We measure the two-point correlation function, ξAG, between galaxies and quasar absorption-line systems at z < 1, using the data set of Morris & Jannuzi on 16 lines-of-sight (LOS) with ultraviolet (UV) spectroscopy and galaxy multi-object spectroscopy (Paper I). The measurements are made in 2D redshift space out to π= 20 h−1 Mpc (comoving) along the LOS and out to σ= 2 h−1 Mpc projected; as a function of H i column density in the range NH I= 1013–1019 cm−2, also for C iv absorption systems, and as a function of galaxy spectral type. This extends the absorber–galaxy pair analysis of Paper I. We find that the amplitude of the peak in ξAG at the smallest separations increases slowly as the lower limit on NH I is increased from 1013 to 1016 cm−2, and then jumps sharply (albeit with substantial uncertainties) for NH I > 1017 cm−2. For C iv absorbers, the peak strength of ξAG is roughly comparable to that of H i absorbers with NH I > 1016.5 cm−2, consistent with the finding that the C iv absorbers are associated with strong H i absorbers.
We do not reproduce the differences reported by Chen et al. between 1D ξAG measurements using galaxy subsamples of different spectral types. However, the full impact on the measurements of systematic differences in our samples is hard to quantify. We compare the observations with smoothed particle hydrodynamical (SPH) simulations and discover that in the observations ξAG is more concentrated to the smallest separations than in the simulations. The latter also display a ‘finger of god’ elongation of ξAG along the LOS in redshift space, which is absent from our data, but similar to that found by Ryan-Weber for the cross-correlation of quasar absorbers and H i-emission-selected galaxies. The physical origin of these ‘fingers of god’ is unclear, and we thus highlight several possible areas for further investigation.
We are investigating the nature and extent of the relationship between gas, as probed by neutral hydrogen quasar absorption-line systems, and the luminous baryonic matter traced by galaxies at cosmic epochs z < 1. In this paper, we extend the work presented by Morris & Jannuzi (2006) (hereafter Paper I), where we set out the motivation for the project, defined the 16 lines-of-sight (LOS) observational data set and established the existence of an absorber–galaxy correlation using pair count analysis. We extend the analysis of this data set to compute the absorber–galaxy two-point correlation function, ξAG, as a function of H i column density and compare the results with other measurements and simulations.
As discussed and referenced extensively in Paper I, the history of work in this area has been characterized by a debate between two extreme positions: (i) that low-redshift Lyα absorbers arise in the haloes of luminous galaxies; or (ii) that they are part of a filamentary network pervading the intergalactic medium (IGM) and are related to galaxies only to the extent that they both trace the underlying dark matter distribution. This polarized picture is undoubtedly a simplification of a reality which now seems likely to require a mixture of the two components in proportions which vary as a function of galaxy type, absorber column density and cosmic epoch. A further complication arises from the expectation that at high redshift galaxies are expected to blow most of their star-forming material out into the IGM as ‘superwinds’. Such outflows are hypothesized to pollute the IGM with metals (Aguirre et al. 2001), to prevent the formation of overluminous galaxies at z= 0 (Benson et al. 2003) and to account for the low-fraction of z= 0 baryons locked in stars. The measurement of ξAG provides a method to characterize these feedback processes and to facilitate a direct comparison with simulations. At z∼ 2–3, attempts have been made to measure the impact of superwinds on the IGM by cross-correlating H i and C iv absorption systems with ultraviolet (UV)-selected galaxies, but the early results were ambiguous (Adelberger et al. 2003). Subsequent measurements have clarified the situation (Adelberger et al. 2005) and reveal that strong Lyα absorption is produced in intergalactic gas within 1 h−1 comoving Mpc of ∼2/3 of such galaxies, and that strong C iv absorption (NC IV≫ 1014 cm−2) extends out to impact parameters of 40 kpc (proper) with a velocity range Δv > 260 km s−1. Whether such superwind events have imprinted a relic signature on the galaxy–IGM relationship which persists to z < 1 is not known, but the measurements presented in the present paper may provide some constraints on this issue (see also Rauch et al. 2005).
