Probing the Origins of the CIV and Fe Kalpha Baldwin Effect
Jian Wu, Daniel E. Vanden Berk, W.N.Brandt, Donald Schneider, Robert Gibson, Jianfeng Wu
aa r X i v : . [ a s t r o - ph . C O ] J u l Probing the Origins of the C iv and Fe K α Baldwin Effects
Jian Wu , Daniel E. Vanden Berk , , W. N. Brandt , Donald P. Schneider , Robert R. Gibson , ,andJianfeng Wu [email protected] ABSTRACT
We use UV/optical and X-ray observations of 272 radio-quiet Type 1 AGNs andquasars to investigate the C iv Baldwin Effect (BEff). The UV/optical spectra aredrawn from the
Hubble Space Telescope , International Ultraviolet Explorer and SloanDigital Sky Survey archives. The X-ray spectra are from the
Chandra and
XMM-Newton archives. We apply correlation and partial-correlation analyses to the equivalent widths,continuum monochromatic luminosities, and α ox , which characterizes the relative X-rayto UV brightness. The equivalent width of the C iv λ α ox and luminosity. We find that by regressing l ν (2500 ˚A) with EW(C iv )and α ox , we can obtain tigher correlations than by regressing l ν (2500 ˚A) with onlyEW(C iv ). Both correlation and regression analyses imply that l ν (2500 ˚A) is not theonly factor controlling the changes of EW(C iv ); α ox (or, equivalently, the soft X-rayemission) plays a fundamental role in the formation and variation of C iv . Variabilitycontributes at least 60% of the scatter of the EW(C iv )- l ν (2500 ˚A) relation and at least75% of the scatter of the of the EW(C iv )- α ox relation.In our sample, narrow Fe K α α exhibits a BEff similar to that of C iv , its equivalent widthhas almost no dependence on either α ox or EW(C iv ). This suggests that the majorityof narrow Fe K α emission is unlikely to be produced in the broad emission-line region.We do find suggestive correlations between the emission-line luminosities of C iv andFe K α , which could be potentially used to estimate the detectability of the Fe K α lineof quasars from rest-frame UV spectroscopic observations. Subject headings: quasars: emission lines Department of Astronomy & Astrophysics, the Pennsylvania State University, 525 Davey Lab, University Park,PA, 16802, USA Department of Physics, Saint Vincent College, 300 Fraser-Purchase Road, Latrobe, PA, 15650, USA Department of Astronomy, University of Washington, Box 351580, Seattle, WA, 98195, USA
1. Introduction
One of the important properties of AGNs is the relation between the emission-line strength,characterized by the equivalent width (EW), and continuum luminosity, because it reveals that theregions emitting these two spectral components are associated. Baldwin (1977a) found that the EWof C iv λ iv ) is inversely correlated with the quasar monochromatic luminosity at 1450 ˚A, l λ (1450 ˚A), namely, log EW(C iv ) = k log l ν (1450 ˚A) + b . Carswell & Smith (1978) referred tothis trend as the “Baldwin Effect” (BEff), a designation now widely used to describe line strength-luminosity relations. Baldwin (1977a) identified this relation using only 20 quasi-stellar objects with29 . . log l ν (1450 ˚A) . . . < z < .
53. Subsequent UV/optical surveys have enabledinvestigation of this relation with wider luminosity and redshift ranges (e.g., Kinney, Rivolo & Ko-ratkar 1990; Zamorani et al. 1992). It has been found that the BEff exists for not only C iv but manyother broad emission lines such as Ly α , C iii ] λ iv λ ii λ ii ] λ v ] λ α BEff), in which the EW of the narrow Fe K α line at 6.4 keV(hereafter abbreviated to Fe K α ) is anti-correlated with X-ray luminosity, l ν (2 keV), was discoveredin the early 1990s from observations by the X-ray observatory Ginga (Iwasawa & Taniguchi 1993).This relation has been subsequently confirmed using data from
ASCA (Tanaka, Inoue & Holt 1994;Nandra et al. 1997) and from
Chandra and XMM-
Newton (Page et al. 2004; Zhou & Wang 2005;Jiang et al. 2006; Bianchi et al. 2007). Possible sites of origin for narrow Fe K α emission includethe broad emission-line region (BELR), the outskirts of the accretion disk, and the molecular torus(e.g., Weaver et al. 1992, Antonucci 1993; Krolik, Madau & Zycki 1994).Although it is well accepted that the BEff exists for many UV/optical emission lines (e.g.,Osmer & Shields 1999; Shields 2007), there is currently no theoretical model that provides acompelling and complete explanation of this well-known phenomenon. Several physical explanationshave been proposed to account for the UV/optical BEff.One promising explanation is that the continuum shape may be luminosity dependent. In thismodel, the UV/optical BEff is due to the softening of the spectral energy distribution (SED) at highluminosity, which lowers the ion populations having high ionization potentials (Netzer, Laor & Gondhalekar1992; Korista, Baldwin & Ferland 1998). It has been found, using Einstein Observatory data,that the quasar SED, parameterized by α ox1 (Tananbaum et al. 1979), depends on UV luminos- Defined as α ox = log ˆ l ν (2 keV) /l ν (2500 ˚A) ˜ / log ˆ ν (2 keV) /ν (2500 ˚A) ˜ = 0 . ˆ l ν (2 keV) /l ν (2500 ˚A) ˜ . α ox is used to characterize the spectral hardness in the UV to X-ray band (e.g., Avni & Tananbaum 1982, 1986; Anderson α ox with UV luminosity forthese sources. The idea that the UV/optical BEff is attributable to SED-driven ionization ef-fects is supported both observationally (Zheng & Malkan 1993; Green 1996, 1998) and theoreti-cally (Netzer, Laor & Gondhalekar 1992). Recent work on a sample of non-Broad Absorption Line(BAL), radio-quiet, optically selected quasars indicates that the EW of C iv depends both on UVand X-ray luminosity. The physics of the C iv BEff is apparently associated with both UV andX-ray emission (e.g., Gibson, Brandt & Schneider, 2008, hereafter GBS08, and references therein).Other proposed BEff drivers include the Eddington ratio,
L/L
Edd (Baskin & Laor 2004; Bachev et al.2004; Warner, Hamann & Dietrich 2004; Zhou & Wang 2005), the black-hole mass (Netzer, Laor & Gondhalekar1992; Wandel, Peterson & Malkan 1999; Shields 2007), and the luminosity dependence of metallic-ity (Warner, Hamann & Dietrich 2004).In this paper we investigate the origin of the BEff for the C iv emission line in a sample of272 Type 1 AGNs and quasars. Although C iv is not the only UV/optical broad emission line thatexhibits a BEff, we selected it to study this phenomenon not only because it is a representativeand well-accepted BEff emission line, but also because C iv resides in a relatively clean spectralregion where the local continuum can be well approximated as a single power-law, with few blendswith other emission lines (in particular the iron emission forest) and limited contamination fromthe AGN host galaxy. These properties make it relatively straightforward to perform spectralfitting and obtain accurate emission-line parameters for C iv . We also use partial-correlationanalysis (PCA) and linear-regression regression analysis to investigate the correlations betweenEW, monochromatic luminosity, and α ox for C iv and narrow Fe K α emission lines.Over the past three decades, there have been a large number of studies of the BEff. Our workon the C iv /Fe K α lines combines the following important features (1) a wide range in redshift(0 . . z . . . . log l ν (2500 ˚A) . .
