Ionization corrections in a multi-phase interstellar medium: Lessons from a z~2 sub-DLA
Nikola Milutinovic, Sara L. Ellison, J. Xavier Prochaska, Jason Tumlinson
aa r X i v : . [ a s t r o - ph . C O ] J un Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 21 November 2018 (MN L A TEX style file v2.2)
Ionization corrections in a multi-phase interstellar medium: Lessonsfrom a z abs ∼ sub-DLA. Nikola Milutinovic , Sara L. Ellison , J. Xavier Prochaska , Jason Tumlinson Department of Physics and Astronomy, University of Victoria, Victoria, B.C., V8P 1A1, Canada Department of Astronomy and Astrophysics, UCO / Lick Observatory, University of California, 1156 High Street, Santa Cruz, CA 95064, USA Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
21 November 2018
ABSTRACT
We present a high resolution (FWHM = . − ), high S / N echelle spectrum for the z em = .
26 QSO J2123 − z abs = .
06 sub-DLA in its line of sight. This high redshift sub-DLA has a complex kinematic structure andharbours detections of neutral (S i , C i ), singly (e.g. C ii , S ii ) and multiply ionized (e.g. C iv ,Si iv ) species as well as molecular H and HD. The plethora of detected transitions in variousionization stages is indicative of a complex multi-phase structure present in this high redshiftgalaxy. We demonstrate that the ionization corrections in this sub-DLA are significant (up to ∼ / H] = + . / H] = − .
19. The theoretical impact of a multi-phase medium is investigated through Cloudy mod-elling and it is found that the abundances of Si, S and Fe are always over-estimated (by up to0.15 dex in our experiments) if a single-phase is assumed. Therefore, although Cloudy mod-els improve estimates of metal column densities, the simplification of a single phase mediumleaves a systematic error in the result, so that even ionization-corrected abundances may stillbe too high. Without ionization corrections the properties of this sub-DLA appear to requireextreme scenarios of nucleosynthetic origins. After ionization corrections are applied the ISMof this galaxy appears to be similar to some of the sightlines through the Milky Way.
Key words: quasars: absorption lines, galaxies: high redshift
The measurement of rest-frame ultra-violet resonance lines indamped Lyman alpha (DLA) systems is currently the most success-ful technique for determining chemical abundances at high redshift(e.g. Prochaska et al. 2003; Wolfe, Gawiser & Prochaska 2005).The largest compilations of DLA abundances include column den-sities for over a dozen di ff erent elements in some 200 absorbinggalaxies (e.g. Prochaska et al. 2007b; Dessauges-Zavadsky et al.2009). It is usually assumed that, due to the high N (H i ) columndensity of the absorber, ionization corrections are negligible andthat total elemental column densities can be derived from the dom-inant ionization state, i.e. the lowest energy species where the ion-ization potential is above 13.6 eV. For the majority of elements ob-served in absorption, such as silicon, iron, zinc, sulphur, nickel, ti-tanium and chromium, this is the singly ionized species, leading tothe approximation N(X) ≈ N(X ii ). Exceptions include oxygen andnitrogen whose first ionization potential is close to that of hydrogenand whose ionization balance is governed by charge exchange sothat the neutral atom is the dominant species. Therefore, althoughabsorption from non-dominant species is observed in DLAs (suchas C iv , Mg i and Na i ) their contributions are minor and not usually considered in abundance determinations. The robustness of this ap-proach to abundance calculations has been tested numerous timesin the literature (Viegas 1995; Howk & Sembach 1999; Vladilo etal 2001; Prochaska et al. 2002a), usually through models that em-ploy the ionization code Cloudy (Ferland et al. 1998). Although theexact magnitude of the corrections depends on a variety of input pa-rameters, most notably the shape and normalization of the ionizingbackground (e.g. Viegas 1995; Howk & Semback 1999), in gen-eral the literature agrees that the majority of DLA column densitiesdo not require significant ionization corrections (e.g. Vladilo et al.2001). However, there are a few noteworthy cases where ionizationcorrections may be important (Prochaska et al. 2002a; Prochaska etal. 2002b; Dessauges-Zavadsky et al. 2004; Dessauges-Zavadsky etal. 2006; Ellison et al. 2010).As the column density of neutral hydrogen decreases, the self-shielding approximation becomes less robust as more ionizing pho-tons penetrate the cloud. For example, it has been shown that theratio of Al iii / Al ii (or some proxy for Al ii if it is saturated) tendsto increase as the N (H i ) decreases (Vladilo et al. 2001). As studiesof quasar absorption line systems began to push down the N (H i ) c (cid:13) Milutinovic et al. scale to investigate the nature of sub-DLAs with 19.0 < log N (H i ) < − (e.g. Peroux et al. 2003) it was natural to re-assess theneed for ionization corrections (Dessauges-Zavadsky et al. 2003;Meiring et al. 2007). Once again, it was found that, in general, ion-ization corrections were small (below 0.2 dex) and observed col-umn densities are therefore usually converted directly into metal-licities (e.g. Peroux et al. 2007; Dessauges-Zavadsky et al. 2009).Nonetheless, for some sub-DLAs, ionization corrections appear tobe non-negligible (e.g. Richter et al. 2005; Quast et al. 2008). In this paper we present the case of a low column density sub-DLA towards the QSO J2123 − z abs = .
