Rehabilitating C iv-based black hole mass estimates in quasars

Abstract

INTRODUCTION

Accretion on to a central supermassive black hole is the engine that powers quasars, making the black hole mass a fundamental property of the quasar. As such, the ability to make accurate measurements of the black hole mass is critical for studies of active galactic nuclei (AGNs). There are methods for estimating the black hole mass (see Shen 2013, for a review), but the uncertainties are large and there is room for improvement.

In current practice, black hole masses can be estimated for large numbers of AGNs with single-epoch spectra using the black hole mass scaling relationships (e.g. Vestergaard & Peterson 2006). The scaling relationships take measures of the velocity of gas in the broad-line region (BLR) and the distance from the black hole, and return a virial mass under the assumption that the BLR motions in the vicinity of the black hole are dominated by the gravity of the black hole. The R–L relationship (e.g. Kaspi et al. 2000; Bentz et al. 2009), a reverberation mapping result, allows the use of an easily observed continuum luminosity as a proxy for radius, and a velocity taken from the linewidth of Doppler-broadened emission lines. Commonly used linewidths include full width at half-maximum (FWHM) and line dispersion (σ_l), each with their own strengths and weaknesses (Denney et al. 2009, 2013).

The scaling relationships have been calibrated for multiple emission lines, including Hβ and C iv λ1549 among others. The best calibration is for the Hβ line because it is the basis for the majority of reverberation mapping programmes. However, at redshifts above z = 1.4, Hβ moves out of the optical wavelength window and the C iv line is more easily obtained. The reverberation mapping for C iv is more limited but does establish an R–L relationship for C iv which seems to be consistent with the results from Hβ reverberation mapping (e.g. Peterson et al. 2005). As a result, there exists a C iv-based single-epoch mass scaling relationship that should yield mass estimates consistent with those derived from Hβ.

The reliability of the C iv line to reproduce the more trusted Hβ-based black hole mass estimates is not well established. The main criticism is that the single-epoch C iv profiles do not generally represent the reverberating BLR that provides the basis for virial mass estimates. This issue manifests itself in several specific issues that limit the successful use of C iv as a virial black hole mass estimator.

Many studies find very poor agreement and significant scatter between C iv and Hβ velocity line widths (e.g. Shen & Liu 2012). Reverberation mapping results and virial arguments suggest that the C iv emission originates in a region nearer the central black hole than does the Hβ emission (Peterson et al. 2004). This would imply that C iv linewidth measurements should yield broader widths than are measured for Hβ; however, the C iv linewidths are often narrower than those of Hβ (e.g. Baskin & Laor 2005; Shang et al. 2007; Trakhtenbrot & Netzer 2012). Although their velocity line widths are not expected to be equal, if C iv and Hβ are both emitted from the BLR, they are expected to be correlated. The fact that they are not suggests that the C iv linewidth measurements are not probing the velocity of the virialized C iv gas.

Linewidth measurements may fail to accurately reflect the velocity of the virialized gas because of contamination from other C iv-emitting regions. In regular, type 1 AGNs, the C iv line profile is often shifted from the systematic redshift of the object (Richards et al. 2002; Baskin & Laor 2005; Ho et al. 2012). This implies that the C iv-emitting gas may not be virialized as there may be a strong wind component to the gas. However, Vestergaard & Peterson (2006) find that this issue is exacerbated by including narrow-line Seyfert 1 sources, low-quality data, absorbed objects and objects where the C iv narrow-line component is uncertain in the Baskin & Laor (2005) sample, so this issue may be less significant than it appears.

Reverberation mapping results provide another indication that linewidth measurements of single-epoch spectra may not reflect the velocity of virialized gas in the BLR. Denney (2012) is able to decompose the C iv emission line into a reverberating component and a non-reverberating component by comparing mean spectra, which emulate single-epoch spectra, to rms spectra, which show the emission from gas that responds to changes in the continuum, for objects with reverberation mapping coverage. The non-reverberating component contributes a fairly narrow core to the C iv line that draws the FWHM to lower values. A measure of linewidth in a single-epoch spectrum that might be used in a black hole mass scaling relationship is unable to separate this component from the virialized emission. Denney et al. (2009) has simulated the effects of including a non-virialized narrow component in the linewidths used for black hole mass calculations. The results are conclusive: to obtain accurate and precise linewidth estimates, particularly when using FWHM, such contamination must be removed.

