The Book of Leviticus

The book of Leviticus: critical edition of the Hebrew text printed in colors exhibiting the composite structure of the book / with notes by S.R. Driver ; assisted by H.A. White.https://scholar.csl.edu/ebooks/1017/thumbnail.jp

A log-quadratic relation for predicting supermassive black hole masses from the host bulge Sersic index

We reinvestigate the correlation between black hole mass and bulge concentration. With an increased galaxy sample, updated estimates of galaxy distances, black hole masses, and Sersic indices `n' - a measure of concentration - we perform a least-squares regression analysis to obtain a relation suitable for the purpose of predicting black hole masses in other galaxies. In addition to the linear relation, log(M_bh) = 7.81(+/-0.08) + 2.69(+/-0.28)[log(n/3)] with epsilon_(intrin)=0.31 dex, we investigated the possibility of a higher order M_bh-n relation, finding the second order term in the best-fitting quadratic relation to be inconsistent with a value of zero at greater than the 99.99% confidence level. The optimal relation is given by log(M_bh) = 7.98(+/-0.09) + 3.70(+/-0.46)[log(n/3)] - 3.10(+/-0.84)[log(n/3)]^2, with epsilon_(intrin)=0.18 dex and a total absolute scatter of 0.31 dex. Extrapolating the quadratic relation, it predicts black holes with masses of ~10^3 M_sun in n=0.5 dwarf elliptical galaxies, compared to ~10^5 M_sun from the linear relation, and an upper bound on the largest black hole masses in the local universe, equal to 1.2^{+2.6}_{-0.4}x10^9 M_sun}. In addition, we show that the nuclear star clusters at the centers of low-luminosity elliptical galaxies follow an extrapolation of the same quadratic relation. Moreover, we speculate that the merger of two such nucleated galaxies, accompanied by the merger and runaway collision of their central star clusters, may result in the late-time formation of some supermassive black holes. Finally, we predict the existence of, and provide equations for, a relation between M_bh and the central surface brightness of the host bulge

The Luminosity Function of Low-Redshift Abell Galaxy Clusters

We present the results from a survey of 57 low-redshift Abell galaxy clusters to study the radial dependence of the luminosity function (LF). The dynamical radius of each cluster, r200, was estimated from the photometric measurement of cluster richness, Bgc. The shape of the LFs are found to correlate with radius such that the faint-end slope, alpha, is generally steeper on the cluster outskirts. The sum of two Schechter functions provides a more adequate fit to the composite LFs than a single Schechter function. LFs based on the selection of red and blue galaxies are bimodal in appearance. The red LFs are generally flat for -22 < M_Rc < -18, with a radius-dependent steepening of alpha for M_Rc > -18. The blue LFs contain a larger contribution from faint galaxies than the red LFs. The blue LFs have a rising faint-end component (alpha ~ -1.7) for M_Rc > -21, with a weaker dependence on radius than the red LFs. The dispersion of M* was determined to be 0.31 mag, which is comparable to the median measurement uncertainty of 0.38 mag. This suggests that the bright-end of the LF is universal in shape at the 0.3 mag level. We find that M* is not correlated with cluster richness when using a common dynamical radius. Also, we find that M* is weakly correlated with BM-type such that later BM-type clusters have a brighter M*. A correlation between M* and radius was found for the red and blue galaxies such that M* fades towards the cluster center.Comment: Accepted for publication in ApJ, 16 pages, 4 tables, 24 figure

