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This paper describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. Particular attention is paid to precision. Voigt function derivatives have previously been calculated using numerical finite difference approximations. We show how these can instead be computed analytically using Taylor series expansions and look-up tables. We introduce a new optimisation method for an efficient descent path to the best-fit, combining the principles used in both the Gauss-Newton and Levenberg-Marquardt algorithms. A simple practical fix for ill-conditioning is described, a common problem when modelling quasar absorption systems. We also summarise how unbiased modelling depends on using an appropriate information criterion to guard against over- or under-fitting. The methods and the new implementations introduced in this paper are aimed at optimal usage of future data from facilities such as ESPRESSO/VLT and HIRES/ELT, particularly for the most demanding applications such as searches for spacetime variations in fundamental constants and attempts to detect cosmological redshift drift., 15 pages, 7 figures, to appear in MNRAS

We used adaptive mesh refinement hydrodynamic cosmological simulations of a $z=1$ Milky Way-type galaxy and a $z=0$ Dwarf galaxy and generated synthetic quasar absorption-line spectra of their circumgalactic medium (CGM). Our goal is to assess whether standard observational spectroscopic analysis methods accurately reproduce intrinsic column densities, metallicities [Si/H], and hydrogen densities $n_{H}$, in simulated absorption-line systems. Without knowledge of the intrinsic simulated properties (blind study), we analysed synthetic COS and HIRES spectra with fixed $S/N=30$ to determine the column densities, metallicity, and $n_{H}$, using Voigt profile fitting combined with Markov-Chain Monte-Carlo single-phase {\sc Cloudy} modelling techniques. To quantify the intrinsic simulated absorbing gas properties, we objectively determined which gas cells along a line of sight (LOS) contribute to detected absorption in the spectra and adopt the unweighted geometric mean of these gas cell properties. For this pilot study, we performed this experiment for five LOS in the Milky-Way galaxy and five LOS in the Dwarf galaxy. We found an average agreement between the "observed" and intrinsic metallicity overestimated within $0.8\sigma$ or $0.2$ dex for the "Milky-Way"' CGM and overestimated within $1.4\sigma$ or $0.2$ dex for the Dwarf galaxy CGM. We found that the spectroscopically-derived $n_{H}$ are underestimated within $0.8\sigma$ or $0.4$ dex of the intrinsic $n_{H}$ for the "Milky-Way" CGM and overestimated within $0.3\sigma$ or $0.3$ dex for the Dwarf galaxy CGM. The overall agreement suggests that, for single-phase ionisation modelling of systems where there is substantial spread in gas properties, global metallicity measurements from quasar absorption line studies are capturing the average metallicity and ionisation parameters in a given astrophysical environment.

We present a theoretical study of intergalactic metal absorption lines imprinted in the spectra of distant quasars during and after the Epoch of Reionization (EoR). We use high resolution hydrodynamical simulations at high redshift ($4 6$, consistent with the current picture of the tail of the EoR. The simulated CII exhibits a bimodal distribution with large absorptions in and around galaxies, and some traces in the lower density IGM. We find some discrepancies between the observed and simulated column density relationships among different ionic species at $z=6$, probably due to uncertainties in the assumed UV background. Finally, our simulations are in good agreement with observations of the HI column density distribution function at $z = 4$ and the HI cosmological mass density $\Omega_{HI}$ at $4 < z < 6$., Comment: 17 pages, 11 figures. Published: 03 June 2017

We have developed a parallel code called "VoIgt profile Parameter Estimation Routine (VIPER)" for automatically fitting the H I Ly-$\alpha$ forest seen in the spectra of QSOs. We obtained the H I column density distribution function (CDDF) and line width ($b$) parameter distribution for $z < 0.45$ using spectra of 82 QSOs obtained using Cosmic Origins Spectrograph and VIPER. Consistency of these with the existing measurements in the literature validate our code. By comparing this CDDF with those obtained from hydrodynamical simulation, we constrain the H I photoionization rate ($\Gamma_{\rm HI}$) at $z < 0.45$ in four redshift bins. The VIPER, together with the Code for Ionization and Temperature Evolution (CITE) we have developed for GADGET-2, allows us to explore parameter space and perform $\chi^2$ minimization to obtain $\Gamma_{\rm HI}$. We notice that the $b$ parameters from the simulations are smaller than what are derived from the observations. We show the observed $b$ parameter distribution and $b$ vs $\log {\rm N_{HI}}$ scatter can be reproduced in simulation by introducing sub-grid scale turbulence. However, it has very little influence on the derived $\Gamma_{\rm HI}$. The $\Gamma_{\rm HI}(z)$ obtained here, $(3.9 \pm 0.1) \times 10^{-14} \; (1+z)^{4.98 \pm 0.11} \;{\rm s^{-1}}$, is in good agreement with those derived by us using flux based statistics in the previous paper. These are consistent with the hydrogen ionizing ultra-violet (UV) background being dominated mainly by QSOs without needing any contribution from the non-standard sources of the UV photons., Comment: 17 pages, 10 figures

For around 100 years, hydrogen spectral modelling has been based on Voigt profile fitting. The semi-classical Voigt profile is based on a 2-level atom approximation. Whilst the Voigt profile is excellent for many circumstances, the accuracy is insufficient for very high column density damped Lyman-$\alpha$ absorption systems. We have adapted the quantum-mechanical Kramers-Heisenberg model to include thermal broadening, producing a new profile, the KHT profile. Interactions involving multiple discrete atomic levels and continuum terms, not accounted for in the Voigt model, generate asymmetries in the Lyman line wings. If not modelled, this can lead to significant systematics in parameter estimation when modelling real data. There are important ramifications in particular for measurements of the primordial deuterium abundance. However, the KHT model is complicated. We therefore present a simplified formulation based on Taylor series expansions and look-up tables, quantifying the impact of the approximations made. The KHT profile has been implemented within the widely-used VPFIT code., Comment: 17 pages, 7 figures, 1 table

We present high-resolution optical spectra obtained with the Ultraviolet and Visual Echelle Spectrograph at the Very Large Telescope and 21-cm absorption spectra obtained with the Giant Metrewave Radio Telescope and the Green Bank Telescope of five quasars along the line of sight of which 21-cm absorption systems at 1.17 < z < 1.56 have been detected previously. We also present milliarcsecond-scale radio images of these quasars obtained with the Very Large Baseline Array. We use the data on four of these systems to constrain the time variation of x ≡ gpα2/μ, where gp is the proton gyromagnetic factor, α is the fine structure constant and μ is the proton-to-electron mass ratio. We carefully evaluate the systematic uncertainties in redshift measurements using cross-correlation analysis and repeated Voigt profile fitting. In both cases, we also confirm our results by analysing optical spectra obtained with the Keck telescope. We find the weighted and the simple means of Δx/x to be, respectively, −(0.1 ± 1.3) × 10−6 and (0.0 ± 1.5) × 10−6 at the mean redshift of 〈z〉 = 1.36 corresponding to a look-back time of ∼9 Gyr. This is the most stringent constraint ever obtained on Δx/x. If we only use the two systems towards quasars unresolved at milliarcsecond scales, we get the simple mean of Δx/x = +(0.2 ± 1.6) × 10−6. Assuming the constancy of other constants, we get Δα/α = (0.0 ± 0.8) × 10−6, which is a factor of 2 better than the best constraints obtained so far using the many-multiplet method. On the other hand, assuming that α and gp have not varied we derive Δμ/μ = (0.0 ± 1.5) × 10−6 which is again the best limit ever obtained on the variation of μ over this redshift range. Using independent constraints on Δα/α at z < 1.8 and Δμ/μ at z ∼ 0.7 available in the literature, we get Δgp/gp ≤ 3.5 × 10−6(1σ).

We investigate the properties of triply ionized Carbon (CIV) in the Intergalactic Medium using a set of high-resolution and large box-size cosmological hydrodynamic simulations of a $\Lambda$CDM model. We rely on a modification of the GADGET-2 code that self-consistently follows the metal enrichment mechanism by means of a detailed chemical evolution model. We focus on several numerical implementations of galactic feedback: galactic winds in the energy driven and momentum driven prescriptions and Active Galactic Nuclei (AGN) powered by gas accretion onto massive black holes. We extract mock IGM transmission spectra in neutral hydrogen (HI) and CIV and perform Voigt profile fitting. The results are then compared with high-resolution quasar (QSO) spectra obtained with the UVES spectrograph at the VLT and the HIRES spectrograph at Keck. We find that feedback has little impact on statistics related to the neutral hydrogen, while CIV is more affected by galactic winds and/or AGN feedback. When the same analysis is performed over observed and simulated CIV lines, we find reasonables good agreement between data and simulations over the column density range $N_{\rm CIV}=10^{12.5-15}$ cm$^{-2}$. Also the CIV line-widths distribution appears to be in agreement with the observed values, while the HI Doppler parameters, $b_{\rm HI}$, are in general too large showing that the diffuse cosmic web is heated more than what is inferred by observations. The simulation without feedback fails in reproducing the CIV systems at high column densities at all redshift, while the AGN feedback case agrees with observations only at $z

WOS:000257706200025 Using the binomial expansion theorem, the simple general analytical expressions are obtained for the Voigt function arising in various fields of physical research. As we will seen, the present formulation yields compact closed-form expressions which enable the ready analytical calculation of the Voigt function. The validity of this approximation is tested by other calculation methods. The series expansion relations established in this work are accurate enough in the whole range of parameters. The convergence rate of the series is estimated and discussed. Some examples of this methodology are presented.

