The thickening of the thin disk in the third Galactic quadrant

In the third Galactic quadrant (180 < l < 270) of the Milky Way, the Galactic thin disk exhibits a significant warp ---shown both by gas and young stars--- bending down a few kpc below the formal Galactic plane (b=0). This warp shows its maximum at 240, in the direction of the Canis Major constellation. In a series of papers we have traced the detailed structure of this region using open star clusters, putting particular emphasis on the spiral structure of the outer disk. We noticed a conspicuous accumulation of young star clusters within 2-3 kpc from the Sun and close to b=0, that we interpreted as the continuation of the Local (Orion) arm towards the outer disk. While most clusters (and young stars in their background) follow closely the warp of the disk, our decade-old survey of the spiral structure of this region led us to identify three clusters, Haffner~18(1 and 2) and Haffner~19, which remain very close to b=0 and lie at distances (4.5, 8.0, and 6.4 kpc) where most of the material is already significantly warped. Here we report on a search for clusters that share the same properties as Haffner~18 and 19, and investigate the possible reasons for such an unexpected occurrence. We present UBVRI photometry of 5~young clusters, namely NGC~2345, NGC~2374, Trumpler~9, Haffner~20, and Haffner~21, which also lie close to the formal Galactic plane. With the exception of Haffner~20, in the background of these clusters we detected young stars that appear close to b=0, and are located at distances up to 8 kpc from the Sun, thus deviating significantly from the warp. These populations define a structure that distributes over almost the entire third Galactic quadrant. We discuss this structure in the context of a possible thin disk flaring, in full similarity with the Galactic thick disk.Comment: 53 pages, 12 eps figures, in press in the Astronomical Journa

Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators

Using the generalised invariant formalism we derive a class of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.Comment: 29 page

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete agreement with the results obtained in intrinsic coordinates. In particular, we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

On the Symmetries of the Edgar-Ludwig Metric

The conformal Killing equations for the most general (non-plane wave) conformally flat pure radiation field are solved to find the conformal Killing vectors. As expected fifteen independent conformal Killing vectors exist, but in general the metric admits no Killing or homothetic vectors. However for certain special cases a one-dimensional group of homotheties or motions may exist and in one very special case, overlooked by previous investigators, a two-dimensional homethety group exists. No higher dimensional groups of motions or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure

Growth-quality evaluation of Missouri-grown shortleaf pine (Pinus echinata, Mill.)

Digitized 2007 AES.Includes bibliographical references (pages 57-59)

Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure