The 4Ms Chandra Deep FieldSouth Number Counts Apportioned By Source Class: Pervasive Active Galactic Nuclei and the Ascent of Normal Galaxies Page: 4
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THE ASTROPHYSICAL JOURNAL, 752:46 (23pp), 2012 June 10
02
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101
1011 1017 1016 5 1 1014 1013
S = Flux Limit (ergs cm2 s1)Figure 2. Effective solid angle A(S) vs. intrinsic flux limit S for the SB
(dotted curve), HB (shortdashed curve), UHB (dashdotted curve), and FB
(solid curve). These curves have been computed for a powerlaw SED with
F = 1.0, the median photon index for sources detected in both the SB and
HB. The shaded regions give the effective solid angle curves appropriate for
the interquartile (~25%75%) range F=0.41.5. These curves were computed
following the probabilistic methods discussed in Section 2.1 and account for
uncertainties in measured flux conversions at the lowest flux levels where the
number of detected counts is small. The horizontal dotted line represents the
10 arcmin2 limit, above which we can confidently compute number counts
(see Section 2.1 for details). These curves are qualitatively different in nature
from those produced by X11, which utilize singlevalued countratetoflux
conversions.
photon index F could be detected when present is therefore
A(S, F) =L Pdet,i dQ (hereafter the effective solid angle),
where the summation is over all possible detection cells (i.e.,
all pixels). In Figure 2, we show A(S, F = 1.0) versus S
for the ~4 Ms CDFS in the four bandpasses. The shaded
regions show A(S, F) in the range of F = 0.41.5 (median value
F = 1.0), which represents the interquartile (i.e., 25%75%)
range for the 332 X11 sources with estimates of F that were
not based on limits. We note that generally A(S, F) increases
with increasing F. We find that the A(S, F) curves asymptote
to a value of ~2 arcmin2 approaching S = 0, suggesting
that sources with extremely low fluxes (down to zero) could
in principle produce fluctuations exceeding the probability
threshold defined in Equation (1). However, as discussed above,
such sources would most efficiently be removed using our initial
wavdetect screening. Therefore, we cannot use information
at such flux levels to determine number counts reliably. We
therefore choose to restrict our numbercount computations to
flux levels where >10 arcmin2 solid angle is accessible in our
survey for the case of F = 1.4 (the mean SED of the Xray
background; e.g., Moretti et al. 2009). Our adopted ~10 arcmin2
solidangle limit additionally constrains our flux limits. The
resulting limits are 5.1 x 1018, 3.7 x 1017, 4.6 x 1017, and
2.4 x 1017 erg cm2 s1 for the SB, HB, UHB, and FB,
respectively; these are factors of 1.94.3 times fainter than
those of B04 and G08, the previously deepest numbercount
studies. For the full range of Xray spectral slopes (i.e., F values)
in the X11 sample, ~520 arcmin2 of solid angle is availabletII 111111 IIIIIIII 1 111111 1111111 11
 .......
ji
ii

10arcmin2 limit
 I
.......... 0.52 keV
 .. . .. .28 keV
0.58 keV _
......48 keV
1 1 1I IIIIII 1 I 111 111 I 1 111111 11 111 111(4)
T b bext
T + bext d S model'where the term dN/dSImodel is a Bayesian prior, based on the
differential number counts, which accounts for the Eddington
bias near the sensitivity limit. As noted in B04, the slope of the
number counts of AGNs, normal galaxies, and Galactic stars will
differ at the flux limit of the CDFS. Therefore, dN/dSImodel
for a given source will depend on which source population it
belongs to. Previous studies of Xray number counts (e.g., Rosati
et al. 2002; B04; Kim et al. 2007; G08) have shown that power
laws provide good fits to the overall shapes of the log Nlog S.
To first order, we use priors based on the following powerlaw
parameterizations:
dN AGN
dSKAGN(S/pSrAGN
XK (f/Sref) GN A
[KAGN (fb Sref) 2 I01 N( S/Sref) #2 GdN gal
dS
dN star
dS(S b fAGN
(S > fbAGN)Kga(S/Sref)_,ga
Kstargg re star(5)
where dN/dS(AGN), dN/dS(gal), and dN/dS(star) are differ
ential numbercount parameterizations to be applied to AGNs,
normal galaxies, and Galactic stars, respectively, fbGN is the
flux related to the break in the double power law used to de
scribe the AGN number counts, and Sref 1014 erg cm2 s1
As we show in Section 3.1 below, we characterize each
Xray source using the Xray and multiwavelength data and
provide best estimates of the parameters in Equation (5) (i.e.,
K, ,Q, and fb values) for the AGNs, normal galaxies, and
Galactic stars. For each source, we computed PT down to the
flux limits defined above and normalize Equation (4) using
f PT dS = 1. In Figure 3, we show examples of PT as a
function of 0.52 keV flux for two AGNs in the main Chandra
catalog having AE probability P ~ 1045 (solid curve) and
P ~ 0.003 (dashed curve; near the detection threshold). For this
computation, we utilized values of 1AGN 1.49, 12GN=2.49,
and fbGN = 5.6 x 101 erg cm2 s1 (the normalization is
arbitrary); as we will show in Section 3.1, these values represent
the bestfit parameterizations for AGN SB number counts.4
for numbercount computations at the flux limits (above the
asymptotic regime). We note that the flux limits derived here are
fainter than those presented in X1i, which were ~z_9.1 x 1018
and ~5.5 x 1017 erg cm2 s1 in the SB and HB, respectively
(see also the area curves in our Figure 2 compared with
Figure 23 in X1). This is due to the fact that XI1 considered
only a single countratetoflux conversion factor and did not
use the probabilistic approach adopted here.
To account for the fact that, for each Xraydetected source
in our main catalog, we are only able to measure reliably
the total observed counts s (see above), the local background
bext, and that the intrinsic flux S may be subject to large
uncertainty (particularly in the lowcount regime), we consider
the conversion from counts to flux for each source to be
probabilistic. For each Xraydetected source, we computed the
flux probability distribution as follows:
(S + bext)! T S
PT
S!bext! T + bextLEHMER ET AL.
x (1
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Lehmer, Bret; Xue, Yongquan; Brandt, William Nielsen; Alexander, David M.; Bauer, Franz E.; Brusa, Marcella et al. The 4Ms Chandra Deep FieldSouth Number Counts Apportioned By Source Class: Pervasive Active Galactic Nuclei and the Ascent of Normal Galaxies, article, April 9, 2012; Washington, DC. (digital.library.unt.edu/ark:/67531/metadc849979/m1/4/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.