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暗物质晕（暗晕）中存在的星系数量、光度和质量等与星系的形成与演化理论密切相关。在当前学术界达成共识的星系形成理论框架下，银河系质量的暗晕（约1012h-1M☉）是形成恒星最为高效的场所，拥有最高的恒星-暗晕质量比。大质量暗晕中的星系会由于活动星系核的反馈，遏制星系的进一步增长，在恒星-暗晕质量比上表现为随暗晕质量的下降行为。而在小质量端，由于星风、超新星等反馈机制的作用，小质量暗晕中的恒星形成效率也会快速降低，表现为恒星-暗晕质量比随暗晕质量的减小而下降的行为。如图1左上角小图中的各条虚线所示。
图1：中心星系的恒星-暗晕质量比
近日，上海交通大学物理与天文学院和李政道研究所的杨小虎教授课题组结合 DESI LS DR9、SV3和Y1的测光和光谱观测数据，首次获得了不同质量暗晕中星系条件光度函数和条件恒星质量函数在小质量端的精确测量。研究发现，在低红移情况下，相比以往的外推结果，星系条件光度（恒星质量）函数在109 h-2L☉(h-2M☉)以下表现出显著的斜率改变。这一结果表明：暗晕中存在大量的小质量卫星星系，它们随着暗晕子结构的吸积进入了暗晕。而进一步的分析则显示：星系条件光度（恒星质量）函数在小质量端的斜率与暗晕子结构质量函数(SHMF)在小质量端的斜率呈现出显著的一致性（如图2虚线）。这一结果暗示了在小质量暗晕中星系的恒星形成效率可能是一个常数，这与当前学术界达成共识的星风、超新星反馈的强烈遏制恒星形成理论存在着显著冲突。
图2：红移0.1处的暗晕星系条件光度函数和条件恒星质量函数测量
值得一提的是，由于对星系条件光度函数和条件恒星质量函数的积分就是星系的整体光度函数和恒星质量函数，上述的斜率陡变行为应当在以往的星系观测中有所体现。然而，迄今为止的观测，都没有声称发现过小质量端有如此大斜率的星系光度函数和恒星质量函数。为此，团队针对DESI Y1的光谱完备度、星等极限进行了细致的分析，发现有两个效应会影响整体测量结果：测光红移误差以及我们观测者处于宇宙的近邻空洞区域。通过修正这两种效应后，团队发现：星系的整体光度函数和恒星质量函数同样在小于109 h-2L☉(h-2M☉)处表现出十分显著的斜率改变（见图3中的星号所示结果）。而且，它们的斜率和暗晕质量函数在小质量端的斜率完美相符（图3中的虚线）！由此自洽检验了我们的测量结果。
图3：基于DESI Y1数据获得的星系光度函数和恒星质量函数的测量。修正测光红移的影响以及近邻宇宙空洞效应后的光度函数如星号所示
基于这一星系恒星质量函数测量结果和理论上的暗晕质量函数，我们可以利用丰度匹配模型将星系的恒星质量与所在暗晕质量的关系延伸到暗晕质量108 h-1M☉（见图1中的实线）。我们发现在1010.5 h-1M☉以下暗晕中，星系的恒星-暗晕质量比呈现出显著的水平趋势。这一行为表明：小质量暗晕中仍然存在高效的恒星形成效率，与经典星风、超新星反馈的强烈遏制效应存在着显著冲突。该结果或许和近期韦伯空间望远镜看到更多的高红移星系有对应的机理，为未来建立完善的星系形成与演化理论提供了一项强有力的观测基准。
该工作发表于国际天文期刊《The Astrophysical Journal》，第一作者为上海交通大学2020级博士生王艺蓉，上海交通大学李政道研究所和物理与天文学院杨小虎教授为通讯作者。该工作得到了科技部重点研发、国家自然科学基金、上海自然科学基金以及中国载人航天科学工程项目的支持。
The conditional luminosity function measurements challenge the galaxy formation and evolution theories at low-mass end
The quantification of galaxy number, luminosity and mass distributions within dark matter halos is crucial to constrain galaxy formation and evolution models. In the current paradigm of galaxy formation theory, halos with masses comparable to that of the Milky Way (~1012h-1M☉) are the most efficient locations for star formation, exhibiting the highest stellar-to-halo mass ratio. In more massive halos, galaxy growth is further inhibited by feedback from active galactic nuclei, causing the stellar-to-halo mass ratio to decline as halo mass increases. Conversely, in low-mass halos, star formation efficiency is also markedly reduced by feedback mechanisms such as stellar winds and supernovae, resulting in a lower stellar-to-halo mass ratio as halo mass decreases. This trend is illustrated by the dashed lines in the small inset in Figure 1.
