A Systematic Analysis of Stellar Populations in the Host Galaxies of SDSS Type I QSOs

We used the spectral analysis code STARLIGHT (Cid Fernandes et al. 2005) to study the stellar population of host galaxies in our working sample. This code searches for the linear combination of N_* Simple Stellar Populations (SSP) from evolutionary synthesis models for a best match of the observed spectrum O_λ. The model M_λ is given by

$$\begin{eqnarray*}&&{M}_{\lambda }={M}_{{\lambda }_{0}}\left({\sum }_{j=1}^{{N}_{* }}{x}_{j}{b}_{j,\lambda }{r}_{\lambda }\right)\otimes G({v}_{\star },{\sigma }_{\star }),\end{eqnarray*}$$

where b_j,λ is the normalized flux of the jth SSP at λ₀, ${r}_{\lambda }\equiv {10}^{-0.4({A}_{\lambda }-{A}_{{\lambda }_{0}})}$ is the reddening term, ${M}_{{\lambda }_{0}}$ is the synthetic flux at the normalization wavelength, x_j is the population vector, and ⨂  denotes the convolution operator and G is a Gaussian filter centered at velocity v_⋆ and with dispersion σ_⋆. This method carries out the fitting with a mixture of simulated annealing plus a Metropolis scheme and Markov Chain Monte Carlo techniques to yield the minimum χ² value (${\chi }^{2}\,={\sum }_{\lambda }[({O}_{\lambda }-{M}_{\lambda }){\omega }_{\lambda }]$, where M_λ is the model spectrum and ${{\omega }_{\lambda }}^{-1}$ is the error in O_λ at each wavelength bin). The χ²/N_λ that we used in Section 3.1.2. is the fit χ² divided by the number of λ's used in the fit.

3.1.1. Preliminary Fitting

First, we used STARLIGHT to fit the integrated spectra for all sources in the parent sample to get the luminosity ratio between the stellar population and AGNs. STARLIGHT is a smarter and faster way of fitting a spectrum and it allows us to contain a power law. We use SSP models from Bruzual & Charlot (2003, BC03; with N_⋆ = 150 spectra with 6 metallicities ranging from 0.0001 to 0.05, and 25 different ages, ranging from 1 Myr to 18 Gyr). The reason why we chose BC03 is that it has a wide range of metallicities and it is also widely used in the literature, which allowed us to directly compare comparison our results and previous works. Furthermore, the BC03 is the base model for STARLIGHT, so it is convenient to use them together. Though the BC03 has a new version (CB07, Charlot & Bruzual 2007) that includes the new stellar evolution prescription for the TP-AGB evolution., Zibetti et al. (2013) showed that the BC03 model is still the most successful at reproducing the stellar population of host galaxies. We also add a power-law spectrum ${F}_{\lambda }\propto {\lambda }^{{\alpha }_{\lambda }}$ that represents the contribution of AGN featureless continua for preliminary fitting. The power-law spectra index α is −2, which is a traditional value for type 1 QSOs (Vanden Berk et al. 2001; Letawe et al. 2007; Shen et al. 2011). The Calzetti laws (Calzetti et al. 2000) were used for the reddening during the fitting. We corrected for Galactic extinction using the Schlegel et al. (1998) maps and extinction curves from Fitzpatrick (1999). The input spectra to STARLIGHT contain four columns: the wavelength (λ), the flux (O_λ), the error of flux (e_λ), and the flag_λ, which signals whether a pixel is good or bad. All these features of input spectra are available from SDSS data release 12.

Figure 2 shows the results of the STARLIGHT fitting: panel (a) is about a normal QSO from the control sample and panel (b) represents the objects of the working sample. Figure 2(a) shows that most QSOs are dominated by AGNs (the luminosity fraction of AGNs is almost 100%), which can be described by a power law and shows few stellar features in its spectrum.

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In order to achieve a sample of QSOs with significant stellar components, we calculate the S/Ns of host galaxies by

$$\begin{eqnarray*}&&{({\rm{S}}/{\rm{N}})}_{\mathrm{stellar}}={({\rm{S}}/{\rm{N}})}_{\mathrm{SDSS}}\cdot \sqrt{1-\eta },\end{eqnarray*}$$

where η is the luminosity ratio between the AGN and the (AGN+host) from STARLIGHT fitting; and (S/N)_stellar is the signal-to-noise ratio of host galaxy. We require that the (S/N)_stellar be greater than 15, and the subsample of our sources contains total 82 objects. Figure 2(b) shows an example in the working sample that is dominated by a stellar population with significant stellar features in its spectrum, such as Ca_IIK λ3933, Ca_IIH λ3968, and Balmer absorption lines.

