The NuSTAR Extragalactic Surveys: X-ray spectroscopic analysis of the bright hard-band selected sample
We discuss the spectral analysis of a sample of 63 Active Galactic Nuclei (AGN) detected above a limiting flux of erg s cm in the multi-tiered NuSTAR Extragalactic Survey program. The sources span a redshift range (median 0.58). The spectral analysis is performed over the broad 0.5-24 keV energy range, combining NuSTAR with Chandra and/or XMM-Newton data and employing empirical and physically motivated models. This constitutes the largest sample of AGN selected at keV to be homogeneously spectrally analyzed at these flux levels. We study the distribution of spectral parameters such as photon index, column density (), reflection parameter () and 10-40 keV luminosity (). Heavily obscured () and Compton Thick (CT; ) AGN constitute 25% (15-17 sources) and 2-3% ( 1-2 sources) of the sample, respectively. The observed distribution fairly agrees with predictions of Cosmic X-ray Background population synthesis models (CXBPSM). We estimate the intrinsic fraction of AGN as a function of , accounting for the bias against obscured AGN in a flux-selected sample. The fraction of CT AGN relative to AGN is poorly constrainted, formally in the range 2-56% (90% upper limit of 66%). We derived a fraction () of obscured AGN () as a function of in agreement with CXBPSM and previous X-ray determinations. Furthermore at and agrees with observational measurements/trends obtained over larger redshift intervals. We report a significant anti-correlation of with (confirmed by our companion paper on stacked spectra) with considerable scatter around the median values.
Over the last decade the advent of Chandra and XMM-Newton allowed extragalactic blank-field X-ray surveys to reach sufficient sensitivities (down to erg s cm) and sky coverage (from tenths to several square degrees) to allow the study of distant populations of Active Galactic Nuclei (AGN, Hickox & Markevitch, 2006; Lehmer et al., 2012; Xue et al., 2012; Brandt & Alexander, 2015; Luo et al., 2017). They resolved most (up to 80-90%) of the Cosmic X-ray Background (CXB) at energies below 10 keV (e.g. Hickox & Markevitch, 2006; Cappelluti et al., 2017) as a mixture of obscured and unobscured AGN, in agreement with early population-synthesis model predictions (Setti & Woltjer, 1989; Comastri et al., 1995). The fraction of resolved CXB gradually decreases with energy being of the order of % above 10 keV and only few percents at keV with Swift/BAT & INTEGRAL studies (Krivonos et al., 2007; Ajello et al., 2008).
The missing unresolved AGN population which is needed to account for the remaining high energy CXB flux may be made up of a numerically non-negligible population of heavily obscured () non-local AGNs (Worsley et al., 2005; Xue et al., 2012). It is therefore crucial to directly investigate the distribution of the obscured AGN population at the high column densities contributing to the CXB at high energies. A population of AGN with column densities in excess of cm, called Compton Thick (CT) AGNs, and numerically comparable to the absorbed Compton Thin AGN, has long been posited to be responsible for the unaccounted 10-25% of the CXB flux required by population synthesis models in order to reproduce its peak at 20-30 keV (Comastri et al., 1995; Gilli et al., 2007, hereafter G07). Recent works though suggest that also less obscured sources may contribute significantly to the missing flux at keV once other relevant high-energy spectral complexities of the AGN spectrum are taken into proper consideration (Treister et al., 2009; Akylas et al., 2012; Ueda et al., 2014). The latter would therefore lessen the need for a contributing sizable population of CT sources.
Given their very large column densities, the most obscured sources can effectively be detected in the X-rays at rest-frame energies keV since their primary continuum is strongly suppressed at softer energies. This can be currently done (i) locally () by targeting bright sources (e.g., erg s cm; Baumgartner et al., 2013) Seyfert-type ( erg s) with hard X-ray ( keV) surveys such as those performed by Swift/BAT & INTEGRAL (Krivonos et al., 2007; Ajello et al., 2008) and (ii) at high redshifts () with the most sensitive Chandra/XMM-Newton observations of the deep/medium survey fields (e.g. Civano et al., 2016; Luo et al., 2017). Through either spectral or hardness ratio analysis they allowed to quantify and characterize the obscured Compton Thin () AGN population and further shed light on the known decreasing trend between the numerical relevance of this population compared to all AGN (absorbed fraction) and the source luminosity (Lawrence & Elvis, 1982; Gilli et al., 2007; Burlon et al., 2011; Buchner et al., 2015) and its redshift evolution (La Franca et al., 2005; Treister & Urry, 2006; Ballantyne et al., 2006; Aird et al., 2015a; Buchner et al., 2015; Liu et al., 2017). They also allowed to explore the importance of the CT population although with different constraining power and different non-negligible degrees of bias especially at the highest column densities and lowest luminosities (e.g. Burlon et al., 2011; Brightman et al., 2014; Lanzuisi et al., 2015; Buchner et al., 2015; Ricci et al., 2015). Indeed the large diversity in the spectral shapes as well as poorly explored observational parameters in low counting regimes111i.e. at the highest column densities or at the high/low energy spectral boundaries where the instruments are less sensitive. such as the high energy cut-off and the reflection strength at high energies (Treister et al., 2009; Ballantyne et al., 2011, hereafter BA11), the scattered fractions at low energies (Brightman & Ueda, 2012; Lanzuisi et al., 2015) or physical parameters such as the Eddington ratio (Draper & Ballantyne, 2010), may further introduce uncertainty or biases, enlarging the possible range of the fraction of CT sources to one order of magnitude (Akylas et al., 2012) or even significantly reduce their importance (Gandhi et al., 2007). Indeed, given the paucity of CT sources effectively contributing to the CXB missing flux, the most recent population-synthesis models try to explain the CXB missing component as mainly a pronounced reflection contribution from less obscured sources with a reduced contribution by CT AGN (Treister et al., 2009; Ballantyne et al., 2011; Akylas et al., 2012). Going deeper at high energies while retaining the capability of being greatly less affected by obscuration bias, will enable us to efficiently sample a more distant () and luminous population (i.e. at the knee of the luminosity function, erg s) of obscured sources and better characterize their high energy spectrum, substantially improving constraints on the majority of the obscured AGN contributing to the CXB (e.g., Gilli, 2013). The Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al., 2013) is perfectly tailored for this task. Indeed, as the first hard X-ray focusing telescope in orbit, it provides a two order of magnitude increase in sensitivity compared to any previous hard X-ray detector. With its higher sensitivity, NuSTAR has resolved of the CXB near its peak (Harrison et al., 2016, hereafter H16) and is able to probe the hard X-ray ( keV) sky beyond the local Universe ().
