Theoretical Re-evaluations of Scaling Relations between SMBHs and Their Host Galaxies—1. Effect of Seed BH Mass

We explore the eﬀect of varying the mass of a seed black hole (BH) on the resulting black hole mass ‒ bulge mass relation at z ~ 0, using a semi - analytic model of galaxy formation combined with large cosmological N -body simulations. When the mass of the seed is set at 10 5 M sun , we ﬁnd that the model results become inconsistent with recent observational results of the black hole mass ‒ bulge mass relation for dwarf galaxies. On the other hand, when we employ seed black holes of 10 3 M sun or select their mass randomly within a 10 3­5 M sun range, the resulting relation is consistent with observational results including the dispersion. We also ﬁnd that black hole mass ‒- bulge mass relations for less massive bulges at z ~ 0 put stronger constraints on the seed BH mass than the relations at higher redshifts. Abstract We present the galactic stellar age -velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have an over-massive/under-massive BH against the best-ﬁtting BH mass - velocity dispersion relation. We ﬁnd that galaxies with an over-massive BH have older stellar age. This result is consistent with observational results obtained from Martin-Navarro et al. (2016) and Merriﬁeld et al. (2000). We also ﬁnd that to obtain this result, AGN feedback is one of the key processes; without the AGN feedback, galaxies with larger velocity dispersion have younger stellar age. In this poster, we also present some statistical properties of galaxies and AGNs obtained from the semi-analytic model to conﬁrm that the model results are consistent with recent observational results. In we report to effect of the BH on


INTRODUCTION
Many observations (e.g., Kormendy and Richstone, 1995;Magorrian et al., 1998;Häring and Rix, 2004;McConnell and Ma, 2013) have suggested that the mass of supermassive black holes (M BH ) correlates with the properties of their host galaxies such as stellar mass of bulges (M bulge ) at z ∼ 0. This M BH -M bulge relation might suggest that supermassive black holes (SMBHs) would have co-evolved with their host galaxies.
SMBHs grow to the current mass ( 10 6 M ⊙ ) from their initial mass. The initial mass and its distribution have been debating. Although, there are many theoretical suggestions of formation mechanism and mass of seed BHs (e.g., Begelman et al., 2006), we cannot obtain what is the dominant mechanism by comparing theoretical models with observations since seed BHs are not observable directly.
Here, we focus on the M BH -M bulge relation for galaxies with bulge mass is less than 10 10 M ⊙ to get the constraints on mass of seed BHs. This paper is a summary of Shirakata et al. (2016) in which we investigate the effect of the seed BHs' mass on model predictions of M BH -M bulge relation at M bulge 10 10 M ⊙ by using an semi-analytic model of galaxy formation (hereafter SA model). In section 2 we briefly review the SA model we used. Section 3 includes the main results. Finally, in section 4, we summarize this review and briefly mention future prospects.

MODELS
We use a revised version of an SA model, "New Numerical Galaxy Catalogue" (ν 2 GC ; Makiya et al., 2016, hereafter M16), where the models related to the SMBH and AGNs are described in Enoki et al. (2003), Enoki et al. (2014), and Shirakata et al. (2015). We consider star formation in galactic disk and bulge, mergers of galaxies, atomic gas cooling, gas heating by UV feedback and feedbacks via supernovae and AGNs, and the growth of SMBHs by coalescence and gas accretion from their host galaxies.
Merging histories of dark matter halos are calculated from state-of-the-art cosmological N-body simulations . The cosmological simulations have a high mass resolution and large volume compared to previous simulations (e.g., mass resolution is roughly four times better than those of Millennium simulations, Springel et al., 2005).

Setting of Seed Black Holes
We place a seed BH soon after the time of a galaxy formation. We present results with M BH,seed = 10 3 M ⊙ (hereafter "light seed model") where M BH,seed is the seed BH mass, and 10 5 M ⊙ ("massive seed model"). In addition, we employ the model in which M BH,seed takes uniformly random values in the logarithmic scale in the range of 3 ≤ log(M BH,seed /M ⊙ ) ≤ 5 (hereafter "random seed model").

