Modeling the Statistics of the Cold Neutral Medium in Absorption-selected High-redshift Galaxies
AAstronomy & Astrophysics manuscript no. main_final © ESO 2020November 30, 2020 L etter to the E ditor Modeling the statistics of the cold neutral medium inabsorption-selected high-redshift galaxies
Jens-Kristian Krogager and Pasquier Noterdaeme Institut d’Astrophysique de Paris, CNRS-SU, UMR7095, 98bis bd Arago, 75014 Paris, Francee-mail: [email protected]
November 30, 2020
ABSTRACT
We present a statistical model of the selection function of cold neutral gas in high-redshift ( z = .
5) absorption systems. The model isbased on the canonical two-phase model of the neutral gas in the interstellar medium and contains only one parameter for which wedo not have direct observational priors: namely the central pressure of an L ∗ halo at z = . P ∗ . Using observations of the fraction ofcold gas absorption in strong H i -selected absorbers, we were able to constrain P ∗ . The model simultaneously reproduces the columndensity distributions of H i and H , and we derived an expected total incidence of cold gas at z ∼ . l cnm = × − . Comparedto recent measurements of the incidence of C i -selected absorbers (EW λ > . l cnm from our model indicatesthat only 15% of the total cold gas would lead to strong C i absorption (EW > . i lines are extremely usefulprobes of the cold gas as they are relatively easy to detect and provide direct constraints on the physical conditions. Lastly, our modelself-consistently reproduces the fraction of cold gas absorbers as a function of N H i . Key words. galaxies: high-redshift — galaxies: ISM — quasars: absorption lines
1. Introduction
Our understanding of star formation throughout cosmic time isintimately linked to our ability to observe and constrain the phys-ical properties of the gas in and around galaxies. The neutral gasis of particular interest and tends to split into a warm, di ff use( T ∼ K, n ∼ . − ), and a cold, dense ( T ∼
100 K, n ∼
50 cm − ) phase (Field, Goldsmith, & Habing 1969), the lat-ter being more inclined to Jeans instability and subsequent starformation.Wolfire et al. (1995) described the two neutral phases as aresult of the balance of heating and cooling mechanisms which,for a range in external pressure, exist in equilibrium. The mini-mum pressure required for a stable cold neutral medium (CNM)to exist, P min , depends on several factors, out of which metallic-ity, Z , and ambient ionizing flux, I uv , play central roles. However,while the canonical two-phase description has been intensivelyinvestigated in nearby environments, these all have rather similar Z and I uv . In order to test the current theoretical framework overan increased range of parameter space, it is convenient to lookto high-redshift galaxies as the average I uv is higher (Khaire &Srianand 2019) and the average metallicity is lower (e.g., De Ciaet al. 2018).One powerful way of studying the neutral gas at high red-shift is through damped Ly α absorption systems (DLAs) ob-served in the spectra of distant quasars (see review by Wolfeet al. 2005). However, these high column density absorbers( N H i > × cm − ) predominantly probe the warm and di ff usegas phase (e.g., Srianand et al. 2012; Neeleman et al. 2015).Instead, the cold gas phase can be studied directly by choos-ing appropriate tracers of the CNM (e.g., molecular hydrogen,H , neutral carbon, C i , or absorption from H i at 21-cm, since the21-cm optical depth depends inversely on the temperature). Yet, such cold gas absorbers (hereafter referred to as CNM absorbers)are rare and only a few hundred – compared to tens of thousandsof DLAs – have been identified in large-scale spectroscopic sur-veys (Balashev et al. 2014; Ledoux et al. 2015; Srianand et al.2012; Kanekar et al. 2014). These CNM absorbers are extremelypowerful probes of the physical conditions of the gas (density,temperature, and I uv ) through atomic fine-structure and molec-ular transitions (e.g., Srianand et al. 2005; Noterdaeme et al.2007b). It is thus possible to constrain the interstellar medium(ISM) conditions in galaxies out to high redshift z ∼ directly and resolve the small-scale CNM (e.g.,Nickerson, Teyssier, & Rosdahl 2019; Bellomi et al. 2020).However, the CNM cross section depends heavily on resolutionand on the poorly constrained feedback mechanisms from starformation and supernovae. Nevertheless, the bulk of the CNMcross section arises in a centrally concentrated region with a uni-form covering factor.In this letter, we model the CNM cross section at high red-shift using a simple analytical description of the two-phase ISM.Our approach is based on the work by Krogager et al. (2020,hereafter K20) who present an e ff ective model for DLAs build-ing on the ideas of Fynbo et al. (2008). Here we include a simplepressure-based prescription of the two-phase medium to modelthe total CNM incidence and the fraction of DLAs exhibitingCNM absorption. This way we are able to quantify the fractionof CNM absorbers that were selected using C i absorption lines.Throughout this work, we assume a flat Λ CDM cosmologywith H =
68 kms − Mpc − , Ω Λ = .
