THE SPIN OF THE SUPERMASSIVE BLACK HOLE IN NGC 3783

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Published 2011 July 13 © 2011. The American Astronomical Society. All rights reserved.
, , Citation L. W. Brenneman et al 2011 ApJ 736 103 DOI 10.1088/0004-637X/736/2/103

0004-637X/736/2/103

ABSTRACT

The Suzaku AGN Spin Survey is designed to determine the supermassive black hole spin in six nearby active galactic nuclei (AGNs) via deep Suzaku stares, thereby giving us our first glimpse of the local black hole spin distribution. Here, we present an analysis of the first target to be studied under the auspices of this Key Project, the Seyfert galaxy NGC 3783. Despite complexity in the spectrum arising from a multi-component warm absorber, we detect and study relativistic reflection from the inner accretion disk. Assuming that the X-ray reflection is from the surface of a flat disk around a Kerr black hole, and that no X-ray reflection occurs within the general relativistic radius of marginal stability, we determine a lower limit on the black hole spin of a ⩾ 0.88 (99% confidence). We examine the robustness of this result to the assumption of the analysis and present a brief discussion of spin-related selection biases that might affect flux-limited samples of AGNs.

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1. INTRODUCTION

Ever since the seminal work of Penrose (1969) and Blandford & Znajek (1977), it has been recognized that black hole spin may be an important source of energy in astrophysics. Of particular note is the role that black hole spin may play in relativistic jets such as those seen in radio-loud active galactic nuclei (AGNs)—the magnetic extraction of the rotational energy of a rapidly spinning black hole is the leading contender for the fundamental energy source of such jets. Indeed, it has been suggested that the spin of the central supermassive black hole (SMBH) is a crucial parameter in determining whether an AGN can form powerful jets (i.e., whether the source is radio-quiet or radio-loud; Wilson & Colbert 1995), although the accretion rate/mode must clearly have a role to play (Sikora et al. 2007).

However, the importance of black hole spin goes beyond its role as a possible power source. The spin distribution of the SMBH population (and its dependence on SMBH mass) encodes the black hole growth history (Moderski & Sikora 1996; Volonteri et al. 2005; Berti & Volonteri 2008). In essence, if local SMBHs have obtained most of their mass during prolonged prograde accretion events in a quasar phase of activity, or in major mergers with similar mass SMBHs, we would expect a population of rapidly rotating SMBHs (a > 0.6) due to the angular momentum accreted from the disks or transferred at merger (Rezzolla et al. 2008). Here, we define acJ/GM2, where J is the angular momentum of the black hole and M is its mass. On the other hand, if mergers with much smaller SMBHs (Hughes & Blandford 2003) or randomly oriented accretion events of small packets of material (King & Pringle 2007) have been the dominant growth mechanism, most of the SMBHs would be spinning at a much more modest rate.

To date, the cleanest probe of strong gravitational physics around SMBHs, including the effects of black hole spin, comes from examining relativistically broadened spectral features that are emitted from the surface layers of the inner accretion disk in response to irradiation by the hard X-ray source (Reynolds & Nowak 2003; Miller 2007). These spectral features have been observed and well characterized in both AGNs (Tanaka et al. 1995; Fabian et al. 1995) and stellar-mass black hole systems (Miller et al. 2002; Reis et al. 2008). The strongest feature in this so-called reflection spectrum is the fluorescent Fe Kα line (rest-frame energy of 6.4 keV); in contrast to lines from other elements, its relative abundance, high energy, and fluorescent yield make Fe Kα visible above the typical power-law continuum seen commonly in black hole systems. Extreme Doppler effects and gravitational redshifts combine to give this line (and all other features in the reflection spectrum) a characteristic broadened and skewed profile (Fabian et al. 1989; Laor 1991). Modern high signal-to-noise (S/N) data sets from XMM-Newton and Suzaku, combined with the latest models of reflection from an ionized accretion disk (e.g., Ross & Fabian 2005) and variable-spin relativistic smearing models (e.g., Brenneman & Reynolds 2006; Dauser et al. 2010), are giving us our first glimpses at the spins of SMBHs. However, due to the high S/N required to characterize the subtle effects of SMBH spin, interesting spin constraints have only been determined for a small handful of AGNs at present (MCG–6-30-15, Brenneman & Reynolds 2006; Fairall 9, Schmoll et al. 2009; SWIFT J2127.4+5654, Miniutti et al. 2009; 1H0707–495, Zoghbi et al. 2010; Mrk 79, Gallo et al. 2011; Mrk 335 and NGC 7469, Patrick et al. 2011; see Table 2).

Under the auspices of the Suzaku Key Project program, we have initiated a series of deep quasi-continuous observations of bright, nearby AGNs with the purpose of characterizing relativistic disk features in the spectra and setting constraints on the SMBH spin (Suzaku AGN Spin Survey; PI: C. Reynolds). In this paper, we present results from the first object to be studied under this program, the Seyfert 1.5 galaxy NGC 3783 (z = 0.00973; Theureau et al. 1998). This object possesses a high-column density and multi-component warm absorber (WA) that has been studied well by every spectroscopic X-ray observatory, including a 900 ks campaign by Chandra using the High-Energy Transmission Grating Spectrometer (HETGS; Kaspi et al. 2002; Krongold et al. 2003; Netzer et al. 2003). We show that, despite the presence of this complex WA, reflection signatures from the inner accretion disk can be identified and characterized with sufficient accuracy to constrain SMBH spin. We conclude that the SMBH is rapidly spinning with a > 0.93 (90% confidence). This result is shown to be robust to the exclusion of the complex, soft region of the X-ray spectrum as well as to uncertainties in the X-ray Imaging Spectrometer (XIS)/PIN cross-normalization.

