119779449
Planck intermediate results. XV. A study of anomalous microwave emission in Galactic clouds
Anomalous microwave emission (AME) is believed to be due to electric dipole radiation from small spinning dust grains. T he aim of this paper is a statistical study of the basic properties of AME regions and the environment in which they emit. We used WMAP and Planck maps, combined with ancillary radio and IR data, to construct a sample of 98 candidate AME sources, assembling SEDs for each source using aperture photometry on 1 ◦ -smoothed maps from 0.408 GHz up to 3000 GHz. Each spectrum isfitted with a simple model of free-free, synchrotron (where n ecessary), cosmic microwave background (CMB), thermal dust, and spinning dust components. We find that 42 of the 98 sources have sign ificant ( > 5�) excess emission at frequencies between 20 and 60 GHz. An analysis of the potential contribution of optically thick free- free emission from ultracompact Hii regions, using IR colour criteria, reduces the significant A ME sample to 27 regions. The spectrum of the AME is consistent with model spectra of spinning dust. Peak frequencies are in the range 20‐35 GHz except for the California Nebula (NGC1499), which appears to have a high spinning dust peak frequency of (50± 17) GHz. The AME regions tend to be more spatially extended than regions with little or no AME. The AME intensity is strongly correlated with the sub-millimetre/IR flux densities and comparable to previous AME detections i n the literature. AME emissivity, defined as the ratio of AME to dust optical dep th, varies by an order of magnitude for the AME regions. The AME regions tend to be associated with cooler dust in the range 14‐20 K and an average emissivity index, �d, of +1.8, while the non-AME regions are typically warmer, at 20‐27 K. In agreement with previous studies, the AME emissivity appears to decrease with increasing column density. This supports the idea of AME originating from small grains that are known to be depleted in dense regions, probably due to coagulation onto larger grains. We also find a correlation between the AME emissivity (and to a le sser degree the spinning dust peak frequency) and the intensity of the interstellar radiation field, G0. Modelling of this trend suggests that both radiative and collisional excitation are important for the spinning dust em ission. The most significant AME regions tend to have relatively less ion ized gas (free-free emission), although this could be a sele ction effect. The infrared excess, a measure of the heating of dust associated with Hii regions, is typically > 4 for AME sources, indicating that the dust is not primarily heated by hot OB stars. The AME regions are associated with known dark nebulae and have higher 12µm/25µm ratios. The emerging picture is that the bulk of the AME is coming from the polycyclic aromatic hydrocarbons and small dust grains from the colder neutral interstellar medium phase.
119468667
Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries
We calculate the expected nHz-μHz gravitational wave (GW) spectrum from coalescing massive black hole (MBH) binaries resulting from mergers of their host galaxies. We consider detection of this spectrum by precision pulsar timing and a future pulsar timing array. The spectrum depends on the merger rate of massive galaxies, the demographics of MBHs at low and high redshift, and the dynamics of MBH binaries. We apply recent theoretical and observational work on all of these fronts. The spectrum has a characteristic strain hc(f) ~ 10-15(f/yr-1)-2/3, just below the detection limit from recent analysis of precision pulsar timing measurements. However, the amplitude of the spectrum is still very uncertain owing to approximations in the theoretical formulation of the model, to our lack of knowledge of the merger rate and MBH population at high redshift, and to the dynamical problem of removing enough angular momentum from the MBH binary to reach a GW-dominated regime.