04) that allows one to disentangleevolutionary vs. luminosity, so that we are not narrowing our study for quasars with a particularluminosity or at a certain redshift; (2) a relatively large sample size (272 objects); (3) the use ofpartial correlation analysis; and (4) a high X-ray detection rate ( ∼ § §
3. In §
4, we perform partial-correlation and linear-regression analyses to investigate the roles of α ox inthe C iv and Fe K α BEffs. In §
5, we probe the connections between C iv and Fe K α relationshipsin EWs, fluxes and luminosities. We present our conclusions in §
6. Throughout this work, we & Margon 1987; Wilkes et al. 1994; Vignali, Brandt & Schneider 2003; Strateva et al. 2005; Steffen et al. 2006; Justet al. 2007). M = 0 .
3, Ω Λ = 0 . H = 70 km s − Mpc − .
2. Sample Construction
The quasar sample in our study is drawn from three sources: 50 objects from Jiang et al.(2006), which will be referred to as “Sample A”; 98 objects from GBS08, which will be referred toas “Sample B”; and 124 objects from Just et al. (2007), which is referred to as “Sample C”. Wedefine our “combined sample” as the combination of these three data sets.
Jiang et al. (2006) compiled a dataset of 101 Type 1 AGNs with Fe K α observations from boththe Chandra and
XMM-Newton archives. The detection fraction of the Fe K α line in their combinedsample is around 55%. The redshifts of the AGNs range from 0 .
003 to 3 . z . .
4) AGNs. The monochromatic luminosities, l ν (2500 ˚A), range from10 . to 10 . erg s − Hz − . We chose this dataset because it is the most complete Fe K α BEffsample with high-quality data obtained from the most sensitive X-ray missions. However, becausethe number of AGNs observed in the X-ray band is much smaller than the number observed opticallyand not all X-ray observed AGNs present Fe K α emission lines, the Fe K α sample is significantlylimited in size.We searched for UV/optical spectra of all 101 objects from the archival databases for HST and
IUE . We found 82 spectra covering the wavelength region around the C iv emission line (containingat least the 1500–1600 ˚A band). If observations are available from both HST and
IUE , we selectedthe
HST observations due to their generally higher signal-to-noise (S/N) ratio. For spectra withmultiple observations using the same instrument, we preferentially use spectra with higher S/N.Next, we excluded all the radio-loud (RL) objects from the core sample, because additionalX-ray emission is produced by the radio jet (e.g., Brinkmann et al. 2000) and changes the value of α ox as well as the slope of the Fe K α BEff.We further excluded 3 objects for the following reasons: • MCG-06-30-15 : The Fe K α profile of MCG-06-30-15 is well fit using a broad disk line model(e.g., Tanaka et al. 1995). The narrow component is not well resolved or very weak. In thiswork, we only study the narrow component of Fe K α , so this object is excluded. • IC 4329a : The spectrum has low S/N, and the C iv emission line is cannot be accuratelymeasured (e.g., Crenshaw & Kraemer 2001). • PG 1407 + : This object was termed as an “unusual” quasar (McDowell et al. 1995) be-cause it contains extremely weak Ly α and C iv lines. Because of its peculiarity, we exclude 5 –it from our sample.We removed 5 objects with strong associated absorption lines of C iv λ iv λ α ox .Finally, we exclude 8 objects that are classified as Seyfert 1.5 (Sy 1.5) and Sy 1.9 (Osterbrock1981, 1989). These objects are intermediate between Sy 1 and Sy 2 galaxies and are often subjectedto obscuration along the line of sight. Thus their UV, X-ray luminosities and α ox values are alsopotentially affected.The final version of Sample A consists of 50 AGNs. Among these objects, 34 are found in the HST archive (FOS or STIS ), and 16 are found in the IUE archive (SWP or LWP ). The Fe K α detection rate is 55%, the same as in the entire Jiang et al. (2006) study. Objects in Sample B were selected from 536 SDSS DR5 (Adelman-McCarthy et al. 2007)quasars in GBS08. These quasars, taken from the DR5 Quasar Catalog (Schneider et al. 2007), areat redshift 1 . ≤ z ≤ . Chandra or XMM-
Newton . The lower redshiftlimit ensures that all SDSS spectra in this sample cover the C iv region; the upper redshift limitensures that the rest-frame flux at 2500 ˚A is covered so that α ox can be measured accurately.We excluded the BAL quasars in Table 1 of GBS08. BAL quasars can have strong absorptionfeatures in the C iv spectral region that prohibit accurate fitting of the continuum and emission-line profiles. In addition, BALs are usually associated with relatively strong X-ray absorption(e.g., Brandt, Laor & Wills 2000; Gallagher et al. 2006). We only retain objects with Chandra observations with angular offsets < ′ to avoid large X-ray flux uncertainties caused by variationsof the point spread function. This restriction reduces our sample size to 149. In addition, weexcluded RL objects and strong associated absorption-line (AAL) objects. The final version ofSample B consists of 98 objects with l ν (2500 ˚A) between 10 . and 10 . erg s − Hz − . This is Faint Object Spectrograph Space Telescope Imaging Spectrograph Short Wavelength Prime Long Wavelength Prime
To examine the relations between α ox , l ν (2500 ˚A), and l ν (2 keV), Just et al. (2007) compileda sample of 372 objects, including 26 from their core sample, 332 from Steffen et al. (2006), and14 from Shemmer et al. (2006). BAL quasars, RL quasars, and gravitationally lensed objects havealready been excluded from this sample. The gravitationally lensed quasars are removed becausetheir fluxes are strongly amplified and thus their luminosities are uncertain.Among the 372 objects, 38 are already in Sample A. For the rest of the AGNs, we searchedfor existing spectra with C iv coverage preferentially from SDSS, then the HST and
IUE archives.Finally, we removed 5 AGNs whose spectra contain strong AALs. These restrictions leave 124objects in Sample C, in which 91 objects are from the SDSS DR5 quasar catalog, 13 from the
HST archive, and 20 from the
IUE archive. The redshift of this sample ranges from 0.015 to 4.720 and l ν (2500 ˚A) ranges from 10 . to 10 . erg s − Hz − . The combined sample (Table 1) consists of a total of 272 objects: 189 (69.5%) have spectrafrom SDSS, 47 (17.3%) from
HST , and 36 (13.2%) from
IUE . The redshifts range from 0.009 to4.720 (Fig. 1). The gap between z ∼ . z ∼ . iv coverage must be greater than 1 .