In Paper I, we showed that absorbers and galaxies are correlated out to impact parameters of at least 1.5 Mpc (physical) but that this clustering is weaker than the galaxy–galaxy clustering in the sample. The velocity differences between absorber–galaxy pairs with detected C iv absorption are typically smaller than those with H i absorption only, but variations with H i column density were not assessed. Several other works have cross-correlated absorption-line catalogues with various low-z galaxy samples and reached broadly similar, but not identical, conclusions. Ryan-Weber (2006) cross-correlated galaxies selected in H i 21-cm emission with low column density (NH I < 1015 cm−2) Lyα absorbers and found the clustering to be similar in strength to the clustering of the galaxies in the sample in redshift space, but somewhat stronger in real space on scales of 1–10 h−1 Mpc. At somewhat higher column density, Bouché, Murphy & Péroux (2004) cross-correlated Mg ii absorbers with luminous red galaxies (LRGs) at 0.4 ≤z≤ 0.8, and over comoving scales of 0.05–13 h−1 Mpc found that the Mg ii–LRG cross-correlation amplitude is ≃ 30 per cent weaker than the LRG–LRG clustering. In a series of papers, Prochaska and collaborators have investigated the clustering of z < 0.5 galaxies around absorbers along the sightline to the quasar PKS 0405−123 (Prochaska et al. 2004, 2006; Chen et al. 2005). To the extent that it is possible using a single sightline, they showed that emission-line galaxies and absorbers with NH I > 1014 cm−2 cluster with a strength comparable to the galaxy–galaxy clustering, whilst the absorption-line galaxies in their sample are not correlated with absorbers.1 They also showed that absorbers with NH I < 1013.6 cm−2 are distributed more randomly with respect to galaxies, and that the strength of ξAG is insensitive to NH I for 1013.6 < NH I < 1016.5 cm−2. Also for this sightline, Williger et al. (2006) found that the absorber–galaxy correlation function is significant out to Δv < 250 km s−1 and grows with minimum absorber column density. Some of these conclusions can be tested with our multiple LOS data set and that is our aim here.
For completeness, we note that Chen et al. (2001) presented a sample of quasar LOS with Hubble Space Telescope (HST) Faint Object Spectrograph (FOS) observations together with galaxy redshifts. As mentioned in Paper I, we have chosen not to fold their data into our current analysis due to significant differences in survey strategy.
Throughout this paper, we adopt the cosmological parameters Ωm= 0.3, ΩΛ= 0.7 and H0= 100 h km s−1 Mpc−1.
2 THE ABSORBER–GALAXY TWO-POINT CORRELATION FUNCTION
The absorber–galaxy cross-correlation function, ξAG, is defined through the expression for the conditional probability dP of finding a galaxy in a volume dV at position r2, given that there is an absorber at position r1:
The samples of absorption lines and galaxies which we will use to compute ξAG are identical to those defined in Paper I, where full details can be found. In brief, the data set comprises 16 quasar fields (from the HST Quasar Absorption Line Key Project data set; Jannuzi et al. 1998), whose LOS contain a total of 381 Lyα absorption lines and 30 C iv systems (25 at z < 1), and a total of 685 galaxies with redshifts z < 1. As discussed in Paper I, 49 of these galaxies have recession velocities <500 km s−1 and are most likely stars, but their exact identification is irrelevant for this study because 98 per cent of the H i absorbers are in any case at z > 0.3. The number of galaxies in the redshift range 0.3 ≤z≤ 1 which effectively overlap with the absorption-line sample is 379.
The following estimator, introduced by Davis & Peebles (1983), is used to compute ξAG as a function of projected separation, σ, and LOS separation, π:Bouché et al. (2004), the numbers of pairs in each of the quasar fields are normalized separately such that AR =ΣARiNig/Nir, where the summation is over the 16 fields and Nig and Nir are the numbers of real and random galaxies in field i, respectively. All absorber–galaxy separations are computed in comoving redshift space, and the absorbers are assumed to be located at the sky position of the quasar LOS. For the assumed flat cosmology, the comoving distance to an object at redshift z is given by
Several crucial details of the computational method, namely the generation of the random galaxy catalogue, the binning and smoothing of ξAG and the calculation of uncertainties, are dealt with in the next section.
2.1 Computational method
Random galaxy catalogues
Our method requires a separate random galaxy catalogue for each quasar field in order to reflect any field-to-field differences in the galaxy selection function. The latter mainly arise due to the placement of slits and not from differences in spectroscopic depth. Following Adelberger et al. (2003), we form such catalogues by replacing each real galaxy with 100 random galaxies, whose redshifts are drawn at random from the galaxy redshift distribution of the other fields, i.e. the real and random galaxies have the same positions on the sky, but different redshifts. This reflects the fact that galaxies in the sample must be located at the position of the slits.
Spatial binning and smoothing ofξAG
To reduce the effects of shot noise due to the small number of absorber–galaxy pairs on the measurement of ξAG some consideration must be given to the form of the numerical coordinate grid, (σ, π), on which it is evaluated. There are two approaches. The first approach adopts a grid whose cell size is large enough to include a sufficient number of absorber–galaxy pairs. An adaptively sized mesh would be the best way to handle strong variations in the density of absorber–galaxy pairs, but this would have the tendency to dilute the signal in regions where the paucity of pairs arises from a genuinely strong anticorrelation signal with ξAG≃−1.
An alternative approach is to bin the measurements much more finely (if at all) and then to smooth the resulting field to remove the noise. Again, an adaptively sized smoothing kernel could be the best option. The two underlying density fields, AG (σ, π) and AR(σ, π), must be smoothed first and then ratioed to obtain the smoothed ξAG, as in equation (2).
