes that produce these mysterious, high metallicity objects abundant in the CGM.

More generally, both observational and theoretical studies (e.g. Stinson et al. 2012; Ford et al. 2013; Shen et al. 2013; Suresh et al. 2017) of absorbers reveal the existence of cool (10⁴ K) and warm-hot (10⁵–10⁶ K) phases in the CGM, often all detected along the same sightline to the background quasar. Different ionization states of material trace different phases of gas, which have different densities and temperatures. Cooler, higher density gas is traced by lower ionization species (e.g. Mg ii, Si ii) and shows structure on smaller scales compared to the warmer and/or lower density phase (e.g. C iv or O vi). Length scales of the lower ionization clouds range from ∼1 pc (McCourt et al. 2012; Liang & Remming 2020) to a few kpc. As mentioned above, strong Mg ii absorption is detected along most sightlines within an impact parameter of 50 kpc from a galaxy (Nielsen et al. 2013a), while weaker Mg ii absorption is found at a median impact parameter of 166 kpc (Muzahid et al. 2018). C iv is often seen out to 100 kpc (Chen, Lanzetta & Webb 2001; Bordoloi et al. 2014), while O vi is seen out to at least 150 kpc (Prochaska et al. 2011; Tumlinson et al. 2011; Stocke et al. 2013; Liang & Chen 2014; Pointon et al. 2019) of star-forming galaxies, but not around quiescent galaxies. Gas traced by H i absorption is seen well beyond (Liang & Chen 2014; Borthakur et al. 2015).

Interpretation of the rich absorption-line data is aided by the identification of galaxies near the quasar sightlines. It is expected that the orientations of the galaxies will correlate with absorption properties (Bordoloi et al. 2011; Bouché et al. 2012; Kacprzak, Churchill & Nielsen 2012; Kacprzak et al. 2015; Nielsen et al. 2015). In the simplest view, galactic winds due to episodes of star formation are expected to produce high metallicities in the outflowing gas, and should be seen primarily along the minor axis (Muzahid et al. 2015; Nielsen et al. 2015; Pointon et al. 2019; Schroetter et al. 2019; Peroux et al. 2020). Inflowing pristine gas from the intergalactic medium would be expected to flow in along the major axis. Another important observational result is a bimodality in the metallicity of partial LLSs, with the high metallicity peak at log Z = −0.4 and the low-metallicity peak at log Z = −1.7 (Lehner et al. 2013). It has been hypothesized that this bimodality could be due to the contrast between outflowing and infalling material.

A coherent and logical picture is beginning to emerge from the data (Tumlinson, Peeples & Werk 2017), however, there are some significant problems plaguing interpretations, and the root cause of these problems could be the methods used to derive the properties of the gas from the absorption profiles, particularly the metallicities. Often the total column density (integrating over all components at all velocities) of a given metal-line transition is compared to the total column density of hydrogen, in the context of photoionization models, to derive the metallicity. This overlooks the importance of phase structure, with more than one phase contributing to absorption at a single velocity, i.e. some transitions could have contributions from two different phases which can lead to an inaccurate estimate of ionization parameter, and thus a systematic error in deriving a single metallicity value. In other words, the average parameters inferred for a system may ‘wash out’ contributions from regions of gas that have metallicities and densities that differ significantly from the means, and the possibility of conditions that significantly change with velocity because of changes in physical conditions along the line of sight. Simulations (Churchill et al. 2015; Peeples et al. 2019) indicate absorption arises in lots of places along the sightline, motivating why multiple metallicities are expected.

In a recent study, Zahedy et al. (2019) have carried out a systematic analysis of 16 intermediate-redshift (⁠|$z$| = 0.21–0.55) luminous red galaxies, finding metal-poor absorbing components with < one-tenth solar metallicity in half of the LRG haloes in tandem with solar and supersolar metallicity gas in the same halo, suggestive of poor chemical mixing and complex multiphase structure in these haloes. This highlights the importance of resolving multiple components of an absorption system using high-resolution absorption spectra, which otherwise is missed by ionization studies that make use of only the integrated H i and metal column densities along individual sightlines.

This work improves the efficiency of component by component modelling that has been successful in recovering the physical conditions for various individual absorbers (e.g. Churchill & Charlton 1999; Charlton et al. 2000, 2003; Ding et al. 2003a, 2003b; Zonak et al. 2004; Ding, Charlton & Churchill 2005; Masiero et al. 2005; Lynch & Charlton 2007; Misawa et al. 2008; Jones et al. 2010; Lacki & Charlton 2010; Muzahid et al. 2015; Richter et al. 2018; Rosenwasser et al. 2018). Rather than averaging over components and phases, it is possible to determine how much of the H i is associated with these different phases in order to derive separate metallicities for various clouds. Resolving the individual clouds allows us to break the degeneracy for components on the flat part of the Lyα curve of growth, even with coverage of just saturated H i lines, and derive metallicity constraints for different parcels of gas along the line of sight. It is important to do so because different processes, e.g. outflows (Bouché et al. 2012; Bordoloi et al. 2014; Rubin et al. 2014; Schroetter et al. 2016), pristine accretion (Martin et al. 2012; Rubin et al. 2012; Danovich et al. 2015), recycled accretion (Ford et al. 2014), minor and major mergers (Martin et al. 2012; Anglés-Alcázar et al. 2017), are surely contributing to the same system, and it is expected that conditions will vary significantly along a line of sight which can span hundreds of kpc spatially (Churchill et al. 2015; Peeples et al. 2019). This will lead to a more meaningful comparison to galaxy properties. For example, Pointon et al. (2019) did not find a difference between the metallicities of absorbers found within an impact parameter of 200 kpc along the major and the minor axes of isolated galaxies. Based on cosmological hydrodynamic simulations, a larger metallicity is expected along the minor axis due to outflows and a lower metallicity along the major axis due to inflows (Peroux et al. 2020). However, an observational trend could exist, for example, for the minor axis to have some, but not all, high metallicity components, or for the minor axis to have one or more low metallicity components. Such results would be ‘washed out’ by deriving an average metallicity for all gas along a line of sight, which clearly often has multiple complex origins. For some data sets/projects, the new analysis could be transformative, however, to make it feasible to use for large statistical studies it is important that the analysis is semi-automated and robust.

In this paper, we describe a new method to derive the physical properties of quasar absorption-line systems using the photoionization code cloudy (ver 17.01; Ferland et al. 2017), Bayesian methods, and parallel processing to efficiently obtain results. Though the code requires some human intervention to choose transitions that define the phase structure, it is mostly automated, and provides uncertainties on parameters in the context of the assumed structure. The paper is organized as follows: In Section 2, we describe the spectral observations that are analysed in this work; in Section 3, we describe the methodology used to determine the physical conditions of an absorber; in Section 4, we present the results and discuss our findings, comparing to previous work, applying tests, and discussing possible limitations. We conclude in Section 5 by discussing the limitations and potential of our cloud-by-cloud, multiphase, Bayesian modelling (CMBM) method. Throughout this work, we assume a cosmology with |$H_{0}\, =\, 70$| km s⁻¹ Mpc⁻¹, |$\Omega _{\rm M}\, =\, 0.3$|⁠, and |$\Omega _{\Lambda }\, =\, 0.7.$| Abundances of heavy elements are given in the notation |$\rm [X/Y] = \log (X/Y) - \log (X/Y)_{\odot }$| with solar relative abundances taken from Grevesse et al. (2010). All the distances given are in physical units. All the logarithmic values are presented in base-10.