69, and Ω m = .
31 (PlanckCollaboration et al. 2016).
Article number, page 1 of 7 a r X i v : . [ a s t r o - ph . GA ] N ov & A proofs: manuscript no. main_final
2. Literature data
We have compiled a sample of known CNM absorbers in theliterature at z abs > . N H i . The observable quantities used in this analysis are thecolumn densities of neutral and molecular hydrogen, the gas-phase metallicity, and the thermal gas pressure. We furthermoreincluded impact parameters for the seven absorption systemswhere an emission counterpart has been identified. The collecteddata are presented in Table 1. Only absorption systems with de-tections of C i and / or H were included in the compilation. Themetallicities were calculated based on the elements Zn and Ssince these do not su ff er from strong dust-depletion e ff ects (DeCia et al. 2016).
3. Modeling neutral gas absorption
The modeling of the neutral gas of high redshift galaxies fol-lowed the framework for DLA absorption by K20 and Fynboet al. (2008). Here we provide a brief summary of the model.Galaxies were drawn randomly from the UV luminosity func-tion φ ( L ), which is described by a Schechter function: φ ( L ) = φ ( L / L ∗ ) α exp − L / L ∗ , with α = − .
7. For each randomly drawngalaxy, we assigned an average projected extent of neutral gas( R dla ), a central metallicity ( Z ), and a radial metallicity gradient( γ Z ) based on empirically derived scaling relations, for detailssee K20. An impact parameter ( b ) was assigned with a proba-bility proportional to the area of a circular annulus at a givenprojected radius. The absorption metallicity was then calculatedat the given impact parameter following the assumed metallicitygradient. Based on the absorption metallicity and the N H i valuealong the line of sight (see Sect. 3.2), we calculated the opticalextinction ( A V ) following Zafar & Møller (2019). We includeda mock optical selection similar to large spectroscopic surveysby probabilistically rejecting sightlines with large A V (Krogageret al. 2019). For details regarding the implementation, we referreaders to K20.In this work, we further model the radial pressure of the haloin order to calculate at what radial scales the ISM is able to sup-port the CNM. We do this by assigning a halo mass to a givenluminosity from which we can then calculate a halo pressure andits radial dependence. Since we are including a prescription forthe pressure in this work, we are able to model N H i more ac-curately than in our previous model (K20). The details of thepressure-based model are presented in what follows. Following Elmegreen & Parravano (1994), we assume that P tot ∝ Σ (cid:63) . The radial dependence of the stellar surface density Σ (cid:63) thenleads to a radial dependence on the pressure of the form: P tot ( r ) = P e − r / r e . (1)The e ff ective radius r e scales with luminosity as: r e = r ∗ e (cid:18) LL ∗ (cid:19) t e , (2)where the characteristic scale length of an L ∗ galaxy, r ∗ e , is takento be 3 kpc at z = . t e has a value of 0.3 (Brooks et al. 2011). The centralpressure, P , is calculated as a function of halo mass, M h , as-suming that the central pressure scales with the virial pressure: P ∝ T vir ρ vir ∝ M / h . The halo mass is assigned based on the luminosity according to the luminosity– M h relation by Masonet al. (2015). The central pressure of a halo is then calculated as: P = P ∗ (cid:32) M h M ∗ h (cid:33) / , (3)where M ∗ h = × M (cid:12) at z = − L ∗ galaxy, P ∗ , is not constrained directlyby observations. Instead, we explore a range of 10 − K cm − .We approximate P min following eq. (33) of Wolfire et al.(2003): P min = P ∗ min I uv Z d / Z + . (cid:16) I uv Z d ζ cr (cid:17) . , (4)where I uv is the ambient UV field in units of the Draine field(Draine 1978), Z d is the dust abundance, and ζ cr is the cosmicray ionization rate. In the above expression, P ∗ min refers to theminimum pressure at Solar metallicity with I uv =
