On the detectability of HI 21-cm in MgII absorption system
aa r X i v : . [ a s t r o - ph . C O ] N ov Mon. Not. R. Astron. Soc. , 1–9 (2009) Printed 4 June 2018 (MN L A TEX style file v2.2)
On the detectability of H I II absorption systems S. J. Curran ⋆ School of Physics, University of New South Wales, Sydney NSW 2052, Australia
Accepted —. Received —; in original form —
ABSTRACT
We investigate the effect of two important, but oft neglected, factors which can affect thedetectability of H I II absorption systems: The effect of line-of-sightgeometry on the coverage of the background radio flux and any possible correlation betweenthe 21-cm line strength and the rest frame equivalent width of the Mg II α absorption systems (DLAs). Regarding the former, while theobserved detection rate at small angular diameter distance ratios ( DA abs /DA QSO > . )is a near certainty ( P > . ), for an unbiased sample, where either a detection or a non-detection are equally likely, at DA abs /DA QSO > . the observed detection rate has onlya probability of P < ∼ − of occuring by chance. This > ∼ σ significance suggests that themix of DA abs /DA QSO values at z abs < ∼ is correlated with the mix of detections and non-detections at low redshift, while the exclusively high values of the ratio ( DA abs /DA QSO ∼ )at z abs > ∼ contribute to the low detection rates at high redshift.In DLAs, the correlation between the 21-cm line strength ( R τ dv/N HI ) and the Mg II equivalent width ( W λ ) is dominated by the velocity spread of the 21-cm line. This hasrecently been shown not to hold for Mg II systems in general. However, we do find the signif-icance of the correlation to increase when the Mg II absorbers with Mg I W λ > . ˚A are added to the DLA sample. This turns out to be a sub-set of theparameter space where Mg II absorbers and DLAs overlap and the fraction of Mg II absorbersknown to be DLAs rises to 50% (Rao et al. 2006). We therefore suggest that the width of the21-cm line is correlated with W λ for all systems likely to be DLAs and note a correlationbetween W λ (Mg I ) and N HI , which is not apparent for the singly ionised lines. Further-more, the 21-cm detection rate at DA abs /DA QSO < . rises to > ∼ % for absorbers with W λ > . ˚A and large values of DA abs /DA QSO may explain why the absorbers whichhave similar values of W λ to the detections remain undetected. We do, however, also findthe neutral hydrogen column densities of the non-detections to be significantly lower thanthose of the detections, which could also contribute to their weak absorption. Applying the R τ dv/N HI – W λ correlation to yield column densities for the Mg II absorbers in whichthis is unmeasured, we find no evidence of a cosmological evolution in the neutral hydrogencolumn density in the absorbers searched for in 21-cm. Key words: quasars: absorption lines – cosmology: observations – galaxies: high redshift –galaxies: ISM – radio lines: galaxies
Redshifted radio absorption lines can provide an excellent probeof the contents and nature of the early Universe, through surveyswhich are not subject to the same flux and magnitude limitationssuffered by optical studies. In particular, with the H I ⋆ E-mail: [email protected] the sensitivity provided by the best optical data. (Curran et al. 2004and references therein).However redshifted H I z < ∼ , whichfor the associated systems could be due to the excitation/ionisationcaused by the proximity to the active nucleus, where optical sur-veys tend to select the most UV luminous sources at high redshift(Curran et al. 2008). c (cid:13) S. J. Curran
Table 1.
Searches for intervening redshifted H I z abs ) is given as well as the number of detections andnon-detections ( n det and n non , respectively).Reference Type z abs n det n non Brown & Roberts (1973) DLA 0.69 1 0Roberts et al. (1976) DLA 0.52 1 0Wolfe & Davis (1979) DLA 1.78 1 0Wolfe et al. (1981) DLA 1.94 1 0Brown & Mitchell (1983) ∗ sub-DLA 0.44 1 0Briggs & Wolfe (1983) Mg II ∗ DLA 0.28–0.48 0 2Lane (2000) ∗ Mg II II ∗ Mg II II II ∗ Mg II II ∼ . ∗ Other detections reported, but which also appear in previous papers.
