Confirmation of a correlation between the X-ray luminosity and spectral slope of AGNs in the Chandra Deep Fields

0.89 MB·English

by  C. Saez

Draftversion February2,2008
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
CONFIRMATION OF A CORRELATION BETWEEN THE X-RAY LUMINOSITY AND SPECTRAL SLOPE OF
AGNS IN THE CHANDRA DEEP FIELDS.
C. Saez 1, G. Chartas 1, W. N. Brandt 1, B. D. Lehmer 2, F. E. Bauer 3, X. Dai 4, and G. P. Garmire 1
Draft versionFebruary 2, 2008
ABSTRACT
We present results from a statistical analysis of 173 bright radio-quiet AGNs selected from the
Chandra Deep Field-North and Chandra Deep Field-South surveys (hereafter, CDFs) in the redshift
range of 0.1 . z . 4. We find that the X-ray power-law photon index (Γ) of radio-quiet AGNs
8
is correlated with their 2–10 keV rest-frame X-ray luminosity (L ) at the > 99.5% confidence level
0 X
0 in two redshift bins, 0.3 . z . 0.96, and 1.5 . z . 3.3 and is slightly less significant in the
2 redshiftbin0.96 . z . 1.5. TheX-rayspectralslopesteepensastheX-rayluminosityincreasesfor
AGNs in the luminosity range1042 to 1045 erg s−1. Combiningour results fromthe CDFs with those
n
from previous studies in the redshift range 1.5 . z . 3.3, we find that the Γ−L correlation has
a a null-hypothesis probability of 1.6 ×10−9. We investigate the redshift evolution oXf the correlation
J
betweenthe power-lawphotonindexandthe hardX-rayluminosityandfindthatthe slopeandoffset
3
ofalinearfittothecorrelationchangesignificantly(atthe>99.9%confidencelevel)betweenredshift
2
bins of 0.3 . z . 0.96 and 1.5 . z . 3.3. We explore physical scenarios explaining the origin

of this correlation and its possible evolution with redshift in the context of steady corona models
]
h focusing on its dependency on variations of the properties of the hot corona with redshift.
p Subjectheadings: cosmology: observations—galaxies: active—galaxies: statistics—X-rays: galaxies
-
o
r
t 1. INTRODUCTION tionand luminosity (e.g., Steffen et al.2003; Ueda et al.
s
2003; La Franca et al. 2005; Akylas et al. 2006). We
a It is important to extend the study of quasars to high
[ redshifts in order to understand their evolution and en- note, however, recent work by Dwelly & Page (2006)
vironments. A relevant conclusion from modern studies reporting that the obscurationfraction may be indepen-
1 dent of luminosity. The dependence of the obscuration
is that the quasar luminosity function evolves positively
v
fractiononredshiftisacontroversialissue. Someauthors
9 with redshift, having a comoving space density strongly
detect an increase of the obscuration fraction with red-
9 peaked at z ≈ 2 (e.g., Schmidt 1968; Boyle et al. 1987;
shift (e.g., La Franca et al. 2005; Treister & Urry 2006;
5 Warren et al. 1994). More recent findings suggest that
Tozzi et al. 2006), while others do not find any evidence
3 theevolutionofthespacedensityofAGNsisstronglyde-
for evolution (e.g., Ueda et al. 2003; Akylas et al. 2006;
. pendent on X-ray luminosity (L ), with the peak space
1 X Dwelly & Page 2006).
density of AGNs moving to higher redshifts for more
0 A recent mini-survey of relatively high-redshift (1.5<
luminous AGNs (e.g., Ueda et al. 2003; Hasinger et al.
8
z <4)gravitationallylensedradio-quietquasars(RQQs)
0 2005).
observed with Chandra and XMM-Newton (Dai et al.
: The X-ray band probes the innermost region of the
v 2004)indicated a possible correlationbetween the X-ray
central engines of AGNs. The study of AGNs in the
i power-lawphotonindex andX-rayluminosity. This cor-
X X-rayband provides importantinsights about their cen-
relation, characterizedby an increase of Γ with L , was
tral engines and the evolution of the AGN luminosity X
r foundfor RQQs with 2–10keVluminosities inthe range
a function. In most AGNs, the observed X-ray contin- 1043 to 1045 erg s−1. Such a correlation is not found in
uum can be modeled using a power-law of the form
N(E) = N (E/E )−Γ, where Γ is the photon index. nearbyz .0.1quasars(e.g.,George et al.2000). Several
0 0
studiestodateofhigh-redshiftquasarsdonothavelarge
This power-law is attenuated by material in our Galaxy
enough sample sizes in the 2–10 keV luminosity range
as well as material intrinsic to the host galaxy. Sev-
1043 to 1045 erg s−1 to place any significant constraints
eral recent studies have centered on estimating the dis-
ona possible Γ−L correlation(e.g., Reeves & Turner
tributionofintrinsiccolumndensities(N )andthefrac- X
H
tion of AGNs having N & 1022 cm−2. Recent theo- 2000; Page et al. 2005).
H
One of the concerns with the Dai et al. (2004) analy-
retical studies of AGNs (e.g., Hopkins et al. 2005) sug-
sis was that the limited number of quasars in the sam-
gest that the distribution of N is luminosity depen-
H
ple, combined with the poor signal-to-noise ratio (S/N)
dent; this is supported observationally with the detec-
availableforseveraloftheobservationsandtherelatively
tion of an anti-correlationbetween the obscurationfrac-
largefractionofBAL quasars,may haveled to problem-
1AstronomyandAstrophysicsDepartment,PennsylvaniaState atic systematic effects. The number of available lensed
University,UniversityPark,PA16802, USA radio-quietquasarsusedbyDai et al.(2004)waslimited
2Department of Physics, University of Durham, South Road, toatotalof25sources,ofwhichthe brightest11hadX-
Durham,DH13LE,UK
rayobservations. Inordertoincreasethesizeofthehigh-
3ColumbiaAstrophysicsLaboratory,ColumbiaUniversity,New
redshift radio-quiet quasar sample, we have compiled
York,NY10027, USA
4DepartmentofAstronomy,TheOhioStateUniversity,Colum- a sample of 173 high-redshift AGNs with moderate-to-
bus,OH43210, USA highS/NspectraavailablefromtheChandraDeep-Field-
2
North and Chandra Deep-Field-South surveys (CDF-N
and CDF-S, respectively; jointly CDFs; Giacconi et al.
2002; Alexander et al. 2003).
The main scientific goal of this work is to constrain
better theΓ−L correlationfoundbyDaietal. (2004).
X
The significantincrease in sample size allows us to place
tighter constraints on the significance of the correlation.
We also test the correlation in narrower redshift bands
whichwillallowustodeterminetheepochbywhichpos-
siblechangesintheaverageemissionpropertiesofAGNs
occurred. Currently, the two deepest X-ray surveys are
the CDF-N and CDF-S with ≈2 Ms and ≈1 Ms expo-
sures,respectively. Bothsurveyscover≈300arcmin2 ar-
eas and target different regions of the sky characterized
bylowGalacticcolumndensitiesandanabsenceofbright
stars (Giacconi et al. 2002; Alexander et al. 2003). The
CDFs pointings have sufficient sensitivity to detect the
X-ray emission from AGNs with moderate luminosities
(L ≈1043−1044 erg s−1) out to z ≈2−6.
