The quasar M_bh - M_host relation through Cosmic Time II - Evidence for evolution from z=3 to the present age

We study the dependence of the M_bh - M_host relation on the redshift up to z=3 for a sample of 96 quasars the host galaxy luminosities of which are known. Black hole masses were estimated assuming virial equilibrium in the broad line regions (Paper I), while the host galaxy masses were inferred from their luminosities. With this data we are able to pin down the redshift dependence of the M_bh - M_host relation along 85 per cent of the Universe age. We show that, in the sampled redshift range, the M_bh - L_host relation remains nearly unchanged. Once we take into account the aging of the stellar population, we find that the M_bh / M_host ratio (Gamma) increases by a factor ~7 from z=0 to z=3. We show that Gamma evolves with z regardless of the radio loudness and of the quasar luminosity. We propose that most massive black holes, living their quasar phase at high-redshift, become extremely rare objects in host galaxies of similar mass in the Local Universe.


INTRODUCTION
Many pieces of evidence suggest that supermassive black holes (BHs) and their host galaxies share a joint evolution throughout Cosmic Time. In particular: i-the evolution of the quasar luminosity function (Dunlop & Peacock 1990;Fontanot et al. 2007;Croom et al. 2009) closely matches the trend of the star formation density through Cosmic ages (Madau Pozzetti & Dickinson 1998); ii-massive black holes are found in virtually all massive galaxies (Kormendy & Richstone 1995;Decarli et al. 2007); iii-their mass (MBH) is tightly correlated with the large scale properties (stellar velocity dispersion, σ * ; luminosity, L host ; mass, M host ) of their host galaxies (see Ferrarese 2006;Gultekin et al. 2009, for recent reviews on this topic).
When and how these relations set in, and which are the physical processes responsible of their onset are still open questions, despite the large efforts perfused both from a theoretical (e.g., Silk & Rees 1998;King 2005;Wyithe & Loeb 2006;Robertson et al. 2006;Hopkins et al. 2007;Malbon et al. 2007)  Probing BH-host galaxy relations at high redshift is extremely challenging. Direct measurements of MBH from gaseous or stellar dynamics require observations capable to resolve the BH sphere of influence, which are feasible only for a limited number of nearby galaxies. The only way to measure MBH in distant (> few tens of Mpc) galaxies is to focus on Type-1 AGN, where MBH can be inferred from the width of emission lines Doppler-broadened by the BH potential well and from the AGN continuum luminosity (see, e.g., Vestergaard 2002), assuming the virial equilibrium. Quasars represent therefore the best tool to probe MBH at high redshift, thanks to their huge luminosity. Indeed, large-field spectroscopic surveys allowed the estimate of MBH in several thousands of objects (see, for instance, Shen et al. 2008a;Labita et al. 2009a,b). On the other hand, the AGN light in quasars outshines the emission from the host galaxies, making their detection challenging. Only recently limitations due to intrinsic (e.g. the Nucleus-to-Host galaxy luminosity ratio, N/H) and extrinsic (e.g., the angular size of the host with respect to the angular resolution of the observations) effects could be overcome. Optical images from the Hubble Space Telescope (HST) and NIR observations both from space and ground-based telescopes could resolve ∼ 300 quasar host galaxies up to z ∼ 3 (see, e.g., Kotilainen et al. 2009, and references therein). Preliminary studies suggest that, for a given galaxy mass, black holes in high-z AGN are more massive than their low-z counter-parts (e.g., McLure et al. 2006;Peng et al. 2006a,b).
A number of limitations potentially affect the studies of the MBH-M host relation through Cosmic Time: 1) All the works to date use different MBH proxies as a function of redshift (i.e., based on different broad emission lines: usually Hβ at z ∼ < 0.5, Mg ii for 0.5 ∼ < z ∼ < 2 and C iv at z ∼ > 1.6). 2) Selection biases related to luminosity or flux limits, to the sampled N/H, to the steepness of the bright end of the galaxy and quasar luminosity functions may hinder the study of the evolution of the MBH-M host relation (see, for instance, Lauer et al. 2007). 3) As the properties of quasar host galaxies are directly observed only in a limited number of objects, poor statistics usually affect the available datasets.
This study represents a significant effort in overcoming all these limitations: Thanks to UV and optical spectra of low-redshift quasars (Labita et al. 2006;Decarli et al. 2008) and to optical spectra of mid-and high-redshift quasars , hereafter Paper I) we can probe MBH using both high and low ionization lines in a wide range of redshifts, for the largest dataset adopted so far in this kind of studies.
In Paper I we presented the sample and we inferred BH masses. Here we describe the data sources for the host galaxy luminosities, we infer M host and we address the evolution of the MBH-M host relation.
Throughout the paper, we adopt a concordance cosmology with H0 = 70 km/s/Mpc, Ωm = 0.3, ΩΛ = 0.7. We converted the results of other authors to this cosmology when adopting their relations and data.

