A NEW SAMPLE OF CANDIDATE INTERMEDIATE-MASS BLACK HOLES SELECTED BY X-RAY VARIABILITY^*

We prepared light curves in the 0.5–10 keV band with 512 s bin, and quantified variability with the NXS. Figure 1 shows source and background light curves in the 0.5–10 keV band with 512 s bin. The background rates are normalized to the area of the source light curves. When light curves were made, the redshift-corrected energy band was used for sources with a redshift greater than 0.1. NXS is the variance after correcting for measurement errors (e.g., Nandra et al. 1997; Turner et al. 1999; Vaughan et al. 2003) and is defined by

$$\begin{equation} \sigma ^2_{\rm NXS}=\frac{1}{{\bar{x}}^2}\left[\frac{1}{N-1}\sum ^N_{i=1}(x_i-{\bar{x}})^2-\frac{1}{N}\sum ^N_{i=1}\sigma ^2_i\right], \end{equation} \tag{ 1 }$$

where N and ${\bar{x}}$ are the number of data points and the mean count rate, respectively. x_i is the count rate in the ith bin and its error is σ_i. The error of NXS was estimated by using the expression of Vaughan et al. (2003). Previous studies of variability often used light curves in the 2–10 keV band with 256 s bin to calculate NXS. Light curves of some sources, however, contain bins of zero counts s⁻¹, and NXS cannot be properly calculated. We, therefore, calculated NXS by using light curves in the 0.5–10 keV band with 512 s bin, and only few bins of zero counts s⁻¹ are seen in the light curves. Light curves of J0021−1507 and J1305+1813 still contain one and three bins of zero counts s⁻¹ among 80 and 88 bins, respectively. In these cases, since the fractions of such bins were small and their influence on the NXS calculation is small, we excluded such bins from the calculation of NXS.

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We examined several models to fit spectra of the 15 strongly variable AGN candidates. All the model components were absorbed by the Galactic H i column density using the phabs model in XSPEC. We fixed the Galactic H i column density at the value derived from 21 cm observations (Kalberla et al. 2005). In all spectral fits, if the redshift is known, we used models taking account of the source redshift, to fit the observed spectra.

Spectra of the two sources J0232−0729 and J0324−0256 were explained by a simple power-law model without intrinsic absorption. A combination of power law and blackbody reproduced spectra of the 10 sources: J0152−1347, J1201−1848, J1233+0005, J1305+1813, J1324+3000, J1347+1734, J2008−4440, J2131−4251, J2334+3921, and J2355+0600. The results of these spectral fits are summarized in Table 2. These 12 objects do not require additional absorption intrinsic to the source. We derived upper limits on their intrinsic absorption column densities by adding an additional absorption. The results are also shown in Table 2. Among these objects, the best-fit photon index for one object (J1324+3000) is rather flat (photon index Γ ≈ 0.57), which might be due to intrinsic absorption. Then we applied intrinsic absorption to both the power-law and blackbody components. The spectrum, however, did not require additional intrinsic absorption. Thus, we adopt the result of the fit with the power-law plus blackbody model in the following discussions.

These simple continuum models failed to fit the spectra of J0021−1507, J0113−1442, and J0136+1549 (χ²_ν (dof) = 1.73 (27), 1.54 (23), and 1.51 (18), respectively). When the spectra of J0021−1507 and J0136+1549 were fitted by a combination of power law and blackbody, an edge-like feature was seen at ∼0.7 keV in the residuals. Thus, we added an absorption edge model to represent this feature, and obtained better fits (Δχ² = 24.0 and 10.6 for J0021−1507 and J0136+1549, respectively). The parameters for this model are shown in Table 2.

In the spectral fit to J0113−1442 with a combination of power law and blackbody, the photon index obtained was extremely flat (∼0.4). In order to test whether this flatness is due to absorption, we applied the intrinsic absorption to the power-law and blackbody model. This, however, resulted in an unacceptable fit (χ²_ν(dof) = 1.60(22)). We also tried to fit the spectrum using a partially covered power-law model,

$$\begin{equation} {\tt phabs\times zpcfabs\times zpowerlaw}, \end{equation} \tag{ 2 }$$

where phabs, zpcfabs, and zpowerlaw represent models of Galactic absorption, partial covering absorption, and power law, respectively. Although we obtained a steeper photon index Γ ≈ 2.1, the fit was unacceptable (χ²_ν(dof) = 1.67(23)). In this fit, edge-like residuals were seen at ∼0.7 keV. Then we added an absorption edge model "zedge,"

$$\begin{equation} {\tt phabs\times zpcfabs\times zedge\times zpowerlaw}, \end{equation} \tag{ 3 }$$

and obtained a better fit (χ²_ν(dof) = 1.16(21)) with a photon index Γ ≈ 1.98. The spectral parameters of this model are shown in the first row of Table 3. We also examined the following model:

$$\begin{equation} {\tt phabs\times zpcfabs\times (zpowerlaw+zbbody)}. \end{equation} \tag{ 4 }$$