This paper is organized as follows. Section 2 discusses the Suzaku observation of NGC 3783 and the basic reduction of the data. Section 3 then presents our modeling of the 0.7–45 keV time-averaged spectrum of NGC 3783, including our newly derived constraints on the SMBH spin. Section 4 summarizes our conclusions on NGC 3783 and addresses the role of spin-dependent selection biases in AGN samples.

2. OBSERVATIONS AND DATA REDUCTION

NGC 3783 was observed by Suzaku quasi-continuously for the period 2009 July 10–15, with the source placed in the Hard X-ray Detector (HXD) nominal aim point. After eliminating Earth occultations, South Atlantic Anomaly passages, and other high background periods, the observation contains 210 ks of "good" on-source exposure. The XIS data (XIS 0, XIS 1, and XIS 3; XIS 2 has been inoperable since 2006 November) were reprocessed using the xispi script in accordance with the Suzaku ABC Guide10 along with the latest version of the CALDB (as of 2010 March 29). XIS spectra and light curves were then produced according to the procedure outlined in the ABC Guide. For the XIS spectra, we combined data from the front-illuminated (FI) detectors XIS 0+3 data using the addascaspec script in order to increase S/N. The XIS spectra, responses, and backgrounds were then rebinned to 512 spectral channels from the original 4096 in order to speed up spectral model fitting without compromising the resolution of the detectors. Finally, the XIS spectra were grouped to a minimum of 25 counts per bin in order to facilitate robust χ2 fitting. The merged, background-subtracted, time-averaged FI spectrum has a net count rate of $4.960 \pm 0.002 \hbox{ ${\rm counts}\,{\rm s}^{-1}$}$ for a total of 1.04 × 106 counts. The total number of 2–10 keV counts is 6.26 × 105. The total XIS 1 count rate is $3.043\pm 0.004 \hbox{ ${\rm counts}\,{\rm s}^{-1}$}$ for a total of 6.40 × 105 or 3.14 × 105 when restricting to 2–10 keV. For all of the fitting presented in this paper, we allow for a global flux cross-normalization error between the FI and XIS 1 spectra. The XIS 1/FI cross-normalization is allowed to be a free parameter and is found to be approximately 1.03.

The HXD/PIN instrument detected NGC 3783, though the GSO did not. Data from PIN were again reduced as per the Suzaku ABC Guide. For background subtraction, we used the "tuned" non-X-ray background (NXB) event file for 2009 July from the Suzaku CALDB, along with the appropriate response file and flat-field file for epoch 5 data. The NXB background contributed a count rate of $0.2165 \pm 0.0004\hbox{ ${\rm counts}\,{\rm s}^{-1}$}$ to the total X-ray background from 16 to 45 keV. We modeled the cosmic X-ray background (CXB) contribution as per the ABC Guide, simulating its spectrum in XSPEC (Arnaud 1996). The simulated CXB spectrum contributed a count rate of $0.0237 \pm 0.0002\hbox{ ${\rm counts}\,{\rm s}^{-1}$}$ to the total X-ray background from 16 to 45 keV. The NXB and CXB files were combined to form a single PIN background spectrum. In comparison, the PIN data had a count rate of $0.4561 \pm 0.0027\hbox{ ${\rm counts}\,{\rm s}^{-1}$}$ over the same energy range, roughly twice that of the total background.

Because the PIN data only contain 256 spectral channels (versus the 4096 channels in the unbinned XIS data), rebinning to 25 counts per bin was not necessary in order to facilitate χ2 fitting. Rather, we rebinned the PIN spectrum to have an S/N of 5 in each energy bin, which limited our energy range to 16–45 keV. After reduction, filtering, and background subtraction, the PIN spectrum had a net 16–45 keV count rate of $0.360 \pm 0.002 \hbox{ ${\rm counts}\,{\rm s}^{-1}$}$. We also added 3% systematic errors to the PIN data to account for the uncertainty in the NXB data supplied by the Suzaku calibration team. For most of the spectral fitting presented in this paper, we assume a PIN/XIS-FI cross-normalization factor of 1.18 as per the Suzaku memo 2008-06.11 However, for the final fits used to constrain the black hole spin in Section 3.4, we investigate the effect of allowing this cross-normalization to be a free parameter.

XIS light curves (both hard and soft band) as well as PIN light curves are shown in Figure 1. In the soft band (0.3–1 keV), the source is observed to undergo variability by a factor of almost two. Most of the large amplitude variability occurs on timescales of 50–100 ks, although there are occasional sharp flares/dips that occur much more rapidly. Also noteworthy is that the amplitude of variability decreases as one considers higher-energy bands, suggesting "pivoting" of the spectrum about some energy above the Suzaku/PIN band. The detailed nature of this spectral variability will be the subject of another publication (R. C. Reis et al. 2011, in preparation). For the remainder of this paper, we examine the high S/N spectrum from the time-averaged data set. We restrict our energy range to 0.7–10 keV in the XIS data, ignoring energies below 0.7 keV and from 1.5 to 2.5 keV to avoid areas of significant deviation between the three detectors, i.e., regions of known calibration uncertainty.

Figure 1.

Figure 1. Co-added and background-subtracted XIS light curves in the soft (0.3–1 keV) and hard (2–10 keV) bands, together with the background-subtracted PIN (16–45 keV) light curve. These light curves are shown with 5000 s bins.

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3. ANALYSIS OF THE TIME-AVERAGED SUZAKU SPECTRUM

3.1. A First Look at the Hard-band Spectrum

It is instructive to begin by examining the hard-band (3.5–45 keV) XIS+PIN spectrum. A simple power-law fit to this band reveals significant spectral complexity (Figures 2(a) and (b). A narrow Kα fluorescence line of cold iron (6.4 keV) dominates; structure redward of this line indicates a possible Compton shoulder as well as an extended tail reaching down to ∼4 keV. Both the narrow iron line and the broad red wing likely originate from X-ray reflection and, hence, the convex spectrum between 8 and 40 keV is readily interpreted as the associated Compton reflection hump. Structure above the 6.4 keV line indicates a strong absorption feature at ∼6.6 keV and/or an emission line at ∼7 keV (likely corresponding to a blend of the Kβ line of cold iron and the Lyα line of Fe xxvi).

