Super-Accuracy Calculation for the Half Width of a Voigt Profile

A simple approximation scheme to describe the half width of the Voigt profile as a function of the relative contributions of Gaussian and Lorentzian broadening is presented. The proposed approximation scheme is highly accurate and provides an accuracy better than 10−17 for arbitrary αL/αG ratios. In particular, the accuracy reaches an astonishing 10−34 (quadruple precision) in the domain 0 ≤ αL/αG ≤ 0.2371 ∪ αL/αG ≥ 33.8786.

A Polarization-Insensitive Recirculating Delayed Self-Heterodyne Method for Sub-Kilohertz Laser Linewidth Measurement

A polarization-insensitive recirculating delayed self-heterodyne method (PI-RDSHM) is proposed and demonstrated for the precise measurement of sub-kilohertz laser linewidths. By a unique combination of Faraday rotator mirrors (FRMs) in an interferometer, the polarization-induced fading is effectively reduced without any active polarization control. This passive polarization-insensitive operation is theoretically analyzed and experimentally verified. Benefited from the recirculating mechanism, a series of stable beat spectra with different delay times can be measured simultaneously without changing the length of delay fiber. Based on Voigt profile fitting of high-order beat spectra, the average Lorentzian linewidth of the laser is obtained. The PI-RDSHM has advantages of polarization insensitivity, high resolution, and less statistical error, providing an effective tool for accurate measurement of sub-kilohertz laser linewidth.

The evolution of the low-density H i intergalactic medium from z = 3.6 to 0: Data, transmitted flux and H i column density*†‡

We present a new, uniform analysis of the H i transmitted flux (F) and H i column density ($N_{\rm{H\, {\small I}}}$) distribution in the low-density IGM as a function of redshift z for 0 < z < 3.6 using 55 HST/COS FUV (Δz = 7.2 at z < 0.5), five HST/STIS+COS NUV (Δz = 1.3 at z ∼ 1) and 24 VLT/UVES and Keck/HIRES (Δz = 11.6 at 1.7 < z < 3.6) AGN spectra. We performed a consistent, uniform Voigt profile analysis to combine spectra taken with different instruments, to reduce systematics and to remove metal-line contamination. We confirm previously known conclusions on firmer quantitative grounds in particular by improving the measurements at z ∼ 1. Two flux statistics at 0 < F < 1, the mean H i flux and the flux probability distribution function (PDF), show that considerable evolution occurs from z = 3.6 to z = 1.5, after which it slows down to become effectively stable for z < 0.5. However, there are large sightline variations. For the H i column density distribution function (CDDF, f ∝ $N_{\rm H\, {\small I}}^{-\beta }$) at $\log (N_{\rm{H\, {\small I}}}/1\, {\mathrm{cm}^{-2}})$ ∈ [13.5, 16.0], β increases as z decreases from β = 1.60 at z ∼ 3.4 to β = 1.82 at z ∼ 0.1. The CDDF shape at lower redshifts can be reproduced by a small amount of clockwise rotation of a higher-z CDDF with a slightly larger CDDF normalisation. The absorption line number per z (dn/dz) shows a similar evolutionary break at z ∼ 1.5 as seen in the flux statistics. High-$N_{\rm{H\, {\small I}}}$ absorbers evolve more rapidly than low-$N_{\rm{H\, {\small I}}}$ absorbers to decrease in number or cross-section with time. The individual dn/dz shows a large scatter at a given z. The scatter increases toward lower z, possibly caused by a stronger clustering at lower z.

Three- and two-point spatial correlations of IGM at z ∼ 2: cloud-based analysis using simulations

ABSTRACT Ly α forest absorption spectra decomposed into multiple Voigt profile components (clouds) allow us to study clustering of intergalactic medium (IGM) as a function of H i column density ($N_{\rm H\, \small{I}}$). Here, we explore the transverse three-point correlation (ζ) of Ly α clouds using mock triplet spectra from simulations at z ∼ 2 on scales of 1–5 h−1 cMpc. We find ζ to depend strongly on $N_{\rm H\, \small{I}}$ and scale and weakly on angle of the triplet configuration. We show that the ‘hierarchical ansatz’ is applicable for scales $\ge ~ 3\, h^{-1}$ cMpc, and obtain a median reduced three-point correlation (Q) in the range 0.2–0.7. We show, ζ is influenced strongly by the thermal and ionization state of the gas. As in the case of galaxies, the influence of physical parameters on Q is weaker compared to that on ζ. We show difference in ζ and Q between different simulations are minimized if we use appropriate $N_{\rm H\, \small{I}}$ cut-offs corresponding to a given baryon overdensity (Δ) using the $N_{\rm H\, \small{I}}~versus~\Delta$ relationship obtained from simulations. We study the effect of pressure broadening on ζ using a model with artificially boosted heating rates. However, for models with realistic thermal and ionization histories the effect of pressure broadening on ζ is subdominant compared to other local effects. We find the strong redshift evolution shown by ζ, mainly originating from the redshift evolution of thermal and ionization state of the IGM. We discuss the observational requirements for the detection of three-point correlation, specifically, in small intervals of configuration parameters and redshift.

An adaptive Gaussian quadrature for the Voigt function

We evaluate an adaptive Gaussian quadrature integration scheme suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for “full non-LTE” radiation transfer computations, assuming potential deviations of the velocity distribution of massive particles from the usual Maxwell–Boltzmann distribution. A first validation is made with computations of the usual Voigt profile.