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

We investigate the relationship between host galaxies' stellar content and active galactic nuclei (AGN) for optically selected QSOs with z$<$0.5. There are total 82 QSOs we select from Sloan Digital Sky Survey (SDSS) . These 82 QSOs both have Wide-field Infrared Survey Explorer (WISE) data and measurable stellar content. With the help of the stellar population synthesis code STARLIGHT, we determine the luminosity fraction of AGN ,stellar population ages and star-formation history (SFH) of host galaxies. We find out there is a correlation between the star formation history and AGN property which suggests a possible delay from star formation to AGN. This probably indicates that the AGN activity correlate with the star formation activity which consistent with a co-evolution scheme for black hole and host galaxies.


Introduction
The connection between active galactic nuclei (AGN) and starburst (SB) activity in galaxies have been proposed for a long time, going back to the first discovery of Ultraluminous Infrared Galaxies (ULIRGs) . Many effort has been made to drive out what is the dominant energy output mechanism (Rieke & Low 1972;Rieke & Lebofsky 1979;Zou et al. 1991). More and more works have provided evidence that ULIRGs are powerd by a mixture of SB and AGN (Toomre & Toomre 1972;Toomre 1977; telescope (Gunn et al. 2006) to image the sky in five broad bands (u, g, r, i, z). The QSOs candidates were selected based on their colors (Richards et al. 2002) and then observed with fiber-fed double spectrographs with 3 diameter fiber which result in getting more emission from host galaxies. . SDSS DR7 quasars catalog contains 105,785 QSOs. In this study, we used the reduced one-dimensional spectral data derived from SDSS DR12 pipeline-processed. The spectra have a wavelength coverage of 3800-9200Å at a spectral resolution R ∼ 1500-2500.
In order to have a better understanding on the infrared properties of our sources, we built a parent sample by matching SDSS objects with the Wide-field Infrared Survey Explorer (WISE) in 3 radius. The survey of WISE covers 95% of sky at 3.4 (W1), 4.6 (W2), 12 (W3), 22 (W4) µm with an angular resolution of 6.1 , 6.4 , 6.5 and 12.0 in four bands, achieving, 5σ point source sensitivities better than 0.08, 0.11, 1, and 6 mJy, respectively. We also set the upper limit of the redshift range to z < 0.5 for two reason: 1) to reject the higher redshift QSOs because they have more luminous AGN which will dilutes the stellar feature; 2) this redshift range allows the spectral to covering the absorption line needed for ST ARLIGHT analysis. In summary, the parent sample was built as follows: 1. z < 0.5, 2. (S/N ) W ISE of W1, W2, W3 and W4 > 3,

(S/N ) SDSS ≥ 15,
where the (S/N ) W ISE represents the signal-to-noise ratio of photometry in WISE bands and the (S/N ) SDSS is the signal-to-noise ratio of the SDSS spectra. There are total 8490 objects in our parent sample and Figure 1 shows the redshift distribution (red solid line).
Then, we selected the working sample from the parent sample by adding this criterion: where the (S/N ) stellar is the S/N of stellar composition which were calculated by using synthesis code ST ARLIGHT and the detail of it will be given in section3.1.1.
Since the type I QSOs provide great observational challenge owing to their overwhelming brightness of the AGN with respect to the host galaxy, we use above criterion to ensure that all object in the sample have obvious stellar content. At last, there are total 82 objects in the working sample. Table 1 shows some observational properties of the sources in the working sample. Figure 1 shows the redshift distribution of these source (blue diagonal).
The decrease of number of the sources in the working sample in high redshift (only one higher than 0.3) may result from the selection effect that brighter AGNs are more easy to be observed in high redshift and the host galaxy is overwhelmed by these brighter AGN.
We also extracted from the parent sample a control sample of QSOs which don't have obvious stellar content. The control sample meeting this criteria: (S/N ) stellar < 15.
We also limit the redshift of our control sample to z < 0.3. The final control sample is composed of 2183 objects. Figure 1 shows the redshift distribution of the parent sample (red solid line), the working sample (blued diagonal) and the control smaple (gray filled), respectively. We normalize them to 1.0 as peak of each.
We have to emphasize that the selection method used in this work is different from those preceding ones: 1) This work focuses on the stellar content of type I QSOs which are brighter than M i = −22 mag. In contrast, many works foucused on low-luminosity type II AGNs (Kauffmann et al. 2003;Yesuf et al. 2014;Davies et al. 2007;Kauffmann et al. 2003;Tadhunter et al. 2005;York et al. 2000;Heckman et al. 2004). 2) We attempt to study the stellar population of QSOs host which contain the central region of galaxies while some other's work avoid QSOs contamination by off-axis observation (the spectra are obtained with the slit of the spectrograph located a few arcseconds away from the quasar) (Nolan et al. 2001;Canalizo & Stockton 2013). 3) We don't limit our working sample exclusive to QSOs host with moderate-age stellar population (PSQs), as done by some authors Cales et al. 2013;Wei et al. 2013).