X
Radio-quiet AGNs (RQ AGNs) correspondto the ma-
jority of active galaxies (∼ 90%) that contain a central
activenucleus andshow severaldifferences intheir spec-
tral properties compared to radio-loud AGNs. Radio-
loud AGNs have powerful sub-parsec jet-linked X-ray
Fig. 1.— (upper panel) Number of sources with more than
synchrotron self-Compton (SSC) emission, which intro- S photons (0.5–8keV observed-frame) versus S. The thick line
duces an additional component to their spectra. As a correspondstoallCDFssourceswithmeasuredredshiftsofz&0.1.
consequence RQ AGNs are observed to have, on av- Thedotted lineshows sources ofthe CDF-Nsurveywith z&0.1,
and the dashed line shows sources of the CDF-Ssurvey with z &
erage, steeper X-ray power-laws than radio-loud AGNs
0.1. TheverticaldottedlinecorrespondstoS=170. Notethatthe
(e.g., Reeves et al. 1997). We therefore have chosen to sampleusedto generate this figure contains AGNs (both RQ and
exclude radio-loud AGNs from this study. Throughout radio-loudAGNs), normal galaxies and starburst galaxies. (lower
this paper we adopt a flat Λ-dominated universe with panel) Number of radio-quietAGNs with z &0.1vs. the number
H =70 km s−1Mpc−1, Ω = 0.7, and Ω = 0.3. The ofphotons(S;0.5–8keV)intheirspectra. Thesolidlinerepresents
0 Λ M sourceswithfits performedinthe0.5–8keV observed-frameband
Chandra data were reduced using the CIAO version 3.3 and the dotted line represents sources with fits performed in the
software tools provided by the Chandra X-ray Center 2–10keVrest-frameband.
(CXC), and the spectral analysis was performed using
XSPEC version 12. Forthe ∼40faintsourcesstill lackingredshiftestimates,
we used the BPZ code (Bayesian photometric redshift
2. SAMPLESELECTION estimation; Benitez 2000) and available photometry
Our sources were selected from the CDFs, cur- (Arnouts et al.2001;Barger et al.2003;Giavalisco et al.
rently the two deepest X-ray surveys. The on- 2004) to estimate crude redshifts.
axis sensitivity limits for the CDF-N are ≈ 2.5 × The selection criteria for our sample of RQ AGNs are
10−17 erg cm−2 s−1 (0.5–2.0 keV) and ≈ 1.4 × 10−16 (1) that the sources are radio-quiet(see below), (2) that
erg cm−2 s−1 (2–8 keV). These limits are around two the redshifts of the sources are greater than 0.1, and (3)
times more sensitive than those for the CDF-S that the total number of photons in the full band (0.5–8
(Giacconi et al. 2002; Alexander et al. 2003). The keV) is greater than ∼ 170 counts (S & 170) result-
CDFs are 50–250 times more sensitive than previ- ing in moderate-to-high S/N spectra. The selection of
ous X-ray surveys, detecting ≈ 900 point sources, of a cut-off at ∼ 170 counts allows an accurate estimate
which ≈ 600 are AGNs and galaxies with measured of the photon index, which is not possible for fainter
redshifts (Giacconi et al. 2002; Alexander et al. 2003; sources (Tozzi et al. 2006). Based on the condition that
Barger et al. 2003; Zheng et al. 2004). S &170, the on-axis flux limits of our sample in the full
Spectroscopic and photometric redshifts were band (0.5–8 keV) in the CDF-N and CDF-S surveys are
gathered from the literature (Croom et al. 2001; ≈1×10−15erg cm−2 s−1 and≈2×10−15erg cm−2 s−1 ,
Barger et al. 2003; Steidel et al. 2003; Cowie et al. respectively.
2004; Mobasher et al. 2004; Szokoly et al. 2004; InFigure1(upperpanel),weshowthecumulativedis-
Wirth et al. 2004; Wolf et al. 2004; Zheng et al. tribution for number of X-ray sources having more than
2004; Alexander et al. 2005; Colbert et al. 2005; S counts (0.5-8 keV) for the CDF-N and CDF-S. The
Le F`evre et al. 2005; Vanzella et al. 2006) and vetted to CDFs contain 205 sources with more than 170 counts
remove redshifts which did not appear to belong to the at z > 0.1. Most of these sources are AGNs; however,
most-likely optical counterpart to each X-ray source. in the low-redshift regime of our sample 0.1 . z . 1.0
The latter was assessed by comparing the optical and we expect only a small fraction of starburst and “nor-
X-rayimages,whichwerealignedto between0′.′12–0′.′25; mal” galaxies (Brandt & Hasinger 2005). Following the
this notably affected the redshifts from Zheng et al. classification scheme discussed in 4.1.1 of Bauer et al.
§
(2004), where 47 (≈14%) of the redshifts were rejected (2004a), we found two starburst galaxies and one “nor-
forbeingassociatedwithanunlikelyopticalcounterpart. mal” galaxy, which we remove leaving 202 AGNs in our
3
sample. regions to avoid overlap. Local background extraction
Radio-loud AGNs were classified based on a radio- regionswere chosenas annuli centeredon the sourcepo-
loudness parameter R & 10 (R = f /f ). To find sitions with inner radii equal to that of the source ex-
5GHz B
these sources, we matched the X-ray positions with ra- traction regions and with outer radii selected such that
dio sources using a matching radius of 2 arcsec. The thebackgroundregioncontainedatleast100background
flux-densityat5GHzwasobtainedfromtheflux-density counts and had an area at least fours times that of the
at 1.4 GHz assuming a power law radio spectrum (f ∝ source region.
ν
ν−αr), where α = 0.8 is a characteristic radio spectral We note that in the current analysis we made no at-
r
index of synchrotron radiation5. tempttocorrectforpossiblespectralvariabilityoverthe
ThefluxintheBfilterwasobtainedfromBarger et al. fewyearperiodoftheobservationsoftheCDFs. Spectra
(2003) for the CDF-N sources and from public-domain obtained are therefore time-averaged over the period of
tables of the GOODS and COMBO-17 surveys for the the observations.