06 whose unusualproperties led us to re-assess the issue of ionization corrections forsub-DLAs. Since the methodology of this work di ff ers from pre-vious studies of ionization corrections in sub-DLAs, it is usefulto summarise our approach at the outset. The superb data quality,in terms of both resolution ( R ∼ / N (up to 50 perpixel), has permitted a rare chance to demonstrate the presence of amulti-phase medium, with contributions from both a mostly neutralcomponent, and a more highly ionized component. Although manyworks on sub-DLAs have previously investigated ionization correc-tions in sub-DLAs (see above references), these investigations haveuniformly assumed that the gas measured in absorption originatesfrom a single phase. Since the sightline towards J2123 − ff ect of calculating Cloudy ion-ization corrections with only a single phase?’.In order to address this question we create a range of mod-els with two-phase media, in which we vary the fractions of the‘cold’ and ‘warm’ gas (as characterised by di ff erent ionization pa-rameters). These models yield column densities of species such asSiII, FeII, AlII and AlIII. The key to our model philosophy is thatwe take these column densities as ‘observed’ values and adopt theusual empirical strategies of observers, and the assumption that themedium is a single phase, to attempt to derive the input parameters.In essence, we are attempting to recover the input model, but usingan incorrect assumption about the ionization structure. Ultimately,we will quantify how wrong the derived elemental abundances willbe under the assumption of a single phase ISM. The utility of thisapproach is that the relative contributions of components of realmulti-phase absorbers can rarely be constrained. Multi-phase mod-els are therefore not usually possible in practice. Our models there-fore provide an indication of the likely error associated with the(necessary) single-phase approach. Additional uncertainties, suchas those associated with geometry or in the atomic data, are notconsidered in this investigation.The paper is laid out as follows. In Section 2 we describe theobservations and data reduction of the QSO J2123 − N (H i ) and metal species columndensities. In Section 3 we discuss the puzzling nature of this sub-DLA in the context of its ISM properties, if no ionization correc-tions are applied. The general fidelity of single phase models in themulti-phase case is quantified in Section 5 and evidence for a multi-phase medium in J2123 − Di ff erent naming conventions have emerged for absorbers that exhibitdamping wings, yet do not qualify as DLAs. The most common alternativename is super-Lyman limit system, e.g. O’Meara et al. (2007). to the specific case of J2123 − and HD) of this absorber are in-vestigated in 2 companion papers (Malec et al. 2010; Tumlinson etal. in preparation). The sub-DLA towards J2123 − ∼ >
95% of cases where Ly α is covered in theSDSS spectrum, the H i column density is found to be large and theabsorber would be classed as a DLA (Kaplan et al. 2010). Follow-up of a sub-sample of these metal-line selected DLAs with HIREShas shown that the metallicity of these DLAs is approaching thesolar value, even at z ∼ z abs ∼ .
06 absorber towardsJ2123 − z em = . r = × − and fine structure lines of carbon at z = . ,
800 s but with the E1 decker (0 . R ∼ ,
000 (FWHM ∼ − ). Suchhigh resolution is beneficial when studying the coldest phases ofthe ISM, allowing us to potentially resolve even very narrow com-ponents of the di ff use gas (e.g. Narayanan et al. 2006). All observa-tions were conducted with the blue cross disperser, an echelle angleof 0 ◦ , and cross-disperser angle of 1.0275 ◦ , yielding a total wave-length coverage of approximately 3000 – 6000 Å. For calibrationpurposes, a set of standard trace flats were obtained, as well as thespectra of ThAr lamps (arcs) using the same instrument settings.We also obtained a set of pixel flats (lamp flats) at the beginning ofthe observing run to determine the pixel-to-pixel variation acrossthe detectors.The data were reduced using the HIRedux routine which is apart of the XIDL package . The reduction involved the followingprocedures:(i) A flat field frame was produced from a stack of approxi-mately 30 flat field exposures for each of the detector’s chips.(ii) In a similar manner, a combined trace flat frame is producedas a median over the series of standard flat images taken during theobserving night. This frame is then used to define (trace) the echelleorder boundaries (and find the order of curvature), and to determinethe slit profile, which is used to correct the illumination pattern ofthe science frames.(iii) A wavelength solution is derived from the spectra of a ThArlamp taken with the same setup as in the science frames. HIReduxperforms a 1D wavelength solution by fitting a low-order Legendrepolynomial to the pixel values in the ThAr exposures versus the XIDL is publicly available at http: // / ∼ xavier / IDL / index.htmlc (cid:13) , 000–000 onization corrections in a multi-phase ISM. laboratory wavelengths along the spatial centres of each order. Thecode then performs a 2D fit to all the lines from the 1D solution.Finally, the pipeline derives the 2D wavelength map giving boththe wavelength solution, and the line tilts for all orders over the fullechelle footprint.(iv) After the raw science frame images are flattened and cos-mic rays are flagged, the final step in the reduction process is theextraction of the object and the sky spectra. The sky background isestimated from the pixels that fall well beyond the object aperture,taking into account di ff use scattered light, which is estimated byinterpolating the pixel counts in the gaps between the pixel orders.After this, the procedure derives the spatial profile of the objectpoint spread function, and performs an optimal extraction based onthe order trace.(v) The individual exposures were coadded by combining eachorder separately, yielding a final, unnormalized 2D spectrum.(vi) The continuum is fitted manually using the XIDL routine x continuum . The routine allows the user to select the parts of thecontinuum una ff ected by absorption and then performs a minimum χ fit on the selected data points using a spline function of a givenorder (for the HIRES data presented here the usual value of thespline order is around 8).(vii) The echelle orders are combined after normalization into a1D spectrum. In regions of order overlap, the orders are averaged,weighting by the square of median signal-to-noise ratio. The finalspectrum has a S / N of ∼
15 per pixel at 3100 Å, ∼
30 at 3500 Å,and ∼
40 at 5100 Å. N (H i ) determination To perform the column density measurement of the Ly α absorp-tion, the continuum and the line profile were simultaneously fit ina blaze-corrected section of the spectrum. The fit was performedusing the x fitdla routine of XIDL. The Ly α profile is clearlyasymmetric, with the red wing showing stronger damping. The as-symetry indicated that a two-component fit was necessary. The red-shifts of the components were fixed at the redshifts of the strongestmetal line absorption in the two kinematically distinct metal linecomplexes detected in the system (see the next Section). The fitis presented in Figure 1. The column densities of the separatecomponents are log N (H i z = . = . ± .