The NuSTAR wedding-cake extragalactic survey strategy focuses on several well-known medium-deep fields with extensive multi-wavelength coverage. The core of it includes the EGS (Del Moro et al. in prep.), E-CDFS (Mullaney et al., 2015), COSMOS (Civano et al., 2015) fields, and a wider and typically shallower Serendipitous survey (Lansbury et al., 2017b, L17). A further extension of it with the observation of two deep fields (CDF-N, Del Moro et al. in prep; UDS, Masini et al. submitted) has also recently been completed. This multi-tiered program has already detected 676 AGN out to (Alexander et al., 2013; Civano et al., 2015; Mullaney et al., 2015; Aird et al., 2015b; Lansbury et al., 2017b), of which 228 are significantly detected in the hard 8-24 keV NuSTAR band. In particular, at low redshift, Civano et al. (2015) presented the spectroscopic identification of a local () low-luminosity ( erg s) CT AGN not previously recognized by either Chandra or XMM-Newton with a column density cm. Lansbury et al. (2017a) identified three similar sources at with even higher obscuration in the NuSTAR Serendipitous Survey. At high-redshift, Del Moro et al. (2014) presented the detection of a heavily absorbed ( cm) quasar at .
The redshift range and the luminosities probed by the NuSTAR extragalactic survey program are well matched to CXB population-synthesis models in terms of characterization of the AGN high energy spectral shape and of the dominant obscured populations contributing to the CXB. In the latter case population synthesis models predict the largest CT AGN contributions from sources at 0.4-1.2 with luminosities erg s (e.g., Gilli, 2013) and that their contribution to the residual CXB flux may amount to 90% by . (Treister et al., 2009). We therefore expect NuSTAR to start to evaluate the relative importance of the obscured AGN populations and shed light on the main aspects contributing to the still unaccounted remaining flux on the peak of the CXB (i.e. heavy absorption versus reflection).
In order to elucidate on these aspects in this paper we carry out a systematic broad-band (0.5-24 keV) spectral analysis of 63 sources detected in the core NuSTAR Extragalactic Survey program and selected to have fluxes in the 8-24 keV energy band brighter than erg s cm. We complement the NuSTAR data with archival low-energy data from Chandra and XMM-Newton. We perform broadband (0.5-24 keV) spectral modeling, characterize their spectral properties, obtain a column density distribution, absorbed/CT fractions and source counts and compare with predictions from population-synthesis models and past observational works. A companion paper, Del Moro et al. (2017, DM17), reports on the properties of the average X-ray spectra from all sources detected in the NuSTAR deep and medium survey fields.
This paper is organized as follow. Section 2 presents the sample, with Sections 3 and 4 devoted to the data reduction and spectral characterization of the source properties, respectively. We then discuss the column density distribution (Section 5), fraction of CT AGN (Section 6), fraction of absorbed sources as a function of luminosity and redshift (Section 7) and source counts (Section 8). We discuss the results in Section 9 and present the conclusions in Section 10. Relevant notes on individual sources are presented in the Appendix.
Throughout the paper we adopt a flat cosmology with and . Errors are quoted at the level and upper/lower limits at 90% confidence level (c.l.). The X-ray luminosities are quoted in the standard (for NuSTAR survey studies) rest-frame 10-40 keV energy band.
|Survey||Total Exp.aaTotal exposure time devoted to the survey;||Pointings Exp.bbAverage exposure times of the single pointings; Notice that the Serendipitous survey consists of pointings with a large range of exposure times.||Deepest Exp.ccAverage exposure in the deepest field;||Pointing layoutddTiling design of the survey;||Area||Detected Sources||Sensitivity 50%eeFlux reached at 50% of the survey area coverage. In units of erg s cm.||Ref.|
|(Ms)||(ks)||(ks)||()||3-24 keV||8-24 keV||3-24 keV||8-24 keV|
|SerendipitousffThis is a sub-sample of the Serendipitous survey sample presented in L17 (see Section 2.2)||2.2||20-1000||970||Random||118||38||L17|
2 Description of the sample
We draw our sample from the high-energy NuSTAR catalogs compiled for the COSMOS (Civano et al., 2015, C15), ECDF-S (Mullaney et al., 2015, M15), EGS (Del Moro et al. in prep., DMIP) and Serendipitous Survey fields (L17). In order to have consistent catalogs, the same data-reduction tasks, mosaicing procedures, source detection steps, photometry and deblending algorithm were applied to all survey fields (see C15, M15 and Aird et al. 2015b for details). In the following we briefly outline the source identification procedure adopted in each catalog. The identification of the sources was consistently done through a SExtractor-based procedure on false probability maps generated on the mosaicked images accounting for the corresponding background maps in three energy bands (3-8, 8-24, 3-24 keV). No positional priors from previous low energy X-ray surveys have been used in the source identification. Through simulated data, a proper threshold to set the significance of each source identification in each band has been adopted and the final balance between completeness and reliability in each catalog has been chosen so that the possible spurious sources down to the limiting flux in each catalog do not exceed the number of 2-3. Further details and description of the procedures regarding deblending, photometry, final catalog building and association to low-energy counterparts are reported in each catalog paper. For our purposes in order to minimize obscuration bias, we selected objects with relatively bright fluxes in the hard 8-24 keV band. The fluxes adopted for this selection have been estimated from the 8-24 keV counts collected in apertures222The fluxes reported in C15 are from apertures. They have been estrapolated to aperture fluxes by assuming a 1.47 constant conversion factor. This factor is obtained as ratio between the fluxes in and apertures measured from the on-axis NuSTAR point-spread function. by the catalog papers by assuming a power-law model with 1.8. Whenever possible, we complemented NuSTAR data with archival lower energy data from Chandra and XMM-Newton.
2.1 Deep-medium survey fields
Given the NuSTAR field of view, the survey fields (COSMOS, ECDF-S and EGS) were observed with a mosaicing strategy whereby each neighboring pointing was shifted by half of a field of view. This tile arrangement produces homogenous and continuous coverage in the deep central region with contiguous shallower edges. The main properties of these surveys are reported in Table 1.
Despite NuSTAR being sensitive up to 79 keV, typical faint sources in the deep surveys are not detected to such high energies. In the extragalactic survey work to date, we have therefore only considered three energy bands: 3-24 keV (total), 3-8 keV (soft) and 8-24 keV (hard).