For the intervening systems, many arise in known dampedLyman- α absorption systems, which, at redshifts of z abs > ∼ . ,have the Lyman- α line shifted into the optical band, allowing directmeasurements of the neutral hydrogen column densities ( N HI > × cm − , by definition). Non-detections can be thereby beattributed to high spin temperatures (Kanekar & Chengalur 2003)and/or poor coverage of the background flux (Curran et al. 2005)in the high redshift systems (see Equ. 1, Sect. 2.1).Note, however, of the DLAs, the vast majority detected in 21-cm are also known Mg II absorbers, these traditionally being con-sidered good candidates for the detection of 21-cm absorption at z abs < ∼ . , where the Lyman- α band is attenuated by the atmo-sphere. Two recent surveys of Mg II systems (at . < z abs < . , Gupta et al. 2009 and . < z abs < . , Kanekar et al.2009b), have found a total of 13 new 21-cm absorbers betweenthem, significantly increasing the number known at z abs ≈ (Ta-ble 1). In these works, various parameters (related to the equiva-lent widths of the singly ionised and neutral metal lines) are dis-cussed, although the effects of geometry are generally ignored:Curran & Webb (2006) attribute the high 21-cm detection rate inDLAs identified through Mg II , cf. Lyman- α , absorption to the factthat the Mg II transition traces a lower redshift range ( . < ∼ z abs < ∼ . , with ground-based telescopes, cf. z abs > ∼ . ). At redshifts of z abs > ∼ . , the geometry of our flat expanding Universe, ensuresthat foreground absorbers are always at larger angular diameter dis-tances than the background QSOs, meaning that their effective cov- erage of the background radio continuum is generally reduced com-pared to the z abs < ∼ . absorbers (particularly those at z abs < ∼ . ).In this paper, we address this issue, investigating possible geometryeffects on the Mg II sample as a whole, as well as discussing otherpossible effects on the detectability of 21-cm absorption. The detectability of 21-cm absorption in a system lying along thesight-line to a radio source is determined from the total neutral hy-drogen column density, N HI , via N HI = 1 . × T spin Z τ dv , (1)where T s [K] is the mean harmonic spin temperature of the gas and R τ dv [ km s − ] is the velocity integrated optical depth of the line.The optical depth is defined via τ ≡ − ln (cid:0) − σf S (cid:1) , where σ is thedepth of the line (or r.m.s. noise in the case of a non-detection) and S and f the flux density and covering factor of the background con-tinuum source, respectively. Therefore in the optically thin regime( σ ≪ f.S ), Equ. 1 reduces to N HI = 1 . × T spin f R σS dv ,and so with a measurement of N HI (from the Lyman- α line), thevelocity integrated “optical depth”, R σS dv , gives the ratio of thespin temperature to the covering factor, T spin /f .The importance of each of these terms to the T spin /f degen-eracy is the subject of much debate, i.e. whether the large num-ber of non-detections at high redshift are predominately due tohigh spin temperatures (Kanekar & Chengalur 2003), or whetherthe coverage of the background emission region also plays a rˆole(Curran et al. 2005). For the majority of the Mg II systems, whichhave not been observed in the Lyman- α line, the situation is furthercomplicated by the fact that the total neutral hydrogen column den-sity is unknown, giving a threefold degeneracy from the integratedline strength. Therefore determining the relative spin temperatureand covering factor contributions is currently impossible, althoughwe can investigate possible geometry effects, which are indepen-dent of the assumptions used to determine these three unknownswhile having a direct bearing on the covering factor. As stated above, Curran & Webb (2006) suggested that for DLAs(then 17 detections and 18 non-detections), the 21-cm detectionrate could be influenced by geometry effects, where at redshifts of z abs < ∼ a foreground absorber can have a mix of angular diam-eter distance ratios, DA abs /DA QSO , depending upon the relativeabsorber and QSO redshifts, whereas at z abs > ∼ the diameter dis-tance ratio is always large ( DA abs /DA QSO ≈ ). This is illus-trated in Fig. 1 (top), where we show the DA abs /DA QSO distribu-tion for the whole Mg II absorber sample: While the histogram forthe line strengths appears to have a Gaussian distribution (Fig. 1,bottom), the angular diameter distance ratio histogram is heavilyskewed towards DA abs /DA QSO = 1 , where a large number ofthe searches for intervening 21-cm absorption have recently oc-cured (Gupta et al. 2009; Kanekar et al. 2009b). It is also evidentthat above angular diameter distance ratios of DA abs /DA QSO = c (cid:13) , 1–9 II absorbers Figure 1.
