ACCRETION RATES OF RED QUASARS FROM THE HYDROGEN Pβ LINE

Our sample is drawn from red quasars listed in previous studies (Glikman et al. 2007; Urrutia et al. 2009). The previous studies selected red quasar candidates using a combination of red colors in the optical through NIR (e.g., $R-K\gt 4$ and J − K > 1.7 in Glikman et al. 2007; r' − K > 5 and J − K > 1.3 in Urrutia et al. 2009) and FIRST (Becker et al. 1995) radio detection. Then, they confirmed red quasars with spectroscopic follow-up. The previous studies found ∼80 red quasars, whose redshifts ranged from 0.186 to 3.050. These red quasars are very luminous (−31.61 < M_i < −23.19; e.g., Urrutia et al. 2009) and obscured by dust (0.186 ≤ E(B − V) ≤ 3.05), and they show strong evidence of ongoing interaction (Urrutia et al. 2008; Glikman et al. 2015). Moreover, their spectra are well-fitted by normal type 1 quasar spectrum with a dust reddening law.

Among the red quasars, we select 20 red quasars at z ∼ 0.7 (from 0.56 to 0.84) for our study where the redshifted Pβ line is observable in the sky window at the K-band. Moreover, our sample is bright (K < 15.5 mag) and has a wide range of luminosities (−31.78 < M_K < −26.90 mag).

In order to compare the accretion rates of the red quasars to those of normal type 1 quasars, we select type 1 quasars from the quasar catalog (Schneider et al. 2010) of the Sloan Digital Sky Survey (SDSS) Seventh Data Release (DR7; Abazajian et al. 2009). The catalog contains 105,783 spectroscopically confirmed quasars with wide ranges of redshifts from 0.065 to 5.4, and r' band magnitudes of $15.2\lt r^{\prime} \lt 22.9$. In order to avoid sample bias effects, we choose quasars with the same selection criteria as the red quasars except for the red colors: (i) the same redshift range of 0.56 ≤ z ≤ 0.84; (ii) FIRST radio detection; and (iii) detection in the J-, H-, and K-bands from 2MASS. In the end, 410 SDSS quasars are found and used as the control sample. Figure 1 shows the redshift distribution and the bolometric luminosity (see Section 4.2) versus redshift of these 16 red quasars and 410 normal type 1 quasars. Note that the red quasars have a bolometric luminosity in the range of ∼10⁴⁶–10⁴⁷ erg s⁻¹.

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NIR spectra of the 20 red quasars were obtained using the SpeX instrument (Rayner et al. 2003) on the NASA Infrared Telescope Facility (IRTF). Descriptions of the observations of 11 of the 20 red quasars are given in Glikman et al. (2007, 2012). Additionally, we obtained IRTF NIR spectra for the remaining nine sources. In the observation, we used the short cross-dispersion mode (SXD: 0.8–2.5 μm), whose spectral wavelength range includes redshifted Pβ lines. We performed observation with a 08 slit width to achieve a resolution of R ∼ 750 (400 km s⁻¹ in FWHM), which is sufficient for the measurement of the width of broad emission line. Note that this observational setup is nearly identical to that of Glikman et al. (2007, 2012).

For telluric correction, we obtained the spectrum of an A0V star after the observation of each target. The A0V stars were chosen to be near the red quasar (Δairmass < 0.1 and separation < 15°). We use the Spextool (Vacca et al. 2003; Cushing et al. 2004) package to produce fully reduced spectra.

Our observations were performed under clear weather conditions and with a sub-arcsecond seeing of ∼07, and we detect Pβ emission line for five red quasars (0911+0143, 1248+0531, 1309+6042, 1313+1453, and 1434+0935) with a signal-to-noise ratio (S/N) of >5. We do not detect Pβ line in the remaining four red quasars due to the low S/N of our data (1106+2812, 1159+2914, 1415+0903, and 1523+0030), and they are excluded in the following analysis. In total, we use 16 red quasars at z ∼ 0.7 (from 0.56 to 0.84) among 20 quasars for which we got IRTF spectra. Table 1 summarizes the basic information of these 16 red quasars.

