To know SMGs at which redshift have most association with galaxies, we divided the optically selected galaxies into subsets by photometric redshift with 0.2 intervals. Then we calculated cross correlation function (CCF) between SMGs and the galaxies at different redshift bins. Final we fitted a power-law function to the CCF for every redshift bin and computed the cross correlation length. Detail of the method is described in Ch. 4.
In Fig. 17, we also plotted galaxies auto correlation lengths for comparison. For display purpose, if there are no positive correlation signals, we forced the value r0 = 0. There are almost no clear relation between SMGs and galaxies in each redshift range, except that AzTEC-SMGs have a marginal correlation with galaxies at z ∼ 2.6 and 3.6.
Fig. 17.— Correlation lengths in the COSMOS and ECDF-S fields. The left panel: star symbols are SMGs detected by AzTEC in the COSMOS cross correlated with galaxies. The right panel: triangle and star symbols are cross correlation lengths between galaxies and LABOCA-SMGs and AzTEC-SMGs in the ECDF-S field. (See e-copy for color version)
5. Discussion
Based on galaxy δ results (Ch. 3.1), we found SMGs at most redshifts did not show the overdens signals. It seems against the expectation of hierarchical model. However, even there are photometric redshift estimates for SMGs and galaxies, the accuracy is still a problem. Most of signals may be diluted by many unrelated sources.
For LABOCA-SMGs at z ∼ 2.5 and AzTEC-SMGs at z = 3.3 and 3.7, they seem to be associated with structures, although the signals are about 1-2 σ. We examined the individual sources, they are not caused by one or two SMGs located at very dense region at that redshift. If the signals are real, does it mean different wavelength selected SMGs tend to be associated galaxies at different epoch, or that is caused by cosmic variance. To identify whether it is true or just a coincident, we need spectroscopic redshift data or to consider the probability distribution function of redshift for SMGs and galaxies to derive more reliable results.
Our results of BzK δ show LABOCA-SMGs are more associated with passive BzKs than star-forming BzKs (Fig. 10 and Fig. 11). Passive BzK is a good tracer of dense region, so this result can support the environments of SMGs are dense. For the difference of AzTEC-SMG result, there are two possible explanations. One is that there is a difference of redshift distribution between LABOCA-SMGs and AzTEC-SMGs (see Fig. 4). The redshift distribution of AzTEC-SMGs (mean redshift is 2.6) is a little far from the redshift peaks of star-forming and passive BzKs at z ∼ 1.8 and z ∼ 1.5. Another explanation is the small field (GOODS-S) caused the large cosmic variance, this can be supported by our MC simulation (Fig. 12) that shows the large uncertainty of BzKs δ of AzTEC-SMGs. But we also could not rule out that LAOBCA-SMGs have higher passive BzKs density than AzTEC-SMGs is caused by cosmic variance.
The selection bias of submillimeter wavelengths is one of explanations for our results,
so we did an independent analysis of SMGs of 870µm and 1.1 mm flux ratio. But the result shows no evidence of 2 SMG populations in terms of spectrum (see Appendix Ch. 7.3).
In this work, we find no detectable SMG-LAE cross-correlation signal in our selected fields, unlike the result (Fig. 18) from previous study of SSA22 field (Tamura et al.
2009), which shows a spatial correlation between the two populations. Another high-z proto-cluster, the Francis field, at z = 2.38, was found by Francis et al. (1996, 1997), and Palunas et al. (2004) and Francis et al. (2004) had observed 37 Lyα-emitting objects.
Beelen et al. (2008) had observed 32 submillimeter sources at an overdense region of the proto-cluster using LABOCA. From their analysis they concluded that several of SMGs could be associated with a z = 2.38 large scale structure.
While a close LAE-SMG spatial correlation may have been revealed in the case of the SSA22 and Francis fields which are both toward to high-z structures, our study demonstrates a more spatially detached relationship between these 2 populations based on data outside the structure. We further excluded most SMGs whose redshift far from the redshift of LAEs and found no significant signal appear in the results either, so the background and foreground contaminations may only play a minor role. Combining previous results and our results, we infer that these two populations are not necessary to have correlation outside clusters or structure at high redshift.