Fig. 1 reports the 8-24 keV sensitivity curves as a function of hard-band flux for all the fields. The sensitivities at 50% survey coverage are reported in Table 1. Notice that they are based on the assumption of an unabsorbed power-law spectrum. This is an approximation which is reasonable for Compton-thin sources given that above 8 keV their spectrum is minimally altered at the highest column densities (i.e. ). It may result somewhat inadequate for CT sources whose spectrum substantially deviates from this assumed spectral shape within this hard band. It may therefore give biased results in calculating the intrinsic distribution of physical quantities for the sampled AGN population. We account for this by correcting a-posteriori for this bias (see Sect. 6 and Fig. 11).
2.2 Serendipitous survey fields
The serendipitous fields considered in this work consist of all fields analyzed as part of the Serendipitous Survey through 2015 January 1. This extends the sample presented by Alexander et al. (2013), and is a subset of the program presented in L17. The selection criteria adopted are reported in the following and constitute a slight modification to those employed in Aird et al. (2015b):
we minimize Galactic point-source contamination by requiring Galactic latitudes ;
to emphasize fields where our serendipitous survey follow-up is currently more complete, we only consider fields accessible from the northern hemisphere by requiring declinations ;
we exclude fields with a large contamination from the primary targets by requiring counts within 120 of the aimpoint, and that primary targets contribute % to the extracted emission of the serendip source within the extraction region.
After these cuts, the sky coverage of the serendipitous survey considered here amounts to (see Fig. 1). Further survey details are reported in Table 1. It is worth noting that despite the Serendipitous Survey having sensitivity better than COSMOS over a wider area and comparable faint source sensitivity to ECDF-S, it also has the disadvantage of having less multi-wavelength coverage. This usually translates to lower redshift completeness (from optical spectroscopy) and a poorer quality X-ray coverage at low energies from Chandra and/or XMM-Newton (see L17).
2.3 Selected sample
The final catalogs consist of 91, 49, 39 and 118 objects, respectively, from the NuSTAR COSMOS, ECDF-S, EGS and the Serendipitous Survey. Of these, 32, 19, 14 and 38, respectively, are significantly detected in the hard-band based on a maximum likelihood estimator (see C15, M15, A15 and L17 for details and the adopted thresholds). These objects are shown in Fig. 2 (left panel) which displays the net 3-24 keV counts within a aperture versus their aperture-corrected photometry in the 8-24 keV energy band. From this combined sample we select sources with hard-band flux erg s cm. We are sensitive to fluxes larger than this value in 80% of the surveyed area (see Fig. 1). This sub-sample, corresponding to objects above the dashed line in Fig. 2, includes a total of 31, 3, 5 and 24 objects from the four surveys, respectively selected over a total area of . The resulting sample of 63 sources is the focus of the following analysis. The redshift distribution is reported in the right panel of Fig. 2, compared to the distribution of the 199 local sources detected by Swift-BAT in the energy range 15-55 keV (Burlon et al., 2011). NuSTAR, with its two orders of magnitude greater sensitivity, probes sources well beyond the local Universe. Table 2 reports the position, spectroscopic redshift, Chandra and XMM-Newton counterparts, NuSTAR observation IDs, and NuSTAR survey for all 63 sources. When referring to the single sources we use the catalog IDs listed in column 2 prefixed by ecdfs, egs, cosmos and ser for sources from respectively the NuSTAR- ECDF-S, EGS, COSMOS and Serendipitous catalogs.
Objects from the deep fields all have unique counterparts at lower energies from either the Chandra (Lehmer et al., 2005; Goulding et al., 2012; Xue et al., 2011; Civano et al., 2012, 2016) or XMM-Newton (Brusa et al., 2010; Ranalli et al., 2013) surveys of these same fields, with the exception of one source in the ECDF-S field (ecdfs5; this source has two possible counterparts, one at low and one at high-redshift; see Table 2 and Appendix).
A few sources have nearby potential contaminants (i.e. inside the NuSTAR extraction radius) in the deep survey fields. Contamination ultimately is unimportant or partially negligible in most cases, as discussed for the affected sources in the Appendix. For some cases (cosmos154 and cosmos181) we restrict the NuSTAR low energy bound to 4-5 keV, where the contamination becomes less important. In a few other cases the contamination is such that within the uncertainties it could potentially lower the true hard-band source flux also below the threshold flux used in our sample selection (cosmos107, cosmos178 and cosmos229). For the Serendipitous Survey sources, most have counterparts from at least Chandra or XMM-Newton, the exception being five sources (ser97, ser285, ser235, ser261, ser409; see Table 4) which have not yet been observed by these satellites.
3 Data reduction
In order to perform a proper spectral analysis for these low-count point-like sources (i.e. from tens to hundreds of counts; see Fig. 2), we need to carefully account for: 1. the relatively uniform arcmin-scale NuSTAR point spread function (FWHM=; half power diameter HPD=; Harrison et al., 2013); and 2. the spectrally variable and spatially dependent background (for details, see Wik et al., 2014). In particular, the latter at keV is strongly affected by stray light from unfocussed CXB photons reaching the detectors through the open design of the observatory (called “aperture background”).
