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Imprints of the super-Eddington accretion on the quasar clustering

Imprints of the super-Eddington accretion on the quasar clustering MNRAS 471, L21–L25 (2017) doi:10.1093/mnrasl/slx102 Advance Access publication 2017 June 21 1,2‹ 3 4 5 Taira Oogi, Motohiro Enoki, Tomoaki Ishiyama, Masakazu A. R. Kobayashi, 1,6 2 7 7 Ryu Makiya, Masahiro Nagashima, Takashi Okamoto and Hikari Shirakata Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan Faculty of Education, Bunkyo University, 3337 Minami-Ogishima, Koshigaya-shi, Saitama 343-8511, Japan Faculty of Business Administration, Tokyo Keizai University, 1-7-34, Minami-cho, Kokubunji-shi, Tokyo 185-8502, Japan Institute of Management and Infomation Technologies, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Faculty of Natural Sciences, National Institute of Technology, Kure College, 2-2-11, Agaminami, Kure, Hiroshima 737-8506, Japan Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild Str. 1, D-85741 Garching, Germany Department of Cosmosciences, Graduates School of Science, Hokakido University, N10 W8, Kitaku, Sapporo 060-0810, Japan Accepted 2017 June 15. Received 2017 June 15; in original form 2017 April 5 ABSTRACT Super-Eddington mass accretion has been suggested as an efficient mechanism to grow su- permassive black holes. We investigate the imprint left by the radiative efficiency of the super-Eddington accretion process on the clustering of quasars using a new semi-analytic model of galaxy and quasar formation based on large-volume cosmological N-body simu- lations. Our model includes a simple model for the radiative efficiency of a quasar, which imitates the effect of photon trapping for a high mass accretion rate. We find that the model of radiative efficiency affects the relation between the quasar luminosity and the quasar host halo mass. The quasar host halo mass has only weak dependence on quasar luminosity when there is no upper limit for quasar luminosity. On the other hand, it has significant dependence on quasar luminosity when the quasar luminosity is limited by its Eddington luminosity. In the latter case, the quasar bias also depends on the quasar luminosity, and the quasar bias of bright quasars is in agreement with observations. Our results suggest that the quasar clustering studies can provide a constraint on the accretion disc model. Key words: galaxies: formation – galaxies: haloes – quasars: general – dark matter – large- scale structure of Universe – cosmology: theory. Natarajan 2014; Volonteri, Silk & Dubus 2015), where L is the Edd 1 INTRODUCTION Eddington luminosity L ≡ 4πGM m c/σ , m is the proton Edd BH p T p Some observations (Mortlock et al. 2011;Wuetal. 2015)have mass, and σ is the Thomson scattering cross-section. During the found optically bright quasars even at high redshift, z ∼ 7. These super-Eddington accretion, the photons produced in the accretion quasars are powered by mass accretion on to supermassive black flow are advected inwards by the optically thick flow and cannot holes (SMBHs). The observations suggest that SMBHs with mass be radiated away (e.g. Begelman 1978). This type of the accretion M ∼ 10 M already exist at such high redshift. While some flow is described by a well-known solution called slim disc (e.g. BH physical processes through which these SMBHs form have been Abramowicz et al. 1988; Mineshige et al. 2000; Watarai et al. 2000). proposed (see Volonteri 2010, and references therein), how the The structure of the slim disc becomes geometrically thick. Pacucci, SMBHs form during less than 1 Gyr after the big bang is still Volonteri & Ferrara (2015a) show analytically and numerically that debated. in this condition the outflow by radiative feedback has a negligible Super-Eddington mass accretion, for which the mass accretion role, and the BH can accrete 80–100 per cent of the gas mass of rate exceeds the Eddington rate the host halo. Although there are some observations suggesting that some active galactic nuclei (AGNs) are accreting at super-Eddington M ≡ L /c , (1) Edd Edd rates (e.g. Netzer & Trakhtenbrot 2014;Jin,Done &Ward 2017), it is still uncertain whether the super-Eddington accretion actually has been suggested as an efficient mechanism to grow SMBHs (e.g. occurs or not. Volonteri & Rees 2005; Madau, Haardt & Dotti 2014; Alexander & The luminosity of a quasar with the super-Eddington accretion phase would be limited to several times of the Eddington luminosity L due to the ‘photon trapping’ (e.g. Ohsuga et al. 2005). This E-mail: [email protected] Edd 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society L22 T. Oogi et al. means that the radiative efficiency is low at a high accretion rate. the cold gas is accreted on the SMBH. The accreted mass M is BH This limitation could affect the clustering of quasars, in particular, modelled as follows: at higher redshifts, because accretion rates for quasars tend to be M = f M , (2) BH BH star,burst higher at such higher redshifts (Bonoli et al. 2009; Enoki et al. 2014). If this is true, future wide field surveys may clarify how where M is the total stellar mass formed during the