For estimating virial masses of red quasars, we adopted the Pβ scaling relation (Kim et al. 2010) after adjusting the relation to have a recent virial coefficient of log f = 0.05 (Woo et al. 2015). The modified relation is

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}={10}^{7.04\pm 0.02}{\left(\displaystyle \frac{{L}_{{\rm{P}}\beta }}{{10}^{42}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)}^{0.48\pm 0.03}{\left(\displaystyle \frac{{\mathrm{FWHM}}_{{\rm{P}}\beta }}{{10}^{3}\;\mathrm{km}\;{{\rm{s}}}^{-1}}\right)}^{2}.\end{eqnarray} \tag{ 1 }$$

In this scaling relation, the luminosity and the FWHM of the Pβ line represent the radius and the velocity of the BLR. The measured M_BH values of the red quasars are listed in Table 2.

Table 2.  Pβ Parameters, BH Masses, and Eddington Ratios

Objects	FWHMPβ	$\mathrm{log}({L}_{{\rm{P}}\beta }$)	MBH	Lbol	Eddington Ratio	$\dot{M}$	τ
	(km s−1)	(erg s−1)	(108 M⊙)	(1046 erg s−1)		(M⊙ year−1)	(107 years)
0825+4716	3940 ± 393	43.78 ± 0.04	12.25 ± 2.98	10.40 ± 1.02	0.693	18.45	6.64
0911+0143	2907 ± 206	42.93 ± 0.04	2.59 ± 0.44	1.54 ± 0.16	0.486	2.73	9.48
0915+2418	3527 ± 729	43.88 ± 0.09	10.94 ± 4.92	12.95 ± 3.18	0.967	22.96	4.76
1113+1244	2054 ± 107	43.71 ± 0.03	3.09 ± 0.52	8.92 ± 0.67	2.360	15.82	1.95
1227+5053	2781 ± 446	43.10 ± 0.08	2.87 ± 1.00	2.26 ± 0.49	0.644	4.01	7.16
1248+0531	2697 ± 123	43.03 ± 0.02	2.49 ± 0.32	1.93 ± 0.12	0.633	3.43	7.27
1309+6042	2673 ± 89	43.00 ± 0.02	2.37 ± 0.26	1.80 ± 0.09	0.622	3.20	7.40
1313+1453	3793 ± 96	43.42 ± 0.01	7.62 ± 0.92	4.65 ± 0.17	0.499	8.25	9.24
1434+0935	1398 ± 34	43.34 ± 0.01	0.95 ± 0.11	3.88 ± 0.13	3.350	6.89	1.37
1532+2415	4071 ± 1549	43.09 ± 0.16	6.12 ± 4.87	2.24 ± 1.05	0.299	3.98	15.39
1540+4923	5397 ± 1518	43.18 ± 0.14	11.86 ± 7.13	2.73 ± 1.11	0.188	4.85	24.46
1600+3522	1887 ± 228	43.38 ± 0.06	1.81 ± 0.49	4.26 ± 0.63	1.927	7.55	2.39
1656+3821	3028 ± 246	43.42 ± 0.04	4.87 ± 0.98	4.66 ± 0.53	0.783	8.27	5.88
1720+6156	1818 ± 205	43.16 ± 0.06	1.31 ± 0.33	2.58 ± 0.38	1.613	4.58	2.86
2325−1052	2778 ± 772	43.05 ± 0.13	2.71 ± 1.59	2.02 ± 0.73	0.610	3.58	7.55
2339−0912	2927 ± 140	43.67 ± 0.03	5.95 ± 0.95	8.03 ± 0.55	1.102	14.23	4.18

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For the BH masses of normal type 1 quasars, we use optical or UV spectral properties from Shen et al. (2011) and use the M_BH estimators of McLure & Dunlop (2004). Note that we modified their formula so that it gives log f = 0.05 by multiplying by a factor of 1.122. First, we use λL_5100Å (L5100, hereafter) and FWHM of the Hβ line with the equation

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=5.27{\left(\displaystyle \frac{{\rm{L}}5100}{{10}^{44}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)}^{0.61}{\left(\displaystyle \frac{{\mathrm{FWHM}}_{{\rm{H}}\beta }}{\mathrm{km}\;{{\rm{s}}}^{-1}}\right)}^{2}.\end{eqnarray} \tag{ 2 }$$

We use this M_BH estimator for 406 normal type 1 quasars with the values of L5100 and ${\mathrm{FWHM}}_{{\rm{H}}\beta }$ from Shen et al. (2011). For the remaining four normal type 1 quasars with no Hβ detection, we adopt Mg ii and λL_3000Å (L3000) instead as

$$\begin{eqnarray}&&\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}=3.59{\left(\displaystyle \frac{{\rm{L}}3000}{{10}^{44}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}\right)}^{0.62}{\left(\displaystyle \frac{{\mathrm{FWHM}}_{\mathrm{Mg}{\rm{II}}}}{\mathrm{km}\;{{\rm{s}}}^{-1}}\right)}^{2}.\end{eqnarray} \tag{ 3 }$$