CDF-S sources. When searching the radio catalogs6
provided by Richards (2000) for the CDF-N and 4. SPECTRALANALYSIS
Afonso et al. (2006) for the CDF-S, we find that 29 Two energy bands were used to fit the Chandra spec-
(∼14%)outofthe 202X-raydetectedAGNs wereradio- tra: the 0.5–8 keV observed-frame and the 2–10 keV
loud. This leaves 173 RQ AGNs which we use for our rest-frame. To obtain the maximum S/N we utilized the
analysis out of which 111 have spectroscopic redshifts. observed-frameenergyrangeof0.5–8keV.Theloweren-
ergy bound was chosen because the Chandra effective
3. SPECTRALEXTRACTION area is not well calibrated below 0.5 keV, and the up-
TheX-rayspectraofthesourcesoftheCDFsanalyzed per energybound was chosenbecause the S/N decreases
in our study were extracted using the software routine greatly above this energy for most of the sources in the
acis extractv3.94(hereafterae;Townsleyetal. 2003; sample. Oneadvantageofusingthesameobserved-frame
Broos et al. 2005),included in the Tools for ACIS Real- energyrangeforeveryobjectisthatthesamesystematic
time Analysis (TARA; Oct 20, 2005) software package. instrumentaluncertaintiesapplytoeveryfit. Sincemost
7 ae is ideal for extracting and analyzing the spectra of ofthe detectedspectrumisusedintheanalysis,theS/N
largenumbersofpointanddiffuse sourcesobservedwith is higher than for cases where restricted energy ranges
ACIS over multiple epochs. ae calls procedures from were used.
both CIAO (v3.3)and HEASOFT (v6.0.4)and uses cal- TotesthowtheΓ−L correlationmightbeaffectedby
X
ibrationfilesthatarepartofthe CALDBv3.2.1product absorption and possible contamination from other emis-
provided by the Chandra X-ray Center. sionprocesses,wealsofittedthespectraintherest-frame
The ≈2 Ms CDF-N (≈1 Ms CDF-S) observations are energy range of 2–10 keV. This range was selected to
comprised of 20 (10) event files. The event files were avoid possible contamination from soft-excess emission
corrected for charge transfer inefficiency, bad columns, thatisoftendetectedinAGNsbelowrest-frameenergies
bad pixels, and cosmic ray afterglows. The event files of ∼ 1 keV. The selection of the 2–10 keV rest-frame
were also filtered for time intervals of acceptable as- band also aids in reducing the effects of X-ray absorp-
pect solutionand backgroundlevels. A detailed descrip- tion. For example, assuming a source with a power-law
tion of the data reduction procedures are presented in spectrumofΓ=1.7,z=1,N ∼1022cm−2,andsolarabun-
H
Alexander et al. (2003). Background event files and ex- dances the fraction of absorbed photons is 30% in the
posure maps were created by excluding circular regions 0.5–8 keV observed-frameband and 9% in the 2–10 keV
centered on the detected sources with radii that are a rest-frameband. The 2–10 keV rest-frame also mini-
factor of 1.1 times larger than the 99% encircled energy mizes possible contamination from Compton-reflection
radiiofthepointspreadfunctionsat∼1.49keV.Source emission from circumnuclear material that is thought to
extractionregionswereconstructedtocontain90%ofthe peak at a rest-frame energy of about 20 keV. In gen-
PSF encircled energy derived from the CXC 1.4967 keV eral,2–10keVrest-framespectrahavefewercountsthan
PSF libraries. There were two exceptions to this proce- 0.5–8 keV observed-frame spectra. For fits performed in
dure. First, for sources with greaterthan 1000 counts in the 2–10 keV rest-frame band, we selected sources with
the Alexander et al. (2003) catalog we used extraction morethan170counts inthis band, leavinga sub-sample
regions that contained 99% of the PSF encircled energy. of 144 RQ AGNs.
Second, for sources with 90% encircled energy extrac- The total number of photon counts per source (S)
tion regions that overlapped we reduced the extraction with energies in the 0.5–8 keV observed-frame band lies
in the range 170–13000. In Figure 1 (lower panel) we
5 InAGNsvalues ofαr couldbeflatter than theadopted αr = present the number of z > 0.1 radio-quiet AGNs in
0.8(e.g.,Richardsetal.1998;Muxlowetal.2005),withmeasured
our sample versus the number of photons with energies
standard deviations ∼1 (e.g., Wadadekar 2004). We investigated
how a flatter αr may affect our results and find that choosing a in the 0.5–8 keV observed-frame band. The solid line
value of αr =0.6, forexample, to estimate R willnot change our applies to sources with spectral fits performed in the
sample of RQ AGNs, whereas, a value of αr = 0.4 will result in 0.5–8 keV observed-frame, and the dotted line applies
theexclusionofonlytwosourcesfromoursample(1%oftheentire
to sources with spectral fits performed in the 2–10 keV
sample) inorder to satisfy R.10. We conclude that our sample
selectionandresultsofourstatisticalanalysisarenotsignificantly rest-frame. The mean logarithm of S for sources with
affected byvaluesoftheradiospectralindexaslowasαr =0. spectral fits performed in the 0.5–8 keV observed-frame
6TheradiosurveysofRichards (2000)andAfonsoetal.(2006) is hlog Si=2.74 with a standard deviation of σ ≃ 0.42.
cover the entire CDF-N and CDF-S regions respectively. More
The mean logarithm of S for sources with spectral fits
detailsoftheCDF-S radioobservations arefoundinNorrisetal.
performed in the 2–10 keV rest-frame is hlog Si=2.83
(2006).
7TARAisavailableathttp://www.astro.psu.edu/xray/docs/TARA/ with a standard deviation of σ ≃ 0.41. Based on the
4
TABLE 1
Models usedin fitting thespectra of theRQAGNsof
oursample.a
Modelb Nosources %ofthewholesample
PL 77 44.5
APL 76 43.9
PAPL 9 5.2
IAPL 4 2.3
PL+EL 4 2.3
APL+EL 3 1.7
a The selection criteria for the sample of RQ AGNs of our
present study were that the redshifts of the sources were
greater than 0.1 and the total number of photons in the full
band (0.5–8 keV) was greater than ∼ 170. b PL≡power-law
(XSPEC model wabs(pow)); APL≡absorbed power-law (XSPEC
model wabs*zwabs(pow)); PAPL≡partially absorbed power-law
(XSPEC model wabs*zpcfabs(pow)); IAPL ≡ionized absorbed
power-law (XSPEC model wabs*absori(pow)); PL+EL≡power-
law + emission-line (XSPEC model wabs(pow+zgauss));
APL+EL≡absorbed power-law + emission-line (XSPEC model
wabs*zwabs*(pow+zgauss)).
factthat oursample containssourceswith relativelylow
counts, we used the C-statistic (Cash 1979) to fit spec-
traasadoptedinasimilarstudypresentedinTozzi et al.
Fig. 2.— Number of sources vs. luminosity (upper panel)
(2006). In this study, the authors concluded that the and redshift (lower panel). The solid line represents sources with
C-statistic is more accurate than the χ2-statistic in esti- fitsperformedinthe0.5–8keVobserved-framebandandthedot-
mating the spectralparametersof AGNs with low-count ted line represents sources with fits performed in the 2–10keV
rest-frameband.
spectra (∼ 100 counts); similar arguments are presented
in Nousek & Shue (1989). We also performed spectral the estimation of Γ (see 5.2.6 for details). In Table 1,
fits in the 0.5–8 keV observed-frame band using the χ2- we list the number of sou§rces from our sample (the en-
statistic, with a grouping of 10 counts per bin. The sole tire samplecontains173RQ AGNs)fit with aparticular
purpose ofusing theχ2-statistic was to apply the F-test spectral model. From Table 1, we notice that based on
to assess the use of more complex spectral models. the F-testthere are 92 sourceswith detected absorption
For the CDF-S and CDF-N sources of our sample, we (∼53 % of the whole sample) and 7 cases with detected
assumed Galactic column densities of 8.8×1019 cm−2 iron lines (∼4 % of the whole sample).