5. Most intermediate-redshift AGNs (0 . . z . . IUE and
HST . Our sample exhibits astrong redshift-luminosity correlation (Fig. 1); we discuss this issue further in our analyses below.The l ν (2500 ˚A) of this combined sample ranges between 10 . and 10 . erg s − Hz − ,including Seyfert galaxies to the most-luminous quasars in the Universe. The X-ray detection rateis 94 . iv BEff, while only Sample A will be used to study the Fe K α BEff. 7 –
3. Data Processing3.1. Bad Pixel Removal and Reddening Correction
To ensure that we use high-quality data to perform the continuum and emission-line fitting,we remove bad pixels in the SDSS spectra based on the mask column contained in the SDSS quasarspectral files. We removed all the bad pixels in the spectra of SDSS objects in Sample C. Theexcluded pixels cover less than 10% of the total pixels for over 98% of SDSS objects, and themaximum fraction of removed pixels for a single object is 15%.We perform Galactic reddening corrections to all the spectra using the E ( B − V ) dependent ex-tinction curve of Fitzpatrick (1999). Values of E ( B − V ) are calculated following Schlegel, Finkbeiner & Davis(1998). For each UV/optical spectrum from
HST or IUE , we fit the local continuum in the vicinityof C iv (typically 1300–1700 ˚A) using a single power-law. We do not expect our measurements tobe significantly affected by host-galaxy components because 1) our sample contains only Type IAGNs and quasars in which emission from the nucleus dominates the light from host galaxies inthe UV band; and 2) C iv is in the UV region in which the non-nuclear emission primarily arisesfrom massive stars such as O and B stars. Examination of the spectra does not reveal any stellarabsorption lines, indicating that the contribution from starlight is negligible. We do not subtractthe iron emission forest as this component is usually not strong around the C iv emission line (e.g.,Shen et al. 2008), and the wavelength coverage of the HST and
IUE spectra is frequently toonarrow (only a few hundred Angstroms) to fit this component. The Balmer continuum “small bluebump” only appears in the wavelength range between 2000–4000 ˚A, so its contribution is negligiblearound the C iv region.The emission-line spectrum is obtained after subtracting the power-law continuum. We fit theC iv emission lines using two Gaussian profiles. The model always produces visually acceptablefits. We mask narrow absorption-line features appearing near the emission-lines so as not to under-predict the emission line flux. The equivalent widths, the emission-line luminosities under theassumption of isotropy, and the continuum monochromatic luminosities at 2500 ˚A are calculatedunder our adopted cosmology and are tabulated in Table 2.To first order, we use 2–10 keV luminosities tabulated in Table 1 of Jiang et al. (2006) to For data processing of Sample B, refer to GBS08. l ν (2 keV) under the assumption that the X-ray continuum is a single power-law withphoton index Γ = 2 from 2 keV to 10 keV (e.g., Page et al. 2005; Shemmer et al. 2005; Vignali etal. 2005), so that l ν (2 keV) = L (2–10 keV) ν ln 5 (1)where hν = 2 keV and h is Planck’s constant. To obtain the Fe K α emission-line flux, we furtherassume that the Fe K α emission line resembles a single Gaussian profile: f l ( ν ) = A · e − ( ν − ν ) / σ .This allows one to express the line flux F l in terms of l ν (2 keV) or F (2–10 keV), the Fe K α equivalent width EW(Fe K α ), and the central energy ( ǫ = 6 . f c = C · ν − , we can deriveEW(Fe K α ) = Z + ∞ f l ( ν ) f c ( ν ) dν = AC (cid:20) σ e − ν / σ + ν (cid:18) √ πσ − Z + ∞ ν e − x / σ dx (cid:19)(cid:21) ≈ AC √ πν σ. (2)The Fe K α emission-line flux is F l = Z + ∞ f l ( ν ) dν = A (cid:18) √ πσ − Z + ∞ ν e − x / σ dx (cid:19) ≈ A √ πσ. (3)The approximations are valid because generally ν ≫ σ so ν / σ ≫
1. For instance, ǫ (Fe K α ) =6 . σ (Fe K α ), is usually . . e − ν / σ ≈
0. We can thereforecalculate the Fe K α line flux by F l = EW(Fe K α ) ǫ F (2–10 keV)ln 5 . (4)The Fe K α EWs, emission-line luminosities, and 2 keV monochromatic luminosities of Sample Aare tabulated in Table 3.