The narrow core component is much less significant in Hβ than in C iv, introducing scatter between Hβ- and C iv-based black hole mass estimates. Denney (2012) recommends the shape parameter, S = FWHM/σ_l, for distinguishing between objects with boxy profiles (S ∼ 1.5), indicative of a strong reverberating component, and peaky (S ∼ 0.5) profiles, indicative of a strong non-reverberating component. Furthermore, she provides a prescription for using the shape parameter to remove the bias in C iv black hole mass estimates. The shape parameter depends on the C iv FWHM, and is a clear source of scatter between Hβ and C iv black hole masses.

The shape parameter, which can be used to isolate the component of the C iv emission line that originates in virialized gas and improve the reliability of C iv black hole mass estimates, is actually one among many correlated spectral properties collectively termed ‘Eigenvector 1’ (EV1). EV1 describes the largest amount of variation between quasar spectra (Boroson & Green 1992), and is dominated by the anticorrelation between optical Fe ii and [O iii] λ5007 emission, with objects on one end having strong Fe ii emission and weak [O iii] emission. Originally defined at rest-frame optical wavelengths, EV1 has ultraviolet (UV) indicators (Brotherton & Francis 1999; Shang et al. 2003; Sulentic et al. 2007). There have been suggestions for physical drivers of EV1, including the Eddington ratio at low redshifts (Boroson & Green 1992), but it is not clear if this is the case and whether it holds at higher redshifts (Yuan & Wills 2003). Although the exact relationship between EV1 and black hole mass remains elusive, black hole mass is not the primary driver of EV1. Objects with similar black hole masses exhibit a range of EV1 properties as demonstrated in fig. 6 of Boroson (2002) and therefore, crucially for this work, an object's location on EV1 is not indicative of its intrinsic black hole mass. In some samples (e.g. the Palomar-Green sample) EV1 and black hole mass appear to be correlated but this may be the result of the sample selection and other primary correlations like the one between EV1 and Eddington fraction.

The spectral analysis of Wills et al. (1993a) suggests that it is in fact an EV1 bias that causes disagreement between the C iv and Hβ velocity widths. Their UV spectral composites demonstrate that with increasing C iv FWHM, the peak flux of the C iv line decreases compared to the peak flux of the nearby Si iv+O iv] blend at 1400 Å (which does not vary with the FWHM of C iv, Wills et al. 1993a; Richards et al. 2002) and the line profile changes from peaky to boxy. As a result, the velocity width of the C iv emission line is determined both by the black hole mass and the unknown physical driver of EV1. The shape of C iv is a UV indicator of EV1, suggesting that the shape correction of Denney (2012) is successful largely because of its ability to estimate the EV1 bias in C iv. However, line dispersion, and thus the shape parameter, requires high-signal-to-noise-ratio (high-S/N) spectra to obtain an accurate measurement and is thus not suitable for use with current survey-quality data (Denney et al. 2013). Instead, the application of a peak ratio of Si iv+O iv] to C iv, a UV EV1 indicator that is free of the S/N constraint that plagues the shape parameter, combined with C iv FWHM-based black hole mass estimates might provide a more Hβ-like black hole mass that can be measured for large numbers of quasars.

We investigate the use of the ratio of the Si iv+O iv] to C iv peak fluxes as a method to rehabilitate the C iv-based black hole mass estimates in the spectral energy distribution (SED) atlas of Shang et al. (2011). The quasi-simultaneous optical and UV spectrophotometry available in this data set is particularly valuable to this investigation, allowing us to consider the Hβ and C iv spectral regions free of variability concerns. We show that by using both the linewidth of C iv and the peak ratio it is possible to dramatically reduce the scatter between Hβ- and C iv-based black hole mass estimates and derive prescriptions for predicting the Hβ linewidth and black hole mass from information in the C iv spectral region.

