A COMPARATIVE ANALYSIS OF VIRIAL BLACK HOLE MASS ESTIMATES OF MODERATE-LUMINOSITY ACTIVE GALACTIC NUCLEI USING SUBARU/FMOS

Our primary selection of AGNs is based on their having X-ray emission detected by Chandra (Elvis et al. 2009; Civano et al. 2012) within the central square degree of COSMOS (hereafter C-COSMOS). The high surface density of AGNs (∼2000 deg⁻²) at the limiting depths (f_{0.5–2.0 keV} > 2 × 10⁻¹⁶ erg cm⁻² s⁻¹) of the C-COSMOS field ensures that we make adequate use of the multiplex capabilities of FMOS. In addition, two FMOS pointings were observed further out from the center of the COSMOS field; thus, we relied upon the catalog of optical and near-infrared counterparts to XMM-Newton sources (Brusa et al. 2010) for AGN selection.

We further require that optical spectroscopy (Trump et al. 2007; Lilly et al. 2009) is available for each source that yields a reliable redshift and a detection of at least a single broad (FWHM >2000 km s⁻¹) emission line, namely, Mg ii in many cases. We then specifically targeted those with spectroscopic redshifts that allow us to detect either Hβ (1.2 < z < 1.7 and 1.9 < z < 2.6), Hα (0.6 < z < 1.0 and 1.2 < z < 1.7), or Mg ii (2.8 < z < 3.8 and 4.1 < z < 5.3) in the observed FMOS spectral windows in low-resolution mode, i.e., 1.05–1.34 μm and 1.43–1.77 μm. Fibers are assigned to BLAGNs (for which we can detect emission lines of interest) with a limiting magnitude of J_AB = 23. Those at J_AB < 21.5 are given higher priority to ensure that this sample (of lower density on the sky) is well represented in the final catalog; this also effectively improves upon our success rate of detection of both continuum and line emission. Due to the sensitivity of FMOS and the low number density of AGNs at z > 3, our sample has very few detections of Mg ii in the near-infrared.

In addition, we have acquired FMOS observations of X-ray-selected AGNs in the ECDF-S (Lehmer et al. 2005) survey by including those that are only detected in the deeper 2–4 Ms data (Luo et al. 2010; Xue et al. 2011) in the central region that covers GOODS. This deeper X-ray field offers the potential to extend the dynamic range of our study in terms of black hole mass and Eddington ratio. We specifically select AGNs, as mentioned above, based on their optical properties determined through deep spectroscopic campaigns (Szokoly et al. 2004; Silverman et al. 2010). As with the COSMOS sample, we place higher priority on the brighter AGNs (R_AB < 22) while targeting the fainter cases with lower priority.

We have acquired near-infrared spectra of BLAGNs with Subaru/FMOS from the COSMOS and ECDF-S surveys. The majority of the data was obtained during open use time through NAOJ over three nights in 2010 December (ID: S10B-108) and two nights in 2011 December (ID: S11B-098). Additional targets were observed during other programs being carried out in the COSMOS field through the University of Hawaii in S10B-S11A. Weather conditions were acceptable, although clouds, mainly cirrus, reduced our observing efficiency. The typical seeing was ∼1'' with considerable variation across the nights.

We elected to use the CBS mode while taking two sequential exposures each of 15 minutes for each position (A and B positions hereafter). These pairs of exposures were repeated multiple times in order to reach an effective total integration time of 2.0–3.5 hr on-source. Some time is lost to refocusing and repositioning fibers at regular intervals during the full observation. In the early data, only one spectrograph (IRS1) was available; thus, ∼100 fibers were available for science targets.

