A 6-12 GHz Analogue Lag-Correlator for Radio Interferometry

Aims: We describe a 6-12 GHz analogue correlator that has been developed for use in radio interferometers. Methods: We use a lag-correlator technique to synthesis eight complex spectral channels. Two schemes were considered for sampling the cross-correlation function, using either real or complex correlations, and we developed prototypes for both of them. We opted for the ``add and square'' detection scheme using Schottky diodes over the more commonly used active multipliers because the stability of the device is less critical. Results: We encountered an unexpected problem, in that there were errors in the lag spacings of up to ten percent of the unit spacing. To overcome this, we developed a calibration method using astronomical sources which corrects the effects of the non-uniform sampling as well as gain error and dispersion in the correlator.Comment: 14 pages, 21 figures, accepted for publication in A&

A 6-12 GHz Analogue Lag-Correlator for Radio Interferometry

Aims: We describe a 6-12 GHz analogue correlator that has been developed for use in radio interferometers. Methods: We use a lag-correlator technique to synthesis eight complex spectral channels. Two schemes were considered for sampling the cross-correlation function, using either real or complex correlations, and we developed prototypes for both of them. We opted for the ``add and square'' detection scheme using Schottky diodes over the more commonly used active multipliers because the stability of the device is less critical. Results: We encountered an unexpected problem, in that there were errors in the lag spacings of up to ten percent of the unit spacing. To overcome this, we developed a calibration method using astronomical sources which corrects the effects of the non-uniform sampling as well as gain error and dispersion in the correlator.Comment: 14 pages, 21 figures, accepted for publication in A&

The Galactic distribution of magnetic fields in molecular clouds and HII regions

{Magnetic fields exist on all scales in our Galaxy. There is a controversy about whether the magnetic fields in molecular clouds are preserved from the permeated magnetic fields in the interstellar medium (ISM) during cloud formation. We investigate this controversy using available data in the light of the newly revealed magnetic field structure of the Galactic disk obtained from pulsar rotation measures (RMs).} % {We collected measurements of the magnetic fields in molecular clouds, including Zeeman splitting data of OH masers in clouds and OH or HI absorption or emission lines of clouds themselves.} % {The Zeeman data show structures in the sign distribution of the line-of-sight component of the magnetic field. Compared to the large-scale Galactic magnetic fields derived from pulsar RMs, the sign distribution of the Zeeman data shows similar large-scale field reversals. Previous such examinations were flawed in the over-simplified global model used for the large-scale magnetic fields in the Galactic disk.} % {We conclude that the magnetic fields in the clouds may still ``remember'' the directions of magnetic fields in the Galactic ISM to some extent, and could be used as complementary tracers of the large-scale magnetic structure. More Zeeman data of OH masers in widely distributed clouds are required.}Comment: Typo fixed in this new versio

Rotation and differential rotation of active Kepler stars

We present rotation periods for thousands of active stars in the Kepler field derived from Q3 data. In most cases a second period close to the rotation period was detected, which we interpreted as surface differential rotation (DR). Active stars were selected from the whole sample using the range of the variability amplitude. To detect different periods in the light curves we used the Lomb-Scargle periodogram in a pre-whitening approach to achieve parameters for a global sine fit. The most dominant periods from the fit were ascribed to different surface rotation periods, but spot evolution could also play a role. Due to the large number of stars the period errors were estimated in a statistical way. We thus cannot exclude the existence of false positives among our periods. In our sample of 40.661 active stars we found 24.124 rotation periods $P_1$ between 0.5-45 days. The distribution of stars with 0.5 < B-V < 1.0 and ages derived from angular momentum evolution that are younger than 300 Myr is consistent with a constant star-formation rate. A second period $P_2$ within $\pm30$% of the rotation period $P_1$ was found in 18.619 stars (77.2%). Attributing these two periods to DR we found that the relative shear $\alpha=\Delta\Omega/\Omega$ increases with rotation period, and slightly decreases with effective temperature. The absolute shear $\Delta\Omega$ slightly increases between $T_{eff}=3500-6000$ K. Above 6000 K $\Delta\Omega$ shows much larger scatter. We found weak dependence of $\Delta\Omega$ on rotation period. Latitudinal differential rotation measured for the first time in more than 18.000 stars provides a comprehensive picture of stellar surface shear, consistent with major predictions from mean-field theory. To what extent our observations are prone to false positives and selection bias is not fully explored, and needs to be addressed using more Kepler data.Comment: 19 pages, 18 figures, accepted by A&A. A table containing all periods, KIC number, etc. can be found here: http://www.astro.physik.uni-goettingen.de/~reinhold/period_table.te

Rotational properties of the binary and non-binary populations in the Trans-Neptunian belt

We present results for the short-term variability of Binary Trans-Neptunian Objects (BTNOs). We performed CCD photometric observations using the 3.58 m Telescopio Nazionale Galileo, the 1.5 m Sierra Nevada Observatory telescope, and the 1.23 m Centro Astronomico Hispano Aleman telescope at Calar Alto Observatory. We present results based on five years of observations and report the short-term variability of six BTNOs. Our sample contains three classical objects: 2003MW12, or Varda, 2004SB60, or Salacia, and 2002 VT130; one detached disk object: 2007UK126; and two resonant objects: 2007TY430 and 2000EB173, or Huya. For each target, possible rotational periods and/or photometric amplitudes are reported. We also derived some physical properties from their lightcurves, such as density, primary and secondary sizes, and albedo. We compiled and analyzed a vast lightcurve database for Trans-Neptunian Objects (TNOs) including centaurs to determine the lightcurve amplitude and spin frequency distributions for the binary and non-binary populations. The mean rotational periods, from the Maxwellian fits to the frequency distributions, are 8.63+/-0.52 h for the entire sample, 8.37+/-0.58 h for the sample without the binary population, and 10.11+/-1.19 h for the binary population alone. Because the centaurs are collisionally more evolved, their rotational periods might not be so primordial. We computed a mean rotational period, from the Maxwellian fit, of 8.86+/-0.58 h for the sample without the centaur population, and of 8.64+/-0.67 h considering a sample without the binary and the centaur populations. According to this analysis, regular TNOs spin faster than binaries, which is compatible with the tidal interaction of the binaries. Finally, we examined possible formation models for several systems studied in this work and by our team in previous papers.Comment: Accepted for publication in Astronomy and Astrophysics (June 26th, 2014); minor changes with published version; 21 pages, 17 figures, 7 table

Automorphic Lie Algebras and Cohomology of Root Systems

A cohomology theory of root systems emerges naturally in the context of Automorphic Lie Algebras, where it helps formulating some structure theory questions. In particular, one can find concrete models for an Automorphic Lie Algebra by integrating cocycles. In this paper we define this cohomology and show its connection with the theory of Automorphic Lie Algebras. Furthermore, we discuss its properties: we define the cup product, we show that it can be restricted to symmetric forms, that it is equivariant with respect to the automorphism group of the root system, and finally we show acyclicity at dimension two of the symmetric part, which is exactly what is needed to find concrete models for Automorphic Lie Algebras. Furthermore, we show how the cohomology of root systems finds application beyond the theory of Automorphic Lie Algebras by applying it to the theory of contractions and filtrations of Lie algebras. In particular, we show that contractions associated to Cartan $\mathbb{Z}$-filtrations of simple Lie algebras are classified by $2$-cocycles, due again to the vanishing of the symmetric part of the second cohomology group.Comment: 26 pages, standard LaTeX2

KPD 0422+5421: A New Short Period Subdwarf B/White Dwarf Binary

The sdB star KPD 0422+5421 was discovered to be a single-lined spectroscopic binary with a period of P=0.0901795 +/- (3\times 10^{-7}) days (2 hours, 10 minutes). The U and B light curves display an ellipsoidal modulation with amplitudes of about 0.02 magnitudes. The sdB star contributes nearly all of the observed flux. This and the absence of any reflection effect suggest that the unseen companion star is small (i.e. R_comp ~ 0.01 solar radii) and therefore degenerate. We modeled the U and B light curves and derived i = 78.05 +/- 0.50 degrees and a mass ratio of q = M_comp/M_sdB = 0.87 +/- 0.15. The sdB star fills 69% of its Roche lobe. These quantities may be combined with the mass function of the companion (f(M) = 0.126 +/- 0.028 solar masses) to derive M_sdB = 0.72 +/- 0.26 solar masses and M_comp = 0.62 +/- 0.18 solar masses. We used model spectra to derive the effective temperature, surface gravity, and helium abundance of the sdB star. We found T_eff = 25,000 +/- 1500K, log g = 5.4 +/- 0.1, and [He/H] = -1.0. With a period of 2 hours and 10 minutes, KPD 0422+5421 has one of the shortest known orbital periods of a detached binary. This system is also one of only a few known binaries which contain a subdwarf B star and a white dwarf. Thus KPD 0422+5421 represents a relatively unobserved, and short-lived, stage of binary star evolution.Comment: 9 pages, 8 figures, to appear in MNRAS, LaTeX, uses mn.st

Frame Theory for Signal Processing in Psychoacoustics

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field