Top: The absorber/quasar angular diameter distance ratio versus the absorption redshift. Note the mix of DA abs /DA QSO ratios at z abs < ∼ ,whereas at z abs > ∼ the ratio is always large. The filled symbols/hatched histogram represent the 21-cm detections and the unfilled symbols/histogram thenon-detections, with the shapes designating the transition through which the absorber was discovered. The inset shows the detail around the z abs = 1 . − . region. Bottom: The velocity integrated optical depths versus the absorption redshift, where the arrows designate upper limits (for these the line-widths havebeen estimated from W λ , see Sect. 2.3.2). In both plots we show the DLAs plus all of the Mg II absorption ( W λ > ˚A) systems searched in 21-cm. . , that the ratio of detections to non-detections drops drastically(shown by the upper two histogram bars in Fig. 1, top) .This, however, is based on a relatively small sample at DA DLA /DA
QSO . and so we refer to the binomial prob-abilities of such a distribution occuring by chance: Assumingthat there is an equal probability of either a detection or a non-detection occuring in either DA abs /DA QSO bin, we see that at DA abs /DA QSO < . there is a near certainty of obtaining theobserved number detections of detections, P ( > k/n ) > . (Ta-ble 2). However, in the DA abs /DA QSO > . bin, the probabil-ity of the observed number of non-detections or more occuring bychance is very small, P ( > k/n ) < ∼ − .For the W λ > . ˚A Mg II absorbers with < W λ / W λ < AND W λ > . ˚A, i.e. those in which ≈ are known to be DLAs (Rao et al. 2006), we obtain a sim-ilar distribution at DA abs /DA QSO > . , although the proba-bilities are much higher (row 3 of Table 2), due to the smallersample. However, a probability of P ( > k/n ) = 1 . × − isstill significant at . σ , assuming Gaussian statistics, comparedwith P ( > k/n ) = 0 . ⇒ . σ for the confirmed DLAs only(Curran & Webb 2006), where there were 16 non-detections out ofa sample of 22 at DA abs /DA QSO > . .From the bottom panel of Fig. 1, it is apparent that the 21-cm The choice of a cut at DA abs /DA QSO = 0 . is somewhat arbitrary,but, as Curran & Webb (2006), we use this value since it is the lowest whichgives an appreciable enough sample size in the lower bin. Combined with the > / detections at DA abs /DA QSO < . , thisgives an overall probability of . ⇒ . σ ) for the whole distribu-tion. surveys cover a wide range of sensitivities and with no knowledgeof the total neutral hydrogen column densities in many of these,it is not possible to normalise out the observational biases (Sect.2.1). However, the histogram in Fig. 1 shows that, on the whole,the non-detections have been searched as deeply as the detectionsand, given that the observed distribution may be driven by othereffects , all else being equal, the angular diameter distance ratiodoes appear to be correlated with the detection rate.To recap, for all of the Mg II absorption systems the observeddetection rate at low angular diameter distance ratios has a highprobability of occuring by chance, while that at high ratios is ex-tremely unlikely and, when placing conditions on the sample, byselecting those which could be DLAs, there is an extremely highdetection rate at low angular diameter distance ratios, while therate remains low at high ratios. Since, on the basis that a givenabsorption cross-section will cover a given emission region less ef-fectively when these are at similar angular diameter distances, itstands to reason that the observed distribution is, at least in part,driven by the line-of-sight geometry. II equivalent width While the above work demonstrates that the detection rate ap-pears to be dependent upon the angular diameter distance ratio, the Such as different T spin /f ratios (see Curran et al. 2007c) or column den-sities (see Sect. 3).c (cid:13) , 1–9 S. J. Curran
Table 2.
