THE SLOAN DIGITAL SKY SURVEY REVERBERATION MAPPING PROJECT: POST-STARBURST SIGNATURES IN QUASAR HOST GALAXIES AT z < 1

We aim to extract host-galaxy information from the observed spectra with as little ambiguity as possible. This is a challenge, since different combinations of quasar and stellar spectral models give rise to similar total spectra at UV-to-optical wavelengths. For the present analysis, we choose the rest-frame spectral window from λ = 3700 to 5400 Å, which includes a wealth of stellar absorption features as well as important nebular lines such as [O ii] λ3727, Hβ, and [O iii] $\lambda \lambda 4959$, 5007. We devise a method to apply a series of spectral fits to the data in such a way that degeneracies between model components are minimized. The following models are used to represent the relevant emission components, namely, the quasar accretion disk, gas in the broad line region (BLR), narrow line region (NLR), and interstellar medium (ISM), and stars in the host galaxy.

• 1.  
  Accretion disk: the emission from the quasar accretion disk can be represented by a single power-law continuum (${f}_{\lambda }\propto {\lambda }^{{\alpha }_{\mathrm{pl}}}$) in our spectral window, with the amplitude and slope being free parameters. Previous observations have found slopes spanning the range of $-2.5\lt {\alpha }_{\mathrm{pl}}\lt 0.0$, with a typical value of ${\alpha }_{\mathrm{pl}}\simeq -1.5$ (Richstone & Schmidt 1980; Francis 1996; Vanden Berk et al. 2001; Ivezić et al. 2002; Pentericci et al. 2003).
• 2.  
  Gas in the BLR, NLR, and ISM:

  • (a)  
    $3700\;\mathring{\rm A} \lt \lambda \lt 4450\;\mathring{\rm A}$: numerous high-order Balmer lines and metal lines as well as the Balmer continuum make up a pseudo-continuum in this spectral region. It is modeled by subtracting the power-law contribution from the SDSS quasar composite spectrum provided by Shen et al. (2011). We take the composite of the highest-luminosity bin (${L}_{5100}={10}^{45.5}$ erg s⁻¹) so that the host contamination is minimized; Shen et al. (2011) report that the contamination at $\lambda =5100$ Å is negligible in a quasar with ${L}_{5100}\gt {10}^{45.0}$ erg s⁻¹. The power-law contribution is determined in two continuum windows (in which strong emission lines are absent) at λ = 4200–4230 and 5470–5500 Å. This pseudo-continuum template also includes individual BLR, NLR, and ISM lines present in the original composite spectrum, although the ISM contribution should be minimal at this highest quasar luminosity. We consider seven additional narrow lines or line complexes, namely, [O ii] λ3727, [Fe vii] λ3760, [Ne iii] λ3870, He i + H8 λ3890, [Ne iii] λ3969, Hδ, and Hγ, to fit the ISM lines. They are each modeled with Gaussian profiles sharing the same velocity dispersion (${\sigma }_{{\rm{g}}}$) and velocity offset relative to the object's formal redshift (${v}_{{\rm{g}}}^{\mathrm{off}}$), both of which are free parameters.
  • (b)  
    $4450\;\mathring{\rm A} \lt \lambda \lt 5400\;\mathring{\rm A}$: the dominant contributors to this spectral region are the Fe ii pseudo-continuum, Hβ, and [O iii] λ4959, λ5007 lines. We use the empirical Fe ii template of Véron-Cetty et al. (2004) created from an observed spectrum of I Zw 1, a prototype narrow-line Seyfert 1 galaxy (e.g., Osterbrock & Pogge 1985). This template is velocity-broadened with a Gaussian kernel with ${\sigma }_{\mathrm{Fe}{\rm{II}}}=1,500$ km s⁻¹; we test a different value of ${\sigma }_{\mathrm{Fe}{\rm{II}}}$ later. Hβ is modeled with three Gaussian emission profiles with variable amplitudes, widths, and velocity offsets, while the two [O iii] lines are each modeled with two Gaussians. The widths of these lines are varied independently from those of the above ISM lines. We assume that the two [O iii] lines have the theoretical intensity ratio λ5007/λ4959 = 3.0 and that the two lines share the same profile (i.e., widths and velocity offsets).
• 3.  
  Stars: we use simple stellar population (SSP) models of Maraston & Strömbäck (2011) to represent the stellar emission. SSP is a single generation of stars formed in an instantaneous starburst; it is the simplest assumption for a stellar population and is suitable for the present analysis, in which the dominant quasar light makes it difficult to exploit full details of the stellar properties. We test more complicated stellar population models in Section 3.3. For SSP models, we adopt the STELIB (Le Borgne et al. 2003) stellar spectral library, the Chabrier (2003) initial mass function (IMF), and solar metallicity. Stellar age (t_*) takes values from 30 Myr to the age of the universe at the redshift of each object. The SSP spectra are velocity broadened in accordance with the stellar velocity dispersion (${\sigma }_{*}$) and the instrumental resolution¹¹ assumed to be ${\sigma }_{\mathrm{inst}}=65$ km s⁻¹, and offset in wavelength by ${v}_{*}^{\mathrm{off}}$ relative to the object's redshift; both ${\sigma }_{*}$ and ${v}_{*}^{\mathrm{off}}$ are free parameters. The amplitude of the SSP model determines the stellar mass ${M}_{*}.$ We test different choices of stellar library, IMF, and metallicity in Section 4.

