Feynman graph polynomials

The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.Comment: 35 pages, references adde

Revisiting soliton contributions to perturbative amplitudes

Open Access funded by SCOAP3. CP is a Royal Society Research Fellow and partly supported by the U.S. Department of Energy under grants DOE-SC0010008, DOE-ARRA-SC0003883 and DOE-DE-SC0007897. ABR is supported by the Mitchell Family Foundation. We would like to thank the Mitchell Institute at Texas A&M and the NHETC at Rutgers University respectively for hospitality during the course of this work. We would also like to acknowledge the Aspen Center for Physics and NSF grant 1066293 for a stimulating research environment

Hydrodynamic Processes in Young Binary Systems as a Source of Cyclic Variations of Circumstellar Extinction

Hydrodynamic models of a young binary system accreting matter from the remnants of a protostellar cloud have been calculated by the SPH method. It is shown that periodic variations in column density in projection onto the primary component take place at low inclinations of the binary plane to the line of sight. They can result in periodic extinction variations. Three periodic components can exist in general case. The first component has a period equal to the orbital one and is attributable to the streams of matter penetrating into the inner regions of the binary. The second component has a period that is a factor of 5-8 longer than the orbital one and is related to the density waves generated in a circumbinary (CB) disk. The third, longest period is attributable to the precession of the inner asymmetric region of CB disk. The relationship between the amplitudes of these cycles depends on the model parameters as well as on the inclination and orientation of the binary in space. We show that at a dust-to-gas ratio of 1:100 and and a mass extinction coefficient of 250 cm$^2$ g$^{-1}$, the amplitude of the brightness variations of the primary component in the V-band can reach $1^m$ at a mass accretion rate onto the binary components of $10^{-8} M_{\odot}$ yr$^{-1}$ and a $10^{\rm o}$ inclination of the binary plane to the line of sight. We discuss possible applications of the model to pre-main-sequence stars.Comment: 13 pages, 6 figures, published in Astronomy Letters (v.33, 2007

Probing the formation of intermediate- to high-mass stars in protoclusters II. Comparison between millimeter interferometric observations of NGC 2264-C and SPH simulations of a collapsing clump

The earliest phases of massive star formation in clusters are still poorly understood. Here, we test the hypothesis for high-mass star formation proposed in our earlier paper (Peretto et al. 2006). In order to confirm the physical validity of this hypothesis, we carried out IRAM Plateau de Bure interferometer observations of NGC 2264-C and performed SPH numerical simulations of the collapse of a Jeans-unstable, prolate dense clump. Our Plateau de Bure observations reveal the presence of a new compact source (C-MM13) located only \~ 10000 AU away, but separated by ~ 1.1 km/s in (projected) velocity, from the most massive Class 0 object (C-MM3) lying at the very center of NGC 2264-C. Detailed comparison with our numerical SPH simulations supports the view that NGC 2264-C is an elongated cluster-forming clump in the process of collapsing and fragmenting along its long axis, leading to a strong dynamical interaction and possible protostar merger in the central region of the clump. The present study also sets several quantitative constraints on the initial conditions of large-scale collapse in NGC 2264-C. Our hydrodynamic simulations indicate that the observed velocity pattern characterizes an early phase of protocluster collapse which survives for an only short period of time (i.e., < 10^5 yr). To provide a good match to the observations the simulations require an initial ratio of turbulent to gravitational energy of only ~ 5 %, which strongly suggests that the NGC 2264-C clump is structured primarily by gravity rather than turbulence. The required "cold'' initial conditions may result from rapid compression by an external trigger.Comment: 15 pages, 8 figures, accepted for publication in A&

Cluster scaling relations from cosmological hydrodynamic simulations in dark energy dominated universe