The statistics of the whole sample [Fig. 1], that of the absorbers with W λ > . ˚A, those likely to be DLAs according to Rao et al. (2006), as well asthose likely to be DLAs by our definition [Sect. 2.3.1]. We show the number of detections/total with angular diameter distance ratios of DA abs /DA QSO < . and the number of non-detections/total with DA abs /DA QSO > . with the binomial probability of this number or more of occuring by chance. “rate” gives thedetection rate for each DA abs /DA QSO bin.Sample Lyman- α and Mg II Mg II only DETECTIONS NON - DETECTIONS DETECTIONS NON - DETECTIONS < . P ( > k/n ) rate > . P ( > k/n ) rate < . P ( > k/n ) rate > . P ( > k/n ) rateWhole 11/29 0.93 38% 111/133 . × −
17% 9/26 0.96 35% 95/109 . × − λ > . ˚A 11/14 0.029 79% 88/106 . × −
17% 9/11 0.033 82% 72/82 . × − . × −
27% 7/7 0.0078 100% 33/42 . × − W λ > . ˚A 9/10 0.011 90% 44/64 0.0020 31% 7/7 0.0078 100% 33/46 0.0023 28% strength of the 21-cm absorption (normalised by the neutral hy-drogen column density, R τ dv/N HI ) may itself be related to theMg II equivalent width, as shown to apply to the confirmed DLAs(Curran et al. 2007c). However, no such correlation was found be-tween τ and W λ , with only a weak trend existing between R τ dv and W λ . The correlation therefore appears to be domi-nated by the velocity spread of the 21-cm profile (both FWHM andtotal velocity spread), “significant” at . σ , which rises to . σ when the outlier 1622+238 is removed : With a FWHM = 235km s − and an impact parameter of ≈ kpc (Curran et al. 2007band references therein), this is a most unusual DLA in which we be-lieve the 21-cm profile width is dominated by large-scale dynamics.Gupta et al. (2009); Kanekar et al. (2009b) report no correla-tion between the FWHM and W λ for the Mg II absorbers andin Fig. 2 we show the confirmed DLAs (where N HI > × cm − ) together with various sub-sets of Mg II absorbers detected in21-cm and do find that the addition of the Mg II absorbers degradesthe correlation (top panel). This regains a similar significance tothat of the DLAs only (Curran et al. 2007c) when only the Mg II absorbers with W λ > ˚A are added (second panel) and de-grades once more with the condition of Rao et al. (2006) appliedto the Mg II absorbers which overlap the same W λ / W λ — W λ space as the confirmed DLAs (third panel).Through various trials, we only find a significant increase inthe correlation for the Mg II absorbers with W λ > . ˚A addedto the confirmed DLAs (bottom panel). Although found empiri-cally, our condition actually selects a sub-set of the range speci-fied by Rao et al. (2006), where ≈ % of the Mg II absorbers areDLAs. At W λ > . ˚A, 16 of the 30 absorbers are DLAs(50%), cf. 16 out of 49 (30%) at < W λ / W λ < AND . < W λ < . ˚A (figure 11 of Rao et al. 2006). Above W λ ≈ ˚A, all of the Mg II absorbers are DLAs, although be-ing a sample of only four severely restricts the significance of this .Note that, although our W λ > . ˚A selection is a sub-set of the DLA range of Rao et al. (2006), our FWHM– W λ correlation is significantly higher than when applying their con- Curran et al. (2007c) previously reported a significance of . σ ( . σ without 1622+238) for the FWHM– W λ correlation, but here we ex-clude 0248+430 (at W λ = 1 . ˚A, FWHM = 19 km s − ) which,while generally being regarded as a DLA, has an unknown neutral hydrogencolumn density. Also, we have included 2003–025 (Kanekar et al. 2009b),which at W λ = 0 . ˚A, FWHM = 40 km s − , is somewhat of anoutlier. For example, applying this condition to the 21-cm absorbers gives onlythree Mg II systems in addition to the DLAs (cf. the already low number offive when applying W λ > . ˚A, Fig. 2). These three do increase thesignificance of the correlation slightly to . σ ( . σ without 1622+238). Figure 2.
The full width half maximum of the 21-cm absorption profileversus the Mg II II ab-sorption systems. All of the panels show the confirmed DLAs (small blacksquares) overlain with the unfilled symbols, which show various Mg II ab-sorber sub-samples – all Mg II absorbers detected in 21-cm, those with2796 ˚A equivalent widths of W λ > ˚A, those which could beDLAs according to Rao et al. (2006) [ < W λ / W λ < AND W λ > . ˚A, where . W λ < . ˚A] and finally thosewith just W λ > . ˚A. In each panel we give the significance of thecorrelation for the DLAs plus Mg II absorbers with and without the outlier1622+238, with the line showing the least-squares fit to the latter.c (cid:13) , 1–9 II absorbers dition. This can be attributed to the inclusion of the end pointat W λ = 4 . ˚A and FWHM = 30 km s − (towardsJ0850+5159, Gupta et al. 2009) , as well as a tighter selectionwhich introduces some differences in the sample at W λ < ∼ ˚A (the third cf. the bottom panel of Fig. 2). Although the normalised 21-cm line strength may be correlatedwith the Mg II W λ maybe a diagnostic of the 21-cm line strength ( R τ dv/N HI ∝ f/T spin ),it cannot predict whether or not 21-cm will be detected. Onepossible explanation is that the non-detections are disadvantagedthrough geometry effects, as discussed in Sect. 2.2.In Fig. 3 we show the line strength against the equivalent widthtogether with the angular diameter distance ratios. From this, wesee that the non-detections are indeed disadvantaged, with most ofthese being at angular diameter distance ratios of > ∼ . , whereasthe detections have a range of ratios, with the large spiral galaxieslocated at the high end with the strongest line strengths (see figure6 of Curran et al. 2007c). This is strong evidence that the geometryis, once again, a dominant effect, although applying a survival anal-ysis to the non-detections , raises the significance of the correla-tion of the whole sample quite dramatically: . σ ( . σ without1622+238), cf. . σ ( . σ without 1622+238) for the detec-tions only (Curran et al. 2007c). Hence, if the 21-cm line strengthand Mg II equivalent width are related, this suggests that many ofthe non-detections may only require slightly deeper searches.The values used to derive the limits for the 21-cm non-detections (Fig. 3) will of course be biased by the use of the correla-tion for the detections to estimate the FWHM of the non-detections.This gives FWHM ≈