We again obtained a good fit (χ²_ν(dof) = 1.13(21)) as shown in the second row of Table 3. The spectrum of J0113−1442 was almost equally well reproduced by the models (3) and (4).

Spectra of all the sources with the best-fit model are shown in Figure 2. The model (3) is shown as the best-fit model for J0113−1442. Observed fluxes and absorption-corrected luminosities in the 2–10 keV band were calculated by using the best-fit model, where luminosities are derived only for objects with known redshifts. We obtained luminosities in the range of 10⁴¹–10⁴³ erg s⁻¹ as summarized in Table 4.

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We estimated BH masses based on a correlation between BH mass (M_BH) and NXS. Such correlations have been studied by various authors (O'Neill et al. 2005; Papadakis 2004; Miniutti et al. 2009; Nikołajuk et al. 2009; Zhou et al. 2010). These studies used NXS calculated from light curves in the 2–10 keV band with 256 s bin. We, however, calculated NXS by using light curves in the 0.5–10 keV band with 512 s bin. Then a correlation between BH mass and NXS in 0.5–10 keV was derived by using a reverberation-mapped sample consisting of 20 AGNs. These AGNs are the same as used in Zhou et al. (2010). PG 0026+129 in their sample, however, was excluded from our analysis because no XMM-Newton data were available. We obtained

$$\begin{equation} M_{\rm BH}=10^{5.76\pm 0.13}\big(\sigma ^2_{\rm NXS,0.5\hbox{--}10}\big)^{-0.64\pm 0.04}\;M_\odot, \end{equation} \tag{ 5 }$$

where σ²_{NXS, 0.5–10} is corrected to the common duration (50 ks) and the common bin size (256 s) by using the method of Awaki et al. (2006), since NXS depends on the duration and time bin size. The energy band we use (0.5–10 keV) is different from that used in the previous studies (2–10 keV). The 2–10 keV band is likely to be mainly from intrinsic emission unless absorption to the nucleus is large and variable, and suitable to study the timescales of phenomena just around BHs. The softer energy band below 2 keV, however, is more affected by changes in absorber and soft excess emission, of which the origin is still unknown, and should be treated with caution. Note also that NXS in the soft X-ray band is strongly correlated with that in the hard X-ray band (Ponti et al. 2012) despite the different composition of spectral components in the soft and hard bands. This result strongly suggests that NXS in 0.5–10 keV is well correlated with that in 2–10 keV.

In order to use Equation (5) for BH mass estimation, we corrected NXS for our sample to the common duration (50 ks) and the common bin size (256 s). Awaki et al. (2006) showed the conversion between two NXSs (σ²_{NXS, 1}, σ²_{NXS, 2}) calculated with different duration (T₁, T₂) and different bin size (Δt₁, Δt₂) as

$$\begin{equation} \frac{\sigma ^2_{\rm NXS,1}}{\sigma ^2_{\rm NXS,2}}=\frac{(2\Delta t_1)^{\alpha -1}-(T_1)^{\alpha -1}}{(2\Delta t_2)^{\alpha -1}-(T_2)^{\alpha -1}}, \end{equation} \tag{ 6 }$$

where α is the slope of the PSD and is assumed to be 2.25. In Table 5, the values of NXS before and after the corrections of duration and bin size, and estimated BH masses are listed. The time spans from the first bin to last bin of the light curves, which corresponds to T₁ in Equation (6), are also shown in Table 5.

We assumed the PSD slope in 0.5–10 keV to be 2.25, which is typically observed in 2–10 keV (Papadakis et al. 2002; Uttley et al. 2002; Edelson & Nandra 1999; Markowitz et al. 2003, 2007; Vaughan & Fabian 2003; McHardy et al. 2004, 2005; Vignali et al. 2004; Awaki et al. 2005; Markowitz & Uttley 2005; Uttley & McHardy 2005). Although the number of AGNs studied is very limited, PSD slopes in the soft X-ray band appear to be similar to or only somewhat steeper than those in the 2–10 keV band (Papadakis et al. 2002; McHardy et al. 2004; Markowitz et al. 2007). We examined the dependence of a scaling factor of NXS on the duration of the light curve for the PSD slope of 1.50, 2.25, and 3.00 to estimate an effect of the assumed PSD slope on BH mass estimation. These slopes were chosen because PSD slopes of most AGNs likely lie within this range. The scaling factor was calculated from Equation (6) by substituting T₁, Δt₁, and Δt₂ for 50 ks, 256 s, and 512 s, respectively. The dependence of the scaling factor on the duration of the light curve is shown in Figure 3. The shortest and longest durations in our sample are 14.8 ks and 77.8 ks, respectively. According to Figure 3, the influence on NXS by difference of PSD slopes is larger at 14.8 ks than at 77.8 ks. The scaling factor for α = 1.50 and 3.00 divided by those for α = 2.25 at 14.8 ks are 0.47 and 2.4, respectively. If NXS multiplied by 0.47 or 2.4 are substituted for σ²_{NXS, 0.5–10} in Equation (5), BH masses become smaller or larger by ∼60%, respectively.

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The BH masses for our sample were estimated by using Equation (5) and are in the range of (0.58–6.6) × 10⁶ M_☉. The estimated masses for relatively low-mass BHs could be incorrect due to the effect of a break in PSD. NXS represents an integration of the PSD in a certain frequency range normalized by the mean count rate squared (Vaughan et al. 2003). If the break frequency is in the frequency range, BH mass based on NXS would be underestimated. The break time, the reciprocal of the break frequency, is proportional to BH mass as M_BH/10^6.5 M_☉ day (Markowitz et al. 2003). In the case of our sample, if the break time is shorter than either the duration of the light curve or 50 ks, BH mass would be underestimated. We calculated the break times of the estimated BH masses for our sample using the equation in Markowitz et al. (2003). The break times of seven sources (J0113−1442, J0136+1549, J0324−0256, J1201−1848, J1347+1734, J2008−4440, and J2131−4251) are shorter than 50 ks. The estimated break times for all the other objects are longer than 50 ks and the length of their light curves. BH masses of these sources are likely to be underestimated, since NXS are overestimated due to the scaling using an inappropriate PSD. We tried to obtain their BH masses taking into account the effect of the break, by assuming a universal shape of PSD, a power law of frequency Af^−α with α = 0 and 2.25 at lower and higher frequencies than the break frequency, where A is a normalization.

First, we calculated the integrals of the PSD with and without the break from 1/T to 1/2Δt, where T and Δt are 50 ks and 256 s, respectively. The integration of the PSD with the break divided by that of the PSD without the break was calculated. We multiplied this value by scaled NXS listed in Table 5 to obtain new NXS and re-estimated BH mass based on new NXS by using Equation (5). The true BH mass should be lower than this re-estimated mass, since the re-estimated mass is calculated by using the break time for the underestimated mass. We then found a self-consistent solution for a mass, NXS, and a break frequency inside the mass range determined by the upper and lower bound of mass derived above. Finally, we obtained the BH masses of the four sources listed in Table 5. Thus, the BH mass range for our sample becomes (1.1–6.6) × 10⁶ M_☉, and BH masses of the seven sources are 2 × 10⁶ M_☉ or less, which are in the range for IMBHs. If the PSD slope of 1.50 or 3.00 is used instead of 2.25, the BH masses estimated by these steps are changed by only 1%–9%.

Growing BHs are expected to have a combination of relatively low masses and high accretion rates. We calculated Eddington ratios L_bol/L_Edd for nine objects with known redshifts, where the Eddington luminosity is 1.26 × 10³⁸ (M_BH/M_☉) erg s⁻¹. Bolometric luminosities are derived from the intrinsic 2–10 keV luminosities by assuming a bolometric correction factor of 20 (Vasudevan & Fabian 2007). The Eddington ratios L_bol/L_Edd thus obtained are listed in Table 4 and the relation between M_BH and bolometric luminosities is shown in Figure 4(a). Six among nine sources have L_bol/L_Edd greater than 0.2. This result and the estimated M_BH imply that we successfully selected relatively low-mass BHs with a large mass accretion rates, which are likely to be growing BHs.