3.1.2. Formal Fitting and Stellar Populations

To make our results more reliable, we calculate the best-fit metallicity and power-law index by using the method proposed by Meng et al. (2010). We adopted a wide range of AGN power-law slopes α_λ over the optical and UV range from −3.0 to 0 (no power-law fitting with α_λ = 0) at intervals of 0.5 to search for the best power-law index. To search for the best-fit metallicity, we carried out a metallicity test with six metallicities (Z = 0.0001, 0.0004, 0.004, 0.008, 0.02, 0.05) of the BC03 model for each power-law index. Figure 3 shows the test fitting results for one example object with a different power-law index α_λ and six metallicities. We evaluate the fitting quality by the minimum χ²/N_λ, which was suggested by Cid Fernandes et al. (2005). We averaged it over 100 times by fitting with different seeds (which are the random numbers that need to be appointed during the STARLIGHT fitting).

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As for the given metallicity and power-law index, there is a total of 100 fitting results. Though differences occur, the random seeds will not change the overall population distribution, and a ∼10% variation can be added to the individual component x_j (Meng et al. 2010). In order to get a statistically reliable result, as the best fitting we selected fitting results with minimal χ²/N_λ values (if available) or those with mean values over 100 . Figure 4 shows the distributions of luminosity fractions of AGN (frac_AGN) and χ²/N_λ for two objects in our working sample: we adopt the minimal and mean values in the left and right panels, respectively. In addition to the χ²/N_λ value, we also use the adev vale as an indicator of the quality of fit. The adev gives the percentage mean $| {O}_{\lambda }-{M}_{\lambda }| /{O}_{\lambda }$ deviation over all fitted pixels. Figure 5 shows the distribution of the χ²/N_λ value (Panel a) and adev (Panel b). Most sources have reliable fitting results with χ²/N_λ ∼ 1. Of these sources, 22% (18/82) have χ²/N_λ ≥ 1.3. We find that the main reason accounting for this high χ²/N_λ value is related the fact that some high frac_AGN objects are more difficult to fit because of lower stellar content. We have compared the main results from the data that contained these 18 objects and the data that do not contain these objects and found that there is no bias between them. So we keep these 18 objects in our work. The adev value distribution is shown in Figure 5(b) and presents adev values ≲6% for all objects, indicating that the model reproduces the observed underlying spectra very well.

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We calculate the luminosity of the stellar component from the UV to the optical over the past ∼1 Gyr by reconstructing the UV-to-optical spectrum. Detailed descriptions of these calculations can be found in Meng et al. (2010) and are briefly described below.

Because the 3'' diameter fiber does not cover the whole galaxy, aperture corrections (Meng et al. 2010) are necessary. It is known that the luminosity of the galaxy is dominated by young stellar populations and the AGN, which can both be better traced by the u band, so we adopt the aperture correction for the stellar component at the u band derived from

$$\begin{eqnarray*}&&A=\tfrac{{L}_{\star \mathrm{Petro}}}{L\star \mathrm{fiber}}=\tfrac{{10}^{-0.4({m}_{\mathrm{petro}}-{m}_{\mathrm{AGN}})-1}}{{10}^{-0.4({m}_{\mathrm{fiber}}-{m}_{\mathrm{AGN}})-1}}.\end{eqnarray*}$$

We rebuild the rest-frame model spectrum ${F}_{i}(\lambda ,t)$ of the stellar components with the UV-to-optical wavelength coverage (912 ∼ 9000 Å) corrected for extinction by

$$\begin{eqnarray*}&&{F}_{i}(\lambda ,t)=\mathrm{Mcor}\_\mathrm{tot}{\sum }_{j=1}^{N}\tfrac{{\mu }_{j}}{{f}_{\star ,j,{t}_{0}}}{f}_{\star ,j,t}{B}_{\lambda ,j,t},\end{eqnarray*}$$

where ${F}_{i}(\lambda ,t)$ is the stellar spectrum (corrected for extinction) at a given time t. t can be the time in the past or at the present (equal t₀). Mcor_tot is present stellar mass obtained from the spectral synthesis after aperture correction, μ_j is the mass-weighted fraction, ${B}_{\lambda ,j,t}$ are BC03 SSP templates without normalization, ${f}_{\star ,j,{t}_{0}}$ is the present (t₀) fraction of remaining stellar mass to the initial mass of population j, and ${f}_{\star ,j,t}$ is such a fraction at a given time t. We estimate the UV-to-optical luminosity of the past 25, 100, 290, 500, and 900 Myr separately.