In this work, we present results obtained using both the above approaches: (i) on a uniform grid sampled as σ= 0, 0.4, 0.8, … , 2 h−1 Mpc, π= 2, 4, 6, … , 20 h−1 Mpc – referred to as the ‘binned’ results (the 2 h−1 Mpc bin size in the π direction reflects the ≃200 km s−1 spectral resolution; in the σ direction, the field sizes dictate that galaxies are present out to maximum comoving impact parameters of ≃2 h−1 Mpc, which we have arbitrarily split into five equally spaced bins); (ii) on a finely space grid with the underlying density fields smoothed by a Gaussian of full width at half-maximum (FWHM) = 0.8 × 4 h−1 Mpc, referred to as the ‘smoothed’ results. We did not experiment with any adaptively sized grids or smoothing kernels.
Using the same method as Ryan-Weber (2006), we attempted to measure the uncertainties on ξAG using jackknife resampling in which the correlation function is computed N= 16 times with one sightline removed each time
A disadvantage of this method is that at locations where there are no absorber–galaxy pairs in the full sample (i.e. ξAG=−1), all the individual ξi=−1 and hence σξ= 0. This highlights another problem of assessing the significance of the measured ξAG values, namely that there is no obvious figure of merit analogous to a signal-to-noise ratio, i.e. ξAG/σξ is not a straightforward indication of a correlation's significance. A simpler alternative to characterize the significance of the observed correlation is to use Poisson statistics, i.e. to calculate the probability of observing the real number of absorber–galaxy pairs (AG) in a given cell, given the expected number (AR). We will utilize both these approaches.
3 RESULTS AND COMPARISON WITH OTHER WORKS
In so far as the sizes of our absorber and galaxy samples permit, our goal is to measure ξAG as a function of both H i column density and galaxy spectral type, and to compare with other results in the literature.
3.1 Dependence of absorber–galaxy cross-correlation function (ξAG) on absorber H i column density
The absorption-line sample spans a range of H i column density from NH I= 1013 to 1019 cm−2, with the bulk of the lines being at the lower end of this range, as shown by the distribution in Table 1. As discussed in Paper I, the modest resolution of the HST FOS (R= 1300; 230 km s−1) means that the Lyα absorption features were typically unresolved, so column densities were inferred from the equivalent width assuming a Doppler b-parameter of 30 km s−1. As shown in fig. 1 of Weymann et al. (1998), the 4.5σ lower detection limit on the rest equivalent width (REW) of absorption features in these quasars decreases from 0.2 Å at z= 0.3 to 0.1 Å at z= 1. Considering that the overlap between the galaxy and absorber sample is skewed toward the lower end of this redshift range, the lower detection limit for the absorber sample is effectively REW ≃ 0.2Å, equating to NH I≃ 1013.6 cm−2. We note, however, that the Key Project absorption-line sample is not strictly complete for any REW value, but has a detection limit which varies with both LOS and redshift (as discussed at length in Paper I).
|log NH Ia||Number of absorbers|
|log NH Ia||Number of absorbers|
aInfrared assuming Doppler parameter b= 30 km s−1.
In the first calculation of ξAG, we use the entire absorption-line sample, i.e. NH I > 1013 cm−2. The results are shown in Fig. 1 where we also display the jackknife errors σξ and the distributions of absorber–galaxy real (AG) and random (AR) pairs. The vertical banding in the distribution of random pairs results from an increased volume per cell at larger projected distances and a fall-off in the galaxy density at the largest radii in our sample. Observe that whilst the correlation function itself clearly peaks in the cell at the smallest separations, the peak in the absolute number of absorber–galaxy pairs is spatially offset, due to volume effects. This highlights the value of basing inferences about statistical associations on ξAG rather than on the raw pair counts. The peak ‘signal-to-noise’ ratio, ξAG/σξ, is approximately 3.
The evaluation of ξAG for various absorber subsamples is presented in Fig. 2, with the same binning scheme as that used in Fig. 1. As the lower threshold on the H i, column density is increased from 1013 to 1016 cm−2, the strength of the central peak in ξAG also increases smoothly from ≃4.5 to ≃6.7. At NH I > 1017 cm−2, the peak strength jumps dramatically to ≃15 although the formal jackknife error is substantial. For absorber samples with a lower maximum H i column density, the peak in ξAG is of lower amplitude, ≃3. For the absorbers with NH I= 1013–1015 cm−2, the peak is spatially offset from the central position. These results are summarized in Table 2 where we list the peak values of ξAG, their jackknife uncertainties and statistical significance assuming Poisson statistics. In Fig. 3, we show cross-correlation functions for the same H i column density intervals evaluated on a fine grid but with the underlying pair count fields heavily smoothed, as described in Section 2.1.
