Black hole scaling relations of active and quiescent galaxies: Addressing selection effects and constraining virial factors

Local samples of quiescent galaxies with dynamically measured black hole masses (Mbh) may suffer from an angular resolution-related selection effect, which could bias the observed scaling relations between Mbh and host galaxy properties away from the intrinsic relations. In particular, previous work has shown that the observed Mbh-Mstar (stellar mass) relation is more strongly biased than the Mbh-sigma (velocity dispersion) relation. Local samples of active galactic nuclei (AGN) do not suffer from this selection effect, as in these samples Mbh is estimated from megamasers and/or reverberation mapping-based techniques. With the exception of megamasers, Mbh-estimates in these AGN samples are proportional to a virial coefficient fvir. Direct modelling of the broad line region suggests that fvir~3.5. However, this results in a Mbh-Mstar relation for AGN which lies below and is steeper than the one observed for quiescent black hole samples. A similar though milder trend is seen for the Mbh-sigma relation. Matching the high-mass end of the Mbh-Mstar and Mbh-sigma relations observed in quiescent samples requires fvir~15 and fvir~7, respectively. On the other hand, fvir~3.5 yields Mbh-sigma and Mbh-Mstar relations for AGN which are remarkably consistent with the expected `intrinsic' correlations for quiescent samples (i.e., once account has been made of the angular resolution-related selection effect), providing additional evidence that the sample of local quiescent black holes is biased. We also show that, as is the case for quiescent black holes, the Mbh-Mstar scaling relation of AGN is driven by velocity dispersion, thus providing additional key constraints to black hole-galaxy co-evolution models.Comment: 15 pages, 5 Figures. MNRAS, accepte

The quasar epoch and the stellar ages of early-type galaxies

We investigate the hypothesis that quasars formed together with the stellar populations of early-type galaxies. This hypothesis, in conjunction with the stellar ages of early-type galaxies from population synthesis models, the relation of black hole mass to bulge velocity dispersion, and the velocity dispersion distribution from the Sloan Digital Sky Survey, completely determines the cosmic accretion hystory of supermassive black holes and the redshift evolution of the characteristic luminosity. On the other hand the precise shape of the luminosity function of quasars depends on the light curve of quasars and, in the optical, but not so much in X-rays, on the covering factor of the dust surrounding the AGN. We find a plausible set of assumptions for which the coeval formation of supermassive black holes and elliptical galaxies is in good agreement with the observed B-band and X-ray luminosity functions of quasars.Comment: 8 pages, 5 figures, accepted for publication in MNRA

Approximation to a parabolic system modeling the thermoelastic contacts of two rods

In this article, we study a sequence of finite difference approximate solutions to a parabolic system, which models two dissimilar rods that may come into contact as a result of thermoelastic expansion. We construct the approximate solutions based on a set of finite difference schemes to the system, and we will prove that the approximate solutions converge strongly to the exact solutions. Moreover, we obtain and prove rigorously the error bound, which measures the difference between the exact solutions and approximate solutions in a reasonable norm. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:1–25, 1998Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34948/1/1_ftp.pd

Kinetics of extraction and in situ transesterification of oils from spent coffee grounds

Resource limits, environmental concerns and unstable petroleum costs have led to an increased effort to develop alternative liquid fuels. Purpose grown feedstocks are expensive and demand additional resources such as land and water. Spent coffee grounds (SCGs) are a good potential low-cost feedstock, however, processing times and costs must be lowered in order to be cost competitive with fossil fuels. In this work, we investigated the kinetics of oil extraction from SCGs to explore if current methods of oil extraction could be hastened and if an integrated process which couples oil extraction and conversion to biodiesel stages in one single step (in situ transesterification) was viable. Kinetics of oil extraction from SCGs using n-hexane as solvent was studied as a function of temperature, solvent to solid ratio and water content. We have found that oil extraction times could be as low as 10 min due to higher diffusion coefficients of oils from SCGs. Further, we demonstrate, for the first time, the successful in situ transesterification of SCGs using different concentrations of sodium hydroxide as a catalyst and methanol to oil mole ratios. Both of these outcomes show promise for lowering biodiesel production costs from SCGs, a ubiquitous waste product around the world