L host AND M host IN DISTANT QUASARS
For the purposes of this work, we have to define a homogeneous compilation of quasar host galaxy luminosities from data available in the literature. After that, we use the restframe R-band luminosities to infer the host galaxy stellar masses. We refer to Kotilainen et al. (2009) for a detailed discussion of technicalities in the luminosity estimate of quasar host galaxies from high-resolution imaging.

Host galaxy luminosities from the literature
For a complete list of data sources, we refer to the sample description in Paper I. Apparent magnitudes in the filters of the observations are converted to rest-frame R-band absolute magnitude as follows: where f is the original filter of the observations, DL(z) is the luminosity distance of the quasar in the cosmological frame we adopted, C(z) is a term accounting for filter and kcorrection, as derived by assuming an elliptical galaxy template (Mannucci et al. 2001), and A f is a term accounting for the Galactic extinction, as derived from the H i maps in Schlegel Finkbeiner & Davis (1998). We remark that, in order to minimize filter and colour corrections, we selected observations performed using filters roughly sampling the rest-frame R-band. Moreover, the R-band luminosity is only marginally sensitive to the age of the stellar content. Thus, uncertainties in C(z) due to the chosen host galaxy template are negligible ( ∼ < 0.1 mag) for the purposes of this work. Low-z data taken with the HST-Wide Field Camera have been analyzed by many authors, and different m f estimates are available for the same object and on the same data. In particular, the studies of Bahcall et al. (1997); Hamilton et al. (2002); Dunlop et al. (2003) significantly overlap onto the recent re-analysis presented by Kim et al. (2008a,b). When comparing the reported apparent host galaxy and nuclear magnitudes, we find that the average offset is usually negligible ( ∼ < 0.2 mag), but a significant scatter is present (rms∼ 0.3 − 0.5 mag). When more than one estimate of m f was available, we adopted the most recent one. No images of the mid-and high-z quasars in our sample were analyzed independently by different groups, thus no superposition happens for these objects.

Host galaxy masses
In order to infer the stellar mass from the host galaxy luminosity, we have to adopt a stellar R-band Mass-to-Light ratio and consider its dependence on Cosmic Time. If the majority of the stellar population of massive galaxies did form at high redshift, as suggested by several pieces of evidence (Gavazzi et al. 2002;Thomas et al. 2005;Renzini 2006;Cirasuolo et al. 2008;Cappellari et al. 2009), one may assume that the Mass-to-Light ratio passively evolves from the formation (z = z burst ) to the present age. On the other hand, if quasar host galaxies suffer intense star formation episodes from z = 3 to z = 0 (for instance, due to merger events), the evolution of the stellar Mass-to-Light ratio becomes more complex and is, in principle, different from object to object. For the sake of simplicity, following Kotilainen et al. (2009) we will consider here only the scenario of a passively evolving stellar population with z burst = 5. This is justified by the selection of quasars with bulge-dominated host galaxies, where old stellar populations are expected. Furthermore, as we will discuss in section 4, this assumption is conservative with respect to the main results of our study.
With this caveat in mind, we find that the redshift dependence of the host galaxy luminosity observed, e.g., in Kotilainen et al. (2009) is practically removed when we take into account the evolution of the stellar population. The stellar mass of the host galaxies in our sample is nearly constant, with an average value of few times 10 11 M⊙. Table 1 lists our final estimates of the host galaxy luminosities and masses for the quasars in our sample. The MBH-L host relation appears rather insensitive to the Cosmic Time, independently on which line is adopted

Host galaxy
Host galaxy Quasar Name   suggesting that galaxies with similar stellar masses harbour BHs ∼ 7 times more massive at z = 3 than galaxies at z = 0.
In Figure 3 we study separately Radio Loud (RLQs) and Radio Quiet quasars (RQQs), finding that both samples are consistent with the log Γ-z relation found for the whole sample. The only remarkable difference is in the offset, in the sense that, at any redshift, both black holes and host galaxies in RLQs are ∼ 0.2 dex more massive than in RQQs (e.g., Dunlop et al. 2003;Labita et al. 2009c). Table 2 and Figure 4 report the slopes of the best linear fit of log Γ as a function of z in each subsample.