Figure 2.

Figure 2. Left panel: simple power-law fit to the 3.5–45 keV XIS-FI+PIN spectrum. Middle panel: zoom-in on the 4–8 keV region of the simple power-law fit. Note the probable "Compton shoulder" on the immediate low-energy side of the strong 6.4 keV emission line. Right panel: residuals remaining when the broad iron line component is removed from a simple phenomenological fit to the 3.5–45 keV data (see Section 3.1). In all panels the black points correspond to XIS 0+3 data, the red to XIS 1 data, and the blue to PIN data. The green line represents a data-to-model ratio of unity.

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Guided by these identifications, we construct a heuristic model of the hard spectrum consisting of a power-law continuum, a narrow Fe xxvi emission line (modeled as a Gaussian line centered at 6.97 keV with σ = 10 eV), reflection from distant, low-velocity, cold matter (described by the pexmon model12), and a relativistically broadened cold iron Kα line (described by the laor model; Laor 1991). This model produces an excellent fit to the data (χ2/ν = 573/544 (1.05)) with the following parameters: photon index Γ = 1.68+0.01− 0.01, reflection fraction ${\cal R}=0.87^{+0.02}_{-0.06}$, emission line equivalent widths $W_{{\rm Fe\,\mathsc{xxvi}}}=28^{+4}_{-5}\;{\rm eV}$, Wbroad = 263+23− 23 eV, inner edge of line emitting disk rin = 3.0+0.1− 0.8rg, index of line emissivity across disk q = 3.3 ± 0.1, and disk inclination i < 9°. If we replace the pexmon model with a pexrav and three separate Gaussian lines for narrow Fe Kα (6.4 keV, σ = 0.015 keV), Fe Kβ (7.06 keV, σ = 0.015 keV), and Compton shoulder (6.25 keV, σ = 0.1 keV), their equivalent widths are W = 98+5− 5 eV, W ⩽ 8 eV, and WCS = 22+8− 6 eV, respectively. We note that, in this fit, the intrinsic widths of the iron lines were taken from their Chandra/HETG values (Yaqoob et al. 2005). Substituting the individual Gaussian lines and pexrav component for the pexmon model results in a modest change in the global goodness of fit (Δχ2/Δν = −32/ − 3), likely owing to the free normalizations of the emission lines (they are set at fixed ratios within pexmon). No statistically significant change is seen in the other model parameters.

For illustrative purposes only, Figure 2(c) shows the residuals that remain when the broad iron line is removed from this spectral model, and the remaining model parameters are re-fit. An obvious broad line remains. However, there are two reasons why this cannot be interpreted as "the broad line profile" for this object. First, NGC 3783 has a well-known, high-column density WA that, while principally affecting the soft spectrum, can also introduce subtle spectral curvature up to 10 keV or more. Second, the broadened iron line is just the tip of the iceberg; in particular when the accretion disk is ionized, the rest of the reflection spectrum has a sub-dominant but significant contribution that must be considered. The statistically unlikely value of the disk inclination derived from the simple fit (i < 9°) is a signal of these issues. For these reasons, we are forced into global modeling of the full 0.7–45 keV spectrum.

3.2. Guidance from the Long Chandra/HETG Observation

It is well known that NGC 3783 possesses a high-column density WA (e.g., Reynolds 1997); this is the greatest complexity we face when modeling the X-ray spectrum of this source. For guidance, we turn to the long (900 ks) observation of NGC 3783 with the HETGS on Chandra. Extensive analyses of the HETG data have been published (Kaspi et al. 2002; Krongold et al. 2003; Netzer et al. 2003); however, to retain consistency and utilize the latest calibrations, we have reanalyzed the first-order MEG+HEG spectra.

We obtained the Chandra HETG data for NGC 3783 from tgcat for each of the ObsIDs corresponding to the 900 ks campaign and co-added together spectra for a given order of a given grating. As a result, we obtain four spectral files corresponding to the time-average ±first-order spectrum from each of the HEG and the MEG. These were binned to a minimum of 15 photons per spectral bin in order to validate the use of χ2 techniques while still maintaining spectral resolution. We then jointly analyzed these spectra, noticing the 0.5–7 keV range in the MEG data and the 1–7.5 keV range in the HEG data. We permitted the overall cross-normalization between these four spectra to be free parameters; in all cases, the best-fitting cross-normalization is within 5% of unity.

Fitting these data with a power law modified by the effects of Galactic absorption (NH = 9.91 × 1020 cm−2; described using the phabs model of XSPEC) results in a very poor fit with χ2/ν = 58962/13112 (4.50). The residuals suggest a soft excess component, soft X-ray absorption by a WA, and a prominent fluorescent iron Kα line at 6.4 keV. The effect of the WA is modeled using the XSTAR code (Kallman & Bautista 2001); for an absorber of a given column density NH and ionization parameter ξ, XSTAR is used to compute the absorption imprinted on a power-law X-ray spectrum. We compute a grid of XSTAR models, logarithmically sampling a range of column densities in the range NH: 1020–1024 cm−2 and a range of ionization parameters in the range ξ: 1–104 erg cm s−1, for use in spectral fitting. In the construction of the WA grids it is assumed that the irradiating power law has a spectral index of Γ = 2, that elemental abundances are fixed to solar values,13 and that the turbulent velocity of the WA is 200 km s−1. Dramatic improvements in the goodness of fit are found by the inclusion in the model of three zones of WA. To begin with, each WA component is included assuming that the absorbing gas is at rest with respect to NGC 3783; the improvement in the fit upon the addition of each WA component was Δχ2 = −26316, −3096, and −2490. The inclusion of a fourth zone led to a much smaller improvement in the fit and hence was deemed inappropriate. The residuals from the three-zone WA fit do indicate a soft excess. Following Krongold et al. (2003), we model the soft excess with a blackbody component (this is intended to be a phenomenological, not a physical, description of the soft excess; see discussion in Section 3.3) resulting in an improvement in the fit of Δχ2/Δν = −480/ − 2 (i.e., χ2/ν = 26582/13104 (2.03)).

