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Register a new userWhat Do Statistics Reveal About the Black Hole versus the Bulge Mass Correlation and Co-evolution?
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Chien Y. Peng
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Observational data show that the correlation between supermassive black holes (MBH) and galaxy bulge (Mbulge) masses follows a nearly linear trend, and that the correlation is strongest with the bulge rather than the total stellar mass (Mgal). With increasing redshift, the ratio Gamma=MBH/Mbulge relative to z=0 also seems to be larger for MBH >~ 10^{8.5} Msol. This study looks more closely at statistics to better understand the creation and observations of the MBH-Mbulge correlation. It is possible to show that if galaxy merging statistics can drive the correlation, minor mergers are responsible for causing a *convergence to linearity* most evident at high masses, whereas major mergers have a central limit convergence that more strongly *reduces the scatter*. This statistical reasoning is agnostic about galaxy morphology. Therefore, combining statistical prediction (more major mergers ==> tighter correlation) with observations (bulges = tightest correlation), would lead one to conclude that more major mergers (throughout an entire merger tree, not just the primary branch) give rise to more prominent bulges. With regard to controversial findings that Gamma increases with redshift, this study shows why the luminosity function (LF) bias argument, taken correctly at face value, strengthens rather than weakens the results. However, correcting for LF bias is unwarranted because the BH mass scale for quasars is bootstrapped to the MBH-Sigma* correlation in normal galaxies at z=0, and quasar-quasar comparisons are internally consistent. In Monte-Carlo simulations, high Gamma objects are under-merged galaxies that take longer to converge to linearity via minor mergers. Another evidence that the galaxies are undermassive at z >~ 2 for their MBH is that the quasar hosts are very compact for their expected mass.
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We constrain the ratio of black hole (BH) mass to total stellar mass of type-1 AGN in the COSMOS survey at 1<z<2. For 10 AGN at mean redshift z~1.4 with both HST/ACS and HST/NICMOS imaging data we are able to compute total stellar mass M_(*,total), based on restframe UV-to-optical host galaxy colors which constrain mass-to-light ratios. All objects have virial BH mass-estimates available from the COSMOS Magellan/IMACS and zCOSMOS surveys. We find zero difference between the M_BH--M_(*,total)-relation at z~1.4 and the M_BH--M_(*,bulge)-relation in the local Universe. Our interpretation is: (a) If our objects were purely bulge-dominated, the M_BH--M_(*,bulge)-relation has not evolved since z~1.4. However, (b) since we have evidence for substantial disk components, the bulges of massive galaxies (logM_(*,total)=11.1+-0.25 or logM_BH~8.3+-0.2) must have grown over the last 9 Gyrs predominantly by redistribution of disk- into bulge-mass. Since all necessary stellar mass exists in the galaxy at z=1.4, no star-formation or addition of external stellar material is required, only a redistribution e.g. induced by minor and major merging or through disk instabilities. Merging, in addition to redistributing mass in the galaxy, will add both BH and stellar/bulge mass, but does not change the overall final M_BH/M_(*,bulge) ratio. Since the overall cosmic stellar and BH mass buildup trace each other tightly over time, our scenario of bulge-formation in massive galaxies is independent of any strong BH-feedback and means that the mechanism coupling BH and bulge mass until the present is very indirect.
In the present paper, we investigate the cosmographic problem using the bias-variance trade-off. We find that both the z-redshift and the $y=z/(1+z)$-redshift can present a small bias estimation. It means that the cosmography can describe the supernova data more accurately. Minimizing risk, it suggests that cosmography up to the second order is the best approximation. Forecasting the constraint from future measurements, we find that future supernova and redshift drift can significantly improve the constraint, thus having the potential to solve the cosmographic problem. We also exploit the values of cosmography on the deceleration parameter and equation of state of dark energy $w(z)$. We find that supernova cosmography cannot give stable estimations on them. However, much useful information was obtained, such as that the cosmography favors a complicated dark energy with varying $w(z)$, and the derivative $dw/dz<0$ for low redshift. The cosmography is helpful to model the dark energy.
The growth of black holes and the formation and evolution of galaxies appear to be linked at such a fundamental level that we think of the two as `co-evolving. Recent observations show that this co-evolution may be complex and the result of several different pathways. While it is clear that black hole accretion is linked to specific phases of the evolution of the host galaxy, the impact of the energy liberated by the black hole on the evolutionary trajectory of the host by feedback is less clear. In this contribution, I review the motivations for co-evolution, the current state of the observational picture, and some challenges by black hole feedback.
We investigate a mechanism for a super-massive black hole at the center of a galaxy to wander in the nucleus region. A situation is supposed in which the central black hole tends to move by the gravitational attractions from the nearby molecular clouds in a nuclear bulge but is braked via the dynamical frictions by the ambient stars there. We estimate the approximate kinetic energy of the black hole in an equilibrium between the energy gain rate through the gravitational attractions and the energy loss rate through the dynamical frictions, in a nuclear bulge composed of a nuclear stellar disk and a nuclear stellar cluster as observed from our Galaxy. The wandering distance of the black hole in the gravitational potential of the nuclear bulge is evaluated to get as large as several 10 pc, when the black hole mass is relatively small. The distance, however, shrinks as the black hole mass increases and the equilibrium solution between the energy gain and loss disappears when the black hole mass exceeds an upper limit. As a result, we can expect the following scenario for the evolution of the black hole mass: When the black hole mass is smaller than the upper limit, mass accretion of the interstellar matter in the circum-nuclear region, causing the AGN activities, makes the black hole mass larger. However, when the mass gets to the upper limit, the black hole loses the balancing force against the dynamical friction and starts spiraling downward to the gravity center. From simple parameter scaling, the upper mass limit of the black hole is found to be proportional to the bulge mass and this could explain the observed correlation of the black hole mass with the bulge mass.
Observations of nearby galaxies reveal a strong correlation between the mass of the central dark object M and the velocity dispersion sigma of the host galaxy, of the form log(M/M_sun) = a + b*log(sigma/sigma_0); however, published estimates of the slope b span a wide range (3.75 to 5.3). Merritt & Ferrarese have argued that low slopes (<4) arise because of neglect of random measurement errors in the dispersions and an incorrect choice for the dispersion of the Milky Way Galaxy. We show that these explanations account for at most a small part of the slope range. Instead, the range of slopes arises mostly because of systematic differences in the velocity dispersions used by different groups for the same galaxies. The origin of these differences remains unclear, but we suggest that one significant component of the difference results from Ferrarese & Merritts extrapolation of central velocity dispersions to r_e/8 (r_e is the effective radius) using an empirical formula. Another component may arise from dispersion-dependent systematic errors in the measurements. A new determination of the slope using 31 galaxies yields b=4.02 +/- 0.32, a=8.13 +/- 0.06, for sigma_0=200 km/s. The M-sigma relation has an intrinsic dispersion in log M that is no larger than 0.3 dex. In an Appendix, we present a simple model for the velocity-dispersion profile of the Galactic bulge.
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