Is the trend of Γ an artifact?
In this section, we discuss the possible effects that could bias the estimate of Γ, in order to probe the reliability of the trend observed in Figures 1-3. 3.1.1 The luminosity function bias Lauer et al. (2007) showed that, because of the steepness of the bright end of the galaxy luminosity (mass) function and the presence of intrinsic scatter in the MBH-L host (M host ) relation, very massive BHs are preferentially found in relatively faint (less massive) galaxies rather than in extremely bright (massive) galaxies, which are very rare. Since high-z samples are dominated by massive objects, the bias increases with z, possibly mimicking an evolution in Γ.  Figure 1. The best linear fits are plotted. The average points with rms as error bars of the Hβ subsample (big square), of the low-and high-z C iv data (big circles) and of the Mg ii data with redshift < 1 and > 1 (big triangles) are also shown.
In order to quantify the relevance of this bias, we assume that MBH mostly depends on the quasar luminosity. This is consistent with the relatively small range of Eddington ratios we sample. If σµ, the cosmic scatter of the MBH-L host , is constant in L host , at a given redshift the bias depends on the shape of the luminosity function of quasars, Ψ(M ) (see equation 25 in Lauer et al. 2007). We assume the quasar luminosity function and its purely-luminosity evolution as reported by Boyle et al. (2000), basing on the 2QZ survey: M * (z) = −22.0 − 2.5 (1.34 z − 0.27 z 2 ). As a consequence, as long as we sample the same range of the quasar luminosity function at any redshift, the bias is kept constant. A constant bias is irrelevant for the purposes of our study, since our main aim is to probe the redshift dependence of the BHhost galaxy relations, not their absolute normalization.
From Figure 1 of Paper I, we note that the constant luminosity cut at −26 > MV > −27 and the M * > MV > M * − 1 cut roughly braket the objects in our sample over 5 magnitudes in MV . Hence, if we consider the whole sample, the bias on MBH will lie within the expectations from these two cases. Our estimate of the redshift evolution of the bias in these two cases is plotted in Figure 5, for two different values of σµ, namely 0.39 from Bettoni et al. (2003) and the conservative value σµ = 0.5. We conclude that the bias accounts for ∼ < 0.11 dex ≈ a factor 1.3 moving from z = 0 to z = 3. As the observed dependence of Γ is ∼ 6 times larger, it cannot be explained in terms of this selection effect. As a further check, Figure 6 shows the log Γ-z plane only for the objects lying in the two luminosity cuts considered in this discussion. The observed trend is unchanged, independently on the adopted luminosity cut (see Table 2 and Figure 4).

The effects of the N/H ratio
All the objects in our reference sample are selected on the basis of their total luminosity, which is dominated by the nuclear light in quasars. This possibly introduces a bias in the sense that the higher is the Nuclear-to-Host luminosity ratio (N/H), the harder is the measure of the host galaxy luminosity, especially at high-z. In Figure 7 we show that the redshift dependence of Γ in objects with high-and low-N/H is similar. Moreover, we stress that if we include the unresolved quasars to this analysis, the trend would be even steeper, as they all lie at high-z. Analogously, this argument can be applied for possible contaminations from discdominated galaxies at high redshift, where the morphology classification may be more doubtful. In this case, as MBH is sensitive to the bulge mass rather than to the total galaxy . The slope of the log Γ versus z linear fit in our data, for each subsample. Error bars are the 1-σ uncertainties as derived from the fit algorithm (see Table 2). All the subsets have consistent slopes around ∼ 0.3 dex. A non-evolving scenario (horizontal, dotted line) mismatches with the observations in all the cases. mass, we should consider smaller values of M host for such galaxies, which would increase the value of Γ at high z. Marconi et al. (2008Marconi et al. ( , 2009 suggest that the virial estimates of MBH may yield lower limits to the true BH mass, as the radiation pressure is not taken into account. As long as the BLR clouds are virialized, a correction can be applied by adding a term depending on the BLR column density NH and the quasar luminosity. There is still no strong constrain on the values of NH. X-ray variability studies performed on nearby, lower luminosity AGN suggest that the column densities may be relatively high (e.g. Turner & Miller 2009;Risaliti et al. 2009, and references therein), thus preventing radiation pressure from sustaining BLR clouds motion. However, as a clear comprehension of the radiation pressure role in the BLR is still missing, especially in the most luminous AGN, we limit our discussion to the following consideration: Since the average luminosity of our data increase with z, the radiation pressure effect is expected to become more severe at higher z, leading to an even steeper trend of Γ than the one observed in Figures 1 and 2.

Comparison with previous results
As a key result of this analysis, we find that the MBH/M host ratio significantly increases with redshift. Hereafter we com- Figure 5. The bias on the prediction of M BH from the M BH -L host relation with respect to the expectation from the luminosity functions of galaxies and quasars, plotted as a function of redshift. The bias estimates are obtained by integrating the luminosity function of quasars over the adopted luminosity cuts: −26 > M V > −27 (dot-dashed and dotted lines) and M * > M V > M * − 1 (dashed and solid lines). We plot the limit cases with σµ = 0.5 (dot-dashed and dashed lines) and σµ = 0.3 (dotted and solid lines). We note that, in the worst case, the bias increases of 0.22 dex (that is, a factor 1.66) from z = 2.5 to z = 0. pare these findings with those of other studies available in the literature. McLure et al. (2006) match the average trend of MBH observed in 38 Radio Loud quasars at z < 2 with the typical stellar masses of massive radio galaxies in the same redshift bins. This approach relies on the assumption that quasar host galaxies are comparable, at any redshift, with massive radio galaxies. The major caveat here is that their results may be biased by the different histories of quasar and radio galaxies (for instance, note that the luminosity functions of AGN evolves differently for various luminosity subclasses). Nevertheless, McLure et al. (2006) find an increase of Γ comparable to the one observed in the present study (see Figure  8). Our results extend these findings to RQQs and beyond the peak age of quasar activity. Peng et al. (2006a,b) address the evolution of the MBH-M host relation as a function of redshift in ∼ 20 low-z quasars and in ∼ 30 high-z lensed quasars imaged with the HST. Their data show a larger scatter than ours, possibly due to uncertainties in the modelling of the lens mass distribution and the lens light subtraction. They find that there is practically no evolution in the MBH-L host relation. On the other hand, when correcting for the evolution of the stellar population, they find an excess (a factor 3-6) in the MBH values at high-z with respect to the prediction from the lo- cal MBH-M host relation, in qualitative agreement with our findings. Merloni et al. (2009) study the MBH-M host ratio in a sample of 89 type-1 AGN with 1 < z < 2.2 from the zCOS-MOS survey. Black hole masses are derived through the standard virial assumption, while the host galaxy luminosities and stellar masses are inferred from multi-wavelength fitting of the spectral energy distribution of the targets (with no direct information about the morphology of the galaxies). This technique is effective with intermediate to low-luminosity AGN, while it cannot be applied to quasars as bright as ours, where the nuclear light overwhelms the galaxy contribution. They find that the average Γ is higher than what observed in the Local Universe, the excess scaling as (1 + z) 0.74 , consistently with the trend observed in our data in the same redshift bin. Jahnke et al. (2009) observed 10 of the targets in Merloni's sample with the HST and independently derived host galaxies luminosities with a procedure similar to the one adopted in our data sources (see, e.g., Kotilainen et al. 2009). They find no evolution in the MBH-M host (total) ratio. However, clues of the occurrence of discs are present, thus the MBH-M host (bulge) ratio is expected to evolve as (1 + z) 1.2 , in agreement with our findings. Bennert et al. (2009) address the MBH-L host relation in a sample of 23 Seyfert galaxies with 0.3 < z < 0.6. They study the morphology of the host galaxies of these objects using NIR observations from the HST. A careful modelling is adopted in order to disentangle nuclei, bulges and disc components. Black hole masses are derived in a way similar to that presented in paper I. Once corrected for the evolution of the stellar population, they find Γ ∝ (1 + z) (1.4±0.2) , in good agreement with our results.
Additional indication of an evolution of Γ comes from the relation of MBH with the stellar velocity dispersion, σ * , of the host galaxy. In particular, it is remarkable that these works suggest that the higher is the redshift, the more massive is the black hole for a given σ * . For instance, Salviander et al. (2007) use the width of the [O iii] narrow emission line as a proxy of the stellar velocity dispersion and study the MBH-σ * relation in a sample of ∼ 1600 quasars up to z = 1.2 taken from the SDSS. They find that MBH at high redshift are ∼ 0.2 dex larger than what expected from local MBH-σ * relation. A smaller evolution ( ∼ < 0.1 dex), albeit with small significance, is also proposed by Shen et al. (2008b), based on a sample of 900 Type-1 AGN with z ∼ < 0.4. More recently, Woo et al. (2008) and Woo et al. (in preparation) address the MBH-σ * relation in Seyfert galaxies up to z ∼ 0.6, and find an overall MBH excess at high redshift with respect to the prediction from low-z relationships. These findings support our results, notwithstanding the different characteristic luminosities, morphologies and stellar contents of the sampled targets with respect to those examined in our analysis.
It is interesting to note that the z = 6.42 quasar SDSS J1148+5251 has a black hole mass of few ×10 9 M⊙ (Willott, McLure & Jarvis 2003) and a dynamical mass of the host galaxy of ∼ 5 × 10 10 M⊙ (Walter et al. 2003(Walter et al. , 2004, yielding Γ ∼ 0.1, which is in agreement with the extrapolation of our results at that redshift (Γ ≈ 0.13) and well beyond the Γ = 0.002 value observed in the Local Universe.
These results as a whole support a picture where, for a given quasar host galaxy, its central black hole at high redshift is 'over-massive' with respect to its low-z counterparts. This picture is also consistent with the constrains on the MBH-M host evolution derived from the comparison between the galaxy stellar mass function and the quasar luminosity function (Somerville 2009).