Clusters are potentially powerful tools for cosmology provided their observed properties such as the Sunyaev-Zel'dovich (SZ) or X-ray signals can be translated into physical quantities like mass and temperature. Scaling relations are the appropriate mean to perform this translation. It is therefore, important to understand their evolution and their modifications with respect to the physics and to the underlying cosmology. In this spirit, we investigate the effect of dark energy on the X-ray and SZ scaling relations. The study is based on the first hydro-simulations of cluster formation for diferent models of dark energy. We present results for four dark energy models which differ from each other by their equations of state parameter, $w$. Namely, we use a cosmological constant model $w=-1$ (as a reference), a perfect fluid with constant equation of state parameter $w=-0.8$ and one with $w = -1.2$ and a scalar field model (or quintessence) with varying $w$. We generate N-body/hydrodynamic simulations that include radiative cooling with the public version of the Hydra code, modified to consider an arbitrary dark energy component. We produce cluster catalogues for the four models and derive the associated X-ray and SZ scaling relations. We find that dark energy has little effect on scaling laws making it safe to use the $\Lambda$CDM scalings for conversion of observed quantities into temperature and masses.Comment: 9 pages, 7 figures, submitted to A&

3D Simulations of Betelgeuse's Bow Shock

Betelgeuse, the bright, cool red supergiant in Orion, is moving supersonically relative to the local interstellar medium. The star emits a powerful stellar wind which collides with this medium, forming a cometary structure, a bow shock, pointing in the direction of motion. We present the first 3D hydrodynamic simulations of the formation and evolution of Betelgeuse's bow shock. The models include realistic low temperature cooling and cover a range of plausible interstellar medium densities and stellar velocities between 0.3 - 1.9 cm-3 and 28 - 73 km/s. We show that the flow dynamics and morphology of the bow shock differ substantially due to the preferential growth of Rayleigh-Taylor or Kelvin-Helmholtz instabilities in the models. The former dominate the models with slow stellar velocities resulting in a clumpy bow shock sub-structure, whereas the latter produce a smoother, more layered sub-structure in the fast models. If the mass in the bow shock shell is low, as seems to be implied by the AKARI luminosities (~0.003 Msun), then Betelgeuse's bow shock is very young and is unlikely to have reached a steady state. The circular nature of the bow shock shell is consistent with this conclusion. Thus, our results suggest that Betelgeuse entered the red supergiant phase only recently.Comment: Minor revisions, replaced Fig. 1, 15, and 16, added movies. For a pdf version with higher resolution, see A&A: Forthcomin

Precision measurements of large scale structure with future type Ia supernova surveys

Type Ia supernovae are currently the best known standard candles at cosmological distances. In addition to providing a powerful probe of dark energy they are an ideal source of information about the peculiar velocity field of the local universe. Even with the very small number of supernovae presently available it has been possible to measure the dipole and quadrupole of the local velocity field out to z~0.025. With future continuous all-sky surveys like the LSST project the luminosity distances of tens of thousands of nearby supernovae will be measured accurately. This will allow for a determination of the local velocity structure of the universe as a function of redshift with unprecedented accuracy, provided the redshifts of the host galaxies are known. Using catalogues of mock surveys we estimate that future low redshift supernova surveys will be able to probe sigma-8 to a precision of roughly 5% at 95% C.L. This is comparable to the precision in future galaxy and weak lensing surveys and with a relatively modest observational effort it will provide a crucial cross-check on future measurements of the matter power spectrum.Comment: 18 pages, 9 figures, submitted to JCA

Representing complex data using localized principal components with application to astronomical data

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex''. In these cases, simple principal component analysis (PCA) as a tool for dimension reduction can fail badly. Of the many alternative approaches proposed so far, local approximations of PCA are among the most promising. This paper will give a short review of localized versions of PCA, focusing on local principal curves and local partitioning algorithms. Furthermore we discuss projections other than the local principal components. When performing local dimension reduction for regression or classification problems it is important to focus not only on the manifold structure of the covariates, but also on the response variable(s). Local principal components only achieve the former, whereas localized regression approaches concentrate on the latter. Local projection directions derived from the partial least squares (PLS) algorithm offer an interesting trade-off between these two objectives. We apply these methods to several real data sets. In particular, we consider simulated astrophysical data from the future Galactic survey mission Gaia.Comment: 25 pages. In "Principal Manifolds for Data Visualization and Dimension Reduction", A. Gorban, B. Kegl, D. Wunsch, and A. Zinovyev (eds), Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 180--204, http://www.springer.com/dal/home/generic/search/results?SGWID=1-40109-22-173750210-