13 W λ (figure 6 of Curran et al. 2007c),and, where the Mg II equivalent widths are not available (gener-ally at z abs > ∼ . ), we estimate these from the metallicity via W λ ≈ . / H]+4 . (figure 7 of Curran et al. 2007c). Whennone are available, we apply the average 20 km s − of the DLAsdetected in 21-cm absorption (Curran et al. 2005). Here, the 21-cm detections span a FWHM of 8 to 50 km s − (or 235 km s − including 1622+238), giving an average value of 26 km s − andapplying the methods above gives 5 to 28 km s − for the non-detections, with an average value of 15 km s − . If instead we justassume the average value of the detections as the FWHM of eachnon-detection, each of these moves these further up the ordinate inFig. 3, while reducing the significance of the correlation to . σ ( . σ without 1622+238).The fact that, for the DLAs, the normalised line strength ex-hibits the strongest correlation with equivalent width (followed bythe FWHM then R τ dv , Curran et al. 2007c), suggests that theseparameters are inseparable, giving W λ ∝ f/T spin , where f is generally lower for the non-detections as a result of the higherangular diameter distance ratios. In the absence of measured neu-tral hydrogen column densities, this means that we cannot use themajority of the Mg II absorbers to verify this. Conversely, the corre- Excluded in the . W λ < . ˚A Rao et al. (2006) sample. Via the
ASURV package (Isobe et al. 1986). Updated from Curran et al. (2007c), as per the changes described in foot-note 4.
Figure 4.
The column density–redshift distribution of the Mg II absorberssearched for in 21-cm, where the black markers denote the detections andthe coloured markers the non-detections Top: The individual column den-sities, where the filled markers show the actual column density measure-ments and the unfilled markers show the column density calculated fromthe 21-cm line strength as per the fit in Fig. 3. We do not include the limitsdetermined from the 21-cm non-detections for which there are no measure-ments of N HI . Middle: The total values in ∆ z = 1 redshift bins. Bottom:The mean N HI per absorber within each bin . The error bars on the ordinateshow the σ uncertainty to the fit in Fig. 3 and the unfilled squares showthe detected and non-detected values combined. lation may provide a method with which to estimate these columndensities, one use of which we now explore. Using the fit from the 21-cm line strength–Mg II II absorbers for which theseare unavailable, which we show in Fig. 4. What is immediatelyclear is that the 21-cm non-detections have systematically lowercolumn densities than the absorbers detected in 21-cm, particularlyat low redshift ( < z abs < , where many do have a measured c (cid:13) , 1–9 S. J. Curran
Figure 3.
The 21-cm line strength versus the rest frame equivalent width of the Mg II N HI ) . Although there is considerable overlap in the column den-sities between the detections and the non-detections, the lower val-ues combined with the geometry issues addressed above, could ac-count for the paucity of strong 21-cm absorption in these objects.Curran et al. (2005) previously noted a correlation between the ve-locity integrated optical depth and the column density for the con-firmed DLAs, which is found to be significant at . σ when thenon-detections are also included (Curran et al. 2009).In the middle panel of Fig. 4 we show the total column den-sity for all of the 21-cm searched absorbers, which have a mea-sured/estimated value of this. It is apparent that, after a possiblepeak in the < z abs < bin, N HI decreases with redshift. How-ever, this will be heavily influenced by the relative paucity of highredshift searches, due to the availability of specific radio bands inconjunction with a severe radio interference environment, whichcan hamper searches at these frequencies. This effect, in additionto the geometry effects discussed above, could explain the steep de-crease in the number of 21-cm absorbers with redshift (Gupta et al.2009), which runs contrary to the increase in the number of DLAs(Rao et al. 2006).Therefore in the bottom panel we show the mean column den-sity per bin which, although limited by the very few points in thehigh redshift bins, shows no evidence of an evolution of N HI . Usingthese combined averages ( N HI ), we may calculate the cosmologi-cal mass density of the neutral gas in the Universe as a function ofredshift, via: Ω neutral gas = µ m H H c ρ crit n DLA N HI z + 1) H z H , where µ = 1 . is a correction for the 75% hydrogen composition, m H is the mass of the hydrogen atom, H = 71 km s − is thepresent Hubble parameter, c the speed of light, ρ crit ≡ H / π G is the critical mass density of the Universe and H z H = p Ω matter ( z + 1) + (1 − Ω matter − Ω Λ ) ( z + 1) + Ω Λ , where H z is the Hubble parameter at redshift z and we use Although the column density is normalised out in Fig. 3, suggesting that,apart from the angular diameter distance ratios, these have been searchedsufficiently deeply. Where G is the gravitational constant. Figure 5.
