消除具有动力学测量超大质量黑洞的星系样本中疑似存在的选择偏差
Quashing a suspected selection bias in galaxy samples having dynamically-measured supermassive black holes
AI总结：
本研究针对有动力学测量黑洞质量的早型星系样本疑似存在的选择偏差问题，通过交叉匹配S⁴G与SDSS星系样本验证发现，此前的恒星质量偏移源于光学与红外观测使用的质光比不一致，纠正了相关本征关系推导的错误假设，并强调了υ项在避免质光比失配中的作用。
摘要：
据报道，拥有直接测量黑洞质量$M_{\rm bh}$的局地早型星系，相较于整体星系族群而言是一个有偏差的样本。据称，拥有斯皮策空间望远镜（Spitzer Space Telescope）成像数据的这类星系，在给定星系恒星质量$M_{\rm *,gal}$的情况下，其速度弥散$σ$比斯隆数字巡天（Sloan Digital Sky Survey, SDSS）观测到的数千个早型星系的典型值至少大~0.1 dex。这一明显的偏移促使Shankar等人将观测到的$M_{\rm bh} \propto σ^5$关系的归一化值降低了至少~0.5 dex，从而得到他们的“本征关系”，其中包括对$M_{\rm bh}$-$M_{\rm *,gal}$关系的基于$σ$的修正。这些修正基于一个未经检验的假设：两个样本的恒星质量推导方式是一致的。本文中，我们利用同时属于星系恒星结构斯皮策巡天（Spitzer Survey of Stellar Structure in Galaxies, S$^4$G）和SDSS的星系，开展了这项必要的检验。我们发现，拥有和未拥有直接测量黑洞的星系，其恒星质量之所以呈现偏移，是因为光学和红外数据使用了不一致的恒星质光比$Υ_*$。我们简要讨论了“本征关系”，以及为何其中部分关系在应用于基于同样不一致的$Υ_*$值的数据时，有时会显得部分有效。最后，我们重申了$\upsilon$（小写$Υ$）项的重要性——我们此前已将该项引入$M_{\rm bh}$-$M_{\rm *}$关系中，以帮助避免与$Υ_*$相关的不匹配问题。
英文摘要：
Local early-type galaxies with directly-measured black hole masses, $M_{\rm bh}$, have been reported to represent a biased sample relative to the population at large. Such galaxies with Spitzer Space Telescope imaging have been purported to possess velocity dispersions, $σ$, at least $\sim$0.1 dex larger for a given galaxy stellar mass, $M_{\rm *,gal}$, than is typically observed among thousands of early-type galaxies imaged by the Sloan Digital Sky Survey. This apparent offset led Shankar et al. to reduce the normalisation of the observed $M_{\rm bh} \propto σ^5$ relation by at least $\sim$0.5 dex to give their "intrinsic relations", including $σ$-based modifications to the $M_{\rm bh}$-$M_{\rm *,gal}$ relation. These modifications were based on the untested assumption that the stellar masses had been derived consistently between the two samples. Here, we provide the necessary check using galaxies common to the Spitzer Survey of Stellar Structure in Galaxies (S$^4$G) and the Sloan Digital Sky Survey (SDSS). We find that the stellar masses of galaxies with and without directly measured black holes had appeared offset from each other due to the use of inconsistent stellar mass-to-light ratios, $Υ_*$, for the optical and infrared data. We briefly discuss the "intrinsic relations" and why some of these will at times appear to have had partial success when applied to data based on similarly inconsistent values of $Υ_*$. Finally, we reiterate the importance of the $\upsilon$ (lower-case $Υ$) term, which we previously introduced into the $M_{\rm bh}$-$M_{\rm *}$ relations to help avoid $Υ_*$-related mismatches.
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