pdf - SRON

CHAPTER 4: CLUSTERING OF AXIS AND XMS SOURCES
tion function [17]. Formally, the integral constraint can be estimated by:
W =
∫ ∫
dΩ1 dΩ 1 w(θ)
∫ ∫
dΩ1 dΩ 2
(4.3.5)
where the integral is carried out over the whole area of the survey. However,
given the complicated dependence of the sensitivity with the area of our survey,
we decided to evaluate the integral constraint empirically. To do that, we
calculated the angular correlation function that would have been detected in
the absence of correlation w IC (θ) via the average of N sim simulated realisations
of w(θ), where the real data were replaced by random samples simulated independently
using the method described in section 4.3.1. The w IC (θ) points at
each angular scale are overplotted as triangles in Figs. 4.1 and 4.2, and have
been used to increase the corresponding w(θ), convolving the error bars using
Gaussian statistics.
Our first results to the full sample resulted in a ∼3-σ significant bump at scales
about 200 arcsec, which was also present in the simulations but at lower significance.
The origin of this bump turned out to be in only two fields: HD 111812
and HD 117555. Both fields have stellar clusters in their field of view ([60])
and, since we are only interested in the extragalactic large-scale structure, we
have opted to exclude these two fields from all subsequent angular clustering
analysis.
The observed w(θ) values can be fit to a power law model in the form:
w(θ) =
( θ
θ 0
) −γ
(4.3.6)
The best χ 2 fits to this model are overplotted in Figs. 4.1 and 4.2. The best
fit parameters are listed in table 4.1 along with the significance of the detection
from an F-test, comparing the χ 2 value of a power law model a w(θ) = 0,
no-clustering model. The F-test suggests significant correlation at the ∼99%
confidence level in the Soft and XID bands, whereas no significant clustering
detection is seen the the Hard and Ultrahard bands.
In [72], they find significant angular correlation in the XMM-LSS sample ([183])
in the Soft band with a similar slope γ = 1.2 ± 0.2, and a lower correlation
length θ 0 = 7 ± 3 arcsec, but compatible with ours within ∼1-σ. In [229] find
γ = 0.7 ± 0.3 and θ 0 = 4 ± 3 arcsec, again a lower correlation length than in our
90