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

1. 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 ($\gtrsim 10^6{M}_{\odot }$) 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 $10^{10}{M}_{\odot }$ 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 $M_{\text{bulge}}\lesssim 10^{10}{M}_{\odot }$ 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.

2. Models

We use a revised version of an SA model, “New Numerical Galaxy Catalogue” (ν²GC ; 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 (Ishiyama et al., 2015). 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). Here we employ a simulation with L = 70.0 [h⁻¹ Mpc] of box size and 512³ particles, which corresponds to $M_{\text{min}}=2.20\times 10^8\left[h^{-1}{M}_{\odot }\right]$ of minimum halo mass.

We assume a ΛCDM universe which have the following parameters: Ω₀ = 0.31, λ₀ = 0.69, Ω_b = 0.048, σ₈ = 0.83, n_s = 0.96, and a Hubble constant of $H_0=100h\text{ km }{\text{s}}^{-1}$ Mpc⁻¹, where h = 0.68 (Planck Collaboration et al., 2014).

2.1. Setting of Seed Black Holes

We place a seed BH soon after the time of a galaxy formation. We present results with $M_{\text{BH},\text{seed}}=10^3{M}_{\odot }$ (hereafter “light seed model”) where M_{BH, seed} is the seed BH mass, and $10^5{M}_{\odot }$ (“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”).

2.2. 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 ν²GC is based on Hopkins et al. (2009). We consider that mergers of galaxies occur both by dynamical friction (central-satellite merger) and random collision (satellite-sattelite 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 ν²GC 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 :

$\begin{array}{ll}{M}_{\text{acc}}=f_{\text{BH}}\Delta M_{\text{*},\text{burst}},& (1)\end{array}$

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, ΔM_{*, 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.

FIGURE 1

Figure 1. M_BH – M_bulge relations at z ~ 0 for different M_{BH, seed}; the massive (top), random (middle), and light (bottom) seed models. Black solid lines track the median, and shaded regions indicate 10–90 percentile of the models of the model result. Red filled symbols indicate observational results obtained from McConnell and Ma (2013), Kormendy and Ho (2013), and GS15³(triangles, diamonds, and squares, respectively). Blue open symbols are AGN sample obtained from GS15, (see the text for more details). Blue asterisks correspond LEDA 87300 (Baldassare et al., 2015; Graham et al., 2016).

We find all of the models reproduce the relation at $M_{\text{bulge}}\gtrsim 10^{10}{M}_{\odot }$, while the massive seed model has an inconsistency in the observational results for less massive galaxies ($M_{\text{bulge}}\lesssim 10^{10}{M}_{\odot }$). Random and light seed models, on the other hand, provide the consistent results in the range of $M_{\text{BH}}\gtrsim 10^{5.5}{M}_{\odot }$, 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 $~10^3{M}_{\odot }$.

We note that since the number of samples of galaxies with $M_{\text{BH}}\lesssim 10^{5.5}{M}_{\odot }$ (corresponds to $M_{\text{bulge}}\lesssim 10^{10}{M}_{\odot }$) 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 $3\times 10^9{M}_{\odot }$ 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.

FIGURE 2

Figure 2. The difference of averaged SMBH mass due to the seed BH mass at z ~ 2 (dash-doted line in blue), z ~ 1 (dashed line in purple), and z ~ 0 (solid line in pink) as a function of their bulge stellar mass with the ν²GC -H2 simulation. The difference becomes smaller at higher redshift.

4. 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 $10^5{M}_{\odot }$ 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 $M_{\text{bulge}}\lesssim 10^{10}{M}_{\odot }$. Obtaining stronger constraints of the detailed mass distribution of seed BHs observations of $M_{\text{BH}}\lesssim 10^{5.5}{M}_{\odot }$ 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 ν²GC. In addition, HS analyze the output data obtained from ν²GC. TK, TakO, and TaiO gave comments for the analysis. TI provides merger trees obtained from cosmological N-body simulations for ν²GC. 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 Grant-in-Aid (25287041 and 17H02867) from the MEXT of Japan.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Footnotes

3. ^Originally obtained from Scott et al. (2013).

References

Baldassare, V. F., Reines, A. E., Gallo, E., and Greene, J. E. (2015). A ~ 50,000 M_⊙ solar mass black hole in the nucleus of RGG 118. Astrophys. J. Lett. 809:L14. doi: 10.1088/2041-8205/809/1/L14

CrossRef Full Text | Google Scholar

Begelman, M. C., Volonteri, M., and Rees, M. J. (2006). Formation of supermassive black holes by direct collapse in pre-galactic haloes. Mon. Not. R. Astron. Soc. 370, 289–298. doi: 10.1111/j.1365-2966.2006.10467.x

CrossRef Full Text | Google Scholar

Cole, S., Lacey, C. G., Baugh, C. M., and Frenk, C. S. (2000). Hierarchical galaxy formation. Mon. Not. R. Astron. Soc. 319, 168–204. doi: 10.1046/j.1365-8711.2000.03879.x

CrossRef Full Text | Google Scholar

Enoki, M., Ishiyama, T., Kobayashi, M. A. R., and Nagashima, M. (2014). Anti-hierarchical evolution of the active galactic nucleus space density in a hierarchical universe. Astrophys. J. 794:69. doi: 10.1088/0004-637X/794/1/69