Our default models do not incorporate the effect of dust extinction. In fact, the amount of extinction observed in optically selected broad-line quasars is usually quite small (Richards et al. 2003; Hopkins et al. 2004; Salvato et al. 2009; Matute et al. 2012) and its effect is limited. Recently, Krawczyk et al. (2014) investigated a large sample of SDSS broad-line quasars and found that the vast majority are consistent with ${E}_{B-V}\lt 0.1\;\mathrm{mag}$. Here we assume no dust extinction for both quasar nuclei and host galaxies, and later confirm that non-zero ${E}_{B-V}$ values have little impact on our qualitative conclusions. We note that there are dust-reddened broad-line quasars that can be identified in the near-infrared, although their surface density is much lower than that of optically selected quasars (e.g., Glikman et al. 2012). Urrutia et al. (2008) presented an enhanced merger fraction in dust-reddened quasars, hence their host stellar properties may be quite different from those of normal optically selected quasars.

We perform a series of spectral fits rather than fitting all the model components simultaneously. First, we determine the stellar age t_* by fitting the spectrum over the rest-frame wavelength range λ = 3700–4050 Å with the quasar power-law slope fixed to ${\alpha }_{\mathrm{pl}}=-1.5$. This spectral window is chosen because (i) a wealth of strong stellar absorption features are present, including the Ca HK lines and the 4000 Å break; (ii) the quasar emission is relatively featureless; and (iii) the precise value of ${\alpha }_{\mathrm{pl}}$ is not important, since the flux ratio between the two edges of the window (${f}_{4050}/{f}_{3700}$) changes only by ∼10% when ${\alpha }_{\mathrm{pl}}$ varies from $-1.5$ to the extreme values of 0.0 or $-2.5$. Second, the wider spectral range of $\lambda =3700$–4750 Å and 5050–5400 Å (i.e., the full 3700–5400 Å spectral window excluding the Hβ region) is fit by varying all parameters but ${t}_{*}$, which is fixed to the value determined above. We then return to the first step and update t_* with the latest ${\alpha }_{\mathrm{pl}}.$ These two steps are iterated until t_* converges, but in most cases the convergence occurs with no more than two iterations. Finally, we subtract the best-fit model from the full spectrum and fit the residual with the Hβ and [O iii] line models in the range λ = 4750–5050 Å.

We apply the above algorithm to all the 191 SDSS-RM quasars found at $z\lt 1;$ our spectral window (λ = 3700–5400 Å) is shifted beyond the spectrograph coverage at higher redshifts. The standard ${\chi }^{2}$ method is used for the model fitting with the IDL routine MPFIT (Markwardt 2009). As described above, the pixel flux errors were taken from the BOSS spectroscopic pipeline and propagated appropriately through the co-addition process. Figure 2 shows four typical examples of the decomposition results. While the spectra are usually dominated by quasar light, most of the small-scale features are fit by the stellar models. The median reduced ${\chi }^{2}$ of the fits over the whole spectral window is about five; as seen in Figure 2, this rather large value is caused by the systematic discrepancy at certain wavelengths between the observed spectra and the models, the latter being not complex enough to provide perfect fits to every emission and absorption feature across the spectrum. The uncertainties in the best-fit parameters are estimated following the Monte Carlo method outlined in Shen et al. (2011). We create 50 mock spectra by adding random noise to the original spectrum, using the Gaussian probability density function (PDF) with the standard deviation equal to the flux error at each pixel, and process them through the decomposition algorithm. The measurement errors are evaluated from the 68% central intervals of the parameter distributions of the 50 trials. We add additional 20% error to the derived stellar age, which accounts for the minimum uncertainty arising from non-continuous coverage of ages in the SSP models. We perform further assessment of possible systematic uncertainties in the next section.

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Figure 3 presents the histogram of the fractional contribution of the stellar component to the total flux (f_*) measured at λ = 4000 Å in the rest frame. We exclude the 31 objects with ${f}_{*}\lt 0.1$ from the following analysis; we will demonstrate in the next section that their host results are unreliable. An additional four objects are excluded because they have particularly large statistical uncertainties in the host stellar mass, Δlog$({M}_{*}/{M}_{\odot })\gt 0.5\;\mathrm{dex}$. These excluded objects tend to have high quasar luminosities, as shown in Figure 1. Our final sample consists of the remaining 156 quasars, more than 80% of the initial 191 objects. The median redshift and absolute magnitude of the 156 quasars are $\langle z\rangle =0.72$ and $\langle {M}_{i}\rangle =-22.2\;\mathrm{mag}$, respectively.

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We focus on six physical quantities in this work, namely, stellar age ${t}_{*}$, stellar mass ${M}_{*}$, SFR, stellar velocity dispersion ${\sigma }_{*}$, [O iii] λ5007 luminosity ${L}_{[{\rm{O}}{\rm{III}}]}$, and SMBH mass ${M}_{\bullet }$. The parameters ${t}_{*},$ ${M}_{*},$ ${\sigma }_{*},$ and ${L}_{[{\rm{O}}{\rm{III}}]}$ are taken directly from the decomposition results. Since the quantity ${\sigma }_{*}$ is poorly constrained in many cases, its measurement is rejected if the best-fit value lies outside the physically plausible range ($10\lt {\sigma }_{*}\lt 400$ km s⁻¹) or smaller than three times the estimated statistical error. SFRs are estimated from the [O ii] λ3727 luminosity. As shown in Figure 2, the [O ii] line is comprised of two components, i.e., the quasar BLR/NLR template and the host ISM line with Gaussian profile. The former contribution is tied to the overall amplitude of the BLR/NLR template, which is fit over the full spectral window. We use the luminosity of the latter ISM component (${L}_{[{\rm{O}}{\rm{II}}]}^{\prime }$) for SFR estimates, assuming the Kennicutt (1998) calibration:

$$\begin{eqnarray}&&\mathrm{SFR}\ ({M}_{\odot }\ {\mathrm{yr}}^{-1})\ =\ (1.4\pm 0.4)\times {10}^{-41}\ {L}_{[{\rm{O}}{\rm{II}}]}^{\prime }\ ({\mathrm{erg}\ {\rm{s}}}^{-1}).\end{eqnarray} \tag{ 1 }$$

Since the NLR usually contributes only weakly to this low-ionization line, it may be a good tracer of star formation in quasar host galaxies even without spectral decomposition (Ho 2005). On the other hand, Kim et al. (2006) found that the [O ii]/[O iii] ratios observed in SDSS AGNs at $z\lt 0.3$ are fully consistent with AGN photoionization, hence there is no need to invoke any additional [O ii] source such as star formation. Although the mean quasar contribution is properly subtracted with the BLR/NLR template in this work, we conservatively treat the derived SFRs as rough estimates only, given that our single BLR/NLR template cannot trace object-to-object variation of the [O ii] strength. Another concern is the effect of dust extinction, which we discuss later.

SMBH masses are estimated with the single-epoch virial estimator (Vestergaard & Peterson 2006):

$$\begin{eqnarray}\mathrm{log}\left(\displaystyle \frac{{M}_{\mathrm{BH}}}{{M}_{\odot }}\right)\ & = & \ \mathrm{log}\left({\left[\displaystyle \frac{\mathrm{FWHM}\ ({\rm{H}}\beta )}{1000\ \mathrm{km}\ {{\rm{s}}}^{-1}}\right]}^{2}{\left[\displaystyle \frac{\lambda {L}_{\lambda }(5100\ \mathring{\rm A} )}{{10}^{44}\ \mathrm{erg}\ {{\rm{s}}}^{-1}}\right]}^{0.5}\right)\\ & & +(6.91\pm 0.02).\end{eqnarray} \tag{ 2 }$$

It is believed that this Hβ-based estimator is more reliable than other single-epoch estimators, such as those based on Civ λ1549 or Mg ii λ 2800 (Shen & Liu 2012; Shen 2013). In some cases our Hβ models apparently fit the underlying continuum residuals rather than the line itself, especially when the S/N around Hβ is low. The ${M}_{\bullet }$ measurements were rejected for 16 such fits identified by visual inspection. We will eventually obtain more precise SMBH masses for all the objects with RM analysis.

