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Astron. Astrophys. 357, 37-50 (2000)

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6. Ly[FORMULA] absorption systems

We now describe the Ly[FORMULA] forest lines observed in the spectra of HS 1216+5032 A and B. The projected separation between LOSs samples well the expected cloud sizes of hundreds of kpc if the QSO pair is real (see next subsection). However, the effective redshift path where Ly[FORMULA] lines can in principle be detected is blocked out by the broad absorption lines in the B spectrum, so the line samples will be small.

6.1. Lensed or physical pair?

The nature of the double images in HS 1216+5032 is not clearly established yet. Maybe the strongest arguments favoring HS 1216+5032 AB as a physical-pair instead of a gravitational lens origin are: (1) BALs are observed only in the spectrum of the B image; 2(2) no extended, luminous object is detected between (or even close to) the QSO images down to [FORMULA]; and (3) gravitationally lensed QSO pairs normally have image separations [FORMULA] (e.g., Kochanek et al. 1999). In addition, the absence of a trend for equivalent widths of intervening Ly[FORMULA] lines common to both spectra to become similar at redshifts closer to [FORMULA] (see Fig. 4 and Table 3) also argues for a physical-pair; however, this argument is weak as the sample of common lines is too small. Unfortunately, for reasons given in Sect. 2.2, it is not possible to establish whether there are differences between A and B in the emission line redshifts and line shapes in the spectral region covered by the FOS.


[TABLE]

Table 3. Ly[FORMULA] Lines with [FORMULA] in HS 1216+5032 A and B.
Notes:
1 Three sigma detection limits in B [FORMULA](A).
2 Spectral region covered by the BAL troughs in B.
3 CIV associated.
4 Maybe SIV [FORMULA]944 BAL.
5 Absorption feature present in B at low significance.
6 Associated system.


The intriguing point here is that two [FORMULA] Ly[FORMULA] systems are detected in both spectra at almost identical redshifts to within [FORMULA] km s-1 (see Sect. 6.6 for more details). Under the physical-pair hypothesis, these absorbers should extend over transverse scales greater than [FORMULA]kpc. If, on the other hand, HS 1216+5032 AB is a gravitationally lensed pair, the detection of these systems in both spectra can easily be explained by the fact that the separation between light paths approaches zero.

In consequence, the gravitational lens nature of HS 1216+5032 cannot be yet ruled out. Let us note that in a simple lens geometry the virial mass implied by the velocity span of the CIV absorbers at [FORMULA] (see Sect. 4.1) is consistent with the deflector mass required to produce an angular separation between QSO images of [FORMULA]. In such a model the separation between light paths at the source position is derived to be [FORMULA]". Therefore, confirmation of HS 1216+5032 as a gravitationally lensed QSO would have dramatic consequences for our understanding of the BAL phenomenon. As pointed out by Hagen et al. (1996), if HS 1216+5032 AB were indeed the mirror images of one unique QSO, the coverage fraction of BAL clouds would have to be very small. Incomplete coverage of the continuum source or the BLR in BAL clouds have been confirmed using high-resolution spectra (Hamann et al. 1997; Barlow & Sargent 1997). In fact, the cloud sizes derived from BAL variability could be [FORMULA] times smaller than the distances to the source derived from photoionization models (Hamann et al. 1995), implying subtended angles not much larger than [FORMULA]. Therefore, the scenario in which only one light path crosses the BAL clouds is not unrealistic, and the non-BAL spectrum of HS 1216+5032 A can also be considered if the QSO pair is lensed. 3

In summary, there are reasons to believe that HS 1216+5032 is a binary QSO, but a gravitational lens origin of the double images cannot yet be excluded. A definitive assessment of this issue must await medium resolution optical spectra to better derive emission redshifts and to establish differences in the continuum or emission lines. Alternatively, deep infrared or radio observations would help determining the nature of the double QSO images. The non-detection of the lensing galaxy/cluster would be a strong proof for the binary QSO hypothesis, since wide separation ([FORMULA]) "dark lenses" enter in conflict with current models of structure formation (Kochanek et al. 1999), which predict few wide separation gravitational lenses (e.g., Kochanek 1995).