(Stark et al.1992)and1.3×1020cm−2(Lockman 2004), The spectral-fitting results are presented in Table 2
respectively. The spectral analysis was performed us- for fits performed in the 0.5–8 keV observed-frameband
ing XSPEC version 12. The default spectral model (173RQ AGNs), and the fits performed in the 2–10keV
used is a power law (PL; POW) with Galactic ab- rest-frame band (144 RQ AGNs). In Table 2 we pro-
sorption (WABS). Additional model components were vide the photon index Γ (errors at the 90% confidence
added to the default model in cases where the F-test level), the intrinsic column density N (errors at the
H
showed an improvement in the fit at the 95% confi- 90%confidencelevel)inunits of1022 cm−2,andthe log-
dencelevel(0.5–8keVobserved-frame)whenthese addi- arithm of the hard X-ray luminosity in the rest-frame
tional components were used. We refer to models com- 2–10 keV band in units of erg s−1(hereafter referred to
prised of the default model plus additional model com- as L2−10). Table 2 also includes the X-ray identification
ponents as alternative models. Alternative models in- ofthesourcesbasedontheirRAandDECpositions,the
cluded an absorbed-power-law model (APL) at the red- photoncountsin the fitted range,the number ofdegrees
shift of the source (WABS ZWABS POW), an ionized- of freedom, and the values of the C-statistic. The last
absorbed-power-law model (IAPL) (WABS ABSORI two quantities provide an estimate of the quality of the
POW), a partial-absorbed-power-law model (PAPL) fits.
(WABS ZPCFABS POW) and/or models that included In Figure 2, we show the distributions of 2–10 keV
an ironline (PL+EL;APL+EL)(WABSZGAUSS POW; luminosities (upper panel) and redshifts (lower panel)
WABS ZWABS ZGAUSS POW). We also considered of the sources in our sample with fits performed in
models that contained a Compton-reflection component the 0.5–8 keV observed-frame band (solid line; 173 RQ
(PEXRAV),butwedidnotfindanyimprovementinthe AGNs) and the 2–10 keV rest-frame band (dotted line;
fits using such models. Our finding, that none of the 144 RQ AGNs). The luminosities of the sources in our
sourcesinoursamplerequireaCompton-reflectioncom- samplecoverthe range3×1041−6×1044 erg s−1 where
ponent,isinagreementwithTozzi et al.(2006)whofind the lower limit is mostly determined by the sensitivity
thatonly14outof321CDF-SsourcesrequireCompton- limit of the CDF-N survey, while the upper limit is a
reflection components. We note that none of these 14 statistical consequence of the fact that luminous AGNs
sources are part of our sample mostly because they con- (L2−10 & 1045 erg s−1) are less numerous than lower
tainless than170counts. Eventhoughwe do notdetect luminosity AGNs (see e.g., Brandt & Hasinger 2005).
asignificantreflection-componentinourspectralfits,an ThemeanredshiftandmeanlogarithmicX-rayluminos-
unaccountedreflection-componentcouldstillbeaffecting ity of the sources with fits performed in the 0.5–8 keV
5
TABLE 2
Propertiesof oursampleof RQAGNs selected fromtheChandra DeepField Surveys.
Xida z b Countsc Γ NHd logL2−10 C-stat dof typee modelf
RESULTSBASEDONFITSPERFORMEDINTHE0.5–8KEVOBSERVED-FRAME.
CXOJ123521.32+621628.1 0.559sp 513.4 1.51+−00..1077 .. 42.79 519.2 510 non-type1 PL
CXOJ123528.77+621427.8 0.850ph 183.2 1.19+−00..9422 4.95+−41..5997 43.06 542.0 509 non-type1 APL
CXOJ123529.45+621822.8 3.000ph 205.8 0.81+−00..2244 .. 43.93 516.1 510 non-type1 PL
CXOJ123535.21+621429.1 2.240ph 310.5 1.64+−00..3422 2.57+−12..8567 43.80 467.8 509 non-type1 APL
CXOJ123537.10+621723.6 2.050sp 451.1 1.82+−00..2116 .. 43.95 488.5 510 type1 PL
CXOJ123539.14+621600.3 2.575sp 729.8 1.91+−00..2156 1.98+−01..8185 44.33 489.1 509 type1 APL
CXOJ123546.07+621559.9 1.930ph 242.6 1.09+−00..2200 .. 43.49 474.8 510 non-type1 PL
CXOJ123548.37+621703.3 0.850ph 396.8 1.66+−00..1155 .. 42.92 440.5 510 non-type1 PL
CXOJ123548.53+621931.2 3.100ph 226.0 1.22+−00..2165 .. 43.95 439.5 510 non-type1 PL
CXOJ123550.42+621808.6 1.300ph 955.9 1.41+−00..1166 2.04+−00..6692 43.95 518.3 509 non-type1 APL
RESULTSBASEDONFITSPERFORMEDINTHE2–10KEVREST-FRAME.
CXOJ123521.32+621628.1 0.559sp 320.5 1.49+−00..2233 .. 42.80 386.6 349 non-type1 PL
CXOJ123535.21+621429.1 2.240ph 256.7 1.89+−00..7602 3.18+−33..6188 43.81 176.0 165 non-type1 APL
CXOJ123537.10+621723.6 2.050sp 365.7 1.88+−00..2243 .. 43.94 220.0 177 type1 PL
CXOJ123539.14+621600.3 2.575sp 604.0 1.84+−00..4420 1.96+−21..2906 44.33 161.0 149 type1 APL
CXOJ123546.07+621559.9 1.930ph 182.6 0.85+−00..3333 .. 43.53 218.8 184 non-type1 PL
CXOJ123548.37+621703.3 0.850ph 261.3 1.69+−00..2264 .. 42.91 268.3 293 non-type1 PL
CXOJ123550.42+621808.6 1.300ph 789.5 1.69+−00..2336 3.49+−11..1602 43.99 274.8 234 non-type1 APL
CXOJ123551.75+621757.1 1.910ph 1016.8 1.65+−00..3208 1.67+−11..3221 44.37 179.0 181 non-type1 APL+EL
CXOJ123553.13+621037.3 1.379sp 1329.0 1.85+−00..1390 0.88+−00..9711 44.22 225.8 226 type1 APL
CXOJ123555.08+621610.7 1.022sp 188.7 1.25+−00..8308 14.88−+193.4.235 43.29 341.0 266 non-type1 PAPL
Note.—Table2ispresentedinitsentiretyintheelectroniceditionoftheAstronomicalJournal. Aportionisshownhereforguidance
regardingitsformandcontent.