Why does Γ evolve?
The interpretation of the observed evolution in the MBH-M host ratio is challenging. Exotic scenarios involving black hole ejection from their host galaxies due to gravitational wave recoil or to 3-body scatter may be applicable for few peculiar targets (e.g., see Komossa, Zhou & Lu 2008, but see also Bogdanovic et al., 2009, Heckman et al., 2009and Dotti et al., 2009 for alternative explanations), but they are not applicable to the general case. Thus, if high-z quasars are destined to move towards the local MBH-M host , the unavoidable consequence of our results is that, at a given MBH, galaxy masses increase from z = 3 to the present age.
Hereafter we sketch three possible basic pictures for that. We also present an alternative scenario, in which the fate of high-z quasars may be different, the remnants of high-z quasars keeping high Γ values down to the present age.
Galaxy growth by mergers -A first scenario involves substantial mass growth of quasar host galaxies through merger events. It is remarkable that strong gravitational interactions may trigger intense gas infall in the centre of galaxies and may even lead to the activation of BH accretion. This is observed in a number of relatively low-redshift AGN (e.g., Bennert et al. 2008Bennert et al. , 2009 showing dense close environments or disturbed morphologies, and confirmed by the presence of young stellar populations in some quasar host galaxies (Jahnke, Kuhlbrodt & Wisotzki 2004;Jahnke et al. 2007). Two arguments disfavour this scenario. First, theoretical models based on the structure evolution in a ΛCDM cosmology (e.g., Volonteri et al. 2003) predict that a massive galaxy experience only few (1-2) major merger events from z = 3 to z = 0. However, our study shows that a factor ∼ 7 increase of the stellar mass of the host galaxies is required from z = 3 to z = 0, which means that the host galaxies have to suffer 3 major mergers in this redshift range. Secondly, several pieces of evidence suggest that massive inactive galaxies, as well as quasar host galaxies, have already formed/assembled the majority of their mass in very remote Cosmic epochs (z ∼ > 3; see, e.g., Kotilainen et al. 2009, and references therein). The stellar population may experience episodic rejuvenation, but this only marginally affects the mean age of the stellar content: The stellar shells observed, e.g., by Canalizo et al. (2007) and Bennert et al. (2008) in low-redshift quasar host galaxies account for 5 -10 per cent of the total stellar population. Similarly, in a comparison with inactive galaxies of similar mass, Jahnke, Kuhlbrodt & Wisotzki (2004) find that quasar host galaxies are on average only 0.3 mag bluer. If the galaxies enter the quasar phase ∼ 1 Gyr after the activation of the starburst, as suggested by the authors of that study, then the involved mass is ∼ 30 per cent of the initial mass of the galaxy. Moreover, if the quasar host galaxies contain a significant fraction of young stellar populations, then the Mass-to-Light ratio would be smaller. Therefore, young host galaxies at high-z would yield a Γ-z relation even steeper than that reported in Figure 2.
Stellar mass growth through gas consumption -Another possible interpretation is that high redshift quasar host galaxies are gas rich, and form a significant fraction of their stellar content in relatively recent Cosmic epochs. This is consistent with a picture in which the black hole mass is somehow sensitive to the energetic budget of the galaxy or its dynamical mass rather than its stellar mass (see for instance Hopkins et al. 2007). This scenario is disfavoured as all the quasar host galaxies in our sample are massive elliptical, and the stellar content of these galaxies is usually old. Moreover, if significant star formation occurred in quasar host galaxies in the redshift range explored in this work, the evolution of Γ would be much steeper, making this scenario even less realistic.
