On Some Geometric Properties of Slice Regular Functions of a Quaternion Variable

The goal of this paper is to introduce and study some geometric properties of slice regular functions of quaternion variable like univalence, subordination, starlikeness, convexity and spirallikeness in the unit ball. We prove a number of results, among which an Area-type Theorem, Rogosinski inequality, and a Bieberbach-de Branges Theorem for a subclass of slice regular functions. We also discuss some geometric and algebraic interpretations of our results in terms of maps from $\mathbb R^4$ to itself. As a tool for subordination we define a suitable notion of composition of slice regular functions which is of independent interest

The luminous late-time emission of the type Ic supernova iPTF15dtg - evidence for powering from a magnetar?

iPTF15dtg is a Type Ic supernova (SN) showing a broad light curve around maximum light, consistent with massive ejecta if we assume a radioactive-powering scenario. We study the late-time light curve of iPTF15dtg, which turned out to be extraordinarily luminous for a stripped-envelope (SE) SN. We compare the observed light curves to those of other SE SNe and also with models for the $^{56}$Co decay. We analyze and compare the spectra to nebular spectra of other SE SNe. We build a bolometric light curve and fit it with different models, including powering by radioactivity, magnetar powering, as well as a combination of the two. Between 150 d and 750 d past explosion, iPTF15dtg's luminosity declined by merely two magnitudes instead of the six magnitudes expected from $^{56}$Co decay. This is the first spectroscopically-regular SE SN showing this behavior. The model with both radioactivity and magnetar powering provides the best fit to the light curve and appears to be the more realistic powering mechanism. An alternative mechanism might be CSM interaction. However, the spectra of iPTF15dtg are very similar to those of other SE SNe, and do not show signs of strong CSM interaction. iPTF15dtg is the first spectroscopically-regular SE SN whose light curve displays such clear signs of a magnetar contributing to the powering of the late time light curve. Given this result, the mass of the ejecta needs to be revised to a lower value, and therefore the progenitor mass could be significantly lower than the previously estimated $>$35 $M_{\odot}$.Comment: 9 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

On the accuracy of retrieved wind information from Doppler lidar observations

A single pulsed Doppler lidar was successfully deployed to measure air flow and turbulence over the Malvern hills, Worcester, UK. The DERA Malvern lidar used was a CO2 µm pulsed Doppler lidar. The lidar pulse repetition rate was 120 Hz and had a pulse duration of 0.6 µs The system was set up to have 41 range gates with range resolution of 112 m. This gave a theoretical maximum range of approximately 4.6 km. The lidar site was 2 km east of the Malvern hill ridge which runs in a north-south direction and is approximately 6 km long. The maximum height of the ridge is 430 m. Two elevation scans (Range-Height Indicators) were carried out parallel and perpendicular to the mean surface flow. Since the surface wind was primarily westerly the scans were carried out perpendicular and parallel to the ridge of the Malvern hills. The data were analysed and horizontal winds, vertical winds and turbulent fluxes were calculated for profiles throughout the boundary layer. As an aid to evaluating the errors associated with the derivation of velocity and turbulence profiles, data from a simple idealized profile was also analysed using the same method. The error analysis shows that wind velocity profiles can be derived to an accuracy of 0.24 m s-1 in the horizontal and 0.3 m s-1 in the vertical up to a height of 2500 m. The potential for lidars to make turbulence measurements, over a wide area, through the whole depth of the planetary boundary layer and over durations from seconds to hours is discussed

Is a ‘quiet eye’ all it takes to be successful? Comment on Vickers

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The Luminosity Function of the NoSOCS Galaxy Cluster Sample

We present the analysis of the luminosity function of a large sample of galaxy clusters from the Northern Sky Optical Cluster Survey, using latest data from the Sloan Digital Sky Survey. Our global luminosity function (down to M_r<= -16) does not show the presence of an upturn at faint magnitudes, while we do observe a strong dependence of its shape on both richness and cluster-centric radius, with a brightening of M^* and an increase of the dwarf to giant ratio with richness, indicating that more massive systems are more efficient in creating/retaining a population of dwarf satellites. This is observed both within physical (0.5 R_200) and fixed (0.5 Mpc) apertures, suggesting that the trend is either due to a global effect, operating at all scales, or to a local one but operating on even smaller scales. We further observe a decrease of the relative number of dwarf galaxies towards the cluster center; this is most probably due to tidal collisions or collisional disruption of the dwarfs since merging processes are inhibited by the high velocity dispersions in cluster cores and, furthermore, we do not observe a strong dependence of the bright end on the environment. We find indication that the dwarf to giant ratio decreases with increasing redshift, within 0.07<z<0.2. We also measure a trend for stronger suppression of faint galaxies (below M^*+2) with increasing redshift in poor systems, with respect to more massive ones, indicating that the evolutionary stage of less massive galaxies depends more critically on the environment. Finally we point out that the luminosity function is far from universal; hence the uncertainties introduced by the different methods used to build a composite function may partially explain the variety of faint-end slopes reported in the literature as well as, in some cases, the presence of a faint-end upturn.Comment: 16 pages, 12 figures. Accepted for publication in MNRA

The bumpy light curve of supernova iPTF13z

A Type IIn supernova (SN) is dominated by the interaction of SN ejecta with the circumstellar medium (CSM). Some SNe IIn (e.g., SN 2006jd) have episodes of re-brightening ("bumps") in their light curves. We present iPTF13z, a SN IIn discovered by the intermediate Palomar Transient Factory (iPTF) and characterised by several bumps in its light curve. We analyse this peculiar behaviour trying to infer the properties of the CSM and of the SN explosion, as well as the nature of its progenitor star. We obtained multi-band optical photometry for over 1000 days after discovery with the P48 and P60 telescopes at Palomar Observatory. We obtained low-resolution optical spectra in the same period. We did an archival search for progenitor outbursts. We analyse our photometry and spectra, and compare iPTF13z to other SNe IIn. A simple analytical model is used to estimate properties of the CSM. iPTF13z was a SN IIn showing a light curve with five bumps during its decline phase. The bumps had amplitudes between 0.4 and 0.9 mag and durations between 20 and 120 days. The most prominent bumps appeared in all our different optical bands. The spectra showed typical SN IIn characteristics, with emission lines of H$\alpha$ (with broad component FWHM ~$10^{3}-10^{4} ~{\rm ~km ~s^{-1}}$ and narrow component FWHM ~$10^2 \rm ~km ~s^{-1}$) and He I, but also with Fe II, Ca II, Na I D and H$\beta$ P-Cygni profiles (with velocities of ~$10^{3}$ ${\rm ~km ~s^{-1}}$). A pre-explosion outburst was identified lasting $\gtrsim 50$ days, with $M_r \approx -15$ mag around 210 days before discovery. Large, variable progenitor mass-loss rates (~> 0.01 $M_{\odot} \rm ~yr^{-1}$) and CSM densities (~> 10$^{-16}$ g cm$^{-3}$) are derived. We suggest that the light curve bumps of iPTF13z arose from SN ejecta interacting with denser regions in the CSM, possibly produced by the eruptions of a luminous blue variable star.Comment: Version 2: Update to match published paper. 21 pages, 14 figures, abstract abridged to comply with arXiv length limit. In version 1 of the paper on arXiv, Table 3 had some erroneous entries. Table 3 is now corrected and available via VizieR. Version 1 comment: Accepted for publication in Astronomy & Astrophysics (24 pages, 14 figures, abstract abridged by 20 % not to exceed the arXiv length limit