a Xid with RA+DEC coordinates.b Spectroscopic (sp) and photometric (ph) redshifts gathered from the literature (see 2).c Back-
§
ground subtracted source counts in the 0.5–8keV observed-frame band for fits performed in the 0.5–8keV observed-frame band
and counts in the 2–10keV rest-frame band for fits performed in the 2–10keV rest-frameband.d In units of 1022 cm−2.e Based
on Baueretal. (2004a), source classifications from 4.1.1 (http://www.astro.psu.edu/∼niel/hdf/hdf-chandra.html) f PL≡power-law
(XSPECmodelwabs(pow));APL≡absorbed-power-law§(XSPECmodelwabs*zwabs(pow));PAPL≡partially-absorbed-power-law(XSPEC
modelwabs*zpcfabs(pow));IAPL≡ionized-absorbed-power-law(XSPECmodelwabs*absori(pow)); PL+EL≡power-law+emission-line
(XSPEC model wabs(pow+zgauss)); APL+EL≡absorbed-power-law + emission-line (XSPEC model wabs*zwabs*(pow+zgauss)).g The
estimated values of Γ, NH, and X-ray luminosities presented in this table are based on spectral fits performed in the 0.5–8 keV
observed-frame.
observed-frame band are hzi ≃ 1.41 and hlog L2−10i ≃ solidline(92/173),andsourceswithfitsperformedinthe
43.6, respectively. The mean redshift and mean loga- 2–10 keV rest-frame band are indicated with the dotted
rithmic X-ray luminosity of the sources with fits per- line (82/144). In the two fitted energy ranges, the peak
formed in the 2–10 keV rest-frame band are hzi ≃ 1.38 ofintrinsiccolumndensitydistributionislog N ∼22.6,
H
and hlog L2−10i≃43.6, respectively. and there is a fraction of ∼40% sources from the to-
In Figure 3 (upper panel), we show the distributions tal sample having log N > 22. We note that there
H
of the photon indices of the sources with fits performed are likely systematic errors on these column density es-
in the 0.5–8 keV observed-frame band (solid line) and timates due to unmodeled absorptioncomplexity. These
the 2–10 keV rest-frame band (dotted line). We find parametervaluesanddistributionsareinagreementwith
the mean photon indices and their standard deviations those found in Tozzi et al. (2006) and Dwelly & Page
for fits performed in the 0.5–8 keV observed-frame and (2006).
2–10 keV rest-frame bands to be hΓi ≃ 1.60 ± 0.27 and InFigure4,wepresentadiagramcomparingestimates
hΓi ≃ 1.70 ± 0.29, respectively. In Figure 3 (lower of Γ obtained from fits performed in the 2–10 keV rest-
panel), we show the distributions of the intrinsic col- frame (Γ ) and fits in the 0.5–8 keV observed-frame
rest
umndensitiesofsourceswithsignificantabsorption(only (Γ ). ThesizeofeachsymbolinFigure4increaseswith
obs
sources where the F-test indicated significant intrinsic redshift. Deviations from the straight line (Γ =Γ )
obs rest
absorption at the >95% confidence level are included are most likely statistical in nature, however, a few may
in the distributions); sources with fits performed in the beassociatedwiththeeffectsofintrinsicabsorption,soft
0.5–8 keV observed-frame band are indicated with the excesses, non-detected spectral lines, and Compton re-
6
Fig. 4.— Spectral index for fits performed in the 2–10 keV
rest-frame band (Γrest) versus spectral index for fits performed
in the 0.5–8 keV observed-frame band (Γobs). The size of each
symbol increases with redshift. The solid line represents the case
ofΓobs=Γrest. NoticethatvaluesofΓrest andΓobs canbefound
inTable2.
Fig. 3.— Number of sources vs. photon index (upper panel)
and column density (lower panel). In the lower panel we show
onlythesourceswithasignificantdetectionofabsorptionintheir
spectra. The solid line represents sources with fits performed in
the0.5–8keVobserved-framebandandthedottedlinerepresents
sourceswithfits performedinthe2–10keVrest-frameband.
flection.
In general, the agreement between Γ and Γ is
rest obs
good;thisisfirstquantifiedbyahighPearsonlinearcor-
relation coefficient (∼0.73) and a very low null hypoth-
esis probability (∼ 4.8×10−25). Secondly, this agree-
ment is quantified by testing whether the linear relation
between Γ and Γ is consistent with Γ = Γ .
rest obs rest obs
To verify the later we performed a χ2 fit to the data
assuming Γ = αΓ , where α was a free parame-
rest obs
ter.8 We considered the errors in both variables Γ
rest
and Γ when performing the least-squares fit. We
obs
obtained α = 0.996 ± 0.08 (error at the 68% confi-
dence level) with χ2 = 99.3 for 143 degrees of freedom
(dof). As a basic check for the luminosity dependence
of the linear relation between Γ and Γ we per-
rest obs
formedχ2 fitsofthemodelΓ =αΓ tosourceswith
rest obs
log L2−10 . 43.6 and sources with log L2−10 & 43.6.
We obtained α = 0.995±0.011 (χ2 = 43.8; dof=70) for
sources with log L2−10 . 43.6 and α = 0.997± 0.010
(χ2 =55.6; dof=72) for sources with log L2−10 &43.6.
Fig. 5.— Estimated best-fit column densities versus 2–10 keV
5. RESULTSANDDISCUSSION luminosities(upper panel), and 2–10 keV luminosities versus red-
shifts(lower panel) ofthe z>0.1RQAGNs. Filledcirclesrepre-
5.1. Selection Effects. sent sources with fits performed in the 0.5–8keV observed-frame
band and open squares represent sources with fits performed in
We begin this section by describing several selection the 2–10keV rest-frame band. In the upper panel, the two lines
effects that are intrinsic to our sample. Having an ex- indicate the maximum column density that can be detected for
posure of ≈2 times greater than the CDF-S survey, the a source with 0.1 ≤ z ≤ 4.0, and a total of 170 counts in the
0.5–8keVobserved-frame(dashed)and2–10keVrest-frame(dot-
CDF-Nsurveydrivesthesensitivitylimitsofoursources,
ted). Inthelowerpanelthelinesindicatetheminimumluminosity
sothefollowingdiscussionwillbefocusedonthissurvey. requiredfor the detection of a source as a function of redshift. A
Figure 5 shows the estimated best-fit column density totalof170countsinthe0.5–8keVobserved-frameband(dashed)
versus the 2–10 keV luminosity (upper panel), and the oratotal of170 counts inthe 2–10keV rest-frameband (dotted)
isassumed. For the limits shownin this figure itis assumed that
the source is detected at the ACIS-I aim-point with an exposure
8Aχ2fitusingtherelationy=αxtomodelsomebivariatesam- timeof≈2Ms.
ple(xi,yi)witherrorsinboth variables(σxi, σyi)isobtained by
minimizingχ2=X (yi−αxi)2
σ2 +α2σ2
i yi xi
7
Fig. 6.— Spearman correlation coefficients of the Γ−L2−10
relationasafunctionofthemeanredshiftwithineachsub-sample.