1. We assumea fiducial value of P ∗ min = K cm − (Wolfire et al. 2003). Wefurther assume that I uv /ζ cr is constant as both the cosmic ray ion-ization rate and the ambient UV field depend on the star forma-tion activity. We model Z d / Z as a broken power-law followingBialy & Sternberg (2019, their eq. 5).The I uv is calculated based on the star formation rate surfacedensity: I uv ∝ Σ sfr ∝ ψ (cid:63) r e . (5)The star formation rate, ψ (cid:63) , is taken to be directly proportional tothe UV luminosity, whereas the disk scale length is given abovein Eq. (2).The total I uv is given as the sum of the extragalactic UVbackground and the UV field related to on-going star formation.Hence, combining equations (5) and (2), assuming that the am-bient UV field of an L ∗ galaxy is one in units of the Draine field,results in an e ff ective scaling between I uv and L of the form: I uv = I + (cid:18) LL ∗ (cid:19) − t e = I + (cid:18) LL ∗ (cid:19) . , (6)where I = .
16 is the extragalactic UV background integratedover 6 − . z = . R cnm , within which the total pressure isgreater than P min , and hence the ISM is able to support a stableCNM. This radial scale is determined as: R cnm = r e ln (cid:32) P P min (cid:33) . (7)For the ensemble of random sightlines drawn in the modeldescribed above, we then refer to sightlines as CNM absorbers ifthe impact parameter is less than R cnm , that is to say we implicitlyassume a covering factor of one for the CNM for r < R cnm . Thevalidity of this assumption is discussed in Sect. 5. Given the inclusion of the halo pressure as a function of ra-dius, we were able to model the neutral hydrogen in more de-tail than the average radial profile assumed by K20. We started
Article number, page 2 of 7ens-Kristian Krogager and Pasquier Noterdaeme: Modeling CNM statistics in high- z quasar absorbers out by modeling the total hydrogen column, N H , as a functionof radius. Motivated by the universality of the exponential formas observed by Bigiel & Blitz (2012), we used a central valueof log N H ( r = = . − for all galaxies.The exponential scale length was then matched to reproducelog N H i = . R dla , which was set to match theobserved incidence of DLAs (see K20). In doing so, we assumedthat N H is dominated by H i at these large radii, which is consis-tent with Bigiel & Blitz (2012).We subsequently split the total hydrogen column densityinto separate atomic and molecular column densities using thepressure-based prescription by Blitz & Rosolowsky (2006): f H = N H N H i = (cid:18) P tot P (cid:48) (cid:19) . , (8)with P (cid:48) = × K cm − . Here, P tot was calculated at the posi-tion of the random impact parameter following Eq. (1).In order to properly reproduce the distribution function of N H i , we included a random scatter on N H of 0.4 dex, mimick-ing the scatter in the observed radial profiles (Bigiel & Blitz2012). The molecular fraction of a given absorber was further-more given a random scatter of 0.1 dex according to the obser-vations (Bigiel & Blitz 2012). We verified that this modeling of N H i and N H reproduces the distribution function of N H i . Theagreement is only slightly worse than the fit by K20.
4. Results
Based on a stacking experiment performed on SDSS spectra,Balashev & Noterdaeme (2018, hereafter BN18) infer the av-erage covering fraction of self-shielded H -bearing gas amongH i -selected absorption systems of 4 . ± . stat ± . sys % and37 ± stat ± sys %, for log(N H i / cm − ) > . > .