CrossRef Full Text | Google Scholar

Enoki, M., Nagashima, M., and Gouda, N. (2003). Relations between galaxy formation and the environments of quasars. Publ. Astron. Soc. Jpn. 55, 133–142. doi: 10.1093/pasj/55.1.133

CrossRef Full Text | Google Scholar

Graham, A. W., Ciambur, B. C., and Soria, R. (2016). Does the intermediate-mass black hole in LEDA 87300 (RGG 118) follow the near-quadratic M_BH–M_Spheroid relation? Astrophys. J. 818:172. doi: 10.3847/0004-637X/818/2/172

CrossRef Full Text | Google Scholar

Graham, A. W., and Scott, N. (2015). The (black hole)-bulge mass scaling relation at low masses. Astrophys. J. 798:54. doi: 10.1088/0004-637X/798/1/54

CrossRef Full Text | Google Scholar

Häring, N., and Rix, H.-W. (2004). On the black hole mass-bulge mass relation. Astrophys. J. Lett. 604, L89–L92. doi: 10.1086/383567

CrossRef Full Text | Google Scholar

Hopkins, P. F., Cox, T. J., Younger, J. D., and Hernquist, L. (2009). How do disks survive mergers? Astrophys. J. 691, 1168–1201. doi: 10.1088/0004-637X/691/2/1168

CrossRef Full Text | Google Scholar

Ishiyama, T., Enoki, M., Kobayashi, M. A. R., Makiya, R., Nagashima, M., and Oogi, T. (2015). The ν²GC simulations: quantifying the dark side of the universe in the Planck cosmology. Publ. Astron. Soc. Jpn. 67:61. doi: 10.1093/pasj/psv021

CrossRef Full Text | Google Scholar

Kormendy, J., and Ho, L. C. (2013). Coevolution (or not) of supermassive black holes and host galaxies. Annu. Rev. Astron. Astrophys. 51, 511–653. doi: 10.1146/annurev-astro-082708-101811

CrossRef Full Text | Google Scholar

Kormendy, J., and Richstone, D. (1995). Inward bound—the search for supermassive black holes in galactic nuclei. Annu. Rev. Astron. Astrophys. 33:581.

Google Scholar

Magorrian, J., Tremaine, S., Richstone, D., Bender, R., Bower, G., Dressler, A., et al. (1998). The demography of massive dark objects in galaxy centers. Astron. J. 115, 2285–2305.

Google Scholar

Makiya, R., Enoki, M., Ishiyama, T., Kobayashi, M. A. R., Nagashima, M., Okamoto, T., et al. (2016). The new numerical galaxy catalog (ν²GC): an updated semi-analytic model of galaxy and active galactic nucleus formation with large cosmological N-body simulations. Publ. Astron. Soc. Jpn. 68:25. doi: 10.1093/pasj/psw005

CrossRef Full Text | Google Scholar

McConnell, N. J., and Ma, C.-P. (2013). Revisiting the scaling relations of black hole masses and host galaxy properties. Astrophys. J. 764:184. doi: 10.1088/0004-637X/764/2/184

CrossRef Full Text | Google Scholar

Mo, H. J., Mao, S., and White, S. D. M. (1998). The formation of galactic discs. Mon. Not. R. Astron. Soc. 295, 319–336. doi: 10.1046/j.1365-8711.1998.01227.x

CrossRef Full Text | Google Scholar

Ade, P. A. R., Aghanim, N., Alves, M. I. R., Armitage-Caplan, C., Arnaud, M., et al. (2014). Planck 2013 results. I. Overview of products and scientific results. Astron. Astrophys. 571:A1. doi: 10.1051/0004-6361/201321529

CrossRef Full Text

Scott, N., Graham, A. W., and Schombert, J. (2013). The supermassive black hole mass-spheroid stellar mass relation for sérsic and core-Sérsic galaxies. Astrophys. J. 768:76. doi: 10.1088/0004-637X/768/1/76

CrossRef Full Text | Google Scholar

Shankar, F., Bernardi, M., Sheth, R. K., Ferrarese, L., Graham, A. W., Savorgnan, G., et al. (2016). Selection bias in dynamically-measured super-massive black holes: its consequences and the quest for the most fundamental relation. Mon. Not. R. Astron. Soc. arXiv:1603.01276.

Google Scholar

Shirakata, H., Kawaguchi, T., Okamoto, T., Makiya, R., Ishiyama, T., Matsuoka, Y., et al. (2016). Theoretical re-evaluations of the black hole mass-bulge mass relation - I. Effect of seed black hole mass. Mon. Not. R. Astron. Soc. 461, 4389–4394. doi: 10.1093/mnras/stw1798

CrossRef Full Text | Google Scholar

Shirakata, H., Okamoto, T., Enoki, M., Nagashima, M., Kobayashi, M. A. R., Ishiyama, T., et al. (2015). The impact of dust in host galaxies on quasar luminosity functions. Mon. Not. R. Astron. Soc. 450, L6–L10. doi: 10.1093/mnrasl/slv035

CrossRef Full Text | Google Scholar

Springel, V., White, S. D. M., Jenkins, A., Frenk, C. S., Yoshida, N., Gao, L., et al. (2005). Simulations of the formation, evolution and clustering of galaxies and quasars. Nature 435, 629–636. doi: 10.1038/nature03597

PubMed Abstract | CrossRef Full Text | Google Scholar