Throughout this section we will assume that HS 1216+5032 AB is a physical pair. The proper separation [FORMULA] between LOSs obeys then the relation [FORMULA], where [FORMULA] is the angular separation between the A and B QSO images, and [FORMULA] is the angular-diameter distance between the observer and a cloud at redshift z. For the redshift range of interest [FORMULA] [FORMULA] kpc.

6.2. Line list

Table 3 lists Ly[FORMULA] lines detected at the [FORMULA] level in HS 1216+5032 A and B. Fig. 3 shows [FORMULA] detection thresholds as a function of redshift. Out of 36 lines in the spectrum of A, a total of 23 lines within [FORMULA] to 1.43 have [FORMULA] Å. This redshift interval excludes lines within [FORMULA] km s-1 from the QSO redshift to avoid the "proximity effect" (Bechtold et al. 1994). The derived number density is [FORMULA] at [FORMULA], in very good agreement with the results of the HST Key Project (Weymann et al. 1998). The scarce sample of lines in B is clearly explained by the shorter redshift path allowed by the BAL profiles.

[FIGURE] Fig. 3. Three [FORMULA] rest-frame detection limits of Ly[FORMULA] lines in HS 1216+5032 A (thick line) and B.

6.3. Definition of line samples

To define the number of coincidences and anti-coincidences we have selected from all 36 Ly[FORMULA] lines observed in A (the spectrum with better signal-to-noise) those ones (1) at [FORMULA]; (2) not associated with metal lines; (3) at wavelengths not covered by the BAL troughs in B; and (4) at wavelengths where [FORMULA] detection limits in B are lower than the measured equivalent width of the line in A. Lines in B that had [FORMULA] and fulfilled criteria (1) to (3) were also selected. In some cases, lines in A have a corresponding absorption feature at the same wavelength in B, but at a too low significance level to unambiguously designate the line pair as a coincidence. These lines in A were excluded (A26, A36, A44). Notice that criterion (3) automatically prevents comparing line equivalent widths for which the uncertainties introduced by the placement of the B continuum are large.

The final sample of Ly[FORMULA] lines suitable for this study is composed of [FORMULA] redshift systems within [FORMULA], a range not much smaller than the one allowed by conditions (1) to (4). Out of this number, [FORMULA] systems show Ly[FORMULA] lines in both spectra, and [FORMULA] lines are detected in only one spectrum. The rest-frame equivalent widths range from 0.14 to 0.76 Å in A, and from 0.23 to 1.16 Å in B. This sample is hereafter called "full sample".

Coincident lines are shown in Fig. 4, where the thick line represents the flux of A and the zero velocity point corresponds to the redshift of the A line. Only the first six panels show lines in the "full sample"; the remaining lines arise in Ly[FORMULA] clouds likely to be influenced by the QSO flux. All coincident lines are separated by less than 100 km s-1. Anti-coincident lines are all uniquely defined, as there are no corresponding lines in the other spectrum within several hundred km s-1.

[FIGURE] Fig. 4. Ly[FORMULA] lines present both in HS 1216+5032 A and B, with [FORMULA], [FORMULA] km s-1, and no metals associated. These lines lie at wavelengths not covered by the BAL troughs in B. The right number indicates to which sample the line pair belongs. The three bottom panels show lines that fall within [FORMULA] km s-1 from the QSO redshift. The thick line represents the flux of A. The abscissa is in km s-1 and the zero-velocity point is defined by the redshift of each A line.

However, there are two exceptions that must be pointed out. The first one is line 29 in B, separated by 198 km s-1 from the nearest Ly[FORMULA] line in A (37). These lines in A and B have been counted as anti-coincidences, though we are suspicious of this interpretation as the line profiles suggest line B29 is blended with an absorption feature seen in both spectra. The second is another of the anti-coincidences, line B50, which could alternatively be identified with MgI at [FORMULA]. These cases will introduce unavoidable uncertainties in the results presented here. Let us recall that the exclusion of any one line from the samples would lead to significantly different results for [FORMULA]. This illustrates the real uncertainties dominating simulations with such a small number of observed lines. Moreover, the samples are limited by the large redshift path blocked out by the BAL troughs in B, so there must be a considerable loss of information.

A line significance level of 5 for lines in A has been chosen to perform the likelihood analysis described in the next subsection. This selection automatically excludes two of the redshift systems in the full sample and defines the following sub-samples:

  1. Strong-line sample (sample 1): lines for which SNR(A) [FORMULA], SNR(B) [FORMULA], and [FORMULA] Å. This selection yields [FORMULA] coincidences and [FORMULA] anti-coincidences.