7, re-spectively. Here, we consider this molecular covering fractionas a proxy for the CNM fraction, that is to say the fraction ofsightlines showing CNM absorption.The only a priori unknown parameter in our CNM model, P ∗ , was constrained by matching the CNM fractions by BN18using χ -minimization. For this purpose, we used an e ff ectiveuncertainty on the observed CNM fractions, combining the sys-tematic and statistical uncertainties in quadrature. The best-fitvalue is log( P ∗ / k B / K cm − ) = . ± .
11, for which we findthe following average CNM fractions of 4.5% and 34.8% forlog(N H i / cm − ) > . > .
7, respectively. This value of P ∗ is consistent with the central pressure inferred for the MilkyWay of log( P / K cm − ) ≈ P r = R (cid:12) / K cm − ) = . R (cid:12) = r h = (cid:104) log( P th / K cm − ) (cid:105) = . ± .
1, and our modelpredicts a value of (cid:104) log( P th / K cm − ) (cid:105) = .
8. Taking into ac-count the caveat that the observations are neither homogeneousnor representative, the average pressure predicted by our modelagrees well with the observations.The predicted column density distribution functions f ( N , X )of H i and H are presented in Fig. 1. Overall, our model si-multaneously reproduces the observed statistics of N H i and N H .The power-law inferred from the stacking experiment by BN18represents the average shape of f ( N , X ) and it is not sensitiveto the "knee" at higher column densities. The disagreement at
18 19 20 21 22 23 log( N / cm ) l o g f ( N , X ) H optical selectionH intrinsicHI optical selectionHI intrinsicBalashev & Noterdaeme (2018)Noterdaeme et al. (2012) Fig. 1.
Predicted column density distribution functions of N H i (blue) and N H (red) at z ∼ .
5. The dashed lines indicate the intrinsic distributionsand the solid lines are the "observable" distribution in optically-selectedsamples similar to SDSS-DR7. log( N H ) ∼
22 is therefore not surprising. We note that the lo-cation of the knee depends on the adopted central value of N H ,which is motivated by observations by Bigiel & Blitz (2012).The expected incidence of CNM absorbers was calculated asthe integral: l cnm = d n d z = c (1 + z ) H − ( z ) (cid:90) ∞ L min σ ( L ) φ ( L ) d L , (9)where we adopted L min = − L ∗ following K20; σ ( L ) denotesthe luminosity dependent absorption cross section, and the Hub-ble parameter is given as: H ( z ) = H (cid:112) Ω m (1 + z ) + Ω Λ . (10)The CNM absorption cross section was calculated based on theluminosity-dependent R cnm : σ ( L ) = π R cnm , which yields an inci-dence of l cnm = . × − at z = . i -selected absorbers inferred by Ledouxet al. (2015) at similar redshifts is l C i = . ± . × − , whichwas corrected for incompleteness due to the limiting equivalentwidth. In order to compare our predicted l cnm with that inferredby Ledoux et al. (2015), we restricted our calculation to modelpoints with log( Z abs / Z (cid:12) ) > − .
6, which corresponds to the min-imum metallicity in the C i -selected sample by Ledoux et al.(2015). This yields an expected C i incidence of l (cid:48) C i = . × − .A comparison between the overall expected incidence of coldgas and that traced by C i absorption is discussed in Sect. 5.Lastly, in Fig. 2 we show the distribution of impact parame-ters as a function of N H i and metallicity for the modeled CNMabsorbers compared to the overall absorber population. In thisfigure, we show the seven CNM absorbers for which emissioncounterparts have been identified (see Table 1). For comparisonpurposes, we show the compilation of emission counterparts ofH i -selected absorbers by Møller & Christensen (2020). As men-tioned in the discussion by Krogager et al. (2018), the averageprojected radial extent of CNM gas at high redshift is expectedto be roughly a factor of ten smaller than the typical extent ofDLAs. This is in good agreement with our model where the me-dian impact parameter of CNM absorbers is a factor 11 smallerthan the median for DLAs. Article number, page 3 of 7 & A proofs: manuscript no. main_final log( N HI / cm ) l og ( b / kp c ) GRBs (Lyman et al. 2017) 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.5 log( Z abs / Z ) Fig. 2.