Spetral Synthesis with Starlight
We used the spectral analysis code ST ARLIGHT (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 matches of observed spectrum O λ . The models M λ is given by: where b j,λ is the normalized flux of the jth SSP at λ 0 , r λ ≡ 10 −0.4(A λ −A λ 0 ) is the reddening term, M λ 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 Metropolis scheme and Markov Chain Monte Carlo techniques to yield the where M λ is the model spectrum and ω λ −1 is the error in O λ at each wavelength bin). The χ 2 /N λ which we used in Section3.1.2. is the fit χ 2 divided by the number of λ's used in the fit.

Preliminary Fitting
Firstly, we used ST ARLIGHT to fit the integrated spectra for all sources in the parent sample to get the luminosity ratio between the stellar population and AGN. The ST ARLIGHT is a smarter and fast way of fitting a spectrum and it allows us to contain a power-law. We use SSPs models from Bruzual & Charlot (2003, BC03) (2007)) which includes the new stellar evolution prescription for the TP-AGB evolution., the work (Zibetti et al. 2013) shown that the BC03 model is still the most successful in reproducing the stellar population of host galaxies. We also add a power-law spectrum F λ ∝ λ α λ which represent the contribution of AGN featureless continuum for preliminary fitting. The power-law spectra index α is -2 which is a traditional value of type 1 QSOs Vanden Berk et al. 2001;Shen et al. 2011). The Calzetti law (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 ST ARLIGHT contain 4 columns: the wavelength (λ), the flux (O λ ), the error of flux (e λ ) and the f lag λ which signals if that pixcel is good or bad. All these message of input spectrum are get from SDSS data release 12.  Figure 2 (a) shows that most QSOs are dominated by AGN (the luminosity fraction of AGN is almost 100%) which can described by a power-law and shows little stellar feature in its spectrum.
In order to gain a sample of QSOs with significant stellar component, we calculate the S/N of host galaxy by where η is the luminosity ratio between the AGN and (AGN+host) getting from ST ARLIGHT fitting; The (S/N ) stellar is the signal-to-noise ratio of host galaxy. We require the (S/N ) stellar greater than 15 and the subsample of our sources is total 82 objects.

Formal Fitting and Stellar Populations
To make the result more reliable, we get the best-fit metallicity and power-law index by using method proposed by Meng et al. (2010). We adopted a wide range of AGN power-law slop 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 carry 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 different power-law index α λ and six metallicities. We evaluate the fitting quality by the minimum χ 2 /N λ which is suggested by Cid Fernandes et al. (2005). We averaged it over 100 times fitting with different seed (the random number that need to be appointed during the ST ARLIGHT fitting).
As for the given metallicity and power law index, there are total 100 fitting results.
Though difference result from random seeds will not change the overall population distribution, a ∼ 10% variation may added to the individual component x j (Meng et al. 2010). In order to get a statistically reliable result, we selected the fitting result of minimal χ 2 /N λ value (if we have) or mean value over 100 fitting as the best fitting. Figure 4 shows the distribution of luminosity fraction of AGN (f rac AGN ) and χ 2 /N λ for two objects in our working sample: we adopt the minimal and mean value in left and right panel, respectively.
Besides the χ 2 /N λ value, we also use the adev vale as an indicator of the quality of fit. The adev gives the percentage mean |O λ − M λ |/O λ deviation over all fitted pixels. The Figure 5 shows the distribution of χ 2 /N λ value (Panel.a) and adev (Panel.b). Most of sources has a reliable fitting result with χ 2 /N λ ∼ 1. There are 22% (18/82) sources have χ 2 /N λ ≥ 1.3 . We find that the main reason accounting for this high χ 2 /N λ value is related to the fact that some high f rac AGN objects are more difficult to fit because of lower stellar content.
We have compare the main result getting 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 valus distribution is shown in Figure 5 (b) and presents values adev 6 per cent for all objects, indicating that the model reproduces very well the observed underlying spectra.