While providing a decent fit to the global spectrum, the model thus described leaves prominent unmodeled emission and absorption lines, the most prominent of which is the iron fluorescent emission line at 6.4 keV. Fitting the iron line with a simple Gaussian model improves the goodness of fit by Δχ2/Δν = −593/ − 3, with a line energy E = 6.398 ± 0.002 keV (confirming the identification of cold iron Kα), FWHM = 2000  ±  300 km s−1, and equivalent width W = 88 ± 6 eV. However, since we believe that this component originates from reflection, we shall henceforth model it using pexmon; replacing the simple Gaussian with the pexmon model convolved with a Gaussian velocity profile (with FWHM = 1800 ± 300 km s−1) results in a slightly better fit (Δχ2 = −18). At the soft end of the spectrum, the Kα emission triplet of O vii (at 0.574 keV, 0.569 keV, 0.561 keV) as well as the Kα emission line of O viii (at 0.654 keV) are clearly visible. Modeling these as Gaussian lines at the redshift of NGC 3783 with common velocity width yields a further improvement in the goodness of fit (Δχ2 = −218) with best-fitting FWHM = 700 ± 150 km s−1 and equivalent widths W0.574 = 26 ± 6 eV, W0.569 = 14 ± 6 eV, W0.561 = 47 ± 9 eV, and W0.654 = 23 ± 5 eV.

It is well known that the WA in this and many other objects corresponds to outflowing gas. Relaxing the constraint that the WA zones are at the systemic redshift of NGC 3783 yields a large improvement in the fit (Δχ2/Δν = 4247/ − 3; χ2/ν = 21532/13094 (1.64)), with implied line-of-sight outflow velocities in the 500–1000 km s−1 range. These velocities as well as the other parameters defining the best-fit model for the HETG data are listed in Table 1. The spectral model described in this section (power-law continuum, three-zone WA, blackbody soft excess, reflection from distant neutral material, and emission lines from O vii and O viii) describes the vast majority of spectral features seen in the HETG data (see Figure 3).

Figure 3.

Figure 3. Folded Chandra/HETG spectrum and best-fitting model as a function of observed energy. As described in the text (Section 3.2), the model is fitted simultaneously to the ±1 MEG (0.5–7 keV) and HEG (1–7.5 keV) data. However, for clarity, we only show here the −first-order MEG data (black; first three panels) and the −first-order HEG data (blue; bottom panel).

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Table 1. Spectral Fit Parameters

Model Component Parameter HETG Suzaku (0.7–45 keV) Suzaku (>3 keV)
Galactic column    NH    9.91(f)    9.91(f)    9.91(f)
WAbs1    NWA    51.7+0.8− 0.7    90+10− 14    90(f)
     log  ξ    1.15+0.01− 0.01    1.47+0.03− 0.03    1.47(f)
     Δz    −(1.4+0.07− 0.07) × 10−3    0(f)    0(f)
WAbs2    NWA    127+1.8− 2.0    159+31− 21    159(f)
     log  ξ    2.08+0.01− 0.01    1.93+0.02− 0.01    1.93(f)
     Δz    −(1.0+0.3− 0.3) × 10−3    0(f)    0(f)
WAbs3    NWA    268+10− 12    168+48− 42    168(f)
     log  ξ    2.83+0.01− 0.01    2.53+0.05− 0.02    2.53(f)
     Δz    −(3.4+0.4− 0.4) × 10−4    0(f)    0(f)
PL    Γ    1.62+0.01− 0.01    1.81+0.10− 0.05    1.84+0.06− 0.05
     Apl    (1.49+0.01− 0.01) × 10−2    (1.46+0.09− 0.04) × 10−2    (1.52+0.10− 0.08) × 10−2
BB    kT (eV)    107+3− 3    60+3− 4    60(f)
     Abb    (1.4+0.1− 0.1) × 10−4    (8.45+5.98− 2.67) × 10−3    8.45 × 10−3(f)
Scattered fraction    fsc    (2.3+0.4− 1.0) × 10−2    0.17+0.02− 0.02    0.17(f)
Cold reflection    $\cal R_{\rm cold}$    0.49+0.04− 0.03    0.46+0.12− 0.07    0.62+0.31− 0.20
  PL cutoff (keV) ...    200(f)    200(f)
GAU line    E (keV) ...    6.97(f)    6.97(f)
     σ (keV) ...    0.0154(f)    0.0154(f)
     $W_{{\rm Fe \mathsc{xxvi}}}$ (eV) ...    22+5− 5    18+6− 5
     $A_{{\rm Fe \mathsc{xxvi}}}$ ...    (1.28+0.29− 0.31) × 10−5    (1.11+0.39− 0.31) × 10−5
Accretion disk    ZFe ...    3.7+0.9− 0.9    2.2+2.4− 0.9
     ξ ...    <8    <67
     $\cal R_{\rm rel}$ ...    0.21+1.56− 0.07    0.23+14.66− 0.03
     i ...    22+3− 8    19+6− 14
     rin ...    ISCO(f)    ISCO(f)
     q1 ...    5.2+0.7− 0.8    4.7+1.9− 1.2
     rbr ...    5.4+1.9− 0.9    6.0+16.9− 1.9
     q2 ...    2.9+0.2− 0.2    2.8+0.3− 0.5
     rout ...    400(f)    400(f)
PIN/XIS norm   ...    1.18(f)    1.15+0.07− 0.07
SMBH spin    a ...    ⩾0.98    0.98+0.02− 0.34
χ2      21532/13094 (1.64)    917/664 (1.38)    499/527 (0.95)

Notes. All errors are quoted at the 90% confidence level for one interesting parameter (Δχ2 = 2.7). Parameters marked with an "(f)" had their values fixed during the fit. Units of normalization are in $\hbox{${\rm ph}\rm {otons}\,\rm {cm}^{-2}\,\rm {s}^{-1}$ }$, column density is in units of 1020 cm−2, ionization parameter is in erg cm s−1, iron abundance is relative to solar (linked between the reflionx and pexmon reflection components), inclination is in degrees, radii are in rg, and spin parameter is dimensionless, but is defined as acJ/GM2. See Section 3 for details.

