Searching for High-Redshift Galaxies:
Lensing Clusters vs Field Searches
Over the past few years there has been extensive discussion regarding the best approach for finding large samples of high redshift galaxies and determining their overall properties.
Highly-magnified high redshift galaxies clearly are a unique product of lensing cluster observations. The source plane resolution in HST images of strong lensing clusters approaches (or exceeds) that expected from 30 m class telescopes with adaptive optics. While valuable pathfinders to the detailed structure of high redshift galaxies, such sources are extremely rare. Lensing clusters can also, in principle, enable the detection of highly-magnified, very low luminosity sources. These are potentially very valuable since the absolute magnitude levels being sampled through such sources are beyond even what can be done in the Hubble Ultra Deep Field (HUDF).
However, over the years we have been struck by the very small numbers of highly-magnified high redshift z~6-7 galaxies that have been found behind lensing clusters, both in our own searches behind lensing clusters, and in the searches of others reported in the literature. Furthermore, the actual detection rate appeared to be far less than what has been claimed from models, as highlighted in presentations at meetings and proposals for telescope time, suggesting to us that the models were not fully representative of real clusters.
In our first major paper on this topic we discussed aspects of the challenge of using clusters.
z ~ 7-10 Galaxies Behind Lensing Clusters: Contrast with Field Search Results, Bouwens, R. J., Illingworth, G. D., Bradley, L. D., Ford, H., Franx, M., Zheng, W., Broadhurst, T., Coe, D., Jee, M. J., ApJ, 690, 1764-1771, 2009. The abstract is given below.
Given our disappointment with what we recovered at z~7-10, we recently tried an experiment whereby we searched a sample of clusters (6 "classical" large strongly-lensing clusters) for z~4-6 galaxies. The volume density of such galaxies from field searches as a function of luminosity is extremely well understood to very faint levels from the HUDF data, and the field samples are now very large (over 5000 galaxies!). A comparison between field and lensing cluster searches at these redshifts would therefore be very instructive.
What we found was quite remarkable. There was a striking paucity of detections in the lensing clusters. In these 6 clusters, with over 120 orbits of HST ACS observations we found just 11 z~4, 5 z~5, 3 z~6 highly-magnified (magnification >7) galaxies. The same number of orbits in a typical HUDF depth observation in field regions (reaching similar luminosities to the cluster probe) would have returned about 200 z~4 galaxies, 50 z~5 galaxies, and ~45 z~6 galaxies (Bouwens et al. 2007). Per orbit one finds ~0.09 z~4, 0.04 z~5 and 0.03 z~6 galaxies behind lensing clusters, compared to 1.7 z~4, ~0.4 z~5 and ~0.4 z~6 galaxies in field searches. Thus cluster searches appear to be intrinsically far less cost-effective (per orbit of HST time) at finding high redshift galaxies. And this reduced effectiveness is by a large factor (over an order of magnitude!).
Sample of 20 Highly Magnified (>7x magnification) z~4-6 Galaxies
Images of all the highly magnified (>7) z~4-6 galaxies found behind 6 lensing clusters. In total, 11 z~4, 5 z~5, and 3 z~6 candidates are found, most of which are known from specific papers in the literature, i.e., Franx et al. (1997), Ellis et al. (2001), Kneib et al. (2004). Two of the z~5 V-dropout candidates are images of the same candidate (from Ellis et al. 2001). We were surprised at how few highly magnified z~4-6 galaxies were found behind lensing clusters, given the predictions by a number of teams.
Credit:Bouwens
It is a fascinating question as to why such a difference exists but a couple of thoughts come to mind (but this clearly requires some serious assessment and modelling to resolve) — e.g., (i) the foreground galaxies make it harder to detect faint sources; and (ii) the faint end slope of the luminosity functions is not as steep as needed to fall in the regime where the reduced source plane volume due to the lensing is offset by having many more fainter sources.
| Region | Galaxy Candidates per 400 orbits (HUDF) |
||
| z~4 | z~5 | z~6 | |
| Clustera | 36 |
16 | 12 |
| Ultra-Deep Fieldb | 680 | 160 | 160 |
aSources identified with model magnification factors >= 7 in HST observations reaching depths of ~27 AB mag
bHST Observations that reach depths of ~29.5-30.0 AB mag
In addition, there is another problem. A key requirement of these searches is establishing the volume density of high redshift sources. This is non-trivial in the field, but it is routinely done through simulations of the detection efficiency as a function of wavelength (redshift) and the volume density can be established to typically <10-15% given adequate numbers of sources (and adequate volume to limit cosmic variance).