star- star, burst mass accretion occurs. In this Letter, we focus on the slim disc so- burst. We set f = 0.005 to match the observed correlation be- BH lution, although alternative radiatively inefficient models exist, e.g. tween masses of host bulges and SMBHs at z = 0. Our model also ZEro-BeRnoulli Accretion (ZEBRA; Coughlin & Begelman 2014) reproduces the observationally estimated SMBH mass function. We and the ADiabatic Inflow–Outflow Solution (ADIOS; Blandford & assume that the time evolution of the accretion rate is as follows: Begelman 1999). BH M (t) = exp(−t/t ), (3) BH life In the previous study with our semi-analytic model (Oogi et al. life 2016; hereafter O16), we have shown that the model quasars with where t is the quasar lifetime, and that t scales with the dy- life life a given host halo mass have various Eddington ratios, L/L = Edd namical time-scale of the host DM halo, that is, t ∝ t . We note ˙ ˙ life dyn ηM /M , and various luminosities due to a variety of elapsed BH Edd that we allow for super-Eddington accretion in this model. The cold times from the beginning of the quasar activity. As a consequence gas accretion leads to quasar activity. We assume that a fraction of of this, the median mass of quasar host haloes depends only weakly the rest mass energy of the accreted gas is radiated. The radiative on the quasar luminosity. In O16, we did not take into account efficiency is determined by the models we describe below. Further the fact that the radiative efficiency depends on the accretion rate details of our model of galaxy and quasar formation are given in when considering the super-Eddington accretion (e.g. Pacucci et al. Enoki et al. (2014) and Makiya et al. (2016). 2015a). This effect changes the Eddington ratios and luminosities We also consider the radio-mode gas accretion and the feedback of model quasars with a given host halo mass. This suggests that process. In this mode, the accreted gas powers radio jet that puts the behaviour of the luminosity for the accretion rate in the slim energy into the hot halo gas and prevents the hot gas from cooling disc affects the estimated host halo mass and the spatial clustering and resultant star formation. The radio-mode feedback occurs when of quasars. (i) the time-scale of gas cooling is sufficiently long compared with In this Letter, we investigate the imprint left by the radiative the dynamical time-scale of the halo, and (ii) the cooling luminosity efficiency of the super-Eddington accretion process on the clustering of the gas, which is assumed to balance the heating luminosity by the of quasars. For this purpose, we use a new semi-analytic model AGN, is sufficiently low compared with the Eddington luminosity. of galaxy and quasar formation based on high-resolution N-body Although this gas accretion grows the mass of SMBHs, this is simulations. not significant contribution for the entire mass growth of SMBHs. The remainder of this Letter is organized as follows. In Section 2, This is because the mass growth of SMBHs is dominated by the we outline our semi-analytic model and the models of radiative gas accretion during major mergers (Makiya et al. 2016). Further efficiency of SMBHs. Section 3 gives the mass distribution of the details of the implementation of the radio-mode feedback are given quasar host haloes and the quasar bias for our models. In Section 4, in Makiya et al. (2016). we discuss the BH growth at high redshift via the super-Eddington To examine the effect of the photon trapping in the accretion flow accretion, and summarize our results. on the quasar host halo mass and the clustering, we adopt a simple model for the radiative efficiency η ≡ L/Mc of a quasar, which imitates the effect of photon trapping for a high mass accretion rate, −1 1 m ˙ 2MODEL η = + , (4) agn Edd We use a semi-analytic model, ν GC (Makiya et al. 2016), which is ˙ ˙ an extension of the Numerical Galaxy Catalog (νGC) (Nagashima where m ˙ is the normalized mass accretion rate m ˙ ≡ M /M and BH Edd et al. 2005; Enoki et al. 2014; Shirakata et al. 2015). In this model,  is a free parameter. The form of the model is the same as Sakurai, agn we adopt merger trees of dark matter (DM) haloes using state- Inayoshi & Haiman (2016). In this model, the radiative efficiency of-the-art cosmological N-body simulations (Ishiyama et al. 2015) decreases with increasing accretion rate, while it is constant for low with the Planck cosmology (Planck Collaboration XVI 2014). The accretion rates (m ˙  10). The parameter,  , provides a constant agn simulation used in this Letter contains 4096 DM particles within radiative efficiency at such low accretion rates. f corresponds to Edd −1 a comoving box of 560 h Mpc, and the minimum halo mass is the maximum Eddington ratio for high mass accretion rates. In our 9 −1 8.79 × 10 h M (see Ishiyama et al. 2015 for details). This sim- previous work, O16, f corresponded to ∞, which leads to  = Edd agn ulation enables us to investigate quasar host haloes with statistical η. We set the parameter f = 1, 2 and 10 to examine the effects of Edd significance. The model includes all the main physical processes in- the maximum Eddington ratio on the quasar clustering. We call the volved in galaxy formation: formation and evolution of DM haloes; models with these parameters η , η and η model, respectively. 