The cosmological mass density versus redshift for the Mg II absorbers searched for in 21-cm. The error bars show the com-bined uncertainties from N HI (above) and n DLA in each redshift bin(Prochaska & Herbert-Fort 2004; Rao et al. 2006). The dashed–dotted barsin the . < z abs . bin show the result if the W λ > . ˚Acondition of Kanekar et al. (2009b) is applied. Ω matter = 0 . and Ω Λ = 0 . . From the redshift number densityof DLAs, n DLA (Prochaska & Herbert-Fort 2004; Rao et al. 2006)and deriving the mean column densities according to how the n DLA values are binned in redshift, we obtain the cosmological mass den-sity distribution shown in Fig. 5.From this we see a near constant Ω neutral gas ≈ × − , as previously noted by Rao & Turnshek (2000);Prochaska & Herbert-Fort (2004); Rao et al. (2006), where the cos-mological mass density of the neutral gas remains unchanged up toredshifts of z abs ≈ . This is not surprising as our Mg II /DLAsample is comprised of sub-sets of the aforementioned samples. Note that while all of the sample is not necessarily comprised of DLAs,from Fig. 4 it is apparent that at least all of the 21-cm detections have N HI > × cm − , including the column densities estimated fromthe 21-cm detections (unfilled markers). Although some of the 21-cm non-c (cid:13) , 1–9 II absorbers The fact that our value at . < ∼ z abs < ∼ . is consistent withthat of Rao et al. (2006), provides a check on 21-cm line strength–Mg II Ω neutral gas calculated at this redshift byKanekar et al. (2009b) , although this work assumes an averageH I column density at these redshifts, whereas our value is esti-mated using the correlation. Following the recent surveys of Mg II absorbers at . < z abs < . (Gupta et al. 2009; Kanekar et al. 2009b), there has been alarge increase in the number of intervening 21-cm absorption sys-tems detected at these redshifts. Both these works discuss variousreasons regarding the detection of 21-cm absorption in Mg II sys-tems, but these focus upon the various equivalent widths of thesingly ionised and neutral metal lines, without considering the pos-sible line-of-sight geometry effects, although these have been foundto bias the detection rate for confirmed damped Lyman- α absorp-tion systems (Curran & Webb 2006). Considering this effect, wefind for the Mg II absorbers:(i) For the sample as a whole (or limiting this to strong Mg II ab-sorbers, e.g. W λ > ˚A), the mix of detections at low redshiftsis what would be expected purely from chance, although the highnon-detection rate at z abs > ∼ is highly unlikely.(ii) When restrictions are applied to the sample, so that a largefraction of the Mg II absorbers are expected to consist of DLAs (ac-cording to Rao et al. 2006), detection rates of ≈ % are reachedat low redshift, while the low detection probabilities at z abs > ∼ remain significant.Although other factors may contribute (such as lower column den-sities for the 21-cm non-detections, Sect. 3), which may be un-measurable (i.e. T spin /f in the absence of N HI ), it is apparentthat the likelihood of detecting 21-cm absorption is correlatedwith the angular diameter distance ratio for all intervening absorp-tion systems, where the absorbers at low redshift are subject toa range of DA abs /DA QSO ratios and thus exhibit a mix of de-tections and non-detections, whereas those at z abs > ∼ all have DA abs /DA QSO ∼ , while tending to be non-detections.Since a given absorber will occult the background flux muchmore effectively at a lower angular diameter distance ratio, thissuggests a strong contribution by the covering factor, which isindependent from the measured 21-cm line strength, from whichthe spin temperature/covering factor degeneracy cannot be broken(Sect. 2.1): In some cases the covering factor has been estimatedas the ratio of the compact unresolved component’s flux to the to-tal radio flux (Briggs & Wolfe 1983; Kanekar et al. 2009a). How-ever, even if high resolution radio images at the redshifted 21-cmfrequencies are available, this method gives no information on theextent of the absorber (or how well it covers the emission). Fur-thermore, the high