Model prediction for impact parameters as a function of N H i and absorption metallicity. The blue-filled contours indicate the 99th, 95th,and 68th percentiles of the model distribution of CNM absorbers. The dashed contours in gray mark the percentiles of the model distribution ofoverall H i absorbers. Red and black data points show CNM and H i absorbers (Møller & Christensen 2020), respectively, with identified emissioncounterparts. The open circles in the left panel show data points for GRBs from Lyman et al. (2017). The majority of the GRBs do not havemetallicity measurements and are therefore not shown in the right panel.
5. Discussion
An implicit assumption in our analysis is that the strong H lines( N H > cm − ) analyzed by BN18 are complete tracers ofthe CNM in our model. One independent way to probe the CNMgas in DLAs is through H i z > . + − % (Kanekar et al. 2014). At face-value, thisindicates that the CNM fraction of DLAs is higher than the 4 %obtained from H statistics and assuming CNM always bearsself-shielded H (BN18). However, given the low-number statis-tics of high-redshift 21-cm absorbers, this fraction should be in-terpreted with great care. The CNM fraction derived from 21-cmabsorbers depends strongly on the redshift criteria, for example,for z > .
5, which is more comparable to the sample analyzed byBN18, and the fraction drops to ∼ /
14; see also Srianandet al. 2012). The assumption that strong H absorption systemstrace the bulk of the CNM is therefore consistent with 21-cmabsorption statistics.Absorption from C i is a good tracer of CNM gas at highmetallicity due to the increasing detectability with an increasingmetal column and due to the more e ffi cient cooling and dust-shielding from UV photons in high-metallicity gas. A compari-son between our model prediction and the incidence derived forstrong C i absorption lines with W C i , > . ∼
30 % of the CNM gas at log( Z abs / Z (cid:12) ) > − . was identified by selecting based on strong C i absorption.However, the simplifying assumptions in our model about theCNM covering factor and geometry a ff ect the estimated fractionof the CNM identified using C i -selection.We assume that the covering factor of CNM within R cnm isunity. While this may be an over-simplification, it is consistent This metallicity cut corresponds to the lowest metallicity observed inthe sample by Ledoux et al. (2015). with observations at lower redshifts (e.g., Wiklind et al. 2018)and the observation of several C i absorption components to-wards both lines of sight in the lensed quasar observed by Kro-gager et al. (2018). We also assume a spherical distribution ofthe cross section similar to K20. While this may work well forthe more extended warm gas phase dominating the strong H i absorbers, the CNM on smaller scales may be distributed in amore flattened disk-like structure. Taking such a flattening intoaccount would decrease the cross section of the CNM by roughlya factor of two. Accounting for such a geometrical e ff ect wouldbring the model expectation for l cnm of metal-rich systems intocloser agreement with the observed l C i . Nonetheless, some partof the cold, molecular gas may arise outside a flattened disk, forexample, in accretion streams or material carried out in outflows.This may decrease the projected ellipticity on average, therebylending more support to our spherical approximation.Taking our model at face value, we find that strong C i -selected absorbers represent only a fraction of the total observ-able CNM (i.e., not obscured by dust). The inferred total l cnm of11 . × − yields a fraction of 13 ± i absorption in current spectroscopicsurveys of quasars.As alluded to above, a non-negligible part of the CNM hasa dust obscuration that is too high in order to be identified inoptical surveys. Based on our model, we find that the fractionalcompleteness of l cnm is ∼
95 % due to dust obscuration, giving atotal unobscured CNM incidence of l cnm , tot ≈ × − .We have so far only considered data from intervening quasarabsorption systems. Another powerful probe of high-redshiftgalaxies is absorption systems observed in γ -ray burst afterglowspectra at the redshift of the host galaxy, the so-called GRB-DLAs. The GRB-DLAs probe very central regions of their hostgalaxies with impact parameters less than (cid:46) Article number, page 4 of 7ens-Kristian Krogager and Pasquier Noterdaeme: Modeling CNM statistics in high- z quasar absorbers a sample of GRB-DLAs. The small impact parameters overlapwith the expected impact parameters of CNM sightlines fromour model. This is consistent with the high fraction ( (cid:38)
25 %) ofGRB-DLAs showing absorption from H or C i (Bolmer et al.2019; Heintz et al. 2019). The GRB sightlines, however, tendto probe higher N H i , which may be a result of GRBs arising inregions of recent star formation where the gas column could behigher than the average galactic environment. A formal analysisof the GRB statistics in the context of our model is beyond thescope of this letter, yet we highlight that the similarities of ES-DLAs (log(N H i / cm − ) > .