We use the publicly available software FMOS Image-based Reduction package (Iwamuro et al. 2012). The reduction routines are based on IRAF tasks, although several steps are processed by additional tools written by the FMOS instrument team. Since our observations are carried out using an ABAB nodding pattern in the CBS mode of the telescope, an effective sky subtraction (A−B) can be performed using the two different sky images: A_n − B_{n − 1} and A_n − B_{n + 1} taken before and after the nth exposure. After the initial background subtraction, a crosstalk signal is removed by subtracting 0.15% and 1% of the counts from the bright region of each quadrant for IRS1 and IRS2, respectively (see Kimura et al. 2010, for more details on the crosstalk). The difference in the bias between the quadrants is corrected to make the average over each quadrant equal. We further apply a flat-field correction using a dome lamp exposure. Bad pixels are masked throughout the reduction procedure. Additional steps include distortion correction and the removal of residual airglow lines. This procedure is carried out for both positions A and B. Individual frames are combined into an averaged image and an associated noise image. Finally, the wavelength calibration is carried out based on a reference image of a Th–Ar emission spectrum. Both individual one-dimensional science and error spectra are extracted to be used for the fitting of emission line profiles.

We perform a first attempt at flux calibration by using the spectra of bright stars, usually one to two per spectrograph. A single stellar spectrum for each spectrograph is chosen to apply a correction based on the spectroscopic magnitude and photometry from the Two Micron All Sky Survey. An improvement of the absolute flux level is required to account for aperture effects. Therefore, we scale the flux of each FMOS spectra of our AGNs to match the deep infrared photometry using the total magnitudes available from the UltraVISTA survey (McCracken et al. 2012) over the COSMOS field. While scale factors can reach as high as ∼4, the median value, mean value, and dispersion are 1.64, 1.82, and 0.80, respectively.

We have observed over 100 type 1 AGNs in the combined COSMOS and ECDF-S fields to date. In Figure 1, we show the X-ray flux and NIR magnitude distribution of the 108 AGNs (originally identified as Chandra X-ray sources) in the COSMOS field that have 0.6 < z < 1.8, a redshift interval where we are capable of detecting Hα in the FMOS spectroscopic window. The distributions are shown for both the observed objects and the 56 AGNs having a significant detection of a broad Hα emission line (at the expected wavelength) that subsequently yielded a black hole mass estimate.

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Prior to our observations, we had no empirical assessment of the performance of FMOS; thus, AGNs were targeted to faint infrared magnitudes, now understood not to be feasible using the low-resolution mode for the faintest objects (J_AB ∼ 23). As shown in Figure 1(b), we have had a reasonable level of success (71%) with the detection of broad emission lines at brighter magnitudes (J_AB < 21.5). Unfortunately, the success rate is significantly lower at fainter magnitudes, thus dropping to 50% for the entire sample with J_AB < 23. It is worth highlighting that a survey depth of J_AB < 21.5 is about 2 mag fainter than current near-infrared spectroscopic observations of SDSS quasars (Shen & Liu 2012) at similar redshifts. In Figure 2, we demonstrate this by plotting the bolometric luminosity (based on L₃₀₀₀ and a bolometric correction of 5.15; Shen et al. 2011) of our AGNs compared to those from SDSS surveys.

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Greene & Ho (2005) describe in detail the benefits of using Hα for black hole mass measurements. In particular, the Hα emission line is stronger (∼3 ×), and thus more easily detected as compared to Hβ. This is clearly evident from our observations. We successfully detect a broad Hα line in ∼50% of the cases (as mentioned above), while the detection of Hβ is very low (17%). Even so, we do detect Hβ in a fair number of cases up to z ∼ 2.6 that will be presented in the full emission-line catalog (J. D. Silverman et al., in preparation). Any future FMOS campaign designed to detect the Hβ emission line (both broad and narrow) should increase the exposure time significantly and/or use the high-resolution mode that has roughly three times higher throughput in the H band as compared to the low-resolution mode (see Figure 19 of Kimura et al. 2010).

We perform a fit to the Hα emission line (if detected within the FMOS spectral window) in order to measure line width and integrated emission-line luminosity. Based on the spectroscopic redshift as determined from optical spectroscopy, we select the spectrum at rest wavelengths centered on the emission line and spanning a range that enables an accurate determination of the continuum characterized by a power law, f_λ∝λ^−α.