angular resolution images are of the continuumonly and so do not give any information about the depth of theline when the extended continuum emission is resolved out. By us-ing the angular diameter distance ratios, we completely circumventthese issues, although we can only discuss generalities which can-not determine values of T spin or f for individual systems. What we detections have N HI < ∼ cm − , from the bottom panel of Fig. 4 themean value exceeds the defining DLA column density in all redshift bins. Even when applying their W λ > . ˚A criterion (Fig. 5). do find, however, from our statistically large sample (a total of 162absorption systems), is that 21-cm detection rates are much lowerwhen the absorber and background QSO are at similar angular di-ameter distances.Saying this, the recent surveys (Gupta et al. 2009;Kanekar et al. 2009b) yield 13 new detections between themat z abs ∼ , where the angular diameter distance ratios arehigh ( DA abs /DA QSO > ∼ . , Fig. 1). However, each of thesesurveys also yields a large number of non-detections, with bothexhibiting a 25% detection rate . This is about double the ratefor the whole DA DLA /DA
QSO > . sample, but very closeto that when restrictions are applied to include those Mg II ab-sorbers which may also be DLAs (Table 2). This is not surprisingsince the Kanekar et al. (2009b) survey selects only those with W λ > . ˚A (the minimum equivalent width of a DLA in theRao et al. 2006 sample – see their figure 2) and Gupta et al. (2009)select those with W λ > ˚A, restricting this further.Another possible factor affecting the detection of 21-cm ab-sorption could be the correlation between the 21-cm line strength( R τ dv/N HI ∝ f/T spin ) and the Mg II W λ , Curran & Webb 2006). However, the same range ofequivalent widths is also spanned by the non-detections, makingthis a questionable diagnostic with which to find 21-cm absorptionsystems. We do find, however, that eight of the ten non-detectionshave DA abs /DA QSO > . , whereas the 13 detections are muchmore spread out, spanning . < DA abs /DA QSO < , whichsuggests that geometry effects may again be responsible for thedetection rate. If the R τ dv/N HI ∝ f/T spin – W λ correlationholds up, the fact that the non-detections increase the significance,suggests that these absorbers may be close to 21-cm detection. Inany case, we suggest that W λ in conjunction with the valueof DA abs /DA QSO may provide a diagnostic with which to find21-cm absorption.As discussed by Curran et al. (2007c), the strongest con-tributer to this correlation appears to be the 21-cm profile width,which is not surprising as at W λ > ∼ . ˚A, the range discussedhere, the Mg II profile is dominated by velocity structure (Ellison2006). Including all of the Mg II absorbers degrades the correla-tion (as found by Gupta et al. 2009; Kanekar et al. 2009b), althoughthrough the testing of many different equivalent widths and their ra-tios (e.g. W λ , W λ & W λ / W λ ), we find that thecorrelation increases for the Mg II absorbers for which the Mg I W λ > . ˚A. At 13.60 eV, H I has a similar ionisation potential to the singly ionised metal species(15.04 for Mg II & 16.18 eV for Fe II ), although it is not surpris-ing that the cooler component (i.e. the 21-cm) is better traced bythe neutral metal species (i.e. Mg I , which has a potential of 7.65eV). Furthermore, the fact that W λ > . ˚A is a sub-set of the W λ / W λ — W λ space which contains all of the DLAsof Rao et al. (2006), suggests that the W λ > . ˚A selectionis (mostly) adding further DLAs to the confirmed DLA sample(Curran et al. 2007c). That is, in general, the 21-cm profile widthis correlated with W λ when N HI > × cm − .Investigating this further, in Fig. 6 we show the total neutralhydrogen column density versus the Mg I z abs < . absorbers for which both measurements areavailable. Although there is no clear partitioning, all (in an admit- The binomial probability of 26 or more non-detections out of a sampleof 35 is P ( > k/n ) = 0 . (Gupta et al. 2009, where at . < z abs < . all of the systems have DA abs /DA QSO ∼ ).c (cid:13) , 1–9 S. J. Curran
Figure 6.