|log NH I||Peak ξAG||Peak pair real (random) countsa||Peak significanceb|
|13–19||4.4 ± 1.7||13 (2.4)||2 × 10−6|
|14–19||5.2 ± 2.5||13 (2.1)||4 × 10−7|
|15–19||6.0 ± 3.8||13 (1.9)||1 × 10−7|
|16–19||6.7 ± 5.2||9 (1.2)||4 × 10−6|
|17–19||15 ± 12||7 (0.44)||4 × 10−7|
|13–15c||3.0 ± 2.0||5 (1.3)||9 × 10−3|
|15–17||3.3 ± 1.1||6 (1.4)||3 × 10−3|
|C iv systems||11 ± 9.9||11 (0.94)||1 × 10−8|
|log NH I||Peak ξAG||Peak pair real (random) countsa||Peak significanceb|
|13–19||4.4 ± 1.7||13 (2.4)||2 × 10−6|
|14–19||5.2 ± 2.5||13 (2.1)||4 × 10−7|
|15–19||6.0 ± 3.8||13 (1.9)||1 × 10−7|
|16–19||6.7 ± 5.2||9 (1.2)||4 × 10−6|
|17–19||15 ± 12||7 (0.44)||4 × 10−7|
|13–15c||3.0 ± 2.0||5 (1.3)||9 × 10−3|
|15–17||3.3 ± 1.1||6 (1.4)||3 × 10−3|
|C iv systems||11 ± 9.9||11 (0.94)||1 × 10−8|
aNumber of real (random) absorber–galaxy pairs in cell at ξAG peak.
bPoisson probability of observing ≥ peak pair counts. These are included for completeness but substantially overestimate the significance level of any signal; the jackknife errors offer a more reliable significance measure.
cPeak not in central bin.
In Fig. 3, we also show the auto-correlation function of the galaxies in the sample. We note that whilst the peak value is comparable to other measurements of the galaxy–galaxy two-point correlation function on scales of 1–2 h−1 Mpc (The 2dF Galaxy Redshift Survey (2dFGRS); Hawkins et al. 2003), it is formally lower than the peak in ξAG for the NH I= 1017–1019 cm−2 sample, which appears surprising. However, in view of the substantial uncertainty on the peak value of ξAG for the latter subsample (see Table 2), any such differences in peak amplitude are not significant. We also note that other authors have compared the absorber–galaxy cross-correlation function to the galaxy–galaxy auto-correlation function to estimate the mass of the dark matter haloes in which the absorbers are embedded. Whilst this procedure is acceptable for Damped Lyman Alpha absorbers (which are likely to be galaxies) (e.g. Bouché et al. 2004), it is not appropriate for diffuse Lyα absorbers below NH I= 1015 cm−2. The latter are likely to arise in unbound cosmological filaments (e.g. Davé et al. 1999) so we do not pursue such calculations here. Indeed, Ryan-Weber (2006) used this method and found that weak Lyα absorbers should arise in 1014 M⊙ groups; this seems unphysical since gas in such groups would be quite hot, while the individual galaxies' interstellar media do not have nearly the cross-section to reproduce the counting statistics of weaker Lyα forest absorbers.
For C iv absorbers, Fig. 2 shows that the peak strength of ξAG is comparable to that of H i absorbers with NH I > 1016.5 cm−2. This is not surprising as in our data set the median H i column density of C iv absorbers is 1017.7 cm−2, while the median of the full Lyα absorber sample is 1014.2 cm−2. The median H i column density of Lyα absorbers with NH I > 1016.5 cm−2 is 1017.45 cm−2.
3.2 Dependence of ξAG on galaxy spectral type
Chen et al. (2005) reported that the strength of the absorber–galaxy cross-correlation may be dependent on galaxy spectral type, in the sense that a strong correlation signal is found for emission-line galaxies but not for absorption-line galaxies. Here, we investigate this issue by splitting our galaxy sample into two subsamples, according to whether the redshift assigned in Paper I was obtained by identification of a strong emission line or where no such emission line could be seen. The resulting emission- and absorption-line galaxy samples contain 406 and 225 galaxies, respectively. Of the original full galaxy sample of 685, a total of 54 galaxies could not be classified and were not included in this analysis: eight of them have spectra with an ambiguous classification, and the redshifts of 46 galaxies were obtained from the literature without associated spectral information (see Paper I for full details). The 225 absorption-line galaxies include most of the 49 very low z objects which were classified as probable stars in Paper I, but this is not critical because such objects are too low in redshift to overlap with the absorption-line sample.
These two galaxy samples were cross-correlated with the full H i absorption-line catalogue (i.e. NH I > 1013 cm−2) and the results are displayed in Fig. 4. For the emission-line sample, the form of ξAG is qualitatively similar to the result obtained with the full galaxy sample (Fig. 1), but the peak strength is now marginally (but not significantly) higher at ≃5.8, compared to 4.4 ± 1.7 for the full galaxy sample. With just the absorption-line galaxies, the central peak in ξAG is observed to be displaced from the central bin to 2–4 h−1 Mpc along the LOS, although we do not claim that this is necessarily a statistically significant finding in view of the much smaller size of the absorption-line galaxy sample. A more direct comparison with the 1D results of Chen et al. is presented in the next section.
