Planetary nebulae in the elliptical galaxy NGC 821: kinematics and distance determination

Using a slitless spectroscopy method with the 8.2 m Subaru telescope and its FOCAS Cassegrain spectrograph, we have increased the number of planetary nebula (PN) detections and PN velocity measurements in the flattened elliptical galaxy NGC 821. A comparison with the detections reported previously by the Planetary Nebula Spectrograph (PN.S) group indicates that we have confirmed most of their detections. The velocities measured by the two groups, using different telescopes, spectrographs and slitless techniques, are in good agreement. We have built a combined sample of 167 PNs and have confirmed the keplerian decline of the line-of-sight velocity dispersion reported previously. We also confirm misaligned rotation from the combined sample. A dark matter halo may exist around this galaxy, but it is not needed to keep the PN velocities below the local escape velocity as calculated from the visible mass. We have measured the m(5007) magnitudes of 145 PNs and produced a statistically complete sample of 40 PNs in NGC 821. The resulting PN luminosity function (PNLF) was used to estimate a distance modulus of 31.4 mag, equivalent to 19 Mpc. We also estimated the PN formation rate. NGC 821 becomes the most distant galaxy with a PNLF distance determination. The PNLF distance modulus is smaller than the surface brightness fluctuation (SBF) distance modulus by 0.4 mag. Our kinematic information permits to rule out the idea that a shorter PNLF distance could be produced by the contamination of the PNLF by background galaxies with emission lines redshifted into the on-band filter transmission curve.Comment: Accepted for publication in ApJ; 16 figure

A Case Study on Artefact-based RE Improvement in Practice

Most requirements engineering (RE) process improvement approaches are solution-driven and activity-based. They focus on the assessment of the RE of a company against an external norm of best practices. A consequence is that practitioners often have to rely on an improvement approach that skips a profound problem analysis and that results in an RE approach that might be alien to the organisational needs. In recent years, we have developed an RE improvement approach (called \emph{ArtREPI}) that guides a holistic RE improvement against individual goals of a company putting primary attention to the quality of the artefacts. In this paper, we aim at exploring ArtREPI's benefits and limitations. We contribute an industrial evaluation of ArtREPI by relying on a case study research. Our results suggest that ArtREPI is well-suited for the establishment of an RE that reflects a specific organisational culture but to some extent at the cost of efficiency resulting from intensive discussions on a terminology that suits all involved stakeholders. Our results reveal first benefits and limitations, but we can also conclude the need of longitudinal and independent investigations for which we herewith lay the foundation

Time delay of light signals in an energy-dependent spacetime metric

In this note we review the problem of time delay of photons propagating in a spacetime with a metric that explicitly depends on the energy of the particles (Gravity-Rainbow approach). We show that corrections due to this approach -- which is closely related to DSR proposal -- produce for small redshifts ($z<<1$) smaller time delays than in the generic Lorentz Invariance Violating case.Comment: 5 pages. This version contains two new references with respect to the published versio

On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras $sl(2,\mathbb{R})$ or $su(2)$ according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential. PACS: 03.65.-w; 03.65.Fd MSC: 81R05; 20C35; 22E70Comment: 49 pages. No figures. Version to appear in JP