A near-infrared and optical photometric study of the Sculptor dwarf spheroidal galaxy: implications for the metallicity spread

We present here a detailed study of the Sculptor dSph galaxy red giant branch (RGB) and horizontal branch (HB) morphology, combining new near-infrared photometry from CIRSI, with optical data from the ESO WFI. For a Sculptor-like old and generally metal-poor system, the position of RGB stars on the colour-magnitude diagram is mainly metallicity dependent. The advantage of using optical-NIR colours is that the position of the RGB locus is much more sensitive to metallicity than with optical colours alone. In contrast the horizontal branch (HB) morphology is strongly dependent on both metallicity and age. Therefore a detailed study of both the RGB in optical-NIR colours and the HB can help break the age-metallicity degeneracy. Our measured photometric width of the Sculptor giant branch corresponds to a range in metallicity of 0.75 dex. We detect the RGB and AGB bumps in both the NIR and optical luminosity functions, and derive from them a mean metallicity of [M/H] = -1.3 +/- 0.1. From isochrone fitting we derive a mean metallicity of [Fe/H] = -1.42 with a dispersion of 0.2 dex. These photometric estimators are for the first time consistent with individual metallicity measurements derived from spectroscopic observations. No spatial gradient is detected in the RGB morphology within a radius of 13 arcmin, twice the core radius. On the other hand, a significant gradient is observed in the HB morphology index, confirming the `second parameter problem' present in this galaxy. These observations are consistent with an early extended period of star formation continuing in time for a few Gyr. (Abridged)Comment: 9 pages, 10 figures. Accepted for publication in MNRA

When are projections also embeddings?

We study an autonomous four-dimensional dynamical system used to model certain geophysical processes.This system generates a chaotic attractor that is strongly contracting, with four Lyapunov exponents $\lambda_i$ that satisfy $\lambda_1+ \lambda_2+\lambda_3<0$, so the Lyapunov dimension is $D_L=2+|\lambda_3|/\lambda_1 < 3$ in the range of coupling parameter values studied. As a result, it should be possible to find three-dimensional spaces in which the attractors can be embedded so that topological analyses can be carried out to determine which stretching and squeezing mechanisms generate chaotic behavior. We study mappings into $R^3$ to determine which can be used as embeddings to reconstruct the dynamics. We find dramatically different behavior in the two simplest mappings: projections from $R^4$ to $R^3$. In one case the one-parameter family of attractors studied remains topologically unchanged for all coupling parameter values. In the other case, during an intermediate range of parameter values the projection undergoes self-intersections, while the embedded attractors at the two ends of this range are topologically mirror images of each other

A Comparison of Tests for Embeddings

It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions

CP violation conditions in N-Higgs-doublet potentials

Conditions for CP violation in the scalar potential sector of general N-Higgs-doublet models (NHDMs) are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model (2HDM) potential, a minimum set of conditions for explicit and spontaneous CP violation is presented. The conditions can be given a clear geometrical interpretation in terms of quantities in the adjoint representation of the basis transformation group for the two doublets. Such conditions depend on CP-odd pseudoscalar invariants. When the potential is CP invariant, the explicit procedure to reach the real CP-basis and the explicit CP transformation can also be obtained. The procedure to find the real basis and the conditions for CP violation are then extended to general NHDM potentials. The analysis becomes more involved and only a formal procedure to reach the real basis is found. Necessary conditions for CP invariance can still be formulated in terms of group invariants: the CP-odd generalized pseudoscalars. The problem can be completely solved for three Higgs-doublets.Comment: RevTeX4 used. Minor modifications, in particular, the parameter counting of $Z$. v3: Eqs.(28)-(31) correcte

Climbing the cosmic ladder with stellar twins

Distances to stars are key to revealing a three-dimensional view of the Milky Way, yet their determination is a major challenge in astronomy. Whilst the brightest nearby stars benefit from direct parallax measurements, fainter stars are subject of indirect determinations with uncertainties exceeding 30%. We present an alternative approach to measuring distances using spectroscopically-identified twin stars. Given a star with known parallax, the distance to its twin is assumed to be directly related to the difference in their apparent magnitudes. We found 175 twin pairs from the ESO public HARPS archives and report excellent agreement with Hipparcos parallaxes within 7.5%. Most importantly, the accuracy of our results does not degrade with increasing stellar distance. With the ongoing collection of high-resolution stellar spectra, our method is well-suited to complement Gaia.Comment: published online on MNRA

Astrometric Effects of Gravitational Wave Backgrounds with non-Luminal Propagation Speeds

A passing gravitational wave causes a deflection in the apparent astrometric positions of distant stars. The effect of the speed of the gravitational wave on this astrometric shift is discussed. A stochastic background of gravitational waves would result in a pattern of astrometric deflections which are correlated on large angular scales. These correlations are quantified and investigated for backgrounds of gravitational waves with sub- and super-luminal group velocities. The statistical properties of the correlations are depicted in two equivalent and related ways: as correlation curves and as angular power spectra. Sub-(super-)luminal gravitational wave backgrounds have the effect of enhancing (suppressing) the power in low-order angular modes. Analytical representations of the redshift-redshift and redshift-astrometry correlations are also derived. The potential for using this effect for constraining the speed of gravity is discussed

Extragalactic Background Light and Gamma-Ray Attenuation

Data from (non-) attenuation of gamma rays from active galactic nuclei (AGN) and gamma ray bursts (GRBs) give upper limits on the extragalactic background light (EBL) from the UV to the mid-IR that are only a little above the lower limits from observed galaxies. These upper limits now rule out some EBL models and purported observations, with improved data likely to provide even stronger constraints. We present EBL calculations both based on multiwavelength observations of thousands of galaxies and also based on semi-analytic models, and show that they are consistent with these lower limits from observed galaxies and with the gamma-ray upper limit constraints. Such comparisons "close the loop" on cosmological galaxy formation models, since they account for all the light, including that from galaxies too faint to see. We compare our results with those of other recent works, and discuss the implications of these new EBL calculations for gamma ray attenuation. Catching a few GRBs with groundbased atmospheric Cherenkov Telescope (ACT) arrays or water Cherenkov detectors could provide important new constraints on the high-redshift star formation history of the universe.Comment: 12 pages, 8 multi-panel figures, Invited talk at the 25th Texas Symposium on Relativistic Astrophysics, Heidelberg December 6-10, 201