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3.3. Global Modeling of the 0.7–45 keV Spectrum

To extract the maximal information from the full-band (0.7–45 keV) Suzaku spectrum of NGC 3783, we must compare the data to a global spectral model which is as physically self-consistent and realistic as possible. In constructing this global model, we draw guidance from our heuristic analysis of the hard-band spectrum (Section 3.1) as well as the results from the Chandra/HETG (Section 3.2). The primary continuum emission is taken to be a power law (photon index Γ) with a soft excess which we describe as a blackbody (temperature T). X-ray reflection of this continuum from cold, distant material (possibly associated with the dusty/molecular torus of unified Seyfert schemes) is described using the pexmon model (see Section 3.1). As discussed in Section 3.1, the inclination of the pexmon is fixed at i = 60° and the abundances are fixed to be solar, as defined in Nandra et al. (2007). These emission components are then absorbed by a three-zone WA modeled using the XSTAR tables described in Section 3.2; the column density NW and ionization parameter ξ of each zone are taken to be free parameters rather than being fixed to the HETG value. Since the Suzaku/XIS detectors do not have the spectral resolution capable of constraining the outflow velocities of the various WA zones, we have elected to hold the redshifts of these components fixed at the cosmological value for NGC 3783. Statistically indistinguishable results are obtained if we, instead, fix the outflow velocities to the HETG-derived values. For completeness, we also allow for some fraction fsc of the continuum to be scattered around (or to leak through) the WAs, i.e., our model allows for "partial covering."

Fitting this model to the 0.7–45 keV Suzaku data results in a poor fit (χ2/ν = 1206/679 (1.78)) and strong residuals which indicate the presence of the broad iron line as well as additional reflection beyond that associated with the narrow iron line (Figure 4). This leads us to include relativistically smeared reflection from an ionized accretion disk into the spectral model; operationally, we use the ionized reflection model reflionx (Ross & Fabian 2005) convolved with the variable-spin relativistic smearing model relconv (Dauser et al. 2010). The relconv model is a further evolution of the kerrconv model of Brenneman & Reynolds (2006), employing faster and more accurate line-integration schemes and allowing black hole spin to be fit as a free parameter for prograde, non-spinning, and retrograde spins (a ∈ [ − 0.998, 0.998]). While the fit achieved with this blurred reflection model is not statistically ideal (χ2/ν = 917/664 (1.38)), there are no broadband residuals (Figure 5(a)), and much of the contribution to the excess χ2 originates from fine details of the WA-dominated region below 1.5 keV. The model is shown in Figure 5(b), and the best-fitting parameter values are shown in Table 1.

Figure 4.

Figure 4. Results of fitting the XIS+PIN spectrum with a model that includes the warm absorbers, distant reflection, and scattering/leaked soft component but not the relativistic ionized accretion disk. While the fitting is performed on the 0.7–45 keV spectrum, we show for clarity only the residuals above 3 keV. Left: strong residuals indicative of a broad iron line and Compton reflection hump are clearly visible. This motivates the inclusion of a relativistic disk component into the spectral model. The XIS 0+3 data are shown in black and XIS 1 data are in red, while the HXD/PIN data are in blue. The solid green line represents a data-to-model ratio of unity. Right: zoom-in on the Fe K line region.

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Figure 5.

Figure 5. Global modeling of the 0.7–45 keV XIS-FI+PIN data. The left panel shows the resulting residuals from fitting the model (including the relativistic accretion disk) discussed in Section 3.3. Data point colors are as in Figure 2. The right panel shows the best-fitting model color coded as follows: (a) green line, continuum power-law emission; (b) dark blue line, cold and ionized iron line emission from distant matter; (c) red line, soft excess modeled as blackbody; (d) magenta line, significant emission that scatters around or leaks through the warm absorber; (e) light blue line, relativistically smeared disk reflection; and (f) thick black line, total summed model spectrum. Warm absorption affects all components apart from (d).

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The parameters defining the best-fitting model for the 0.7–45 keV data are shown in Table 1 along with their 90% confidence ranges. Under the assumption that we can identify the low-, medium-, and high-ionization components seen in the 2001-HETG observation with those seen in our 2009-Suzaku data, we see that both the column density and the ionization state of the low-ionization absorber have increased somewhat (Δlog ξ ≈ 0.28, ΔNWA ≈ 3 × 1021 cm−2). In contrast, the medium- and high-ionization absorbers have slightly dropped in ionization parameter. Given that these different zones are likely at very different distances from the central engine with very different plasma densities, they will possess very different recombination/photoionization timescales and hence will respond to changes in the ionization flux on different timescales. Thus, it is not surprising that we see a mixture of increasing and decreasing ionization states in the various WA zones.