7; Noterdaeme et al. 2014; Ranjanet al. 2020) and GRB-DLAs in terms of the high fraction of themshowing signs of CNM and their small impact parameters are inagreement with our model.
6. Summary
We have presented a simple model to reproduce the statisticsof high-redshift absorption systems featuring either H or C i absorption lines as tracers of the CNM. The aim of the modelis to test the canonical two-phase model of the neutral ISM athigh redshifts where the environment is significantly di ff erentfrom local galaxies (mainly in terms of metallicity and ambi-ent ionizing flux). The main principle of the model relies on apressure gradient throughout the galactic halo which determinesat which point the neutral medium is able to support a stableCNM. The criterion for CNM to exist is determined by the min-imum pressure, P min , calculated following theoretical consider-ations by Wolfire et al. (2003). This pressure-based prescriptionwas incorporated into the model framework by K20 in order topredict the H i and Z abs of CNM absorption systems.We were able to constrain the single a priori unknown modelparameter by matching the fraction of high-redshift ( z ≈ . ; BN18). Our modelthen simultaneously reproduces the distribution functions of N H i and N H . Furthermore, the distributions of metallicity, N H i , andimpact parameters are all in qualitative agreement with observa-tions. However, due to the heterogeneous sample selection andlimited statistics, it was not possible to formally quantify thegoodness of fit.We find that the fraction of CNM identified by strong C i absorption lines (with equivalent widths in excess of 0.4 Å)amounts to ∼
15 % of the total CNM observable in optically-selected quasar surveys, and that the total incidence of CNM ab-sorption is underestimated by ∼ Acknowledgements.
We thank R. Srianand for helpful discussions and com-ments on the manuscript. We thank Sergei Balashev for the very constructivereview. The research leading to these results has received funding from theFrench
Agence Nationale de la Recherche under grant no ANR-17-CE31-0011-01 (project “HIH2” – PI Noterdaeme).
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Article number, page 5 of 7 & A proofs: manuscript no. main_final
Table 1.
Auxiliary data: Compilation of cold gas absorption systems.
Quasar z abs log (cid:16) N H i / cm − (cid:17) log ( Z / Z (cid:12) ) log (cid:16) N H / cm − (cid:17) log (cid:16) P th / K cm − (cid:17) b / kpc ReferenceJ0000 + . ± .
10 0 . ± .
45 20 . + . − . . ± . − . ± . − . ± .
05 18 . + . − . – – (23)Q0027 − . ± . − . ± .
10 17 . + . − . – – (17)J0136 + . ± . − . ± .
03 18 . + . − . . ± . + . ± . − . ± .
10 15 . + . − . – – (29, 5)J0216 − . ± . − . ± .
10 – – – (15)Q0347 − . ± . − . ± .
09 14 . + . − . – – (27)Q0405 − . ± . − . ± .
12 18 . + . − . – – (27, 13)Q0551 − . ± . − . ± .
09 17 . + . − . – 15 . ± . − . ± . − . ± .
09 18 . + . − . . ± . + . ± . − . ± .
17 – – – (15)J0812 + . ± . − . ± .
10 19 . + . − . . ± . + . ± . − . ± .
11 – – – (15)J0816 + . ± . − . ± .