This investigation is organized as follows. In Section 2, we present the sample and discuss our methods for making spectral measurements. Section 3 presents an analysis of the dependence of velocity line width residuals on the ratio of peak fluxes of Si iv+O iv] to C iv, including a correction for the observed effect that decreases the scatter between C iv- and Hβ-based black hole masses. The results are discussed in the context of other work in Section 4 and conclusions are presented in Section 5. Throughout this work, back hole masses and luminosities are calculated using a cosmology with H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.7 and Ω_m = 0.3.

SAMPLE, DATA AND MEASUREMENTS

For this work we use the SED sample from Shang et al. (2011). The atlas includes 85 objects, 58 of which are radio loud (RL) and 27 of which are radio quiet (RQ), with redshifts in the range z = 0.030–1.404 and bolometric luminosities of |$45.1< {\rm log}(L_{\rm bol})<47.3$| in units of erg s⁻¹.

Most objects have quasi-simultaneous optical and UV spectrophotometry. All of the objects were observed in the UV either with the Hubble Space Telescope Faint Object Spectrograph (FOS) or with the Space Telescope Imaging Spectrograph and most were followed up within a few weeks by low-resolution ground-base optical spectrophotometry either from the McDonald Observatory or from the Kitt Peak National Observatory.

The SED atlas does not comprise a complete sample, but it does include a nearly-complete subsample. The PGX subsample has 22 out of 23 Palomar–Green (PG) quasars selected to study the soft-X-ray regime (Laor et al. 1994b, 1997), is UV bright and has z ≤ 0.4. This subsample was presented in Shang et al. (2007), who found that the linewidths for these objects do not indicate a purely stratified ionization structure in the BLR. Furthermore, these objects have also been used to illustrate the issues associated with C iv linewidths (e.g. Trakhtenbrot & Netzer 2012). The atlas also includes the higher redshift, higher luminosity RL subsample and the FUSE subsample that contains mostly RQ objects with redshifts of a few tenths.

This atlas is particularly suited to this investigation for two reasons. First, the quasi-simultaneous optical and UV spectrophotometry makes this sample less susceptible to variability issues than similar investigations (e.g. Trakhtenbrot & Netzer 2012), allowing a meaningful comparison between physical properties calculated from the C iv and Hβ wavelength regimes. Secondly, the inclusion of the PGX subsample ensures that the total atlas covers the full range in EV1 properties. This is important because the sample contains a large number of RL sources which are isolated on one end of EV1 with strong [O iii] and weak Fe ii (e.g. Boroson & Green 1992; Bachev et al. 2004; Sulentic et al. 2007). The sample will exhibit EV1 properties within the range defined by the PGX subsample, making our conclusions robust; the fact that the overabundance of RL sources may cause the distribution of those properties to be biased does not compromise this.

The spectra have been corrected for Galactic extinction, reddening and host contamination in the optical (although these objects are optically bright and the host contribution is minimal). The redshift is determined from the [O iii] λ5007 line and the spectra were shifted to the rest frame. Shang et al. (2011) provides more details on these corrections.

Spectral fitting was done by Tang et al. (2012) following the method of Shang et al. (2007). Fitting is done by minimizing χ² between the model and the data using the iraf package specfit (Kriss 1994). The Hβ, C iv λ1549and Si iv+O iv] λ1400 regions were fitted individually with model spectra consisting of a power-law continuum and two Gaussian components per broad emission line. In the case of the Si iv+O iv] blend, which we will hereafter refer to as ‘λ1400’, the fit was made between 1350 and 1460 Å and the power-law continuum is separated from that of C iv. The Gaussians ascribed to Si iv and O iv] were identical except in their centroids which were appropriate for their respective line centres. For the C iv doublet, the Gaussian pairs were also identical except in their centroids and they did not include a component to model emission from the narrow-line region (NLR) because, according to Wills et al. (1993b), there is no strong NLR component present in C iv. The Hβ broad emission line does include a contribution to emission from the NLR which was modelled with an additional Gaussian that is not included when measuring linewidths. An Fe ii template derived from the narrow-line Seyfert 1 I Zw1 (Boroson & Green 1992) was also included in the Hβ region and was allowed to vary in amplitude and velocity width in order to match the observed spectrum.