For objects in Sample B, we directly adopt the fitting results from GBS08. In their paper, theSDSS spectral continua were fit with polynomials, and the C iv emission lines were fit with Voigtprofiles. The different model in GBS08 from our work used to fit the C iv spectral region will notcause significant differences; because the continuum around C iv is not contaminated with otheremission/absorption lines, the polynomial fit will produce almost the same result as the simplepower-law fit. In addition, since both multiple Gaussian and Voigt profiles produce acceptable fitsto the emission line, they will give nearly the same line flux. The X-ray spectral continua were fitusing a broken power-law with the power-law break fixed at 2 keV in the rest-frame in order toobtain l ν (2 keV). 9 – We fit the UV/optical spectra from the SDSS using a routine, described by Vanden Berk et al.(2009, in preparation), developed for SDSS quasar spectra. This routine fits the “underlying contin-uum” using three components simultaneously: a power-law, the iron emission forest, and the smallblue bump. We adopt the UV iron emission template (1075–3090 ˚A) from Vestergaard & Wilkes(2001) and the optical template (3535–7534 ˚A) from V´eron-Cetty, Joly & V´eron (2004). We firstmake a preliminary estimate of the power-law component by connecting two “line-free” points inthe spectra. This provides initial estimates of the power-law parameters for the subsequent com-prehensive processing in which the spectra are fit by considering all three components mentionedabove. We evaluate the fitting quality by calculating χ values within some “line-free” windows.Finally, the continuum fit is subtracted from the original spectrum and the residuals are used toconduct emission-line fitting. For Sample C, the C iv emission-lines are fit by superpositions oftwo Gaussian profiles, which always yields acceptable fits for the data. We then calculate the C iv EW, emission-line luminosity, and monochromatic luminosity at 2500 ˚A (Table 2). We adopt thevalues of α ox and 2 keV monochromatic luminosity from Just et al. (2007).Examples of continuum and emission-line fits of the HST , IUE and SDSS spectra are presentedin Fig. 2.
In order to estimate the uncertainties in the measured quantities for objects in Samples Aand C, we ran Monte Carlo simulations assuming a model with a perfect correlation betweenEW(C iv ), f (C iv ), and f ν (2500 ˚A). For each spectrum, we add random noise to the originalbest fit to produce artificial spectra. The random noise follows a Gaussian distribution, and itsamplitude is determined in one of two ways. For a spectrum from the HST or IUE database, weapply a low band pass filter, filtering out low-frequency signals via fast Fourier transformation. The residual signal is mostly noise. We then calculate the root-mean-square (RMS) of the noiseand take this value as the random noise amplitude to be added onto the model spectrum. For aspectrum from the SDSS database, we simply use the uncertainty level associated with each pixelas the noise amplitude. For each spectrum, we produce 100 artificial spectra and fit them in exactlythe same way as the observed spectrum. The error bar of a spectral parameter is then calculatedas the RMS of 100 fitting results. The typical error bar shown in each plot (e.g., Fig. 3) is themedian of all the error bars of points in that plot.When evaluating the uncertainties of monochromatic luminosities, e.g., l ν (2500 ˚A), we mustconsider the contribution from the error in the luminosity distances (important for the low-redshift
10 –objects). To validate this, we calculate the ratio of luminosity uncertainties without consideringdistance errors ( δ f ; the error in the flux measurement) to luminosity uncertainties after consideringdistance errors ( δ f,d ) for objects in Sample A, and denote it as δ f /δ f,d , in which f stands for fluxand d stands for distance. Assuming that the square of total uncertainty can be expressed as thequadratic summation of the uncertainties of flux and distance individually, the square of the ratio,( δ f /δ f,d ) , is more relevant than the ratio itself. We find that there are 5 out of 50 objects (inSample A) whose ratios are above 0.1; three of them are even greater than 0.5. These objects havevery low redshifts but large redshift uncertainties ( δ z > . Theseuncertainties are treated as noise amplitudes to be added to the redshift values. The luminosityuncertainties are calculated using the following error-propagation equation: δL = 4 πd L q ( d L δf ) + 4 f ( δd L ) We adopt a 20% uncertainty for each X-ray continuum luminosity, e.g., l ν (2 keV); their mea-surement errors are not available in the literature. The relative uncertainty varies considerablydepending on the number of X-ray counts. For Sample A, when the Fe K α emission lines aredetected, the total number of counts is at least ∼ α emission-line luminosity andflux errors are calculated using the maximum error estimates. For instance, the upper bound of L (Fe K α ) is calculated using the upper bounds of both EW(Fe K α ) and L (2–10 keV); the upperbound of f (Fe K α ) is calculated using the upper bound of L (Fe K α ) and the lower bound of lumi-nosity distance d L − δd L . This uncertainty ignores any systematic uncertainty produced by errorsin the cosmological model.For Sample B, because the parameter uncertainties are not given in GBS08, we simply applya 20% uncertainty for all luminosity values as a first-order approximation.
4. Drivers of the C iv Baldwin Effect4.1. Comparison with Previous Work
We will first examine some important relations to determine if our measurements are consistentwith previous work. It has been argued that α ox has no detectable redshift dependence (e.g.,Strateva et al. 2005; Steffen et al. 2006; but see Kelly et al. 2007), so in this paper we neglect anyredshift evolution of α ox .
11 –Fig. 3 displays the plot of EW(C iv ) against l ν (2500 ˚A) for the combined sample, distinguishedby luminosity. We use the monochromatic luminosity at 2500 ˚A rather than the traditional BEffwavelength (1450 ˚A) because our choice is more convenient to compare the BEff with the correlationbetween C iv and α ox . The luminosities at these two wavelengths are well correlated. The quantity f /f is Gaussian distributed with a dispersion of σ ∼ .
15 (Fig. 3 in Gibson et al. 2009), sousing l ν (2500 ˚A) instead of l ν (1450 ˚A) should only add a small dispersion to the data points but willnot significantly affect the slope of the BEff. We fit the data points linearly in logarithmic spaceusing the EM (Expectation-Maximization) method (Dempster, Laird & Rubin 1977; Table 4). Itis clear that EW(C iv ) decreases with l ν (2500 ˚A) (Fig. 3).It has been reported that the slope of the BEff becomes steeper for high-luminosity quasars.For example, Dietrich et al. (2002) obtained a C iv BEff slope ( − . ± . − . ± .
05, Green 1996; also see Osmer, Porter &Green 1994; Laor et al. 1995). Using only the EW(C iv ) measurements for their high-luminositysubsample with λL λ (1450 ˚A) & erg s − , Dietrich et al. (2002) obtained a steeper slope of theBEff of − . ± .