3.3 Comparison with other works
Of the ξAG measurements mentioned in Section 1, the one mentioned by Chen et al. (2005) is the most similar to our work in its methodology, as it is based on an optical magnitude-limited galaxy redshift survey along the LOS to a single quasar (PKS 0405−123 at z= 0.5726). Here, we make a comparison between our results and their 1D measurements of ξAG as a function of galaxy type. We begin with a summary of the Chen et al. data set. Their galaxy sample comprises 482 galaxies with R≤ 20 mag and spectroscopic redshifts over a 1600 arcmin2 area within a 5 h−1 Mpc (comoving) impact parameter of the quasar LOS; the redshift distribution has a broad peak at z≃ 0.2. For their ξAG analysis, they restrict their attention to galaxies with impact parameter <1 h−1 Mpc of the LOS, of which there are 61 (46 emission-line galaxies and 15 absorption-line galaxies; no details of the spectral classification method are given). The redshift distribution of this small impact parameter subsample is skewed towards lower redshifts compared to the entire sample, with a median redshift z≃ 0.1. They claim a galaxy redshift accuracy of Δz=±0.0002, or ∼40 km s−1.
The Chen et al. absorption-line sample comprises 112 Lyα systems at redshifts 0.01 ≤z≤ 0.557 with H i column densities log NH I= 12.5–16.5 (80 per cent of the lines are at log NH I < 13.6, the regime in which our absorption-line sample is most incomplete). The bulk of the lines was derived from observations with the HST Space Telescope Imaging Spectrograph (STIS) with spectral resolution of 6.7 km s−1. The latter is substantially higher than the ∼230 km s−1 resolution of the FOS spectra from which our absorption-line sample was derived. Compared to our data set, the Chen et al. sample can thus in principle probe ξAG on (i) smaller velocity scales; (ii) for weaker absorption lines; (iii) with fewer complications arising from absorption-line blending. The first two of these differences can be handled by comparing on appropriate Δv scales and for sufficiently high NH I, but the issue of line blending in the FOS spectra is less straightforward and will be discussed later.
Mindful of the above differences between the data sets, we restrict our attention to a comparison with the Chen et al. ξAG measurements for absorption lines with log NH I= 14.0–16.5. Chen et al. computed ξAG for galaxies within 1 h−1 Mpc comoving of the LOS for the entire galaxy sample and its emission- and absorption-line galaxy subsamples, computed out to LOS velocity separations of Δv= 5000 km s−1. Converting Δv to comoving distance, we plot the Chen et al. measurements along with our results out to LOS separations of 20 h−1 Mpc in Fig. 5. Error bars on our data points were derived using jackknife resampling; Chen et al. give no details of their error bar computation.
The plots in Fig. 5 demonstrate that we do not reproduce the high peak in ξAG at the smallest separations (comoving LOS separations <2 h−1 Mpc) found by Chen et al. for the entire galaxy sample: our peak values are more than 2σ apart. Possibly related to this, we also do not substantiate their finding of much stronger ξAG for the emission-line galaxies as compared with the absorption-line galaxies. Whilst our data set is substantially larger than that of Chen et al. in terms of the numbers of galaxies (our study: 179 galaxies with impact parameters <1 h−1 Mpc overlapping with the absorption-line redshift distribution; Chen et al: 61 galaxies) and absorbers (our study: 180; Chen et al: 15), a much larger data set will be needed to address more conclusively any dependence of ξAG on galaxy type. It should also be borne in mind that the Chen et al. study is effectively at redshift z∼ 0.1 (in terms of maximal overlap between absorber and galaxy samples), whereas our study is at z∼ 0.5. Concerning the possible impact of different degrees of absorption-line blending in quasar spectra from the FOS and STIS, we refer to Penton, Stocke & Shull (2004): they smoothed their STIS/Goddard High Resolution Spectrograph (GHRS) spectra to FOS resolution and found a 15–25 per cent increase in the line density at REW > 0.24 Å (NH I≃ 1014 cm−2 for b= 30 km s−1) due to the blending of weaker lines. Since Chen et al. found that these weaker absorption lines correlate much less strongly with galaxies, this alone would suppress our peak ξAG values by 25–35 per cent relative to their measurements, going some way to explaining the differences in Fig. 5. However, the full impact on the ξAG measurements of differences between our respective galaxy and absorption-line samples merits further investigation. Finally, we note that the 1D ξAG in Fig. 5 exhibits possible minima at LOS separations ≃10 h−1 Mpc, similar to the feature in the smoothed 2D plots of Fig. 3; the physical origin of this feature is not known.