1 2 10 radiative gas cooling and disc formation in DM haloes; star forma- For comparison, we also adopt f =∞ as a model in which we Edd tion, supernova feedback and chemical enrichment; galaxy mergers. allow for any super-Eddington luminosity (η model). We set t ∞ life Free parameters related to galaxy formation processes are set to the (z = 0) and  to match the luminosity function of quasars with agn values adopted in Makiya et al. (2016). the observation at z = 2in η model. We obtain t (z = 0) = 2 × ∞ life Our model also includes SMBH growth and quasar formation. 10 yr and  = 0.03. In O16, we employ this model. To examine agn We assume that major mergers of galaxies trigger starbursts in the the photon trapping effect, we fix all parameters except for f and Edd nuclear regions and cold gas accretion on to SMBHs. We define a examine the effect of the change of f on the results. We show Edd major merger as that with the mass ratio M /M ≥ 0.1, where M and the Eddington ratio in the models used here as a function of the 2 1 1 M are the baryonic masses of the more and less massive galaxies, accretion rate in Fig. 1. To obtain the quasar B-band luminosity, we respectively. During major mergers, we assume that a fraction of use the bolometric correction from Marconi et al. (2004). MNRASL 471, L21–L25 (2017) Imprints of the super-Eddington accretion L23 Fig. 3 clearly shows that the radiative efficiency, in other words, the maximum value of the quasar luminosity affects the quasar host halo mass distribution. We see that decreasing the upper limit of the quasar luminosity, the median host halo mass increases. For η model, there is only a weak dependence of median halo mass on quasar magnitude. On the other hand, for η model, there is a strong dependence of the median halo mass on quasar magnitude. While, for η model, the difference between the median halo masses of bright and faint quasars is ∼0.5 dex, for η model, the difference reaches ∼1.2 dex. This trend can be understood as follows. Because of the fact that more massive haloes have more massive BHs in our model, when two quasars in haloes with different masses have same luminosity, the quasar in the less massive halo needs to have a high Eddington ratio. As a result, decreasing the upper limit of the quasar luminosity, the median host halo mass increases. This trend appears Figure 1. The Eddington ratios as a function of the accretion rate in our in the quasar bias described in Section 3.3. models. In all magnitude range, the median host halo mass increases with the decreasing upper limit of quasar luminosity, although the up- per limit affects the median stronger for bright quasars than that of faint quasars. The median host halo mass of bright quasars in- creases more than that of faint quasars by adopting the upper limit of quasar luminosity. This is because more luminous quasars within less massive haloes have higher Eddington ratios. Therefore, in this case, the median host halo mass depends on the quasar luminosity. 3.3 Quasar bias We estimate the quasar bias using the median host halo mass and the following equation derived by Sheth, Mo & Tormen (2001). This is because the bias of quasars is primarily determined by the median host halo mass. Sheth et al. (2001) relates the halo bias and its mass: Figure 2. Evolution of normalized accretion rates for quasars. The solid line √ √ 2 2 1−c denotes the median. The dashed lines show the 10th and 90the percentiles. b(M, z) = 1 + √ a(aν ) + ab(aν ) aδ Note that we use equation (1) for the definition of M . The Eddington ratio Edd c ˙ ˙ L/L = ηM /M ,where η ≤ 0.03 in our model. Thus, the luminosity Edd BH Edd 2 c (aν ) of most quasars is sub-Eddington at z ∼ 0. − , (5) 2 c (aν ) + b(1 − c)(1 − c/2) 3 RESULTS where a = 0.707, b = 0.5, c = 0.6, δ = 1.686 is the critical overdensity required for collapse and ν = . D(z) is the linear σ (M)D(z) 3.1 Accretion rate distribution growth factor and σ (M) is the variance of mass fluctuations. We have confirmed that this method works well in O16. The redshift To show the importance of the model of the radiative efficiency evolution of the bias is shown in Fig. 4, where we show different during super-Eddington accretion, in particular, at high redshift, we models of radiative efficiency in different panels. Decreasing the first show the redshift evolution of the normalized accretion rate for upper limit of the quasar luminosity, the quasar bias increases. The our model quasars in Fig. 2. This figure shows that the normalized upper limit of the quasar luminosity affects the bias for brighter accretion rate increases with redshift. The super-Eddington accre- quasars and at higher redshift more strongly. At z  2, the bias of tion is expected to occur, in particular, at high redshift. We expect bright quasars increases significantly for η and η models. This 1 2 that the slim accretion disc model affects the quasar clustering more is because of the following two reasons. First, in these cases only strongly