The mapping class group and the Meyer function for plane curves

For each d>=2, the mapping class group for plane curves of degree d will be defined and it is proved that there exists uniquely the Meyer function on this group. In the case of d=4, using our Meyer function, we can define the local signature for 4-dimensional fiber spaces whose general fibers are non-hyperelliptic compact Riemann surfaces of genus 3. Some computations of our local signature will be given.Comment: 24 pages, typo adde

Recovering the H II region size statistics from 21-cm tomography

We introduce a novel technique, called ‘granulometry’, to characterize and recover the mean size and the size distribution of H II regions from 21-cm tomography. The technique is easy to implement, but places the previously not very well-defined concept of morphology on a firm mathematical foundation. The size distribution of the cold spots in 21-cm tomography can be used as a direct tracer of the underlying probability distribution of H II region sizes. We explore the capability of the method using large-scale reionization simulations and mock observational data cubes while considering capabilities of Square Kilometre Array 1 (SKA1) low and a future extension to SKA2. We show that the technique allows the recovery of the H II region size distribution with a moderate signal-to-noise ratio from wide-field imaging (SNR 3), for which the statistical uncertainty is sample variance dominated. We address the observational requirements on the angular resolution, the field of view, and the thermal noise limit for a successful measurement. To achieve a full scientific return from 21-cm tomography and to exploit a synergy with 21-cm power spectra, we suggest an observing strategy using wide- field imaging (several tens of square degrees) by an interferometric mosaicking/multibeam observation with additional intermediate baselines (∼2−4 km) in an SKA phase 2

Spectral performance of SKA log-periodic antennas I: Mitigating spectral artefacts in SKA1-LOW 21 cm cosmology experiments

This paper is the first in a series of papers describing the impact of antenna instrumental artefacts on the 21-cm cosmology experiments to be carried out by the low frequency instrument (SKA1-LOW) of the Square Kilometre Array telescope (SKA), i.e., the Cosmic Dawn (CD) and the Epoch of Reionization (EoR). The smoothness of the passband response of the current log-periodic antenna being developed for the SKA1-LOW is analyzed using numerical electromagnetic simulations. The amplitude variations over the frequency range are characterized using low-order polynomials defined locally, in order to study the impact of the passband smoothness in the instrument calibration and CD/EoR Science. A solution is offered to correct a fast ripple found at 60~MHz during a test campaign at the SKA site at the Murchison Radio-astronomy Observatory, Western Australia in September 2015 with a minor impact on the telescope's performance and design. A comparison with the Hydrogen Epoch of Reionization Array antenna is also shown demonstrating the potential use of the SKA1-LOW antenna for the Delay Spectrum technique to detect the EoR

Gravitational detection of a low-mass dark satellite at cosmological distance

The mass-function of dwarf satellite galaxies that are observed around Local Group galaxies substantially differs from simulations based on cold dark matter: the simulations predict many more dwarf galaxies than are seen. The Local Group, however, may be anomalous in this regard. A massive dark satellite in an early-type lens galaxy at z = 0.222 was recently found using a new method based on gravitational lensing, suggesting that the mass fraction contained in substructure could be higher than is predicted from simulations. The lack of very low mass detections, however, prohibited any constraint on their mass function. Here we report the presence of a 1.9 +/- 0.1 x 10^8 M_sun dark satellite in the Einstein-ring system JVAS B1938+666 at z = 0.881, where M_sun denotes solar mass. This satellite galaxy has a mass similar to the Sagittarius galaxy, which is a satellite of the Milky Way. We determine the logarithmic slope of the mass function for substructure beyond the local Universe to be alpha = 1.1^+0.6_-0.4, with an average mass-fraction of f = 3.3^+3.6_-1.8 %, by combining data on both of these recently discovered galaxies. Our results are consistent with the predictions from cold dark matter simulations at the 95 per cent confidence level, and therefore agree with the view that galaxies formed hierarchically in a Universe composed of cold dark matter.Comment: 25 pages, 7 figures, accepted for publication in Nature (19 January 2012

The Hubble Constant

I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individual astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of all-sky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, object-based measurements give $H_0$ values of around 72-74km/s/Mpc , with typical errors of 2-3km/s/Mpc. This is in mild discrepancy with CMB-based measurements, in particular those from the Planck satellite, which give values of 67-68km/s/Mpc and typical errors of 1-2km/s/Mpc. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the object-based methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the all-sky methods.Comment: Extensively revised and updated since the 2007 version: accepted by Living Reviews in Relativity as a major (2014) update of LRR 10, 4, 200

A review of elliptical and disc galaxy structure, and modern scaling laws

A century ago, in 1911 and 1913, Plummer and then Reynolds introduced their models to describe the radial distribution of stars in `nebulae'. This article reviews the progress since then, providing both an historical perspective and a contemporary review of the stellar structure of bulges, discs and elliptical galaxies. The quantification of galaxy nuclei, such as central mass deficits and excess nuclear light, plus the structure of dark matter halos and cD galaxy envelopes, are discussed. Issues pertaining to spiral galaxies including dust, bulge-to-disc ratios, bulgeless galaxies, bars and the identification of pseudobulges are also reviewed. An array of modern scaling relations involving sizes, luminosities, surface brightnesses and stellar concentrations are presented, many of which are shown to be curved. These 'redshift zero' relations not only quantify the behavior and nature of galaxies in the Universe today, but are the modern benchmark for evolutionary studies of galaxies, whether based on observations, N-body-simulations or semi-analytical modelling. For example, it is shown that some of the recently discovered compact elliptical galaxies at 1.5 < z < 2.5 may be the bulges of modern disc galaxies.Comment: Condensed version (due to Contract) of an invited review article to appear in "Planets, Stars and Stellar Systems"(www.springer.com/astronomy/book/978-90-481-8818-5). 500+ references incl. many somewhat forgotten, pioneer papers. Original submission to Springer: 07-June-201

