In the previous section, we noted that, on scales of 30 kpc/h < rp <
100 kpc/h, there seem to be more galaxies around bright absorbing QSOs than
around weak absorbing QSOs. Indeed, over the noted range bright absorbing QSOs have almost twice as many galaxies around them as do faint absorbing QSOs. This is true not only for the full sample split in half by absorbing QSO apparent magnitude, but also of the weak and strong sub-samples after they had been similarly split. The presence of the same phenomenon in all three plots indicates some effect which we have not yet taken into account, and which does not originate in potential differences between weak and strong absorption systems. In this section, we investigate this effect.
Figures 4.10 and 4.11 were constructed by taking the ratio of faint to
our absorber sample, though, this corresponds to a range of angular separations. If there is some angular scale over which bright QSOs tend to be surrounded by more galaxies than faint QSOs, it is being smeared by the redshift distribution of absorbers in our previous figures. To more cleanly investigate whether bright QSOs are surrounded by more galaxies on some scale, we should repeat our analysis using angular separations. In what follows, we plot angular scales only out to 1 arcminute, as this is approximately the range in angle over which our sample is complete. Recall from Section 2.2 that we selected only those galaxies whose projected comoving
separation from the QSO fell within the range 19.3kpc/h≤rp ≤880kpc/h, because
that was the range of separations accessible over the entire redshift range of the
sample. For the highest redshift of our sample (z = 0.8197), a projected comoving
separation of 880 kpc/h corresponds to an angular separation of 91.3 arcseconds,
or 1.52 arcminutes. Beyond this angular scale, only the lowest redshift absorbers contribute.
To begin our investigation, we once again split the full absorber sample in half by absorbing QSO apparent magnitude. Recall that the split occurred at
mr = 18.86. We now count the number of galaxies whose angular separations from
the central QSO lie within the range θ−∆θ ≤ θ ≤ θ+ ∆θ. In the top panel of
Figure 4.13, we plot the raw counts per bin measured from the faint and bright sub- samples. Notice that, on scales less than 0.06 arcminutes (or 3.6 arcseconds), there are clearly more galaxies around faint QSOs. This is likely due to QSO glare, as we determined in Section 4.3.2; note that 3.6 arcseconds corresponds to a projected
comoving separation of 27kpc/hat the mean redshift of our sample (z= 0.598). On
angular scales 0.08 ≤θ≤ 0.12 arcminutes, though, there are clearly more galaxies
around bright QSOS. This is more plainly seen when we take the ratio of bright
to faint galaxy counts per θbin and plot them in the bottom panel of Figure 4.13.
approximately 1.7 times as many galaxies around them as do faint QSOs.
To more carefully account for the different mean apparent magnitudes of weak and strong absorbing QSOs, we repeat our tactic of splitting the full sample in half by equivalent width (at an equivalent width of 1.28˚A) and then by absorbing
QSO apparent magnitude. Recall from Section 4.3.2 that the split occurs at mr =
18.75 for the weak sub-sample and mr= 18.96 for the bright one. The top left and
bottom left panels of Figure 4.14 show the galaxy counts per θ bin around bright
(orange histogram) and faint (purple histogram) QSOs for each sub-sample. The counts around weak sub-sample absorbing QSOs are plotted in the top left, whereas the counts around strong sub-sample absorbing QSOs are plotted in the bottom left. Turning our attention first to the strong sub-sample, we clearly see more galaxies near faint QSOs within 0.06 arcminutes (3.6 arcseconds). No such excess is noted for the weak sub-sample. Indeed, only 1 galaxy is found within 0.05 arcminutes (3 arcseconds) of a weak absorber. In both plots, though, we see an excess of galaxies
around bright QSOs over scales 0.08≤θ≤0.12 arcminutes. The excess is somewhat
more noticeable for the weak sub-sample than it is for the strong sub-sample. In the top right and bottom right panels of Figure 4.14, we plot the ratio of bright to faint
galaxy counts perθbin for the weak and strong sub-samples, respectively. Over the
range 0.08≤θ≤0.12 arcminutes, we see that bright QSOs in the weak sub-sample
have roughly 1.7 as many galaxies around them, compared to the faint QSOs; for the strong sub-sample, bright QSOs have about 1.3 times as many galaxies around them as do the faint QSOs. The presence of a similar excess over the same range for both the weak and strong sub-samples indicates that, whatever the cause, it does not likely originate in differences between the two absorbing populations.