The spectral fits for λ1400 were done at the same time as the Hβ and C iv regions but not presented in Tang et al. (2012), so we present them here. A sample spectrum is given in Fig. 1 and the results of the fitting are given in Tables 1 and 2.

Figure 1.

Spectral fitting for the wavelength region around λ1400 for PG 1415+451. The observed spectrum is shown by the dotted grey line, the total model spectrum by the red line, the power-law continuum by the orange line, the two Si iv components by the gold lines and the two O iv] components by the green lines.

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In most cases, errors on the fit parameters were calculated by Tang et al. (2012) (see also Shang et al. 2007; Laor et al. 1994a). For spectra with high S/N, the largest uncertainty comes from placing the continuum in each wavelength region rather than formal errors from the fitting process. Therefore, they estimated the errors in the continuum placement by calculating the 1σ errors on the flux in the observed spectrum at each end of the local continuum. They then calculate four new continua, corresponding to adding and subtracting the 1σ flux errors at each end of the local continuum, and recalculate the measured quantities. The largest positive and negative changes in the measured quantities were taken to be the errors. Uncertainties in the equivalent width (EW) and flux in the line measurements for the Hβ and C iv regions that are not listed here are given in Tang et al. (2012) and calculated via the above method.

The above method for calculating uncertainties is problematic for some parameters (namely line dispersion), which led us to perform a Monte Carlo fitting procedure similar to that of DiPompeo et al. (2012) to determine the uncertainties on these parameters. The resulting errors on all fit parameters were very small, indicating that the formal errors on our fitting procedure are small. The uncertainties on each parameter are actually a combination of the fit uncertainties and systematic uncertainties, where the systematic uncertainties likely dominate in our sample.

For the FWHM measurements, which are at the core of this analysis, it is particularly important not to underestimate the measurement uncertainties by ignoring systematic uncertainties. A comparison of measurements of the FWHM of C iv made with similar but not identical methodologies in the literature (Vestergaard & Peterson 2006; Shang et al. 2007) for some objects in our sample shows that measurements typically vary by 15 per cent. This is larger than all but two of the per cent errors listed for C iv FWHM (the largest of which is 16 per cent) in Table 2, suggesting that the errors on FWHM may be underestimated. We expect that the uncertainty in the line dispersion parameter will be at least as large as for FWHM, indicating that these are likely also at least 15 per cent. While applying our fitting procedure across the literature might yield more consistent results than this, we must also consider the possibility that different fitting procedures behave systematically differently for different line profiles. Thus, in order to be appropriately conservative, we adopt 15 per cent uncertainty for all velocity line width measurements.

Measurements associated with the optical and UV indicators of EV1 are provided in Table 1. Runnoe, Brotherton & Shang (2012) measured continuum luminosities for this sample in the Hβ and C iv wavelength regimes that are listed in Table 2 along with linewidth measurements.

ANALYSIS

The EV1 bias in C iv

The trend of the FWHM of C iv with the ratio Peak(λ1400/C iv) illustrated by Wills et al. (1993a) suggests that both EV1 and black hole mass play a role in determining the C iv line profile. Because this effect is not present in Hβ, we expect that it contributes significantly to the disagreement between velocity widths measured from Hβ and C iv.

Fig. 2 demonstrates that the ratio Peak(λ1400/C iv) is correlated with the significant scatter between the FWHM of Hβ and the FWHM of C iv. We distinguish between RL and RQ points in the figure and find that they do not clearly populate separate relationships, though they do tend to occupy opposite ends of EV1.

Figure 2.

Residuals in FWHM for C iv and Hβ versus Peak(λ1400/C iv) (top panel) and residuals in the fit (bottom panel). The Spearman rank correlation coefficient and associated probability that this distribution of points occurs by chance are listed in the upper left-hand corner. The significant correlation indicates that the disagreement between C iv and Hβ linewidths that we hope to reduce depends on Peak(λ1400/C iv). The fitted line is given in red with the shaded region indicating the 95 per cent confidence interval. RL objects are indicated by the solid circles and the open circles indicate RQ objects.