Figure 1：The steller-to-halo mass ratio as a function of halo mass for central galaxies
Professor Xiaohu Yang's research team at the Tsung-Dao Lee Institute and the School of Physics and Astronomy, Shanghai Jiao Tong University, has recently, for the first time, attained precise measurements of the conditional luminosity function and conditional stellar mass function of galaxies at the very faint/low-mass ends. This was accomplished using photometric and spectroscopic data from DESI LS DR9, SV3, and Y1. The research shows that at low redshift, the slope of the conditional luminosity (stellar mass) function of galaxies below 109 h-2L☉(h-2M☉) diverges from extrapolations of earlier work with significantly enhanced low mass end slope. This finding points to the existence of numerous low-mass satellite galaxies within dark halos, which were accreted into halos along with substructures.
Further analysis revealed that the slope of the conditional luminosity (stellar mass) function at the low-mass end is notably consistent with the slope of the subhalo mass function (SHMF) at the low-mass end, as indicated by the dashed lines in Figure 2. This finding suggests that the star formation efficiency in low-mass halos may be roughly constant, which significantly conflicts with the widely accepted theory that stellar winds and supernova feedback strongly suppress star formation.
Figure 2：The conditional luminosity function (upper panels) and conditional stellar mass functions in halos of different masses at redshift z~0.1.
It is important to highlight that the integral of the conditional luminosity function and the conditional stellar mass function of galaxies results in the total luminosity function and stellar mass function. Thus, the pronounced slope change mentioned earlier should have been detected in prior galaxy observations. Yet, so far, no research has indicated such a notable slope variation at the low-mass end within the galaxy luminosity and stellar mass functions.
To explore this, the research team performed an in-depth analysis of the spectroscopic completeness and magnitude limits of DESI Y1 and discovered two factors that could affect the overall measurement results: photometric redshift errors and the fact that we, as observers, are located in a nearby cosmic void region. After correcting for these two factors, the team observed that the overall luminosity function and stellar mass function of galaxies also undergo a significant slope change below 109 h-2L☉(h-2M☉), as denoted by the stars in Figure 3. Furthermore, the slopes of these functions align almost perfectly with the slope of the halo mass function at the low-mass end (as indicated by the dashed lines in Figure 3), thus providing a self-consistent validation of their measurement results.
Figure 3：The galaxy luminosity (left panel) and stellar mass (right panel) functions measured from DESI Y1. The ones corrected for the photometric redshift and the local void effects are represented using the dots and stars, respectively.
Utilizing the galaxy stellar mass function measurements and the theoretical dark halo mass function, we can apply the abundance matching method to model the connection between a galaxy's stellar mass and its host halo mass to halo masses as low as 108 h-1M☉ (as depicted by the solid line in Figure 1). Our findings reveal that for halos with masses under 1010.5 h-1M☉, the stellar-to-halo mass ratio of galaxies exhibits a significant flattening trend. This trend reveals that efficient star formation continues in low-mass halos, which contrasts sharply with the strong suppression effects anticipated by the traditional stellar wind and supernova feedback theory.
This outcome could be linked to the recent discoveries made by the James Webb Space Telescope, which identified a large population of high-redshift galaxies, hinting at a comparable underlying process. These results offer a strong observational foundation for upcoming attempts to develop a more thorough and coherent theory of galaxy formation and evolution.
This work was published in The Astrophysical Journal. The first author is Yirong Wang, a Ph.D. student from the 2020 cohort at Shanghai Jiao Tong University. Professor Xiaohu Yang from the Tsung-Dao Lee Institute and the School of Physics and Astronomy at Shanghai Jiao Tong University is the corresponding author. The research was supported by the National Key R&D Program of China, the National Natural Science Foundation of China, the Shanghai Natural Science Foundation, and the China Manned Space Program.
Article Link: https://iopscience.iop.org/article/10.3847/1538-4357/ad5294