2 OBSERVATIONS

We apply our methods to four low redshift absorption-line systems from the COS-Weak sample (Muzahid et al. 2018). The background quasars in this study have UV spectra from the Cosmic Origins Spectrograph (COS) instrument on the Hubble Space Telescope (HST) and optical spectra from High Resolution Echelle Spectrometer (HIRES) installed on the Keck telescope or Ultraviolet and Visual Echelle Spectrograph (UVES) installed on the Very Large Telescope (VLT). The four absorption systems that we consider have spectroscopic redshifts |$z$| < 0.30. These weak, low-ionization systems are relatively simple ones compared to some stronger low-ionization absorbers, but they are expected to have multiple gas phases and provide good test cases for our methodology. Table 1 presents the details of the observations of the four systems studied in this work.

2.1 COS, FUSE, and STIS spectra

The UV spectra in the COS-Weak sample are taken from the archive of HST/COS observations using the G130M and G160M gratings spanning observed wavelength ranges 1135–1457 and 1399-1794 Å, respectively. The spectra have an average resolving power of R ≈ 20 000 and cover a range of ions including the H i Lyman series, C ii, C iii, C iv, N v, O vi, Si ii, Si iii, and Si iv. The HST/COS spectra were obtained from the archive already reduced using the calcos pipeline software (Massa et al. 2013), with individual exposures aligned and co-added, weighted by their exposure times. The spectra are rebinned to the Nyquist sampling rate. FUSE spectra for three absorbers in our sample were available. The observations were obtained already processed with the calfuse pipeline (ver. 3.2.3). Zero-point offset correction was carried out on this pre-processed data using the approach described in Wakker (2006). The spectra have an average resolving power of R ≈ 15 000. STIS spectra for three absorbers in our sample were available. We make use of COS data when STIS and COS both have coverage of a transition of interest because the COS spectra have significantly higher signal-to-noise (S/N), ratio compared to the STIS data. When a transition is not covered by COS, we make use of STIS observations.

We perform continuum normalization of the data by fitting a cubic spline to the spectrum. We estimated the uncertainties in the continuum fits using ‘flux randomization’ Monte Carlo simulations (e.g. Peterson et al. 1998), varying the flux in each pixel of the spectrum by a random Gaussian deviate based on the spectral uncertainty. The pixel-error weighted average and standard deviation of 1000 iterations were adopted as the flux and uncertainty of the continuum fit, respectively.

2.2 Ground-based optical quasar spectra

When available, we use higher resolution optical spectra to complement the UV spectra because transitions including Mg i, Mg ii, Fe ii, and Ca ii are especially useful in revealing the presence of multiple components for absorption systems at redshifts of |$z$|_abs ≳ 0.1. The spectra have an average resolving power of R ≈ 45 000. The HIRES spectra were reduced using the makee (Mauna Kea Echelle Extraction) package. The UVES spectra were reduced using the European Southern Observatory (ESO) pipeline (Dekker et al. 2000) and the UVES Post-Pipeline Echelle Reduction (UVES popler) code (Murphy 2016; Murphy et al. 2019). The program numbers and dates of these observations are also listed in Table 1.

3 METHODOLOGY

We model the observed absorption system using the photoionization code cloudy, and synthesize the expected absorption profiles and compare them to the observed profiles in order to infer the physical conditions of the absorbing gas. What makes this method different from other researchers’ methods is that we model the entire absorption system across all transitions by splitting it into its constituent clouds.

We begin by choosing a ‘trustworthy’ low-ionization species (the ‘optimized ion’) for a Voigt profile (VP) fit, meaning one with lines that are unsaturated, and observed at a high resolution, and with a large S/N. The starting point is a fit of VPs to all transitions within this single ionization species (each parcel of gas described by a single VP will be called a ‘cloud’). For this optimized transition, we determine the parameters of column density (N), Doppler parameter (b), and redshift (⁠|$z$|⁠) for each cloud using a Monte Carlo technique employed using PyMultiNest (Buchner et al. 2014). PyMultiNest is a python implementation of MultiNest (Feroz, Hobson & Bridges 2009), which is a robust nested sampling method that draws a new, uniformly random point with higher likelihood through an ellipsoidal rejection sampling scheme (Shaw, Bridges & Hobson 2007). It is efficient at sampling from a multimodal posterior distribution. We model VPs using an analytic approximation (Tepper-García 2006) for the Voigt–Hjerting function as implemented in the VoigtFit package (Krogager 2018). We obtain VP fits to the absorption profiles for the optimized ion, allowing for more than one component. We fit the profiles of the optimized ion with a VP model corresponding to the highest log-evidence and the least model complexity. After we determine the observed values of log N, b, and |$z$| for each cloud, we use the parameters of that VP fit for the optimized ion as a starting point for models in cloudy.

cloudy has many parameters that can be adjusted. The two most important parameters are metallicity relative to solar abundance (Z) and ionization parameter (U), defined by U = n_γ/n_H, where n_γ is the volume density of ionizing photons. Ionization parameter serves as a direct proxy for the hydrogen number density, but may be more intuitive when thinking of contributions of different clouds to the observed ionization states. We adopt the Haardt & Madau (2012, hereafter HM12) model for the EBR to determine n_γ at the given redshift. The systematic effects arising from the choice of the EBR are discussed in Keeney et al. (2017). We adopt the HM12 model as it best reproduces the low-redshift H i column density distribution for |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}] \gt $| 14 (Shull et al. 2015). We assume a solar abundance pattern (Grevesse et al. 2010) for our modelling. Detailed constraints on abundance pattern are not possible without higher S/N coverage of a larger number of transitions.

It is a time-consuming endeavor to construct cloudy models component-by-component and phase-by-phase for individual absorbers because of the limitations imposed by serial computing. However, it is clear that doing so will lead to a significant gain in our ability to correctly infer the presence of metallicity structure in the CGM. To increase efficiencies, we have developed robust python-based codes that employ distributed parallel processing on the CyberLAMP infrastructure¹ to obtain models in a shorter time.

The cloudy photoionization equilibrium (PIE) models are generated for the identified optimized ion tracing the low-ionization gas phase for a broad range of values over the log Z × log U grid in the range: log Z ∈ [−3.0,1.5] and log U ∈ [−6.0, 0.0], obtained with a step-size of 0.1. The cloudy models are then linearly interpolated on to the log Z × log U grid with a spacing of 0.01 dex. The interpolating function is generated by triangulating the input data with Qhull (Barber, Dobkin & Huhdanpaa 1996), and on each triangle performing linear barycentric interpolation. The interpolation error is of the order ∼O(h²), h being 0.1, and introduces only small errors ∼0.01 dex in log Z and log U. The total column density of hydrogen, N(H), is adjusted for each model until the column density of the optimized ion is matched for each point on the log Z × log U grid. We allow for an uncertainty of 0.05 dex in the column density matching when generating the cloudy models. The uncertainties arising due to the interpolation error and the error in column density are not accounted for in our error estimation, but are usually negligible in comparison to other sources of error. We quote 2σ uncertainties in our results for the best model parameter values, which account only for the photon noise in the comparison between the synthesized model profiles and the observed spectra.