The total neutral hydrogen column density versus the Mg I z abs < . absorbers (P´eroux et al. 2004). Thecoloured symbols/arrows designate upper limits to W λ . The horizontaldashed line shows N HI = 2 × cm − , above which the absorbers areconsidered to be DLAs and the dotted line shows the least-squares fit to allof the points (taking account of the limits via ASURV ). Figure 7.
As the left panel of Fig. 3, but with the velocity integrated opticaldepth of the 21-cm line on the ordinate and the equivalent width of the Mg I W λ > . ˚A, all of the21-cm non-detections have DA abs /DA QSO > . . tedly small sample) of those with W λ > . ˚A have N HI > ∼ cm − , and unlike P´eroux et al. (2004), who find no signifi-cant correlation between metal line equivalent widths ( W λ & W λ ) and N HI , we find W λ to correlate with log N HI ata . σ significance.In Fig. 7 we extend this to the sample searched for 21-cmabsorption. Ideally, we would show the normalised line strength( R τ dv/N HI ∝ f/T spin , as in Fig. 3), however there are only 12absorbers with measurements of both (comprising of seven 21-cmdetections and five non-detections) . From this, we see a weakcorrelation between R τ dv and W λ , although, as was notedin Curran et al. (2007c), the neutral hydrogen column density is re-quired in order to obtain the full picture (and f/T spin ). The absence Although these few points do give a . σ correlation between R τ dv/N HI and W λ . Figure 8.
As Fig. 7, but with the equivalent width of the Mg II of a measured N HI could be responsible for the fairly weak corre-lation, especially considering that the non-detections tend to havelower column densities (Sect. 3).Finally, for completeness, in Fig. 8 we show R τ dv versusthe Mg II W λ − [M/H] correlations ofthe detections (Sect. 2.3.2), which will tend to increase any sig-nificance derived for these. This will be tempered somewhat bythe optical depth limits for the non-detections, which are known.Therefore the significance of each of these correlations should beconsidered to lie somewhere between the two quoted values.To summarise our findings regarding the detectability of 21-cm absorption in intervening Mg II absorption systems: • On the basis of a 21-cm detection and non-detection be-ing equally probable, at small angular diameter distance ratios( DA abs /DA QSO < ∼ . ) the observed distribution is expected forthe whole sample, whereas at high ratios the observed distributionis very improbable. This suggests that the angular diameter distance( DA abs ) plays a crucial rˆole in the detection of 21-cm absorption,which in turn suggests a strong covering factor dependence. • Large angular diameter distance ratios may also explain whythe non-detections span a similar range of Mg II W λ correlation. Note also, that, in general, the non-detectionshave considerably lower neutral hydrogen column densities, whichcould contribute to making these harder to detect over the wholeMg II sample . • Using this correlation to estimate the column densities for theabsorbers in which these are unmeasured (particularly at . < ∼ z abs < ∼ . ), we find that the cosmological mass density of the neu-tral gas does not deviate significantly from Ω neutral gas ≈ × − over the redshifts spanned by the optically selected absorbers( . < ∼ z abs < ∼ . ). This consistency with the general optically Although N HI is normalised out in our definition of line strength in thecase of the R τ dv/N HI — W λ correlation.c (cid:13) , 1–9 II absorbers selected population supports the 21-cm line strength– W λ cor-relation.Curran et al. (2007c) suggested that the R τ dv/N HI — W λ cor-relation was dominated by the 21-cm profile width in confirmedDLAs, although this does not appear to be the case for the Mg II sample in general (Gupta et al. 2009; Kanekar et al. 2009b). How-ever, we find this significance to increase when only the absorberswith Mg I W λ > . ˚A areadded. This happens to be a sub-set of the Mg II absorbers with < W λ / W λ < AND W λ > . ˚A, ≈ of which are known to be DLAs (Rao et al. 2006). The FWHM– W λ correlation does therefore appear to hold for absorbers inwhich the neutral hydrogen column density exceeds N HI ∼ cm − . Finally, we note a (somewhat scattered) correlation betweenthe total neutral hydrogen column density and the equivalent widthof the Mg I ACKNOWLEDGMENTS
I wish to thank the referee for their helpful comments, whichaided in clarifying the manuscript. This research has made use ofthe NASA/IPAC Extragalactic Database (NED) which is operatedby the Jet Propulsion Laboratory, California Institute of Technol-ogy, under contract with the National Aeronautics and Space Ad-ministration. This research has also made use of NASA’s Astro-physics Data System Bibliographic Service and
ASURV
Rev 1.2(Lavalley et al. 1992), which implements the methods presented inIsobe et al. (1986).
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