|Name||aaIdentification name for each source. This is made from a prefix indicating the source parent catalog plus the ID from NuSTAR parent catalogs (Section 2). The prefixes of each parent catalog are cosmos for COSMOS, ecdfs for ECDF-S egs for EGS and ser for the Serentipitous Survey.||R.A.||DEC.||bbAll the redshifts are spectroscopic. They are taken from: Brusa et al. 2010 (COSMOS), Lehmer et al. 2005, Xue et al. 2011 and Ranalli et al. 2013 (ECDF-S), Nandra et al. 2015 (EGS) and L17 (NuSTAR Serendipitous Survey).||ccChandra IDs are from Elvis et al. 2009 and Civano et al. 2016 (COSMOS, with prefix cid and lid respectively), Lehmer et al. 2005 (ECDF-S), Nandra et al. 2015 (EGS).||ddXMM-Newton IDs are from Brusa et al. 2010 (COSMOS) and Ranalli et al. 2013 (ECDF-S).||NuSTAR Observation IDseeTo obtain the full NuSTAR observation IDs for the COSMOS, ECDF-S and EGS fields, the six digit survey identification numbers 60021, 60022 and 60023 must be prefixed, respectively.||Catalog|
|NuSTAR J100129013636||cosmos97||150.372537||+1.610073||0.104||cid1678||2021||098001 099001||COSMOS|
|NuSTAR J100249013851||cosmos107||150.705859||+1.647561||0.694||lid1688||5496||101002 103001||COSMOS|
|NuSTAR J100101014752||cosmos129||150.256432||+1.797837||0.907||cid284||54490||037002 038001 060001||COSMOS|
|NuSTAR J095815014932||cosmos130||149.564437||+1.825731||1.509||lid961||5323||090001 091001||COSMOS|
|NuSTAR J095926015348||cosmos145||149.860885||+1.896815||0.445||cid209||293||012001 018001 062001 063001||COSMOS|
|NuSTAR J100055015633||cosmos154||150.233212||+1.942588||0.219||cid1105||131||029001 030001 035002 036002||COSMOS|
|NuSTAR J100024015858||cosmos155||150.104087||+1.982873||0.373||cid358||1||023001 024001 029001 030001||COSMOS|
|NuSTAR J095840020437||cosmos178||149.668862||+2.077021||0.340||cid168||417||004001 005001 087001 088002||COSMOS|
|NuSTAR J100141020348||cosmos181||150.423842||+2.063424||0.125||cid482||2608||040001 041001 050001 051001||COSMOS|
|NuSTAR J095918020956||cosmos194||149.826665||+2.165826||1.157||cid320||5||003001 004001 009002-B 010001||COSMOS|
|NuSTAR J100308020917||cosmos195||150.785979||+2.154816||1.470||lid1646||5321||109001 111001||COSMOS|
|NuSTAR J095857021320||cosmos206||149.738507||+2.222475||1.024||cid329||2||003001 004001||COSMOS|
|NuSTAR J100307021149||cosmos207||150.782581||+2.197149||0.582||lid1645||5370||111001 113001||COSMOS|
|NuSTAR J095817021548||cosmos216||149.573824||+2.263384||0.707||lid633||54514||086001 087001||COSMOS|
|NuSTAR J100032021821||cosmos217||150.133457||+2.305840||1.598||cid87||18||020002 021001 026001 027002||COSMOS|
|NuSTAR J095902021912||cosmos218||149.761712||+2.320121||0.345||cid440||3||002001 003001 008001 009002||COSMOS|
|NuSTAR J095909021929||cosmos229||149.789727||+2.324908||0.378||cid420||23||002001 003001 008001 009002||COSMOS|
|NuSTAR J095957022244||cosmos232||149.990626||+2.378889||0.931||cid530||212||013001 014001 019001 020002||COSMOS|
|NuSTAR J100228024901||cosmos249||150.620155||+2.817155||0.213||lid3218||5014||067001 120001||COSMOS|
|NuSTAR J095945024750||cosmos251||149.941358||+2.797420||1.067||lid545||5620||076001 077001-A 078001||COSMOS|
|NuSTAR J100238024651||cosmos253||150.658422||+2.780956||0.212||lid484||5114||120001 121001||COSMOS|
|NuSTAR J095908024310||cosmos263||149.785525||+2.719548||1.317||lid549||5230||077001 079001 080001||COSMOS|
|NuSTAR J100243024025||cosmos272||150.682309||+2.673758||0.669||lid492||5400||118001 119001 120001 121001||COSMOS|
|NuSTAR J100204023726||cosmos282||150.520310||+2.623974||0.519||lid294||7||046002 046004 065002 066001||COSMOS|
|NuSTAR J095837023602||cosmos284||149.656383||+2.600703||0.735||lid1856||2076||082001 083001||COSMOS|
|NuSTAR J100232023538||cosmos287||150.635807||+2.593895||0.658||lid280||5133||046002 116001 117001-B 118001 119001||COSMOS|
|NuSTAR J095849022513||cosmos296||149.704281||+2.420472||1.108||cid513||126||001002 002001||COSMOS|
|NuSTAR J095848022419||cosmos297||149.700185||+2.405449||0.375||cid417||135||001002 002001||COSMOS|
|NuSTAR J100229023223||cosmos299||150.624855||+2.539961||0.432||lid278||5222||046002 046004 065002 116001 118001||COSMOS|
|NuSTAR J095839022350||cosmos322||149.662604||+2.397242||0.356||lid622||1429||001002 002001 084001 085001||COSMOS|
|NuSTAR J100259022033||cosmos330||150.747792||+2.342593||0.044||lid1791||5371||113001 115001||COSMOS|
|NuSTAR J033136280132||ecdfs5||52.901946||-28.025645||0.141||103||-||001003 001002 001003||E-CDFS|
|NuSTAR J033207273736||ecdfs20||53.032301||-27.626858||0.976||301||358||013001 013002 014001 014002||E-CDFS|
|NuSTAR J033328275642||ecdfs51||53.370361||-27.945068||0.841||712||-||004001 004002 008001 008002||E-CDFS|
|NuSTAR J141736523029||egs1||214.400911||+52.508258||0.987||37||-||001002 001004 001006 001008||EGS|
|NuSTAR J141754524138||egs9||214.475905||+52.694030||0.464||294||-||001002 001004 001008 002002||EGS|
|002003 002004B 002005|
|NuSTAR J142047525809||egs26||215.196713||+52.969305||0.201||669||-||006002 006003 006004 006005||EGS|
|007001 007003 007005 007007|
|NuSTAR J142052525630||egs27||215.220076||+52.941858||0.676||622||-||006002 006004A 006005 007001||EGS|
|NuSTAR J142027530454||egs32||215.113227||+53.081728||0.997||863||-||007001 007003 007005 007007||EGS|
|008001 008002 008003 008004|
|NuSTAR J023228202349||ser37||38.119089||+20.397218||0.029||-||-||60002047006 60002047004||Serendip|
|NuSTAR J051617001340||ser97||79.073788||-0.227904||0.201||-||-||60001044004 60001044002||Serendip|
|NuSTAR J061640710811||ser107||94.167546||+71.136661||0.203||-||-||60002048010 60002048006 60002048004||Serendip|
|NuSTAR J081909703930||ser153||124.789365||+70.658570||1.278||-||-||30001031005 30001031003 30001031002||Serendip|
|NuSTAR J095512694739||ser184||148.800066||+69.794361||0.675||-||-||80002092011 80002092009 80002092008||Serendip|
|80002092007 80002092006 80002092004|
|NuSTAR J110740723234||ser235||166.919819||+72.542882||2.100||-||-||60002042004 60002042002||Serendip|
|NuSTAR J112829583151||ser243||172.122122||+58.530861||0.410||-||-||50002041003 50002041002||Serendip|
|NuSTAR J115912423242||ser254||179.802748||+42.545158||0.177||-||-||60001148004 60001148002 60061217006||Serendip|
|NuSTAR J151654561744||ser363||229.225216||+56.295566||1.310||-||-||30002039005A 30002039003 30002039002||Serendip|
|NuSTAR J204020005609||ser451||310.087027||-0.936058||0.601||-||-||30001120005 30001120004 30001120003||Serendip|
Given the flux levels of the sources in our sample, it is necessary to maximize and carefully account for their contribution relative to the backgrounds (especially with respect to the spatially dependent “aperture background”). We therefore optimize the spectral extraction radius to maximize the signal-to-noise ratio (SNR) and, within the Poissonian uncertainties, the number of collected net counts. To do this we started with the level 2 data products and simulated background maps where the latter were created using the software nuskybgd (Wik et al., 2014) as described in C15 and M15. The simulated background maps reproduce the “aperture background” across the FoV and the normalization of the total background in each observation. In detail we determined from all the observations pertaining to a given source, the total counts in increasing circular apertures centered on the source position, calculating both source+background counts () from the event files and background counts alone () from the simulated maps. Then we calculated the radial profile for the net source counts and . The radius for spectral extraction is chosen as the radius which maximizes the SNR profile and, within its range, maximizes also . In the few (nine for COSMOS and one for ECDFS) cases in which a source is blended with a nearby source (closer than arcmin), we further reduced so that the source flux from the contaminating source is reduced, within the aperture, to levels of . Table 4 reports values for all the sources in our sample.