Typically, all of the observed line transitions cannot be reproduced with one phase of gas. It is often the case that a model that fits the low-ionization transitions (e.g. Mg ii, Fe ii) cannot produce the observed amount of high-ionization absorption (e.g. C iv, O vi), or adequately match the profiles of the full Lyman series. In such cases, we will use more than one optimized ion. The other optimized ions represent the different phases of gas, with distinct regions having different densities along the line of sight. For example, we would typically optimize on Mg ii for the low-ionization gas, and on C iv for high-ionization gas. In some intervening absorbers, O vi, because of its comparatively high ionization potential (∼114 eV), arises in gas with T > 10⁵ K where the ionization is governed by collisions between energetic free electrons and metal ions (Pradeep et al. 2020). We model the gas phase traced by O vi to be under collisional ionization equilibrium (CIE). For such collisional ionization models, the cloudy grids are run over log Z × log T space: log Z ∈ [−3.0,1.5] and log [T/K] ∈ [5.0, 5.8]. Similar to the PIE modelling, the CIE models are obtained by varying the total column density of hydrogen, N(H), until the column density of O vi is matched for each point on the log Z × log T grid. In Fig. 1, we show for a metallicity of log Z = −1.0 and different gas densities that cloudy can produce accurate results when modelling gas in CIE. The column density ratios of C iv/O vi agree well with the CIE model (Gnat & Sternberg 2007) for temperatures in the range of 10⁵−10^5.8 K, and are independent of the hydrogen number densities. We contrast the modelling results obtained with cloudy ver6.02d and ver17.01 to show that the apparent discrepancy with the Gnat & Sternberg (2007) model arises because of the evolving atomic data base (Chatzikos et al. 2015). The cloudy models are generated for an assumed value of log n_H = −3.9, based on the Milky Way halo density at 50 kpc (Kaaret et al. 2020).

Figure 1.

Comparison of CIE model (black; Gnat & Sternberg (2007) and collisional ionization models obtained with cloudy ver6.02d (left-hand panel) and ver17.01 (right-hand panel) for a metallicity of log Z = −1 and different hydrogen densities (log n(H)). The disagreement of the CIE model with collisional ionization models obtained with cloudy ver17.01 for log T > 5.5 is attributed to the evolving atomic data base (Chatzikos et al. 2015). We use cloudy ver17.01 and adopt log [n(H)/cm⁻³] = −3.9 for collisional ionization modelling.

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To summarize, we start with the assumption that a single, low-ionization phase describes an absorption system. If such a simple, one-phase model fails to account for the observed column densities in all the transitions, we incorporate additional phases until the synthesized spectra from cloudy best match the observed spectra for all transitions. Generally, we find that a single phase is insufficient to explain the observed abundances of all the transitions even when the transitions coincide in velocity space. If the synthetic spectra fit the data for all transitions, then it is plausible that the physical conditions in the cloudy model match those in the gas that produces the absorption. This allows us to determine precise allowed ranges of metallicity, density, and temperature for each individual cloud that create the observed transition lines. A summary of the methodology is given in the form of a flowchart in Fig. 2.

Figure 2.

A flowchart showing the workflow involved in obtaining the models that best describe the conditions present in an absorption system.

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4 RESULTS

4.1 Application to four quasar absorption-line systems

We discuss the findings from the application of our methodology to four, weak low-ionization absorption-line systems, and compare our results to those obtained from earlier studies adopting the HM12 model for the EBR.

4.2 The z = 0.077 76 absorber towards the quasar PHL1811

A system plot of the |$z$| = 0.077 76 absorber, with the constraining transitions shown, is given in Fig. 3. This system has weak absorption detected in Si ii and C ii. Though Mg ii is not covered in the STIS/G230MB spectrum, it is expected to be weak as well. The Fe ii, covered in the COS/G160M and STIS/G230MB spectra, is not detected. The intermediate-ionization transitions, Si iii, and C iii, are detected, however, Si iv and C iv are not detected. The O vi is detected in the λ1031 transition, but not in the λ1037 transition. O vi λ1031 is contaminated at −35 km s⁻¹ by Galactic Fe ii λ1112. We account for the contribution of Fe ii λ1112 using other Galactic Fe ii lines from COS data, and display the corrected O vi λ1031 profile. The Lyα transition was covered by HST/COS observations, however, all constraining higher order Lyman series lines plotted (down to H i λ930) come from FUSE observations. The lines H i λ937, and H i λ930 are affected by contamination due to the Galactic molecular hydrogen lines. H i λ937 is affected by H₂ W 8 − 0 Q(2)λ1010.94 at 59 km s⁻¹, and H i λ930 by H₂ L 8 − 0 P(1)λ1003 at 26 km s⁻¹. We divide out the contribution due to these blends using several of the Galactic hydrogen molecular lines present in the FUSE observations. The lines H₂ L 6 − 0 R(0)λ 1024.37 and H₂ L 6 − 1 R(1)λ 1024.99 affect the continuum placement of H i λ949 on its redward side. We omit H i λ949 as a constraining ion. The H i λ972 is blended at 10 km s⁻¹ with Galactic Ar i λ1048; we divide out its contribution to the H i λ972 profile using the Ar i λ1066 line. The Lyβ is strongly contaminated by Galactic Si iii λ1205 (Savage et al. 2014), and though the contamination is at the centre of the saturated profile, Lyβ is still not used as one of the constraining transitions.

Figure 3.

cloudy models for the |$z$| = 0.077 76 absorber towards the quasar PHL1811 obtained using the MLE values. The spectral data are shown in grey with 1σ error. The instruments used for observation in different regions of the spectrum are indicated in the panels. The centroids of absorption components as determined from the VP fits to optimized ions are indicated by the vertical tick marks on top of each panel. The low-ionization photoionized phase is traced by three clouds – the blueward cloud optimized on C iii (shown as a blue curve), and the blended redward clouds optimized on Si iii (shown as a red curve). The high ionization collisionally ionized phase (shown by a green curve) is obtained by optimizing on O vi. The superposition of these three models is shown by the black dashed curve. The models are obtained using the maximum likelihood parameter values. The region shaded in grey shows the pixels that were not used in the evaluation of the log likelihood. The lines H i λ930, H i λ937, H i λ972, and O vi λ1031 are corrected for blending as described in Section 4.2 and earmarked with an asterisk.

