Slicing Sets and Measures, and the Dimension of Exceptional Parameters

We consider the problem of slicing a compact metric space \Omega with sets of the form \pi_{\lambda}^{-1}\{t\}, where the mappings \pi_{\lambda} \colon \Omega \to \R, \lambda \in \R, are \emph{generalized projections}, introduced by Yuval Peres and Wilhelm Schlag in 2000. The basic question is: assuming that \Omega has Hausdorff dimension strictly greater than one, what is the dimension of the 'typical' slice \pi_{\lambda}^{-1}{t}, as the parameters \lambda and t vary. In the special case of the mappings \pi_{\lambda} being orthogonal projections restricted to a compact set \Omega \subset \R^{2}, the problem dates back to a 1954 paper by Marstrand: he proved that for almost every \lambda there exist positively many $t \in \R$ such that \dim \pi_{\lambda}^{-1}{t} = \dim \Omega - 1. For generalized projections, the same result was obtained 50 years later by J\"arvenp\"a\"a, J\"arvenp\"a\"a and Niemel\"a. In this paper, we improve the previously existing estimates by replacing the phrase 'almost all \lambda' with a sharp bound for the dimension of the exceptional parameters.Comment: 31 pages, three figures; several typos corrected and large parts of the third section rewritten in v3; to appear in J. Geom. Ana

Super star clusters and Supernovae in interacting LIRGs unmasked by NIR adaptive optics

We report on an on-going near-IR adaptive optics survey targeting interacting luminous IR galaxies. High-spatial resolution NIR data are crucial to enable interpretation of kinematic, dynamical and star formation (SF) properties of these very dusty objects. Whole progenitor nuclei in the interactions can be missed if only optical HST imaging is used. Here we specifically present the latest results regarding core-collapse supernovae found within the highly extincted nuclear regions of these galaxies. Direct detection and study of such highly obscured CCSNe is crucial for revising the optically-derived SN rates used for providing an independent measurement of the SF history of the Universe. We also present thus-far the first NIR luminosity functions of super star cluster (SSC) candidates. The LFs can then be used to constrain the formation and evolution of SSCs via constraints based on initial mass functions and cluster disruption models.Comment: 6 pages. To appear in proceedings of 'Galaxies and their Masks' (Namibia, April 2010), published by Springer, New York, eds. D.L. Block, K.C. Freeman, I. Puerar

On the nature of the progenitors of three type II-P supernovae: 2004et, 2006my and 2006ov

The pre-explosion observations of the type II-P supernovae 2006my, 2006ov and 2004et, are re-analysed. In the cases of supernovae 2006my and 2006ov we argue that the published candidate progenitors are not coincident with their respective supernova sites in pre-explosion Hubble Space Telescope observations. We therefore derive upper luminosity and mass limits for the unseen progenitors of both these supernovae, assuming they are red supergiants: 2006my (log L/Lsun = 4.51; mass < 13Msun) and 2006ov (log L/Lsun = 4.29; mass < 10Msun). In the case of supernova 2004et we show that the yellow-supergiant progenitor candidate, originally identified in Canada France Hawaii Telescope images, is still visible ~3 years post-explosion in observations from the William Herschel Telescope. High-resolution Hubble Space Telescope and Gemini (North) adaptive optics late-time imagery reveal that this source is not a single yellow supergiant star, but rather is resolved into at least three distinct sources. We report the discovery of the unresolved progenitor as an excess of flux in pre-explosion Isaac Newton Telescope i'-band imaging. Accounting for the late-time contribution of the supernova using published optical spectra, we calculate the progenitor photometry as the difference between the pre- and post-explosion, ground-based observations. We find the progenitor was most likely a late K to late M-type supergiant of 8 +5/-1 Msun. In all cases we conclude that future, high-resolution observations of the supernova sites will be required to confirm these results.Comment: 43 pages (pre-print format), 12 figures, 10 tables. Significant revision following referee's comments. Accepted for publication in MNRA

Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.Comment: 20 pages, 1 figur

Supernovae and radio transients in M 82

We present optical and near-infrared (IR) photometry and near-IR spectroscopy of SN 2004am, the only optically detected supernova (SN) in M 82. These demonstrate that SN 2004am was a highly reddened type II-P SN similar to the low luminosity type II-P events such as SNe 1997D and 2005cs. We show that SN 2004am was located coincident with the obscured super star cluster M 82-L, and from the cluster age infer a progenitor mass of 12 +7/-3 Msun. In addition to this, we present a high spatial resolution Gemini-N K-band adaptive optics image of the site of SN 2008iz and a second transient of uncertain nature, both detected so far only at radio wavelengths. Using image subtraction techniques together with archival data from the Hubble Space Telescope, we are able to recover a near-IR transient source co-incident with both objects. We find the likely extinction towards SN 2008iz to be not more than Av ~ 10. The nature of the second transient remains elusive and we regard an extremely bright microquasar in M 82 as the most plausible scenario.Comment: 14 pages, 8 figures, accepted for publication in MNRA

Metal-ligand interplay in strongly-correlated oxides: a parametrized phase diagram for pressure induced spin transitions

We investigate the magnetic properties of archetypal transition-metal oxides MnO, FeO, CoO and NiO under very high pressure by x-ray emission spectroscopy at the K\beta line. We observe a strong modification of the magnetism in the megabar range in all the samples except NiO. The results are analyzed within a multiplet approach including charge-transfer effects. The pressure dependence of the emission line is well accounted for by changes of the ligand field acting on the d electrons and allows us to extract parameters like local d-hybridization strength, O-2p bandwidth and ionic crystal field across the magnetic transition. This approach allows a first-hand insight into the mechanism of the pressure induced spin transition.Comment: 5 pages, 3 figure

Infrared Spectroscopy of the Diffuse Ionized Halo of NGC 891

We present infrared spectroscopy from the Spitzer Space Telescope at one disk position and two positions at a height of 1 kpc from the disk in the edge-on spiral NGC 891, with the primary goal of studying halo ionization. Our main result is that the [Ne III]/[Ne II] ratio, which provides a measure of the hardness of the ionizing spectrum free from the major problems plaguing optical line ratios, is enhanced in the extraplanar pointings relative to the disk pointing. Using a 2D Monte Carlo-based photo-ionization code which accounts for the effects of radiation field hardening, we find that this trend cannot be reproduced by any plausible photo-ionization model, and that a secondary source of ionization must therefore operate in gaseous halos. We also present the first spectroscopic detections of extraplanar PAH features in an external normal galaxy. If they are in an exponential layer, very rough emission scale-heights of 330-530 pc are implied for the various features. Extinction may be non-negligible in the midplane and reduce these scale-heights significantly. There is little significant variation in the relative emission from the various features between disk and extraplanar environment. Only the 17.4 micron feature is significantly enhanced in the extraplanar gas compared to the other features, possibly indicating a preference for larger PAHs in the halo.Comment: 35 pages in ApJ preprint format, 8 figures, accepted for publication in ApJ. Minor change to Introduction to give appropriate credit to earlier, related wor