We calculate the UV-to-optical luminosity history of the host galaxies by

$$\begin{eqnarray*}&&{L}_{\mathrm{UV}\_\mathrm{Optical},t}={\int }_{912}^{9000}[{F}_{i}(\lambda ,t)]d\lambda .\end{eqnarray*}$$

To test the feasibility of our method, we also reconstructed the spectrum in present time (t₀) by adding the dust extinction and double-index power. The formula is

$$\begin{eqnarray*}&&{F}_{0}(\lambda ,{t}_{0})=[{L}_{\mathrm{UV}\_\mathrm{Optical},0}+{F}_{p}(\lambda )]\times {10}^{-0.4({A}_{\lambda }-{A}_{V})},\end{eqnarray*}$$

where ${F}_{p}(\lambda )$ is a double power-law spectrum of AGN. The spectral indexes we used here are given by α = −1 for λ < 1250 Å (Hatziminaoglou et al. 2008) and α is given by starlight for λ > 1250 Å. The A_V is obtained from the spectral synthesis. Figure 6 shows the reconstructed model spectrum (red solid line) superimposed onto the observed one (green solid line). This model spectrum is used as ${F}_{0}(\lambda ,{t}_{0})$.

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We give a simple classification of our working sample based on the SFH (${L}_{\mathrm{UV}\_\mathrm{Optical},t}$) of the host galaxy. In summary, these SFHs have two main features: one is a dramatically enhanced star formation about 900 Myr ago, and a moderate one recently (within 500 Myr). Since their prototypes are unknown, we focus on these two features and attempt to classify our source according to their SFHs in our work. We classify our working sample into four types:

• (1)  
  typeO: do not have obvious star formation activity in the past 900 Myr. The star formation activity in these objects could have taken place 1 Gyr ago. There is a total of 16 sources of this type.
• (2)  
  typeA: only have moderate star formation activity within 500 Myr. There is a total 20 sources of this type.
• (3)  
  typeB: only have dramatically enhanced star formation activity about 900 Myr ago. There is a total of 11 sources of this type.
• (4)  
  typeAB: have both two main features of SFHs (a dramatically enhanced one and a moderate one). There is a total of 35 sources of this type.

Figure 7 shows the mean star formation histories of these four different types (dark line), which are added with individual objects (gray lines) for corresponding classes.

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In order to characterize the spectrum-to-spectrum differences for these four SFH types, we make combine each type by normalizing each individual spectrum at 5100 Å and then computing the average value of F_λ in bins of λ.

Figure 8 shows the composite spectra of the working source sample. We divide the spectrum into two panels. In panel (a) we compare the composite spectrum of the sources in the working sample (blue solid line) with those of other sample. For example, we plot the QSO spectra from Shang et al. (2011), which presented the SEDs of 85 optically bright, non-blazar QSOs (27 radio-quiet and 58 radio-loud) from radio to X-ray wavelengths. The purple solid line represents the radio-loud QSOs and the purple dashed line represents the radio-quiet QSOs. We also show other spectra in Figure 8: the black solid line represents the control sample, the orange solid line represents the PSQ from Cales et al. (2011), the dark green solid line represents the Mrk 231 spectra (IR-QSOs, Moustakas & Kennicutt 2006), the dark red solid line represents the Arp 220 spectra (ULIRGs, Moustakas & Kennicutt 2006), and the cyan blue solid line represents the M82 spectra (SB galaxy, Kennicutt 1992). When compared to the control sample, the spectra of the working sample are more luminous in the red (wavelengths longer than 5100 Å) and are close to the PSQs, indicating that the sources in the working sample have significant contributions from stellar content, and this conclusion is consistent with the results of Cales & Brotherton (2015) that PSQs are overall red compared to typical QSOs' colors, with a significant contribution from a post-starburst stellar population. It is clear from panel (a) in Figure 8 that the slopes of the spectra of the sources in the working sample are intermediate between those of IR-QSOs and QSOs, which implies that our objects could be in an evolutionary stage between that of IR-QSOs and typical optical QSOs.