We employ multiple Gaussian components to describe the line profile. It is common practice to make such an assumption on the intrinsic shape of individual components even though it has been demonstrated that broad emission lines in AGNs are not necessarily of such a shape (e.g., Collin et al. 2006). The Hα line is fit with two or three Gaussians (including a narrow component) and the [N ii] λ6548,6583 lines with a pair of Gaussians. The ratio of the [N ii] lines is fixed at the laboratory value of 2.96. The narrow width of the [N ii] lines is fixed to match the narrow component of Hα. The width of the narrow components is limited to 420–800 km s⁻¹ (a range not corrected for intrinsic dispersion). The velocity profile of the broad components is characterized by the FWHM, which is measured using either one Gaussian or the sum of two Gaussians. We then correct the velocity width for the effect of instrumental dispersion to achieve an intrinsic profile width. The Hα luminosity discussed throughout this work is the sum of the broad components.

There are cases for which the fitting routine returns a solution with the width of the narrow component pegged at the upper bound of 800 km s⁻¹. It is worth highlighting that this minimization routine stops the fitting procedure when a parameter hits a limit; thus, the returned values are not the true best-fit values. For these, we inspect all fits by eye and decide whether such an additional broad component is real. For many cases, we can use the [O iii] λ5007 line profile, within the FMOS spectral window, to determine whether such a fit to the narrow line complex is accurate. In addition, we can use the available optical spectra for such comparisons. When the level of significance of the narrow line is negligible, we rerun the fitting routine and fix the narrow line width to the spectral resolution of FMOS, ∼420 km s⁻¹. In Figure 3, we show three examples of our fits to the Hα emission line that span a range of line properties.

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We fit the Mg ii emission line, as done in Schramm & Silverman (2012), observed in the optical spectra primarily from zCOSMOS (Lilly et al. 2009), Magellan/IMACS (Trump et al. 2007), and SDSS (York et al. 2000). The emission line is modeled by a combination of one or two broad Gaussian functions to best characterize the line shape. We first remove the continuum (before attempting to deal with the emission lines) by fitting the emission in a window surrounding the line. As with Hα, a power-law function is chosen to best characterize the featureless, non-stellar light attributed to an accretion disk. We further include a broad Fe emission component based on an empirical template (Vestergaard & Wilkes 2001) that is convolved by a Gaussian of variable width and straddles the base of the Mg ii emission line. A least-square minimization is implemented to determine the best-fit parameters. When possible, we optimize the residuals of the fits on a case-by-case basis by trying to minimize the number of components. Absorption features are either masked out or interpolated across. The fit returns two parameters required for black hole mass estimates: FWHM and monochromatic luminosity at 3000 Å. Examples of our fits to the Mg ii line are presented in Figure 4.

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Our first concern is to determine whether the Hα emission-line luminosity scales appropriately with the UV continuum luminosity. For the following analysis, we do not correct for extinction due to dust and any contamination by the host galaxy; the impact of these, thought to be small, will be quantified in a later study. In Figure 5, the continuum luminosity, λL_λ at 3000 Å, is plotted against the emission-line luminosity of Hα. Our data (as shown by the red points) spans two decades in luminosity and exhibits a clear correspondence between continuum and line emission. Based on our AGN sample, we determine the best-fit linear relation to be log (λL₃₀₀₀) = (0.82 ± 0.08) × log L_Hα + (9.31 ± 3.47). For the linear fitting, we adopt a FITEXY method (Press et al. 1992; Park et al. 2012). The level of dispersion of the data about this fit that will contribute to the dispersion in the final mass estimates is 0.20 dex.