We used the task “nuproducts” in NUSTARDAS v.1.4.1 with the NuSTAR calibration database (CALDB version 20150123) for the spectral extractions and the creation of relative response files.
The background spectrum for each source spectrum was simulated from the best-fit models of the background across the detectors obtained with nuskybgd. This software performs iterative joint fits of the observed backgrounds across the field extracted in arcmin apertures placed in each chip of each focal plane module. The joint modeling aims to determine the normalization of the different background components and hence characterize them at the position of the source. The fits are performed using spectral models of the instrumental (continuum + line activation due to particle background), cosmic focused (CXB) and cosmic unfocussed background (straylight) components and information on their spatial dependence across the detectors. We checked each best-fit to ensure that no significant spatial or spectral residuals were present. After this procedure we are in principle able to well reproduce the background spectrum at each position of the detector. We further verify this by creating background-subtracted images and visually inspect them for spatial gradients indicative of poor background modeling. As a final step, the best fit spectral model is used by nuskybgd to simulate the background within the source extraction aperture but using a 100 times higher exposure time to ensure high SNR.
We then co-added for each source and in each detector spectra, simulated backgrounds and response files. Table 4 reports NuSTAR net counts and total exposure time collected for each source.
3.2 XMM-Newton and Chandra
For the ECDF-S and COSMOS fields we employed all spectra reduced and extracted by previous works. Specifically, for the deep ECDF-S field we used Chandra data reduced by Lehmer et al. (2005) and Xue et al. (2016), and extracted spectra following procedures discused in Del Moro et al. (2014). For ecdfs20, which only has an XMM-Newton spectrum, the data reduction and spectral extraction are from Ranalli et al. (2013) and Georgantopoulos et al. (2013). For the COSMOS field we use spectra reduced and extracted for XMM-Newton by Mainieri et al. (2007) and for Chandra by Lanzuisi et al. (2013), with the only exception being source cosmos330 for which a spectrum from the COSMOS-Legacy field has been used (Marchesi et al., 2016).
For the Serendipitous Survey fields we reduced and extracted the Chandra and XMM-Newton data. In the selection of archival observations, we only use data from observations in which CCD detectors are primary instruments (i.e., we exclude Chandra grating observations). In the case of XMM-Newton we almost always only use data from PN, the exception being ser107 which was located in a CCD gap of the PN camera. For this source we use the MOS data. For the Chandra data we used both ACIS-S and ACIS-I detectors whenever available (see Table 3 for details). When multiple archival datasets were available we chose the data closest in time to the NuSTAR observation, if available, in order to minimize source variability. Table 3 reports the selected observations for each source.
Note. – Notes: (1) Chandra/ACIS-I detector; (2) XMM-Newton/MOS data; (3) Observations chosen to be closest in time to the NuSTAR data; (4) the source is on the Chandra /ACIS-S2 chip; (5) the source is on the Chandra /ACIS-S3 chip; (6) see Ricci et al. (2016) for details on data reduction and spectral extraction;
We reduced the Chandra data using CIAO v. 4.7333http://cxc.harvard.edu/ciao4.7/ with CALDB v. 4.6.7. We re-processed the data using the chandra_repro script to produce new re-calibrated level=2 event files. The spectral extraction was done with the script specextract, which automates the creation of source and background spectral files and the relative ARF and RMF. The source and background spectral extractions were performed on user-selected circular and annular concentric regions, respectively, in order to maximize the source flux and avoid point source contamination to background measurements. We finally combined the resulting spectra using the FTOOLs script addascaspec, available in HEASOFT v. 6.16444http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/, and produced combined RMFs and ARFs using the tasks addrmf and addarf. The resulting exposure times and collected net-source counts are reported in Table 4.
For the XMM-Newton data we used SAS v14.0.0555https://www.cosmos.esa.int/web/xmm-newton/sas. For each observation we screened the event files for time intervals impacted by soft proton flares by adopting an observation dependent 10-12 keV count-rate threshold ( being the average and standard deviation of the applied threshold), above which data were removed. For the spectral extraction and creation of response files we followed the standard procedures outlined in the XMM-Newton science threads666http://www.cosmos.esa.int/web/xmm-newton/sas-threads. We extracted events with pattern for the PN camera and for the MOS detectors. We combined the MOS1 and MOS2 spectra using the SAS task epicspeccombine. For sources with more than one data set, we produced combined source spectra, background spectra, ARF and RMF as per the Chandra data. Exposure times and net-source counts for each source are reported in Table 4.
For the EGS field, Chandra data products from Goulding et al. (2012) have been used. The spectral extraction, specifically carried out for this work777CIAO v. 4.8 with CALDB v. 4.7.0 has been used., has been performed using specextract for each individual observation. Background regions were taken from annuli with â– (with the latter being the radius enclosing 90% of the point spread function) with other detected sources masked out. Spectra and backgrounds were combined for the different observations using combine_spectra in CIAO.