To obtain bolometric luminosities of red quasars, we use several relations between the line luminosity, the continuum luminosity, and the bolometric luminosity. We bootstrap the relations between ${L}_{{\rm{P}}\beta }$ and ${L}_{{\rm{H}}\alpha }$ (Kim et al. 2010), L_Hα and L5100 (Jun et al. 2015), and L5100 and L_bol (Shen et al. 2011) to relate L_Pβ to L_bol. The combined relationship is

$$\begin{eqnarray}&&\mathrm{log}(\displaystyle \frac{{L}_{\mathrm{bol}}}{{10}^{44}\;\mathrm{erg}\;{{\rm{s}}}^{-1}})=1.29+0.969\;\mathrm{log}(\displaystyle \frac{{L}_{{\rm{P}}\beta }}{{10}^{42}\;\mathrm{erg}\;{{\rm{s}}}^{-1}}).\end{eqnarray} \tag{ 4 }$$

The measured L_bol values of the red quasars are listed in Table 2.

For the normal type 1 quasars for which BH masses are estimated by a Hβ BH mass estimator, we convert L5100 to the bolometric luminosity with a bolometric correction factor of 9.26 (Shen et al. 2011) for L5100. We also measure the bolometric luminosities of four normal type 1 quasars without Hβ detection from L3000 with a bolometric correction factor of 5.15 (Shen et al. 2011).

Five of the red quasars in our sample overlap with the thirteen red quasars studied by Urrutia et al. (2012). We are thus able to compare the L_bol and the M_BH values of these five red quasars (0825+4716, 0915+2418, 1113+1244, 1532+2415, and 1656+3821) from our method versus the method adopted by Urrutia et al. (2012). Urrutia et al. (2012) obtained L_bol by applying a bolometric correction to their monochromatic luminosity at 15 μm (L15, hereafter), and derived M_BH values using L15 as a proxy for R_BLR and FWHM of broad emission lines (either Balmer or Paschen lines depending on the availability). For  comparison, the M_BH values of Urrutia et al. (2012) are rescaled to match the virial factor adopted in this paper. Figure 3 shows a comparison of L_bol and M_BH, which show a reasonable agreement between two independent estimates, except for one outlier (1532+2415, a red circle in Figure 3). The Pearson correlation coefficients are 0.863 and 0.370 for the L_bol and the M_BH, respectively, but the Pearson correlation coefficient for ${M}_{\mathrm{BH}}$ values increases to 0.683 if we exclude the outlier. We note that the outlier has the largest uncertainty of the Pβ line properties among the 16 red quasars used in this study, with the fractional errors of the FWHM and the flux as 38% and 45.5%, respectively.

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The rms scatters (including measurement uncertainties) of the L_bol and the M_BH values with respect to the one-to-one correlations are 0.306 dex and 0.479 dex, respectively. In order to derive the intrinsic scatters by removing the contribution from measurement uncertainties, we performed a Monte-Carlo simulation 10,000 times by assuming that the L_bol and the M_BH values from Urrutia et al. (2012) are identical to those from Pβ measurements and adding measurement uncertainties randomly. The median values of the scatters from this simulation are taken to be the contribution to the rms scatter due to measurement uncertainties, and they are subtracted from the original rms scatters in quadrature to obtain intrinsic scatter. Through this process, we find that the intrinsic scatters in the correlations are 0.294 dex and 0.446 dex, respectively, suggesting that the scatters in the two quantities are not due to measurement errors.

In Figure 4, we compare the Eddington ratios from Pβ to those from Urrutia et al. (2012). The comparison shows a reasonable agreement between two values with an rms scatter of 0.514 with respect to the one-to-one correlation. However, if the outlier is excluded, the Eddington ratios from Urrutia et al. (2012) are a bit larger than those from Pβ by a factor of 1.85 (0.267 dex).