15 cm − , andlog N (H i z = . = . ± .
30 cm − , yielding a total columndensity of neutral hydrogen of log N (H i ) = . ± . − . Notethat these uncertainties are dominated by systematic (e.g. contin-uum fitting), not statistical error. In order to derive the total column density of multi-componentmetal line complexes VPFIT 9.3 was used on the normalized data.VPFIT is a multiple Voigt profile fitting code that calculates a max-imum likelihood fitting function to the data. The code is adaptedto fit multiple lines simultaneously, which allows for e ffi cient iden-tification of blends. The goodness of fit is assessed in VPFIT by χ statistics. The error estimates of the fitting parameters also in-clude the uncertainties induced by self-blends, as well as blendsdue to unidentified lines. The errors on individual components arefairly poorly constrained, but the total column density error canbe more accurately quantified and may be quite small, especially / ∼ rfc / vpfit.html −1500 −1200 −900 −600 −300 0 300 600 900 1200 1500050100150200250 || Velocity (km s −1 ) Figure 1.
Fit to the Ly α line with total log N (H i ) = . ± . − (redline). The blue dotted line represents the continuum fit and green lines arethe 3 σ bounds respectively. A two component fit (shown by tick marks)is required to adequately fit the asymmetric profile. The column densi-ties of separate components are log N (H i z = . = . ± .
15 cm − ,and log N (H i z = . = . ± .
30 cm − . The lower solid (cyan) lineshows the 1 σ error array. SI 1808 | |01
SI 1473 | |01
CI 1157 | |−40 −20 0 20 4001
CI 1158 | | 01
CI* 1189 | |01
CI* 1279 | |01
CI** 1329 | |−40 −20 0 20 4001
CI** 1277 | |
Velocity (km s −1 ) Velocity (km s −1 ) Figure 2.
Fit to neutral carbon and sulphur lines towards J2123 − z = . (cid:13) , 000–000 Milutinovic et al. NI 1135c | | | | | | CII* 1335 | | | | | | | | SII 1254 | | | | | | | | −100 0 10001
SiII 1808 | | | | | | | | SiII 1527 | | | | | | | | | | | | | | | | | FeII 1608 | | | | | | | | | | | | | | | | FeII 1145 | | | | | | | | | | | | | | | | AlII 1670 | | | | | | | | | | | | | | | | | AlIII 1854 | | | | | | | | | | | | | | | | | CIV 1550 | | | | | | | | | | | | | | | | | −200 −100 0 10001
SiIV 1402 | | | | | | | | | | | | | | | |
Velocity (km s −1 ) Velocity (km s −1 ) | |||| Figure 3.
Metal lines towards J2123 − z = . if several species are fit simultaneously with the same structuralmodel. Lower limits are reported for species with only saturatedtransitions and 3 σ upper limits are quoted for non-detections us-ing the following equations: W obs (3 σ ) = × FWHM / ( S / N ) , (1) W r = W obs / (1 + z ) , (2) N = . e × W r / ( λ r × f ) , (3)where W r , and λ r are rest-frame equivalent width and wavelength, f is oscillator strength, and ( S / N ) is signal to noise ratio at theobserved line wavelength. Eqn 3 comes from the linear part of thecurve of growth (e.g. Pagel 1997). Table 1.
Neutral carbon and silicon column densities from Voigt profile fits.z b log N(CI) log N(CI*) log N(CI**) log N(SI)(km s − ) (cm − ) (cm − ) (cm − ) (cm − )2.05930 1.8 ± ± ± ± ± ± ± ± ± ± ± ± ± (cid:13) , 000–000 on i z a ti on c o rr ec ti on s i na m u lti - pha s e I S M . z b log N(SiII) log N(FeII) log N(NiII) log N(AlII) log N(AlIII) log N(SII) log N(NI) log N(CII) log N(CII*)(km s − ) (cm − ) (cm − ) (cm − ) (cm − ) (cm − ) (cm − ) (cm − ) (cm − ) (cm − )2.05684 5.2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± > ± ± ± > ± Table 2.
Metal ions column densities from Voigt profile fits. The upper section (separated by double horizontal lines) shows fits for the satellite complex, the lower section for the main complex, as defined in thetext. Totals in the bottom row are only for the main complex (lower section) c (cid:13) R A S , M N R A S , Milutinovic et al.
Table 3.
CIV and SiIV column densities from Voigt profile fits. The uppertable section shows fits for the satellite complex, the lower section for themain complex, as defined in the text. The totals in the bottom row also referonly to the main complex.z b log N(CIV) log N(SiIV)(km s − ) (cm − ) (cm − )2.05685 9.0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± The same kinematic structure (i.e. combination of Doppler( b ) parameter and z ) was used for singly ionized species, N i andAl iii , but this model was not applicable to the more highly ionizedspecies of C iv and Si iv . We also adopted an independent model forS i and C i , since these atoms likely trace gas in a cooler kinematicphase. The fits for the measured species are given in Tables 1 to 3and shown in Figures 2 and 3. Molecular transitions of hydrogen from both Lyman and Wernerbands up to rotational level J = lines are located at the same redshifts as the neutral linesof carbon, which are also aligned with the strongest singly ionizedmetal ion lines. Fitting the H absorption features is complicated bysaturation of the lowest J states and by the need for continuum andzero-level adjustment. Molecular HD is also detected in this sys-tem, only the third such detection in a DLA (see also Varshalovichet al 2001; Srianand et al. 2008). The HD and H lines are anal-ysed in two separate papers (Malec et al. 2010; Tumlinson et al. inpreparation). The molecular lines are not considered further in thispaper, but their presence is noted here for completeness. The abundances, calculated on the basis of the raw column den-sity measurements (uncorrected for ionization), in the sub-DLA to-wards J2123 − Table 4.