Classification with SFH
We calculate the luminosity of the stellar component from UV to optical during the past ∼ 1Gyr by reconstructing the UV-to-Optical spectrum. The detailed descriptions of calculation can be found in Meng et al. (2010) and we briefly described the method here.
Because the 3 diameter fiber does not cover the whole galaxy, a 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 stellar component at the u band derived from We rebuild the rest-frame model spectrum F i (λ, t) of stellar with whole UV-to-Optical wavelengths coverage (912 ∼ 9000Å) corrected for extinction by where F i (λ, 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 t 0 ). M cor tot is present stellar mass obtained from the spectral synthesis after aperture correction, µ j is mass-weighted fraction, B λ,j,t are BC03 SSP templates without normalization, f ,j,t 0 is the present (t 0 ) fraction of remaining stellar mass to the initial mass of population j, f ,j,t is such 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 To test the feasibility of our method, we also reconstructed the spectrum in present time (t 0 ) by adding the dust extinction and double-index power. The formula is where F p (λ) is a double power-law spectrum of AGN. The spectral indexes we used here are given by α = −1 for λ < 1250Å (Hatziminaoglou et al. 2008) and α given by starlight for λ > 1250Å. The A V is obtained from the spectral synthesis. Figure ?? shows the reconstructed model spectrum (red solid line) superimposed by the observed one (green solid line). This model spectrum is used as F 0 (λ, t 0 ).
At last, we give a simple classification of our working sample based on the SFH (L U V Optical,t ) of the host galaxy. In summary, there are two main features of these SFH: one is a dramatically enhanced star formation about 900 Myr ago, and moderate one recently (with in 500 Myr). Since their prototypes are unknown, we focus on these two features and attempt to classify our source according to their SFH in our work. At last, we classify our working sample into 4 types: (1)typeO : Don't have obvious star formation activity in the past 900 Myr. The star formation activity in this objects could took place 1 Gyr ago. There are total 16 sources in this type.
(2)typeA : Only have moderate star formation activity within 500Myr. There are total 20 sources in this type; (3)typeB : Only have dramatically enhanced star formation activity about 900 Myr ago. There are total 11 sources in this type; (4)typeAB : Have both two main feature of SFH ( dramatically enhanced one and moderate one). There are total 35 sources in this type. Figure 7 shows the mean star formation histories of these four different type (dark line) which is added with individual objects ( gray lines ) for corresponding classes.

Composite Spectra
In order to characterize the spectrum-to-spectrum difference for these four SFH types, we make a combination for each type by normalizing each individual spectrum at 5100Å and then computing the average value of F λ in bins of λ. Figure 8 shows the composites spectral of sources sample in the working . For more explicit, we divide the spectrum into two panels. In the panel (a), we compare composite spectrum of the souses in the working sample (blue solid line) with those of others. For example, we plot the QSOs spectra from Shang et al. (2011), which presented the SEDs of 85 optically bright, non-blazar QSOs (27 radio-quiet and 58 radio-loud) over the wavelength from radio to X-ray. The purple solid line represents the radio-loud QSOs and the purple dashed line represents the radio-quiet QSOs. Additionally, we also show the spectra of others in Figure