  2. Strong+weak line sample (sample 2): same as previous sample but with [FORMULA] Å. This selection yields [FORMULA] and [FORMULA].

6.4. Maximum likelihood analysis

In the following we discuss a likelihood analysis on cloud sizes in front of HS 1216+5032. The technique is based on the definition of a likelihood function [FORMULA] that gives the probability of getting the observed number of coincidences and anti-coincidences. Evidently, such a function must depend on the shape of the absorber. Here we concentrate on two possible cloud geometries for which [FORMULA] can be derived analytically: spheres and cylinders.

For coherent spherical clouds, the probability that one cloud at redshift z is intersected by one LOS is given by McGill (1990) as:

[EQUATION]

where [FORMULA] and [FORMULA] is the cloud radius. The samples consider only redshifts where at least one LOS intersects a cloud (otherwise one should make assumptions on the cloud distribution along the LOS). Therefore, one must compute the probability that, given that a line appears in one spectrum, a line will appear in the other spectrum. This probability is given by Dinshaw et al. (1997) as:

[EQUATION]

Finally, the probability of getting the observed number of coincidences and anti-coincidences is given by the product

[EQUATION]

where the indexes i and j number the coincidences and anti-coincidences, respectively. Note that if there is at least one anti-coincidence, then [FORMULA] has a maximum value. Otherwise it grows monotonically.

The solid curve in Fig. 6 shows the results of the likelihood function [FORMULA] normalized to its peak intensity for the various samples. The figure also shows the cumulative distribution of [FORMULA]. The estimated [FORMULA] limits on cloud diameters for HS 1216+5032 - derived from the cumulative distribution - are listed in Table 4. The peak intensity of [FORMULA] is used to find the most probably radii, i.e., 96 [FORMULA] kpc for the strong line sample and 128 [FORMULA] kpc for the strong+weak line sample. From the cumulative distribution, the respective median values are 145 and 173 [FORMULA] kpc. In both cases, the derived sizes are larger if weaker lines are used. This result provides evidence that Ly[FORMULA] clouds must have a smooth density distribution.

[FIGURE] Fig. 5. Ly[FORMULA] lines present either in HS 1216+5032 A or B, with [FORMULA], [FORMULA] km s-1, and no metals associated. These lines lie at wavelengths not covered by the BAL troughs in B. The right number indicates to which sample the line pair belongs. The abscissa is in km s-1 and the zero-velocity point is defined by the redshift of each present line.

[FIGURE] Fig. 6. Likelihood function [FORMULA] normalized to its peak intensity vs. cloud radius [FORMULA], and cumulative distribution for spherical (solid line) and cylindric absorbers.


[TABLE]

Table 4. Diameter D of spherical and cylindric Ly[FORMULA] clouds in HS 1216+5032 in the redshift interval [FORMULA] as derived from the likelihood function defined in (3). Values are in kpc and represent [FORMULA] limits. [FORMULA] km s-1 Mpc-1 and [FORMULA].
Notes:
Sample 1: Lines with [FORMULA] Å; 2 coincidences, 4 anti-coincidences.
Sample 2: Lines with [FORMULA] Å; 4 coincidences, 5 anti-coincidences.
Sample 3: Full sample: 6 coincidences, 5 anti-coincidences.


In a second model, let us suppose that Ly[FORMULA] lines occur in filamentary structures lying perpendicular to the LOSs. Such structures can be idealized as cylinders with a radius-to-length ratio [FORMULA]. For cylindric clouds, the probability that one LOS intersects a cloud at redshift z given that the other LOS already does, reads (A. Smette, private communication):

[EQUATION]

where [FORMULA] and [FORMULA] is the radius of the cylinder. The dotted curve in Fig. 6 shows the results of the likelihood function [FORMULA] normalized to its peak intensity and the cumulative distribution for the various samples. Most probably cylinder radii are 49, 65, and 85 [FORMULA] kpc for the strong, strong+weak and full line samples, respectively. The respective median values are 70, 87 and 115 [FORMULA] kpc. Two sigma bounds are displayed in Table 4. Again, the derived sizes are larger if weaker lines are used , providing evidence that the density distribution in Ly[FORMULA] clouds must be smooth (see, e.g., Monier et al. 1999). These size estimates are almost 50% lower than for spherical absorbers. This can be explained by the fact that, in general, elongated structures can more easily reproduce the observed number of coincidences for a given radius than a sphere; in fact, the probability [FORMULA] for spherical absorbers vanishes for [FORMULA], while for cylinders [FORMULA] for all nonzero values of [FORMULA]. The lengths of such structures are much larger than these values, but undefined in the model.