The limited aperture size of the BOSS spectrograph fibers does not include all the light from the extended hosts. The fiber diameter of 2'' corresponds to approximately 14 kpc at the median redshift of our sample (z = 0.72). We correct the stellar mass, derived from the decomposed galaxy flux (${f}_{{\rm{g}}}^{\mathrm{fiber}}$), for the aperture loss as follows. Since the spectrophotometry of the BOSS spectroscopic pipeline is tied to the PSF magnitude of standard stars, the quasar flux decomposed from each spectrum (${f}_{{\rm{q}}}$) should correctly represent the total flux of the unresolved quasar nucleus. The SDSS imaging pipeline measures the total nuclear plus host flux (${f}_{\mathrm{tot}}$) with the cModel algorithm (Abazajian et al. 2004), which fits galaxy models to the observed image profile. Therefore, the total host flux (${f}_{{\rm{g}}}$) is given by ${f}_{{\rm{g}}}={f}_{\mathrm{tot}}-{f}_{{\rm{q}}}$. Multiplying the stellar mass of each source measured from the spectra by the ratio ${f}_{{\rm{g}}}/{f}_{{\rm{g}}}^{\mathrm{fiber}}$ provides a crude estimate of the total stellar mass, with the implicit assumptions that the mass-to-luminosity ratio in the fiber represents that in the whole galaxy and that quasar variability between the epochs of imaging (before 2005) and spectroscopic (2014) observations does not introduce a significant bias. This aperture correction is calculated in the observed-frame r band. The correction is not applied to the SFRs, since broadband magnitudes are a poor tracer of the spatial extent of the [O ii] line emission. When we later discuss the relation between SFR and stellar mass, we use the stellar mass within the fiber (${M}_{*}^{\mathrm{fiber}}$; the stellar mass before the aperture correction) so that the two quantities refer to the same central part of the galaxies. Therefore, the present analysis does not map SFR and its relation to stellar mass to extended regions of the galaxies outside the fibers.

Here the reliability of the present method is evaluated with Monte Carlo simulations. We generate 1000 mock spectra by combining spectral models of quasar accretion disk, gas in the BLR, NLR, ISM, and host stellar population, as described in Section 3.1, with realistic PDFs for the parameter values. The power-law slope ${\alpha }_{\mathrm{pl}}$ is assumed to follow a Gaussian PDF with mean $-1.5$ and standard deviation 0.3, which approximately reproduces past measurements (Ivezić et al. 2002; Pentericci et al. 2003). The SSP age is randomly drawn from 14 logarithmically spaced values between ${t}_{*}=30$ Myr and 10 Gyr, while the stellar mass is distributed uniformly on a logarithmic scale between log(${M}_{*}/{M}_{\odot }$) = 9 and 12. The ratio between the mean amplitudes of the stellar model and the quasar power law is assumed to follow a logarithmically uniform PDF between 0.01 and 10.0. The stellar velocity dispersion is drawn from a logarithmically uniform PDF between 50 and 400 km s⁻¹. All other model parameters are assumed to follow the Gaussian PDFs best describing the distributions derived in our own measurements. For each of the mock spectra, we randomly select a SDSS-RM quasar at $z\lt 1$ and apply its redshift and pixel flux errors to mimic a real spectrum.

These mock spectra are processed through the decomposition algorithm used for the real data. Figure 4 presents the comparisons between the intrinsic (input) and measured (output) parameter values. The stellar age and mass show relatively large scatter, reflecting the ambiguity in decomposing the nuclear and stellar components from the observed spectra. The scatter is significant at ${t}_{*}^{0}\lesssim 0.1\;\mathrm{Gyr}$ (the superscript "0" represents the input parameter), where the relatively blue spectra of young stars are difficult to distinguish from those of quasar nuclei. These degeneracies result in overestimated ages up to ${t}_{*}\sim 0.5\;\mathrm{Gyr}$, hence we conservatively regard measured stellar ages at ${t}_{*}\leqslant 0.5\;\mathrm{Gyr}$ as upper limits (although we find only few such cases in the real quasars; see below). At larger ages, most of the scatter is caused by spectra with ${f}_{*}\lt 0.1$ or Δ log ${M}_{*}\;\gt$ 0.5 dex. When these simulated quasars are eliminated, as we did for the real sample, all six parameters are constrained within a scatter of roughly 0.15 dex; the actual rms scatter of each parameter is reported in each panel of the figure. Figure 4 also reports for each parameter the fraction (${f}_{\mathrm{id}}$) of the simulated spectra whose output value is consistent with the input (i.e., the ordinate value is consistent with zero) within 1σ statistical error. The fraction for ${\sigma }_{*}$ is low, due to the systematic overestimation of this parameter at small ${\sigma }_{*}^{0}$ where the measurement is most difficult. For the other five parameters, ${f}_{\mathrm{id}}$ are somewhat smaller than but roughly comparable to the expected 68%.