Ryan-Weber (2006) cross-correlated quasar absorption-line systems with 12.4 ≤ log NH I≤ 14.8 against a H i-selected galaxy catalogue from the H i Parkes All-Sky Survey (HIPASS). As in the Chen et al. absorption-line sample, this absorption-line sample is based on HST STIS and GHRS spectra and thus provides considerably higher velocity resolution and weak line sensitivity compared to our sample. The galaxy sample is biased towards gas-rich galaxies, including gas-rich dwarf and low surface brightness galaxies often absent from magnitude-limited optical catalogues such as ours. These differences, together with the lower redshift of her measurements (which are effectively at z≃ 0), might account for the extreme LOS elongation seen in her ξAG measurements – out to 10 h−1 Mpc comoving – which we do not reproduce. Indeed, morphological analysis of the optical counterparts to the 1000 brightest HIPASS sources confirms that the majority are late-type gas-rich galaxies (Zwaan et al. 2003). The origins of this LOS elongation are explored further in Section 4.2 with the help of smoothed particle hydrodynamical (SPH) simulations. In seeking to compare our ξAG results with those of Ryan-Weber, an important first step is to compare the ranges of galaxy mass probed by the two surveys. Ryan-Weber states that the geometric mean H i mass of galaxies contributing to absorber–galaxy pairs is log (MHI/M⊙) = 8.8 h−2, with a corresponding dark halo mass of log (M/M⊙) = 11.0 h−1[as inferred from modelling by Mo et al. (2005)]. In contrast, our galaxy sample was selected by R-band imaging and follow-up spectroscopy and is thus expected to contain a higher fraction of early-type galaxies. In Paper I (section 2.3.5), we attempted to place bounds on the rest-frame B-band absolute magnitudes of our galaxy sample: confining our attention to galaxies at redshifts 0.35 ≤z≤ 0.8 which overlap with the absorption-line sample, we find that the vast majority of these galaxies have −22 ≤MB≤−18 mag, with a median MB≃−20.5 mag. With reference to models of the conditional probability distribution of halo masses (e.g. Cooray 2005 and references therein), we expect galaxies at this median luminosity to be hosted by dark matter haloes of mass ∼1012−13h−1 M⊙.
We note that not only are our galaxies hosted by more massive haloes than those of Ryan-Weber, but also the two samples fall either side of a critical halo mass, at which the nature of gas accretion on to galaxies is thought to change. Using SPH simulations, Keres et al. (2005) find that galaxies hosted by haloes with Mhalo≤ 1011.4 M⊙ (or, equivalently, baryonic mass Mgal≤ 1010.3 M⊙) acquire most of their gas via ‘cold mode’ accretion in which gas at T < 105 K is efficiently drawn in from large distances along filaments. For more massive galaxies, the dominant mechanism is quasi-spherical accretion of hot shocked gas at the virial temperature of the halo, more akin to the classical picture outlined by White & Rees (1978). Moreover, this transition in accretion mode is a strong function of halo mass over the range of interest: from Mhalo= 1011 to 1012 M⊙, the fraction of gas accreted by the ‘cold mode’ accretion varies from >0.9 to <0.1, virtually independent of redshift. Similar results have been found by Dekel & Birnboim (2006). We do not wish to claim that this switch from cold mode filamentary accretion in Ryan-Weber's HIPASS galaxies to hot mode accretion in our galaxies can wholly explain the different degrees of LOS elongation in ξAG measurements using the two samples, but it may be a useful signpost to fruitful areas of future investigation.
4 COMPARISON WITH SPH SIMULATIONS
In this section, we use cosmological simulations to generate synthetic 2D absorber–galaxy correlation functions to compare with the observations, and to gain insight into the physical origin of features such as the ‘finger of god’ which is seen in the results of Ryan-Weber (2006).
We ran a simulation using gadget-2 (Springel & Hernquist 2003) with improvements as described in Oppenheimer & Davé (2006) in a cubic comoving volume of 64 h−1 Mpc on a side. We employed the momentum-driven outflow model ‘vzw’ as described in Oppenheimer & Davé, and a cosmology concordant with 3rd-year Wilkinson Microwave Anisotropy Probe (WMAP) results (Spergel et al. 2006): Ωm= 0.26, ΩΛ= 0.74, H0= 71 km s−1 Mpc−1, σ8= 0.75 and Ωb= 0.044. The force resolution is 5 h−1 kpc, and the mass per gas particle is 2.72 × 108 M⊙. The galaxy finding procedure is described in Finlator et al. (2006), using a minimum-resolved galaxy stellar mass of 8.7 × 109 M⊙.
The simulation volume was pierced by 1000 randomly located sightlines to simulate quasar spectra, and absorption-line profiles were fitted using AutoVP (Davé et al. 1997). Absorber–galaxy pairs were measured and tabulated from these spectra for LOS separations Δv < 1600 km s−1 and projected separations of Δr < 16 Mpc (physical). Following conversion of pair separations into comoving redshift space, these catalogues were used to create 2D absorber–galaxy correlation functions. Two such absorber–galaxy pair catalogues were created in order to compare with our observational results and those of Ryan-Weber, as described below.
