Application of Bayesian model averaging to measurements of the primordial power spectrum

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model Evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940 < n_s < 1.000, where n_s is specified at a pivot scale 0.015 Mpc^{-1}. For the tensors model averaging can tighten the credible upper limit, depending on prior assumptions.Comment: 7 pages with 7 figures include

Origin of Complex Quantum Amplitudes and Feynman's Rules

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued function of this number pair. By making use of elementary symmetry conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes.Comment: v2: Clarifications, and minor corrections and modifications. Results unchanged. v3: Minor changes to introduction and conclusio

Efficiency of Nonlinear Particle Acceleration at Cosmic Structure Shocks

We have calculated the evolution of cosmic ray (CR) modified astrophysical shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of diffusive shock acceleration (DSA) in 1D quasi- parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We model shocks similar to those expected around cosmic structure pancakes as well as other accretion shocks driven by flows with upstream gas temperatures in the range $T_0=10^4-10^{7.6}$K and shock Mach numbers spanning $M_s=2.4-133$. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc \gsim 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. For these models the time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number. The modeled high Mach number shocks all evolve towards efficiencies $\sim 50$%, regardless of the upstream CR pressure. On the other hand, the upstream CR pressure increases the overall CR energy in moderate strength shocks ($M_s \sim {\rm a few}$). (abridged)Comment: 23 pages, 12 ps figures, accepted for Astrophysical Journal (Feb. 10, 2005

Effects of electronic correlations and disorder on the thermopower of NaxCoO2

For the thermoelectric properties of NaxCoO2, we analyze the effect of local Coulomb interaction and (disordered) potential differences for Co-sites with adjacent Na-ion or vacancy. The disorder potential alone increases the resistivity and reduces the thermopower, while the Coulomb interaction alone leads only to minor changes compared to the one-particle picture of the local density approximation. Only combined, these two terms give rise to a substantial increase of the thermopower: the number of (quasi-)electrons around the Fermi level is much more suppressed than that of the (quasi-)holes. Hence, there is a particle-hole imbalance acting in the same direction as a similar imbalance for the group velocities. Together, this interplay results in a large positive thermopower. Introducing a thermoelectric spectral density, we located the energies and momenta regions most relevant for the thermopower and changes thereof.Comment: 23 pages, 27 figures, accepted at PR

Radio Emission from a Young Supernova Remnant Interacting with an Interstellar Cloud: MHD Simulation with Relativistic Electrons

We present two-dimensional MHD simulations of the evolution of a young Type Ia supernova remnant during its interaction with an interstellar cloud of comparable size at impact. We include for the first time in such simulations explicit relativistic electron transport, including spectral information using a simple but effective scheme that follows their acceleration at shocks and subsequent transport. From this information we also model radio synchrotron emission, including spectra. The principal conclusions from these experiments are: 1) Independent of the cloud interaction, the SNR reverse shock can be an efficient site for particle acceleration in a young SNR. 2) At these early times the synchrotron spectral index due to electrons accelerated at the primary shocks should be close to 0.5 unless those shocks are modified by cosmic-ray pressures. However, interaction with the cloud generates regions of distinctly steeper spectra, which may complicate interpretation in terms of global dynamical models for SNR evolution. 3) The internal motions within the SNR become highly turbulent following the cloud interaction. 4) An initially uniform interstellar magnetic field is preferentially amplified along the magnetic equator of the SNR, primarily due to biased amplification by instabilities. Independent of the external field configuration, there is a net radial direction to this field inside the SNR. 5) Filamentary radio structures correlate well with magnetic filaments, while diffuse emission follows the electron distribution. 6) Interaction with the cloud enhances both the electron population and the radio emission.Comment: 29 pages of Latex generated text with 6 figures in gif format. Accepted for publication in the Astrophysical Journal. High resolution postscript figures can be obtained by anonymous ftp from ftp://ftp.msi.umn.edu/pub/users/twj/sn