We also note a change in the both the temperature and normalization of the blackbody component between the 2001-HETG and 2009-Suzaku data. This merits some discussion. The blackbody component used to phenomenologically parameterize the soft excess was first employed by Krongold et al. (2003), who found kT = 0.10 ± 0.03 keV and Abb = (2.0 ± 0.7) × 10−4, where the normalization is in units of L39/D210 (L39 is luminosity of the component in units of 1039 erg s−1 and D10 is distance to the source in units of 10 kpc). Our analysis of the same HETG data confirms the Krongold et al. (2003) result. By contrast, our analysis of the Suzaku/XIS+PIN spectra finds a lower temperature (kT = 0.060+3− 4keV) and a normalization that is almost two orders of magnitude greater (Abb = 8.4+6.0− 2.7 × 10−3). We stress that neither the use of a blackbody to model the soft excess nor the precise change in the parameters of the blackbody should be interpreted literally. In particular, the significant change in the normalization of this component is misleading—the lower energy cutoffs in both the HETG analysis (0.5 keV) and the XIS analysis (0.7 keV) are much higher than the peak of this blackbody component and, thus, only the Wien tail of this component is playing any role in the spectral fitting. Given this fact, even a modest drop in the temperature must be compensated for by a large increase in normalization in order to have a comparable contribution to the observed energy band. While the physical nature of the soft excess is of intrinsic interest, it is beyond the scope of this paper. We have verified that different treatments of the soft excess (replacing the blackbody spectrum with bremsstrahlung or a steep power-law component) do not affect the interpretation of the spectrum above 2 keV.

The principal focus of this work is the signature of the relativistic accretion disk. Our global fit finds reflection from a rather low-ionization accretion disk (ξ < 9 erg cm s−1) extending down to the innermost stable circular orbit (ISCO) of a rapidly rotating black hole (a ⩾ 0.98). The emissivity/irradiation profile defining the reflection spectrum, modeled as a broken power law, is found to have an inner power-law index of q1 = 5.2+0.7− 0.8 breaking to q2 = 2.9 ± 0.2 at a radius of rbr = 5.4+1.9− 0.9rg. If these indices are tied together in the model, i.e., if q1 = q2, the fit worsens considerably (Δχ2/Δν = +21/ + 1, with q1 = q2 = 3.0 ± 0.3) and the black hole spin is also less tightly constrained: a ⩾ 0.25.

The iron abundance of the disk has been constrained to lie between 2.8 and 4.6 times solar. To probe the robustness of this constraint we have refitted the data in three different ways, each allowing for slight differences in the way the iron abundance was handled in our model: (1) fixing Fe/solar of the distant reflector (pexmon) to that of the inner disk reflection (reflionx), with both values frozen at Fe/solar = 1; (2) allowing these linked abundances allowed to vary freely; and (3) allowing both abundances to vary freely and independently. Compared with the global best fit, scenario (1) resulted in a worsening of the goodness of fit by Δχ2 = 33 and unconstrained black hole spin at the 90% confidence level, scenario (2) resulted in a marginal decrease in the goodness of fit by Δχ2 = 7 (no change in spin constraints), and scenario (3) yielded no change in the goodness of fit (no change in spin constraints). In summary, the high iron abundance of the reflionx is statistically preferred to the solar value; the high-spin value is dependent upon the high iron abundance, but the high abundance is strongly preferred in the fit. Because the iron abundance of the distant reflector could not be constrained independently of the relativistic reflector, the pexmon and reflionx iron abundances have been linked in our best model fit.

To gauge the importance of the (complex) soft spectrum on our global fit, we have also conducted a restricted hard-band (3–45 keV) fit. Since a hard-band fit cannot constrain the parameters of the WA or soft excess, these parameters are constrained to lie within their 90% confidence ranges as derived from the 0.7–45 keV analysis. To be most conservative, we also relax the constraint on the XIS/PIN cross-normalization, allowing it to be a free parameter. The resulting fit is listed in the last column of Table 1. For this fit χ2/ν = 499/527 (0.95), a great improvement over the 0.7–45 keV fit and confirmation that the small residuals below ∼1.5 keV are the primary contribution to the large reduced χ2 of the full spectral fit. While the parameter values are equivalent to those of the 0.7–45 keV fit within errors, the uncertainties on the parameters are larger when only the hard spectrum is considered. This is especially true for the inner disk emissivity and break radius of the relconv model, which exhibit a strong degeneracy without the soft spectrum data. Figure 6 shows the confidence contours on the (q1, q2)-plane for this hard-band fit; we see that the outer disk emissivity index, q2, is well constrained, whereas the constraints on the inner disk emissivity index, q1, are clearly worse. Fixing the XIS/PIN cross-normalization at the nominal value of 1.18 tightens the constraints but still leaves a significant degeneracy between q1 and rbr (Figure 6).

Figure 6.

Figure 6. Confidence contours on the (q1, q2)-plane for the 3–45 keV band fit assuming a XIS/PIN cross-normalization that is free (left panel) or fixed at the nominal value of 1.18 (right panel). Blue, red, and green lines show the 68%, 90%, and 99% confidence contours for two interesting parameters (Δχ2 = 2.3, 4.6, 9.2), respectively. The dot-dashed black line represents q1 = q2.

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Using the best-fitting 0.7–45 keV spectral model with the XIS 0 normalization, the 2–10 keV observed-frame flux of NGC 3783 is F2–10 = 6.04 × 10−11 erg cm−2 s−1. Adopting a standard cosmological model ($H_0=71\;\hbox{$\hbox{${\rm km}\;{\rm s}^{-1}$}\;{\rm Mpc}^{-1}$}$, ΩM = 0.3, $\Omega _\Lambda =0.7$), this implies a rest-frame luminosity of L2–10 = 1.26 × 1043 erg s−1. The hard X-ray band yields a 16–45 keV flux of F16–45 = 1.07 × 10−10 erg cm−2 s−1 for a rest-frame luminosity of L16–45 = 2.24 × 1043 erg s−1.