4.1 Tuning the simulations to compare with the observational results
First, to compare with the observational results presented in Section 3 of this paper, the simulation output was extracted at z= 0.5 (giving a total redshift pathlength of Δz= 26.4). The pixel scale of the quasar spectra was set to 70 km s−1 and convolved with a Gaussian of 230 km s−1 FWHM in order to match the resolution of the HST FOS. H i absorption lines were selected with REW > 0.056 Å, corresponding to column densities NH I > 1013 cm−2 for b= 30 km s−1. The strength of the ionizing background radiation was increased by a factor of 4 over the Haardt & Madau (1996) value in order to normalize the dN/dz value for REW > 0.24Å lines to the HST Absorption Line Key Project results (Weymann et al. 1998). The entire resolved galaxy population was used for the comparison with a galaxy density of 0.01145 per cubic h−1 Mpc comoving above the 8.7 × 109 M⊙ baryonic mass limit. As shown by, for example, the Deep Evolutionary Exploratory Probe 2 (DEEP2) Galaxy Redshift Survey (Willmer et al. 2006), this is comparable to the space density of galaxies at this redshift in an absolute range which matches our observed galaxy sample (−22 ≤MB≤−18 mag; see Section 3).
The second absorber–galaxy pair catalogue was extracted from the simulations at redshift z= 0 (giving a total redshift pathlength of Δz= 21.3) to compare with the Ryan-Weber results. The spectral resolution of the artificial quasar sightlines was set to 8 km s−1 to mimic the higher resolution HST STIS and GHRS spectra, and H i absorption lines were extracted for REW = 0.0126–0.45 Å, corresponding to 1012.4 < NH I < 1014.8 cm−2 for b= 30 km s−1. Mimicking the HIPASS selection of galaxies in H i emission by means of a simple cut in baryonic mass is a crude approximation, but it is the only tool at our disposal with the current simulation. Somewhat arbitrarily, we use an upper baryonic mass cut-off for galaxies of 2 × 1010 M⊙. To put this figure in context, we refer to some results from Durham semi-analytic models of galaxy formation [Cedric Lacey, private communication; for the latest implementation of such models see Bower et al. (2006)]. Such models track the behaviour of gas and stars in dark matter haloes with simple physical prescriptions. At redshift z= 0, dark halo masses of 1011, 1012, 1013 and 1014h−1 M⊙ contain galaxies of total baryonic mass (hot gas, cold gas and stars) of 1010, 8.6 × 1010, 1012 and 1013 M⊙, respectively. The corresponding cold gas masses are 1.7 × 109, 6.7 × 109, 3.3 × 1010 and 2.7 × 1011 M⊙, respectively. A baryonic mass cut-off of 2 × 1010 M⊙ corresponds to a cold gas mass of 4.2 × 109 M⊙ and a dark halo mass of 2.5 × 1011h−1 M⊙. As stated in Section 3, the HIPASS galaxies contributing to Ryan-Weber's absorber–galaxy pairs have mean H i and dark halo masses of 108.8h−2 and 1011h−1 M⊙, respectively. The space density of these simulated galaxies is 0.006107 per cubic h−1 Mpc comoving.
4.2 Results: the simulated ξAG and the origin of the ‘finger of god’
The two-dimensional ξAG which results from the simulations described in Section 4.1 is displayed in Fig. 6. Plots with two types of binning/smoothing are presented, first binned coarsely to match our results in Fig. 2 (although the simulated plots extend out to slightly smaller LOS distances), and secondly using the technique of Ryan-Weber. The latter evaluates ξAG on a fine grid (0.1 × 0.1 h−1 Mpc) and then smoothes the resulting ξAG by 9 × 9 pixels. Note that this differs from the smoothing procedure we used to generate Fig. 3, where the underlying pair counts were smoothed before computing ξAG.
Comparing the simulations of Fig. 6 with our observational results in Fig. 2 and with the results of Ryan-Weber, we note that both sets of observed ξAG are much more strongly peaked at the smallest separations than the simulations, i.e. we observe much more gas at small velocity offset and/or close to the galaxies than present in the simulations. Redshift measurement errors in the observations would tend to weaken such peaks, so this cannot be the origin of the discrepancy. A related issue is the asymmetric elongation of the simulated ξAG in redshift space along the LOS, which is qualitatively similar to that found by Ryan-Weber but which appears to be absent from our measurements. Such a feature is analogous to that seen in the auto-correlation function of galaxies (see e.g. Hawkins et al. 2003), where it arises from departures from Hubble flow due to virialized motions in groups and clusters. Commonly referred to as the ‘finger of god’, the effect was seen in ξAG in an earlier generation of cosmological simulations (e.g. Davé et al. 1999) but its physical interpretation is not as clear as in the galaxy–galaxy case. Ryan-Weber (2006) interpreted it as arising from the draining of gas from low-density regions into collapsed structures. In a subsequent paper, we will address the role of galaxy outflows in causing the ‘finger of god’, and also investigate the dependence of ξAG on galaxy mass and absorption-line column density. A more ambitious goal is to simulate the full observational data set, including the selection of the galaxies in a somewhat more realistic manner, than is possible with the existing cuts in total baryonic mass.