However, lensing clusters present us with another challenge. The magnification maps are very model dependent and the magnification uncertainty remains a major factor. The differences between the magnification maps in the same cluster from different teams can be factors >2-3. Such errors are much larger than is typically quoted by any team from internal estimates. These very large, external estimates of the magnification uncertainty suggests that further work is badly needed to understand and to establish reliable and consistent magnification maps.
The problem can be seen in these two figures where we compare magnifications for the well-studied clusters Abell 1689 and CL0024:
Abell 1689
(A) A z-band image of Abell 1689 with the high magnification regions (magnification factors µ >40) for three different lensing models shaded in different colors (the cyan regions are for the Limousin et al. 2006 model, the magenta regions are for the Halkola et al. 2006 ENFW (elliptical Navarro, Frenk & White 1997) model, the grey curves are for the Broadhurst et al. [2008, in prep] model, and the yellow curves are for the D. Coe et al. [2009, in prep] model). (B) The median 1σ differences (quantified in terms of the logarithm) between the magnification factors derived by Limousin et al. (2008) for Abell 1689 and those derived from four other lensing models (lines) versus magnification factor as derived by Limousin et al. (2007). The four other lensing models are the non-singular isothermal sphere model of Halkola et al. (2006: solid black line), the ENFW model of Halkola et al. (2006: dotted blue line), the Broadhurst et al. (2010, in prep: dashed green line) model, and the Coe et al. (2009, in prep: dashed magenta line) LensPerfect model. The thick black and dotted blue line shows the median logarithmic differences between the Limousin et al. (2007) model and the Halkola non-singular isothermal sphere model and ENFW models, respectively. This diagram allows us to estimate how model dependent the magnification factor is as a function of this magnification factor. For magnification factors of ∼10, the small median 1σ dispersion is 0.15 dex (factor of 1.4) for the Halkola et al. (2006) non-singular isothermal sphere model,
but is typically much larger (e.g., 0.35 dex: factor of 2.2). At magnification factors of 100 and 500, the 1σ dispersion is ~1 dex (a factor of 10). eClearly, the model magnification factors show the greatest dispersion with respect to other models precisely in those regions where the magnification factors are the highest!
Credit:Bouwens
CL 0024
Similar to the figure on Abell 1689, but for CL0024. In the top panel (A), the shaded regions show the high magnification regions (magnification factors µ >40) predicted for three different lensing models (the cyan regions are for the Kneib et al. 2003 model, the magenta regions are for the Zitrin et al. 2009 model, and the yellow curves are for the Jee et al. 2007 model). In the lower panel (B), we plot the median logarithmic differences between the Zitrin et al. (2009) lensing model and that of Kneib et al. (2003: solid black line).
Credit:Bouwens
This will be discussed more fully in an upcoming paper. (Bouwens, Illingworth et al, to be submitted to ApJ, 2010).
In summary, it is becoming clear that using lensing clusters to find samples of faint high redshift galaxies is a very inefficient approach compared to field studies (by over an order of magnitude) and that even their value for finding very faint lower luminosity sources will not be realized without further improvements in the models to remove the very large inconsistencies seen in the current magnification maps of any individual cluster.
Abstract from our first published paper discussing this issue:
"We conduct a search for z >~ 7 dropout galaxies behind 11 massive lensing clusters using 21 arcmin**2 of deep Hubble Space Telescope NICMOS, ACS, and WFPC2 image data. In total, over this entire area, we find only one robust z ~ 7 z-dropout candidate (previously reported around Abell 1689). Four less robust z-dropout and J-dropout candidates are also found. The nature of the four weaker candidates could not be precisely determined due to the limited depth of the available optical data, but detailed simulations suggest that all four are likely to be low-redshift interlopers. By contrast, we estimate that our robust candidate A1689-zD1 has <0.2% probability of being a low-redshift interloper. We compare these numbers with what we might expect using the z ~ 7 UV luminosity function (LF) determined from field searches. We predict 2.7 z ~ 7 z-dropouts and 0.3 z ~ 9 J-dropouts over our cluster search area, in reasonable agreement with our observational results, given the small numbers. The number of z>~7 candidates we find in the present search is much lower than that which has been reported in several previous studies of the prevalence of z>~7 galaxies behind lensing clusters. To understand these differences, we examined z >~ 7 candidates in other studies and conclude that only a small fraction are likely to be z>~7 galaxies. Our findings support models that show that gravitational lensing from clusters is of the most value for detecting galaxies at magnitudes brighter than L* (H <~27) where the LF is expected to be very steep. Use of these clusters to constrain the faint-end slope or determine the full LF is likely of less value due to the shallower effective slope measured for the LF at fainter magnitudes, as well as significant uncertainties introduced from modeling both the gravitational lensing and incompleteness."