03 for C iv . To investigate the slope change with luminosity, we fit our datapoints with l ν (2500 ˚A) < .
5. We find that the slope of the low-luminosity sample is consistentwith the slope of the entire sample within 1 σ (Table 4). Therefore, although our dataset exhibitsa suggestive trend which disagrees with Dietrich et al. (2002), we do not find significant changes ofslope over luminosity.The large scatter in the BEff could have several causes, including observational error, intrinsicvariation of the BEff (Osmer & Shields 1999; Shields 2007 and references therein), luminositydependence of the BEff slope, and the redshift dependence of the BEff. Vanden Berk et al. (2009,in preparation) found that the slope of the BEff does not change across redshift, but its scalingfactor (or equivalently, the EW of a broad emission line at a fixed monochromatic luminosity)exhibits a significant change Our BEff slope is an overall average across the redshift and luminosityrange we covered; remember that there is a strong redshift-luminosity correlation in our sample.We examined the l ν (2500 ˚A)- l ν (2 keV) and l ν (2500 ˚A)- α ox relations for both Sample A and thecombined sample using survival analysis (ASURV, Lavalley, Isobe & Feigelson, 1992) if censoreddata are involved, and find that all the results are consistent with previous work. When we calculatethe slope of the Fe K α BEff, we apply the Buckley-James method (Table 4, Buckley & James 1979;Lavalley, Isobe & Feigelson 1992) included in ASURV to perform linear regression because theEW(Fe K α ) contains censored values. The slope of the Fe K α BEff of Sample A ( − . ± . − . ± . α ox on the C iv and Fe K α BEffs
Fig. 4 shows the plot of EW(C iv ) against α ox for the combined sample; the regression resultfrom the EM algorithm for the linear relation islog EW(C iv ) = (1 . ± . α ox + (3 . ± . P < . Because α ox is an indicator ofthe hardness of the SED which controls the ionization level of C iv surrounding the central engine,Fig. 4 demonstrates that as the ionizing flux becomes harder ( α ox increases), the C iv emission hasa strong positive response to α ox .Both α ox and l ν (2500 ˚A) are correlated with EW(C iv ); which is a more fundamental driver?To investigate this issue, we applied PCA to EW(C iv ), l ν (2500 ˚A), and α ox using the combinedsample, Sample A, and a reduced sample. Table 5 presents Pearson, Spearman, and Kendall’scorrelation and partial-correlation coefficients (if available), along with significance levels for thesethree samples. We present the statistical results of Sample A for comparing the correlation resultsof C iv and Fe K α . Because the combined sample contains censored data for the α ox values, wemust use survival analysis to calculate the correlation coefficients. However, algorithms are notavailable for calculating all the correlation and partial-correlation coefficients for censored data.For example, the empty entries in Table 5 are due to the unavailability of corresponding algorithms.In order to compare the changes of correlation strength when the third parameter is controlled, weconstruct a reduced sample with the censored data removed, considering that this only excludesa small fraction ( ∼ iv BEff is significantly weakened when α ox is held fixed; thecorrelation coefficient drops from − .
580 to − .
224 (Spearman). On the other hand, the correlationcoefficient between EW(C iv ) and α ox also drops significantly when l ν (2500 ˚A) is held fixed, from0.615 to 0.332. This implies that both α ox and l ν (2500 ˚A) are driving the change of EW(C iv ).The Fe K α BEff plot (not shown) of our sample (Sample A) is very similar to the correlationshown of Fig. 4 in Jiang et al. (2006) except that our sample size is smaller. Fig. 5 shows EW(Fe K α )plotted against α ox . The Spearman test gives a much weaker correlation coefficient ( − .
230 with P = 0 . iv ( − .
304 with P < . χ fitting produces aslope of 0 . ± . α ) is not correlated with α ox . Because of the ubiquity of AGN variability, combined with the different times of the opticaland X-ray observations, our values of α ox do not reflect the spectral hardness at a specific time P is the confidence level of the null hypothesis. Therefore, the smaller P is the more likely the correlation exists.
13 –but are randomly distributed around their mean values. The deviation of α ox from its mean valuewould be ∼ . l ν (2500 ˚A) and 40% for l ν (2 keV) (e.g., Strateva et al. 2005, GBS08).To check how much of the scatter of our correlations could be attributed to variability, weperformed two simple tests on our combined sample. We follow the method used in § iv ) and the EWcalculated from linear regression (Eq. 7), i.e., ∆ log EW = log EW − log EW( l ν (2500 ˚A)). Wedefine µ and σ as the mean and dispersion of the distribution of ∆ log EW. To calculate µ and σ ,we maximize the likelihood function (Maccacaro et al. 1988): L = Y i q π (cid:0) σ i + σ (cid:1) exp h − (∆ log EW i − µ ) / σ i + σ ) i (6)in which the subscript i represents each object and σ i is the uncertainty of ∆ log EW associatedwith each ∆ log EW i . The maximization of L requires µ = 0 .
01 and σ = 0 . l ν (2500 ˚A)). To first approximation, EW ∼ f line /f cont in which f line is the emission-line flux and the f cont is the continuum flux. The emission-line variabilityof six luminous quasars at z = 2 . . F var11 is ≈ .
096 by averaging the fractional variation of C iv λ iv emission-line variability of a number of Seyfert galaxies has been studied,including Fairall 9 (Rodriguez-Pascual et al. 1997), NGC 5548 (Clavel et al. 1991), NGC 7469(Wanders et al. 1997), NGC 3783 (Reichert et al. 1994), and 3C 390.3 (O’Brien et al. 1998). Byaveraging the fractional variations of Seyferts and quasars above, we obtain an average emission-line variation h F var i = 0 . l ν (2500 ˚A) is ∼
30% (e.g., Strateva et al.2005). Therefore, the scattering of log EW contributed from variability is estimated (assuming allindependent variables are Gaussian distributed) as σ (∆ log EW) = 1ln 10 s(cid:18) δf line f line (cid:19) + (cid:18) δf cont f cont (cid:19) + a (cid:20) δl ν (2500 ˚A) l ν (cid:21) ≈ . . In the calculation above, a = 0 .
198 (Eq. (7)). This exercise indicates that at least 60% of thescatter around the BEff in our sample can be attributed to AGN variability.We performed a similar test for the α ox -EW(C iv ) relation. Because the set of α ox containscensored data, we can only use the reduced data set (258 objects). The maximization of L (Eq. 6)yields µ = 0 .