Elemental abundances before ([X / H] raw ) and after ([X / H] corr )ionization corrections (IC(X / H). Values are for the main complex whose N (H i ) = ± − . Errors in [X / H] account for the error in N (H i )and N(X) and are added in quadrature. For presentation purposes, the errorsare only quoted for the final corrected abundance, but the errors on the rawabundance are identical.log N(SiII) log N(FeII) log N(SII) log N(NI)(cm − ) (cm − ) (cm − ) (cm − )Total 14.69 ± ± ± ± / H) ⊙ − . − . − . − . / H] raw + . − . + . − . / H) + . + . + . − . / H] corr − . ± . − . ± . − . ± . − . ± . the main absorption complex in this analysis, using an N (H i ) = Uncorrected for ionization, the metallicity of the sub-DLA (maincomplex) appears to be super-solar, i.e. [Si / H] = + .
00 and [S / H] = + .
36. Super-solar metallicities have previously been presentedfor a small number of sub-DLAs in the literature (e.g. Prochaskaet al. 2006; Peroux et al. 2006; Peroux et al. 2008; Meiring et al.2008; Dessauges-Zavadsky et al. 2009), based on a similar analysis(i.e. assuming small or negligible ionization corrections). Such highmetallicities are somewhat surprising at high redshift for a num-ber of reasons. First, the emission line abundances measured fromactively star-forming galaxies at z > / or local enrichment. However, although the magni-tude of H ii -to-H i region abundance disagreements is still debated(e.g. Lebouteiller et al. 2009 and references therein), it would be ex-pected that any discrepancy would tend towards higher abundancesfor emission lines. Moreover, emission line abundances measureonly the metallicities of the actively star-forming regions, whereasabsorption line measurements probe the entire galaxy along a givensightline and therefore yield average ISM measurements. Even incases where a sightline probes regions near active star-formation,such as the case for GRB-absorbers, metallicities are typicallyaround 1 /
10 Z ⊙ (Prochaska et al. 2007a). Although the range of elements probed by our spectra is some-what limited, there are two notable abundance ratios of interest.The first are indicators of α element enhancement, which can beobtained from the ratios of [S / Fe] = + / Fe] = + ff ects have been discussed by many au-thors (e.g. the review by Wolfe et al. 2005). What is striking in thecase of J2123 − / Fe] com-pared to previous measurements (e.g. Prochaska & Wolfe 2002). c (cid:13) , 000–000 onization corrections in a multi-phase ISM. log(N/O) log(O/H)+12 Figure 4. N / O ratio plotted against the system metallicity on the solar scale.Metallicities are determined from O / H or Si, S / H corrected by the solar ra-tio of Si / O or S / O (see Table 4). The sub-DLA towards J2123 − ii regions (open blue circles) assembled by Pettini et al. (2008). The dashedlines show predicted contributions from primary and secondary N produc-tion. The arrow points to the J2123 − The main complication here is the unquantified e ff ect of dust de-pletion, particularly for Fe ii which can raise these ratios far abovetheir intrinsic values.A second ratio which reveals a surprising result is N / S. Theutility of nitrogen as a cosmic clock, thanks to its primary and sec-ondary contributions, has been discussed extensively in the liter-ature (e.g. Pettini et al. 2002, Prochaska et al. 2002a; Centurionet al. 2003; Henry & Prochaska 2007; Petitjean et al. 2008). Inbrief, the dominant contribution of α elements to the ISM comesfrom prompt enrichment by massive stars which result in Type IISN. Secondary nitrogen is released on a longer timescale, once theseed nuclei of carbon have been established from previous genera-tions of stars. Hence, the secondary component of nitrogen steadilybuilds with time once the metallicity is approaching the solar value.The source of primary nitrogen is still a contentious issue, but thesubstantial scatter of N / α in DLAs has led to the suggestion that pri-mary nitrogen production occurs in low or intermediate mass starsand its release is hence is delayed relative to the α elements (Pettiniet al. 2002; Henry & Prochaska 2007).The sub-DLA towards J2123 − ii regions show N / α ratiosthat are correlated with metallicity (usually measured from O / H)as expected from the secondary production mechanism describedabove. In Figure 4 we show the ratio of N / α in the J2123 − ii regions. The sub-DLA lies in a previously unpop-ulated part of the diagram – high metallicity, but relatively low N / α .This is a puzzling result. On the one hand, this DLA has apparentlyexperienced su ffi cient star formation to enrich its ISM to above so-lar values, but is only experiencing primary nitrogen enrichment.One explanation of this combination of abundances would be thatthe galaxy is both chemically young, but has experienced intenseand productive star formation. The sub-DLA towards J2123 − ii ∗ λ µ m emission from the strength ofthe C ii ∗ λ P / , from which a 158 µ m photon is spontaneouslyemitted during the decay to the P / fine-structure state in theground 2s
2p term of C ii . The [C ii ] 158 µ m transition is a prin-cipal coolant of interstellar neutral gas in the Galaxy (Wright et al.1991). By assuming that cooling is dominated by the 158 µ m line,the heating rate can be calculated by determining the [C ii ] coolingrate l c .The emissivity of [C ii ] 158 µ m can be calculated from the col-umn density of C ii ∗ λ l c = N ( CII ∗ ) h ν ul A ul N ( HI ) ergss − Hz − (4)where A ul is the Einstein A coe ffi cient, and h ν ul is the energy ofthe 158 µ m transition. For the sub-DLA towards J2123 − l c = . × − ergs s − Hz − . Wolfe et al. (2008) haverecently shown that l c in DLAs follows a bimodal distribution witha transition at l c ∼ − ergs s − Hz − . Absorbers above this crit-ical value exhibit higher metallicities, velocity widths and dust-to-gas ratios. Furthermore, Wolfe et al. (2008) suggest that galaxieswith cooling rates higher than the critical value are located in moremassive halos with active star formation occuring in ‘bulge mode’,i.e. removed from the gas halo. Although the sub-DLAs towardsJ2123 − ii leads to lowerlimits for l c , especially at high N (H i )), and is also larger than theaverage Galactic disk value. The neutral inter-stellar medium is generally divided into two com-ponents – a warm neutral medium (WNM) with temperatures ofseveral thousand degrees K and densities ∼ − , andthe cold neutral medium (CNM) with T ∼
100 K and n ∼
10 atomscm − (Field et al. 1969). Spin temperatures of high redshift DLAsare generally high (e.g. Kanekar et al. 2006 and references therein),with only one DLA exhibiting a value below 350 K at z abs > z abs ∼ .