Eachsub-samplecontains38RQAGNs. Thesolidlinecorresponds
tothefitsperformedinthe0.5–8keVobserved-frameband(Table
2). The dashed-line corresponds to the fits performed in the 2–
10keVrest-frameband(Table2). Thedotted linescorrespondto
threedifferentlevelsofsignificance(68%,90%and99%),assuming
38independent measurementsofΓvs. L2−10.
2–10 keV luminosity versus redshift (lower panel), for Fig. 7.— Spearman correlation coefficients of the Γ−L2−10
relationasafunctionofredshiftfortheRQAGNswithineachin-
our z > 0.1 RQ AGNs. Spectral fits performed in the dependent redshiftbin. In the upper panel each redshiftbin con-
0.5–8keVobserved-framebandand2–10 keVrest-frame tains∼55RQAGNsandthefitswereperformedinthe0.5–8keV
observed-frame band (Table 2). In the lower panel each redshift
band are shown with filled circles and open squares re-
bin contains ∼45 RQ AGNs, and the fits were performed in the
spectively. IntheupperpanelofFigure5,thedashedline 2–10 keV rest-frameband (Table 2). Thedotted lines correspond
shows the maximum column density that can be found tothreedifferentlevelsofsignificance(68%,90%and99%);these
for a source with 0.1 ≤ z ≤ 4.0 assuming the source areobtainedassuming55sourcesintheupperpaneland45sources
inthelowerpanel.
is detected at the ACIS-I aim-point with an exposure
5.2. Luminosity and Photon index
time of≈2Ms (Alexander et al.2003)andatotalof170
counts in the 0.5–8 keV observed-frame band (dashed One of the goals of this work is to examine a possible
line) and 2–10 keV rest-frame band (dotted line). Each correlation between L and Γ in a sample of RQ AGNs
X
point on these curves is obtained by fixing NH and find- which was previously reported by Dai et al. (2004). To
ing the minimum luminosity that can be obtained with improve on the Dai et al. analysis we significantly in-
0.1 ≤ z ≤ 4.0 assuming a source with Γ = 1.6, Galac- creased the sample size using the CDFs, considered a
tic column density of 1.3×1020cm−2 and 170 counts in larger redshift range, and used X-ray spectra that con-
each fitted energy range. For low-luminosity sources tainedmorethan170countsinthefullband(0.5–8keV).
(L2−10 . 1042 erg s−1), the threshold column density The resultsofthis analysisis shownin the followingsec-
is ≈1024 cm−2, which increases by a factor of ∼10 for tions. For the following analysis we use the X-ray lumi-
higher luminosity sources (1044 − 1045 erg s−1). The nosity in the 2–10 keV rest-frame band (L2−10).
maximum column density observed at a specific lumi-
nosity is set by AGNs with z = 0.1 in most of the ob- 5.2.1. Possible evolution of the strength and significance of
served luminosity range; however, for luminous sources the Γ−LX correlation
(L2−10 & 1044 erg s−1) higher redshift AGNs (z ∼ 1–4) As a first approach, we searched for a Γ – LX corre-
establish the limit in NH because these are less affected lation as a function of redshift selecting sub-samples or-
by absorption. dered in redshift. We used sub-samples containing 38
In the lower panel of Figure 5, the curves indicate sources for fits performed in the 0.5–8 keV observed-
the minimum luminosity required for the detection of framebandandthe 2–10keVrest-frameband(Table2).
a source as a function of redshift. We have assumed We calculated the mean redshift of each sub-sample and
a source free of intrinsic absorption, positioned at the computed the Spearmanrank correlationcoefficient and
AΓC=IS1-I.6,aigmal-apcotiinctcowluitmhnadnenesxiptyosoufre1.3ti×m1e02o0cfm≈−22 aMnsd, psirgonciefiscsanwcaesorfetpheeactoedrreblyatisohnifbtientgwetehneΓsaamndplLin2g−1w0.inTdhowis
with170photoncountsinthe 0.5–8 keVobserved-frame acrosstheentireobservedredshiftrange. Figure6shows
(dashed line) or 170 counts in the 2–10 keV rest-frame the values of the significance of the correlations and the
f(odrotzte≈d0l.i5nea)n.dT≈he3×th1r0e4s3heorlgdslu−m1finoroszit≈y i2s.5≈.1T04h2eedragshs−ed1 Stipoenaramsaanfcuonrcrteiloantioonf ctoheeffimcieeanntsroedfsthhieftΓo−f tLh2e−1s0ourreclaes-
curve in Figure 5 is obtained by assuming no intrinsic within each sub-sample, using the best-fit parameters
absorption; however, the presence of NH, which might from Table 2. The solid line in Figure 6 corresponds
beevolving(e.g.,La Franca et al.2005;Treister & Urry to sources fitted in the 0.5–8 keV observed-frame band
2006;Tozzi et al.2006),couldbeincreasingtheobserved andthe dashedline correspondsto those fitted in the 2–
threshold luminosity. 10 keV rest-frame band. We notice that the correlation
8
TABLE 3
Correlation tableof Γversus LX.
Γvs. L2−10
Cor. Coeff. Redshiftbin FittedEnergyRange Na rC %signb
Spearman 0.3.z.0.96 0.5–8keVobserved-frame 53 0.48 >99.9
Kendall 0.3.z.0.96 0.5–8keVobserved-frame 53 0.33 >99.9
Pearsonc 0.3.z.0.96 0.5–8keVobserved-frame 53 0.42 99.8
Spearman 0.96.z.1.5 0.5–8keVobserved-frame 54 0.29 96.7
Kendall 0.96.z.1.5 0.5–8keVobserved-frame 54 0.19 95.9
Pearsonc 0.96.z.1.5 0.5–8keVobserved-frame 54 0.31 97.5
Spearman 1.5.z.3.3 0.5–8keVobserved-frame 57 0.45 >99.9
Kendall 1.5.z.3.3 0.5–8keVobserved-frame 57 0.32 >99.9
Pearsonc 1.5.z.3.3 0.5–8keVobserved-frame 57 0.43 >99.9
Spearman 0.3.z.0.96 2–10keV rest-frame 44 0.62 >99.9
Kendall 0.3.z.0.96 2–10keV rest-frame 44 0.42 >99.9
Pearsonc 0.3.z.0.96 2–10keV rest-frame 44 0.530 >99.9
Spearman 0.96.z.1.5 2–10keV rest-frame 46 0.22 84.9
Kendall 0.96.z.1.5 2–10keV rest-frame 46 0.14 83.3
Pearsonc 0.96.z.1.5 2–10keV rest-frame 46 0.23 87.8
Spearman 1.5.z.3.3 2–10keV rest-frame 48 0.43 99.8
Kendall 1.5.z.3.3 2–10keV rest-frame 48 0.31 99.8
Pearsonc 1.5.z.3.3 2–10keV rest-frame 48 0.43 99.7
a Number of RQ AGNs in each redshift bin. b Percentile significance of the
correlation.c CalculatedfromΓversuslogLX.
