Hole Sphere Research Articles

THEM-σ ANDM-LRELATIONS IN GALACTIC BULGES, AND DETERMINATIONS OF THEIR INTRINSIC SCATTER

We derive improved versions of the relations between supermassive black hole mass (M_BH) and host-galaxy bulge velocity dispersion (sigma) and luminosity (L) (the M-sigma and M-L relations), based on 49 M_BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (epsilon_0) in both relations. We find log(M_BH / M_sun) = alpha + beta * log(sigma / 200 km/s) with (alpha, beta, epsilon_0) = (8.12 +/- 0.08, 4.24 +/- 0.41, 0.44 +/- 0.06) for all galaxies and (alpha, beta, epsilon_0) = (8.23 +/- 0.08, 3.96 +/- 0.42, 0.31 +/- 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-sigma relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-sigma relation. We estimate the M-L relationship as log(M_BH / M_sun) = alpha + beta * log(L_V / 10^11 L_sun,V) of (alpha, beta, epsilon_0) = (8.95 +/- 0.11, 1.11 +/- 0.18, 0.38 +/- 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.

HUBBLE SPACE TELESCOPESPECTROSCOPIC OBSERVATIONS OF THE NARROW-LINE REGION IN NEARBY LOW-LUMINOSITY ACTIVE GALACTIC NUCLEI

We present Space Telescope Imaging Spectrograph observations of 14 nearby low-luminosity active galactic nuclei, including 13 LINERs and 1 Seyfert, taken at multiple parallel slit positions centered on the galaxy nuclei and covering the Hα spectral region. For each galaxy, we measure the emission-line velocities, line widths, and strengths to map out the inner narrow-line region structure -— typically within ~100 pc from the galaxy nucleus. There is a wide diversity among the velocity fields: in a few galaxies the gas is clearly in disk-like rotation, while in other galaxies the gas kinematics either appear chaotic or are dominated by radial flows with multiple velocity components. In most objects, the emission-line surface brightness distribution is very centrally peaked. The [S II] line ratio indicates a radial stratification in gas density, with a sharp increase within the inner 10-20 pc, in the majority of the Type 1 (broad-lined) objects. The electron-density gradients of the Type 1 objects exhibit a similar shape that is well fit by a power law of the form ne = n0(r/1 pc)α, where α = –0.60 ± 0.13. We examine how the [N II] λ6583 line width varies as a function of the aperture size over a range of spatial scales, extending from scales comparable to the black hole's sphere of influence to scales dominated by the host galaxy's bulge. For most galaxies in the sample, we find that the emission-line velocity dispersion is largest within the black hole's gravitational sphere of influence, and decreases with increasing aperture size toward values similar to the bulge stellar velocity dispersion measured within ground-based apertures. We construct models of gas disks in circular rotation and show that this behavior can be consistent with virial motion, although for some combinations of disk parameters we show that the line width can increase as a function of aperture size, as observed in NGC 3245. Future dynamical modeling to determine black hole masses for a few objects in this sample may be worthwhile, although disorganized motion will limit the accuracy of the mass measurements.

The Star‐forming Torus and Stellar Dynamical Black Hole Mass in the Seyfert 1 Nucleus of NGC 3227

We report R ~ 4300 VLT SINFONI adaptive optics integral field K-band spectroscopy of the nucleus of the Seyfert 1 galaxy NGC 3227 at a spatial resolution of 0085 (7 pc). We present the morphologies and kinematics of emission lines and absorption features and give the first derivation of a black hole mass in a Seyfert 1 nucleus from stellar dynamics (marginally resolving the black hole's sphere of influence). We show that the gas in the nucleus has a mean column density of order 1024 cm-2 and that it is geometrically thick, in agreement with the standard molecular torus scenario. We discuss possible heating processes responsible for maintaining the vertical height of the torus. We also resolve the nuclear stellar distribution and find that within a few parsecs of the AGN there has been an intense starburst, the most recent episode of which began ~40 Myr ago but has now ceased. The current luminosity of stars within 30 pc of the AGN, ~3 × 109 L☉, is comparable to that of the AGN. We argue that the star formation has been occurring in the obscuring material. Finally, we apply Schwarzschild orbit superposition models to our full two-dimensional data and derive the mass of the black hole, paying careful attention to the input parameters, which are often uncertain. Our models yield a 1 σ range for the black hole mass of MBH = 7 × 106-2 × 107 M☉.

The black hole in NGC 3379: a comparison of gas and stellar dynamical mass measurements with HST and integral-field data

We combine Hubble Space Telescope spectroscopy and ground-based integral-field data from the SAURON and OASIS instruments to study the central black hole in the nearby elliptical galaxy NGC 3379. From these data, we obtain kinematics of both the stars and the nuclear gaseous component. Axisymmetric three-integral models of the stellar kinematics find a black hole of mass 1.4 +2.6 -1.0 x 10 8 M ⊙ (3σ errors). These models also probe the velocity distribution in the immediate vicinity of the black hole and reveal a nearly isotropic velocity distribution throughout the galaxy and down to the black hole sphere of influence R BH . The morphology of the nuclear gas disc suggests that it is not in the equatorial plane; however the core of NGC 3379 is nearly spherical. Inclined thin-disc models of the gas find a nominal black hole of mass (2.0 ± 0.1) x 10 8 M ⊙ (3a errors), but the model is a poor fit to the kinematics. The data are better fit by introducing a twist in the gas kinematics (with the black hole mass assumed to be 2.0 x 10 8 M ⊙ ), although the constraints on the nature and shape of this perturbation are insufficient for more detailed modelling. Given the apparent regularity of the gas disc appearance, the presence of such strong non-circular motion indicates that caution must be used when measuring black hole masses with gas dynamical methods alone.

Difficulties with Recovering the Masses of Supermassive Black Holes from Stellar Kinematical Data

We investigate the ability of three-integral, axisymmetric, orbit-based modeling algorithms to recover the parameters defining the gravitational potential (M/L ratio and black hole mass Mh) in spheroidal stellar systems using stellar kinematical data. We show that the potential estimation problem is generically under-determined when applied to long-slit kinematical data of the kind used in most black hole mass determinations to date. A range of parameters (M/L, Mh) can provide equally good fits to the data, making it impossible to assign best-fit values. We illustrate the indeterminacy using a variety of data sets derived from realistic models as well as published observations of the galaxy M32. In the case of M32, our reanalysis demonstrates that data published prior to 2000 are equally consistent with Mh in the range 1.5x10^6-5x10^6 solar masses, with no preferred value in that range. While the HST/STIS data for this galaxy may overcome the degeneracy in Mh, HST data for most galaxies do not resolve the black hole's sphere of influence and in these galaxies the degree of degeneracy allowed by the data may be substantial. We investigate the effect on the degeneracy of enforcing smoothness (regularization) constraints. However we find no indication that the true potential can be recovered simply by enforcing smoothness. For a given smoothing level, all solutions in the minimum-chisquare valley exhibit similar levels of noise. These experiments affirm that the indeterminacy is real and not an artifact associated with non-smooth solutions. (Abridged)

Effect of the Spin-Orbit Interaction on the Fermi Surface of LaSn3

Electronic structure is calculated for LaSn 3 by a self-consistent relativistic APW method with the one-electron potential in the local-density approximation. LaSn 3 is a reference for the mixed-valence compound CeSn 3 in which the 4f electrons have recently been proven to be itinerant and contribute directly to the formation of the Fermi surface. Here, the relation between the Fermi surfaces of LaSn 3 and CeSn 3 is investigated. The main Fermi surface of LaSn 3 consists of a distorted hole sphere and a network with slender arms, both of which are connected with small necks. These sheets can explain the de Haas-van Alphen effect and the high-field magnetoresistance reasonably well. The distorted hole sphere in LaSn 3 and the hole sheet in CeSn 3 originate from the eighth band, and look similar to each other. In CeSn 3 , the electron sheet exists as a result of compensation.

Sphere and distance models for binary disordered systems

Abstract First-neighbour geometrical models are presented and shown to provide a good approximation for the structural description of binary disordered systems with metallic, covalent or ionic bonding. Sphere mixture models taking into account atomic size and chemical order effects are first studied and analytical expressions for the partial coordination numbers are derived which only involve packing fraction, diameter ratio, concentration and chemical order parameter. Relations between the concentration thresholds separating different chemical order regimes and site percolation theory are established. Close-packed sphere mixtures are finally shown to be a good representation of liquid or glassy alloys. Hole sphere models are then introduced and shown to provide a satisfactory approximation to the structure of loose-packed covalent glasses of silicon and germanium. Finally, first-neighbour distance models are presented and the variations of their partial structure factors with non-additivity parameter are...