01 and σ = 0 .
22. The potential dispersion of this relation assuming all scatter comes F var is defined as the RMS of the intrinsic variability relative to the mean flux (Rodriguez-Pascual et al. 1997).
14 –from variability is estimated (assuming Gaussian distributions) as σ (∆ log EW) = 1ln 10 vuut(cid:18) δf line f line (cid:19) + (cid:18) δf cont f cont (cid:19) + (0 . a ) "(cid:18) δl ν (2500 ˚A) l ν (2500 ˚A) (cid:19) + (cid:18) δl ν (2 keV) l ν (2 keV) (cid:19) ≈ . . In the calculation above, a = 1 .
035 (Eq. 5). This indicates that variability produces at least 75%of the scatter around the α ox -EW(C iv ) relationship.In summary, the above two tests demonstrate that a substantial fraction, if not the majority,of the scatter in the correlations above can be attributed to X-ray and UV/optical variability. Itshould be possible to make the correlations tighter if the UV/optical and X-ray data are observedsimultaneously. The BEff provides a potential avenue to infer the luminosity of a quasar from emission-lineobservations. Type Ia supernovae (SNe) are treated as classical standard candles (e.g., Phillips1993; Burrows 2000), but only a few are observed beyond z ∼ .
5. If quasars, which are mucheasier to detect than SNe and can be observed to much a higher redshift, can be used as standardcandles, they would be an important tool for cosmological studies. Soon after the discovery of theBEff, many investigations considered the possibility of treating emission-line EW as a luminosityindicator (e.g., Baldwin 1977b; Wampler 1980). Unfortunately, the C iv BEff usually has a largescatter (Osmer & Shields 1999; Shields 2007); given the small slope in the log EW-log l ν plot (onthe order of − . iv BEff is redshift dependent (Francis & Koratkar 1995; Vanden Berk et al. 2009, in preparation),making it a less valuable probe of cosmology.Because we are focusing on the influence of α ox at the moment, and will put the redshift factoraside, we will concentrate on the issue of whether the scatter can be reduced if we regress EW(C iv )with l ν (2500 ˚A) and/or α ox , and if the prediction of luminosity can be made more accurate withthis approach. The linear-regression results of EW(C iv ) with α ox are already shown in Eq.(5).Similar regressions from l ν (2500 ˚A) and both of l ν (2500 ˚A) and α ox , using the fully parametric EMalgorithm, arelog EW(C iv ) = ( − . ± . l ν (2500 ˚A) + (7 . ± . iv ) = ( − . ± . l ν (2500 ˚A) + (0 . ± . α ox + (5 . ± . . (8)in which EW(C iv ) is in ˚A and l ν (2500 ˚A) is in erg s − Hz − . The last regression was performedon the combined sample without the censored data (258 objects) because the EM algorithm inASURV does not allow both independent variables to contain censored data points.To evaluate the scatter, we subtract the predicted EW values calculated using the aboveequations from the observed values and compute the RMS values of the residuals. We see a slight 15 –improvement of the RMS values, using α ox and both l ν (2500 ˚A)+ α ox (Table 6). The last regressionresult (Eq.(8)) is consistent with Eq.(11) in GBS08, indicating that at least part of the scatter ofthe BEff is due to α ox .Next, we regress luminosity against EW(C iv ) and/or α ox , using the combined sample. Theresults arelog l ν (2500 ˚A) = ( − . ± . iv) + (34 . ± . l ν (2500 ˚A) = ( − . ± . iv ) − (2 . ± . α ox + (27 . ± . . (10)The last regression was performed on the censored-data-excluded sample. We then calculate theRMS values of the residuals after subtracting the predictions from the equations above (Table 6).The RMS value shrinks by 18% using EW(C iv )+ α ox , compared to using EW(C iv ) alone. Weuse the standard F -test to check if the two sets of residuals have consistent variance. The testinggives an F -statistic of 1.48 with a significance 0 . < .
1. This cannot be achieved using our current dataset and controlledparameters.
5. Relation Between Fe K α and C iv Fe K α is important in AGN studies because it is the strongest emission line appearing inthe X-ray band. However, the strength of this emission line varies significantly from object toobject, and the line is not detected in most X-ray observations of quasars. Given this lack of directobservational measurement, it would be useful to develop a way to predict the expected strengthof the line empirically.The EW(C iv ) and EW(Fe K α ) do not exhibit a significant correlation (Fig. 6) in Sample A;the correlation has a low Spearman rank-correlation coefficient (0 .
319 with P = 0 . .
529 ( P < . .
551 ( P < . L (Fe K α ) = (0 . ± . L (C iv ) + (16 . ± . f (Fe K α ) = (0 . ± . f (C iv ) − (2 . ± . . (12)One must always question the significance of relations such as (11) because even if there is nocorrelation between the observed fluxes of the lines, the fact that the line luminosities for a givenobject contain the same distance factor will introduce an apparent correlation in the luminosities.To investigate whether this effect is important for our study, we perform a test in which we conduct 16 –correlation and regression analysis for a sub-sample of Sample A. Objects in this sub-sample havesimilar redshifts, and thus they have approximately the same distances. First, we use objects with0 . < z < .