15621530
Constraining large–scale structure theories with the cosmic background radiation
The case is strong that cosmic microwave background (CMB) and large scale structure (LSS) observations can be combined to determine the theory of structure formation and the cosmological parameters that define it. We review: the relevant (10+) parameters associated with the inflation model of fluctuation generation and the matter content of the universe; the relation between LSS and primary and secondary CMB anisotropy probes as a function of wavenumber; how COBE constraints on energy injection rule out explosions as a dominant source of LSS; and how current anisotropy band–powers in multipole–space, at levels ca. 10−5)2, strongly support the gravitational instability theory and suggest the universe could not have reionized too early. We use Bayesian analysis methods to determine what current CMB and CMB+LSS data imply for inflation–based Gaussian fluctuations in tilted &Lgr;CDM, &Lgr;hCDM and oCDM model sequences with cosmological age 11 – 15 Gyr, consisting of mixtures of baryons, cold ‘c’ (and possibly hot ‘h’) dark matter, vacuum energy &Lgr;, and curvature energy ‘o’ in open cosmologies. For example, we find the slope of the initial spectrum is within about 5% of the (preferred) scale–invariant form when just the CMB data are used, and for &Lgr;CDM when LSS data are combined with CMB; with both, a non–zero value of Ω&Lgr; is strongly preferred (ca. ⅔ for a 13 Gyr sequence, similar to the value from SNIa). The oCDM sequence prefers Ωtot < 1, but is overall much less likely than the flat Ω&Lgr; ≠ 0 sequence with CMB+LSS. We also review the rosy forecasts of angular power spectra and parameter estimates from future balloon and satellite experiments when foreground and systematic effects are ignored to show where cosmic parameter determination can go with CMB information alone.
122687802
Imaging the early universe with the BOOMERanG Experiment
The BOOMERanG experiment has recently detected temperature fluctuations the Cosmic Microwave Background (CMB), the otherwise isotropic radiation coming from the early Universe. These anisotropies have a low contrast (about 30 ppm) and feature a peculiar angular power spectrum at angles corresponding to sub-horizon scales at recombination. In the current cosmological model, these structures result from acoustic oscillations in the primeval plasma. In the framework of the Hot Big Bang theory with the inflationary hypothesis, the statistical properties of the image of the CMB allow us to measure most of the cosmological parameters.
119408227
CMB likelihood functions for beginners and experts
Although the broad outlines of the appropriate pipeline for cosmological likelihood analysis with CMB data has been known for several years, only recently have we had to contend with the full, large-scale, computationally challenging problem involving both highly-correlated noise and extremely large datasets (N>1000). In this talk we concentrate on the beginning and end of this process. First, we discuss estimating the noise covariance from the data itself in a rigorous and unbiased way; this is essentially an iterated minimum-variance mapmaking approach. We also discuss the unbiased determination of cosmological parameters from estimates of the power spectrum or experimental bandpowers.
17460509
Simultaneous Estimation of Noise and Signal in Cosmic Microwave Background Experiments
To correctly analyse data sets from current microwave detection technology, one is forced to estimate the sky signal and experimental noise simultaneously. Given a time-ordered data set we propose a formalism and method for estimating the signal and associated errors without prior knowledge of the noise power spectrum. We derive the method using a Bayesian formalism and relate it to the standard methods; in particular we show how this leads to a change in the estimate of the noise covariance matrix of the sky signal. We study the convergence and accuracy of the method on two mock observational strategies and discuss its application to a currently-favoured calibration procedure.
116317881
Constructive Gauge Theory
Here we provide some insight into mathematical methods to analyze quantized gauge theories. This approach is being used to establish existence as well as to prove properties of gauge field models. Up to now, only abelian gauge fields are known to exist, namely the U(1) Higgs model on ℝ2 and ℝ3 and electrodynamics on the tori T2 and T3. In these lectures we study infrared properties of some of these models. The non-Abelian gauge models are interesting for additional reasons: First, they have a natural geometric interpretation. Furthermore, because of asymptotic freedom, non-Abelian models have better local regularity properties than Abelian theories. Furthermore, they provide a rich analytic structure.