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In order to characterize the accretion rates of red quasars, we compare the distribution of the Eddington ratios (L_bol/L_Edd, where L_Edd denotes the Eddington luminosity) of red quasars and those of normal type 1 quasars. The median Eddington ratios of the red quasars and the normal type 1 quasars are 0.69 and 0.16, respectively. Moreover, Figures 5 and 6 show that the distributions of the Eddington ratios of the red quasars and the normal type 1 quasars are clearly different, with the red quasars having larger L_bol/L_Edd values than the normal type 1 quasars. In order to quantify how significantly these two distributions differ from each other, we perform the Kolmogorov–Smirnov test (K–S test). For the K–S statistics, the maximum deviation between the cumulative distributions of these two Eddington ratios, D, is 0.71, and the probability of the null hypothesis in which L_bol/L_Edd values of the two samples are drawn from the same distribution, p, is only 9.07 × 10⁻⁸, confirming that the Eddington ratios of the red quasars are clearly skewed toward higher values in comparison to those of the normal type 1 quasars.

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Because Eddington ratios can vary with BH mass, we also show the Eddington ratio distribution of the sample divided into BH mass bins to account for any difference in the Eddington ratio distribution arising from the BH mass effect (e.g., Shen et al. 2011). We divided the red quasars and the normal type 1 quasars into a low-mass ($7.9\lt \mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })\lt 8.5$) and a high-mass ($8.5\lt \mathrm{log}({M}_{\mathrm{BH}}/{M}_{\odot })\lt 9.1$) sample. For the low-mass sample, 9 red quasars and 67 normal type 1 quasars are selected, and their $\mathrm{log}({L}_{\mathrm{bol}}/\mathrm{erg}\;{{\rm{s}}}^{-1})$ values have ranges of 46.19–46.95 and 45.36–46.57 for the red quasars and the normal type 1 quasars, respectively. The D and the p values from a K–S test for these samples are 0.64 and 0.0015, respectively. The high-mass sample includes 7 red quasars and 177 normal type 1 quasars. The $\mathrm{log}({L}_{\mathrm{bol}}/\mathrm{erg}\;{{\rm{s}}}^{-1})$ values range have ranges of 46.35–47.11 and 45.44–47.31 for the red quasars and the normal type 1 quasars, respectively. The D value is 0.61, and the p is 0.0074 between these two distributions. Again, we find that the Eddington ratio distribution of red quasars is significantly different from that of normal type 1 quasars, independent of the BH mass. The Eddington ratio values of red quasars are about 0.6–0.8 dex larger than those of normal type 1 quasars.

There are three potential biases that could affect the result—(i) the uncertainty in E(B − V), (ii) the application of the M_BH estimator that is derived from normal type 1 quasars, and (iii) the omission of four red quasars without Pβ detection in the analysis. We discuss below how much each item could affect the result.

First, the Eddington ratios of the red quasars could be overestimated or underestimated, since the E(B − V) values (Glikman et al. 2007; Urrutia et al. 2012) of the red quasars can vary by as much as ∼0.5, depending on how they are derived. For example, for the case of 1227+5053 of which E(B − V) value is 0.38 (continuum-derived) or −0.23 (Balmer decrement-derived),⁵ the extinction-corrected Pβ luminosity can be over/underestimated by a factor of 1.6 depending on the method for estimating the $E(B-V)$ value. If we adopt an $E(B-V)$ value of −0.23 from the Balmer decrement, the Eddington ratio of 1227+5053 would decrease from 2.87 to 2.26. Note that this is a rather extreme case. Even if we decrease the Eddington ratios of all of 16 red quasars by a factor of 1.6, the median Eddington ratios of red quasars is 0.55, which is still significantly higher than that of normal type 1 quasars of 0.16. Therefore, the uncertainty in the reddening correction does not affect the result about the Eddington ratios of red quasars, and this demonstrates the power of using the NIR emission line in dusty systems, as outlined in the introduction.

Second, the Pβ M_BH estimator that is derived from normal type 1 quasars may not be applicable to red quasars if the BLR physics of red quasars is very different from that of normal type 1 quasars to the extent that the virial M_BH estimator does not hold for red quasars. This is an open question, but we note that our red quasars are moderately obscured quasars for which the BLR is expected to be well-established. Therefore, the characteristics of the BLR physics of red quasars should be very similar to those of normal type 1 quasars.