(0.3.z .0.96 and 0.96.z .1.5) were selected to ob-
tainindependentredshiftbinswithcomparablenumbers
ofsourceswithinthem. Eachredshiftbincontained∼55
sources in the 0.5–8 keV observed-frame band and ∼45
sources in the 2–10 keV rest-frame band. In Figure 7
and Table 3 we show the Spearman rank correlation co-
efficientandthesignificanceoftheSpearmancorrelation
coefficientineachbin. TheupperpanelofFigure7corre-
spondstofitsperformedinthe0.5–8keVobserved-frame
and the lower panel to fits performed in the 2–10 keV
rest-frame. The height of each bar is the significance of
the Γ−L2−10 Spearmancorrelation. The correlationfor
fitsperformedinthe 0.5–8keVobserved-frameis signifi-
cantforthe threeredshift bins; however,we findaslight
decrease in the strength and significance in the second
redshiftbinforfitsperformedinthe2–10 keVrest-frame.
The significance of the correlation in the first and third
redshift bins is >99.5% for both fitting ranges. A sig-
nificant expansion of our sample made by incorporating
additionaldeepAGNsurveyswillberequiredtoconfirm
thepossibledecreaseofthestrengthofthecorrelationin
the second redshift bin.
InFigure8,weplotΓvs. L2−10forsourcesineachred-
shift bin of Figure 7, for fits performed in the 0.5–8 keV
Fig. 8.—Γversus2–10keVluminosityofradio-quietAGNsinthe
redshiftrangeof0.3.z.3.3. Intheupperpanelweshowsources observed-frame (upper panel) and the 2–10 keV rest-
withfitsperformedinthe0.5–8keV observed-frameband. Inthe frame(lowerpanel). Sourcesinoursamplewithredshifts
lower panel we show sources with fits performed in the 2–10keV intherange0.3.z .0.96havealowermeanluminosity
rest-frame band. The symbol size increases with redshift. Filled
squares are sources with 0.3 .z .0.96, open circles are sources ofhlog L2−10i∼43.1(σlogL2−10 ∼0.5)thansourceswith
with 0.96 . z . 1.5, and filled triangles are sources with 1.5 . redshifts in the range 1.5 . z . 3.3 which have a mean
hza.vin3g.30..3Th.ezd.ott0e.d96l.inTehienddiacsahteeds tlihneelsehaostw-ssqtuhaerelesafistt-stqousaoruerscfiest lluummiinnoossiittyy odfishtlroibguLti2o−n1s0ifo∼r s4o4u.1rc(eσsloignL2t−h1e0r∼ed0s.h4i)ft. bTihnes
tosourceshaving1.5.z.3.3.
0.3.z .0.96 and 1.5.z .3.3 are shown in Figure 9.
Wenoticethatthepeakofthedistributionofthesources
has two significant peaks (∼99%) in both energy bands
inthehigh-redshiftbinissignificantlyhigherinluminos-
fitted, one with a mean redshift of ∼ 0.7, and the other
ity than the peak of the distribution of the sources in
with a mean redshift of ∼2.2.
the low-redshift bin. This shift in luminosity distribu-
As a second approach, we selected three independent
tionsis mainly aselectioneffect(see Figure5)combined
redshift bins covering the redshift range 0.3 < z < 3.3.
with the fact that luminous sources are more numerous
The high redshift bin (1.5.z .3.3) was chosen to
at high redshift (Ueda et al. 2003; Hasinger et al. 2005).
match the redshift range where Dai et al. (2004) found
the Γ−L correlation while the other two redshift bins The Spearman correlation index of the Γ−L2−10 data
X
9
Fig. 9.—2–10 keV rest-frameluminosity(L2−10) distributions
for radio-quiet AGNs with 0.3 . z . 1.5 (thick line) and 1.5 .
z . 3.3 (dashed line). The fits are performed in the 0.5–8keV
observed-frameband.
for the whole sample (173 RQ AGN) is ∼0.24 (99.8%
significance) and ∼0.16 (94.1% of significance) for the
0.5–8 keV observed-frame and the 2–10 keV rest-frame
spectral fits. These correlation coefficients are signifi-
Fig. 10.— Γ versus 2–10 keV luminosity of radio-quiet AGNs
cantly lower than those found in the 0.3.z .0.96 and
with0.3.z.0.96 (upper panel)andwith1.5.z.3.3 (lower
1.5.z .3.3redshiftbins(seeTable3formoredetails). panel). The values of the X-ray luminosities and spectral indices
In Table 4, we show the results of a test of the Γ−L wereobtained byfitting thespectra inthe observed-frameenergy
X
correlation using only sources with spectroscopic red- rangeof0.5–8keV (seeTable2). Thedashedlinesindicatelinear
fitstothedatausingtheleast-squaresmethod. Theopensymbols
shifts. We find that the Γ−L correlation of the sub-
X correspondtosources havinglogNH .22, andthefilledsymbols
sample of sources with spectroscopic redshifts is signif- aresourceswithlogNH >22. Circlescorrespondtotype1AGNs
icant in the three redshift bins; however, as indicated andsquarestonon-type1AGNs.
in Table 4, this sub-sample includes a larger fraction of
type 1 AGNs and contains more sources with log N .
H (a) Observed-Frame (b) Rest-Frame
22 than that of the whole sample. In addition, the size
99.9%
99.9%
ofthis sub-sampleis significantlysmallerthanthe whole 68% 68%
sample. Wecautionthatthestrengthsofthecorrelations
providedbythenon-parametrictestsusedinouranalysis
of sub-samples containing a small number of sources N
withthe presentuncertaintiesinthe photonindices may
be inaccurate since the variance of the Spearman corre- 99.9%
68% 68%
lation coefficient is σ2= 1 . Photometric redshifts are
N−1 99.9%
subject to larger errors than spectroscopic ones and for
sources with z > 1 the error is approximately given by
∆z/(1+z)=0.05 (e.g, Cohen et al. 2000). In our anal-
ysis, the uncertainties in the redshifts will mainly affect
the estimation of the X-rayluminosities. For example, a Fig. 11.— 68% and 99.9% confidence contours of the slope α
sourceatz ∼2willhaveanuncertaintyintheestimated and offset β∗ of the Γ−LX correlation for AGNs in the 0.3 <
z < 0.96 (solid contours) and 1.5 < z < 3.3 (dotted contours)
luminosity of ∆LX/LX ∼ 0.3. This level of uncertainty redshift ranges. The parameters α and β∗ were derived from fits
wvoilllvensotesstiigmniafitcinagntclyhaanffgeecstionurthreespuhltostsoinnciendouexrsotvuedrytwino- ofthe linearmodelΓ = αlog (104L42−er1g0s/s) + β∗. Thefits were
performed in the 0.5–8 keV observed-frame band (a) and in the
orders of magnitude in X-ray luminosity.