Concluding this section, we comment on another possible explanation for the ‘finger of god’ which merits further investigation. It may be a geometrical effect which leads to a bias towards observing large numbers of galaxy–absorber pairs at small projected sky separations when a LOS is oriented directly down an IGM filament with clumpy H i absorption. At redshifts z≤ 2, simulations show that absorbing gas with NH I < 1015 cm−2 resides in a filamentary network (e.g. Davé et al. 1999), whereas at higher redshifts such gas is distributed more diffusely. This basic structure evolves little over 0 ≤z≤ 2 but absorbing material of a given column density becomes increasingly clumpy towards lower redshifts. This might partially account for the increased LOS elongation measured by Ryan-Weber at z≃ 0 compared to our measurements at z≃ 0.5, but further investigations are needed. If only a very small proportion of sightlines are fortuitously aligned with filaments, it is much more likely that such chance alignments occur in the simulations (1000 LOS; Δz∼ 25) which have a much higher redshift pathlength than our data set (16 LOS; Δz∼ 3) or that of Ryan-Weber (27 LOS; Δz∼ 1).
In summary, our measurements show that the strength of the correlation function between H i quasar absorption systems and galaxies increases with H i column density, certainly for comoving separations <0.4 h−1 Mpc (projected) and <2 h−1 Mpc (LOS) where the signal-to-noise ratio of our measurements is greatest. The peak strength of the absorber–galaxy clustering increases only slowly as the lower NH I limit is increased from 1013 to 1016 cm−2, but then jumps considerably (albeit with substantial uncertainty) above 1017 cm−2. If real, such a jump may reflect the transition from absorption within the filamentary IGM to absorption within the haloes of individual galaxies. The peak strength of the C iv absorber–galaxy cross-correlation is comparable to that of the H i absorber–galaxy signal for NH I > 1016.5 cm−2.
Our results are broadly consistent with the finding of Chen et al. (2005), based on the sightline to the quasar PKS 0405−123, that the absorber–galaxy cross-correlation strength is insensitive to H i column density in the range 1013.6≤NH I < 1016.5 cm−2, although Table 2 shows evidence for a weak increase with NH I. We find tentative but inconclusive evidence for differences in the 2D absorber–galaxy cross-correlation function for our subsamples of emission- and absorption-line galaxies, but we do not substantiate the claim of Chen et al. that the 1D cross-correlation signal is much higher for emission-line galaxies than for absorption-line galaxies. This discrepancy between our results and those of Chen et al. is not fully understood, but it may be partially ascribed to the effects of line blending in the FOS spectra compared with the higher resolution STIS quasar spectra.
Comparison was also made with the results of Ryan-Weber (2006) on the cross-correlation of H i-selected galaxies with quasar absorbers with 1012.4≤NH I < 1014.8 cm−2, who find a marked ‘finger of god’ elongation out to 10 h−1 Mpc along the sight. Such a feature appears to be absent from our measurements, but we demonstrated that there are significant differences in the characteristic mass of our respective galaxy samples which may account for such differences. The dark matter halo masses of the two samples fall either side of a critical dark halo mass of 1011.4 M⊙ (with the Ryan-Weber sample being lower in mass), at which simulations show that the nature of the dominant mode of gas accretion on to galaxies changes fundamentally from cold filamentary accretion in low-mass haloes to hot quasi-spherical accretion (Keres et al. 2005).
We also constructed synthetic absorber–galaxy two-point correlation functions using output from a 64 h−1 Mpc box SPH simulation aimed at reproducing our own observational results and those of Ryan-Weber (2006). The simulations revealed somewhat less gas at the smallest separations from galaxies than present in the observations and a strong ‘finger of god’ elongation of ξAG along the LOS. These discrepancies may originate in true deficiencies in the physics of the SPH simulations, or in a failure to accurately mimic the observed galaxy selection functions, or through some more subtle selection effect.
For future work, we suggest that effort be invested to understand the dominant contribution to the ‘finger of god’ elongation in ξAG, and the nature of the apparent transition in ξAG between NH I= 1016 and 1017 cm−2. On the theoretical side, comparison should be made with a variety SPH simulations matching the observational selection function more closely. On the observational side, it would also be valuable to conduct surveys for higher redshift galaxies around existing HST Quasar Absorption Line Key Project sightlines to ensure a better match between the redshift distributions of the absorption lines and the galaxies, and around higher resolution HST STIS quasar sightlines. It would also be valuable to survey some of these sightlines with large-format Integral Field Units to enhance sensitivity to emission-line galaxies which may be preferentially missed by our existing broad-band optical selection techniques.
This work has been partially financed by a Rolling Grant at Durham University from the UK Particle Physics and Astronomy Research Council. BTJ acknowledges partial support from NASA through HF-1045.01-93A and from the National Optical Astronomy Observatory, operated by AURA, Inc., on behalf of the US National Science Foundation. Support for RD was provided in part by NASA through grant HST-AR-10308.01-A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. We thank Bob Carswell, Cedric Lacey and Neil Crighton for useful conversations, and the anonymous referee for an extensive and constructive report.