2. At higher redshift, absorption from a range ofhigh and low ionization species indicates that a multi-phase struc-ture in DLAs is common (e.g. Wolfe & Prochacka 2000; Fox etal. 2007; Lehner et al. 2008; Quast et al. 2008). In this section, weexamine the evidence for a multi-phase medium in the sub-DLAtowards J2123 − − − invelocity space requiring 15 components for a reasonable Voigt pro-file fit, see Figure 3. Although such a wide velocity spread is notunique amongst quasar absorbers, this sub-DLA is unusual in therange of species that are detected. In addition to the often-observed c (cid:13) , 000–000 Milutinovic et al. singly ionized species, such as Si ii and Fe ii , the much less com-mon C i line is present and a rare detection of S i (see also Quastet al. 2008). Substantial column densities of more highly ionizedspecies are also measured, for example, for Al iii , C iv and Si iv .The singly and multiply ionized metal species are clearly separatedinto a main complex centred at z abs = . z abs = . ∼
250 km s − ). The neutralspecies, such as C i and S i are detected in only two components ofthe main complex. The same is true for the molecular absorption(Malec et al. 2010; Tumlinson et al. in prep) which is observed inonly one (HD) or two (H ) velocity components associated withthe main complex. The simultaneous presence of such a variety ofionized species for a given element and the kinematic diversity isstrongly suggestive of a multi-phase medium in which neutral andmolecular species occupy only a fraction of the interstellar volume.Further evidence for a multi-phase medium comes from thedetails of the Voigt profile fit. The neutral carbon and sulphur linesrequire a very small b -parameter of only 1.8 km s − . These verynarrow lines are unresolved even in this high resolution spectra( R ∼ , g f valuesin which C i transitions are observed, the b-parameters of theselines are constrained well. The singly ionized species are more thantwice as broad with b -parameters ∼ − , such di ff erencesare common signatures in the Galactic ISM (e.g. Spitzer & Jenkins1975). Ignoring the contribution of turbulence in line broadening,for a given chemical element that is detected in multiple ionizationstages, the ratio of Doppler parameters scales as the square root ofthe ratio of temperatures, a factor of seven in the case of neutraland singly ionized sulphur. The sub-DLA studied here thereforepresents a clear case of a multi-phase medium at high redshift. As discussed in the Introduction, ionization corrections are usuallyassumed to be negligible for DLAs, and have also been reported tobe < . ffi cient to mask nucleosyntheticsignatures (e.g. Prochaska et al. 2002a; Quast et al. 2008). Previ-ous attempts to model ionization corrections have assumed a singlephase model. Our observations of J2123 − N (H i ) is associated with each phase. Asdiscussed by Ellison et al. (2007), it is extremely di ffi cult to sepa-rate DLA Ly α profiles into separate components , although speciessuch as O I may provide clues in this respect (e.g. Fox et al. 2007).To assess the impact of the single-phase assumption we use Cloudy(Ferland et al. 1998) to construct a multi-phase model and then testhow accurately the column densities can be recovered under thesingle-phase assumption.The modelling procedure is as follows.(i) A model with two phases is constructed, where the ‘phase’is defined by the ionization parameter, i.e., the ratio of H ionizingphotons to H atoms. The ‘cold’ phase gas is defined as having anionization parameter of log U = − .
0, while the ‘warm’ phase isset to log U = − .
0. The total combined neutral column densityof the cloud in both phases is set to be N (H i ) = . cm − . Nine At lower column densities, asymmetries in the Ly α wing become moreobvious and separation becomes easier versions of the model were constructed with di ff erent fractions ofthe N (H i ) in the warm and cold phases ranging from completelycold to completely warm gas (essentially these extrema are single-phase clouds).(ii) The metallicity of the cloud is fixed at [M / H] = − .