10 18 . + . − . . ± . + . ± . − . ± .
09 21 . + . − . . ± . + . ± .
20 0 . ± .
25 – – – (15)J0854 + . ± . − . ± .
08 – – – (15)J0857 + . ± . − . ± .
21 – – – (15)J0858 + . ± . − . ± .
02 19 . + . − . . ± . + . ± . − . ± .
07 18 . + . − . . ± . + . ± . − . ± .
12 20 . + . − . – – (15, 22)J0918 + . ± . − . ± .
05 17 . + . − . – 16 . ± . + . ± . − . ± .
21 – – – (15)J0946 + . ± . − . ± .
01 19 . + . − . . ± . − . ± . − . ± .
11 – – – (13, 27)J1047 + . ± . − . ± .
12 – – – (15)J1117 + . ± .
10 0 . ± .
14 18 . + . − . – – (15, 22)J1122 + . ± . − . ± .
15 – – – (15)J1133 − . ± . − . ± .
31 – – – (15)J1143 + . ± . − . ± .
06 18 . + . − . – 0 . ± . + . ± . − . ± .
02 18 . + . − . . ± . + . ± . − . ± .
12 19 . + . − . . ± . + . ± . − . ± .
04 19 . + . − . . ± . + . ± .
15 0 . ± .
12 19 . + . − . . ± . + . ± . − . ± .
17 – – – (15)J1302 + . ± . − . ± .
10 – – – (15)J1306 + . ± .
20 0 . ± .
22 – – – (15)J1311 + . ± . − . ± .
14 19 . + . − . – – (15, 22)J1314 + . ± .
10 0 . ± .
12 – – – (15)Q1331 + . ± . − . ± .
04 19 . + . − . . ± . Article number, page 6 of 7ens-Kristian Krogager and Pasquier Noterdaeme: Modeling CNM statistics in high- z quasar absorbers Table 1. continued.
Quasar z abs log (cid:16) N H i / cm − (cid:17) log ( Z / Z (cid:12) ) log (cid:16) N H / cm − (cid:17) log (cid:16) P th / K cm − (cid:17) b / kpc ReferenceJ1337 + . ± . − . ± .
22 14 . + . − . . ± . + . ± .
09 0 . ± .
11 19 . + . − . – 38 a (18, 26)J1441 + . ± . − . ± .
10 18 . + . − . – – (14)Q1444 + . ± . − . ± .
09 18 . + . − . . ± . + . ± . − . ± .
11 17 . + . − . – – (20)J1513 + . ± . − . ± .
23 21 . + . − . . ± . . ± . + . ± . − . ± .
15 – – – (15)J1623 + . ± . − . ± .
26 – – – (15)J1646 + . ± .
10 0 . ± .
18 18 . + . − . – – (15, 22)J1705 + . ± .
12 0 . ± .
14 – – – (15)J2100 − . ± . − . ± .
15 18 . + . − . . ± . − . ± .
15 0 . ± .
15 17 . + . − . – – (15, 22)J2140 − . ± . − . ± .
13 20 . + . − . . ± . + . ± . − . ± .
15 19 . + . − . – 5 . ± . + . ± .
15 0 . ± .
25 – – – (15)J2232 + . ± . − . ± .
05 18 . + . − . – – (25)Q2231 − . ± . − . ± .
16 – 3 . ± . − . ± .
07 0 . ± .
18 19 . + . − . – – (15, 22)Q2318 − . ± . − . ± .
06 15 . + . − . – – (17)J2331 − . ± . − . ± .
15 20 . + . − . – – (15, 22)J2334 − . ± . − . ± .
11 – 3 . ± . − . ± . − . ± .
10 19 . + . − . – – (15, 22)J2340 − . ± . − . ± .
03 18 . + . − . . ± . + . ± . − . ± .
10 13 . + . − . – – (17)J2347 − . ± . − . ± .
04 19 . + . − . . ± . − . ± . − . ± .
10 18 . + . − . . ± . . ± . Notes. ( a ) No uncertainty was reported by Rudie et al. (2017).