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We also perform a set of simulations that replace the input SSP models with composite stellar population (CSP) models with exponentially declining star formation history. CSP spectra are calculated as

$$\begin{eqnarray}&&{f}_{\lambda }({t}_{*}^{\mathrm{CSP}})={\displaystyle \int }_{0}^{{t}_{*}^{\mathrm{CSP}}}\psi ({t}_{*}^{\mathrm{CSP}}-t){f}_{\lambda }^{\mathrm{SSP}}(t){dt};\psi (t)={e}^{-t/\tau },\end{eqnarray} \tag{ 3 }$$

where ${t}_{*}^{\mathrm{CSP}}$ is the time since the onset of star formation (i.e., the maximum CSP age), $\psi (t)$ is the star formation history with the exponentially declining timescale τ, and ${f}_{\lambda }^{\mathrm{SSP}}(t)$ is an SSP spectrum. We create 1000 mock spectra by combining these CSP models with other emission components as above, and process them through the decomposition algorithm (which uses the SSP models to represent stellar spectra). The results are shown in Figure 5 for stellar age and mass; the other parameters are less sensitive to the choice of star formation history. The decomposition is unreliable for input ${t}_{*}^{\mathrm{CSP}}\lesssim 0.1\;\mathrm{Gyr}$, which is similar to the situation described above. At larger ${t}_{*}^{\mathrm{CSP}},$ the output SSP age is consistent with ${t}_{*}^{\mathrm{CSP}}$ when τ is less than a few 100 Myr, while the former becomes systematically small at larger τ due to the prolonged star formation. There is little systematic offset between the output SSP mass and the input CSP mass, the latter being the mass accumulated during the whole star formation history.

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Finally, we compare our measurements of ${M}_{\bullet }$ and ${\sigma }_{*}$ with the previous measurements by Shen et al. (2015b), who investigated the ${M}_{\bullet }-{\sigma }_{*}$ relation of the SDSS-RM quasars at $z\lt 1$ using the same co-added spectra as in this work. They performed spectral decomposition with the principal component analysis (PCA) method following Vanden Berk et al. (2006). The PCA method has the advantage of being highly efficient in reproducing observed spectra with an optimal number of empirical eigenspectra, but the interpretation of the reconstructed spectra is usually not straightforward. The SMBH masses were derived with the Vestergaard & Peterson (2006) estimator as in this work, while the stellar velocity dispersion was measured with the vdispfit routine in the idlspec2d package and with the penalized pixel-fitting code (Cappellari & Emsellem 2004) in the spectral window λ = 4125–5350 Å. Figure 6 compares the ${M}_{\bullet }$ and ${\sigma }_{*}$ values measured by the two studies. They are in good agreement with each other, although there is a slight systematic offset in ${\sigma }_{*};$ our measurements give ∼10 km s⁻¹ larger values than those of Shen et al. (2015b) on average. The rms scatter around this offset is ∼40 km s⁻¹, while the typical measurement error is ∼15 km s⁻¹ in the both studies.¹² Our decomposition procedure is not optimized for the ${\sigma }_{*}$ measurements, since the spectral resolution of the adopted stellar library ($\sigma \sim 80$ km s⁻¹) is not sufficiently high for this analysis; we chose this library since it covers the whole of our spectral window with a wide range of stellar parameters, which is crucial for a detailed study of the decomposed stellar emission. In contrast, the emphasis is on the most reliable ${\sigma }_{*}$ measurements in Shen et al. (2015b), who used two dedicated routines adopting spectral libraries with high resolution ($\sigma \leqslant 25$ km s⁻¹). Our fitting procedure also includes Ca H and K lines, which tend to overestimate ${\sigma }_{*}$ (Kormendy & Illingworth 1982; Bernardi et al. 2003; Greene & Ho 2006).

