A Novel Statistical Method for Measuring the Temperature–Density Relation in the IGM Using the b–N_{H i} Distribution of Absorbers in the Lyα Forest

Abstract

We present a new method for determining the thermal state of the intergalactic medium based on Voigt profile decomposition of the Lyα forest. The distribution of Doppler parameter and column density (b-N HI distribution) is sensitive to the temperature density relation T = T 0 (ρ/ρ 0 ) γ−1 , and previous work has inferred T 0 and γ by fitting its low-b cutoff. This approach discards the majority of available data, and is susceptible to systematics related to cutoff determination. We present a method that exploits all information encoded in the b-N HI distribution by modeling its entire shape. We apply kernel density estimation to discrete absorption lines to generate model probability density functions, then use principal component decomposition to create an emulator which can be evaluated anywhere in thermal parameter space. We introduce a Bayesian likelihood based on these models enabling parameter inference via Markov chain Monte Carlo. The method's robustness is tested by applying it to a large grid of thermal history simulations. By conducting 160 mock measurements we establish that our approach delivers unbiased estimates and valid uncertainties for a 2D (T 0 , γ) measurement. Furthermore, we conduct a pilot study applying this methodology to real observational data at z = 2. Using 200 absorbers, equivalent in pathlength to a single Lyα forest spectrum, we measure log T 0 = 4.092 +0.050 −0.055 and γ = 1.49 +0.073 −0.074 in excellent agreement with cutoff fitting determinations using the same data. Our method is far more sensitive than cutoff fitting, enabling measurements of log T 0 and γ with precision on log T 0 (γ) nearly two (three) times higher for current dataset sizes.

A consistent and robust measurement of the thermal state of the IGM at 2 ≤ z ≤ 4 from a large sample of Ly α forest spectra: evidence for late and rapid He ii reionization

“…spectra. The lower envelope of the b − log NHI distribution has been used to measure the thermal parameters (Schaye et al 1999;Bolton et al 2014;Gaikwad et al 2017b;Rorai et al 2018;Hiss et al 2018Hiss et al , 2019Telikova et al 2019). Fitting Voigt profiles to Lyα forest spectra is challenging and somewhat subjective.…”

“…The lower envelope in the b − log NHI distribution is shown to be sensitive to thermal parameters (Webb & Carswell 1991;Schaye et al 2000;Bolton et al 2014;Gaikwad et al 2017b;Rorai et al 2018). However, the lower envelope method utilizes fewer points that define the lower cutoff in b values at given log NHI (but see Hiss et al 2019;Telikova et al 2019). Recently, Hiss et al (2019) have proposed to use the full b-log NHI 2D distribution to simultaneously measure T0 and γ.…”

“…However, the lower envelope method utilizes fewer points that define the lower cutoff in b values at given log NHI (but see Hiss et al 2019;Telikova et al 2019). Recently, Hiss et al (2019) have proposed to use the full b-log NHI 2D distribution to simultaneously measure T0 and γ. However, this requires to sample the b − log NHI plane densely enough to reduce any statistical fluctuations introduced by binning.…”

“…Fitting a lower envelope to the b − log NHI distribution although well motivated, is somewhat subjective. Finding a lower envelope in an objective way is difficult (but see Telikova et al 2019;Hiss et al 2019). The lower envelope is found by iteratively rejecting the lines with low b parameter until convergence is achieved.…”

Thermal State of the Intergalactic Medium at z ∼ 2–4

“…Although the selected shape fits the data well, the choice of the model for the distribution can impose some systematic uncertainties. Recently, Hiss et al (2019) developed a method for comparison of the observed (N, b) distribution with model distributions resulting from the analysis of the mock Lyα forest generated based on the hydrodynamical simulations of the IGM. The simulations are carried out on a grid of the IGM thermal parameters (T 0 and γ) and extended to the inter-grid values by means of the Gaussian process interpolation of the principal components of the kernel-density smoothed (N, b) maps.…”