33 in allmodels, with a solar abundance pattern as given in Cloudy version07.02.(iii) The two-phase cloud is radiated with a mix of the Haardt-Madau (H&M) extragalactic spectrum (Haardt & Madau 1996) andthe average Galactic ISM spectrum of Black (1987), which primar-ily a ff ects the ions with ionization potential lower than 1Ryd, suchas C i , and S i .(iv) For each of the nine models (which sample di ff erent frac-tions of cold and warm gas), Cloudy outputs the column densitiesof Fe ii , S ii , Si ii , Al ii and Al iii separately for the cold and warmphase. The column densities of a given species in the cold and warmphases are summed to give the column densities that would be ob-served in a real spectrum.The procedure described above yields nine sets of columndensities for two-phase models. The next step is to recover themetallicity of the theoretical input cloud by following the steps thatan observer would execute in trying to model the cloud with a sin-gle phase. This requires adopting a metallicity and an indicator oflog U and then running Cloudy over a parameter grid until the ob-served values are reproduced. All grids are calculated using a mixof the H&M and the average Galactic ISM spectrum stopping thecalculations when the column density of neutral hydrogen reaches N (H i ) = . cm − . The details of this stage in the modelling are:(i) For the metallicity, we assume [M / H] = [Fe ii / H i ] (where thecolumn densities come from the Cloudy output). In order to testwhether this approximation of metallicity introduces a significanterror, we also repeat the experiment with the ‘true’ metallicity of[M / H] = − .
33 (in practice, this is unknown to the observer).(ii) The ionization parameter of the single-phase model of eachof the theoretical clouds is inferred from the column density ra-tio of Al ii / Al iii . This ratio is commonly used as an indicator ofionization in sub-DLAs and DLAs (Dessauges-Zavadsky et al.2003; Prochaska et al 2002b). One of the empirical motivationsfor using Al ii / Al iii is its correlation with neutral hydrogen col-umn density (Vladilo et al 2001, Dessauges-Zavadsky et al 2002).Narayanan et al (2008) speculated that this anti-correlation mightextend also to the lower column denisty QALs, such as weakMg ii absorbers. However, other work has questioned the utility ofAl ii / Al iii for constraining the ionization parameter (e.g. Howk &Sembach 1999), whose atomic data is additionally poorly known(e.g. Vladilo et al. 2001; Dessauges-Zavadsky 2003). However,since our methodology is to adopt standard observational strate-gies to quantify errors in derived properties, we follow the com-mon practice of using Al ii / Al iii to constrain ionization parameter.Figure 5 presents the inferred value of log U for each of the ninetheoretical two-phase clouds. The left-hand panels show the resultsof the models in which the metallicity is estimated from Fe ii / H i ,whereas the right-hand panels show the models using the correctmetallicity. The left-hand panels are almost identical to those on theright, indicating that, for these models, using Fe ii / H i as an estimatefor metallicity is a good approximation. As expected, Al ii / Al iii in-creases monotonically with log U . Perhaps more surprising is thatthis approach fairly faithfully recovers the ionization parameter ofthe warm phase even if its contribution to the total neutral hydrogendensity is as small as 10%. The di ff erence between the real and re-covered log U for the warm phase is only on the order of 0.10 dex. c (cid:13) , 000–000 onization corrections in a multi-phase ISM. Figure 5.
Derivation of the ionization parameter from aluminium ionic ra-tios calculated for theoretical two phase clouds, assuming a single phase.The top panels show a monotonic relation between Al ii / Al iii and the in-ferred log U . The lower panels show the inferred ionization parameter asa function of the fraction of N(H i ) in the warm phase. The left hand col-umn is for the single-phase models that assume [M / H] = − .
33, while theright is for models with [M / H] = [Fe ii / H i ]. Even if the contribution of thewarm phase to the total column density of H i is as small as 10% the modelsrecover the log U of the warm phase to within ∼ (iii) After the ionization parameter is derived for each model, theionization corrections are calculated. The fractional column densityof an element in a given ionization state is given as f (X i + ) = N (X i + ) N (X) ,and similarly for hydrogen f ( HI ) = n (HI) n (H) = N (HI) N (H) . The ionizationcorrections IC (X / H) are then given by: IC (X / H) = log N (X i + ) N (HI) ! − log N (X) N (H) ! , (5)which is simply: IC (X / H) = log f (X i + ) f (HI) ! , (6)These values are subtracted from the ionic abundances to obtain thefinal abundance of an element. Comparing these corrected abun-dances to the input values of the original two-phase model allowsus to assess how accurately ionization corrections for a single phasemodel recover the input abundances of a truly two-phase medium.The results of this experiment are presented in Figure 6 for thecase where the intrinsic metallicity is known, and Figure 7, for thecase which uses the ‘observed’ metallicity. The top panel presentsthe ‘observed’ ionic abundance for Si ii , S ii and Fe ii , the middlepanel shows the ionization corrections, and the bottom panel givesthe corrected metallicities. The black line indicates the input metal-licity of [M / H] = − .
33. Only the results for Si ii , S ii and Fe ii areshown, as these are the ions meausred in our study. For complete-ness, we also show in the Appendix a more complete set of modelsfor a further six elements commonly measured in DLAs. The re-covered metallicity for all of the two-phase models over-estimatesthe input value. However, the deviation from the [M / H] = − . Figure 6.
Ionization corrections for the theoretically modeled medium with[M / H] = − .