3.4. The Spin of the Black Hole

Our fiducial spectral model discussed above yields a spin constraint of a ⩾ 0.98 (90% confidence) or a ⩾ 0.88 (99% confidence). However, given the subtle nature of the spin measurements, it is useful to address the systematic issues that may be introduced by the modeling and analysis techniques.

We can assess the role of different analysis-related assumptions on the derived spin by comparing the variation of χ2 with a. Figure 7 (black line) shows Δχ2(a) = χ2(a)  −  χ2best–fit from our fiducial analysis that underlies the constraint just quoted. It is interesting to note the non-monotonic nature of the χ2-space above a ∼ 0.75. We consider a few variants from this fiducial analysis in order to probe the sensitivity of the spin measurement. An important issue is the extent to which the WA parameters are trading off with the derived black hole spin. Thus, we repeat the analysis with the WA parameters (column densities and ionization parameters for all three zones) fixed at their best-fit values from the fiducial model. The resulting spin constraints are shown in Figure 7 (a ⩾ 0.98; red line) and are very similar to the fiducial model, indicating little or no degeneracy between spin and the WA parameters.

Figure 7.

Figure 7. Goodness-of-fit parameter Δχ2 as a function of the assumed black hole spin for our fiducial model (black line), the fiducial model except with frozen WA parameters (red line), the fiducial model except with free XIS/PIN normalization (blue line), and a hard-band (>3 keV) fit only (green line). Confidence levels (90%, 95%, and 99%) are indicated with horizontal black lines and are derived for one interesting parameter. See the text in Section 3.4 for details.

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Second, to the extent that the strength of the Compton reflection hump is important, we may be concerned about the effect of cross-calibration errors in the flux normalization between the XIS and the PIN spectra. Thus, we repeat the spectral analysis, leaving the cross-normalization factor as a free parameter. The best-fit value is slightly smaller than our fiducial value (1.15 versus 1.18), but the improvement in the goodness of fit is only marginally significant (Δχ2 = 6 for one additional degree of freedom). The spin is constrained to be slightly smaller than that of the fiducial model (to 90% confidence, a = 0.92–0.95; Figure 7, blue line).

Lastly, we may be concerned that the spin fits are being driven by the contribution of the ionized disk to the high S/N by highly complex region of the spectrum below 1.5 keV. Thus, we have repeated our analysis including data only above 3 keV. Here, too, we allow the XIS/PIN cross-normalization to be a free parameter. Given the lack of data at soft energies to constrain them, the WA, blackbody, and scattered fraction components were frozen to their best-fitting values for the full-band, free cross-normalization case (which is, within errors, identical to the WA parameters for the fiducial model). Yet again, the best-fit spin parameter is similar to that of the fiducial model (a ⩾ 0.95; Figure 7, green line). This indicates that the fitted spin value is indeed driven by the Fe K band.

4. DISCUSSION AND CONCLUSIONS

The X-ray spectrum of NGC 3783 is complicated; in addition to the effects of a multi-zone WA, there are suggestions that some fraction (17%) of the primary X-ray emission can scatter around or leak through the WA. However, despite this complexity, the high S/N and broad bandpass of Suzaku allows us to robustly detect and study the relativistically smeared X-ray reflection spectrum from the surface of the inner accretion disk. Assuming that the region within the general relativistic radius of marginal stability does not contribute to the reflection spectrum (Reynolds & Fabian 2008) we determine a lower limit of a ⩾ 0.98 (90% confidence) to the dimensionless spin parameter of the black hole. Even at the 99% confidence level, we can constrain the spin to be a ⩾ 0.88. Relaxing the assumed XIS/PIN cross-normalization or neglecting the soft-band data (but then freezing the WA parameters) allows the model to find a slightly better fit and makes the constraints slightly lower (a = 0.92–0.95, a ⩾ 0.95 at 90% confidence, respectively; a ⩾ 0.88, a ⩾ 0.90 at 99% confidence, respectively).

Including this result, four out of the eight AGNs with reliable spin measurements may have spins greater than a = 0.8 (see Table 2). Spin measurements for more sources are required before we can draw any conclusions about the spin distribution function, but here we note that there are potentially important selection effects biasing any flux-limited sample toward high-spin values. For standard accretion models, the efficiency of black hole accretion increases as the spin of the black hole increases. So, all else being equal, an accreting, rapidly spinning black hole will be more luminous than an accreting, slowing spinning black hole and hence will be overrepresented in flux-limited samples.

Table 2. Summary of Black Hole Spin Measurements Derived from Relativistic Reflection Fitting of SMBH Spectra

AGN a W q1 Fe/solar ξ log M Lbol/LEdd Host WA
MCG–6-30-15a ⩾0.98 305+20− 20 4.4+0.5− 0.8 1.9+1.4− 0.5 68+31− 31 6.65+0.17− 0.17 0.40+0.13− 0.13 E/S0 Yes
Fairall 9b 0.65+0.05− 0.05 130+10− 10 5.0+0.0− 0.1 0.8+0.2− 0.1 3.7+0.1− 0.1 8.41+0.11− 0.11 0.05+0.01− 0.01 Sc No
SWIFT J2127.4+5654c 0.6+0.2− 0.2 220+50− 50 5.3+1.7− 1.4 1.5+0.3− 0.3 40+70− 35 7.18+0.07− 0.07 0.18+0.03− 0.03 Yes
1H0707–495d ⩾0.98 1775+511− 594 6.6+1.9− 1.9 ⩾7 50+40− 40 6.70+0.40− 0.40 ∼1.0−0.6 No
Mrk 79e 0.7+0.1− 0.1 377+47−34 3.3+0.2− 0.1 1.2* 177+6− 6 7.72+0.14− 0.14 0.05+0.01− 0.01 SBb Yes
Mrk 335f 0.70+0.12− 0.01 146+39− 39 6.6+2.0− 1.0 1.0+0.1− 0.1 207+5− 5 7.15+0.13− 0.13 0.25+0.07− 0.07 S0a No
NGC 7469f 0.69+0.09− 0.09 91+9− 8 ⩾3.0 ⩽0.4 ⩽24 7.09+0.06− 0.06 1.12+0.13− 0.13 SAB(rs)a No
NGC 3783g ⩾0.98 263+23− 23 5.2+0.7− 0.8 3.7+0.9− 0.9 ⩽8 7.47+0.08− 0.08 0.06+0.01− 0.01 SB(r)ab Yes