We now check to see if a similar phenomenon is seen in the reference sample. Again, we split it in half according to reference QSO apparent magnitude;
Figure 4.13 Left: Absorbing QSO–galaxy pair counts, as a function ofθ, for faint QSOs (purple histogram) and bright QSOs (orange histogram). Right: Ratio of bright absorbing QSO to faint absorbing QSO pair counts as a function of theta.
Figure 4.14 Top left: Absorbing QSO–galaxy pair counts, as a function of θ, for faint QSOs (purple histogram) and bright QSOs (orange histogram) in the weak sub-sample. Bottom left: Absorbing QSO–galaxy pair counts, as a function ofθ, for faint QSOs (purple histogram) and bright QSOs (orange histogram) in the strong sub-sample. Right: Ratio of bright absorbing QSO to faint absorbing QSO pair counts as a function of theta, plotted for the weak sub-sample (top) and the strong sub-sample (bottom).
counts per θ bin are measured for the bright and faint sub-samples and plotted in the top panel of Figure 4.15. Again, the effects of QSO glare are seen at the smallest scales (though note that faint QSOs have only slightly more galaxies near them than
do bright QSOs). Looking at the range 0.8 ≤θ ≤0.12 arcminutes, over which we
saw a clear excess of galaxies near bright QSOs for the absorbing sample, we note
that only for the bin at θ ≈ 0.9 arcminutes do we see such a clear excess in the
reference sample. Over the rest of the range, the counts around bright and faint QSOs are consistent with each other. This is more obvious in the bottom panel of Figure 4.15, wherein we plot the ratio of bright to faint pair counts. For the most part, the ratio is consistent with one over scales of 0.8≤θ≤0.12 arcminutes. These findings indicate that the reason bright absorbing QSOs have more galaxies around them than do faint absorbing QSOs must lie in the presence of a galaxy along the line of sight, for it is the one thing that differs between the absorbing and reference QSOs. If it did not, we would observe the same effect for reference QSOs; however, we find no evidence of bright QSOs having more galaxies around them than faint QSOs over the noted range in our reference sample.
One possible explanation of the trends we have seen is weak gravitational lensing of the background QSOs. The cosmic magnification of background QSOs
by foreground galaxies has been detected by Scranton et al. (2005), who found an
8σ detection of magnification on scales ranging from 0.6–10 Mpc/h using 200,000
QSOs and 13,000,000 galaxies. If the absorbing QSOs are being lensed by the
foreground absorber host galaxies, we might see a similar effect–although with much
less significance. Lundgren et al. (2009) measured the QSO–LRG angular cross-
correlation function over angular scales of 0.7–10 arcminutes to determine if weak lensing was affecting their measurements. They find that this function is strongly
dependent on QSOi−band magnitude. On scales of≈0.1 arcminutes, they find that
Figure 4.15 Left: Reference QSO–galaxy pair counts, as a function of θ, for faint QSOs (purple histogram) and bright QSOs (orange histogram). Right: Ratio of bright reference QSO to faint reference QSO pair counts as a function of theta.
The ratio of bright to faint galaxy counts around our absorbing QSOs is slightly smaller than 2 for our sample, but we do notice a similar overdensity of galaxies near
bright QSOs. Further, the range over which we detect this excess–0.8 ≤ θ ≤ 0.12
arcminutes–is roughly the same range over which the QSO–LRG angular cross-
correlation function measured by Lundgren et al. (2009) differs the most between
QSO apparent magnitude bins. Thus it seems as though weak gravitational lensing of absorbing QSOs by the Mg II absorber host galaxies is a plausible explanation for the overdensity we see. We strongly caution that this is not an unambiguous lensing detection; there is a possibility that some of the high redshift absorbers may be associated with the lowest redshift QSOs (to which we shall return below), and we have not done a full correlation function analysis with a significant number of systems. We also have made no attempt to correct absorbing QSO magnitudes for reddening due to the intervening Mg II absorber host galaxy. A more robust measurement would be an interesting subject for future work. Nonetheless, weak lensing provides a simple, plausible explanation for the overdensity of galaxies near bright QSOs that we see. In passing, we note that we did not detect a cosmic magnification signal from our reference sample. This is likely because the effect is
small, and we do not have a large sample of reference QSOs; Scranton et al.(2005)
used ∼ 200,000 QSOs in their measurement of cosmic magnification, whereas our
reference sample only contains 5640.