Cosmology and Nongalactic Astrophysics · arXiv:1012.2385 v1 · submitted 10 Dec 2010
Mapping systematic errors in helium abundance determinations using Markov Chain Monte Carlo
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“In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra.”
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Abstract
Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H II regions. The helium abundance is sensitive to several physical parameters associated with the H II region. In this work, we introduce Markov Chain Monte Carlo (MCMC) methods to efficiently explore the parameter space and determine the helium abundance, the physical parameters, and the uncertainties derived from observations of metal poor nebulae. Experiments with synthetic data show that the MCMC method is superior to previous implementations (based on flux perturbation) in that it is not affected by biases due to non-physical parameter space. The MCMC analysis allows a detailed exploration of degeneracies, and, in particular, a false minimum that occurs at large values of optical depth in the He I emission lines. We demonstrate that introducing the electron temperature derived from the [O III] emission lines as a prior, in a very conservative manner, produces negligible bias and effectively eliminates the false minima occurring at large optical depth. We perform a frequentist analysis on data from several "high quality" systems. Likelihood plots illustrate degeneracies, asymmetries, and limits of the determination. In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.30 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.96 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Monte Carlo techniques have been used to evaluate the statistical and systematic uncertainties in the helium abundances derived from extragalactic H~II regions. | background 0.69 | 0.35 | 0.05 | asserted 1.00 |
| The helium abundance is sensitive to several physical parameters associated with the H~II region. | background 1.00 | 0.07 | 0.02 | asserted 1.00 |
| In this work, we introduce Markov Chain Monte Carlo (MCMC) methods to efficiently explore the parameter space and determine the helium abundance, the physical parameters, and the uncertainties derived from observations of metal poor nebulae. | contribution 0.88 | 0.93 | 0.08 | asserted 0.99 |
| Experiments with synthetic data show that the MCMC method is superior to previous implementations (based on flux perturbation) in that it is not affected by biases due to non-physical parameter space. | result 0.90 | 0.86 | 0.17 | asserted 1.00 |
| The MCMC analysis allows a detailed exploration of degeneracies, and, in particular, a false minimum that occurs at large values of optical depth in the He~I emission lines. | result 0.65 | 0.86 | 0.09 | asserted 1.00 |
| We demonstrate that introducing the electron temperature derived from the [O~III] emission lines as a prior, in a very conservative manner, produces negligible bias and effectively eliminates the false minima occurring at large optical depth. | result 0.49 | 0.95 | 0.18 | asserted 1.00 |
| We perform a frequentist analysis on data from several "high quality" systems. | method 0.88 | 0.95 | 0.03 | asserted 0.98 |
| Likelihood plots illustrate degeneracies, asymmetries, and limits of the determination. | method 0.44 | 0.85 | 0.04 | asserted 0.99 |
| In agreement with previous work, we find relatively large systematic errors, limiting the precision of the primordial helium abundance for currently available spectra. | result 0.76 | 0.89 | 0.67 | asserted 1.00 |
What kind of paper the classifier reports this is: method or tool 1.00 · evidence from analysis of existing data 0.67
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- references and citing sentences
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- P abstract
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,928 input tokens, $0.0003 reported.
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Cited by 12 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- The LBT Y$_{\rm p}$ Project VI: Gas-Phase Chemical Abundance Patterns of Metal-Poor Nebulae astro-ph.GA · Oct 2026
- How Massless Neutrinos Affect the Cosmic Microwave Background Damping Tail astro-ph.CO · Apr 2011
- Constraining the cosmic radiation density due to lepton number with Big Bang Nucleosynthesis astro-ph.CO · Nov 2010
- Fifty years of primordial helium abundances: A statistical reanalysis astro-ph.CO · Jun 2026
- Improving Helium Abundance Determinations with Leo P as a Case Study astro-ph.CO · Oct 2020
- The effects of He I 10830 on helium abundance determinations astro-ph.CO · Mar 2015
- Increasing Neff with particles in thermal equilibrium with neutrinos astro-ph.CO · Jul 2012
- Cosmological lepton asymmetry with a nonzero mixing angle \theta_{13} astro-ph.CO · Apr 2012
- An analysis of constraints on relativistic species from primordial nucleosynthesis and the cosmic microwave background astro-ph.CO · Dec 2011
- A robust upper limit on N_eff from BBN, circa 2011 astro-ph.CO · Mar 2011
- The primordial helium abundance from updated emissivities astro-ph.CO · Aug 2013
- Sterile neutrinos with eV masses in cosmology -- how disfavoured exactly? astro-ph.CO · Aug 2011
How the literature uses it
12 arXiv papers cite this in 29 sentences
Papers citing it · 15 sentences without a confident label
Uses its method or tool 3 papers
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Our method for determining the 4 abundance in an individual H II region is based on a Markov Chain Monte Carlo (MCMC) analysis [ref] .