Notes. Data are taken with Suzaku except for 1H0707–495, which was observed with XMM-Newton, and MCG–6-30-15, in which the data from XMM and Suzaku are consistent with each other. Spin (a) is dimensionless, as defined previously. W denotes the equivalent width of the broad iron line relative to the continuum in units of eV. Parameter q1 represents the inner disk emissivity index and is unitless. Fe/solar is the iron abundance of the inner disk in solar units, while ξ is its ionization parameter in units of erg cm s−1. M is the mass of the black hole in solar masses, and Lbol/LEdd is the Eddington ratio of its luminous output. Host denotes the galaxy host type and WA denotes the presence/absence of a warm absorber. Values marked with an asterisk either were fixed in the fit or have unknown errors. All masses are from Peterson et al. (2004) except MCG–6-30-15, 1H0707–495, and SWIFT J2127.4+5654, which are taken from McHardy et al. (2005), Zoghbi et al. (2010), and Malizia et al. (2008), respectively. All bolometric luminosities are from Woo & Urry (2002) except for the same three sources. The same references for MCG–6-30-15 and SWIFT J2127.4+5654 are used, but host types for 1H0707–495 and SWIFT J2127.4+5654 are unknown. aBrenneman & Reynolds (2006) and Miniutti et al. (2007). bSchmoll et al. (2009), though note some discrepancies with Patrick et al. (2011). cMiniutti et al. (2009), though note some discrepancies with Patrick et al. (2011). dZoghbi et al. (2010) and de la Calle Pérez (2010). eGallo et al. (2005, 2011). fPatrick et al. (2011). gThis work.

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We illustrate this effect by calculating the selection bias given some very simple assumptions. Suppose that a flux-limited sample is constructed in some band B. The accretion luminosity in that band will be given by

Equation (1)

where KB is the fraction of luminosity appearing in band B (i.e., the reciprocal of the bolometric correction), η is the accretion efficiency, and $\dot{M}$ is the mass accretion rate. Now let us assume that $\dot{M}$ has no explicit spin dependence (e.g., is determined by the larger circumnuclear environment), and that the spectral energy distribution and hence KB is independent of spin. Thus, the space density of sources with accretion rates in the range $\dot{M}\rightarrow \dot{M}+d\!\dot{M}$ and spins in the range aa + da, denoted $\Phi (\dot{M},a)\,d\!\dot{M}\,{\it da}$, can be taken as a given function set by the astrophysics of black hole growth.

We assume a Euclidean universe, valid for the local/bright AGN samples relevant for spin measurements with the current generation of X-ray observatories. The number of sources in a flux-limited sample with luminosity in the range LL + dL and spins in the range aa + da is then

Equation (2)

where Φ(L, a) dLda is the space density of sources with luminosity in the range LL + dL and spins in the range aa + da. Transforming into the $(\dot{M},a)$-plane gives

Equation (3)

Using our assumption that the mass accretion rate is independent of spin, we can separate $\Phi (\dot{M},a)$ into an accretion-rate-dependent space density $n(\dot{M})$ and a spin distribution function f(a), $\Phi (\dot{M},a)=n(\dot{M})f(a)$. We can then integrate Equation (3) over $\dot{M}$ in order to determine the number of sources in a flux-limited sample with spins in the range aa + da:

Equation (4)

For illustration purposes, let us examine Equation (4) in the case of a completely flat spin distribution where f(a) = constant for a ∈ [0, amax] and is zero otherwise. Thus, half of the parent population as a whole has a > amax/2. We find that if amax = 0.95, then half of the sources in the flux-limited sample will have a > 0.67; for amax = 0.99 we find that half of the sources in the sample have a > 0.73.

Generalizing away from a flat spin distribution, we can consider spin distribution functions of the form f(a)∝ap. Within this simple framework, we require f(a)∝a (i.e., p = 1.0) in order to produce flux-limited samples where half of the sources have a > 0.84 (assuming amax = 0.95). For high-spin-weighted distribution functions such as this, the selection bias is stronger; only 20% of objects in the volume-limited parent sample actually have a > 0.84. Of course, given the small number statistics and highly inhomogeneous selection functions for the current spin measurements, it is too early to draw any conclusions about the need for a high-spin-biased distribution function.

We are extremely grateful to our NASA and JAXA colleagues in the Suzaku project for enabling these Key Project data to be collected. We thank Martin Elvis and Cole Miller for insightful conversations throughout the course of this work, and the anonymous referee, who provided useful feedback that has improved this manuscript. This work was supported by NASA under the Suzaku Guest Observer grant NNX09AV43G.

Footnotes

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    The pexmon model (Nandra et al. 2007) is a modification of the commonly used pexrav model (Magdziarz & Zdziarski 1995) which, in addition to the Compton backscattered reflection continuum, also models the Kα and Kβ emission lines of iron, the Compton shoulder of the iron Kα line, and the Kα line of nickel. The lines are included at the appropriate normalization for the assumed inclination, abundance, and reflection fraction. Hence, pexmon is superior to the usual "pexrav+gaussian" model since the strengths of the Compton reflection continuum and fluorescent lines are forced to be self-consistent. Assumptions do need to be made, however, when employing this model. In particular, we fix the inclination parameter of this component to be i = 60° and assume solar abundances (Wilms et al. 2000).

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10.1088/0004-637X/736/2/103