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We can compare our data set to more luminous quasars from the SDSS. In particular, we identify 327 quasars from the SDSS sample in Shen et al. (2011) with 0.35 < z < 0.40 that cover a similar luminosity range as our high-redshift sample. These were selected from 1178 quasars at 0.35 < z < 0.40 based on high-quality data determined by adopting the following criteria: error in log (M_BH/M_☉) < 0.5, log (FWHM_Hα/km s⁻¹) > 2.9, and $\log ({\rm FWHM}_{\rm Mg\,{\scriptsize{II}}} / {\rm km \ s^{-1}}) > 2.9$. In addition, we include data from a recent study by Shen & Liu (2012) that provide the emission-line properties, including the Hα line of high-luminosity quasars from the SDSS with 1.5 < z < 2.2. These samples are added to our data shown in Figure 5. We clearly see that SDSS quasars fall along the λL₃₀₀₀–L_Hα relation as established above. Furthermore, the SDSS quasars have similar dispersion at both low-z and high-z samples to our sample, σ = 0.20 and σ = 0.15, respectively. We highlight that our AGN sample nicely extends such comparisons between continuum luminosity and line emission at higher redshifts and to lower luminosities. We are able to effectively establish a wider dynamic range that is not present in the high-z SDSS sample due to the limited luminosity range around log (λL₃₀₀₀) ∼ 46.2. By merging all three samples, we find the following relation based on a linear fit: log (λL₃₀₀₀) = (0.96 ± 0.01) × log L_Hα + (3.00 ± 0.53).

While there is very good agreement between the UV continuum and emission-line luminosity, there is a small difference that may impact, even slightly, our comparison of the masses. Based on the FMOS sample, the mean ratio 〈log (λL₃₀₀₀/L_Hα)〉 is 1.54 ± 0.03, which is slightly higher than that found for both the low-z and high-z SDSS quasar samples mentioned above; 〈log (λL₃₀₀₀/L_Hα)〉 = 1.40 ± 0.01 and 〈log (λL₃₀₀₀/L_Hα)〉 = 1.36  ±  0.02, respectively. This can be seen in the inset histogram in Figure 5. If this was due to the effect of dust extinction, then one would find the opposite trend with reduced UV continuum relative to the Hα line emission. There may be other explanations, such as an underlying spectral energy distribution that may be different for X-ray-selected samples (Elvis et al. 2012; Hao et al. 2012) and which has an impact on the response seen in photoionized gas, or the effect of the host galaxy on the aperture corrections that differ in each band. While this issue is important, we reserve a detailed investigation for subsequent work since it is beyond the scope of this paper to adequately demonstrate such effects. Here, we are primarily concerned with the magnitude of a luminosity offset and whether it contributes to an offset between the masses. With the black hole mass scaling with the square root of the luminosity (see below), the offset in luminosity, as determined above, amounts to a very small offset of 0.07 in log (M_BH/M_☉).

A second pillar for the use of Mg ii as a black hole mass indicator is that the emitting-line gas is located essentially within the same clouds that emit Balmer emission. While there are claims that this is the case by comparing the velocity profile of Mg ii with Hβ (e.g., McLure & Jarvis 2002; Shen et al. 2011), there are reported differences and trends that are not well understood (Wang et al. 2009; Shen & Liu 2012; Trakhtenbrot & Netzer 2012). For example, Mg ii tends to be narrower than Hβ, with a difference significantly larger at higher velocity widths (see Figure 2 of Wang et al. 2009).

