Molecular Line Profile Fitting with Analytic Radiative Transfer Models

We present a study of analytic models of starless cores whose line profiles have ``infall asymmetry,'' or blue-skewed shapes indicative of contracting motions. We compare the ability of two types of analytical radiative transfer models to reproduce the line profiles and infall speeds of centrally condensed starless cores whose infall speeds are spatially constant and range between 0 and 0.2 km s-1. The model line profiles of HCO+ (J=1-0) and HCO+ (J=3-2) are produced by a self-consistent Monte Carlo radiative transfer code. The analytic models assume that the excitation temperature in the front of the cloud is either constant (``two-layer'' model) or increases inward as a linear function of optical depth (``hill'' model). Each analytic model is matched to the line profile by rapid least-squares fitting. The blue-asymmetric line profiles with two peaks, or with a blue shifted peak and a red shifted shoulder, can be well fit by the ``HILL5'' model (a five parameter version of the hill model), with an RMS error of 0.02 km s-1. A peak signal to noise ratio of at least 30 in the molecular line observations is required for performing these analytic radiative transfer fits to the line profiles.Comment: 48 pages, 20 figures, accepted for publication in Ap

Universal analytic properties of noise. Introducing the J-Matrix formalism

We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an infinite time-series, we build an Hilbert space operator, a J-Operator, where each bound state (inside the unit circle in the complex plane) is simply associated to one damped oscillator while the continuous spectrum of the J-Operator, which lies on the unit circle itself, is shown to represent the noise. Signal and noise are thus clearly separated in the complex plane. For a finite time series of length 2N, the J-operator is replaced by a finite order J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different classes of input noise, such as blank (white and uniform), Gaussian and pink, are discussed in detail, the J-Matrix formalism allowing us to efficiently calculate hundreds of poles of the Z-transform. Evidence of a universal behaviour in the final statistical distribution of the associated poles and zeros of the Z-transform is shown. In particular the poles and zeros tend, when the length of the time series goes to infinity, to a uniform angular distribution on the unit circle. Therefore at finite order, the roots of unity in the complex plane appear to be noise attractors. We show that the Z-transform presents the exceptional feature of allowing lossless undersampling and how to make use of this property. A few basic examples are given to suggest the power of the proposed method.Comment: 14 pages, 8 figure

Systematic Continuum Errors in the Lyman-Alpha Forest and The Measured Temperature-Density Relation

Continuum fitting uncertainties are a major source of error in estimates of the temperature-density relation (usually parametrized as a power-law, $T \propto \Delta^{\gamma - 1}$) of the inter-galactic medium (IGM) through the flux probability distribution function (PDF) of the Lyman-$\alpha$ forest. Using a simple order-of-magnitude calculation, we show that few percent-level systematic errors in the placement of the quasar continuum due to e.g. a uniform low-absorption Gunn-Peterson component, could lead to errors in $\gamma$ of order unity. This is quantified further using a simple semi-analytic model of the Lya forest flux PDF. We find that under-(over-)estimates in the continuum level can lead to a lower (higher) measured value of $\gamma$. Within current observational uncertainties, continuum biases double the error in $\gamma$ from $\sigma_{\gamma} \approx 0.1$ to $\sigma_{\gamma} \approx 0.2$ within our model. We argue that steps need to be taken to directly estimate the level of continuum bias in order to make recent claims of an inverted \tdr\ more robust.Comment: 8 pages, 8 figures. Accepted by Ap

CMB power spectrum estimation using noncircular beams

The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy has proved crucial to the emergence of cosmology as a precision science in recent years. In this remarkable data rich period, the limitations to precision now arise from the the inability to account for finer systematic effects in data analysis. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. We present an analytic framework for studying the leading order effects of a non-circular beam on the CMB power spectrum estimation. We consider a non-circular beam of fixed shape but variable orientation. We compute the bias in the pseudo-$C_l$ power spectrum estimator and then construct an unbiased estimator using the bias matrix. The covariance matrix of the unbiased estimator is computed for smooth, non-circular beams. Quantitative results are shown for CMB maps made by a \emph{hypothetical} experiment with a non-circular beam comparable to our fits to the WMAP beam maps described in the appendix and uses a \emph{toy} scan strategy. We find that significant effects on CMB power spectrum can arise due to non-circular beam on multipoles comparable to, and beyond, the inverse average beam-width where the pseudo-$C_l$ approach may be the method of choice due to computational limitations of analyzing the large datasets from current and near future CMB experiments.Comment: 23 pages, 12 eps figures, uses RevTeX 4. Matches version accepted to Phys. Rev. D. Corrected minor typographical error in the final expression [eqn (3.23)] (post publication