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Before discussing the results, we first compare our measurements with those of Matsuoka et al. (2014a). They studied host galaxies of SDSS broad-line quasars at $z\lt 0.6$ with the imaging decomposition technique (see Section 1), which uses completely different data and methods from those in the present analysis. The two studies share no common objects. We calculated the host colors of the present sample by convolving the decomposed galaxy spectra (in the rest frame; they are extrapolated to $\lambda \lt 3700\;\mathring{\rm A} ,$ i.e., outside our fitting window, with the best-fit stellar models) with the SDSS filter transmissions and created the CMD as shown in Figure 11. As a reference, we also plot the distribution of inactive galaxies at $0.5\lt z\lt 1.0$ taken from the COSMOS/UltraVISTA K-band selected catalog (Muzzin et al. 2013); the rest-frame $u-r$ colors were calculated with the best-fit spectral model of each object given in the catalog. The two measurements of the quasar hosts broadly agree in distributions of stellar mass and color, demonstrating that the quasars are preferentially hosted by massive galaxies distributed from the massive tip of the blue cloud to the red sequence. The median stellar age of the present sample, ${t}_{*}\sim 1\;\mathrm{Gyr},$ corresponds to the gap of the bimodal color distribution of inactive galaxies. It is intriguing that the quasars occupy the colors centered on this gap, where star-forming galaxies may be rapidly transitioning to the quiescent phase due to the quenching of star formation. The stellar masses of the quasar hosts (${M}_{*}\sim {10}^{11}\;{M}_{\odot }$) broadly agree with the turnover mass of the local galaxy mass function at the high-mass end (e.g., Bell et al. 2003). Galaxy growth is significantly suppressed above this mass (Peng et al. 2010), for which quasar activity may be playing an important role.

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Figure 12 displays the relation between SFRs and stellar masses within the spectroscopic fibers,¹⁴ along with the so-called "main sequence" of star-forming galaxies (e.g., Brinchmann et al. 2004; Daddi et al. 2007; Elbaz et al. 2007, 2011; Noeske et al. 2007; Steinhardt et al. 2014). The ratio between these two quantities defines specific SFR, which is not very sensitive to the dust extinction in the present analysis as discussed in Section 4. The majority of the quasar hosts fall below the main sequence at z = 1, i.e., their star formation efficiencies are considerably lower than those of normal star-forming galaxies at similar redshifts. On the other hand, SFRs measured in host galaxies of dust-obscured, X-ray-selected AGNs at similar redshifts tend to be higher than estimated here and trace the main sequence of star-forming galaxies (Mullaney et al. 2012; Santini et al. 2012). However, Mullaney et al. (2015) demonstrated recently that these SFR estimates are biased toward higher values due to bright outliers in stacking analysis of infrared data, and that the actual SFR distribution of obscured AGNs is broader than, and has ∼0.4 dex lower peak of, that of main-sequence galaxies. These findings are broadly consistent with our results for broad-line quasars presented in Figure 12. The decreased specific SFRs were also reported recently by Shimizu et al. (2015), based on the Herschel far-infrared measurements of X-ray AGNs selected from the Swift Burst Alert Telescope catalog.

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The intermediate stellar ages and relatively low SFRs of the present sample suggest that the quasar hosts are linked to post-starburst populations. Since the first discovery by Dressler & Gunn (1983), post-starburst galaxies have been recognized as an important stage of galaxy evolution. They are characterized by the presence of strong Balmer absorption lines and the absence of emission lines, which are commonly interpreted as evidence for starburst activity within the past ∼1 Gyr, which was quenched abruptly (e.g., Quintero et al. 2004; Goto 2005). The cause of this quenching is still unknown, but the present study indicates that the formation of at least some of post-starburst galaxies is related to the nuclear activity. Quasars detected in post-starburst galaxies (e.g., Brotherton et al. 1999, 2002) may represent the relevant phase. In the Hopkins et al. (2006) merger-driven co-evolution model, a galaxy experiences various transition phases after a gas-rich merger, including a luminous infrared galaxy phase with intense star formation and dust production, an obscured AGN/quasar phase with activated central SMBHs, and an unobscured AGN/quasar phase before settling into a quiescent early-type galaxy. Our results point to the link between quasar hosts and post-starburst galaxies, suggesting that merger-induced starbursts are largely quenched before the dust obscuring the nuclear region is cleared away and the central quasar becomes optically visible. Recently Pattarakijwanich et al. (2014) estimated the number density of post-starburst galaxies to be roughly 10⁻⁶ Mpc⁻³ mag⁻¹ for ${M}_{5000}\gt -20$ mag at $0\lt z\lesssim 1$, where M₅₀₀₀ is the absolute magnitude at rest-frame 5000 Å. This value is roughly comparable to the number density of broad-line quasars at similar redshifts and luminosities (Richards et al. 2006; Croom et al. 2009). Kauffmann et al. (2003) noted that the strong Hδ absorption observed in low-z ($z\sim 0.05$) SDSS narrow-line AGNs indicates they experienced a burst of star formation that ended within the past ∼1 Gyr. Yesuf et al. (2014) demonstrated that the AGN fraction is three times higher in post-starburst galaxies than in inactive galaxies. However, they also reported that the (obscured) AGN phase is delayed by a few 100 Myr relative to post-starburst phase, and hence cannot play a primary role in the quenching of starbursts.