at higher redshift. massive BHs become bright quasars due to the upper limit L , max which is proportional to M ,i.e. L ∼ L ∝ M . Secondly, in BH max Edd BH our model, more massive BHs reside in more massive haloes, which 3.2 Quasar host halo mass is in agreement with the observations (e.g. Ferrarese 2002; Fine et al. Here, we investigate the impact of the model of radiative efficiency 2006, but see also Sabra et al. 2015). Therefore, luminous quasars on the quasar host halo mass. Fig. 3 shows the mass distributions having massive BHs show the strong clustering in these cases. On of the quasar host haloes for three quasar-magnitude bins and their the other hand, the quasar bias hardly changes for all magnitude bins median halo masses (dashed lines) at z = 2.5 when the number at low redshift (z ∼ 1) even for η and η models. This is because 1 2 density of quasars has a noticeable peak. We define bright, inter- most quasars have luminosities below the Eddington luminosity in mediate and faint quasars as those with B-band magnitudes M − this epoch. These quasars are not influenced by the upper limit. 5log h < −24.5, −24.5 < M − 5log h < −23.0 and −23.0 < M − We compare our results with observations. We compile observa- B B 5log h < −21.0, respectively. We show different models of radiative tional results by the large-scale surveys of SDSS and 2QZ (Porciani, efficiency in different panels. Magliocchetti & Norberg 2004; Croom et al. 2005; Padmanabhan MNRASL 471, L21–L25 (2017) L24 T. Oogi et al. Figure 3. Mass distributions of DM haloes hosting bright (red, thick solid), intermeiate (green, dashed) and faint (blue, thin solid) quasars at z = 2.5. Each panel corresponds to a different model of radiative efficiency, as indicated by the legend. The vertical dashed lines are the median masses of the distributions. Figure 4. Redshift evolution of the bias of bright (red, thick solid), intermediate (green, dashed) and faint (blue, thin solid) quasars. Each panel corresponds to a different model of radiative efficiency, as indicated by the legend. Observational results by the large-scale surveys of SDSS and 2QZ (Porciani et al. 2004; Croom et al. 2005; Padmanabhan et al. 2009; Ross et al. 2009; Shen et al. 2009) are also plotted (small filled circles and error bars), whose magnitudes are converted to M . The colour coding represents the luminosity of quasars in the same way as for the models. et al. 2009;Rossetal. 2009;Shenetal. 2009). For η model, the 1 Eddington accretion using our semi-analytic model, ν GC. We have bias of bright quasars is in agreement with the general increasing shown that the model of radiative efficiency strongly affects the trend of the bias shown in observational data. In addition, for η 2 quasar clustering. While the quasar bias has no significant depen- model, the bias is in agreement with the observation at 1.5  z dence on quasar luminosity for the no-limit model, it has significant 2. Future surveys of quasars will allow us to make more accurate dependence on quasar luminosity for the model in which quasar comparison to the model. luminosity is limited by its Eddington luminosity. This is because only massive BHs become high luminosity quasars due to the limit, and, in general, such massive SMBHs reside in massive haloes. 4 SUMMARY AND DISCUSSION The luminosity dependence of the quasar bias is a reflection of In this Letter, we have investigated the large-scale clustering of the super-Eddington accretion model. This indicates that quasar quasars, including the models of radiative efficiency during super- clustering studies provide a constraint on the accretion disc model. MNRASL 471, L21–L25 (2017) Imprints of the super-Eddington accretion L25 The existence of the super-Eddington accretion discs is observa- REFERENCES tionally suggested. Netzer & Trakhtenbrot (2014) have estimated Abramowicz M. A., Czerny B., Lasota J. 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R., was supported by World Premier International Research Center Ishiyama T., Makiya R., 2015, MNRAS, 450, L6 Initiative (WPI), the Ministry of Education, Culture, Sports, Sci- Volonteri M., 2010, A&A Rev., 18, 279 ence and Technology (MEXT), Japan and by MEXT as ‘Prior- Volonteri M., Rees M. J., 2005, ApJ, 633, 624 ity Issue on Post-K computer’ (Elucidation of the Fundamental Volonteri M., Silk J., Dubus G., 2015, ApJ, 804, 148 Laws and Evolution of the Universe, JICFuS and the Japan Society Watarai K.-y., Fukue J., Takeuchi M., Mineshige S., 2000, PASJ, 52, 133 for the Promotion of Science (JSPS). This study has been funded Wu X. -B. et al., 2015, Nature, 518, 512 by MEXT/JSPS KAKENHI Grant Number 25287041, 15K12031 and by Yamada Science Foundation, MEXT HPCI STRATEGIC PROGRAM. RM acknowledge support from JSPS KAKENHI Grant Numbers JP 15H05896. TO has been supported by MEXT KAKENHI Grant 16H01085. MN has been supported by MEXT KAKENHI Grant 17H02867. This paper has been typeset from a T X/LT X file prepared by the author. E E MNRASL 471, L21–L25 (2017) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society Letters Oxford University Press

Imprints of the super-Eddington accretion on the quasar clustering