Summary of Bulge and SMBH Growth Model
We assume that the bulge grows via starbursts and the migration of disk stars. Starbursts are triggered by mergers of galaxies (major and minor) or disk instability. The model of merger driven bulge formation in ν 2 GC is based on Hopkins et al. (2009). We consider that mergers of galaxies occur both by dynamical friction (central-satellite merger) and random collision (satellitesattelite merger). We also introduce the spheroid formation by disk instability following Mo et al. (1998) and Cole et al. (2000). In both cases, the gas supplyed from galactic disk to the bulge is completely exhausted by a starburst and fueling onto their central SMBHs.
SMBHs in ν 2 GC are mainly grown by gas accretion from their host galaxy. When a starburst occurs in a bulge, a part of cold gas gets accreted by the SMBH : where M acc is the cold gas mass accreted onto the SMBH, which is assumed to be proportional to the stellar mass formed by a current starburst, M * ,burst .
Here we set f BH = 0.01. SMBHs also grow via coalescence of BHs which occurs with mergers of host galaxies. For simplicity, we assume BHs merge instantaneously when their host galaxies merge.  3. RESULTS Figure 1 shows the main result which depicts the M BH -M bulge relation at z ∼ 0 obtained from the model and observations. Each panels correspond to the results of massive seed model (top), random seed model (middle), and light seed model (bottom), respectively. Red solid lines represents the model result, blue and green points represents the observational data. We find all of the models reproduce the relation at M bulge 10 10 M ⊙ , while the massive seed model has an inconsistency in the observational results for less massive galaxies (M bulge 10 10 M ⊙ ). Random and light seed models, on the other hand, provide the consistent results in the range of M BH 10 5.5 M ⊙ , with observational estimates. We thus conclude that to explain recent observational data of the M BH -M bulge relation at z ∼ 0, seed BH mass should dominate with ∼ 10 3 M ⊙ .
We note that since the number of samples of galaxies with M BH 10 5.5 M ⊙ (corresponds to M bulge 10 10 M ⊙ ) are not sufficient. Observational data with the mass range are thus necessary to investigate the detailed mass distribution of the seed BHs. It is however difficult to estimate BH and bulge mass of less massive galaxies. We thus investigate whether the M BH -M bulge relation at higher redshifts could be useful for getting further constraints on the mass of seed BHs. Figure 2 displays the ratio of the average BH masses in the light seed model (≡ M BH 3 ) and those in the massive seed model (≡ M BH 5 ), as a function of bulge masses. The difference in the seed mass significantly appears in galaxies with bulge mass below 3×10 9 M ⊙ at z ∼ 0, 1, and 2. We also find that the difference becomes smaller at higher redshift for a given M bulge . Observations of less massive bulges at z ∼ 0 would thus be more important than at higher redshifts for investigating the mass distribution of seed BHs.

SUMMARY AND FUTURE PROSPECTS
We investigate how the mass of the seed BHs affects model predictions of the local M BH -M bulge relation by using an SA model. The results suggest that seed BHs with as massive as 10 5 M ⊙ should not be dominant for reproducing the observed M BH -M bulge relation at z ∼ 0 over a wide range of bulge masses down to M bulge 10 10 M ⊙ . Obtaining stronger constraints of the 3 Originally obtained from Scott et al. (2013). detailed mass distribution of seed BHs observations of M BH 10 5.5 M ⊙ would be required.
We have shown results of the local M BH -M bulge relations varying the mass of seed BHs. According to Shankar et al. (2016), M bulge obtained from observations could be biased in favor of larger stellar masses. If so, we might have to use M BH -velocity dispersion relation instead of the local M BH -M bulge . We leave it for future studies.
The spheroids formed through disk instability might be classified as so-called "pseudo bulges". There are some debates whether pseudo bulges and classical bulges follow the same M BH -M bulge relation (e.g., Kormendy and Ho, 2013). We might need the model of the properties of pseudo bulges in the near future.

AUTHOR CONTRIBUTIONS
HS, RM, MN, ME, and MK have developed ν 2 GC . In addition, HS analyze the output data obtained from ν 2 GC . TK, TakO, and TaiO gave comments for the analysis. TI provides merger trees obtained from cosmological N-body simulations for ν 2 GC . YM gave fruitful comments from a standpoint of AGN observations. FUNDING TK was supported in part by an University Research Support Grant from the NAOJ and JSPS KAKENHI (17K05389). TakO was supported by JSPS Grant-in-Aid for Young Scientists (16H01085). RM was supported in part by MEXT KAKENHI (15H05896). TI was supported by MEXT HPCI STRATEGIC PROGRAM and MEXT/JSPS KAKENHI (15K12031) and by Yamada Science Foundation. MN was supported by the Grantin-Aid (25287041 and 17H02867) from the MEXT of Japan.