Our aim here is to compare the FWHM of the Mg ii and Hα emission lines using a sample not yet explored, namely, the moderate-luminosity AGNs at high redshifts in survey fields such as COSMOS. In Figure 6, we plot the emission-line velocity width between Hα and Mg ii emission lines. Based on the FMOS sample only, a positive linear correlation is seen between the velocity width of the two emission lines with the mean ratio of $\langle \log ({\rm FWHM}_{\rm Mg\,{\scriptsize{II}}} / {\rm FWHM}_{\rm H\alpha }) \rangle = 0.089\pm 0.022$ (σ = 0.143). Our data is in very good agreement with those from the SDSS, i.e., $\langle \log ({\rm FWHM}_{\rm Mg\,{\scriptsize{II}}} / {\rm FWHM}_{\rm H\alpha }) \rangle = 0.033$ (σ = 0.176) for the low-z sample from Shen et al. (2011), $\langle \log ({\rm FWHM}_{\rm Mg\,{\scriptsize{II}}} / {\rm FWHM}_{\rm H\alpha }) \rangle = 0.00$ (σ = 0.076) for the high-z sample from Shen & Liu (2012), and recent FMOS results from Subaru XMM-Newton Deep Survey (see Nobuta et al. 2012). Based on a linear fit to the data shown in Figure 6, we measure a slope that is consistent with unity; (0.898  ±  0.132 for FMOS only and 1.001  ±  0.001 for FMOS+SDSS), and that cannot substantiate the claim by Wang et al. (2009) for a shallower value. These results support a scenario where the Mg ii and the Hα emitting regions are essentially cospatial with respect to the central ionizing source.

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There are a few noticeable outliers well outside the dispersion of the sample. These objects then appear as outliers when comparing their masses based on different lines in the next section. Upon inspection, we find that these are the result of the FMOS spectra having low S/N. In some cases, there may be a fit to the Hα emission line, based on different parameter constraints, that is equally acceptable to the original fit as assessed by a chi-square goodness of fit and has a velocity width in closer agreement with Mg ii. However, we refrain from such selective fitting in order to present results that may be obtained from using similar fitting algorithms on larger data sets where such close inspection is not feasible.

We now calculate black hole masses (M_BH) based on our single-epoch spectra using both (1) L₃₀₀₀ and FWHM$_{\rm Mg\,{\scriptsize{II}}}$, and (2) L_Hα and FWHM_Hα. This calculation can be expressed as follows:

$$\begin{eqnarray} &&\log \left(\frac{M_{\rm BH}}{M_\odot }\right) = a + b \log \left(\frac{\lambda L_\lambda \ {\rm or} \ L_{\rm line}}{10^{44} \ {\rm erg \ s}^{-1}} \right) + c \log \left(\frac{{\rm FWHM}}{{\rm km \ s}^{-1}} \right). \nonumber\\ \end{eqnarray} \tag{ 1 }$$

We explicitly use the recipes provided by Greene & Ho (2005) and McLure & Dunlop (2004) for the cases of the Hα and Mg ii lines, respectively:

$$\begin{eqnarray*} (a,b,c) &=& (1.221,0.550,2.060) \quad {\rm for \ H\alpha },\\ (a,b,c) &=& (0.505,0.620,2.000) \quad {\rm for \ \rm Mg\,{\scriptsize{II}}}. \end{eqnarray*}$$

We note that the calibration of the relation for Mg ii has been carried out by many studies (e.g., Vestergaard & Peterson 2006; McGill et al. 2008) and there are known differences between them.

In Figure 7, we show M_BH for our sample derived from Hα and Mg ii. Our sample spans a range of 7.2 ≲ log (M_BH/M_☉) ≲ 9.5 that is consistent with that reported by previous studies of type 1 AGNs in COSMOS (Merloni et al. 2010; Trump et al. 2011) and that is complementary to the higher-L quasar sample at similar redshifts with log (M_BH/M_☉) ≳ 9 (Shen & Liu 2012). We find that the average (dispersion) in the black hole mass ratio of $\langle \log (M_{\rm Mg\,{\scriptsize{II}}}/M_{\rm H\alpha }) \rangle$ is 0.17 (σ = 0.32) for our FMOS sample. These results are similar to that determined from the SDSS sample; the average (dispersion) in the black hole mass ratio is −0.05 (σ = 0.39) at low z and −0.03 (σ = 0.20) at high z. While an offset of 0.17 dex is seen in the FMOS sample, we conclude that the recipes established using local relations give consistent results between Mg ii- and Hα-based estimates.

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