4 Data analysis
We performed the spectral analysis using XSPEC v. 12.8.2 using the Cash statistic (Cash, 1979) with the direct background subtraction option (Wachter et al., 1979). In the limit of a large number of counts per bin, the distribution of this statistic, called the statistic (), approximates the distribution with degrees of freedom (, where is the number of independent bins and is the number of free parameters). We performed all our modeling with spectra binned to 5 net-counts (i.e., background subtracted) per bin with the exception of sources with low number of counts (i.e. counts from both NuSTAR detectors) for which we resorted to a finer binning of 1 net-count per bin.
The spectral modeling has been performed: (a) for the NuSTAR-only data in the energy range keV assuming a power-law, with absorption and reflection (Sect. 4.1), and (b) jointly together with XMM-Newton and Chandra over the broader keV energy band using more complex models (Sect. 4.2).
Notice that despite the spectral analysis being performed up to 24 keV, on average, our spectra are sensitive to slightly lower energies. The median and semi-interquartile range for the highest energy bin in the FPMA and FPMB spectra are keV and keV, respectively.
4.1 NuSTAR spectral analysis
For the NuSTAR-only analysis ( keV) we first used a power-law model. We freeze the cross-calibration between FPMA and FPMB since, given the few percent level of accuracy measured by Madsen et al. (2015) and the limited counts of the majority of our spectra (up to a few hundreds) we do not expect to distinguish these small calibration levels (i.e., the statistical uncertainties exceed the systematic ones). The left panel of Fig. 3 presents the power-law photon index values plotted against the net counts in the keV band. The values are, on average, flatter than the canonical 1.8-2 values (e.g. Piconcelli et al., 2005; Dadina, 2008) with a mean (median) of 1.5 (1.6). The distribution of is reported by the black histogram in the right-upper panel. Spectra with fewer counts than the median have slightly flatter photon indices than high-count sources, compared to . The average hardening of faint sources agrees with the shape of the CXB in approximately the same energy range (Marshall et al., 1980) as already found at lower energies (e.g., Mushotzky et al., 2000; Giacconi et al., 2001; Brandt et al., 2001). There is one notable outlier with a negative value, the CT thick source in the COSMOS field reported by C15 (cosmos330 in Table 2). The average flat values of point to a more complex spectral shape in the NuSTAR energy band.
|NuSTAR ID||NuSTAR FPMA||NuSTAR FPMB||Chandra||XMM-Newton|
|net cts||exp aaExposure time in ksec.||bbExtraction radius in arcsec.||net cts||exp aaExposure time in ksec.||bbExtraction radius in arcsec.||net cts||exp aaExposure time in ksec.||Ref.||net cts||exp aaExposure time in ksec.||Ref.|
|cosmos181||75 ccCounts in the energy range 4.5-24 keV. See Appendix for details on this source.||95.0||40||55 ccCounts in the energy range 4.5-24 keV. See Appendix for details on this source.||94.9||40||62||92.4||3||99||53.5||2|
|ser107||80||127.6||30||130||127.4||50||-||-||-||50 ddMOS spectrum; the source falls in a chip gap in PN.||49.8 ddMOS spectrum; the source falls in a chip gap in PN.||8|
Note. – References: (1) Marchesi et al. 2016; (2) Mainieri et al. 2007; (3) Lanzuisi et al. 2013; (4) Lehmer et al. 2005; (5) Xue et al. 2016; (6) Ranalli et al. 2013; (7) Goulding et al. 2012; (8) this work and (9) data reduction as in Ricci et al. 2016
In order to identify a more suitable model which would bring the power-law photon indices to the canonical 1.8-2 values, we explored two modifications to the simple power-law model. We first allowed for low-energy photoelectric absorption by the circumnuclear interstellar matter using the zwabs model in XSPEC. Given the 3 keV lower bound of the NuSTAR energy range, this model modification did not change appreciably the distribution of , producing a median of 1.6 and only a few outliers (% of the sample) at values much larger than 3 (see red dashed histogram in Fig. 3). An alternative modification is the inclusion, beside the simple power-law component, of an additional cold Compton-reflection component to account for the disk/torus reflectors. This component is particularly important in the NuSTAR hard-energy band. We used the pexrav model (Magdziarz & Zdziarski, 1995) which assumes that the reflector is an infinite slab with infinite optical depth illuminated by the primary power-law continuum, subtending an angle , where is the reflection parameter. For a source of isotropic emission , hence . We tied both the photon index and the normalization of the reflection model to those of the primary power-law and let vary. In our modeling throughout the paper we set this parameter in XSPEC to be negative, as for pexrav this will switch on the reflection-only solution as opposed to the reflection+power-law solution activated by positive values. Throughout the text we quote the absolute value of the parameter. We left the abundance at its default solar value, (i.e., inclination angle deg, the default value in the model), and set the exponential cut-off () for the incident power-law primary continuum at 200 keV (as assumed by G07 and consistent with recent determinations by NuSTAR; see Fabian et al. 2015 for a compilation). This additional component shifts the mean and median photon index to higher values ( and , respectively), but at the cost of increasing the dispersion of the distribution (see blue histogram in Fig. 3). There is no trend in the median with the number of counts except for the dispersion with low-count sources having an interquartile range of 1.2 as opposed to high counts sources which have an interquartile range of 0.6. Histograms of the distribution for the three models are reported in the right panels of Fig. 3.
4.2 Joint broad band analysis
In order to improve the modeling and obtain tighter constraints on the spectral parameters, we added lower energy data from XMM-Newton and Chandra , thereby extending the spectral range down to E keV (observed frame). Table 4 reports details on the low energy data used for each source.
We first consider an empirical model (hereafter called baseline model) expressed in XSPEC as:
constantwabs(powerlaw+zwabspowerlaw + zgauss + pexrav)
where powerlaw represents the primary coronal component modified at low energies with photoelectric absorption (model zwabs) and complemented at high energies with the addition of a cold Compton-reflection component (model pexrav). We further add at low-energy a power-law (powerlaw) to account, when needed, for residual low energy flux for absorbed sources (hereafter called scattered component) consisting either of primary component flux scattered outside the nuclear absorbing region or of circumnuclear photoionized gas. At high energy we add a line (zgauss) to account for neutral Fe K emission at 6.4 keV produced by the surrounding reflecting cold medium and let its normalization free to vary. The entire model is modified by photoelectric absorption (wabs) from Galactic interstellar gas using values reported by Kalberla et al. (2005) at the position of each source.