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We performed a regression analysis to describe the dependence of the FWHM residuals on the ratio Peak(λ1400/C iv) and determined an expression for predicting the Hβ FWHM. Line fitting in this investigation is done with an ordinary least-squares Y on X [OLS(Y|X)] fit. The OLS(Y|X) method is to be used in instances where X is used to predict Y (Isobe et al. 1990), as is the case for our analysis. In the OLS(Y|X) fit, uncertainties are used only in the Y-direction, so uncertainties on the peak ratio do not enter into the fit. The assumption that the errors in the peak ratio are small certainly seems reasonable, given the values in the peak fluxes in Table 1; however, if the systematic errors dominate over the errors in the fitting procedure, these may be underestimated. Because the velocity width measurements have equal per cent uncertainties, the points are all weighted equally in the fit.

In order to determine the uncertainty in the slope and intercept used to predict the FWHM of Hβ, we employ the model-independent Monte Carlo simulation used in Peterson et al. (1998). This method simulates uncertainties associated with the measurement uncertainties and with the individual points in the sample. For our observed data set of N = 69 objects, we do the following. First, we generate NY values within the 1σ Gaussian uncertainties around the measured values to form a data set. Then, similar to the ‘bootstrapping’ technique, N sources are selected randomly from the synthetic data set, without regard to whether a point has been previously selected or not. Duplicate points that are sampled multiple times are then discarded from the sample, typically cutting the sample down by the Poisson probability of not selecting any given point, or ∼1/e ≈ 37 per cent. After duplicates are discarded, the data set is fitted following the procedure used on the actual data. This process is realized 10⁵ times to build a distribution in the slope and intercept parameters. The standard deviations of these distributions are taken to be the uncertainties on the slope and intercept.

This expression treats the RL and RQ sources together. We have investigated the relationships for RL and RQ objects separately and find that they are not significantly different within the 95 per cent confidence intervals, as is suggested by the distribution of RL and RQ points in Fig. 2. We note that, in the case of the RL sources, the correlation appears to be driven by two outliers in the peak ratio. A Monte Carlo bootstrapping simulation that would likely reveal any sample dependence of RL correlation is beyond the scope of this paper, but we do wish to draw the readers attention to this possible caveat.

The FWHM predicted for Hβ based on C iv and λ1400 shows less scatter with the true FWHM of Hβ than does C iv alone. Fig. 3 shows the relationship between the Hβ FWHM and C iv FWHM compared to Hβ and the predicted Hβ from equation (1). Independent of the assumed relationship between the FWHM of C iv and the FWHM of Hβ, the initial scatter between them is 0.20 dex. This is reduced to 0.15 dex and the points become fairly well centred around the one-to-one relationship by using equation (1). This scatter reduction is in the dispersion of the distribution of the log(FWHM) residuals only, and is independent of assuming a relationship between the C ivFWHM and Hβ FWHM. Our goal here is to be able to effectively predict the Hβ FWHM; thus, the reduction in scatter allows a more precise measurement.

Figure 3.

The FWHM of Hβ versus C iv (left-hand panel) and versus the FWHM predicted for Hβ based on UV spectral information (right-hand panel). In the left-hand panel, we do not expect the linewidths to be equal and rather illustrate the scatter between Hβ and C iv measurements. In the right-hand panel, we have used equation (1) to predict the Hβ linewidth and expect the data to fall around the dashed one-to-one line. The scatter decreases from 0.20 to 0.15 dex after including a Peak(λ1400/C iv) term and the points are fairly evenly distributed around the one-to-one line. RL objects are indicated by the solid circles and the open circles indicate RQ objects.

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Improved black hole masses

Figure 4.

5100 Å luminosity versus 1450 Å luminosity (top panel) and residuals in the fit (bottom panel). The dashed black line indicates where the luminosities are the same and the solid red line is the fitted line with the shaded region indicating the 95 per cent confidence interval. The Spearman rank correlation coefficient and associated probability of finding this distribution of points by chance are listed in the upper left-hand corner. RL objects are indicated by the solid circles and open circles indicate RQ objects.

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The uncertainties on the slope and intercept are calculated via the same Monte Carlo method, assuming 5 per cent error in the luminosities, consistent with Shang et al. (2007).

With the ability to predict the 5100 Å luminosity and Hβ linewidth from UV spectral parameters comes the possibility of better predicting the black hole mass using spectral properties in the C iv wavelength region. We calculated rehabilitated C iv masses from the predicted FWHM of Hβ using equation (1), the predicted 5100 Å continuum luminosity using equation (2), and the Hβ scaling relationship from Vestergaard & Peterson (2006). We found better agreement between Hβ-based black hole masses and those calculated from C iv and Peak(λ1400/C iv) than those calculated from C iv alone. Fig. 5 shows the before and after with Hβ versus C iv and Hβ versus predicted Hβ-based black hole masses. The improvement is significant, with a reduction in scatter from 0.43 to 0.33 dex. This method is independent of the choice in scaling relationship; it is not necessary to use the Vestergaard & Peterson (2006) scaling relationship; any relation using FWHM Hβ and 5100 Å continuum luminosity could be substituted.

Figure 5.

Hβ-based black hole masses versus C iv-based black hole masses (left-hand panel) and the mass calculated from the predicted Hβ based on UV spectral information (right-hand panel). The one-to-one line is shown. The scatter, originally 0.43 dex in the left-hand panel, is reduced to 0.33 dex by including Peak(λ1400/C iv) and equations (1) and (2) when calculating the black hole mass from spectral information in the C iv region. RL objects are indicated by the solid circles and the open circles indicate RQ objects.

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The reduction in scatter between Hβ- and C iv-based black hole masses can also be seen in the reduction in the width of the distribution of mass residuals. Fig. 6 shows ‘before’ and ‘after’ histograms for the FWHM-based black hole mass estimates. It is clear that the scatter is reduced by the width reduction in the distribution.

Figure 6.

Before and after histograms of the residuals between masses derived from FWHM. The shaded histogram shows black hole mass residuals ‘before’ using the difference between C ivand Hβ-based masses. The thick histogram shows black hole mass residuals ‘after’ using the difference between predicted Hβ [using equations (1) and (2)] and Hβ-based masses. The primary effect of predicting the FWHM of Hβ and using it to calculate the black hole mass is a reduction in width of the distribution.

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Figure 7.

Residuals in M_BH for C iv and Hβ versus the Peak(λ1400/C iv) (top panel) and residuals in the fit (bottom panel). The Spearman rank correlation coefficient and associated probability that this distribution of points occurs by chance are listed in the upper left-hand corner. The significant correlation indicates that there is a Peak(λ14020/C iv) dependence in the mass residuals similar to what was found for the FWHM. The fitted line is given in red with the shaded region indicating the 95 per cent confidence interval. RL objects are indicated by the solid circles and the open circles indicate RQ objects.

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This expression assumes the C iv single-epoch scaling relationship of Vestergaard & Peterson (2006) and the resulting predicted Hβ black hole masses are akin to using the Hβ scaling relationship from the same authors. The reduction in scatter achieved by using this correction is comparable to propagating the predicted optical measurements through the mass scaling relationship, although this method is less flexible because you cannot choose your mass scaling relationship.

A new mass scaling relationship for C iv based on an updated reverberation mapping sample and methodology has recently become available from Park et al. (2013). We do not re-derive equation (3) for the new scaling relationship, since the motivation for a ready-made mass correction was backward compatibility with catalogues like Shen et al. (2011). The effect of adopting this new mass scaling relationship in our sample is to increase the initial scatter between Hβ- and C iv-based masses from 0.43 to 0.45 dex. Points in the left-hand panel of Fig. 5 move towards the left-hand side, generally farther from the one-to-one line, and the scatter is increased. Thus, the reduction in scatter achieved by correcting Park et al. (2013) C iv-based masses with equations (1) and (2) is even more significant than for masses calculated from Vestergaard & Peterson (2006).