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 i
ncreasing 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.
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting algorithms
by allowing for irregular, curved, logarithmic and power-law spirals, ring and truncated shapes in otherwise traditional parametric functions like the Sersic, Moffat, King, Ferrer, etc., profiles. One can mix and match these new shape features freely, with or without constraints, apply them to an arbitrary number of model components and of numerous profile types, so as to produce realistic-looking galaxy model images. Yet, despite the potential for extreme complexity, the meaning of the key parameters like the Sersic index, effective radius or luminosity remain intuitive and essentially unchanged. The new features have an interesting potential for use to quantify the degree of asymmetry of galaxies, to quantify low surface brightness tidal features beneath and beyond luminous galaxies, to allow more realistic decompositions of galaxy subcomponents in the presence of strong rings and spiral arms, and to enable ways to gauge the uncertainties when decomposing galaxy subcomponents. We illustrate these new features by way of several case studies that display various levels of complexity.
Supermassive black hole (BH) masses (MBH) are strongly correlated with galaxy stellar bulge masses (Mbulge) and there are several ideas to explain the origin of this relationship. This study isolates the role of galaxy mergers from considerations of
other detailed physics to more clearly show how a linear BH-galaxy mass relation (MBH-Mgal) can naturally emerge regardless of how primordial BHs were seeded inside galaxies, if the galaxy mass function declines with increasing mass. Under this circumstance, the MBH-Mgal relation is a passive attractor that eventually converges to a tight linear relation because of two basic statistical effects: a central limit-like tendency for galaxy mergers which is much stronger for major mergers than minor mergers, and a convergence toward a linear relation that is due mainly to minor mergers. A curious consequence of this thought experiment is that, if galaxy bulges are formed by major mergers, then merging statistics naturally show that MBH would correlate more strongly with bulge dominated galaxies, because of stronger central-seeking tendencies, than with disk dominated galaxies. Even if some other physics is ultimately responsible for causing a linear MBH-Mbulge relationship, this thought experiment shows that, counter to intuition, random merging of galaxies that harbor random BH masses tends to strengthen rather than weaken a pre-existing, linear, correlation. This idea may be generalized to other gravitationally bound systems (dark matter halo, compact nuclear objects) that retain their physical identities after experiencing mergers.
