iHM
-2 -1 0 1 2 3 4 5
i775 - H160
-2 -1 0 1 2 3 4 5
H160 - IRAC4.5
All X-ray sources iHM (SF + P) Interlopers (z<3.5)
iHM-SF iHM-P
0 1 2 3 4
0 5 10 15 20
0 1 2 3 4
Redshift 0
5 10 15 20
Number
iHM
Figure 5.4: Left: iHM-selected AGNs in GOODS-S (Area 1). Red dashed lines indicate the color criteria; orange triangles represent the sources selected by the method; the filled circles indicate all the X-ray sources, while the low-redshift interlopers are marked in blue.
Right: Redshift distribution for V J L selected sources.
in Section 5.5.
5.3 High-z selection via P (z)
In the previous sections we defined the “interlopers” as those sources that did not have photo-z or spec-z within the targeted range. However, redshifts have an error associated with them and in particular photo-z carry information in the P(z) on the entire redshift range from 0 to 7. Using this information, we can further investigate the efficiency of the LBGV09, BzK, V J L, and iHM methods by studying the purity (Ps) and completeness (C) of samples selected using these methods. To do this, we introduce the concept of the weight factor w (e.g., Aird et al., 2010). The value is obtained by measuring the fraction of area under the curve of P(z) at a given redshift range (zlow < z < zup), which reflects the confidence that a given source falls within a target redshift range (as illustrated in Figure 5.5). For each individual source with photo-z, we estimated the value of w as determined in Equation 5.1. 1
w= Rzup
zlowP(z)dz R7
0 P(z)dz (5.1)
1Note that theoretically the integration ofP(z) should be from 0 to∞. However we integrate from 0 to 7 which is the range of redshift obtained from our photo-z computation with codeLeP hare.
106 5. High-redshift AGN
For the sources with reliable spec-z 2, we assigned a weight of w= 1 if the spec-z falls within the target redshift range, while we setw= 0 if it is outside the target range.
ID: 5375, photo-z =0.7
0 1 2 3 4 5 6 7
Redshift 0.0
0.2 0.4 0.6 0.8 1.0
P(z)
w(0.5<z<1)= 0.52 w(2<z<3)= 0.10
Figure 5.5: Example of measuring the value of weightwfrom theP(z). The fraction of red shaded area (w = 0.52) represents the photo-z weight in the redshift range 0.5 < z < 1.
The fraction of blue shaded area (w = 0.1) represents the photo-z weight in the redshift range 2< z <3. The dashed line is the best solution of the photo-z, zp = 0.7.
We use w to estimate theC andPs for each of the methods introduced in the previous section and verify which is the most efficient method, i.e., the sample with the highest (C+Ps). We define the completeness as:
C =
Nsample
P
j=1
wj
Ntotal
P
i=1
wi
(5.2)
2Here we select reliable spec-z by the criterion of spec-z qualityQsz ≤2, see the detailed explanation in Table A.4
5.3 High-z selection via P(z) 107 And the purity as:
Ps = 1−
Nsample
P
j=1
(1−wj)
Nsample (5.3)
Ntotal is the total number of entire sample, and P
wi gives an effective total number of the sample. Nsample is the total number of the high-z sample selected by a given threshold of weight (wth) at a certain redshift range zlow < z < zup, and P
wj is an effective total number of the high-z sample.
Figure 5.6 shows how the values of C and Ps change with wth. With larger wth, less sources are selected among the entire sample, which leads to a lower completeness (C). In contrast, the purity (Ps) becomes higher with higherwth, which indicates that the fraction of interlopers is decreasing. The goal is to find the value of w that maximizes the sum of C and Ps. We do that by calculating the values of (C+Ps) as a function ofwwith a step of 0.05 and find the maximum value of (C+Ps) that fall at wth.
We computed the value of wth for each of the typical target redshift ranges of the color techniques, i.e., LBGV09, BzK, V J L and iHM.The best wth for each redshift range and each selection criterion are listed in Table 5.2 and indicated with a red line in Figure 5.6.
In order to understand whether the efficiency of a given selection is depending on the type of sources, we have also used the LBGV09and theBzK-like selections on non-X-ray sources and similarly computed w, C and Ps.