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We begin by optimizing on the column density of C iii for the blueward cloud and Si iii for the redward cloud. We find that the VP fit to C iii yields a large uncertainty on its b-parameter (⁠|$3.2^{+3.7}_{-1.0}$| km s⁻¹). The best-fitting cloudy model for the C iii cloud corresponds to log Z = −1.36, log U = −3.00, and log [T/K] = 4.87. However, this temperature is too high to be consistent with the best VP fit b-parameter for C iii. We therefore tried a 2σ higher b-parameter (b(C iii) = 7.00 km s⁻¹) for the C iii cloud and found the temperature (log [T/K] = 4.42) to be considerably lower because of the resulting higher metallicity (log Z = 0.85). We find a similar high value of metallicity for a b-parameter only 1σ higher than the best-fitting value (b(C iii) = 5.00 km s⁻¹). In Table 2, we present the model with b(C iii) = 5.00 km s⁻¹.

For the redward Si iii cloud, we find that a single component fit results in overproduction of Lyβ and underproduction of C iii on the redward side of the profiles. An adjustment of the b of the optimized Si iii cannot resolve both of these discrepancies. A two-component fit is thus preferred for Si iii, and the column densities and Doppler parameters for the optimized Si iii are listed in Table 2. Again, we found that the best VP fit b-parameters for the two Si iii components resulted in a model with a temperature too high to be self-consistent. Therefore, we adopt 1σ higher values for the b-parameters of the two redward components in Si iii. The posterior distributions for |$z$|⁠, b and log N for the C iii and two Si iii components are presented in Figs A1 and A2. For the redward cloud, the lower ionization Si ii and C ii transitions might have been used as optimized transitions, however, the VP fits would be quite uncertain due to their noisier profiles. Also, C iii is affected by line saturation, so Si iii is the best choice for the optimized transition for the redward cloud. It is clear that the ionization parameters of the three low-ionization clouds must be relatively low, since Si iv and C iv are not detected, such that O vi could not be produced in the same phase with the C iii and Si iii. We therefore determine that this absorber is best explained by invoking the presence of a high-ionization phase giving rise to the O vi absorption. The VP fit posterior distribution for O vi is presented in Fig. A3.

In Table 2, we present the posterior results for the low-ionization phase, which are summarized in Figs A4–A6 for the C iii component and the two Si iii components, respectively. Fig. 3 shows cloudy models, using the maximum-likelihood estimate (MLE) values superimposed on the data. These plots show that the metallicities of the two redward components (red curve) are constrained to be |$\log Z = -0.32^{+0.12}_{-0.12}$| and |$\log Z = -0.85^{+0.08}_{-0.07}$| in order to fit the Lyα profile, and several of the Lyman series transitions. The metallicity of the weaker, blueward C iii component is constrained to be |$\log Z = 0.85^{+0.11}_{-0.18}$|⁠, and it fits the blue wing of Lyα in combination with the middle Si iii cloud and the O vi cloud.

Table 2 summarizes the constraints placed on the metallicities, ionization parameters, number density of hydrogen, |$N({H \rm {\small {I}}})$| values, thickness, and temperatures for the two low-ionization clouds. The blueward cloud has a thickness of ∼6 pc, and the two redward clouds have thicknesses of ∼35 pc and ∼0.5 kpc, respectively. The three clouds fall far short of producing a partial Lyman limit break (combined |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}]\sim 15.75$|⁠).

This low-ionization phase does not produce O vi absorption. While it is possible that the absorption is a broad Lyα component unrelated to the detected broad O vi absorption, a collisionally ionized phase, such as a Coronal Broad Lyman-alpha Absorber (CBLA; Richter 2020), optimized on O vi, is also consistent with the data. This CBLA would have a temperature of log [T/K] = 5.38, so as not to produce detectable C iv absorption, and to fit the wings of the Lyα line. For |$b({O \rm {\small {VI}}}) \sim 47$| km s⁻¹, the wings of Lyα are fit for a metallicity of |$\log Z=-1.16^{+0.34}_{-0.33}$|⁠. The posterior results for this high-ionization phase are summarized in Fig. A7.

We also investigate the alternative of a photoionized phase in O vi. A photoionized model with log U = −1.5 and a supersolar metallicity could fit the O vi profile, and also well explains the observed abundances of other transitions; however, the blueward wing of Lyα is unexplained as shown in Fig. 4. A model with lower ionization parameter could fit the wing of Lyα but would overproduce the C iv. Hence, we favour a collisional ionization model for the O vi phase.

Figure 4.

cloudy photoionization models for some chosen transitions for the |$z$| = 0.077 76 absorber towards PHL1811. Symbols, labels, and masked pixels are the same as shown in Fig. 3 but the high phase producing O vi is modelled as a photoionized phase. In such a model the blueward wing of Lyα is unexplained.

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4.2.1 Comparison to previous models

Our modelling reveals three components seen in the low-ionization transitions, and required by the observed profiles. The responsible photoionized clouds are found to differ from each other in metallicity, from approximately one-tenth solar metallicity to highly supersolar. There is also a separate, collisionally ionized phase (log [T/K] = 5.38) that produces broad O vi and H i absorption. The total H i column density from our model is |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}]=15.75$|⁠.

Lacki & Charlton (2010) conducted multiphase modelling for this system, using a wider grid of log U and log Z, and the HM01 (Haardt & Madau 2001) EBR. Also, C iv appears to be detected in the HST/STIS spectrum that they used, which we do not detect in our HST/COS coverage. For the blueward cloud in C iii, they determine log Z = −1.0 and log U = −1.0 producing C iv and O vi. In contrast to their metallicity, we find |$\log Z = 0.85^{+0.11}_{-0.18}$| with a lower ionization parameter of |$\log U = -3.11^{+0.08}_{-0.06}$| such that C iv is not produced. We find that a low metallicity, log Z ∼ −1.0, with our lower ionization parameter, would yield a high-temperature phase that violates equation 3.

For the redward low-ionization absorption, they find a single low metallicity value of log Z = −1.0 and log U = −3.0. In agreement with their result, we determine two separate low metallicities of |$\log Z = -0.32^{+0.12}_{-0.12}$| and |$-0.85^{+0.08}_{-0.07}$| with ionization parameters of |$\log U = -3.68^{+0.07}_{-0.06}$| and |$-3.04^{+0.03}_{-0.02}$|⁠, respectively.

Other recent models for this system find average values using a single, low-ionization component. Keeney et al. (2017) found log Z = −0.15 and log U = −3.05, using |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}]=15.4$|⁠, and using the same HM12 as we have. Muzahid et al. (2018) measured |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}]=16.0$| and, using the KS15 (Khaire & Srianand 2015) EBR, found log Z = −0.4 and log U = −3.6. In our models, the centred Si iii cloud has a similar metallicity, and produces nearly all of the absorption in higher order Lyman series lines because of its larger H i column density. The redward Si iii cloud is, however, essential to producing the Lyα absorption in the base of the profile, and is thus required to have a lower metallicity. Our conclusions regarding the presence and properties of a collisionally ionized O vi phase contributing to this system are consistent with those of Savage et al. (2014) who determine |$\log [T/K] = 5.49^{+0.14}_{-0.19}$| and [O/H] = |$-1.93^{+1.32}_{-0.11}$|⁠.