The first and second data releases of the Kilo-Degree Survey

Context. The Kilo-Degree Survey (KiDS) is an optical wide-field imaging survey carried out with the VLT Survey Telescope and the OmegaCAM camera. KiDS will image 1500 square degrees in four filters (ugri), and together with its near-infrared counterpart VIKING will produce deep photometry in nine bands. Designed for weak lensing shape and photometric redshift measurements, its core science driver is mapping the large-scale matter distribution in the Universe back to a redshift of ~0.5. Secondary science cases include galaxy evolution, Milky Way structure, and the detection of high-redshift clusters and quasars. Aims. KiDS is an ESO Public Survey and dedicated to serving the astronomical community with high-quality data products derived from the survey data. Public data releases, the first two of which are presented here, are crucial for enabling independent confirmation of the survey’s scientific value. The achieved data quality and initial scientific utilization are reviewed in order to validate the survey data. Methods. A dedicated pipeline and data management system based on ASTRO-WISE, combined with newly developed masking and source classification tools, is used for the production of the data products described here. Science projects based on these data products and preliminary results are outlined. Results. For 148 survey tiles (≈160 sq.deg.) stacked ugri images have been released, accompanied by weight maps, masks, source lists, and a multi-band source catalogue. Limiting magnitudes are typically 24.3, 25.1, 24.9, 23.8 (5σ in a 2′′ aperture) in ugri, respectively, and the typical r-band PSF size is less than 0.7′′. The photometry prior to global homogenization is stable at the ~2% (4%) level in gri (u) with some outliers due to non-photometric conditions, while the astrometry shows a typical 2D rms of 0.03′′. Early scientific results include the detection of nine high-z QSOs, fifteen candidate strong gravitational lenses, high-quality photometric redshifts and structural parameters for hundreds of thousands of galaxies

A LOFAR observation of ionospheric scintillation from two simultaneous travelling ionospheric disturbances

This paper presents the results from one of the first observations of ionospheric scintillation taken using the Low-Frequency Array (LOFAR). The observation was of the strong natural radio source Cassiopeia A, taken overnight on 18–19 August 2013, and exhibited moderately strong scattering effects in dynamic spectra of intensity received across an observing bandwidth of 10–80 MHz. Delay-Doppler spectra (the 2-D FFT of the dynamic spectrum) from the first hour of observation showed two discrete parabolic arcs, one with a steep curvature and the other shallow, which can be used to provide estimates of the distance to, and velocity of, the scattering plasma. A cross-correlation analysis of data received by the dense array of stations in the LOFAR “core” reveals two different velocities in the scintillation pattern: a primary velocity of ~20–40 ms−1 with a north-west to south-east direction, associated with the steep parabolic arc and a scattering altitude in the F-region or higher, and a secondary velocity of ~110 ms−1 with a north-east to south-west direction, associated with the shallow arc and a scattering altitude in the D-region. Geomagnetic activity was low in the mid-latitudes at the time, but a weak sub-storm at high latitudes reached its peak at the start of the observation. An analysis of Global Navigation Satellite Systems (GNSS) and ionosonde data from the time reveals a larger-scale travelling ionospheric disturbance (TID), possibly the result of the high-latitude activity, travelling in the north-west to south-east direction, and, simultaneously, a smaller-scale TID travelling in a north-east to south-west direction, which could be associated with atmospheric gravity wave activity. The LOFAR observation shows scattering from both TIDs, at different altitudes and propagating in different directions. To the best of our knowledge this is the first time that such a phenomenon has been reported

Foreground modelling via Gaussian process regression: An application to HERA data

The key challenge in the observation of the redshifted 21-cm signal from cosmic reionization is its separation from the much brighter foreground emission. Such separation relies on the different spectral properties of the two components, although, in real life, the foreground intrinsic spectrum is often corrupted by the instrumental response, inducing systematic effects that can further jeopardize the measurement of the 21-cm signal. In this paper, we use Gaussian Process Regression to model both foreground emission and instrumental systematics in $\sim 2$ hours of data from the Hydrogen Epoch of Reionization Array. We find that a simple co-variance model with three components matches the data well, giving a residual power spectrum with white noise properties. These consist of an "intrinsic" and instrumentally corrupted component with a coherence-scale of 20 MHz and 2.4 MHz respectively (dominating the line of sight power spectrum over scales $k_{\parallel} \le 0.2$ h cMpc$^{-1}$) and a baseline dependent periodic signal with a period of $\sim 1$ MHz (dominating over $k_{\parallel} \sim 0.4 - 0.8$h cMpc$^{-1}$) which should be distinguishable from the 21-cm EoR signal whose typical coherence-scales is $\sim 0.8$ MHz