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MNRAS 471, L21–L25 (2017) doi:10.1093/mnrasl/slx102 Advance Access publication 2017 June 21 1,2‹ 3 4 5 Taira Oogi, Motohiro Enoki, Tomoaki Ishiyama, Masakazu A. R. Kobayashi, 1,6 2 7 7 Ryu Makiya, Masahiro Nagashima, Takashi Okamoto and Hikari Shirakata Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan Faculty of Education, Bunkyo University, 3337 Minami-Ogishima, Koshigaya-shi, Saitama 343-8511, Japan Faculty of Business Administration, Tokyo Keizai University, 1-7-34, Minami-cho, Kokubunji-shi, Tokyo 185-8502, Japan Institute of Management and Infomation Technologies, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Faculty of Natural Sciences, National Institute of Technology, Kure College, 2-2-11, Agaminami, Kure, Hiroshima 737-8506, Japan Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild Str. 1, D-85741 Garching, Germany Department of Cosmosciences, Graduates School of Science, Hokakido University, N10 W8, Kitaku, Sapporo 060-0810, Japan Accepted 2017 June 15. Received 2017 June 15; in original form 2017 April 5 ABSTRACT Super-Eddington mass accretion has been suggested as an efficient mechanism to grow su- permassive black holes. We investigate the imprint left by the radiative efficiency of the super-Eddington accretion process on the clustering of quasars using a new semi-analytic model of galaxy and quasar formation based on large-volume cosmological N-body simu- lations. Our model includes a simple model for the radiative efficiency of a quasar, which imitates the effect of photon trapping for a high mass accretion rate. We find that the model of radiative efficiency affects the relation between the quasar luminosity and the quasar host halo mass. The quasar host halo mass has only weak dependence on quasar luminosity when there is no upper limit for quasar luminosity. On the other hand, it has significant dependence on quasar luminosity when the quasar luminosity is limited by its Eddington luminosity. In the latter case, the quasar bias also depends on the quasar luminosity, and the quasar bias of bright quasars is in agreement with observations. Our results suggest that the quasar clustering studies can provide a constraint on the accretion disc model. Key words: galaxies: formation – galaxies: haloes – quasars: general – dark matter – large- scale structure of Universe – cosmology: theory. Natarajan 2014; Volonteri, Silk & Dubus 2015), where L is the Edd 1 INTRODUCTION Eddington luminosity L ≡ 4πGM m c/σ , m is the proton Edd BH p T p Some observations (Mortlock et al. 2011;Wuetal. 2015)have mass, and σ is the Thomson scattering cross-section. During the found optically bright quasars even at high redshift, z ∼ 7. These super-Eddington accretion, the photons produced in the accretion quasars are powered by mass accretion on to supermassive black flow are advected inwards by the optically thick flow and cannot holes (SMBHs). The observations suggest that SMBHs with mass be radiated away (e.g. Begelman 1978). This type of the accretion M ∼ 10 M already exist at such high redshift. While some flow is described by a well-known solution called slim disc (e.g. BH physical processes through which these SMBHs form have been Abramowicz et al. 1988; Mineshige et al. 2000; Watarai et al. 2000). proposed (see Volonteri 2010, and references therein), how the The structure of the slim disc becomes geometrically thick. Pacucci, SMBHs form during less than 1 Gyr after the big bang is still Volonteri & Ferrara (2015a) show analytically and numerically that debated. in this condition the outflow by radiative feedback has a negligible Super-Eddington mass accretion, for which the mass accretion role, and the BH can accrete 80–100 per cent of the gas mass of rate exceeds the Eddington rate the host halo. Although there are some observations suggesting that some active galactic nuclei (AGNs) are accreting at super-Eddington M ≡ L /c , (1) Edd Edd rates (e.g. Netzer & Trakhtenbrot 2014;Jin,Done &Ward 2017), it is still uncertain whether the super-Eddington accretion actually has been suggested as an efficient mechanism to grow SMBHs (e.g. occurs or not. Volonteri & Rees 2005; Madau, Haardt & Dotti 2014; Alexander & The luminosity of a quasar with the super-Eddington accretion phase would be limited to several times of the Eddington luminosity L due to the ‘photon trapping’ (e.g. Ohsuga et al. 2005). This E-mail: [email protected] Edd 2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society L22 T. Oogi et al. means that the radiative efficiency is low at a high accretion rate. the cold gas is accreted on the SMBH. The accreted mass M is BH This limitation could affect the clustering of quasars, in particular, modelled as follows: at higher redshifts, because accretion rates for quasars tend to be M = f M , (2) BH BH star,burst higher at such higher redshifts (Bonoli et al. 2009; Enoki et al. 2014). If this is true, future wide field surveys may clarify how where M is the total stellar mass formed during the star- star, burst mass accretion occurs. In this Letter, we focus on the slim disc so- burst. We set f = 0.005 to match the observed correlation