There have been a number of studies comparing the color and mass distributions of AGN host galaxies with those of inactive galaxies (e.g., Nandra et al. 2007; Salim et al. 2007; Hickox et al. 2009; Schawinski et al. 2010). Recent work suggests that, using proper mass-limited samples, the AGN fraction is constant as a function of host color, or may be enhanced in blue star-forming galaxies (e.g., Silverman et al. 2009; Aird et al. 2012; Hainline et al. 2012; Rosario et al. 2013). Luminous AGNs are preferentially found in massive host galaxies, which is perhaps due to the presence of massive SMBHs at the centers and/or of large reservoirs of gas in such galaxies. Most of these studies are based on obscured AGNs selected via their X-ray luminosity or optical narrow emission lines. Our work (Figure 11) suggests that broad-line quasar hosts prevail in the color range $1.5\lt u-r\lt 2.5$ above masses of log$({M}_{*}/{M}_{\odot })\sim 10.5$ and that the quasar fraction increases toward bluer colors, a trend that continues to the end of the galaxy color distribution at $u-r\lt 1.5.$ In order to show this trend more clearly, we create a mass-matched sample of inactive galaxies; for each of the quasar hosts, the galaxy with the closest mass and redshift are drawn from the COSMOS/UltraVISTA K-band selected catalog. Figure 13 compares the histograms of the rest-frame ($u-r$) colors of the two samples. The quasar host distribution is shifted toward bluer colors than that of mass-matched inactive galaxies, demonstrating that bluer galaxies are more likely to host quasars.

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Meanwhile, a drawback of the present analysis is the lack of far-infrared information and hence the dust-absorbed part of star formation. Although a galaxy-wide dust screen is unlikely to be present (see Section 4), the present work cannot trace localized star-forming regions hidden by dust at UV-to-optical wavelengths. Such regions can be mapped reliably only with far-infrared observations, which we will exploit in future work. Our analysis is also limited to within the spectroscopic fibers, whose 2'' diameter corresponds to approximately 14 kpc at the median redshift of the sample (see Section 3.2). If the majority of the star formation took place at outside this aperture, then our results would become inconsistent with the past studies that measured the entire host galaxies.

Our analysis provides both stellar velocity dispersions and masses as well as SMBH masses, which allows us to investigate the scaling relations between them. Figure 14 presents the ${M}_{\bullet }-{\sigma }_{*}$ and ${M}_{\bullet }-{M}_{*}$ relations of the present sample. We calculate the linear regression lines with the IDL routine MPFITEXY, taking into account errors in both variables, as

$$\begin{eqnarray}\mathrm{log}\left(\displaystyle \frac{{M}_{\bullet }}{{10}^{8}\;{M}_{\odot }}\right) & = & (0.43\pm 0.05)\\ & & +(1.64\pm 0.29)\ \mathrm{log}\left(\displaystyle \frac{{\sigma }_{*}}{200\ \mathrm{km}\ {{\rm{s}}}^{-1}}\right),\end{eqnarray} \tag{ 5 }$$

and

$$\begin{eqnarray}\mathrm{log}\left(\displaystyle \frac{{M}_{\bullet }}{{10}^{8}\;{M}_{\odot }}\right) & = & (0.21\pm 0.04)\\ & & +(0.36\pm 0.08)\ \mathrm{log}\left(\displaystyle \frac{{M}_{*}}{{10}^{11}\;{M}_{\odot }}\right).\end{eqnarray} \tag{ 6 }$$

