AI 中文总结
本研究用SPARC全部175个星系逐一对比NFW暗物质晕与MOND，发现两者各有胜负，NFW浓度偏低显示核-尖点问题，而总体径向加速度关系紧密但单星系$a_0$弥散大。
AI 中文摘要
将SPARC数据库中175个盘状星系的旋转曲线，在相同条件下逐一与主导了长达四十年缺失质量之争的两种质量模型进行对比：一种是Navarro-Frenk-White (NFW)形式的冷暗物质晕，另一种是加速度常数固定为$a_0=1.2\times10^{-10}$ m s$^{-2}$的米尔格若姆动力学（MOND）。恒星质量光度比、距离和倾角被视为干扰参数，其先验由3.6 $\mu$m测光及SPARC误差预算设定，每个星系均采用马尔可夫链蒙特卡洛方法进行采样。得出三项发现：（i）根据贝叶斯信息准则，自由NFW晕在96个星系中更受青睐，MOND在79个星系中更优；一旦要求晕满足$\Lambda$CDM的浓度-质量关系，得分变为86比89，即平局。两种理论在不同地方失效：MOND在大质量、高表面亮度、以核球为主的系统中失效，NFW在缓慢上升的矮星系旋转曲线中失效。（ii）数据所需的NFW浓度中位数比$\Lambda$CDM预期低0.24 dex，且样本的53%位于该预期2$\sigma$以下，与晕质量无关；这是核-尖点问题以标度关系偏移而非个别轶事的形式呈现。（iii）由全样本构建的径向加速度关系给出$a_0=(1.13\pm0.02)\times10^{-10}$ m s$^{-2}$，观测弥散为0.14 dex，但单个星系偏好的$a_0$值跨度超过一个数量级，并与表面亮度相关。这两种表述并不矛盾：总体层面的关系之所以紧密，是因为它平均了与质量光度比和距离的简并，而这些简并使得$a_0$在逐个星系上难以确定。提供了完整的拟合表。
英文摘要
The rotation curves of the 175 disk galaxies in the SPARC database are confronted, one by one and under identical conditions, with the two mass models that have dominated the missing-mass debate for four decades: a cold dark-matter halo of Navarro-Frenk-White (NFW) form, and Milgromian dynamics (MOND) with the acceleration constant held at $a_0=1.2\times10^{-10}$ m s$^{-2}$. Stellar mass-to-light ratios, distances and inclinations are treated as nuisance parameters with priors set by the 3.6 $μ$m photometry and by the SPARC error budget, and every galaxy is sampled with a Markov-chain Monte Carlo. Three findings emerge. (i) Judged by the Bayesian information criterion, the free NFW halo is preferred in 96 galaxies and MOND in 79; once the halo is required to obey the $Λ$CDM concentration-mass relation the score becomes 86 to 89, i.e. a draw. The two theories fail in different places: MOND loses in massive, high-surface-brightness, bulge-dominated systems, NFW loses in slowly rising dwarf rotation curves. (ii) The NFW concentrations demanded by the data sit a median 0.24 dex below the $Λ$CDM expectation, and 53% of the sample lies more than $2σ$ below it, independent of halo mass; this is the core-cusp problem expressed as a scaling-relation offset rather than as a handful of anecdotes. (iii) The radial acceleration relation built from the full sample has $a_0=(1.13\pm0.02)\times10^{-10}$ m s$^{-2}$ and an observed scatter of 0.14 dex, yet the value of $a_0$ preferred by individual galaxies spans more than a decade and correlates with surface brightness. The two statements are not in contradiction: the population-level relation is tight because it averages over exactly the degeneracies with mass-to-light ratio and distance that make $a_0$ ill-determined galaxy by galaxy. The full table of fits is provided.
Comments16 pages, 8 figures, 6 tables. Also available at Zenodo: doi:10.5281/zenodo.22342521