Evolution of the fundamental plane -A number of studies suggest that inactive, massive elliptical galaxies were more compact in the high redshift than in the Local Universe (Trujillo et al. 2006; but see also Cappellari et al. 2009). In particular, an evolution of the Faber-Jackson relation is predicted, implying that the higher is z, the higher is the galaxy velocity dispersion σ * . If MBH constantly regulates the host galaxy σ * (e.g., Silk & Rees 1998), so that the MBH-σ * relation does not evolve significantly, then even a small (a factor ∼ 1.6) increase of σ * for a given galaxy would yield to an excess of a factor 7 in Γ. The main limit of this picture is that studies of the evolution of the MBH-σ * relation through redshift do find an increase of the average MBH for a given σ * , when moving from the Local to high-z Universe (Salviander et al. 2007;Woo et al. 2008;Bennert et al. 2009).
Remnants of high-z quasars as rare outliers -We propose a scenario in which the local counter-parts of high-z quasars are high-mass outliers above the MBH-M host relation. The more massive is the BH, the earlier it experiences its quasar phase (Marconi et al. 2004;Merloni 2004). Our study shows that these objects have higher expected Γ, but they are extremely rare, and contribute marginally to the presently known MBH-M host relation. In particular, the 2 < z < 3 quasars should appear as inactive massive galaxies with MBH∼ 10 9.5 M⊙ in the nearby Universe. In order to quantify the occurrence of such objects in the Local Universe, we assume the mass function of quasars: Φ(MBH ∼ 10 9.5 M⊙, 2 < z < 3) ≈ 4 × 10 −9 Gpc −3 M⊙ −1 (Vestergaard & Osmer 2009), and take a volume corresponding to the most distant inactive BH for which a direct measurement of the mass is available 1 . Under these assumptions, we expect virtually no objects (0.2 in the whole volume) with such high values of Γ. Using the same arguments for targets at intermediate redshift (1.0 < z < 1.5), we expect few (∼ 2) objects. Quasars at z ∼ 1.2 have Γ values ∼ 0.3 dex larger than that at z = 0. This offset is close to the one observed for the handful of objects populating the high-mass end of the local MBH-M host relation (e.g. Marconi & Hunt 2003). This scenario is thus consistent both with the Γ-z relation of quasars and with the observed shape of the local MBH-M host galaxy relation of nearby inactive galaxies.

CONCLUSIONS
In this paper, we studied the MBH-M host relations as a function of redshift in a sample of 96 quasars from the present age to z = 3, i.e., 85 per cent of the Universe age. We found that the MBH-M host ratio increases by a factor ∼ 7 from z = 0 to z = 3. This trend is not affected by significant contributions due to target selection criteria and observational biases. Moreover it is independent of the quasar luminosity and of the radio loudness.
1 The BH at the centre of the brightest cluster galaxy in Abell 1836, at 147 Mpc; see Dalla Bontà et al. (2009) We interpret this trend as an indication that the most massive black holes, living their quasar phase at high redshift, keep their high Γ down to the present age, becoming very rare objects in the Local Universe. A fully consistent interpretation of these results in terms of the common history of black holes and galaxies requires further efforts in refining the picture sketched here. In particular, two key points are yet to be clarified: i-how the mechanisms of quasar feedback act onto the host galaxies; ii-which is the role of both dry and wet mergers concerning the quasar activity and in triggering star formation. Moreover, a better knowledge of the MBH-host galaxy relations (improving statistics at high masses) will clarify whether very massive, quiescent black holes can actually be found in galaxies in the Local Universe.