09 because this redshift bin contains a large number of objects. This sub-samplecontains 10 objects. The correlation coefficient of f (Fe K α )- f (C iv ) is 0.624 ( P = 0 . L (Fe K α )- L (C iv ) is 0.709 ( P = 0 . L (Fe K α ) = (0 . ± . L (C iv ) + (9 . ± . f (Fe K α ) = (0 . ± . f (C iv ) − (4 . ± . . (14)Both the correlation and regression results of this sub-sample are consistent with the results ofthe entire sample within uncertainties, suggesting that the luminosity correlation of the C iv andFe K α lines may be real and is not a consequence of multiplying the two fluxes of a given objectby the same large distance factor. The luminosity of C iv emission line increases faster than theluminosity of Fe K α .One might be concerned that the correlation between L (Fe K α ) and L (C iv ) is artificial because the calculation of the Fe K α measurements involves L (2–10 keV) (Eq. (4)), which isproportional to l ν (2 keV) (Eq. (1)), and l ν (2 keV) is correlated with l ν (2500 ˚A), which is correlatedwith EW(C iv ), i.e., the C iv BEff. EW(C iv ) is calculated from continuum and emission lineluminosity, so apparently, the L (Fe K α ) and L (C iv ) are not independent before we perform thecorrelation. However, our calculation of Fe K α is simply reversing the F (2–10 keV)/EW calculationof Jiang et al. (2006), so F (Fe K α ) is not actually dependent of F (2–10 keV) and hence l ν (2500 ˚A).In essence, we have the values of F (Fe K α ) independent of F (C iv ). Therefore, our L (Fe K α ) and L (C iv ) correlation, which is expected from existing relations, is not an artifact correlation.That the EWs of C iv and Fe K α are uncorrelated is consistent with the result by Page et al.(2004) and further demonstrates that the C iv and Fe K α emission lines are unlikely to havethe same origin. This result is not surprising because Fe K α and C iv are produced in differentprocesses. The correlation between their luminosities is probably a combination of effects betweentheir EWs (uncorrelated) and continuum (strongly correlated). The flux correlation, althoughempirical and not very tight, is a useful first order estimation of the Fe K α line flux given the UVspectra in the rest-frame of an AGN.
6. Discussions and Conclusions
We have compiled a sample of 272 Type 1 AGNs and quasars that have UV and X-ray mea-surements, among which Fe K α emission lines are detected in 50 objects. The sample covers a widerange of redshift (0 . . z . . . . log l ν (2500 ˚A) . . ∼ iv BEff is driven by both α ox and l ν (2500 ˚A), or equivalently, by l ν (2 keV) and l ν (2500 ˚A). This implies that changes in the ionizing flux induce changes in the ionizationstate of the BELR, producing more C iv ions when the SED becomes harder and vice versa.This is supported both by correlation and regression anlayses: • The partial correlation between EW(C iv ) and l ν (2500 ˚A) when α ox is controlled isweaker than the regular correlation between EW(C iv ) and l ν (2500 ˚A). • The scatter in the linear regression decreases when we regress EW with α ox + l ν (2500 ˚A)compared with l ν (2500 ˚A) alone.Although the reduction of the scatter due to adding another regression parameter is notsufficiently large to treat quasars as standard candles, it demonstrates that a significantfraction of the scatter attributes to α ox , and can be reduced by including it in regressionanalysis.2. EW(Fe K α ) exhibits no strong correlation with either α ox or EW(C iv ). This implies thatFe K α is not likely to have the same origin as C iv .3. There may be a correlation between the luminosities of Fe K α and C iv with a logarithmicslope of 0 . ± . iv emission line luminosity increases faster than the Fe K α .Although α ox is a fundamental influence on EW(C iv ), there is still a significant scatter in theEW(C iv )- α ox diagram. As we have demonstrated, most of the scatter is contributed by variability,but another likely contribution source is the nature of α ox which only connects the flux points at2500 ˚A and 2 keV but misses the Big Blue Bump, which is expected to play an important rolein the photoionization process. The shape of an AGN SED can be very different depending onEddington ratio ( L bol /L Edd ) but still have a fairly constant α ox (Vasudevan & Fabian 2007). It isperhaps more appropriate to use a point near ∼
250 ˚A instead of 2500 ˚A to calculate a revised α ox (Shemmer et al. 2008). This new α ox might be more strongly correlated with EW(C iv ). However,this requires challenging observations that cannot be achieved at present for most AGNs.We thank Jane Charlton for providing a number of HST /FOS spectra of the core sampleAGNs, Eric Feigelson for useful suggestions and advice on statistics, Ohad Shemmer and DennisJust for discussions on linear regression, and Lanyu Mi for help with the statistical computations.This work was partially supported by NSF grant AST-0607634 and NASA LTSA grant NAG5-13035.Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation,the Participating Institutions, the National Science Foundation, the U.S. Department of Energy,the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max 18 –Planck Society, and the Higher Education Funding Council for England. The SDSS website is . REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
22 –Fig. 1.— The luminosity-redshift diagram of the combined sample containing 272 objects distin-guished by observational facilities. The gap for 0 . . z . . HST / IUE and wavelength coverage of the SDSS. The dashed line marks the position where l ν (2500 ˚A)= 30 .
5. 23 –Fig. 2.— Continuum and C iv emission-line fit examples. In each panel, the upper spectrumis the original and the lower spectrum is continuum subtracted; blue solid curves are the fitsto the spectra. The cyan dotted curves are emission-line components. For PG 0947+396 and3C 120, these components include the power-law continua and two Gaussian profiles for C iv .For SDSS J100129.64+545438.0, we also plot the iron emission forest and small Balmer bumpcomponents, although they are so weak that they are almost invisible. The rest-frame spectralresolutions of these spectra are, from top to bottom, ∼ . ∼ ∼ . iv BEff diagram for the combined sample. The EW(C iv ) is given in ˚A, and l ν (2500 ˚A) is in units of erg s − Hz − . Points are distinguished by luminosity; the short solid lineis the best linear fit to low-luminosity points and the long one is the best linear fit to the entiresample. 25 –Fig. 4.— The correlation between EW(C iv ) and α ox . Upper limits on α ox are marked with arrows.The solid line is the best linear fit using the EM algorithm. 26 –Fig. 5.— The correlation between EW(Fe K α ) and α ox for the core sample. The solid line is alinear fit using the ASURV package for the censored data. The typical error bar of the data isdisplayed at the top-right corner of the plot. 27 –Fig. 6.— Plot of log [EW(Fe K α ) / E (Fe K α )] vs. log [EW(C iv ) /λ (C iv )] for the core sample.Because the units of EW(Fe K α ) and EW(C iv ) are different, we divide them by central energyE (Fe K α ) = 6 . λ (C iv ) to make them dimensionless. 28 –Fig. 7.— Plot of log L (Fe K α ) vs. log L (C iv ) (upper panel) and log f (Fe K α ) vs. log f (C iv )(lower panel) for the core sample. Upper limits are denoted as downward arrows. The solid linesare the best linear fits to the data using ASURV. For comparison, we show the best linear fits witha unity slope in dotted lines. The data symbols and typical error bars are labelled at the bottomright corners. 29 –Table 1. Summary of samples. Sample SDSS HST IUE Total Redshift range log l ν (2500 ˚A) rangeA 0 34 16 50 0.009–1.735 27.81–31.69B 98 0 0 98 1.7–2.7 30.53–31.67C 91 13 20 124 0.015–4.720 28.12–33.04Combined 189 47 36 272 0.009–4.720 27.81–33.04 Table 2. UV properties of the combined sample.