The constant accounts for instrument intercalibration and possible source flux variability, as well allowing for a crude accounting of possible contamination from blended sources inside differing extraction radii. We left the constant free to vary between satellites, but always tied between the two NuSTAR FPMs888For the 58 sources with low-energy spectral data, the difference between the estimated best-fit constants is reasonably low being smaller than a factor of for the majority of the sources (50). Four sources (cosmos129, cosmos229, cosmos297 and ser77) show variations larger than a factor of 2-3 in both XMM-Newton and NuSTAR clearly pointing to source variability as main cause of discrepancy. The remaining four sources cosmos249, cosmos263, ser148 and ecdfs5 have variations by factors 2-4 with the latter showing the largest variation which is possibly due to contamination from a nearby source (see Appendix for details). as done in Section 4.1. We left the slope and the normalization of the scattered component free to vary. As in Sect. 4.1 we used the reflection-only component from PEXRAV and tied both and normalization to the corresponding parameters of the primary component. Other PEXRAV parameters are set to the default values as reported in Sect. 4.1. In this way our fits with the baseline model are performed with 5 free parameters. In case of joint fit performed with one or two additional low-energy datasets, one or two intercalibration constants need to be accounted as additional free parameters, respectively. Furthermore in case of sources with soft-excess component two additional free parameters need to be considered for the slope and normalization of the scattered component. In order to speed up our modeling which, using pexrav, can be quite time consuming, the error estimation on all parameters was obtained with the reflection strength parameter and calibration constants fixed to their best-fit values. For error estimation in , we left free to vary only , and normalization of the primary power-law component. Best-fit spectral parameters are reported in Table 5 along with fluxes in the 8-24 keV and 3-24 keV bands, and 10-40 keV unabsorbed and intrinsic coronal luminosities inferred from the best-fit baseline model (see Section 4.4 for details). Fig. 4 shows broad-band spectra for four sources along with their best-fit model. For the few sources exhibiting extreme values below 1.3 or above or reflection parameter larger than , we redid the fits with fixed to 1.8. These sources are cosmos129, cosmos232, cosmos253, cosmos282, ser285, ser77 and ser261. In three cases, mainly unabsorbed sources with high-quality spectra, the baseline parametrization in the soft (ser148) and broad-band (ser37, egs26) was inadequate. Indeed, in these energy ranges absorbed power-law models return slopes in the range with very little absorption. We therefore further modified the absorbed primary power-law by further applying absorption from a partial covering cold (zpcfabs in XSPEC) or partially ionized (zxipcf) medium. Details on these sources are reported in the Appendix.
4.3 Absorption and photon index from the primary power-law
The distribution of the measured peaks at around 1.8-2, with a mean value of , as reported in Fig. 5. Best-fit column density values range from cm to cm. We have upper limits for 23 sources. Twenty are unabsorbed sources with upper limits cm. The two remaining sources have upper limits reaching into the heavily absorbed regime ( cm). These sources, ser285 and ser235, have low-count NuSTAR data and no lower energy data available. For only one source with NuSTAR-only data (ser409) we cannot constrain its value even when fixing . For 17 sources, 27% of the sample, we measure cm. Two sources (% of the sample), cosmos330 and ser261, exhibit CT column densities. The former is the CT AGN discovered by C15. Fig. 5 shows as a function of intrinsic . Error bars in tend to be larger for obscured sources (i.e., cm).
4.4 Luminosity in the 10-40 keV energy band
In the last two columns of Table 5 we report the 10-40 keV luminosities from the baseline model. They are unabsorbed luminosities (, penultimate column) and intrinsic luminosities (, last column). The unabsorbed luminosity is estimated by simply removing the Galactic and intrinsic absorption components from the best-fit baseline model. The intrinsic coronal luminosities are computed from the unabsorbed coronal power-law component by simply removing the reflection contribution to the best-fit baseline model. The uncertainties in due to parameter degeneracy in our modeling are estimated by fitting the baseline model with fixed to its lower and upper error bounds.
In the context of the baseline parametrization, is supposed to reflect more closely the true X-ray radiative output of the primary (direct) X-ray emitting nuclear source. Notice though that the planar geometry assumed in pexrav is an approximate description of the cold reflector which, according to unification schemes, has a toroidal geometry. In any case, in the 10-40 keV band the additional reflection contribution can become relevant compared to the intrinsic coronal one, especially for sources with low-luminosity and large reflection strengths. Including the reflection term in the luminosity calculation may lead to a “double counting” of the intrinsic X-ray radiative output. Indeed in this case the estimate of would include both the primary coronal power-law component and the primary coronal photons reflected from the circum-nuclear material back to the observer. This overestimation of the intrinsic luminosity is negligible (10-30% for =1-6) in the 2-10 keV band where the reflection component is a few percent of the primary emission. The upper panel of Fig. 6 shows, for the 10-40 keV band, the overestimate of the “unabsorbed luminosities” including the reflection component compared to the intrinsic luminosities derived from the unabsorbed primary component only. In the lower panel we report the ratio between these two quantities in order to quantify better the level of overestimation. can be larger by factors up to and the majority of those sources are those with best-fit (red diamonds) at low luminosity (i.e., erg s). This is due to an induced dependence between and luminosity which, if not accounted for, may lead to a biased view of the relationship between luminosity and reflection strength (see Section 4.5.1 and Fig. 8, bottom panels). Notice that few sources at higher luminosities ( erg s) have overestimates of a factor of even though they have low reflection strenghts (i.e., ). This is due to the fact that the ratio in the observed 10-40 keV energy range is an increasing function of the redshift999Indeed the redshift progressively shifts to lower energies (i.e., outside the band) portions of the spectrum where the decreasing primary component still significantly contribute to the total flux. and our sample, selected in flux, contains, on average, higher luminosity sources at higher redshifts.
In order to keep the baseline parametrization simple and suitable for low SNR spectra we did not include a Compton-scattering term which can become important for the most obscured sources. This may lead to an underestimate of the true luminosity for the most obscured sources. We compared our unabsorbed values with the best-fit values obtained by adding a Compton-scattering term parametrized with cabs for the COSMOS sources with , i.e. those for which we have the best-quality broad-band data. We obtained, on average, larger luminosities with values ranging from dex for the less obscured sources up to dex for the most obscured ones. However, cabs approximates the Compton-scattering by only accounting for the scattering of the photons outside of the beam and neglecting photons reflected by surrounding material into the line-of-sight. Hence more appropriate luminosity values may be estimated by accounting for the geometry of the obscurer. For this reason we compared our values with those obtained with the torus modelings employed in Section 4.6 which self-consistently account for Compton-scattering effects due to the toroidal geometry of the obscurer. We found that in the range , the 10-40 keV luminosity is underestimated on average by at most dex with only two exceptions in our sample: cosmos129 and ser261. These sources are among the most obscured sources in our sample and for them we are finding underestimated by 0.2 dex and 0.3-0.4 dex, respectively. No significant difference is found for less-obscured sources.
