Theoretical Predictions for Surface Brightness Fluctuations and Implications for Stellar Populations of Elliptical Galaxies

(Abridged) We present new theoretical predictions for surface brightness fluctuations (SBFs) using models optimized for this purpose. Our predictions agree well with SBF data for globular clusters and elliptical galaxies. We provide refined theoretical calibrations and k-corrections needed to use SBFs as standard candles. We suggest that SBF distance measurements can be improved by using a filter around 1 micron and calibrating I-band SBFs with the integrated V-K galaxy color. We also show that current SBF data provide useful constraints on population synthesis models, and we suggest SBF-based tests for future models. The data favor specific choices of evolutionary tracks and spectra in the models among the several choices allowed by comparisons based on only integrated light. In addition, the tightness of the empirical I-band SBF calibration suggests that model uncertainties in post-main sequence lifetimes are less than +/-50% and that the IMF in ellipticals is not much steeper than that in the solar neighborhood. Finally, we analyze the potential of SBFs for probing unresolved stellar populations. We find that optical/near-IR SBFs are much more sensitive to metallicity than to age. Therefore, SBF magnitudes and colors are a valuable tool to break the age/metallicity degeneracy. Our initial results suggest that the most luminous stellar populations of bright cluster galaxies have roughly solar metallicities and about a factor of three spread in age.Comment: Astrophysical Journal, in press (uses Apr 20, 2000 version of emulateapj5.sty). Reposted version has a minor cosmetic change to Table

Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space \sM_{\dd}^n of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, ACC-coordinates, as those $(n+2) \times (n+2)$ real matrices \bW with \bW^T \bQ_{D,n} \bW = \bQ_{W,n} where $Q_{D,n} = x_1^2 +... + x_{n+2}^2 - \frac{1}{n}(x_1 +... + x_{n+2})^2$ is the $n$-dimensional Descartes quadratic form, $Q_{W,n} = -8x_1x_2 + 2x_3^2 + ... + 2x_{n+2}^2$, and \bQ_{D,n} and \bQ_{W,n} are their corresponding symmetric matrices. There are natural actions on the parameter space \sM_{\dd}^n. We introduce $n$-dimensional analogues of the Apollonian group, the dual Apollonian group and the super-Apollonian group. These are finitely generated groups with the following integrality properties: the dual Apollonian group consists of integral matrices in all dimensions, while the other two consist of rational matrices, with denominators having prime divisors drawn from a finite set $S$ depending on the dimension. We show that the the Apollonian group and the dual Apollonian group are finitely presented, and are Coxeter groups. We define an Apollonian cluster ensemble to be any orbit under the Apollonian group, with similar notions for the other two groups. We determine in which dimensions one can find rational Apollonian cluster ensembles (all curvatures rational) and strongly rational Apollonian sphere ensembles (all ACC-coordinates rational).Comment: 37 pages. The third in a series on Apollonian circle packings beginning with math.MG/0010298. Revised and extended. Added: Apollonian groups and Apollonian Cluster Ensembles (Section 4),and Presentation for n-dimensional Apollonian Group (Section 5). Slight revision on March 10, 200

Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)$\times$(center) is an integer vector. This series of papers explain such properties. A {\em Descartes configuration} is a set of four mutually tangent circles with disjoint interiors. We describe the space of all Descartes configurations using a coordinate system \sM_\DD consisting of those $4 \times 4$ real matrices \bW with \bW^T \bQ_{D} \bW = \bQ_{W} where \bQ_D is the matrix of the Descartes quadratic form $Q_D= x_1^2 + x_2^2+ x_3^2 + x_4^2 -{1/2}(x_1 +x_2 +x_3 + x_4)^2$ and \bQ_W of the quadratic form $Q_W = -8x_1x_2 + 2x_3^2 + 2x_4^2$. There are natural group actions on the parameter space \sM_\DD. We observe that the Descartes configurations in each Apollonian packing form an orbit under a certain finitely generated discrete group, the {\em Apollonian group}. This group consists of $4 \times 4$ integer matrices, and its integrality properties lead to the integrality properties observed in some Apollonian circle packings. We introduce two more related finitely generated groups, the dual Apollonian group and the super-Apollonian group, which have nice geometrically interpretations. We show these groups are hyperbolic Coxeter groups.Comment: 42 pages, 11 figures. Extensively revised version on June 14, 2004. Revised Appendix B and a few changes on July, 2004. Slight revision on March 10, 200

A sub-product construction of Poincare-Einstein metrics

Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincar\'e-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincare metrics we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman-Graham) obstruction tensor vanishes.Comment: 23 pages Minor correction to section 5. References update

Universality of the Small-Scale Dynamo Mechanism

We quantify possible differences between turbulent dynamo action in the Sun and the dynamo action studied in idealized simulations. For this purpose we compare Fourier-space shell-to-shell energy transfer rates of three incrementally more complex dynamo simulations: an incompressible, periodic simulation driven by random flow, a simulation of Boussinesq convection, and a simulation of fully compressible convection that includes physics relevant to the near-surface layers of the Sun. For each of the simulations studied, we find that the dynamo mechanism is universal in the kinematic regime because energy is transferred from the turbulent flow to the magnetic field from wavenumbers in the inertial range of the energy spectrum. The addition of physical effects relevant to the solar near-surface layers, including stratification, compressibility, partial ionization, and radiative energy transport, does not appear to affect the nature of the dynamo mechanism. The role of inertial-range shear stresses in magnetic field amplification is independent from outer-scale circumstances, including forcing and stratification. Although the shell-to-shell energy transfer functions have similar properties to those seen in mean-flow driven dynamos in each simulation studied, the saturated states of these simulations are not universal because the flow at the driving wavenumbers is a significant source of energy for the magnetic field.Comment: 16 pages, 9 figures, accepted for publication in Ap

Characterization and properties of controlled nucleation thermochemical deposited (CNTD) silicon carbide

The microstructure of controlled nucleation thermochemical deposition (CNTD) - SiC material was studied and the room temperature and high temperature bend strength and oxidation resistance was evaluated. Utilizing the CNTD process, ultrafine grained (0.01-0.1 mm) SiC was deposited on W - wires (0.5 mm diameter by 20 cm long) as substrates. The deposited SiC rods had superior surface smoothness and were without any macrocolumnar growth commonly found in conventional CVD material. At both room and high temperature (1200 - 1380 C), the CNTD - SiC exhibited bend strength approximately 200,000 psi (1380 MPa), several times higher than that of hot pressed, sintered, or CVD SiC. The excellent retention of strength at high temperature was attributed to the high purity and fine grain size of the SiC deposit and the apparent absence of grain growth at elevated temperatures. The rates of weight change for CNTD - SiC during oxidation were lower than for NC-203 (hot pressed SiC), higher than for GE's CVD - SiC, and considerably below those for HS-130 (hot pressed Si3N4). The high purity, fully dense, and stable grain size CNTD - SiC material shows potential for high temperature structural applications; however problem areas might include: scaling the process to make larger parts, deposition on removable substrates, and the possible residual tensile stress