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Panel (b) of Figure 8 gives a comparison for our four types. The black, blue, red, and green spectra represent typeO, typeA, typeB, and typeAB, respectively. The typeA and typeAB spectra have significant Balmer absorption lines, such as Hδ, along with steeper continuum in the blue, which may be attributed to a young stellar population or AGN activity. Considering that there is no significant high AGN fraction (see later in Section 4.2) in typeA and typeAB, we suggest that the steeper continuum in the blue is the result of a young stellar population. The typeO spectra have an even steeper continuum in the blue. It has invisible Balmer absorption lines and a significant high AGN fraction, which means that AGN emission is the major contributor for this type. The continua of typeB are much flatter and the Ca_IIK λ3933, Ca_IIH λ3968 absorption lines are also obvious, which suggests the continua this type are hosted in galaxies with significant contributions from older stellar content and are not dominated by AGNs.

As discussed in Cid Fernandes et al. (2004), individual stellar population components are very uncertain because the existence of multiple solutions in stellar populations and the further binning of the ages will give a coarse but more robust description of the SFH. We separate the stellar population into three components as suggested by Cid Fernandes et al. (2004): "young" (X_Y, t ≤ 1.0 × 10⁸ years), "intermediate" (X_I, 1.6 × 1.0⁸ years ≤ t ≤ 1.27 × 10⁹ years), and "old" (X_O, t ≥ 1.43 × 10⁹ years). The diversity among these four types objects is shown in Figure 9, where we present a trigonometric coordinate system as follows: X_Y + X_I + X_O = 1 panel. It is clear that the typeO (black dot) is dominated by an old age stellar population, while typeA (blue dot) is dominated by young stars. typeB (red dot) have a major contribution from intermediate populations and typeAB (green dot) have a mixed contribution from both young and intermediate stellar population,s which is consistent with the results of composite spectra. To be more clear, we depict the same result in the form of histograms (for each stellar population). The black, blue, red, and green histograms in each figure represent typeO, typeA, typeB, and typeAB, respectively.

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WISE has provided the data in the near- and mid-infrared. Stern et al. (2012) presented a simple mid-IR color criterion ($W1-W2$ ≥ 0.8) to identify AGNs. Figure 10 shows the distribution of $W1-W2\ \mathrm{versus}\ W2-W3$ for our 82 objects and the control sample. The median values of each type are also represented by different symbols (typeO: black star, typeA: blue triangle, typeB: red square, typeAB: green open circle). As expected, most objects in the control sample have W1 − W2 ≥ 0.8 (dark red solid line), while some objects of our working sample have W1 − W2 bluer than 0.8. Stern et al. (2012) showed that a bluer W1 − W2 is caused by host galaxy contamination in $z\lt 2$. Additionally, the dark green dotted–dashed line illustrates the selection of AGNs using W1, W2, and W3 (Mateos et al. 2012). Unsurprisingly, the sources in our working sample lie around the AGN boundary, with redder W2 − W3 and bluer W1 − W2. We performed a Kolmogorov–Smirnov (KS) test between the working sample and control sample (Table 2). The results show that the probabilities that the working sample and the control sample are drawn from the same distribution are ${P}_{\mathrm{KS}}\ll 0.001$. The composite AGN/galaxy SED provided by Mateos et al. (2012) also suggested that the blend with host galaxy will lead to objects that lie outside of the AGN wedge. Moreover, their work also showed that galaxies with old stellar content have W2 − W3 colors that are bluer than that of star formation, which is consistent with our results: the W2 − W3 colors of typeO and typeB tend to be bluer than typeA and typeAB in the color–color diagram. So we conduct a KS-test between typeO+typeB and typeA+typeAB in W23 and the resulting probability, ${P}_{\mathrm{KS}}\ll 0.001$, suggests that come from different distributions.

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The [N ii]/Hα versus [O iii]/Hβ diagnostic diagram (BPT diagram) is commonly used to separate star formation from AGN activity (Baldwin et al. 1981; Veilleux & Osterbrock 1987). The AGN sequence branches from the enriched end of the star-forming sequence and moves toward larger [N_II]/H_α and [O_III]/H_β ratios as the AGN fraction increases. Wu et al. (2007) defined a quantity d_AGN that measures the distances of galaxies from the Kewley et al. (2001) theoretical upper bound of pure star formation, along lines parallel to the AGN sequence. Davies et al. (2014) also calculated relative AGN fractions by populating the composite region of the BPT diagram with a starburst-AGN mixing model. With the help of the equivalent width of narrow emission lines from Shen et al. (2011), we plot our working sample in the BPT diagram (Figure 11). We observe a starburst-AGN mixing sequence of the working sample (except typeO) exclusively occupying the region with high frac_AGN.