To date, the properties of LAEs have not been well constrained. Lai et al. (2008) in their work found 30 percent of LAEs have IRAC 3.6 µm detection, and they are different in stellar mass and age from others. We had divided LAEs into two populations by rest frame UV colors, but the results did not show different LAE populations (Appendix Ch. 7.2).
Furthermore, although there are studies showing evidence that part of LAEs appeared to be ULIRGs. But the ULIRGs fraction is quite low at z ∼ 3 and may not change much of our results (Nilsson & Møller 2009; Ono et al. 2010; Nilsson & Møller 2011).
– 41 – source of one population within a unit solid angle as a function of
angular distance from a source of another population, relative to a random distribution. We use an angular cross-correlation function to quantify the degree of cohabitation between the Lya emitters and the bright SMGs. Figure 2 shows the cross-correlation function, which reveals strong correlation signals at angular distances less than 5 arcmin for the bright sample, suggesting close association of the Lya emitters with the bright SMGs that are most probably embedded in the more massive dark haloes. Monte Carlo simulations (Supplem-entary Information) also show a correspondence between the two distributions, at a 97.3% significance level, further supporting the positional association of Lya emitters with bright SMGs.
The gravitational lensing magnification of background galaxies by foreground large-scale structure would immediately preclude the
physical connection between the galaxies and the foreground struc-ture. Some authors20,21 have reported correlations between bright (sub)millimetre sources and optically selected low-redshift galaxies (mostly at z , 1) in other regions of the sky. In general, SMGs are often found at high redshift (median, z 5 2.2; ref. 22), and the maximal gravitational lensing magnification for a background galaxy at z > 2 occurs when the foreground lensing structure is at z < 0.5. Therefore, they concluded that the correlation signal is most probably the result of amplification of background SMGs due to gravitational weak lensing by the foreground low-redshift galaxies. By contrast, the origin of the correlation signals in SSA 22 is most likely intrinsic to the large-scale structure in which both populations, SMGs and Lya emitters, are embedded. Because the redshift estimates for the SMGs place them at distances coeval with the Lya emitters, it is unlikely that the correla-tion seen in SSA 22 is due to amplificacorrela-tion of a much higher-redshift (z ? 3.1) SMG population lensed by the structure traced by the Lya emitters, which are all located at z 5 3.1 (not z < 0.5).
Declination (J2000)
Declination (J2000) Galaxies per arcmin2
+0º 25′ 1.0
Figure 1|The positions of 1,100-mm sources and Lya emitters towards the SSA 22 protocluster region. a, The colour scale shows the map of signal-to-noise ratio at 1,100 mm. The map shows 30 sources with signal-to-signal-to-noise ratios $3.5 (circles). Observations of SSA 22 (field centre at
RA 5 22 h 17 min 36 s, dec. 5 10u 159 0099 (J2000)) were obtained using the AzTEC camera13, operating at 1,100 mm, mounted on the ASTE 10-m submillimetre telescope14during the July–September 2007 observing season.
The data consist of a total of 42 h of integration time on source under excellent conditions (zenith atmospheric opacity at 220 GHz,
t220 GHz50.01–0.10). This resulted in a root-mean-square noise level of 0.68–0.99 mJy per beam over 390 arcmin2. The point spread function of AzTEC on ASTE has a full-width at half-maximum of 28 6 1 arcsec.b, The locations of the bright submillimetre galaxies with S1,100 mm$2.7 mJy (orange filled circles) and the Lya emitters at z 5 3.1 (white dots). The sizes of the orange circles are proportional to their 1,100 mm fluxes. The number density field of the Lya emitters is shown in the colour scale, highlighting the density enhancement of the Lya emitters, which is thought to trace out the underlying large-scale structure at z 5 3.1.