Third, we omitted four red quasars from our analysis (1106+2812, 1159+2914, 1415+0903, and 1523+0030) because their Pβ lines were not detected with S/N > 5, and this may bias the result. Among the four red quasars, we estimated L5100 and ${\mathrm{FWHM}}_{{\rm{H}}\beta }$ values for 1106+2812, 1415+0903, and 1523+0030 using the optical spectra from Glikman et al. (2006, 2012) and NIR spectra from our IRTF data, but we could not estimate the ${\mathrm{FWHM}}_{{\rm{H}}\beta }$ for 1159+2914 due to low-quality data (S/N < 3). From L5100 and ${\mathrm{FWHM}}_{{\rm{H}}\beta },$ we computed L_bol and M_BH values and the Eddington ratios, and we found the Eddington ratios of 1106+2812, 1415+0903, and 1523+0030 are 0.477, 0.186, and 0.266, respectively. If the Eddington ratios of the three red quasars are included in the Eddington ratio comparison, the D and p values from the K–S test are 0.63 and 4.34 × 10⁻⁷, respectively, which are nearly identical to the result without the three red quasars.

We conclude that red quasars have high accretion rates, with L_bol/L_Edd ≃ 0.69. This Eddington ratio is higher than normal type 1 quasars by a factor of 4–5. These results, although limited by the modest size of the sample used in this study, are consistent with the scenario that red quasars are in the intermediate stage between merger-driven star-forming galaxies and normal type 1 quasars, rather than a scenario in which the red colors of red quasars originate from a viewing angle difference in an AGN unification scheme. Under the merger-driven quasar evolutionary scenario as depicted in Figure 7, the early phase of major mergers drives gas toward the central region of the galaxy due to the loss of the gas' angular momentum through a dissipative, violent merging. This process can fuel the BH activities and a rapid BH growth inside a dust-enshrouded host galaxy (Hopkins et al. 2005, 2008). Such a merger-driven quasar evolutionary scenario also has observational support, especially for luminous quasars (e.g., Hong et al. 2015).

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The duration period of quasar activity is uncertain, with a wide range of possible values of 10⁶–10⁸ years (Martini 2004). Quasars shine at the bolometric luminosity of ${L}_{\mathrm{bol}}=\epsilon \dot{M}{c}^{2},$ where is the radiation efficiency that has a value of ≃ 0.1 for luminous quasars (Martini 2004). Under the Eddington-limited accretion (maximal accretion), BH mass can grow exponentially as $\sim \mathrm{exp}(t/{\tau }_{{\rm{S}}})$, where τ_S is the Salpeter time, ${\tau }_{{\rm{S}}}=4.5\times {10}^{7}(\epsilon /0.1)$ years. If the quasar lifetime is < 10⁷ years, this is less than Salpeter time, and it cannot account for the growth of SMBHs to ${M}_{\mathrm{BH}}\sim {10}^{9}\;{M}_{\odot }$ from a seed BH with ${M}_{\mathrm{BH}}\lt {10}^{6}\;{M}_{\odot }.$ Hence, it has been suggested that SMBHs underwent an extended growth period, including a red quasar phase that can last more than a few ×10⁸ years (Kelly et al. 2010).

We can see if such a growth makes sense by estimating the red quasar duration time from the accretion rate and ${M}_{\mathrm{BH}}$ of our red quasar sample. Since the Eddington ratios are roughly 1 for red quasars, we can propose that the BH mass grows exponentially as $\sim \mathrm{exp}(t/\tau )$ and use the characteristic time τ as a rough estimate of the duration of the red quasar phase. Here, $\dot{M}$ is derived using the relations of ${L}_{\mathrm{bol}}=\epsilon \dot{M}{c}^{2}$ (assuming = 0.1), and τ = M_BH/$\dot{M}$.

The derived $\dot{M}$ and τ values are listed in Table 2, and we find that τ values range from 10⁷ to 2 × 10⁸ years, or ∼7 × 10⁷ years on average. We see from Figure 8 that the average BH mass of normal type 1 quasars is a few times larger than that of red quasars. To grow the BH mass this much during the red quasar phase, we need only one to two Salpeter time, which supports the use of τ values as estimates of the duration of the red quasar phase.

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Our estimate of the red quasar duration time is ∼10 times larger than the value presented in Glikman et al. (2012). The estimate in Glikman et al. (2012) relies on the fraction of red quasars to normal type 1 quasars (∼20%) and assumes a duration time of 10⁷ years for normal type 1 quasars. The difference can be reconciled if we adopt a duration time of ∼10⁸ years for normal type 1 quasars as found in Kelly et al. (2010) and Cao (2010). Since the Eddington ratios of normal type 1 quasars are ×5 times lower than those of red quasars, the growth rate of BH masses in normal type 1 quasars is much lower than red quasars and the long duration time does not lead to the over-growth of BH mass. Alternatively, we can reconcile the two results if ≪ 0.1 during the red quasar phase.