The core-cusp problem is a widely cited motivation for the exploration of dark matter models beyond standard cold dark matter. One such alternative is ultralight dark matter (ULDM), extremely light scalar particles exhibiting wavelike properties on kiloparsec scales. Astrophysically realistic ULDM halos are expected to consist of inner solitonic cores embedded in NFW-like outer halos. The presence of the solitonic core suggests that ULDM may resolve the core-cusp discrepancy associated with pure NFW halos without recourse to baryonic physics. However, it has been demonstrated that the density of ULDM halos can exceed those of comparable NFW configurations at some radii and halo masses, apparently exacerbating the problem rather than solving it. This situation arises because, although solitonic cores are flat at their centres, they obey an inverse mass–radius scaling relationship. Meanwhile, the mass of the inner soliton increases with the total halo mass, and therefore the inner core becomes more peaked at large halo masses. We describe a parameterisation of the radial density profiles of ULDM halos that allows for environmental variability of the core–halo mass relation in order to investigate this issue in more detail. For halos up to $10^{12} {\rm M}_\odot$ , we find feasible ULDM profiles for which the central density is lower than their NFW counterparts at astrophysically accessible radii. However, comparisons to observed profiles do not strongly favour either option; both give reasonable fits to subsets of the data for some parameter choices. Consequently, we find that robust tests of the core-cusp problem in ULDM will require more comprehensive observational data and simulations that include baryonic feedback.

中文翻译：

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重新审视核心尖点问题：ULDM 与 CDM

核心-尖端问题是探索标准冷暗物质之外的暗物质模型的一个广泛引用的动机。一种这样的选择是超轻暗物质（ULDM），极轻的标量粒子在千秒差距尺度上表现出波状特性。预计天体物理上真实的 ULDM 晕由嵌入在类似 NFW 的外晕中的内孤子核心组成。孤子核心的存在表明 ULDM 可以解决与纯 NFW 晕相关的核心-尖点差异，而无需求助于重子物理。然而，已经证明 ULDM 晕圈的密度可以在某些半径和晕圈质量上超过类似的 NFW 配置，显然加剧了问题而不是解决了问题。出现这种情况的原因是，尽管孤子核的中心是平的，它们遵循反质量-半径比例关系。同时，内孤子的质量随着总晕质量的增加而增加，因此内核在较大的晕质量处变得更加峰值。我们描述了 ULDM 晕的径向密度分布的参数化，它允许核心-晕质量关系的环境变化，以便更详细地研究这个问题。对于光晕高达 $10^{12} {\rm M}_\odot$ ，我们找到了可行的 ULDM 剖面，其中心密度低于天体物理可接近半径的 NFW 对应剖面。然而，与观察到的配置文件的比较并不强烈支持这两种选择；对于某些参数选择，两者都为数据子集提供了合理的拟合。因此，我们发现对 ULDM 中核心-尖点问题的稳健测试将需要更全面的观测数据和包括重子反馈的模拟。