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The objects in our sample likely host relatively low-mass SMBHs accreting at relatively large mass accretion rates. Narrow-line Seyfert 1s (NLS1s) are a class of AGNs which tend to host relatively low-mass SMBHs with high accretion rates (e.g., Czerny et al. 2001; Boroson 2002; Wang & Netzer 2003) and objects in our sample are expected to share properties similar to NLS1s. Many NLS1s show relatively steep X-ray spectra above ∼2 keV with photon indices 2.0–2.5 and strong soft emission relative to underlying power law compared to broad-line Seyfert 1s (BLS1s; e.g., Boller et al. 1996; Brandt et al. 1997; Leighly 1999; Grupe 2004; Bianchi et al. 2009; Caccianiga et al. 2011). The photon indices observed for 15 sources in our sample are in the range of Γ ≈ 0.57–2.57, which is much broader than those known for BLS1s and NLS1s. Photon indices are likely to be related to Eddington ratios; a correlation between Γ and L_bol/L_Edd is known for objects with L_bol/L_Edd < 1 (e.g., Lu & Yu 1999; Shemmer et al. 2006, 2008; Risaliti et al. 2009). We examined a relationship between photon indices Γ and Eddington ratios L_bol/L_Edd as shown in Figure 4(b). The relation derived by Risaliti et al. (2009) is also shown as a solid line in Figure 4(b) for comparison. The photon indices of about a half of our sources are flatter than expected from Risaliti et al.'s relation. Ai et al. (2011) suggested that some objects show spectral slopes flatter than the relation using a sample of NLS1s with optical broad-line widths narrower than 1200 km s⁻¹ and large Eddington ratios. We strengthened their finding by adding more data points of objects with low BH masses and large accretion rates selected by our own method.

One possible reason for such flatness of the slope could be uncertainties in BH masses. BH mass estimation relying on X-ray variability is uncertain up to a dex. The BH masses M_BH estimated in the present study may be underestimated, because values of NXS from different observations of the same object show nonstationarity and because we tend to select a strongly variable state. Our comparison between BH masses derived from X-ray variability and from reverberation mapping shows that the discrepancy between the two methods is within a factor of four for most of the objects. Even if there are uncertainties of M_BH by an order of magnitude, our sample contains some objects with flat photon indices well below Risaliti et al.'s relation. Therefore, uncertainties in BH mass estimation alone cannot explain the deviation from the relation and the results likely reflect the intrinsic nature of the sources.

We studied also the dependence of photon indices on BH masses. The relationship between these quantities is shown in Figure 4(c). The slopes are again flatter than the extrapolation of the relation of Risaliti et al. (2009). As discussed in the previous paragraph, the change of intrinsic slope could be the reason for the flatness. In addition, there could be an uncertainty in Risaliti's relation because of relatively narrow range of BH masses and Eddington ratios they used. Our results along with other X-ray studies of AGNs with IMBHs (Dewangan et al. 2008; Miniutti et al. 2009; Ai et al. 2011) suggest that in BH mass range of 10⁴–10⁶ M_☉, photon indices become flatter than the extrapolation of Risaliti et al.'s photon index–BH mass relation.

X-ray spectra of NLS1s, many of which have relatively low-mass SMBHs with high accretion rates, often show soft X-ray excess over a power-law model determined at high energies above 2 keV. The shape of the soft X-ray excess can be approximated by blackbody or multicolor disk blackbody. Soft excess emission was also observed in AGNs with IMBHs selected from SDSS (Dewangan et al. 2008). When a blackbody model is fitted to the soft X-ray excess, temperature ranges form 80 to 250 eV for NLS1s and AGNs with IMBHs (Vaughan et al. 1999; Leighly 1999; Dewangan et al. 2008; Ai et al. 2011). Radio-quiet AGNs having more massive BHs of 10⁷–10⁹ M_☉ show a similar range of temperature (Gierliński & Done 2004; Crummy et al. 2006; Bianchi et al. 2009). In our sample, 12 among the 15 sources showed soft X-ray excess expressed by a blackbody model with kT ≈ 83–294 eV. Temperatures of all sources expect for J1324+3000 (kT ≈ 294 eV) are consistent with the range observed for the AGNs mentioned above. Thus, we strengthened the previous results, in which the temperature of soft excess emission approximated by blackbody is in a relatively narrow range (80–250 eV) regardless BH mass.