Mixed Mimetic Spectral Element Method for Stokes Flow: A Pointwise Divergence-Free Solution

In this paper we apply the recently developed mimetic discretization method to the mixed formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic discretization presented in this paper and in [50] is a higher-order method for curvilinear quadrilaterals and hexahedrals. Fundamental is the underlying structure of oriented geometric objects, the relation between these objects through the boundary operator and how this defines the exterior derivative, representing the grad, curl and div, through the generalized Stokes theorem. The mimetic method presented here uses the language of differential $k$-forms with $k$-cochains as their discrete counterpart, and the relations between them in terms of the mimetic operators: reduction, reconstruction and projection. The reconstruction consists of the recently developed mimetic spectral interpolation functions. The most important result of the mimetic framework is the commutation between differentiation at the continuous level with that on the finite dimensional and discrete level. As a result operators like gradient, curl and divergence are discretized exactly. For Stokes flow, this implies a pointwise divergence-free solution. This is confirmed using a set of test cases on both Cartesian and curvilinear meshes. It will be shown that the method converges optimally for all admissible boundary conditions

Joint Cosmological Formation of QSOs and Bulge-dominated Galaxies

Older and more recent pieces of observational evidence suggest a strong connection between QSOs and galaxies; in particular, the recently discovered correlation between black hole and galactic bulge masses suggests that QSO activity is directly connected to the formation of galactic bulges. The cosmological problem of QSO formation is analyzed in the framework of an analytical model for galaxy formation; for the first time a joint comparison with galaxy and QSO observables is performed. In this model it is assumed that the same physical variable which determines galaxy morphology is able to modulate the mass of the black hole responsible for QSO activity. Both halo spin and the occurence of a major merger are considered as candidates to this role. The predictions of the model are compared to available data for the type-dependent galaxy mass functions, the star-formation history of elliptical galaxies, the QSO luminosity function and its evolution (including the obscured objects contributing to the hard-X-ray background), the mass function of dormant black holes and the distribution of black-hole -- bulge mass ratios. A good agreement with observations is obtained if the halo spin modulates the efficiency of black-hole formation, and if the galactic halos at $z=0$ have shone in an inverted order with respect to the hierarchical one (i.e., stars and black holes in bigger galactic halos have formed before those in smaller ones). This inversion of hierarchical order for galaxy formation, which reconciles galaxy formation with QSO evolution, is consistent with many pieces of observational evidence.Comment: 20 pages, figures included, mn.sty, in press on MNRAS, fig 6 changed (new data added at z=4.4

Probing black hole accretion tracks, scaling relations, and radiative efficiencies from stacked X-ray active galactic nuclei

The masses of supermassive black holes at the centres of local galaxies appear to be tightly correlated with the mass and velocity dispersions of their galactic hosts. However, the local Mbh–Mstar relation inferred from dynamically measured inactive black holes is up to an order-of-magnitude higher than some estimates from active black holes, and recent work suggests that this discrepancy arises from selection bias on the sample of dynamical black hole mass measurements. In this work, we combine X-ray measurements of the mean black hole accretion luminosity as a function of stellar mass and redshift with empirical models of galaxy stellar mass growth, integrating over time to predict the evolving Mbh–Mstar relation. The implied relation is nearly independent of redshift, indicating that stellar and black hole masses grow, on average, at similar rates. Matching the de-biased local Mbh–Mstar relation requires a mean radiative efficiency ε ≳ 0.15, in line with theoretical expectations for accretion on to spinning black holes. However, matching the ‘raw’ observed relation for inactive black holes requires ε ∼ 0.02, far below theoretical expectations. This result provides independent evidence for selection bias in dynamically estimated black hole masses, a conclusion that is robust to uncertainties in bolometric corrections, obscured active black hole fractions, and kinetic accretion efficiency. For our fiducial assumptions, they favour moderate-to-rapid spins of typical supermassive black holes, to achieve ε ∼ 0.12–0.20. Our approach has similarities to the classic Soltan analysis, but by using galaxy-based data instead of integrated quantities we are able to focus on regimes where observational uncertainties are minimized

Finite element pressure stabilizations for incompressible flow problems

Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis