Distance Powers and Distance Matrices of Integral Cayley Graphs over Abelian Groups

It is shown that distance powers of an integral Cayley graph over an abelian group are again integral Cayley graphs over that group. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum

The state space of short-range Ising spin glasses: the density of states

The state space of finite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and gaussian probability distribution of interactions are compared. Different measures for the local state density are presented and discussed. In particular the question whether the local density of states grows exponentially or not is considered. The direct comparison of global and local densities leads to consequences for the structure of the state space.Comment: 18 pages (including 6 figures); submitted to Z.f.Physik

The complex environment of the bright carbon star TX Psc as probed by spectro-astrometry

Context: Stars on the asymptotic giant branch (AGB) show broad evidence of inhomogeneous atmospheres and circumstellar envelopes. These have been studied by a variety of methods on various angular scales. In this paper we explore the envelope of the well-studied carbon star TX Psc by the technique of spectro-astrometry. Aims: We explore the potential of this method for detecting asymmetries around AGB stars. Methods:We obtained CRIRES observations of several CO $\Delta$v=1 lines near 4.6 $\mu$m and HCN lines near 3 $\mu$m in 2010 and 2013. These were then searched for spectro-astrometric signatures. For the interpretation of the results, we used simple simulated observations. Results: Several lines show significant photocentre shifts with a clear dependence on position angle. In all cases, tilde-shaped signatures are found where the positive and negative shifts (at PA 0deg) are associated with blue and weaker red components of the lines. The shifts can be modelled with a bright blob 70 mas to 210 mas south of the star with a flux of several percent of the photospheric flux. We estimate a lower limit of the blob temperature of 1000 K. The blob may be related to a mass ejection as found for AGB stars or red supergiants. We also consider the scenario of a companion object. Conclusions: Although there is clear spectro-astrometric evidence of a rather prominent structure near TX Psc, it does not seem to relate to the other evidence of asymmetries, so no definite explanation can be given. Our data thus underline the very complex structure of the environment of this star, but further observations that sample the angular scales out to a few hundred milli-arcseconds are needed to get a clearer picture

Catching the fish - Constraining stellar parameters for TX Psc using spectro-interferometric observations

Stellar parameter determination is a challenging task when dealing with galactic giant stars. The combination of different investigation techniques has proven to be a promising approach. We analyse archive spectra obtained with the Short-Wavelength-Spectrometer (SWS) onboard of ISO, and new interferometric observations from the Very Large Telescope MID-infrared Interferometric instrument (VLTI/MIDI) of a very well studied carbon-rich giant: TX Psc. The aim of this work is to determine stellar parameters using spectroscopy and interferometry. The observations are used to constrain the model atmosphere, and eventually the stellar evolutionary model in the region where the tracks map the beginning of the carbon star sequence. Two different approaches are used to determine stellar parameters: (i) the 'classic' interferometric approach where the effective temperature is fixed by using the angular diameter in the N-band (from interferometry) and the apparent bolometric magnitude; (ii) parameters are obtained by fitting a grid of state-of-the-art hydrostatic models to spectroscopic and interferometric observations. We find a good agreement between the parameters of the two methods. The effective temperature and luminosity clearly place TX Psc in the carbon-rich AGB star domain in the H-R-diagram. Current evolutionary tracks suggest that TX Psc became a C-star just recently, which means that the star is still in a 'quiet' phase compared to the subsequent strong-wind regime. This is in agreement with the C/O ratio being only slightly larger than 1.Comment: 11 pages, 9 figures, 5 table

Hands-On TAROT: Intercontinental use of the TAROT for Education and Public Outreach

The TAROT telescope has for primary goal the search for the prompt optical counterpart of Cosmic Gamma-Ray Bursts. It is a completely autonomous 25cm telescope installed near Nice (France), able to point any location of the sky within 1-2 seconds. The control, scheduling, and data processing activities are completely automated, so the instrument is completely autonomous. In addition to its un-manned modes, we added recently the possibility to remotely control the telescope, as a request of the "Hands-On Universe" (HOU) program for exchange of time within automatic telescopes for the education and public outreach. To this purpose we developed a simple control interface. A webcam was installed to visualize the telescope. Access to the data is possible through a web interface. The images can be processed by the HOU software, a program specially suited for use within the classroom. We experienced these feature during the open days of the University of California Berkeley and the Astronomy Festival of Fleurance (France). We plan a regular use for an astronomy course of the Museum of Tokyo, as well as for French schools. Not only does Hands-On TAROT gives the general public an access to professional astronomy, but it is also a more general tool to demonstrate the use of a complex automated system, the techniques of data processing and automation. Last but not least, through the use of telescopes located in many countries over the globe, a form of powerful and genuine cooperation between teachers and children from various countries is promoted, with a clear educational goal.Comment: 4 pages, Based on a demonstration presented at the ADASS X Conference, Boston, MA, USA, October 2000, to appear in ASP Conf. Serie

The maximal energy of classes of integral circulant graphs

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count $n$ and a set $\cal D$ of divisors of $n$ in such a way that they have vertex set $\mathbb{Z}_n$ and edge set ${{a,b}: a,b\in\mathbb{Z}_n, \gcd(a-b,n)\in {\cal D}}$. For a fixed prime power $n=p^s$ and a fixed divisor set size $|{\cal D}| =r$, we analyze the maximal energy among all matching integral circulant graphs. Let $p^{a_1} < p^{a_2} < ... < p^{a_r}$ be the elements of ${\cal D}$. It turns out that the differences $d_i=a_{i+1}-a_{i}$ between the exponents of an energy maximal divisor set must satisfy certain balance conditions: (i) either all $d_i$ equal $q:=\frac{s-1}{r-1}$, or at most the two differences $[q]$ and $[q+1]$ may occur; %(for a certain $d$ depending on $r$ and $s$) (ii) there are rules governing the sequence $d_1,...,d_{r-1}$ of consecutive differences. For particular choices of $s$ and $r$ these conditions already guarantee maximal energy and its value can be computed explicitly.Comment: Discrete Applied Mathematics (2012

Toward an optimal search strategy of optical and gravitational wave emissions from binary neutron star coalescence

Observations of an optical source coincident with gravitational wave emission detected from a binary neutron star coalescence will improve the confidence of detection, provide host galaxy localisation, and test models for the progenitors of short gamma ray bursts. We employ optical observations of three short gamma ray bursts, 050724, 050709, 051221, to estimate the detection rate of a coordinated optical and gravitational wave search of neutron star mergers. Model R-band optical afterglow light curves of these bursts that include a jet-break are extrapolated for these sources at the sensitivity horizon of an Advanced LIGO/Virgo network. Using optical sensitivity limits of three telescopes, namely TAROT (m=18), Zadko (m=21) and an (8-10) meter class telescope (m=26), we approximate detection rates and cadence times for imaging. We find a median coincident detection rate of 4 yr^{-1} for the three bursts. GRB 050724 like bursts, with wide opening jet angles, offer the most optimistic rate of 13 coincident detections yr^{-1}, and would be detectable by Zadko up to five days after the trigger. Late time imaging to m=26 could detect off-axis afterglows for GRB 051221 like bursts several months after the trigger. For a broad distribution of beaming angles, the optimal strategy for identifying the optical emissions triggered by gravitational wave detectors is rapid response searches with robotic telescopes followed by deeper imaging at later times if an afterglow is not detected within several days of the trigger.Comment: 6 pages, 1 figure, Accepted for publication in MNRAS Letters (2011 April 22