4.2.2 Caveats and tests

Though we do not have wavelength coverage of the key Mg ii transition in any of our spectra for this quasar, we do show the predicted profiles from our favored model in Fig. 3. The Mg ii would most likely classify as a single component, weak Mg ii absorber with W_r = 28 mÅ. Only the blueward Si iii cloud produces detectable Mg ii, though we do see a slight contribution from the C iii cloud.

The four systems we have chosen to model in this paper, demonstrating our methodology, have richer data sets than the typical low |$z$| weak, low-ionization absorber (Muzahid et al. 2018). Most importantly, in many cases, there is no FUSE coverage of the Lyman series lines. To see what the effect would be on constraints, we have run our models considering only the Lyα line. Table 2 lists the constraints from this experiment. We find the values for log Z and log U to be consistent, for all four clouds, with our model that makes use of all the Lyman series coverage. There is, however, a large uncertainty in the values for the ‘Lyα only’ model, particularly for the blueward C iii cloud. The ‘Lyα only’ model is shown in Fig. 5. The ability to constrain parameters using only Lyα is important given that many of the systems in the literature only have one to two H i lines, and thus the robustness of the method to limited H i data is very important.

Figure 5.

cloudy models for Lyman lines for the |$z$| = 0.077 76 absorber showing that a ‘Lyα-only’ model very slightly overpredicts the observed higher order Lyman series lines. Symbols, labels, and masked pixels are the same as in Fig. 3. However, the parameters for this model are consistent with the parameters obtained with the full model.

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As another test of our methodology, we synthesized artificial spectra modelled after this |$z$| = 0.07776 absorber. We add Gaussian noise to the modelled flux of the synthetic spectra, and flux uncertainties are based on the average S/N observed in that part of the spectrum. We included one blueward C iii cloud, two blended Si iii clouds, and a warm/hot O vi cloud, as we found for this absorber. For our experiment, we adopted four different sets of metallicity, log Z, and ionization parameter, log U values, including a combination similar to the real system shown in Fig. 6. These parameter choices for our simulations are listed in Table 3 along with the recovered values. In two cases, we altered the metallicities in the synthetic spectra, and in one other case, we adjusted the ionization parameter of the blueward C iii and the blended redward Si iii clouds while keeping the parameters of O vi cloud fixed at the values of the best-fitting model. In all cases, we were able to recover the correct model parameters, with the errors, that we specified for the synthetic spectra. This provides confidence that our CMBM approach is recovering accurate results from the observed spectra.

Figure 6.

cloudy models overlaid on a mock spectrum modelled after the |$z$| = 0.077 76 absorber towards PHL1811. Symbols, labels, and curves are the same as in Fig. 3. We find that our method recovers the parameters with which the spectrum was generated as described in Section 4.2.2. The 1σ errors on the spectral data correspond to an average error observed in that part of the spectrum.

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The final consideration for this absorber is the relatively large uncertainties in the VP fit parameters for the blended optimized Si iii clouds and for the C iii cloud. The best VP fit for the Si iii yielded b = 2.6 km s⁻¹ for the blueward component and b = 3.7 km s⁻¹ for the redward component, and for C iii we found b = 3.2 km s⁻¹, as noted in Table 2. The photoionization models based on these best VP fit parameters for the blueward C iii and the two redward Si iii produce high temperatures that are not self-consistent with equation 3. We resolved the problem by adopting higher b values within the limits of 2σ uncertainty. If we did adopt the best VP fit b parameters, cloudy models would find consistent values of log Z and log U for the Si iii clouds, but would find a drastically lower metallicity (of log Z = −1.36) for the C iii cloud. This indicates that in the absence of higher resolution coverage of an optimized transition, there is some level of systematic uncertainty in the derived model parameters. The possible effects of different b-values of blended components should always be considered.

4.2.3 Galaxy properties and physical interpretation

The closest galaxy to the sightline, at a coincident redshift, is a quiescent, inclination |$i=50{^\circ }$|⁠, L_g = 0.26L* galaxy at an impact parameter of 237 kpc (Keeney et al. 2017). It is unlikely that the galaxy itself would produce significant absorption for impact parameters >200 kpc (Liang & Chen 2014), however, Muzahid et al. (2018) notes that there are seven galaxies within 1 Mpc and 500 km s⁻¹ of the absorber. This suggests a group environment.

Only one of the three low-ionization clouds in this system, the middle one with |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}]=15.7$|⁠, would produce detectable weak Mg ii absorption. With a metallicity of log Z = −0.32, and a size of ∼30 pc, it is consistent with the weak, low-ionization absorber population at intermediate redshift (Rigby et al. 2002; Charlton et al. 2003; Misawa et al. 2008). However, those absorbers often have a lower density, C iv phase aligned in velocity with the Mg ii. The blueward cloud is also very small and has a supersolar metallicity. The redward cloud, however, has a lower metallicity of log Z = −0.85, and a larger line-of-sight thickness of ∼500 pc. This cloud would be consistent with lines of sight through infalling gas in filamentary structures as seen in numerical simulations (Hafen et al. 2019). It is unclear if the three clouds are structurally related, despite their close proximity in velocity space.

Because of the lack of detected C iv, this absorber is similar to the well studied |$z$| = 0.0053 Virgo cluster absorber found toward 3C 273 (Stocke et al. 2004). Though they are not common (Milutinović et al. 2006), there is reason to believe that the lower amplitude EBR will lead to some systems with less prominent C iv absorption (Narayanan et al. 2005). In this absorber, though C iv is not detected, we do see collisionally ionized gas giving rise to O vi absorption, a transition not often covered for the higher redshift systems. A survey of low redshift, weak low-ionization absorbers is needed to see if such warm/hot gas is commonly found, perhaps arising in an intragroup medium, such as it is observed in the Local group (Bouma, Richter & Fechner 2019), or at the interface between cooler clouds and hotter surrounding regions (Oppenheimer et al. 2016; Pointon et al. 2017).

4.3 The z = 0.080 94 absorber towards the quasar PHL1811

Spectral regions covering constraining transitions for the |$z$| = 0.080 94 absorber, from FUSE, HST/COS, HST/STIS, and Keck/HIRES, are shown in Fig. 7. The low-ionization absorption in Si ii and C ii shows two components, with the redward being the strongest. The system might classify as a multiple component weak Mg ii absorber, but the Mg ii transitions were not covered to confirm that expectation. The H i λ1025, H i λ972, H i λ949, and H i λ937 are affected by blending due to the Galactic molecular hydrogen lines. H i λ1025 is contaminated by H₂:L 0 − 0 R(1) λ1108.63 at −32 km s⁻¹, H i λ972 by H₂:L 4 − 0 P(1) λ1051.03 at −78 km s⁻¹ and by H₂:L 4 − 0 R(2)λ1052.49 at 56 km s⁻¹, H i λ949 by H₂:L 6 − 0 R(2)λ1026.53 at −63 km s⁻¹, and H i λ937 by H₂:L 7 − 0 R(1)λ1013.44 at −95 km s⁻¹. We divide out the contribution of these lines by making use of several other Galactic hydrogen molecular lines observed in the FUSE spectrum.