Bayesian methods of astronomical source extraction

We present two new source extraction methods, based on Bayesian model selection and using the Bayesian Information Criterion (BIC). The first is a source detection filter, able to simultaneously detect point sources and estimate the image background. The second is an advanced photometry technique, which measures the flux, position (to sub-pixel accuracy), local background and point spread function. We apply the source detection filter to simulated Herschel-SPIRE data and show the filter's ability to both detect point sources and also simultaneously estimate the image background. We use the photometry method to analyse a simple simulated image containing a source of unknown flux, position and point spread function; we not only accurately measure these parameters, but also determine their uncertainties (using Markov-Chain Monte Carlo sampling). The method also characterises the nature of the source (distinguishing between a point source and extended source). We demonstrate the effect of including additional prior knowledge. Prior knowledge of the point spread function increase the precision of the flux measurement, while prior knowledge of the background has onlya small impact. In the presence of higher noise levels, we show that prior positional knowledge (such as might arise from a strong detection in another waveband) allows us to accurately measure the source flux even when the source is too faint to be detected directly. These methods are incorporated in SUSSEXtractor, the source extraction pipeline for the forthcoming Akari FIS far-infrared all-sky survey. They are also implemented in a stand-alone, beta-version public tool that can be obtained at http://astronomy.sussex.ac.uk/$\sim$rss23/sourceMiner\_v0.1.2.0.tar.gzComment: Accepted for publication by ApJ (this version compiled used emulateapj.cls

CMB anisotropy power spectrum using linear combinations of WMAP maps

In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of CMB. This has required removal of foreground contamination as well as detector noise bias with reliability and precision. Recently, a novel {\em model-independent} method for the estimation of CMB angular power spectrum solely from multi-frequency observations has been proposed and implemented on the first year WMAP data by Saha et al. 2006. All previous estimates of power spectrum of CMB are based upon foreground templates using data sets from different experiments. However our methodology demonstrates that {\em CMB angular spectrum can be reliably estimated with precision from a self contained analysis of the WMAP data}. In this work we provide a detailed description of this method. We also study and identify the biases present in our power spectrum estimate. We apply our methodoly to extract the power spectrum from the WMAP 1 year and 3 year data.Comment: 38 pages, 17 figure

Statistics of gamma-ray point sources below the Fermi detection limit

An analytic relation between the statistics of photons in pixels and the number counts of multi-photon point sources is used to constrain the distribution of gamma-ray point sources below the Fermi detection limit at energies above 1 GeV and at latitudes below and above 30 degrees. The derived source-count distribution is consistent with the distribution found by the Fermi collaboration based on the first Fermi point source catalogue. In particular, we find that the contribution of resolved and unresolved active galactic nuclei (AGN) to the total gamma-ray flux is below 20% - 25%. In the best fit model, the AGN-like point source fraction is 17% +- 2%. Using the fact that the Galactic emission varies across the sky while the extra-galactic diffuse emission is isotropic, we put a lower limit of 51% on Galactic diffuse emission and an upper limit of 32% on the contribution from extra-galactic weak sources, such as star-forming galaxies. Possible systematic uncertainties are discussed.Comment: 26 pages, 10 figures, 1 table; v2: clarifications and references added, v3: more detailed presentation of the metho

On the detection of spectral ripples from the Recombination Epoch

Photons emitted during the epochs of Hydrogen ($500 \lesssim z \lesssim 1600$) and Helium recombination ($1600 \lesssim z \lesssim 3500$ for HeII $\rightarrow$ HeI, $5000 \lesssim z \lesssim 8000$ for HeIII $\rightarrow$ HeII) are predicted to appear as broad, weak spectral distortions of the Cosmic Microwave Background. We present a feasibility study for a ground-based experimental detection of these recombination lines, which would provide an observational constraint on the thermal ionization history of the Universe, uniquely probing astrophysical cosmology beyond the last scattering surface. We find that an octave band in the 2--6 GHz window is optimal for such an experiment, both maximizing signal-to-noise ratio and including sufficient line spectral structure. At these frequencies the predicted signal appears as an additive quasi-sinusoidal component with amplitude about $8$ nK that is embedded in a sky spectrum some nine orders of magnitude brighter. We discuss an algorithm to detect these tiny spectral fluctuations in the sky spectrum by foreground modeling. We introduce a \textit{Maximally Smooth} function capable of describing the foreground spectrum and distinguishing the signal of interest. With Bayesian statistical tests and mock data we estimate that a detection of the predicted distortions is possible with 90\% confidence by observing for 255 days with an array of 128 radiometers using cryogenically cooled state-of-the-art receivers. We conclude that detection is in principle feasible in realistic observing times; we propose APSERa---Array of Precision Spectrometers for the Epoch of Recombination---a dedicated radio telescope to detect these recombination lines.Comment: 33 pages, 16 figures, submitted to ApJ, comments welcom

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power ``leakage''. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of about 568 days and a 1/f^3 power-law noise component with a noise strength of 1.24 +/- 0.067 10^{-16} cycles^2/sec^2 over the analysis frequency range 0.003 - 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either 1/f^4 power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a companion mass > 3.2 Earth masses.Comment: 53 pages, 9 figures, submitted to MNRAS, abstract condense