H3+ in Diffuse Interstellar Clouds: a Tracer for the Cosmic-Ray Ionization Rate

Using high resolution infrared spectroscopy we have surveyed twenty sightlines for H3+ absorption. H3+ is detected in eight diffuse cloud sightlines with column densities varying from 0.6x10^14 cm^-2 to 3.9x10^14 cm^-2. This brings to fourteen the total number of diffuse cloud sightlines where H3+ has been detected. These detections are mostly along sightlines concentrated in the Galactic plane, but well dispersed in Galactic longitude. The results imply that abundant H3+ is common in the diffuse interstellar medium. Because of the simple chemistry associated with H3+ production and destruction, these column density measurements can be used in concert with various other data to infer the primary cosmic-ray ionization rate, zeta_p. Values range from 0.5x10^-16 s^-1 to 3x10^-16 s^-1 with an average of 2x10^-16 s^-1. Where H3+ is not detected the upper limits on the ionization rate are consistent with this range. The average value of zeta_p is about an order of magnitude larger than both the canonical rate and rates previously reported by other groups using measurements of OH and HD. The discrepancy is most likely due to inaccurate measurements of rate constants and the omission of effects which were unknown when those studies were performed. We believe that the observed column density of H3+ is the most direct tracer for the cosmic-ray ionization rate due to its simple chemistry. Recent models of diffuse cloud chemistry require cosmic-ray ionization rates on the order of 10^-16 s^-1 to reproduce observed abundances of various atomic and molecular species, in rough accord with our observational findings.Comment: Accepted to ApJ, 35 pages, 5 figures, 5 table

Star Formation in M51 Triggered by Galaxy Interaction

We have mapped the inner 360'' regions of M51 in the 158micron [CII] line at 55'' spatial resolution using the Far-infrared Imaging Fabry-Perot Interferometer (FIFI) on the Kuiper Airborne Observatory (KAO). The emission is peaked at the nucleus, but is detectable over the entire region mapped, which covers much of the optical disk of the galaxy. There are also two strong secondary peaks at ~43% to 70% of the nuclear value located roughly 120'' to the north-east, and south-west of the nucleus. These secondary peaks are at the same distance from the nucleus as the corotation radius of the density wave pattern. The density wave also terminates at this location, and the outlying spiral structure is attributed to material clumping due to the interaction between M51 and NGC5195. This orbit crowding results in cloud-cloud collisions, stimulating star formation, that we see as enhanced [CII] line emission. The [CII] emission at the peaks originates mainly from photodissociation regions (PDRs) formed on the surfaces of molecular clouds that are exposed to OB starlight, so that these [CII] peaks trace star formation peaks in M51. The total mass of [CII] emitting photodissociated gas is ~2.6x10^{8} M_{sun}, or about 2% of the molecular gas as estimated from its CO(1-0) line emission. At the peak [CII] positions, the PDR gas mass to total gas mass fraction is somewhat higher, 3-17%, and at the secondary peaks the mass fraction of the [CII] emitting photodissociated gas can be as high as 72% of the molecular mass.... (continued)Comment: 14 pages, 6 figures, Accepted in ApJ (for higher resolution figures contact the author

Extraction of the Electron Self-Energy from Angle Resolved Photoemission Data: Application to Bi2212

The self-energy $\Sigma({\bf k},\omega)$, the fundamental function which describes the effects of many-body interactions on an electron in a solid, is usually difficult to obtain directly from experimental data. In this paper, we show that by making certain reasonable assumptions, the self-energy can be directly determined from angle resolved photoemission data. We demonstrate this method on data for the high temperature superconductor $Bi_2Sr_2CaCu_2O_{8+x}$ (Bi2212) in the normal, superconducting, and pseudogap phases.Comment: expanded version (6 pages), to be published, Phys Rev B (1 Sept 99

Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting

International audienceThe Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the authors prove that some associated estimators are unbiased, for each value of the size n of the systems of replicas and of resampling number k. Here we go beyond and prove these estimator's asymptotic normality when h goes to infinity, for any fixed value of k. The main ingredient is the asymptotic analysis of a functional equation on an appropriate characteristic function. Some numerical simulations illustrate the convergence to rely on Gaussian confidence intervals

Inferring Core-Collapse Supernova Physics with Gravitational Waves

Stellar collapse and the subsequent development of a core-collapse supernova explosion emit bursts of gravitational waves (GWs) that might be detected by the advanced generation of laser interferometer gravitational-wave observatories such as Advanced LIGO, Advanced Virgo, and LCGT. GW bursts from core-collapse supernovae encode information on the intricate multi-dimensional dynamics at work at the core of a dying massive star and may provide direct evidence for the yet uncertain mechanism driving supernovae in massive stars. Recent multi-dimensional simulations of core-collapse supernovae exploding via the neutrino, magnetorotational, and acoustic explosion mechanisms have predicted GW signals which have distinct structure in both the time and frequency domains. Motivated by this, we describe a promising method for determining the most likely explosion mechanism underlying a hypothetical GW signal, based on Principal Component Analysis and Bayesian model selection. Using simulated Advanced LIGO noise and assuming a single detector and linear waveform polarization for simplicity, we demonstrate that our method can distinguish magnetorotational explosions throughout the Milky Way (D <~ 10kpc) and explosions driven by the neutrino and acoustic mechanisms to D <~ 2kpc. Furthermore, we show that we can differentiate between models for rotating accretion-induced collapse of massive white dwarfs and models of rotating iron core collapse with high reliability out to several kpc.Comment: 22 pages, 9 figure