[Paper Review] The current best estimate of the Galactocentric distance of the Sun based on comparison of different statistical techniques

Zinovy Malkin|arXiv (Cornell University)|Feb 28, 2012

Scientific Measurement and Uncertainty Evaluation5 references18 citations

TL;DR

This study evaluates the current best estimate of the Sun's Galactocentric distance, R₀, by comparing 52 published determinations from 1992–2011 using multiple statistical techniques. It finds no significant trend in R₀ over time and derives a final value of R₀ = 7.98 ± 0.15 (stat) ± 0.20 (syst) kpc, representing the most reliable combined estimate to date, with 8.0 ± 0.25 kpc suitable for most practical applications.

ABSTRACT

In this paper, the current best estimate of a fundamental Galactic parameter Galactocentric distance of the Sun $R_0$ has been evaluated using all the available estimates published during the last 20 years. Unlike some other studies, our analysis of these results showed no statistically significant trend in $R_0$ during this period. However we revealed a statistically valuable improvement in the $R_0$ uncertainties with time of about 0.2 kpc for 20 years. Several statistical techniques have been used and compared to obtain the most reliable common mean of 52 determinations made in 1992--2011 and its realistic uncertainty. The statistical methods used include unweighted mean, seven variants of the weighted mean, and two variants of median technique. The $R_0$ estimates obtained with these methods range from 7.91 to 8.06 kpc with uncertainties varying from 0.05 to 0.08 kpc. The final value derived in this analysis is $R_0 = 7.98 \pm 0.15\,|_{stat} \pm 0.20\,|_{syst}$ kpc, which can be recommended as the current best estimate of the Galactocentric distance of the Sun. For most of the practical applications the value of $R_0 = 8.0 \pm 0.25$ kpc can be used.

Motivation & Objective

• To derive a current best estimate of the Galactocentric distance of the Sun, R₀, based on all available published determinations from 1992 to 2011.
• To evaluate the reliability and consistency of different statistical techniques in combining discrepant or inconsistent R₀ estimates.
• To assess whether systematic errors or a 'bandwagon effect' have biased recent R₀ measurements.
• To quantify the improvement in uncertainty of R₀ estimates over the past two decades.
• To provide a robust, up-to-date R₀ value suitable for astronomical modeling and distance scale applications.

Proposed method

• The study compiles 52 R₀ estimates from the literature published between 1992 and 2011, excluding earlier results as they contribute minimally to the final estimate.
• It applies multiple statistical techniques: unweighted mean, seven variants of weighted mean (including classical, robust, and likelihood-based methods), and two median-family techniques (including biweight and trimmed mean approaches).
• The weighted mean methods account for reported uncertainties and assess data consistency, while the median-based methods are used to handle potential outliers and data discrepancies.
• The final estimate is derived by comparing results across methods, with the classical weighted mean and likelihood-based robust methods yielding the most consistent results.
• Systematic uncertainty is estimated by considering residual discrepancies and known error sources in original studies, leading to a separate ±0.20 kpc systematic uncertainty term.
• The final R₀ value is validated by consistency checks with prior average estimates and by testing the stability of results under data subset variations.

Experimental results

Research questions

• RQ1 What is the most reliable current estimate of the Sun's Galactocentric distance R₀ based on all available published determinations from 1992 to 2011?
• RQ2 How do different statistical techniques—especially those designed for inconsistent or discrepant data—compare in estimating the common mean of R₀?
• RQ3 Is there a statistically significant trend in R₀ estimates over the past 20 years, indicating systematic bias or convergence?
• RQ4 To what extent have uncertainties in R₀ estimates improved over time, and is this improvement real or due to inconsistent uncertainty reporting?
• RQ5 What is the realistic combined uncertainty of R₀, accounting for both statistical and systematic error components?

Key findings

• The analysis of 52 R₀ estimates from 1992 to 2011 shows no statistically significant trend in the central value over time, indicating stability in the current best estimate.
• The uncertainty in R₀ estimates has improved by approximately 0.2 kpc over 20 years, reflecting a steady reduction in reported errors.
• The most consistent results across multiple statistical techniques—particularly the classical weighted mean, likelihood-based robust weighted mean, and median-family methods—yield R₀ values between 7.91 and 8.06 kpc.
• The final best estimate is R₀ = 7.98 ± 0.15 (stat) ± 0.20 (syst) kpc, with the statistical uncertainty derived from data consistency and the systematic uncertainty from residual error sources.
• For most practical applications, the value R₀ = 8.0 ± 0.25 kpc is recommended as a sufficiently accurate and robust approximation.
• The study finds no strong evidence of a 'bandwagon effect' biasing recent R₀ estimates, as results from different methods converge and show consistency across time.