33. The ionic abundances ‘measured’ from the Cloudy mod-els are presented in the top panel for Si ii (green line), S ii (blue line) andFe ii (red dotted line). The ionization corrections are given in the middlepanel, and the corrected abundances are shown in the bottom panel. Theblack horizontal line represents the input metallicity of [M / H] = − . ∼ of the corrections increases with increasing warm-phase fraction.The input metallicity is recovered when the model is either 100%warm or 100% cold phase, since in these cases, the single-phaseapproximation is obviously an accurate one. From these models,it is possible to quantify the approximate accuracy to within whichionization corrections can be calculated from a single phase Cloudymodel. The experiment also shows that if even a small fraction ofhydrogen column density is present in the warm phase, applying nocorrections to the elemental abundances can lead to over-estimatesup to 0.5 dex (as is the case for Si in this example). − In this section we derive photo-ionization corrections for the sub-DLA towards J2123 − − As shown in Section 5, for a multi-phase medium, the correctionsderived from the single-phase Cloudy model approximate the val-ues of the warm medium and become increasingly inaccurate as the c (cid:13)000
33. The ionic abundances ‘measured’ from the Cloudy mod-els are presented in the top panel for Si ii (green line), S ii (blue line) andFe ii (red dotted line). The ionization corrections are given in the middlepanel, and the corrected abundances are shown in the bottom panel. Theblack horizontal line represents the input metallicity of [M / H] = − . ∼ of the corrections increases with increasing warm-phase fraction.The input metallicity is recovered when the model is either 100%warm or 100% cold phase, since in these cases, the single-phaseapproximation is obviously an accurate one. From these models,it is possible to quantify the approximate accuracy to within whichionization corrections can be calculated from a single phase Cloudymodel. The experiment also shows that if even a small fraction ofhydrogen column density is present in the warm phase, applying nocorrections to the elemental abundances can lead to over-estimatesup to 0.5 dex (as is the case for Si in this example). − In this section we derive photo-ionization corrections for the sub-DLA towards J2123 − − As shown in Section 5, for a multi-phase medium, the correctionsderived from the single-phase Cloudy model approximate the val-ues of the warm medium and become increasingly inaccurate as the c (cid:13)000 , 000–000 Milutinovic et al.
Figure 7.
Same as in Figure 6, but for an assumed metallicity of[M / H] = [Fe ii / H i ]. medium becomes dominated by a cooler phase. It is unfortunatelynot possible to model the corrections for J2123 − ff ect is typically at the < − N (H i ) = . cm − , a metallicity of + ii and H i ), and a solar abundance pattern. In order to determinethe ionization parameter (which, as we have shown above, approx-imates to that of the warm medium if multiple phases are present),the code matches the observed (Si ii / Al iii ) ratio of 1.63 to the valuesobtained from the model (see top panel of Figure 8). Si ii is used asa proxy for Al ii since the only available Al ii line is saturated andonly a lower limit to aluminium ionic ratio (Al ii / Al iii > .
45) canbe measured from the available spectrum.The upper panel of Figure 8 presents the ionic ratio (Si ii / Al iii )versus the ionization parameter from the model grid. The observedratio of ions intercepts the model curve at the ionization parameter Figure 8.
The top panel shows the predicted Si ii to Al iii column densityratio from the Cloudy models with the photoionizing spectrum containingboth average Galactic ISM and extragalactic HM spectra. The horizontaldashed lines is drawn at the measured ratio. The average ionization param-eter inferred by comparing the observed values to the model has a value of − .
46. The middle panel shows the fraction of each element in the givenstage of ionization. Predicted ionization corrections for the selected metalabundances (see equation 6) from the same models are given in the lowerpanel. of log U = − .
46. The lower panels give the model inferred ion-ization fraction and correction curves for the ions of interest. Ta-ble 4 reports the ionization corrections (IC) for each element, andthe corrected abundance on the solar scale once the ionization hasbeen accounted for. The errors on the column densities are thosedetermined by VPFIT (Table 2), and errors on abundances includethe error in N (H i ) propogated in quadrature. No attempt has beenmade to estimate the error on the ionization correction due to theuncertainties mentioned above. Nitrogen (relative to H i ) is the leasta ff ected by ionization, which is often implicitly assumed, due to itsionization potential of 1.07 Ryd. Indeed, the middle panel of Figure8 shows that the fraction of N i closely tracks the H i as a functionof log U. Si ii is the species requiring the largest ionization cor-rection for the limited species studied here (see the Appendix forcorrections for other elements).In order to examine the influence of the photoionizing spec-trum and the assumed metallicity on the magnitude of the inferredcorrections, additional Cloudy grids of varying metallicity (1 / /
10, 1 /
3, 3, and 10 of theoriginal) were produced. The models with the combination of theseparameters that acceptably reproduce the observed elemental abun- c (cid:13) , 000–000 onization corrections in a multi-phase ISM. dance ratios vary the magnitude of the resulting correction within acouple of tenths of a dex from the value determined by the originalmodel. We now re-examine the metallicity, cooling rate, N / α and α / Feabundances of the sub-DLA towards J2123 − / H] = − .
19 and [Si / H] = − .
71. This sub-DLA there-fore remains metal-rich for its redshift, relative to DLAs at z ∼ ff erence in metallicity only existsat low redshift ( z abs < . ff ect. In the case of the sub-DLA towardsJ2123 − z abs ∼ /
10 to 1 / i column density systems at the same redshift.The determination of the cooling rate includes the N (H i ) col-umn density; for most Galactic interstellar sightlines the total hy-drogen content is indeed dominated by neutral gas so that N (H i )is a reasonable proxy in the calculations (e.g. Pottasch et al. 1979).However, we have shown that this is not the case for the sub-DLAstudied here. We therefore re-calculate the cooling rates as: l c = N ( CII ∗ ) h ν ul A ul N ( H ) ergss − Hz − (7)where the total hydrogen column density determined from our ion-ization model is log N(H) = − . The cooling rate calculatedfor J2123 − l c = . × − ergs s − Hz − to l c = . × − ergs s − Hz − , consistent with the ‘high-cool’population studied by Wolfe et al. (2008).Finally, the corrected N / O ratio has also moved dramaticallyrelative to its ‘raw’ values, due to both corrections in metallicityand N / O (determined from N / S with a correction for the S / O solarabundance). The corrected value (see Figure 4) is now indicativeof a primary plus secondary nitrogen contribution and is consistentwith Galactic H ii regions at a similar metallicity. Concern regard-ing ionization corrections of N / α ratios has been previously raised,e.g. Izotov et al. (2001). Specifically, ionization e ff ects have beenappealed to in order to explain the large scatter of N / α ratios be-low the primary plateau. Although we have shown that a signifi-cant correction is required for the sub-DLA studied here, Pettiniet al. (2002) have argued that such corrections are unlikely to beresponsible for all of the observed scatter. The ISM is expected to exhibit a multi-phase structure and thereis abundant evidence that DLAs are no exception. In this paper we present the case of a z abs = .