AGN Luminosity Fraction and WISE Color
The 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 AGN. Figure 10 shows the distribution of W 1 − W 2 vs W 2 − W 3 for our 82 objects and the control sample.
The median value of each type are also represented by different symbols (typeO: black star, typeA: blue taiangle, typeB: red square, typeAB: green open circle). As expected, most 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 < 2. Additionally, the dark green dot-dashed line illustrates the selection of AGN using W1, W2 and W3 (Mateos et al. 2012). Not surprisingly, the sources in our working sample lie around AGN boundary with redder W2-W3 and bluer W1-W2. We give a Kolmogorov-Smirnov (KS) test between the working sample and control sample ( Table 2). The result shows that the probabilities that the working sample and the control sample are drawn from the same distribution are P KS 0.001. The composite AGN/galaxy SED provided by Mateos et al. (2012) also suggested that the blend with host galaxy will lead the objects lie out the AGN wedge.
Moreover, their work also show that the galaxy with old stellar content has W2-W3 color bluer than that of star-formation, which is consistent with our result: the W2-W3 color of typeO and typeB tend to be bluer than typeA and typeAB in color-color diagram. So we give a KS-test between typeO + typeB and typeA + typeAB in W23 and the resulting probability, P KS 0.001, suggests that they are come from different distribution.  Figure 11). We observe a starburst-AGN mixing sequence of the working sample except typeO exclusively occupy the region with high f rac AGN .

Correlation with AGN Properties
The tight correlation between the black hole and the bulge within which it resides (M BH vs M bulge , L BH vs L bulge , M BH vs σ bulge ) reveals a close connection between black holes and their host galaxies. Heckman et al. (2004) found that in the most present-day accretion occurs onto black hole with masses less than 10 8 M and young stellar population.
In the study of (sub)mm-loud QSOs, Hao et al. (2008) found a trend that the star formation rate increases with the accretion rate. They also found the star formation rate decrease with the central black hole 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 the similar result, at low redshift more massive galaxies tend to have older stellar population.

Shen et al. (2011) presented a compilation of properties of SDSS DR7 quasar catalog.
In this product, they compiled continuum and emission measurements, as well as other quantities such as virial black hole mass and Eddington ratio estimates. With the help of these quasar properties, the expected correlations between AGN properties and stellar population are indeed found.
Panel (a) of Figure 12 shows a strong correlation between black hole mass and Eddington ratio (M BH increases as L/L Edd decreases) for the sources the working sample and control sample (gray dot). By applying the Pearson test, the statistical significance of this two variables is 0.001 and the correlation coefficient is 0.998, which means this two variables are related. Our result indicate that the low-mass black holes are more active than massive ones. In contrast, the more massive black holes are currently experiencing less additional accretion. The blue triangle, red square, green open circle and black star in Figure 12 denote the median value of typeA, typeB, typeAB and typeO, respectively.
By comparing these median value, we find that the QSOs with previous star formation activity (typeA, typeB and typeAB) tend to have high Eddington ratio (stronger black hole active), statistically. Alternatively, the QSOs which have both former and recent star formation (typeAB) tend to have stronger AGN activity, while the typeO which have no obvious star formation activity in the past are the inactive ones. Generally speaking, there may be correlation between the star formation and black hole activity, which may imply a co-evolution between SFH of host galaxies and AGN activity. The KS-test of both M BH and L/L Edd show that the working sample and the control sample are draw from the different distribution with P KS 0.001. We also use the KS-test to test the significant difference of M BH and L/L Edd among these four types and the result are shown in Figure 13 (a) and (b), respectively. The number next to the braces gives the P KS of this two types. Combining with Figure 12, we can see that if the different between the median value of two types is greater, then the difference significance between these two type will also be greater (with small P KS ). The P KS between typeAB (most active among four type) and typeO (most inactive among four type) show that this two type are draw from the different distribution both in M BH and L/L Edd .
Panel (b) of Figure 12 shows a relationship between black holes mass and 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 control QSOs, our working sample seems have lower Eddington ratio as well as lower luminosity which may be result from the selection effect (the high luminosity QSOs tend to have a more powerful AGN and may overwhelm the light of host galaxies).
The KS-test of luminosity show that the working sample and the control sample are draw from the different distribution with P KS 0.001.