Object z log l ν (2500 ˚A) EW(C iv ) α ox Flag UV/Optical Sample(erg s − Hz − ) (˚A) InstrumentNGC4593 0.009 27 . ± .
15 141 . ± . − . ± .
066 0 HST ANGC3783 0.010 28 . ± .
08 144 . ± . − . ± .
045 0 HST AMkn352 0.015 28 . ± .
15 200 . ± . − . ± .
067 0 IUE CMrk1044 0.016 28 . ± .
04 60 . ± . − . ± .
037 0 HST ANGC7469 0.016 28 . ± .
28 129 . ± . − . ± .
111 0 HST AMCG8 − . ± .
19 233 . ± . − . ± .
082 0 IUE CMkn79 0.022 28 . ± .
09 135 . ± . − . ± .
049 0 IUE CMrk335 0.026 29 . ± .
18 75 . ± . − . ± .
077 0 HST ANote. — Table 2 is published in its entirety in the electronic version of the
Astrophysical Journal . The portion isshown here for guidance regarding its form and content. A value of “1” indicates that α ox for this object is an upper limit. Table 3. UV and X-ray properties of Sample A objects.
Object z EW(Fe K α ) log l ν (2 keV) log L (Fe K α ) log f (Fe K α ) log L (C iv ) log f (C iv )(eV) (erg s − Hz − ) (erg s − ) (erg s − cm − ) (erg s − ) (erg s − cm − )NGC4593 0.009 98 . +21 . − . . ± .
09 41 . +0 . − . − . +0 . − . . ± . − . ± . . +14 . − . . ± .
09 41 . +0 . − . − . +0 . − . . ± . − . ± . . +25 . − . . ± .
09 41 . +0 . − . . − .
19 42 . ± . − . ± . . +61 . − . . ± .
09 40 . +0 . − . − . +0 . − . . ± . − . ± . . . . ± . . . . − .
42 42 . ± . − . ± . . +65 . − . . ± .
09 41 . +0 . − . − . +0 . − . . ± . − . ± . . +56 . − . . ± .
09 41 . +0 . − . − . +0 . − . . ± . − . ± . . . . ± . . . . − .
55 42 . ± . − . ± . Astrophysical Journal . The portion is shown here forguidance regarding its form and content.
Table 4. Hypothesis and linear fitting results.
Fig Sample x y ρ ( P ) k l λ (2500 ˚A) log EW λ (C iv ) − . < . − . ± . l ν (2500 ˚A) < . l λ (2500 ˚A) log EW λ (C iv ) − . < . − . ± . α ox log EW λ (C iv ) 0 . < . . ± . α ox log EW eV (Fe K α ) 0 . . . ± . Spearman rank correlation coefficient. Significance levels of Spearman’s rank correlation. Slope from EM algorithm. Calculated for Sample A using the Buckley-James method in the ASURV software package (Lavalley, Isobe & Feigelson1992).
30 –Table 5. Correlation and partial-correlation analysis results. x y z a Spearman Pearson KendallCombined sample (279)log EW(C iv ) log l ν (2500 ˚A) α ox · · · · · · − b log EW(C iv ) log l ν (2500 ˚A) − < · · · − < α ox log EW(C iv ) log l ν (2500 ˚A) · · · · · · α ox log EW(C iv ) 0.607( < · · · · · · Combined Sample Without Censored Data (258)log EW(C iv ) log l ν (2500 ˚A) α ox − . − . − . iv ) log l ν (2500 ˚A) − . < . − . − . < . α ox log EW(C iv ) log l ν (2500 ˚A) 0 .
332 0 .
258 0 . α ox log EW(C iv ) 0 . < . .
587 0 . iv ) log l ν (2500 ˚A) α ox iv ) log l ν (2500 ˚A) − − − α ) log l ν (2 keV) α ox · · · c · · · d < . α ) log l ν (2 keV) − · · · · · · α ox log EW(Fe K α ) log l ν (2 keV) · · · · · · − α ox log EW(Fe K α ) 0.104( 0.470) · · · · · · Note. — The number in the parentheses after a correlation coefficient is its significance level. Because we areconsidering the null hypothesis, a small number indicates a possibility of a strong correlation. a z is the controlled parameter. If a z entry is not empty, we calculate the partial correlation of x and y whilecontrolling for z ; otherwise, we only calculate the correlation of x and y . b For the Kendall’s partial τ correlation coefficients, generally, the sampling distribution is unknown; therefore,the probability values are not available (Kendall 1938, 1970). c ,d Because EW(Fe K α ) is a set of censored data, we have to use a generalized correlation statistics that candeal with censored data to derive the coefficients. For the non-partial correlations, we used the ASURV softwarepackage (Lavalley, Isobe & Feigelson 1992) which only provides Spearman’s ρ and Kendall’s τ correlation correlationcoefficients. For the PCA, we only use the Kendall’s partial τ correlation statistics (Akritas & Siebert 1996). Table 6. The RMS values of residuals after regression from different variables.
Independent variables Dependent variable RMS values l ν (2500 ˚A) EW(C iv ) 0.231 α ox EW(C iv ) 0.228 l ν (2500 ˚A)+ α ox EW(C iv ) 0.217EW(C iv ) l ν (2500 ˚A) 0.747 α ox l ν (2500 ˚A) 0.645EW(C iv )+ α ox l ν (2500 ˚A) 0.615Note. — To consistently compare the RMS values, we com-pute them using the combined sample without the censoreddata.
31 –Table 7. Correlation and regression analysis for EW, emission line luminosity, and flux databetween Fe K α and C iv . Relations ρ ( P ) k EW 0.319( 0.027) 0.291 ± L (line) 0.529( < ± f (line) 0.551( < ± Correlations are tested using Spearman’s ρ and the significance level ( P ) is evaluatedagainst the null hypothesis. We use the Buckley-James method to dolinear regression and kk