AI 中文总结
本研究提出反基本平面IMBH质量估计的有效性判据，发现低爱丁顿比不足以保证有效性，并应用于NGC 4395等系统，定义了SKA/ngVLA时代射电核心的可转换性。
AI 中文摘要
射电/X射线/黑洞质量基本平面（FP）被广泛用于估计吸积中等质量黑洞（IMBH）候选体的质量。仅当射电光度追踪致密喷流核心且X射线来自同一亚爱丁顿硬态吸积流时，其反演使用才合理。我们利用已验证的黑洞X射线双星射电/X射线轨迹作为经验参考，制定了反FP质量的有效性判据。基于21个BHXB及候选体的424次探测，我们发现标准轨迹和弯曲轨迹均存在，且射电/X射线行为发生变化的亮度因源而异。因此，低X射线爱丁顿比本身不足以确立反FP有效性。在标度不变的喷流/热流框架内，轨迹变陡降低了反演的有效质量杠杆，而在更低的吸积率下，主导发射机制和致密核心产生的不确定性可能完全使FP基本假设失效。我们将该判据应用于代表性的IMBH相关系统，而未拟合新平面。NGC 4395为低爱丁顿比但致密射电缺乏：其VLA尺度和VLBI喷流基座光度意味着，若将这种缺乏误读为质量信号，则正式反FP质量被低估约1.0和超过2.8个数量级。NGC 1399和NGC 4472中的球状星团X射线源受源身份限制：71%和67%低于$L_{\rm Edd}(10\\,M_\odot)$，仅高光度尾部不能识别IMBH吸积体。$\omega$ Centauri IMBH候选体的射电未探测约束了气体供应、吸积效率和致密核心产生，而非排除黑洞。由此产生的测试定义了SKA/ngVLA时代哪些射电核心可转换为FP质量，哪些则约束气体供应、源身份或致密核心产生。
英文摘要
The radio/X-ray/black-hole-mass Fundamental Plane (FP) is widely used to estimate masses of accreting intermediate-mass black hole (IMBH) candidates. Its inverse use is justified only when radio luminosity traces a compact jet core and X-rays arise from the same sub-Eddington hard-state accretion flow. We formulate an accretion-state validity criterion for inverse-FP masses using verified BH X-ray binary radio/X-ray tracks as the empirical reference. Using 424 detections from 21 BHXBs and candidates, we find that both standard and curved tracks are present and the luminosity at which radio/X-ray behavior changes is source dependent. A low X-ray Eddington ratio is therefore not, by itself, sufficient to establish inverse-FP validity. Within a scale-invariant jet/hot-flow framework, track steepening reduces the effective mass leverage of the inversion, while at much lower accretion rates uncertainties in the dominant emission mechanism and compact-core production can invalidate the underlying FP assumptions altogether. We apply the criterion to representative IMBH-relevant systems without fitting a new plane. NGC 4395 is low-Eddington but compact-radio deficient: its VLA-scale and VLBI jet-base luminosities imply formal inverse-FP mass underestimates of about 1.0 and more than 2.8 dex if the deficit is misread as a mass signal. Globular-cluster X-ray populations in NGC 1399 and NGC 4472 are source-identity limited: 71% and 67% lie below $L_{\rm Edd}(10\,M_\odot)$, and the high-luminosity tail alone does not identify an IMBH accretor. The radio non-detection of the $ω$ Centauri IMBH candidate constrains gas supply, accretion efficiency, and compact-core production rather than excluding the black hole. The resulting test defines which SKA/ngVLA-era radio cores can be converted into FP masses, and which instead constrain gas supply, source identity, or compact-core production.
Comments15 pages, 6 figures, Under review in The Astrophysical Journal. Comments are welcome
