A Fatou-Bieberbach domain in C^2 which is not Runge

We give an example of a Fatou-Bieberbach domain which is not Runge in C^2

Asymptotics of Invariant Metrics in the normal direction and a new characterisation of the unit disk

We give improvements of estimates of invariant metrics in the normal direction on strictly pseudoconvex domains. Specifically we will give the second term in the expansion of the metrics. This depends on an improved localisation result and estimates in the one variable case. Finally we will give a new characterisation of the unit disk in $\mathbb C$ in terms of the asymptotic behaviour of quotients of invariant metrics

Nuclear embedded star clusters in NGC 7582

We report on the discovery of several compact regions of mid-infrared emission in the starforming circum nuclear disk of the starburst/Seyfert2 galaxy NGC7582. The compact sources do not have counterparts in the optical and near-infrared, suggesting that they are deeply embedded in dust. We use the [NeII]12.8 micron line emission to estimate the emission measure of the ionized gas, which in turn is used to assess the number of ionizing photons. Two of the brighter sources are found to have ionizing fluxes of ~2.5x10^52, whereas the fainter ones have ~1x10^52 photons/s. Comparing with a one Myr old starburst, we derive stellar masses in the range (3-5)x10^5 Msun, and find that the number of O-stars in each compact source is typically (0.6-1.6)x10^3. We conclude that the compact mid-infrared sources are likely to be young, embedded star clusters, of which only a few are known so far. Our observation highlights the need for high resolution mid-infrared imaging to discover and study embedded star clusters in the proximity of active galactic nuclei.Comment: 6 pages, 2 figures, accepted for publication in MNRAS Letter

The influence of AGN nuclear parameters on the FRI/FRII dichotomy

We have investigated the influence of nuclear parameters such as black hole mass and photoionizing luminosity on the FRI/FRII transition in a sample of nearby (z<0.2) radio galaxies from the 3CR catalogue. The sample was observed with medium-resolution, optical spectroscopy and contains some galaxies with unpublished velocity dispersion measurements and emission-line fluxes. The measured velocity dispersions for the sample lie in the range 130-340 km s^(-1) with a mean of 216 km s^(-1). Using the M-σ relation, we convert to black hole mass and find that the black hole mass distribution is identical for FRI and FRII galaxies, with a mean of ≈ 2.5 × 10^8 M_☉. We determine narrow emission-line luminosities from [O III] and [O III] in our spectra, as well as from the literature, and convert them to photoionizing luminosities under the assumption that the gas is ionized by the nuclear UV continuum. Most of the galaxies with FRI morphology and/or low-excitation emission-line spectra have progressively lower black hole masses at lower photoionizing (and jet) luminosities. This agrees with the well-known Ledlow-Owen relation which states that the radio luminosity at the FRI/FRII transition depends on the optical luminosity of the host, L_(radio) ∝ L^(1.8)_(optical), because these two luminosities relate to AGN nuclear parameters. When recasting the Ledlow-Owen relation into black hole mass versus photoionizing luminosity and jet luminosity, we find that the recasted relation describes the sample quite well. Furthermore, the FRI/FRII transition is seen to occur at approximately an order of magnitude lower luminosity relative to the Eddington luminosity than the soft-to-hard transition in X-ray binaries. This difference is also consistent with the Ledlow-Owen relation, which predicts a weak black hole mass dependence in the transition luminosity in Eddington units. We conclude that the FRI/FRII dichotomy is caused by a combination of external and nuclear factors, with the latter dominating

Herculin, a Fourth Member of the MyoD Family of Myogenic Regulatory Genes

We have identified and cloned herculin, a fourth mouse muscle regulatory gene. Comparison of its DNA and deduced amino acid sequences with those of the three known myogenic genes (MyoD, myogenin, and Myf-5) reveals scattered short spans with similarity to one or more of these genes and a long span with strong similarity to all three. This long span includes a sequence motif that is also present in proteins of the myc, achaete-scute, and immunoglobulin enhancer-binding families. The herculin gene is physically linked to the Myf-5 gene on the chromosome; only 8.5 kilobases separate their translational start sites. A putative 27-kDa protein is encoded by three exons contained within a 1.7-kilobase fragment of the herculin gene. When expressed under the control of the simian virus 40 early promoter, transfected herculin renders murine NIH 3T3 and C3H/10T1/2 fibroblasts myogenic. In doing so, it also activates expression of myogenin, MyoD, and endogenous herculin in NIH 3T3 recipients. In adult mice, herculin is expressed in skeletal muscle but is absent from smooth muscle, cardiac muscle, and all nonmuscle tissues assayed. Direct comparison of the four known myogenic regulators in adult muscle showed that herculin is expressed at a significantly higher level than is any of the others. This quantitative dominance suggests an important role in the establishment or maintenance of adult skeletal muscle

The Influence of Black Hole Mass and Accretion Rate on the FRI/FRII Radio Galaxy Dichotomy

We use medium resolution optical spectra of 3CR radio galaxies to estimate their black hole masses and accretion rates. Black hole masses are found from central stellar velocity dispersions and accretion rates are derived from narrow emission-line luminosities. The sample covers both Fanaroff-Riley (FR) classes; the more powerful FRIIs and the less powerful FRIs. We find that FRIs and FRIIs separate in diagrams of black hole mass versus radio luminosity and narrow-line luminosity. This suggests that, at a given black hole mass, the FRIIs accrete more efficiently, or accrete more matter, than FRIs.Comment: 2 pages, 1 figure. Contribution to the proceedings of the conference "Growing Black Holes", Garching, Germany, June 21-24, 2004. Eds. A. Merloni, S. Nayakshin, R. Sunyae