The Properties of Poor Groups of Galaxies: III. The Galaxy Luminosity Function

We obtain R-band photometry for galaxies in six nearby poor groups for which we have spectroscopic data, including 328 new galaxy velocities. For the five groups with luminous X-ray halos, the composite group galaxy luminosity function (GLF) is fit adequately by a Schechter function with Mstar = -21.6 +/- 0.4 + 5log h and alpha = -1.3 +/- 0.1. We also find that (1) the ratio of dwarfs to giants is significantly larger for the five groups with luminous X-ray halos than for the one marginally X-ray detected group, (2) the composite GLF for the luminous X-ray groups is consistent in shape with that for rich clusters, (3) the composite group GLF rises more steeply at the faint end than that of the field, (4) the shape difference between the field and composite group GLF's results mostly from the population of non-emission line galaxies, whose dwarf-to-giant ratio is larger in the denser group environment than in the field, and (5) the non-emission line dwarfs are more concentrated about the group center than the non-emission line giants. This last result indicates that the dwarfs and giants occupy different orbits (i.e., have not mixed completely) and suggests that the populations formed at a different times. Our results show that the shape of the GLF varies with environment and that this variation is due primarily to an increase in the dwarf-to-giant ratio of quiescent galaxies in higher density regions, at least up to the densities characteristic of X-ray luminous poor groups. This behavior suggests that, in some environments, dwarfs are more biased than giants with respect to dark matter. This trend conflicts with the prediction of standard biased galaxy formation models. (Abridged)Comment: 36 pages, AASLaTeX with 8 figures. Table 1 also available at http://atropos.as.arizona.edu/aiz/papers/all_grp_lf_ascii.dat.final . To appear in Ap

Populating Stellar Orbits Inside a Rotating, Gaseous Bar

In an effort to better understand the formation and evolution of barred galaxies, we have examined the properties of equatorial orbits in the effective potential of one model of a rapidly rotating, steady-state gas-dynamical bar that has been constructed via a self-consistent hydrodynamical simulation. Using a ``Restriction Hypothesis'' to determine initial conditions, we find that a significant fraction of orbits in this potential are quasi-ergodic and that regular orbits have a ``bowtie'' shape in contrast to the more typical x1 orbits. This bowtie orbit should give a boxy-peanut shape to such systems.Comment: Accepted for publication in The Astrophysical Journal; 29 pages, 29 gif figure

Can the Future Influence the Present?

One widely accepted model of classical electrodynamics assumes that a moving charged particle produces both retarded and advanced fields. This formulation first appeared at least 75 years ago. It was popularized in the 1940\u27s by work of Wheeler and Feynman. But the most fundamental question associated with the model has remained unanswered: When (if ever) does the two-body problem have a unique solution? The present paper gives an answer in one special case. Imagine two identical charged particles alone in the universe moving symmetrically along the x axis. One is at x(t) and the other is at −x(t). Their motion is then governed by a system of functional differential equations involving both retarded and advanced arguments. This system together with the Newtonian initial data x(0)=x0\u3e0 and x′(0)=0 has a unique solution for all time provided x0 is sufficiently large. Perhaps the existence and uniqueness proof given for this special case will pave the way for more general results on this curious two-body problem

Argumentation in school science : Breaking the tradition of authoritative exposition through a pedagogy that promotes discussion and reasoning

The value of argumentation in science education has become internationally recognised and has been the subject of many research studies in recent years. Successful introduction of argumentation activities in learning contexts involves extending teaching goals beyond the understanding of facts and concepts, to include an emphasis on cognitive and metacognitive processes, epistemic criteria and reasoning. The authors focus on the difficulties inherent in shifting a tradition of teaching from one dominated by authoritative exposition to one that is more dialogic, involving small-group discussion based on tasks that stimulate argumentation. The paper builds on previous research on enhancing the quality of argument in school science, to focus on how argumentation activities have been designed, with appropriate strategies, resources and modelling, for pedagogical purposes. The paper analyses design frameworks, their contexts and lesson plans, to evaluate their potential for enhancing reasoning through foregrounding the processes of argumentation. Examples of classroom dialogue where teachers adopt the frameworks/plans are analysed to show how argumentation processes are scaffolded. The analysis shows that several layers of interpretation are needed and these layers need to be aligned for successful implementation. The analysis serves to highlight the potential and limitations of the design frameworks

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be published in one of the AIP Conference Proceedings serie