We provide a remedy for a recently published formulation of the Voigt function by reformulating the function into a single proper integral with a damped sine integrand. The present formulation clears up concerns highlighted about the original formulation. The reduction of the Voigt function to a single proper integral enables the use of algorithms available in the literature and included in many software packages to integrate the function and to evaluate the line profile with relative simplicity and superior accuracy. Evidence of the usefulness and superior accuracy of the new formulation is provided.

The Voigt-Hjerting function is fundamental in order to correctly model the profiles of absorption lines imprinted in the spectra of bright background sources by intervening absorbing systems. In this work we present a simple analytic approximation to this function in the context of absorption line profiles of intergalactic HI absorbers. Using basic calculus tools, we derive an analytic expression for the Voigt-Hjerting function that contains only fourth order polynomial and Gaussian functions. In connection with the absorption coefficient of intergalactic neutral hydrogen, this approximation is suitable for modeling Voigt profiles with an accuracy of $10^{-4}$ or better for an arbitrary wavelength baseline, for column densities up to $N_{HI} = 10^{22} cm^{-2}$, and for damping parameters $a \lesssim 10^{-4}$, i.e. the entire range of parameters characteristic to all Lyman transitions arising in a variety of HI absorbing systems such as Lyman Alpha Forest clouds, Lyman Limit systems and Damped Lyman Alpha systems. We hence present an approximation to the Voigt-Hjerting function that is both accurate and flexible to implement in various types of programming languages and machines, and with which Voigt profiles can be calculated in a reliable and very simple manner.

We investigate the dependence of QSO Lyman-alpha absorption features on the temperature of the absorbing gas and on the amplitude of the underlying dark matter fluctuations. We use high-resolution hydrodynamic simulations in cold dark matter dominated cosmological models. In models with a hotter intergalactic medium (IGM), the increased temperature enhances the pressure gradients between low and high density regions and this changes the spatial distribution and the velocity field of the gas. Combined with more thermal broadening, this leads to significantly wider absorption features in hotter models. Cosmological models with little small scale power also have broader absorption features, because fluctuations on the scale of the Jeans length are still in the linear regime . Consequently, both the amplitude of dark matter fluctuations on small scales and thermal smoothing affect the flux decrement distribution in a similar way. However, the b-parameter distribution of Voigt profile fits, obtained by deblending the absorption features into a sum of thermally broadened lines, is largely independent of the amount of small scale power, but does depend strongly on the IGM temperature. The same is true for the two-point function of the flux and for the flux power spectrum on small scales. These three flux statistics are thus sensitive probes of the temperature of the IGM. We compare them computed for our models and obtained from a HIRES spectrum of the quasar Q1422+231 and conclude that the IGM temperature at z=3.25 is fairly high, T_0>= 15000K.

(Abridged) We investigate the importance of several numerical artifacts such as lack of resolution on spectral properties of the Lyman alpha forest as computed from cosmological hydrodynamic simulations in a standard cold dark matter universe. We assume an ionising background produced by quasars as computed by Haardt & Madau. We use a new simulation code based on P3M and SPH, which we compare in detail with a modified version of HYDRA (Couchman et al.) and published results of TREESPH (Hernquist et al.). The agreement is very good between all three codes. We then use our new code to investigate several numerical effects such as resolution on spectral statistics deduced from Voigt profile fitting. Our highest resolution simulation has a mass resolution of 2.1x10^5 solar masses. The column density distribution is converged but the b-parameter distribution is only marginally converged. The simulation reproduces both the HI column density and b-parameter distribution when we assume a high baryon density, Omega_B h^2 > 0.028. In addition we need to impose a higher IGM temperature than predicted within our basic set of assumptions. The simulated HI optical depth is in good agreement with observations but the HeII optical depth is lower than observed. Fitting the latter requires a larger jump between the photon flux at the H and He edge than is present in the Haardt & Madau spectrum.