2–10 keV rest-frame band (b). The confidence contours indicate
In the following three sections, we focus on sources thattheparametersofthelinearfittotheΓ−LXcorrelationdiffer
in the first bin (0.3 . z . 0.96) and the third bin at the > 99.9% confidence level between the 0.3 < z < 0.96 and
1.5<z<3.3redshiftranges.
(1.5 . z . 3.3) and test the sensitivity of the Γ−L
X
correlation to the possible presence of intrinsic absorp- 0.5–8 keV (see Table 2). We searched for a correlation
tionandComptonreflectioninthespectraofthesources. between Γ and L by computing the Spearman’s and
X
Kendall’scorrelations(seeTable3). Wefindastrongcor-
5.2.2. Possible evolution of the slope and offset of the
Γ−L correlation relationbetweenΓandL2−10,atthe>99.9%confidence,
X for sources having 0.3.z .0.96 and 1.5.z .3.3. We
InFigure10,weshowΓversusL2−10 forsourcesinthe tested for a linear dependence between Γ and log LX by
rangesof0.3.z .0.96(upperpanel),and1.5.z .3.3 calculatingthe Pearson’scorrelationand finda high sig-
(lower panel). The values of the X-ray luminosities and nificance(>99.8%)forsourceswithin0.3.z .0.96 and
spectralindices showninFigure 10wereobtainedby fit- 1.5.z .3.3 (see Table 3). In Table 5, we also present
ting the spectra in the observed-frame energy range of results of linear least-squares fits to the Γ−L relation
X
10
TABLE 4
Correlation tableof Γversus LX forAGNswith spectroscopic redshifts.
Γvs. L2−10
FittedEnergyFrame Redshiftbin Na rCb %signc fractionoftype1 fractionwithlogNH.22
0.5–8keVobserved-frame 0.3.z.0.96 46 0.47 99.9 0.37 0.70
2–10keVrest-frame 0.3.z.0.96 40 0.64 >99.9 0.40 0.68
0.5–8keVobserved-frame 0.96.z.1.5 31 0.40 97.3 0.42 0.71
2–10keVrest-frame 0.96.z.1.5 26 0.42 96.6 0.50 0.73
0.5–8keVobserved-frame 1.5.z.3.3 26 0.38 94.3 0.62 0.62
2–10keVrest-frame 1.5.z.3.3 24 0.49 98.5 0.67 0.67
aNumberofRQAGNsineachredshiftbin. bSpearmancorrelationcoefficient. cPercentilesignificanceofthecorrelation.
and 1.5 < z < 0.33 redshift ranges and for fits per-
formed in the 2–10 keV rest-frame band (Figure 11a)
and in the 0.5–8keV observed-frameband (Figure 11b).
The parameter β∗ is obtained from fits of the model
Γ = α log (104L42−er1g0s/s) + β∗. L2−10 was re-normalized
forthepurposeofillustratingbetterthefullrangeofthe
contours. The 68%and99.9%confidencecontourslevels
correspondto∆χ2(α,β∗)valuesof2.3and13.81,respec-
tively. The confidencecontoursindicate thatthe param-
etersofthe linear fitto the Γ−L correlationchangeat
X
the > 99.9%confidence levelbetween the 0.3<z <0.96
and 1.5<z <0.33 redshift ranges.
Totestthe sensitivityandstabilityoftheseconfidence
contours to possible outliers in the data we repeated
the confidencecontouranalysisbyexcluding datapoints
with significant deviations from the linear fit. In partic-
ular, we re-fit the Γ−L correlation and re-calculated
X
the confidence contours after excluding data points that
deviated by more than 2σ, 2.5σ and 3σ from the linear
fit. In all cases we find that the parameters of the lin-
earfitto the Γ−L correlationchangebetweenredshift
X
bins1and3atthe>99.9%and>98%confidencelevels
for fits performed in the 0.5–8 keV observed-frame and
Fig. 12.— Γ versus 2–10 keV luminosity of radio-quiet AGNs 2–10 keV rest-frame, respectively.
with0.3.z.0.96 (upper panel) andwith1.5.z.3.3 (lower As discussed in 4 to test the influence of possible ef-
panel). The values of the X-ray luminosities and spectral indices §
fects such as Compton reflection, soft excesses, and in-
wereobtainedbyfittingthespectraintherest-frameenergyrange
of 2–10keV (see Table 2). The dashed lines indicate linear fits trinsic absorption on the Γ – LX correlation,we also fit-
to the data using the least-squares method. The open symbols ted the spectra in the 2–10 keV rest-frame, where these
correspondtosources having logNH .22,andthe filledsymbols effects are expected to be smaller. The results of these
aresourceswithlogNH >22. Circlescorrespondtotype1AGNs spectral fits are presented in Table 2. In Figure 12, we
andsquarestonon-type1AGNs.
present Γ versus L2−10 for sources in the redshift range
of0.3.z .0.96(upperpanel),andintheredshiftrange
with a model of the form Γ = α log L +β. For this
X of1.5.z .3.3 (lower panel) for spectralfits performed
test, we assumed that Γ is the dependent variable with
in the 2–10keVrest-frame band. The results of our cor-
errors given at the 68% confidence level. In Table 5, we
relation analysis applied to the variables Γ and L are
show the best-fit linear fit parameters α and β. We find X
shown in Table 3. We find the Spearman, Kendall and
that the best-fit parameters α and β show a significant
change between the redshift bin 0.3 . z . 0.96 and the Pearsoncorrelation coefficients of Γ vs. L2−10 to be sig-
nificantatthe>99.9%and>99.7%confidencelevels,for
redshift bins of 0.96 . z . 1.5 and 1.5 . z . 3.3. In
sources within 0.3.z .0.96 and 1.5.z .3.3 respec-
particular, for spectral fits performed in the 0.5 – 8 keV
tively. These results suggest that Compton reflection,
observed-frame band we find the following: The slope
softexcesses,andintrinsicabsorptionaremostlikelynot
and offset of the linear fit to the Γ−L correlation in
X drivingtheobservedcorrelationbetweenΓandL inthe
the 0.3 < z < 0.96 redshift range are, α= 0.14 ± 0.02 X
two redshift bins analyzed in this section. In 5.2.3 and
and β = −4.5±0.8, respectively. The slope and offset §
5.3.6,weprovidedetailedanalysestoshowthatintrinsic
of the Γ−LX correlation in the 1.5 < z < 0.33 redshift §absorption and Compton reflection have negligible con-
rangeare,α = 0.23 ± 0.03,β =−8.7±1.2,respectively.
tributions to the Γ−L correlation.
Similarresultarefoundforspectralfitsperformedinthe X
2–10 keV rest-frame. This change in the linear parame-
5.2.3. Dependence of the Γ−L correlation on N
ters can also be seen in Figure 8. X H
In Figure 11 we show the 68% and 99.9% confidence The estimated values of the photon indices used in
contours of α and β∗ for AGNs in the 0.3 < z < 0.96 ourcorrelationanalysisdependpartiallyonthe assumed