Interaction of host galaxies
A long term discussion concerning the properties of the galaxies hosting QSOs is its morphology. To study the host galaxy morphology properties and their interaction, we use images from the SDSS. The main challenge in understanding the host galaxy is the poor spatial resolution of the ground-based observations and combined with the bright nuclei hindered the nature of the QSOs host. We just classify our sources into tow types: Y (30) with obvious interactivity, which was represented with red triangle in Figure 14 and N (14) which don't shows any tidal feature and no companion (black squares). The rest 38 source is hard to be classified by SDSS image. It is interesting that the host galaxies without interaction are exclusive locate in high black hole mass and alliance with typeO and typeB (9/14). This result may indicate that objects without recent star formation and high black hole mass may already relax from the interactivation and evolve to the quiescent ellipse galaxies.

Discussion
By studying the stellar population of host galaxies in type I QSOs among different SFH types, we find that the stellar population is associated with the AGN physical properties.
These result is consistent with the finding of  and  , at least some QSOs are in the advanced merge stage.  Cales et al. (2011) shows that the PSQs have a starburst within 100 Myr which is smaller than our age range. Combined with the analysis in Section 4.1, our objects may in the evolutionary stage from IR-QSOs to typical optical QSOs.

The AGN properties in the evolution
In former analysis, we find a compelling correlation between the star-busts (both former dramatically enhanced and recent moderate star formation) and AGN properties.
Considering the typical QSOs' lifetime are expected to be ∼ 10 8 yr, the dramatically enhanced star formation can't have been triggered at the same time as they occurred few hundred Myr ago. However, there are some theories can explain the correlation between black hole activity and former star formation Walter et al. or interaction, when the AGN has not been triggered yet and then followed by decrease in accretion of AGN with the aging of stellar content 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 firstly the gas move toward center and gives rise to the star formation. Then, the gas flowing further inwards by losing angular momentum and produces a time delay between star formation and AGN activity. What's more, many numerical simulations show that the star formation as well as AGN activity is episodic (Hopkins et al. 2008;Van Wassenhove et al. 2012;Torrey et al. 2012), which depend on the detail of the merge (orbits, morphological type of progenitors). In this picture, the former dramatically enhanced star formation of QSO hosts in the working sample are induced in the early stages of galaxies merger. As the galaxies continue to merge for next few hundred Myr, the gas flowing further inwards central regions, followed by the AGN activity. The recent moderate star formation in our working sample may be triggered by a minor merge due the accretion of a satellite ). Many works (Walter et al. 2002;Hutchings et al. 2003;Letawe et al. 2007) suggest that minor merger that do not produce dramatically enhanced star formation, while still fuelling the AGN. Our result is consistent with that of the former work. Davies et al. (2007) analyzed the star formation in the nuclei of nine Seyfert galaxies, which also show a possible starbursts in the last 10-300 Myr. In the work of Schawinski et al. (2009), the AGN (obscured and unobscured) appear to be prevalent in the "green valley" on the color-magnitude diagram. They suggested that there is a 100Myr time delay between the shutdown of star formation and detectable AGN. The research of Heckman et al. (2004) also used type 2 AGNs to investigate the accretion-driven growth of super-massive black holes and found that bulge formation and black hole formation are tightly coupled in present-day. The study of Santini et al. (2012); Floyd et al. (2013) shows a higher SFRs of AGN host galaxies than that of inactive galaxies with the same stellar mass and redshift.

Summary
We have studies the stellar population of 82 host galaxies of type Considering the AGN properties such as black hole mass and Eddington ratio, we suggest that there is a co-evolution between AGN and host galaxies. Our result also shows there is a time delay between the peak of star formation and black hole accretion and then both of them decrease slowly. In addition, the host galaxies that do not show sign of interactive ( no tidal feature and companion galaxies ) are exclusive reside in the object with big black hole mass and relative old stellar population and imply they are the object relaxed form interactive. Most of our sources may be in the transition phase from IR-QSOs to classical optical QSOs.