be- BH lution, although alternative radiatively inefficient models exist, e.g. tween masses of host bulges and SMBHs at z = 0. Our model also ZEro-BeRnoulli Accretion (ZEBRA; Coughlin & Begelman 2014) reproduces the observationally estimated SMBH mass function. We and the ADiabatic Inflow–Outflow Solution (ADIOS; Blandford & assume that the time evolution of the accretion rate is as follows: Begelman 1999). BH M (t) = exp(−t/t ), (3) BH life In the previous study with our semi-analytic model (Oogi et al. life 2016; hereafter O16), we have shown that the model quasars with where t is the quasar lifetime, and that t scales with the dy- life life a given host halo mass have various Eddington ratios, L/L = Edd namical time-scale of the host DM halo, that is, t ∝ t . We note ˙ ˙ life dyn ηM /M , and various luminosities due to a variety of elapsed BH Edd that we allow for super-Eddington accretion in this model. The cold times from the beginning of the quasar activity. As a consequence gas accretion leads to quasar activity. We assume that a fraction of of this, the median mass of quasar host haloes depends only weakly the rest mass energy of the accreted gas is radiated. The radiative on the quasar luminosity. In O16, we did not take into account efficiency is determined by the models we describe below. Further the fact that the radiative efficiency depends on the accretion rate details of our model of galaxy and quasar formation are given in when considering the super-Eddington accretion (e.g. Pacucci et al. Enoki et al. (2014) and Makiya et al. (2016). 2015a). This effect changes the Eddington ratios and luminosities We also consider the radio-mode gas accretion and the feedback of model quasars with a given host halo mass. This suggests that process. In this mode, the accreted gas powers radio jet that puts the behaviour of the luminosity for the accretion rate in the slim energy into the hot halo gas and prevents the hot gas from cooling disc affects the estimated host halo mass and the spatial clustering and resultant star formation. The radio-mode feedback occurs when of quasars. (i) the time-scale of gas cooling is sufficiently long compared with In this Letter, we investigate the imprint left by the radiative the dynamical time-scale of the halo, and (ii) the cooling luminosity efficiency of the super-Eddington accretion process on the clustering of the gas, which is assumed to balance the heating luminosity by the of quasars. For this purpose, we use a new semi-analytic model AGN, is sufficiently low compared with the Eddington luminosity. of galaxy and quasar formation based on high-resolution N-body Although this gas accretion grows the mass of SMBHs, this is simulations. not significant contribution for the entire mass growth of SMBHs. The remainder of this Letter is organized as follows. In Section 2, This is because the mass growth of SMBHs is dominated by the we outline our semi-analytic model and the models of radiative gas accretion during major mergers (Makiya et al. 2016). Further efficiency of SMBHs. Section 3 gives the mass distribution of the details of the implementation of the radio-mode feedback are given quasar host haloes and the quasar bias for our models. In Section 4, in Makiya et al. (2016). we discuss the BH growth at high redshift via the super-Eddington To examine the effect of the photon trapping in the accretion flow accretion, and summarize our results. on the quasar host halo mass and the clustering, we adopt a simple model for the radiative efficiency η ≡ L/Mc of a quasar, which imitates the effect of photon trapping for a high mass accretion rate, −1 1 m ˙ 2MODEL η = + , (4) agn Edd We use a semi-analytic model, ν GC (Makiya et al. 2016), which is ˙ ˙ an extension of the Numerical Galaxy Catalog (νGC) (Nagashima where m ˙ is the normalized mass accretion rate m ˙ ≡ M /M and BH Edd et al. 2005; Enoki et al. 2014; Shirakata et al. 2015). In this model,  is a free parameter. The form of the model is the same as Sakurai, agn we adopt merger trees of dark matter (DM) haloes using state- Inayoshi & Haiman (2016). In this model, the radiative efficiency of-the-art cosmological N-body simulations (Ishiyama et al. 2015) decreases with increasing accretion rate, while it is constant for low with the Planck cosmology (Planck Collaboration XVI 2014). The accretion rates (m ˙  10). The parameter,  , provides a constant agn simulation used in this Letter contains 4096 DM particles within radiative efficiency at such low accretion rates. f corresponds to Edd −1 a comoving box of 560 h Mpc, and the minimum halo mass is the maximum Eddington ratio for high mass accretion rates. In our 9 −1 8.79 × 10 h M (see Ishiyama et al. 2015 for details). This sim- previous work, O16, f corresponded to ∞, which leads to  = Edd agn ulation enables us to investigate quasar host haloes with statistical η. We set the parameter f = 1, 2 and 10 to examine the effects of Edd significance. The model includes all the main physical processes in- the maximum Eddington ratio on the quasar clustering. We call the volved in galaxy formation: formation and evolution of DM haloes; models with these parameters η , η and η model, respectively. 