First of all, we found that the optimal value of wth is frequently within the range of 0.3 < w < 0.5 and this is valid for normal and X-ray detected galaxies. In addition, we note that in each redshift range, at the value ofwth that maximizes (C+Ps),C andPs are generally higher for X-ray sources than for non-X-ray normal galaxies. This implies that X-ray sources have more confident values of photo-z in the target redshift range. This is because X-ray sources usually have strong emission line features which can help in iden-tifying the photo-z correctly, specially in the presence of Intermediate and Narrow band photoemtry. At z ≥ 4.5, we do not have Xray sources; for normal galaxies the drop of the mean wth at that redshift, is due to the fact that most of the emission lines shift to redder bands which have broader filter bandwidth so that the line flux contribution to the continuum is diluted. This, added to the increased photometric errors for faint sources increases the uncertainty of photo-z and reduces the weight, and also because of the small sample size, thus the trend become unstable at z >4.
Following Table 5.2, we have selected samples by wth that maximize C+Ps (so called P(z)-selected samples) in the redshift ranges: (a) 1.4 < z < 2.5; (b) 2.5 < z < 3.5; (c) 3.5< z < 4.5; (d) 3.1< z < 4.4; (e) 3.4< z < 4.5; as defined from the literature. In the following we will compare these samples with those defined by the color techniques.
108 5. High-redshift AGN
Table 5.2: The values ofwth, completeness (C) and purity (Ps) for which (C+Ps) is maximum for X-ray and non-X-ray detected samples in Area 1.
Non-X-ray X-ray
wth C Ps (C+Ps) wth C Ps (C+Ps)
0.0< z <0.7 0.50 0.77 0.91 1.68 0.50 0.98 1.00 1.98 0.7< z <1.4 0.40 0.76 0.78 1.54 0.50 0.95 0.98 1.93 1.4< z <2.5a 0.30 0.93 0.68 1.62 0.45 0.95 0.89 1.84 2.5< z <3.5b 0.45 0.64 0.80 1.44 0.25 0.93 0.65 1.58 3.5< z <4.5c 0.50 0.52 0.81 1.33 0.40 0.78 0.76 1.54 3.1< z <4.4d 0.45 0.66 0.83 1.49 0.45 0.85 0.91 1.76 3.4< z <4.5e 0.45 0.62 0.80 1.42 0.50 0.78 0.90 1.69
aTypical redshift range ofBzK selection (Daddi et al., 2004).
bTypical redshift range of LBG selection forU-band dropout (Steidel et al., 1996); it is also the range ofV J L selection from Guo et al. (2013)
cRedshift range of iHM selection from Guo et al. (2013)
dRedshift range of LBG selection for B-band dropouts from Vanzella et al.
(2009)
eRedshift range of LBG selection forB-band dropouts from Papovich et al.
(2004)
5.3 High-z selection via P(z) 109 1.4<z<2.5
0.0 0.2 0.4 0.6 0.8 1.0
weight 0.0
0.2 0.4 0.6 0.8 1.0
Completeness Purity (C+P)/2 Non-X-ray sources
1.4<z<2.5
0.0 0.2 0.4 0.6 0.8 1.0
weight 0.0
0.2 0.4 0.6 0.8 1.0
Completeness Purity (C+P)/2 X-ray sources
2.5<z<3.5
0.0 0.2 0.4 0.6 0.8 1.0
weight 0.0
0.2 0.4 0.6 0.8 1.0
Completeness Purity (C+P)/2 Non-X-ray sources
2.5<z<3.5
0.0 0.2 0.4 0.6 0.8 1.0
weight 0.0
0.2 0.4 0.6 0.8 1.0
Completeness Purity (C+P)/2 X-ray sources
3.5<z<4.5
0.0 0.2 0.4 0.6 0.8 1.0
weight 0.0
0.2 0.4 0.6 0.8 1.0
Completeness Purity (C+P)/2 Non-X-ray sources
3.5<z<4.5
0.0 0.2 0.4 0.6 0.8 1.0
weight 0.0
0.2 0.4 0.6 0.8 1.0
Completeness Purity (C+P)/2 X-ray sources
Figure 5.6: (C +Ps) as a function of wth at given redshift ranges of 1.4 < z < 2.5, 2.5< z <3.5, and 3.5< z <4.5 in GOODS-S (Area 1) for non-ray (left panel) and X-ray (right panel) sources. The red dotted line represents thewth selected by the maximum of the (C+Ps).
110 5. High-redshift AGN