Figure 7.

cloudy models for the |$z$| = 0.080 94 absorber towards the quasar PHL1811 obtained using the MLE values. The spectral data are shown in grey along with the 1σ error. The instruments used for observation in different regions of the spectrum are indicated in the panels. The centroids of absorption components as determined from the VP fits for optimized ions are indicated by the vertical tick marks on top of each line. The absorption system is modelled using four clouds. A low- ionization phase traced by the blueward C iii cloud (shown as blue curve), an intermediate-ionization phase traced by C iv (shown as yellow curve), and two coincident phases – a high-ionization phase traced by C iv (shown as red curve) and a low-ionization phase traced by Si ii (shown as green curve). The superposition of these two models are shown by the black dashed curve. The region shaded in grey shows the pixels that were not used in the evaluation of the log likelihood. The lines H i λ937, H i λ949, H i λ972, and H i λ1025 are corrected for blending as described in Section 4.3 and earmarked with an asterisk.

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This system was previously analyzed by Jenkins et al. (2003, 2005), Richter et al. (2016), and Richter (2020). The strongest low-ionization component is also detected in O i, N ii, Fe ii, and Ca ii. There are three components detected in C iii, and the two redward components in C iv as well. In a noisy part of the FUSE spectrum, O vi provides only an upper limit. Lyman series lines, from Lyα down to H i λ920, provide useful constraints on the metallicities of the three components, with the blueward component clearly separated in the higher order lines. The metallicity of the strongest, redward component is best constrained by the redward side of all the Lyman series profiles. A full Lyman break is observed at this redshift in the FUSE coverage (Jenkins et al. 2003). Table 4 summarizes the constraints placed on the metallicities, ionization parameters, number densities, neutral hydrogen column densities, temperatures, and thickness for the four clouds, we find necessary to explain the multiphase absorption.

Since C iii is saturated for the strongest component, and several Si ii lines were covered, the model is optimized on the measured Si ii column density. This cloud was constrained to have metallicity, log Z = −0.30, and gives rise to the Lyman limit break. It also fits the distinctive ‘wing’ on the redward side of the Lyα profile, and also produces a small amount of absorption consistent with the smaller ‘wing’ on the blueward side. For an ionization parameter of log U = −3.81, the observed O i, Fe ii, and N ii are fully produced, but all the higher ionization transitions are underproduced, calling for a separate, higher ionization phase at this same velocity. The Ca ii was not included as a model constraint because it is often depleted on to dust (Richter et al. 2011), and we do find it to be overproduced by 0.75 dex by the log U = −3.8 model. The large |$N({H \rm {\small {I}}})$| needed to reproduce this relatively strong profile results in a cloud thickness of 1.7 kpc.

To account for the C iv, S iv, C iii, Si ii, N iii, and C ii, coincident with the strongest Si ii component, we included an additional cloud, optimized on the C iv at this velocity. This cloud has the highest ionization parameter of log U = −2.8 among the absorbers present in this system, this cloud can produce the observed absorption in all these transitions. Its metallicity must be relatively high (we obtain log Z = 0.6) in order that it does not affect the fit to the Lyman series lines. The thickness of this cloud is 0.7 kpc.

For the middle component, the optimized transition is C iv, since the C iii is saturated, and detections are weak or absent in the low-ionization transitions. This cloud has an ionization parameter of log U = −3.0. A metallicity of log Z = −2.0 allows this cloud to fill in the Lyman series profiles in between the contributions from the other clouds, which themselves are well constrained from the blueward and redward sides of the profiles. Despite its much lower |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}]$| of 15.5, relative to the strongest cloud, the low metallicity leads to a similar cloud thickness of 63 kpc. This model, however, overpredicts the absorption in N iii, but an abundance pattern variation from solar could resolve this discrepancy.

The third, blueward cloud model is optimized on C iii since it is at most weakly detected in Si ii and C ii. Because C iv is not detected, this cloud has a lower ionization parameter of log U = −3.9. A supersolar metallicity (log Z = 0.2) is required in order that Lyman series lines are not overproduced. Though the |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}] = 15.34$| is similar to that for the middle cloud, the thickness is several orders of magnitude smaller, only 5 parsecs. This contrast in thickness is striking, and perhaps surprising, but it seems to be required by the observed profiles.

In Table 4, we present the posterior results for different phases, which are summarized in Figs B4–B7 for the four clouds.

4.3.1 Comparison to other models

It is apparent from our models that the four clouds needed to explain the low-ionization absorption profiles have significantly different properties from one another, pointing to different physical origins of the gas. The metallicities of these clouds are found to be log Z = −0.3 for the strongest low-ionization component, log Z = 0.6 for the coincident higher ionization component, a very low metallicity of log Z = −2.0 for the middle cloud, and log Z = 0.2 for the weak, blueward component. The redward, strong low-ionization component also contributes the bulk of the H i absorption and produces a Lyman limit break, as well as giving rise to the wings on the Lyα profile. Richter (2020) has modelled the right, broad wing of the Lyα absorption as CBLA that traces the collisionally ionized, coronal gas of the CGM host galaxy, however, we find that the wing is explained by the redward Si ii cloud.

The middle cloud has log U = −3.0, while the redward cloud has log U = −3.80. Another startling difference is perhaps the thicknesses of the clouds, with the lower density, high metallicity cloud that is only 5 pc thick, while the redward spans a few kpc.

Previous models by Keeney et al. (2017), Muzahid et al. (2018), and Wotta et al. (2019), which average the components together infer metallicities and ionization parameters consistent (considering differences in EBR models) with those we obtain for the strongest lower ionization component. However, they miss the richness of information available in the profile about two other regions along the sightline which have vastly different properties and physical origins.

4.3.2 Caveats and tests

For this system, we predict the strength of Mg ii. The equivalent width predicted for Mg ii is W_r(2796) = 243 mÅ, dominated by the redward cloud.

We also conduct a test for this system to determine how much information can be derived using a ‘Lyα only’ model. Table 4 summarizes these constraints for the ‘Lyα only’ model compared to the original one. Even without access to the Lyman series lines, the ionization parameters and metallicities of all but the middle C iv clouds agree well within errors. This disagreement arises due to the fact that the higher order lines provide the information necessary to produce the shape of the profile. The ‘Lyα only’ model is shown in Fig. 8.

Figure 8.

cloudy models for Lyman lines for the |$z$| = 0.080 96 absorber towards PHL1811 showing that a ‘Lyα only’ model predicts well the properties of all but the middle C iv cloud (yellow curve). Symbols, labels, and masked pixels are the same as in Fig. 7.