|NuSTAR ID||stat||dof||aa in units of cm.||bbUnits of erg s cm.||bbUnits of erg s cm.||ccUnabsorbed luminosity in the 10-40 keV energy range in units of erg s. See Section 4.4 for details.||ddIntrinsic luminosity in the 10-40 keV energy range in units of erg s. Errors highlights the uncertainty associated to the reflection component modeling|
|egs26eeFor this source we further added a partial covering absorber by partially cold material (zpcfabs in XSPEC). See Appendix for further details||424.4||429||1.4||2.0||43.4|
|ser37ffFor this source we further added a partial covering absorber by partially ionized material (zxipcf in XSPEC). See Appendix for further details||223.3||219||17.7||23.7||42.7|
|ser148ffFor this source we further added a partial covering absorber by partially ionized material (zxipcf in XSPEC). See Appendix for further details||1338.4||1260||47.5||85.7||44.1|
. See Section 4.4 for details.
4.5 The reflection component
We next estimate the significance of the reflection component in our sources. We first evaluated if for the obscured sources ( the absorbed spectral shape could be better modelled in the context of a CT scenario in which the primary continuum is completely suppressed and where the only dominant component other than the soft residual scattered one is the pure cold reflection component. Hence we evaluated a reflection-dominated spectrum obtained by removing the absorbed primary power-law component from the baseline model. Since we are not using statitics, we are not able to use an F-test to evaluate the significance of the baseline model over the simpler reflection-dominated one. We therefore based our evaluation on the presence of: 1) a reasonable input power-law photon index for the pexrav component of the best-fit parametrization of the reflection dominated model; 2) a large fraction of scattered flux at low energies for the baseline model101010I.e., if we are modeling an intrinsic reflection-dominated source with the baseline model, we obtain an overestimate of this quantity. To check for this we tied of the scattered component to the primary one.; 3) the presence of an Fe K emission line with a large equivalent width ( keV); and 4) large residuals for the best-fit parametrization. Based on these criteria, we did not find clear cases of sources deviating from the baseline model or significantly better parametrized by a reflection-dominated model. Similarly we did not find scattered fractions in excess of a few percent, the value that is typically found in heavily obscured sources (e.g. Lanzuisi et al., 2015). Moreover, only for cosmos181 we obtained . Other sources show more moderate . We therefore are unable to discriminate between the two models.
4.5.1 Reflection as a function of obscuration, slope and luminosity of the primary emission
We measured for all the sources (see Table 5 column 6) and obtained upper limits for 23 sources. We considered as upper limits all the best-fit values with . In Fig. 7 we report the distribution of in bins of 0.5 dex111111Notice that the derived values are obtained by fixing the inclination angle () for the reflector to (default in Xspec). Assuming lower/larger inclination angles will decrease/increase . For instance fixing () would lower (increase) our reported by 50% (a factor of 2-3)..
We investigated how reflection correlates with obscuration and luminosity for the whole sample. Fig. 8 presents the reflection parameter as a function of column density (top-left panel) and unabsorbed and intrinsic 10-40 keV luminosity (bottom panels). The color of each point corresponds to redshift with the redder colors representing the more distant sources. Since ours is a flux-selected sample, more distant (i.e., redder) sources in the plane correspond to more luminous, less obscured sources (i.e., see plane).
There is an apparent tendency for obscured and luminous sources to have, on average, maximum values smaller than unobscured and less luminous sources.
We investigated and quantified these trends by: (1) computing the Spearman’s rank correlation coefficient () for censored data using the ASURV package v. 1.2 (Lavalley et al., 1992; Feigelson & Nelson, 1985; Isobe et al., 1986) and (2) calculating the median and its interquartile range (IQR) for the entire sample and the obscured/unobscured and luminous/less luminous sub-samples (the separation between the latter being dictated by the median luminosities of the sample, and ).
|Parameters||aaSpearman’s rho correlation coefficient () and null-hypothesis probability () calculated for censored data from ASURV package (see Section 4.5.1).||aaSpearman’s rho correlation coefficient () and null-hypothesis probability () calculated for censored data from ASURV package (see Section 4.5.1).||Sample||bbMedian () and Interquartile range (IQR) values for computed in each considered sample accounting for errors and upper limits as explained in Section 4.5.1.||IQRbbMedian () and Interquartile range (IQR) values for computed in each considered sample accounting for errors and upper limits as explained in Section 4.5.1.|
|,||-0.25||0.05||unobscuredccWe used a cm threshold value.||0.67||0.10–1.80|
|obscuredccWe used a cm threshold value.||0.28||0.05–1.07|
|,||-0.59||low ddThe median value is adopted as the threshold value.||1.15||0.17–2.56|
|high ddThe median value is adopted as the threshold value.||0.25||0.05–0.68|
|,||-0.37||0.0039||low eeThe median value is adopted as the threshold value.||0.73||0.08–2.17|
|high eeThe median value is adopted as the threshold value.||0.31||0.05–1.00|
For the latter we accounted for measurement errors and upper limits in , and as follows: we performed 10000 realizations of the sample each time with Gaussian and uniform randomization for respectively each of the parameter best-fit values121212We assumed a symmetric distribution centered on the parameter value with 1 standard deviation as the mean of the lower and upper error-bars. and the upper limits. In the case of and , the latter were randomized from their 90% upper value down to a fixed minimum value of and . We computed for each realization the median value and IQR, and adopted as representative for the sample the averaged values over all the realizations. The resulting values are reported in Table 6. Note that accounting for the upper limits may lead to a shift of the lower interquartile bound toward smaller values. Therefore the lower interquartile range may not reflect the true relative distributions. The IQR values are reported as shaded areas in Fig. 8 for the sub-samples and vertical lines for the entire sample.
For the entire sample, the average median value is with an interquartile range .
We find a weak mildly significant anti-correlation between and with and a null hypothesis probability that the two quantities are not related to each other of 0.05. The median values for unobscured and obscured samples are respectively of 0.67 and 0.28. Despite the apparent difference, their IQR have in common a quite large interval of values. The difference in the lower values (with unabsorbed sources having larger values) may reflect the fact that the obscured sample has twice as many upper limits as the unobscured sample. We verified that the presence of such a large number of upper limits does not depend on the SNR of the NuSTAR spectra. The upper bounds of the interquartile range differ by a factor of . Both categories sample AGN with similar range in luminosities (interquartile range