06 sub-DLA which exhibits a com-plex kinematic and ionization structure. The HIRES data obtainedrepresent one of the highest resolution spectra obtained of a high z QSO which facilitates the study of the multi-phase ISM. Absorp-tion transitions detected in this sub-DLA range from species whichtrace cold gas (such as H , HD, S i , C i ) up to highly ionized speciessuch as C iv . Ignoring ionization corrections in this system leads topuzzling properties.We have shown that using a single phase model to deriveionization corrections in a multi-phase medium can only recoverabundances to within ∼ Z ∼ / Z ⊙ , the single-phaseassumption probably does not impact greatly on the conclusions.However, relative abundances, which are used to identify subtle nu-cleosynthetic e ff ects, may be quite susceptible to ionization errors.For example, although our two-phase model was constructed witha solar ratio of Si / Fe, the output abundances (see Figures 6 and7) yielded an over-abundance of Si by up to 0.1 dex. This mightotherwise be interpreted as evidence for dust depletion in Fe, or α -element enhancement in Si.In closing, we note that the sub-DLA studied here is of partic-ularly low N (H i ), and is unusual in the range of ionzation speciesit displays. It may therefore not be typical of the sub-DLA pop-ulation as a whole. However, it does alert us to the real need toassess the ionization state of sub-DLAs on a case by case basis.For example, Quast et al. (2008) recently revisited the z abs = . −
44. Originally estimated by de la Vargaet al. (2000) to have log N (H i ) ≈ N (H i ) = − (Reimers et al. 2003). As forthe sub-DLA studied here, Quast et al. (2008) detect a range of ion-zation species including S i , Si i , Fe i , Si iii and Al iii which confirmthat the sightline intersects a combination of neutral and ionizedgas. In fact, Quast et al. (2008) conclude that the majority of themetal line species in the sub-DLA towards HE0515 −
44, similarlyto the one in J2123 − z abs = .
745 towardsQ1331 +
17. Ellison et al. (2003) previously investigated the com-plex kinematic structure and ionization structure of this absorber. AHIRES spectrum obtained by one of us (JXP) also exhibits Si i andFe i , ions also reported by D’Odorico (2007), although neither ofthese cases has coverage of higher ionization species. The N (H i ) ofthe z abs = .
745 absorber towards Q1331 +
17 is not known, but its D -index (Ellison 2006; Ellison et al. 2008) indicates that it is likelyto be a sub-DLA. There are thus three cases where sub-DLAs ex-hibit absorption from neutral gas, presumably a cold phase, despitetheir relatively low N (H i ). In at least two of these cases, higher ion-ization species are also present, a strong indication that the sightlineis intersecting multi-phase gas. Although it is di ffi cult to draw ro-bust conclusions from such small numbers, one explanation couldbe that the N (H i ) column density of some sub-DLAs is low becauseof ionization from H i to H ii , as well as a conversion of H i to H (e.g. Schaye et al. 2001; Krumholz et al. 2009). Although Noter-daeme et al. (2008) do not find a strong correlation between N (H i )and the probability of H detection, the sample of the sub-DLApopulation is relatively sparse. A more extensive survey of neutralions such as C i in DLAs and sub-DLAs would be most interestingin this regard. c (cid:13) , 000–000 Milutinovic et al.
ACKNOWLEDGMENTS
SLE is supported by an NSERC Discovery Grant. The data pre-sented herein were obtained at the W.M. Keck Observatory, whichis operated as a scientific partnership among the California Insti-tute of Technology, the University of California and the NationalAeronautics and Space Administration. The Observatory was madepossible by the generous financial support of the W.M. Keck Foun-dation. The authors wish to recognize and acknowledge the verysignificant cultural role and reverence that the summit of MaunaKea has always had within the indigenous Hawaiian community.We are most fortunate to have the opportunity to conduct obser-vations from this mountain. NM also wants to acknowledge that asthe University of Victoria a ffi liates we are visitors on the traditionalterritory of the Coast Salish people and we thank the WS’ANEC’(Saanich), Lkwungen (Songhees) and Wyomilth (Esquimalt) peo-ples for an opportunity to work and reside in their lands. REFERENCES
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Figures A1 and A2 show the results of the Cloudy modeling de-scribed in Section 5 for a further six elements commonly observedin DLAs. These are presented here for completeness, but we notethat these corrections are not generally applicable to the sub-DLAor DLA population as they are modelled for the particular parame-ters of J2123 − c (cid:13) , 000–000 onization corrections in a multi-phase ISM. Figure A1.
Ionization corrections for the theoretically modeled mediumwith [M / H] = − .
33. The ionic abundances ‘measured’ from the Cloudymodels are presented in the top panel for di ff erent elemental species com-monly measured in DLAs and sub-DLAs. The ionization corrections aregiven in the middle panel, and the corrected abundances are shown in thebottom panel. The black horizontal line represents the input metallicity of[M / H] = − .
33. The single-phase based corrections recover the metallicityof the clouds to within ∼ Figure A2.
Same as in Figure A1, but for an assumed metallicity of[M / H] = [Fe ii / H i ].c (cid:13)000