1 2 10 radiative gas cooling and disc formation in DM haloes; star forma- For comparison, we also adopt f =∞ as a model in which we Edd tion, supernova feedback and chemical enrichment; galaxy mergers. allow for any super-Eddington luminosity (η model). We set t ∞ life Free parameters related to galaxy formation processes are set to the (z = 0) and  to match the luminosity function of quasars with agn values adopted in Makiya et al. (2016). the observation at z = 2in η model. We obtain t (z = 0) = 2 × ∞ life Our model also includes SMBH growth and quasar formation. 10 yr and  = 0.03. In O16, we employ this model. To examine agn We assume that major mergers of galaxies trigger starbursts in the the photon trapping effect, we fix all parameters except for f and Edd nuclear regions and cold gas accretion on to SMBHs. We define a examine the effect of the change of f on the results. We show Edd major merger as that with the mass ratio M /M ≥ 0.1, where M and the Eddington ratio in the models used here as a function of the 2 1 1 M are the baryonic masses of the more and less massive galaxies, accretion rate in Fig. 1. To obtain the quasar B-band luminosity, we respectively. During major mergers, we assume that a fraction of use the bolometric correction from Marconi et al. (2004). MNRASL 471, L21–L25 (2017) Imprints of the super-Eddington accretion L23 Fig. 3 clearly shows that the radiative efficiency, in other words, the maximum value of the quasar luminosity affects the quasar host halo mass distribution. We see that decreasing the upper limit of the quasar luminosity, the median host halo mass increases. For η model, there is only a weak dependence of median halo mass on quasar magnitude. On the other hand, for η model, there is a strong dependence of the median halo mass on quasar magnitude. While, for η model, the difference between the median halo masses of bright and faint quasars is ∼0.5 dex, for η model, the difference reaches ∼1.2 dex. This trend can be understood as follows. Because of the fact that more massive haloes have more massive BHs in our model, when two quasars in haloes with different masses have same luminosity, the quasar in the less massive halo needs to have a high Eddington ratio. As a result, decreasing the upper limit of the quasar luminosity, the median host halo mass increases. This trend appears Figure 1. The Eddington ratios as a function of the accretion rate in our in the quasar bias described in Section 3.3. models. In all magnitude range, the median host halo mass increases with the decreasing upper limit of quasar luminosity, although the up- per limit affects the median stronger for bright quasars than that of faint quasars. The median host halo mass of bright quasars in- creases more than that of faint quasars by adopting the upper limit of quasar luminosity. This is because more luminous quasars within less massive haloes have higher Eddington ratios. Therefore, in this case, the median host halo mass depends on the quasar luminosity. 3.3 Quasar bias We estimate the quasar bias using the median host halo mass and the following equation derived by Sheth, Mo & Tormen (2001). This is because the bias of quasars is primarily determined by the median host halo mass. Sheth et al. (2001) relates the halo bias and its mass: Figure 2. Evolution of normalized accretion rates for quasars. The solid line √ √ 2 2 1−c denotes the median. The dashed lines show the 10th and 90the percentiles. b(M, z) = 1 + √ a(aν ) + ab(aν ) aδ Note that we use equation (1) for the definition of M . The Eddington ratio Edd c ˙ ˙ L/L = ηM /M ,where η ≤ 0.03 in our model. Thus, the luminosity Edd BH Edd 2 c (aν ) of most quasars is sub-Eddington at z ∼ 0. − , (5) 2 c (aν ) + b(1 − c)(1 − c/2) 3 RESULTS where a = 0.707, b = 0.5, c = 0.6, δ = 1.686 is the critical overdensity required for collapse and ν = . D(z) is the linear σ (M)D(z) 3.1 Accretion rate distribution growth factor and σ (M) is the variance of mass fluctuations. We have confirmed that this method works well in O16. The redshift To show the importance of the model of the radiative efficiency evolution of the bias is shown in Fig. 4, where we show different during super-Eddington accretion, in particular, at high redshift, we models of radiative efficiency in different panels. Decreasing the first show the redshift evolution of the normalized accretion rate for upper limit of the quasar luminosity, the quasar bias increases. The our model quasars in Fig. 2. This figure shows that the normalized upper limit of the quasar luminosity affects the bias for brighter accretion rate increases with redshift. The super-Eddington accre- quasars and at higher redshift more strongly. At z  2, the bias of tion is expected to occur, in particular, at high redshift. We expect bright quasars increases significantly for η and η models. This 1 2 that the slim accretion disc model affects the quasar clustering more is because of the following two reasons. First, in these cases only strongly at higher redshift. massive BHs become bright quasars due to the upper limit L , max which is proportional to M ,i.e. L ∼ L ∝ M . Secondly, in