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Central to our ability to discern accurate model parameters, even from saturated H i lines, is the use of the cloudy model equilibrium temperature in order to determine the thermal/turbulent contributions to the b parameter, and thus to infer |$b({H \rm {\small {I}}})$| for each component. We thus investigated for this system the effect of uncertainties in the temperature given by cloudy, considering values 10 per cent smaller and 10 per cent larger for all four clouds. In order to do this, for each cloudy model we took the output temperature and artificially adjusted it before synthesizing model spectra. When these model spectra, which therefore were produced with different b parameters for non-optimized transitions, were compared to the data, different log Z and log U parameters were found to compensate for the different b values. Results are summarized in Table 5. This table shows that the effects of this assumed uncertainty are quite small. As expected, we find that a lower temperature will lead to a larger thermal contribution and a larger |$b({H \rm {\small {I}}})$|⁠, and thus a slightly smaller inferred metallicity, while a higher temperature will lead to a slightly larger metallicity. Results are overall not very sensitive to the equilibrium cloudy temperatures.

4.3.3 Galaxy properties and physical interpretation

The closest galaxy to the sightline at this redshift is an L_g = 0.56L* early type galaxy at an impact parameter of 35 kpc from the sightline (Keeney et al. 2017). Although the Sloan survey does not show many other galaxies within 1 Mpc and 500 km s⁻¹ of the line of sight (Muzahid et al. 2018), there is one close companion galaxy with L ∼ L* at an impact parameter of 87 kpc (Jenkins et al. 2005), which is possibly interacting with the nearer galaxy.

Our inference of four very different gas clouds points toward there being different processes at work along the sightline. The presence of two nearby galaxies suggests that there could be gas associated with each of the two different galaxies, or with debris that resulted from their interaction. There also could be gas associated with the group of galaxies containing the pair and also possibly dwarf galaxies to these L*/sub-L* galaxies, though no other bright galaxies are present besides the two.

It is very interesting that the smallest of the four clouds is a fairly typical, supersolar, weak, low-ionization absorber. These are typically not associated closely with specific galaxies, however, in this case, there is a galaxy within an impact parameter of 35 kpc. The lowest metallicity cloud (log Z = −2.0) could be gas infalling into the galaxy pair from a more pristine surrounding environment, consistent with expected values for IGM accretion metallicities from simulations, which yield values between −3 < log Z < −1.5 (Hafen et al. 2019). In this case, there is no evidence of hot gas that produces broad O vi absorption, consistent with the previous studies of group environments (Oppenheimer et al. 2016; Pointon et al. 2017). Instead, the wings of the Lyα profile can be fully explained by the low-ionization cloud that produces a full Lyman break.

4.4 The z = 0.13849 absorber towards the quasar PG1116 + 215

Keeney et al. (2017) have modelled this absorber using HST/COS, HST/STIS, and FUSE spectra and determine a metallicity of |$\log Z = -0.19^{+0.07}_{-0.08}$| for a single, low-ionization cloud in this |$z$| = 0.138 49 absorber. However, the higher resolution, Keck/HIRES data reveals the presence of two narrow components in Mg ii (⁠|$b({\rm Mg} \rm {\small {II}}) = 2.5$| and 1.7 km s⁻¹) with W_r(2796) = 95 ± 5 mÅ. It is important to note that relatively broad (8−20 km s⁻¹) low-ionization components may often resolve into narrower components (1−7 km s⁻¹), and the b parameters of these components can substantially affect the constraints on the metallicity in our modelling method. Several of the lines from the |$z$| = 0.138 49 system are affected by blends with other systems along the sightline. The H i λ949 and H i λ923 are affected by the Galactic molecular hydrogen lines. The H i λ949 is contaminated at −62 km s⁻¹ by H₂ L 2-0 P(2) λ1081.265, and H i λ923 at −32 km s⁻¹ by H₂ L 4-0 P(1)λ1051.03. We divide out the contribution of these lines using the several other Galactic hydrogen lines observed in the FUSE spectrum. The H i λ972 line is contaminated by the Lyδ of |$z$| = 0.16612 absorber at 57 km s⁻¹, and the H i λ926 line is contaminated by Lyβ of the |$z$| = 0.02829 absorber at 66 km s⁻¹. We mask their influence in the log-likelihood evaluation.

The low-ionization Mg ii clouds in this absorber are also detected in N ii, Si ii, C ii, and Mg i and marginally in Ca ii and O i. The O ii is contaminated by H₂ W 3−0 R(3)λ948.42, but the profile is still shown for completeness in Fig. 9. The region of the HST/STIS spectrum covering Fe ii λ 2382 is too noisy to provide a useful constraint. The intermediate-ionization states, Si iii, O iii and C iii are detected (though O iii is contaminated by H₂ L 14 − 0 R(2)λ948.47), and though it is not as strong as the Mg ii, C iv is also detected. These transitions are clearly offset by ∼5 km s⁻¹ redward of the low-ionization transitions. A broad, O vi cloud is clearly detected in both doublet members, in the high S/N HST/COS spectrum. The Lyα and Lyβ were covered in the high S/N HST/COS spectrum as well, but the higher order Lyman series lines, down to λ918, were covered by FUSE. It is critical to note that the H i lines appear to be centred on the Si iv and C iv absorption rather than on the low-ionization absorption. These velocity offsets suggest that two phases are needed to fit this system.

Figure 9.

cloudy models for the |$z$| = 0.138 49 absorber towards PG1116 + 215 obtained using the MLE values. The spectral data are shown in grey along with the 1σ error. The instruments used for observation in different regions of the spectrum are indicated in the panels. The centroids of absorption components as determined from the VP fits for optimized ions are indicated by the vertical tick marks on top of each line. The low-ionization photoionized phase consisting of two clouds are shown by the blue and red curves, and is optimized on Mg ii, the intermediate-ionization photoionized phase shown by the yellow curve is optimized on Si iv, and the collisionally ionized phase shown by the green model is optimized on O vi. The superposition of all the three models is shown by the black dashed curve. The region shaded in grey shows the pixels that were not used in the evaluation of the log likelihood. The lines H i λ923 and H i λ949 are corrected for blending as described in Section 4.4 and earmarked with an asterisk.

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³Our modelling yields constraints presented in Table 6, and model curves that are superimposed on the data in Fig. 9. The posterior distributions for the parameters are summarized in Figs C4–C7 for the different phases. The b parameter (⁠|$b({\rm Mg}\rm {\small {II}})$| = 2.9 km s⁻¹) adopted for the blueward Mg ii cloud is 2σ higher than the best VP fit value, because the lower value yielded a cloudy model temperature too high to be consistent with the line width. The two, narrow, low-ionization clouds have high metallicities (log Z = 0.26 and 0.82), low-ionization parameters (log U = −3.43 and −4.14), low temperatures (10⁴ and 10 K), and small thickness (100 pc and <1 pc). With these low-ionization parameters, only a small fraction of the intermediate-ionization absorption can arise in the same phase as the low-ionization absorption. It is also impossible to produce the Lyα and other H i lines with such narrow low-ionization clouds, particularly the redward cloud which is best fit with |$b({\rm Mg}\rm {\small {II}})$| of only 1.7 km s⁻¹.