6.5. Equivalent widths

The sample of Ly[FORMULA] lines common to both spectra gives model-independent information about the size scales of the absorbers. Fig. 7 shows the rest-frame equivalent widths of lines common to both spectra and their [FORMULA] errors, where the dashed straight line has a slope of unity. Only lines without associated metal lines are included. Note that this selection yields line-pairs with [FORMULA] Å, so the influence of uncertainties in the continuum placement (e.g. due to the BAL troughs or to spectral regions with high noise level) over the equivalent-width estimates is minimized. We have included one line pair within 3 000 km s-1 from the QSO's redshift (A52,B49) but not the "associated system". The dotted crosses represent line pairs for which the B line has [FORMULA], i.e., those ones labeled with footnote 5 in Table 3. Additionally, to illustrate the significance of the non-detections we have also included lines detected in only one spectrum, plotted against the corresponding [FORMULA] detection limit in the other spectrum.

[FIGURE] Fig. 7. Rest-frame equivalent widths of Ly[FORMULA] lines common to both spectra, with [FORMULA], [FORMULA] km s-1, and no metal lines associated. Dotted crosses represent line pairs with [FORMULA]. The "associated system" has not been considered. Lines detected in only one spectrum are also shown, with upper limits representing [FORMULA] detection limits in the other spectrum.

Most of the coincident lines are stronger in the B spectrum, which is explained by the difficulty in detecting lines in B (an additional consequence of this is that most anti-coincidences are lines in B). It can be seen that there are some significant deviations from [FORMULA], even excluding the line pair within 3 000 km s-1. For the latter such deviation would be expected, since the QSOs themselves might be an important ionizing agent in clouds next to the QSOs. 4

The equivalent width differences [FORMULA] show no correlation with [FORMULA]. Instead, [FORMULA] and max[FORMULA] seem to be correlated (see Fig. 8), with larger equivalent width differences for larger equivalent widths (e.g. Fang et al. 1996). Both effects, although not statistically significant, suggest coherent structures, i.e., no "cloudlets" at similar redshifts (Charlton et al. 1995). In conclusion, LOS A and B must sample coherent clouds showing small - but otherwise significant - density gradients on spatial scales of [FORMULA]kpc, the linear separation between LOSs in this redshift range.

[FIGURE] Fig. 8. Absolute value of rest-frame equivalent width differences (Å) vs. [FORMULA] of Ly[FORMULA] lines with [FORMULA], [FORMULA] km s-1, and no metal lines associated. The "associated system" has not been considered.

6.6. The [FORMULA] Ly[FORMULA] systems in HS 1216+5032 A and B

Two [FORMULA] Ly[FORMULA] systems are observed in the spectra of both HS 1216+5032 A and B, through the partially resolved Ly[FORMULA] lines A53, A54, A55, and B51 and B52 (see Fig. 4). The lines in A and B differ by [FORMULA] km s-1 and [FORMULA] km s-1. The system in A is blueshifted by 122 km s-1 relative to [FORMULA], while the system in B is redshifted by 280 km s-1 relative to [FORMULA] (but see Sect. 2.2). Line A55 has no clear counterpart in B. No metal lines are found associated with these systems. The total equivalent width of the A lines is larger than in B by a factor of 2.1.

The absence of highly ionized species such as NV and OVI suggests that these systems are probably not physically associated with the QSOs (e.g., Turnshek 1984; Petitjean et al. 1994). Furthermore, the small velocity differences between lines in A and B, and the fact that both systems have two line components well correlated in redshift, strongly suggest they arise in the same absorber (see also Petitjean et al. 1998; Shaver & Robertson 1983). If this is true, the different Ly[FORMULA] line strengths between A and B imply either characteristic transverse sizes of [FORMULA]kpc or maybe even larger clouds with ionization conditions that change on such scales. The size scales are compatible with the idea that these systems arise, for example, in the very extended halo of an intervening galaxy (Weymann et al. 1979), or in the intra-group gas of the QSO host galaxies.