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The tight correlation between the BH and the bulge within which it resides (${M}_{\mathrm{BH}}\ \mathrm{versus}\ {M}_{\mathrm{bulge}}$, ${L}_{\mathrm{BH}}\ \mathrm{versus}\ {L}_{\mathrm{bulge}}$, ${M}_{\mathrm{BH}}\ \mathrm{versus}\ {\sigma }_{\mathrm{bulge}}$) reveals a close connection between BHs and their host galaxies. Heckman et al. (2004) found that most present-day accretion occurs onto BH with masses less than 10⁸ M_⊙ and young stellar populations. In a study of (sub)millimeter-loud QSOs, Hao et al. (2008) found a trend in which the star formation rate increases with the accretion rate. They also found that the star formation rate decreases with the central BH mass and suggested that the higher Eddington ratios of IR-QSOs imply that they are in the evolution stage toward QSOs. Heckman et al. (2004) found similar results, namely that at low redshifts, more massive galaxies tend to have older stellar populations.

Shen et al. (2011) presented a compilation of properties of the SDSS DR7 quasar catalog. In this product, they compiled continuum and emission measurements, as well as other quantities such as virial BH mass and Eddington ratio estimates. With the help of these quasar properties, the expected correlations between AGN properties and stellar populations are indeed found.

Panel (a) of Figure 12 shows a strong correlation between BH mass and Eddington ratio (M_BH increases as L/L_Edd decreases) for the sources of the working sample and control sample (gray dot). By applying the Pearson test, the statistical significance of these two variables is 0.001 and the correlation coefficient is 0.998, which means these two variables are related. Our results indicate that the low-mass BHs are more active than massive ones. In contrast, the more massive BHs are currently experiencing less additional accretion. The blue triangle, red square, green open circle and black star in Figure 12 denote the median values of typeA, typeB, typeAB, and typeO, respectively. By comparing these median values, we find that the QSOs with previous star formation activities (typeA, typeB and typeAB) tend to have high Eddington ratios (stronger BH activity), statistically. Alternatively, the QSOs that have both previous and recent star formation (typeAB) tend to have stronger AGN activity, while typeO, which has no obvious star formation activity in the past, is inactive. Generally speaking, there may be a correlation between star formation and BH activity, which may imply a coevolution between the SFH of host galaxies and AGN activity. The KS-tests of both M_BH and L/L_Edd show that the working sample and the control sample are drawn from different distributions, with P_KS ≪ 0.001. We also use the KS-test to test the significant difference between M_BH and L/L_Edd among these four types and the results are shown in Figures 13(a) and (b), respectively. The number next to the braces gives the P_KS of these two types. Considered alongside with Figure 12, we can see that if the difference between the median values of two types is greater, then the difference significance between these two types will also be greater (with small P_KS). The P_KS between typeAB (most active among the four types) and typeO (most inactive among the four types) shows that these two types are drawn from different distributions both in M_BH and L/L_Edd.

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Panel (b) of Figure 12 shows a relationship between BH mass and the luminosity of the working sample. We quantify the Eddington and BH masses by calculating their mean values and standard errors (SE) for all four types and the control sample (Table 3). Compared with the control QSOs, our working sample seems to have lower Eddington ratios, as well as lower luminosities, which may be the result of selection effects (the high-luminosity QSOs tend to have more powerful AGNs and may overwhelm the lights of their host galaxies). The KS-test of luminosity shows that the working sample and the control sample are drawn from different distributions, with P_KS ≪ 0.001

The exact morphologies of the galaxies hosting QSOs is a longstanding discussion. To study the host galaxy morphology properties and their interactions, we use images from the SDSS. The main challenge for understanding the host galaxy is the poor spatial resolution of the ground-based observations, which, when combined with the bright nuclei, hindered the nature of the QSO hosts. We just classify our sources into two types: Y(30) with obvious interactivity, which was represented by the red triangle in Figure 14 and N (14), which do not show any tidal features and no companions (black squares). The remaining 38 sources are hard to classify using SDSS images. It is interesting that the host galaxies without interactions exclusively have high BH masses and tend to be typeO and typeB (9/14). This result may indicate that objects without recent star formation and high BH mass may have already relaxed from the interactivation and evolved into quiescent ellipse galaxies.