A slightly broader cloud optimized on the Si iv column density (⁠|$b({Si \rm{\small {IV}}}) = 6$| km s⁻¹) was added to the model and a maximum likelihood solution is determined combining with the two low-ionization clouds, and an additional broad O vi cloud to be discussed below. This Si iv cloud produces the majority of the Si iii absorption and all of the observed C iv absorption. It also produces the majority of the Lyα absorption and a substantial fraction of the Lyman series lines as well. The properties of this Si iv cloud are log Z = −1.90, log U = −3.07, and cloud thickness of 60 kpc, and it contributes |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}] = 16.0$| to the model.

In Fig. 9, the model, including the three low-ionization clouds, slightly overproduces the observed C ii λ 1036, but it is apparently consistent with the C ii λ 903 and λ 1334 lines, so we assume there may be a small defect in the C ii λ 1036 data. The results are not dependent on which of the C ii transitions are used as constraints.

The broad O vi cloud (⁠|$b({O \rm {\small {VI}}}) \sim 35$| km s⁻¹) is consistent with collisional ionization with log [T/K] = 5.4, and it can produce the wings on the Lyα line that would otherwise be unexplained. The metallicity to provide that fit to Lyα is log Z = −1.06.

We also test if O vi could arise in a photoionized phase. A photoionized model with log U = −1.6 and a supersolar metallicity could fit the O vi profile, without contributing to the H i, however, it also produces a broad C iv profile, which is clearly inconsistent with the data, as shown in Fig. 10.

Figure 10.

Photoionization only models for the |$z$| = 0.13849 absorber towards PG1116 + 215. Clearly, the photoionized model for O vi is discrepant as it overproduces C iv and the wings of the Lyα are unexplained. Symbols, labels, and masked pixels are the same as in Fig. 9.

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4.4.1 Comparison to previous work

This system might have been fit with just one low-ionization component if it were not for higher resolution and high S/N coverage of Mg ii, which clearly shows two narrow components. These clouds are typical of weak Mg ii absorbers at higher redshifts (⁠|$z$| = 0.4-1.0), with low-ionization parameters log U = −3.4 and −4.1, supersolar metallicities (log Z = 0.3 and log Z = 0.8), and small thickness (100 pc and < 1 pc). Our modelling indicates the presence of two additional phases in order to produce the observed high-ionization and H i absorption, which cannot come from the low-ionization clouds. An intermediate-ionization phase, with log U = −3.1 and with low metallicity (log Z = −1.9) produces Si iii, Si iv, and C iv absorption and is responsible for the majority of H i absorption as well, having |$\log [N({H \rm {\small {I}}})/\hbox{cm$^{-2}$}] = 16.0$|⁠. This intermediate-ionization gas phase is much more extended, with a thickness of 60 kpc. Finally, broad O vi absorption and wings on the Lyα profile constrain the properties of a higher ionization/hotter phase. We find it to be consistent with collisional ionization at log [T/K] = 5.4 in line with the Lyα fit by Stocke et al. (2014) (b = 86 ± 11 km s⁻¹). Richter (2020) successfully fitted an even broader component to the combined STIS and COS data set (b = 150 km s⁻¹). He identified the extended wings of the Lyα profile as part of a CBLA that traces the collsionally ionized, hot coronal gas of the host galaxy of this CGM absorber, in line with the predicted CBLA properties from his semianalytic model (Richter 2020; Section 5.5). In contrast, Savage et al. (2014) inferred a lower temperature of log [T/K] = 4.72, and a contribution from photoionization from their analysis. However, we find that O vi arising in a photoionized phase gives rise to a broad C iv which is inconsistent with the data, as shown in Fig. 10.

Previous investigators (e.g. Keeney et al. 2017; Muzahid et al. 2018; Pointon et al. 2019; Wotta et al. 2019) found metallicities (log Z ∼ −0.3) intermediate between those of our low metallicity, intermediate-ionization cloud, and our supersolar metallicity, low-ionization clouds. The ionization parameters of these earlier models tend to match that of our intermediate-ionization phase, with log U = −3.1, because they are trying to produce all the absorption in a single phase. We see a significant variation in ionization parameter/density across the profiles. Again the possible origin of the absorber through a combination of low metallicity inflowing gas, and high metallicity outflowing gas, may be smeared out through modelling that does not consider multiple components and phases.

4.4.2 Caveats and tests

For this system, a ‘Lyα only’ model provides constraints that qualitatively match those that we obtained with the full model. These constraints, with errors, are compared in Table 6. The best ‘Lyα only’ model slightly under predicts several of the higher order H i lines because of the slightly lower metallicity for the Si iv phase. The ‘Lyα only’ model is shown in Fig. 11.

Figure 11.

cloudy models for Lyman lines for the |$z$| = 0.138 49 absorber towards PG1116 + 215 showing that a ‘Lyα-only’ model noticeably underproduces several of the higher order Lyman lines. Symbols, labels, and masked pixels are the same as in Fig. 9.

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4.4.3 Galaxy properties

There are three galaxies within an impact parameter of 1 Mpc at the redshift of this absorber (Muzahid et al. 2018), with the nearest being an L = 1.2L* galaxy at an impact parameter of 139 kpc (e.g. Keeney et al. 2017). As with the previous systems, this absorber appears to be found in a small group of galaxies.

The low-ionization clouds are again typical of the supersolar metallicity, parsec-scale, weak Mg ii absorbers that are pervasive at intermediate redshifts (Rigby et al. 2002; Narayanan et al. 2008). The Si iv cloud is more characteristic of a sightline through the larger, intragroup medium, since it is 60 kpc in extent along the sightline, and has a low metallicity. It would presumably be gas falling into the group (Hafen et al. 2019), because of its low metallicity of log Z = −1.9. The warm/hot, collisionally ionized O vi phase also has a relatively low metallicity of log Z = −1.06. Perhaps this gas is more related to the nearest galaxy, or perhaps to an unidentified dwarf in the group, or to the low-metallicity coronal gas of the absorber host galaxy.

4.5 The z = 0.225 96 absorber towards the quasar HE0153-4520

This three component, weak Mg ii absorber (with W_r(2796) = 184 ± 6 mÅ) also shows absorption in the low-ionization Si ii, C ii, N ii, and Fe ii transitions. Because the Mg ii is observed with the highest resolution with VLT/UVES, it is used as the optimized transition in our modelling. The detection of Fe ii, in particular, requires a low-ionization parameter/high density for the two blueward, low-ionization clouds. Because of this, the detected Si iii, C iii, N iii, and Si iv cannot be produced in the same phase. Our model thus also includes three intermediate-ionization clouds, optimized on the Si iv doublet. Finally, a strong detection of broad O vi absorption and the corresponding wings in the Lyα profile call for a high ionization, collisionally ionized gas phase for the absorber, possibly related to a CBLA that traces the hot halo of the host galaxy.

Thus, our optimized cloudy models are run incorporating seven clouds in three phases. The VP fit parameters for the three components identified in Mg ii which traces the low-ionization phase, the three component fit for the S iv which traces the intermediate-ionization phase, and the single component fit for the O vi tracing a collisionally high-ionization phase are given in Table 7, along with the model parameters. The marginalized posterior distributions for the VP fit parameters are shown in Figs D1–D3. The marginalized posterior distributions for the physical properties of clouds are shown in Figs D4–D10.