If the radiation field of the QSOs is the main ionization source in the clouds giving rise to these systems (assuming the QSO pair is real), then the systems in B should be less ionized than the A ones. This is because QSO A is intrinsically more luminous than B in the ionizing continuum. Consequently, the different line strengths in A and B can also be explained if the LOSs cross regions of similar density, with LOS B probing regions with more neutral gas. Of course, the latter case does not rule out the intervening nature of these systems.

6.7. Discussion

Fang et al. (1996) have pointed out that there seems to be a trend of larger estimated cloud sizes with increasing LOS separation S (see their Fig. 5). If such a trend were real, it would imply that the scenario of uniform-sized spherical clouds is too idealized. Their data, however, are insufficient to discern whether the effect is due to non-uniform cloud size or simply non-spherical cloud geometry. The results presented in our work (slightly modified by defining a sample of lines with [FORMULA] Å to be consistent with these authors) fit this tendency well because they add a new measurement of relatively small cloud sizes at small LOS separation. We note, however, that D'Odorico et al. (1998), who use a larger database and an improved statistical approach, find no correlation between cloud size and LOS separation. Clearly, more QSO pairs are needed that span a range in LOS separations to confirm or discard the size/separation correlation.

Here we propose that the notion of a single population of uniform-sized clouds must be revised. In fact, if Ly[FORMULA] clouds span a range of sizes between, say, a few hundred kpc to a few Mpc, then LOSs to QSO pairs with arcminute separations would be crossing not only huge and coherent structures, but also smaller clouds correlated in redshift. Further evidence for a more complicated scenario than usually assumed comes from cosmological hydrodynamic simulations made for [FORMULA], which show entities of non-uniform sizes grouped along filamentary structures (e.g., Cen & Simcoe 1997). However, we recall that the situation at lower redshift can be different if such structures do evolve in size.

Size evolution of Ly[FORMULA] absorbers has not yet been observed, in part because the number of adjacent QSOs with suitable angular separations is not statistically significant, but also due to the scarce number of observations at low redshift. In particular, the present data on HS 1216+5032 ([FORMULA]) do not confirm the suggestion (Fang et al. 1996; Dinshaw et al. 1998) that cloud sizes increase with decreasing redshift. This result is in variance with the findings by D'Odorico et al. (1998).

Assuming that the Ly[FORMULA] absorbers are filamentary structures - modelled as cylinders of infinite length - lying perpendicular to the LOSs, our likelihood analysis leads to almost [FORMULA] smaller transverse dimensions than for spherical clouds. Unfortunately, the method presented here is not capable of distinguishing between cylinders and spheres. Moreover, the information provided by two LOSs might be insufficient to make such a distinction possible, so one should use triply imaged QSOs (Crotts & Fang 1998) or, even better, QSO groups (Monier et al. 1999). It is worth saying, however, that flattened structures are more able to simultaneously reproduce the requirements of neutral gas density from photoionization models and the transverse scale lengths derived from double LOSs than spherical absorbers do. Such photoionization models lead to structures with thickness-to-length ratios of [FORMULA] (Rauch & Haehnelt 1995). Indeed, hydrodynamical simulations in the context of hierarchical structure formation have shown that at [FORMULA], high density gas regions (producing [FORMULA] Å Ly[FORMULA] absorption lines) are connected by filamentary and sheet-like structures roughly [FORMULA] times less dense than the embedded condensations. The filaments seem to evolve slowly and still fill the Universe at [FORMULA] (Davé et al. 1999; Riediger et al. 1998), giving rise to the majority of strong Ly[FORMULA] lines. If this picture is correct, the requirement of different cloud populations might not be necessary to explain current observations.

New high-resolution ultraviolet observations of QSO pairs are needed. Despite technical difficulties (close QSO pairs tend to have such different observed fluxes that high dispersion spectroscopy normally leads to at least one spectrum with high noise levels) they should improve considerably our knowledge of the Ly[FORMULA]-cloud geometry by (1) analyzing absorbers that produce only weak ([FORMULA] Å) lines, i.e., those surely not associated with low-brightness galaxies, and (2) testing models that consider column density distributions.

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Online publication: May 3, 2000
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