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Sanders et al. (1988) suggested a evolutionary sequence from ULIRGs to QSOs. Hao et al. (2005) and Cao et al. (2008) also proposed that at last some IR-QSOs are at a transitional stage from ULIRGs to classical QSOs. The work of Treister et al. (2012) showed that most luminous AGNs (QSOs, M_R ≤ −22) seem to be triggered by major mergers. If so, the composite spectra of the working sample will be consistent with the idea that they are hybrids of AGNs and starbursts (or post-starbust). We compared different spectra in Figure 8. As we can see in panel (a), the spectra of QSOs from Shang et al. (2011; both radio-quiet and radio-loud) are brighter at wavelengths shorter than 5100 Å and even much brighter than the control sample. This may be because most objects selected from Shang et al. (2011) are UV-bright-AGNs. The ULIRGs have roughly similar SED to the starburst galaxies, while IR-QSOs are brighter at shorter wavelengths, which is consistent with the evolutionary paths mentioned before. Additionally, the spectra of our working sample are close to the PSQs from Cales et al. (2011), which means they have similar frac_AGN or are even at similar evolution stage. Cale et al. (2011) showed that the PSQs have a starburst within 100 Myr that is smaller than our age range. Combined with the analysis in Section 4.1, our objects may be in an evolutionary stage between IR-QSOs and typical optical QSOs.

In a former analysis, we found a compelling correlation between the starbursts (both former dramatically enhanced and recent moderate star formation) and AGN properties. Considering the typical QSO's lifetime is expected to be ∼10⁸ years, the dramatically enhanced star formation could not have been triggered at the same time, as it occurred few hundred Myr ago. However, there are some theories that can explain the correlation between BH activity and former star formation (Canalizo & Stockton 2000; Walter et al. 2002; Hutchings et al. 2003; Granato et al. 2004; Hopkins et al. 2006; Letawe et al. 2007; Cox et al. 2008; Hopkins 2012).

Previous works suggested that starbursts may occur at the early stage of a merger or interaction, when the AGN has not been triggered yet, which is then followed by a decrease in the accretion of AGNs with the aging of stellar content (Canalizo & Stockton 2000; Granato et al. 2004; Hopkins et al. 2006). Hopkins (2012) showed that such a time delay can occur for purely dynamical reasons. His simulations showed first that the gas moves toward the center and gives rise to star formation. Then, the gas flows further inward by losing angular momentum and producing a time delay between star formation and AGN activity. Furthermore, many numerical simulations show that the star formation and AGN activity are episodic (Hopkins et al. 2008; Torrey et al. 2012; Van Wassenhove et al. 2012), which depends on the detail of the merger (orbits, morphological types of progenitors). In this scenario, the former dramatically enhanced star formation of QSO hosts in the working sample is induced in the early stages of galaxies merger. As the galaxies continue to merge for the next few hundred Myr, the gas flows further inward toward central regions, followed by AGN activity. The recent moderate star formation in our working sample may have been triggered by a minor merger due to the accretion of a satellite (Cox et al. 2008). Many previous works (Walter et al. 2002; Hutchings et al. 2003; Letawe et al. 2007) have suggested that minor mergers do not produce dramatically enhanced star formation, while still fueling the AGNs. Our result is consistent with the former work, in that there is a time delay between star formation and AGN activity, and that the star formation and AGN activity are episodic. Davies et al. (2007) analyzed the star formation in the nuclei of nine Seyfert galaxies, which showed possible starbursts in the last 10–300 Myr. In the work of Schawinski et al. (2009), the AGNs (obscured and unobscured) appeared to be prevalent in the "green valley" on the color–magnitude diagram. They suggested that there is a 100 Myr time delay between the shutdown of star formation and detectable AGNs. The research of Heckman et al. (2004) also used type II AGNs to investigate the accretion-driven growth of super-massive BHs and found that bulge formation and BH formation are tightly coupled in the present-day. The studies of Santini et al. (2012) and Floyd et al. (2013) showed higher SFRs for AGN host galaxies than forinactive galaxies with the similar stellar masses and redshifts.