123628830
The holonomy expansion: Invariants and approximate supersymmetry
Abstract In this paper we give a new expansion, based on cyclicity of the trace, to study regularity properties of twisted expectations 〈 X ( s )〉=Tr H ( γU ( θ )  X ( s )). Here X ( s )= X 0 e − s 0 Q 2 X 1 e − s 1 Q 2 … X k e − s k Q 2 is a product of operators X j , regularized by heat kernels e − s j Q 2 with s j >0. The twist groups γ ∈ Z 2 and U ( θ )∈ U (1) are commuting symmetries of Q 2 . The name “holonomy expansion” arises from picturing 〈 X ( s )〉 as a circular graph, with vertices in the graph representing the operators X j , in the order that they appear in the product, and the linesegment following X j representing the heat kernel e − s j Q 2 . The trace functional is cyclic, so the graph is circular. We generate our expansion by “transporting” a vertex X k around the circle, ending in its original position. We choose an X k that transforms under a one-dimensional representation of Z 2 × U (1). For θ in the complement of the discrete set ϒ sing (where the group Z 2 × U (1) acts trivially on X k ) we obtain an identity between the original expectation and some new expectations. We study an example from supersymmetric quantum mechanics, with a Dirac operator Q ( λ ) depending on a parameter λ and with a U (1) group of symmetries U ( θ ). We apply our expansion to invariants Z ( λ ;  θ )= Z ( Q ( λ );  θ ) suggested by non-commutative geometry. These invariants are sums of expectations of the form above. We investigate this example as a first step toward developing an expansion to evaluate related invariants arising in supersymmetric quantum field theory. We establish differentiability of Z ( λ ; ,  θ ) in λ for λ ∈(0, 1] and show Z ( λ ;  θ ) is independent of λ . We wish to evaluate Z ( λ ;  θ ) at the endpoint λ =0, but Z (0;  θ ) is ill-defined. We regularize the endpoint, while preserving the U ( θ )-symmetry, by replacing Q ( λ ) 2 with H ( e ,  λ )= Q ( λ ) 2 + e 2  | z | 2 . The regularized function Z ( e ,  λ ;  θ ) depends on all three variables e , λ , θ ; for fixed θ , it is differentiable in the unit ( e ,  λ ) square, except at the origin. Using the holonomy expansion, we prove for fixed θ ∉ ϒ sing that Z ( e ,  λ ;  θ ) is also jointly continuous in ( e ,  λ ), at the origin. As a consequence, if θ ∉ ϒ sing , then we can interchange limits and Z ( λ ;  θ )=lim e →0 Z ( e , 0;  θ ). We observe that the joint continuity of Z ( e ,  λ ;  θ ) in ( e ,  λ ) is not uniform in θ , and Z ( e ,  λ ;  θ ) is not jointly continuous for θ ∈ ϒ sing . But the limiting function Z ( λ ;  θ ) is continuous in θ ; so the e -limit also determines Z ( λ ;  θ ) for all θ , including for θ ∈ ϒ sing . We use these facts to calculate Z ( λ ;  θ ). Our regularization destroys supersymmetry, but the holonomy expansion gives quantitative bounds on the error terms.
118881742
Constructive Field Theory, Phase II
It now appears possible to study a realm of problems in CFT which, two years ago, appeared an order of magnitude too difficult to tackle. The finishing touches have just been put on the first paper of this sort1, and in this talk I will describe some of the basic ideas; these ideas are simple, although the details of the paper are complicated. The main question that I will discuss today has been around as long as field theory: Namely how does an interacting field model react to perturbations by an external source? Such perturbations of \(\textup{P}\left (\phi \right )_{2}\), or in fact any reasonable local perturbations of the \(\textup{P}\left (\phi \right )_{2}\) model, have been shown to be regular by James Glimm and myself1. As a consequence, (i) further properties of the original model have been established1, (ii) some new breakthroughs are being made2 and (iii) these methods appear promising for use in the study of more singular models than \(\textup{P}\left (\phi \right )_{2}\).
13103184
An Exchange Identity for Non-linear Fields
We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.
120686550
Instantons in aU(1) lattice gauge theory: A Coulomb dipole gas
We study the decompositionA=AI+ASW of aU(1) lattice gauge field into instanton and spin wave parts. The action also decomposes,A=AI+ASW+R. HereAI is a Coulomb dipole gas,ASW is a zero mass free field, andR is a higher order remainder. We studyAI in detail, ford≧4, in the dilute gas case (which corresponds to the low temperature limit of the gauge field theory). We establish the leading behavior of the free energy:f ∼ ɛ−daζ. Here ɛ is the lattice spacing,a is a geometrical constant and ζ is an activity defined in terms of a small number of instanton configurations. Our methods suggest the absence of screening in the dilute dipole gas,d≧4, in contrast to Debye screening for the dilute monopole gas.