The intrinsic scatters are 0.39 and 0.44 dex for the ${M}_{\bullet }-{\sigma }_{*}$ and ${M}_{\bullet }-{M}_{*}$ relations, respectively. The ${M}_{\bullet }-{\sigma }_{*}$ relation is almost identical to that of Shen et al. (2015b, see Section 3.3), which is not surprising given the consistent measurements of the two quantities (Figure 6). Our sample shows no evolution of the mean ${M}_{\bullet }/$ ${\sigma }_{*}$ ratio from the local universe, while the slope of the relation appears to flatten toward high redshifts. This flattening was also reported by Shen et al. (2015b) and was interpreted as a result of a selection bias; with simple simulations, they concluded that a non-evolving ${M}_{\bullet }-{\sigma }_{*}$ relation is favored at $z\lt 1.$

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We also found similar trends in the ${M}_{\bullet }-{M}_{*}$ relation. Our M_* estimates include a galaxy disk component if it is present, hence they should be regarded as the upper limits of the bulge masses (${M}_{*,\ \mathrm{bulge}}$). A similar comparison between the ${M}_{\bullet }-{M}_{*}$ relation at $z\sim 1.4$ and the local ${M}_{\bullet }-{M}_{*,\ \mathrm{bulge}}$ relation was presented by Jahnke et al. (2009), who found no significant difference between the two. Since their sample shows evidence for substantial disk components, the authors concluded that bulges have grown predominantly via redistribution of the disk mass since z = 1.4 to the present epoch. This conclusion was supported by Sun et al. (2015) with a larger sample at similar redshifts and with a careful assessment of selection biases. Our results are consistent with these findings, but we have no estimate of disk contribution to M_* and cannot provide direct support for the above scenario. The present ${M}_{\bullet }-{M}_{*}$ relation is also similar to that of Matsuoka et al. (2014a), who reported that the relation is offset toward large ${M}_{\bullet }$ compared to the local relation at fixed ${M}_{*}.$ This result is likely due to the shallow slope of the relation, producing systematically large ${M}_{\bullet }/$M_* ratios at ${M}_{*}\lesssim {10}^{11}\;{M}_{\odot }.$

The present spectral decomposition analysis is made possible due to the low-to-moderate luminosities of the quasars, with relative stellar contribution ${f}_{*}\gt 0.1$ measured at $\lambda =4000\;\mathring{\rm A} ,$ and the high S/N of the spectra. Meeting both conditions usually requires significant telescope resources; in this work, we have exploited the co-added SDSS-RM spectra whose net exposure times amount to 65 hr per object. As we demonstrated in the previous sections, clear detection of stellar absorption features allows for reliable extraction of the host components from the observed spectra. In this section, we give a rough guideline for estimating whether the present analysis is applicable to a given spectrum.

The first requirement is a certain fraction (${f}_{*}\gtrsim 0.1$) of host galaxy light in the total spectrum. This fraction can be estimated roughly from the depths of the stellar absorption lines. Figure 15 presents the stellar fraction f_* as a function of EW (Ca K), the rest-frame equivalent width of the Ca K absorption line. Ca K is one of the strongest stellar absorption features in a quasar spectrum at UV-to-optical wavelengths, while Ca H is less visible due to the superposed [Ne iii] λ3969 emission. We measure EW (Ca K) in the wavelength range λ = 3920–3955 Å, with the blue and red continuum levels defined at λ = 3880–3920 Å and λ = 3990–4030 Å, respectively. Figure 15 indicates that EW (Ca K) and f_* are moderately correlated. The majority of the quasars with EW (Ca K) ≳ 2 Å have more than 10% of the light at 4000 Å from the host, and stellar emission is the major contributor to a quasar spectrum on average when one observes EW (Ca K) ≳ 6 Å.

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The second requirement is high S/N. We test the minimum S/N required to perform a reliable decomposition analysis by artificially degrading the SDSS-RM data and determining how the derived uncertainties change as the S/N decreases. We take the original high-S/N spectra with successful decomposition and add noise, assuming a Gaussian PDF with standard deviations of 2, 4, 8, or 16 times the original pixel errors. These mock spectra are processed through the decomposition algorithm. We omit the calibration errors in Equations (1) and (2) in these simulations to view the effect of decreasing S/N directly. Figure 16 displays the resultant uncertainties in the six physical quantities as a function of the S/N per pixel measured at λ = 4000 Å. These plots can be used to infer the required S/N to achieve the desired accuracy in one of the parameters; for example, a rough estimate of stellar mass (Δlog ${M}_{*}\lt 0.5\;\mathrm{dex}$) is possible at S/N ∼3 on average, while stellar age is poorly constrained (${\rm{\Delta }}{t}_{*}/{t}_{*}\sim 1$) at that S/N. All six parameters are moderately well constrained at S/N > 10, where the actual SDSS-RM quasars are located.

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