BH max Edd BH our model, more massive BHs reside in more massive haloes, which 3.2 Quasar host halo mass is in agreement with the observations (e.g. Ferrarese 2002; Fine et al. Here, we investigate the impact of the model of radiative efficiency 2006, but see also Sabra et al. 2015). Therefore, luminous quasars on the quasar host halo mass. Fig. 3 shows the mass distributions having massive BHs show the strong clustering in these cases. On of the quasar host haloes for three quasar-magnitude bins and their the other hand, the quasar bias hardly changes for all magnitude bins median halo masses (dashed lines) at z = 2.5 when the number at low redshift (z ∼ 1) even for η and η models. This is because 1 2 density of quasars has a noticeable peak. We define bright, inter- most quasars have luminosities below the Eddington luminosity in mediate and faint quasars as those with B-band magnitudes M − this epoch. These quasars are not influenced by the upper limit. 5log h < −24.5, −24.5 < M − 5log h < −23.0 and −23.0 < M − We compare our results with observations. We compile observa- B B 5log h < −21.0, respectively. We show different models of radiative tional results by the large-scale surveys of SDSS and 2QZ (Porciani, efficiency in different panels. Magliocchetti & Norberg 2004; Croom et al. 2005; Padmanabhan MNRASL 471, L21–L25 (2017) L24 T. Oogi et al. Figure 3. Mass distributions of DM haloes hosting bright (red, thick solid), intermeiate (green, dashed) and faint (blue, thin solid) quasars at z = 2.5. Each panel corresponds to a different model of radiative efficiency, as indicated by the legend. The vertical dashed lines are the median masses of the distributions. Figure 4. Redshift evolution of the bias of bright (red, thick solid), intermediate (green, dashed) and faint (blue, thin solid) quasars. Each panel corresponds to a different model of radiative efficiency, as indicated by the legend. Observational results by the large-scale surveys of SDSS and 2QZ (Porciani et al. 2004; Croom et al. 2005; Padmanabhan et al. 2009; Ross et al. 2009; Shen et al. 2009) are also plotted (small filled circles and error bars), whose magnitudes are converted to M . The colour coding represents the luminosity of quasars in the same way as for the models. et al. 2009;Rossetal. 2009;Shenetal. 2009). For η model, the 1 Eddington accretion using our semi-analytic model, ν GC. We have bias of bright quasars is in agreement with the general increasing shown that the model of radiative efficiency strongly affects the trend of the bias shown in observational data. In addition, for η 2 quasar clustering. While the quasar bias has no significant depen- model, the bias is in agreement with the observation at 1.5  z dence on quasar luminosity for the no-limit model, it has significant 2. Future surveys of quasars will allow us to make more accurate dependence on quasar luminosity for the model in which quasar comparison to the model. luminosity is limited by its Eddington luminosity. This is because only massive BHs become high luminosity quasars due to the limit, and, in general, such massive SMBHs reside in massive haloes. 4 SUMMARY AND DISCUSSION The luminosity dependence of the quasar bias is a reflection of In this Letter, we have investigated the large-scale clustering of the super-Eddington accretion model. This indicates that quasar quasars, including the models of radiative efficiency during super- clustering studies provide a constraint on the accretion disc model. MNRASL 471, L21–L25 (2017) Imprints of the super-Eddington accretion L25 The existence of the super-Eddington accretion discs is observa- REFERENCES tionally suggested. Netzer & Trakhtenbrot (2014) have estimated Abramowicz M. A., Czerny B., Lasota J. 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R., was supported by World Premier International Research Center Ishiyama T., Makiya R., 2015, MNRAS, 450, L6 Initiative (WPI), the Ministry of Education, Culture, Sports, Sci- Volonteri M., 2010, A&A Rev., 18, 279 ence and Technology (MEXT), Japan and by MEXT as ‘Prior- Volonteri M., Rees M. J., 2005, ApJ, 633, 624 ity Issue on Post-K computer’ (Elucidation of the Fundamental Volonteri M., Silk J., Dubus G., 2015, ApJ, 804, 148 Laws and Evolution of the Universe, JICFuS and the Japan Society Watarai K.-y., Fukue J., Takeuchi M., Mineshige S., 2000, PASJ, 52, 133 for the Promotion of Science (JSPS). This study has been funded Wu X. -B. et al., 2015, Nature, 518, 512 by MEXT/JSPS KAKENHI Grant Number 25287041, 15K12031 and by Yamada Science Foundation, MEXT HPCI STRATEGIC PROGRAM. RM acknowledge support from JSPS KAKENHI Grant Numbers JP 15H05896. TO has been supported by MEXT KAKENHI Grant 16H01085. MN has been supported by MEXT KAKENHI Grant 17H02867. This paper has been typeset from a T X/LT X file prepared by the author. E E MNRASL 471, L21–L25 (2017)

Journal

Monthly Notices of the Royal Astronomical Society Letters – Oxford University Press

Published: Jun 21, 2017

Keywords: galaxies: formation; galaxies: haloes; quasars: general; dark matter; large-scale structure of Universe; cosmology: theory

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