The effects of He I 10830 on helium abundance determinations · Introduction · 0.98
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Their analysis followed the approach in [ref] and they combined their new observations with a large number of observations from the literature.
Improving Helium Abundance Determinations with Leo P as a Case Study · The Primordial Helium Abundance · 0.89
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To account for systematics, a Markov-Chain Monte Carlo approach using the 4 abundance as one of the several input parameters has been adopted [ref] .
Impact of Current Results on Nucleosynthesis · Towards Precision 4 abundance determinations · 0.98
Uses its data or values 6 papers
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For 4, we use here the abundances inferred in nine metal-poor, extragalactic HII regions in [ref] (see also [ref] ).
A robust upper limit on N_eff from BBN, circa 2011 · Procedure · 1.00
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Applying approaches in which physical parameters for each Hii region are determined in a simultaneous fit and errors are computed by Monte Carlo, Izotov & Thuan find $0.2565±0.0010 (stat) ±0.0050 (syst)$ from 93 Hii regions [ref] while Aver et al. find $0.2573 ±0.0033$ [ref] for nine selected low-metallicity objects from the Izotov & Thuan data set.
An analysis of constraints on relativistic species from primordial nucleosynthesis and the cosmic microwave background · $^4$He · 0.93
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A linear regression of data from seven high-quality objects with a careful treatment of systematic uncertainties yields $Y_p = 0.2573^+0.0033_-0.0088$, with the additional restriction to theoretically meaningful positive slopes $dY/dZ > 0$ [ref] .
Sterile neutrinos with eV masses in cosmology -- how disfavoured exactly? · Helium-4 · 1.00
Compares with it 1 paper
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Notice that our upper bound of Eq. ([ref]) is close but slightly more stringent than what is found at 2 $σ$ in [ref] , $Y_p < 0.2639$, since only seven of the nine determinations were used there.
A robust upper limit on N_eff from BBN, circa 2011 · Procedure · 1.00
Cites it as background 1 paper
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More recently, new studies of metal poor H II regions have appeared in the literature [ref] .
Constraining the cosmic radiation density due to lepton number with Big Bang Nucleosynthesis · Results from BBN: constraints on total and electron neutrino asymmetries · 0.87
What it cites · 19 sentences without a confident label
Uses the method or tool of 2 papers
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This work uses the radiative transfer calculations of [ref] [ref] .
Radiative Transfer Effects in He I Emission Lines · Degeneracies at large values of optical depth · 0.97
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This work uses the radiative transfer calculations of [ref] [ref] .
A Realistic Determination of the Error on the Primordial Helium Abundance: Steps Toward Non-Parametric Nebular Helium Abundances · Degeneracies at large values of optical depth · 0.97
Uses data or values from 4 papers
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A regression of Y, the helium mass fraction, versus O/H, the oxygen to hydrogen mass fraction, is used to extrapolate to the primordial value.[This work takes $Z=20(O/H)$ such that $Y=4y(1-20(O/H))/1+4y$] For direct comparison, the O/H values are taken from AOS [ref] .
A Realistic Determination of the Error on the Primordial Helium Abundance: Steps Toward Non-Parametric Nebular Helium Abundances · Results of the MCMC analysis · 0.99
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The 7-year WMAP value for $η$ is $(6.19 ±0.15) ×10^-10$, [ref] .
Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation · Introduction · 1.00
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Additionally, NGC 346 [ref] and I Zw 18SE [ref] are also included, as in AOS.
The Chemical Composition of the Small Magellanic Cloud H II Region NGC 346 and the Primordial Helium Abundance · Application of MCMC to real observations · 0.94
Cites as background 12 papers
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Standard big bang nucleosynthesis (SBBN) using the baryon density determined by WMAP [ref] predicts the initial abundances of D, $^3$He, $^4$He, and $^7$Li [ref] , allowing one to probe the early universe at redshifts of order $10^10$ [ref] .
Primordial Nucleosynthesis: Theory and Observations · Introduction · 0.95
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Standard big bang nucleosynthesis (SBBN) using the baryon density determined by WMAP [ref] predicts the initial abundances of D, $^3$He, $^4$He, and $^7$Li [ref] , allowing one to probe the early universe at redshifts of order $10^10$ [ref] .
A Bitter Pill: The Primordial Lithium Problem Worsens · Introduction · 0.95
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Standard big bang nucleosynthesis (SBBN) using the baryon density determined by WMAP [ref] predicts the initial abundances of D, $^3$He, $^4$He, and $^7$Li [ref] , allowing one to probe the early universe at redshifts of order $10^10$ [ref] .
Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation · Introduction · 0.95
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