Table 1|The bright SMG sample found in SSA 22
Source name Coordinate (J2000) Flux density (mJy) s/n
RA (h:min:s) Dec. Sobserved* Sdeboost{ SSA22-AzTEC1 22:17:32.42 10u 179 35.599 8.7 6 0.7 8:4z0:8{1:0 12.8 SSA22-AzTEC2 22:17:42.38 10u 169 59.399 4.9 6 0.7 4:4z0:9{0:8 7.2 SSA22-AzTEC10 22:17:34.03 10u 139 46.899 3.4 6 0.7 2:8z0:9{0:9 4.8 SSA22-AzTEC11 22:17:29.64 10u 209 24.499 3.3 6 0.7 2:7z0:9{0:9 4.7 SSA22-AzTEC12 22:17:36.04 10u 49 0.299 4.0 6 0.9 3:1z1:1{1:1 4.5 SSA22-AzTEC13 22:18:5.95 10u 119 41.999 3.3 6 0.7 2:7z0:9{1:0 4.5 SSA22-AzTEC14 22:17:0.34 10u 109 42.699 3.7 6 0.9 2:7z1:2{1:2 4.2 SSA22-AzTEC15 22:16:57.60 10u 199 22.899 4.1 6 1.0 2:9z1:4{1:3 4.2 A full list of the 30 submillimetre galaxies is given in Supplementary Table 1. The astrometric accuracy of the catalogue is,10 arcsec.
* Observed flux density before flux bias correction, plus the 1s error.
{ Deboosted flux density (flux density corrected for the flux bias due to confusion noise using the method described elsewhere28), plus the 68% confidence interval.
Angular distance (arcmin)
Figure 2|Angular cross-correlation between submillimetre galaxies and Lya emitters.The two-point angular cross-correlation function shown here is computed for the 166 Lya emitters and the 15 brightest
(S1,100 mm$2.7 mJy) submillimetre galaxies (orange circles). For reference, we also show the two-point angular autocorrelation function for the SSA 22 Ly-a emitters (blue squares). Small-number statistics prevent us from constraining the auto-correlation function well for the submillimetre galaxies. The correlation functions are computed using the estimator of ref.
29. The error bars are estimated from the root mean square of 1,000 bootstrap samples. See Supplementary Information for details.
62
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©2009
Fig. 18.— Spatial correlation between SMGs and LAEs in SSA22 field. Blue squares are ACF of LAEs, yellow circles are CCF between SMGs and LAEs. There is a clear association at angular separation smaller than 5 arcmin. (Tamura et al. 2009)
6. Summary
In this work, we have investigated the environments of SMGs at different redshifts based on multiwavelength data from the COSMOS and ECDF-S (including the GOODS-S) fields. Our first approach is to count the number density of galaxies with photometric redshift and BzKs centered at each SMG. We then did a cross-correlation analysis of SMGs and a young, small and dust free galaxy population, LAEs. Our main results are the following.
(i) Based on the result of galaxy number density, SMGs are not necessarily in the most dense regions, at least in the epochs included in this study. LABOCA-SMGs and AzTEC-SMGs only have marginal signal at z ∼ 2.5 and z ∼ 3.5 (Fig. 7).
(ii) There are overdensities of BzKs around SMGs at separation smaller than 1 Mpc and passive BzKs have higher signal than star forming BzKs (Fig. 10).
(iii) There is no detectable correlation between SMGs and LAEs, suggesting outside galaxy structures (compared with previous results in SSA22 field), SMGs and LAEs seem not associated (Fig. 13).
Although SMGs tend to be located in relatively dense regions, they may not be a population only with very massive galaxy that can always trace the most dense environments such as the center of (proto)clusters.
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7. Appendix
7.1. Galaxy density around SMGs without redshift
Before there are redshift estimates for SMGs, to know which redshift most of SMGs locate at, we did this analysis. If SMGs are highly associated with galaxies, galaxy δ at the redshift SMGs are at should be higher than other redshifts. So starting from z = 1 to 4, we divided galaxies into redshift bins with 0.2 δz interval. In each redshift bin, we computed the mean δ for all SMGs (without considering the redshift of SMGs). All three fields (Fig.
19) show that SMGs tend to be located at relatively dense regions at z > 2.3.
Based on our results of galaxy overdensity (Fig. 19), we find that SMGs tend to be found in relatively dense regions at redshift > 2, which is consistent with the expected merger scenario of SMG origins (see Ch. 1). The result on the contrary suggests that SMGs are not necessarily embedded in overdense regions at 1.5 < z < 2.
Fig. 19.— Average environment δ in a region of radius from r = 0.5 to 2 Mpc centered at SMGs (see text for details).