发表机构
Argelander-Institut für Astronomie, Universität Bonn（波恩大学阿根德天体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于广义帕累托分布的极值统计方法，从P(D)尾部提取亚毫米星系计数斜率及其透镜调制，在Planck和SPIRE数据上验证，并首次在P(D)尾部探测到透镜效应。
AI 中文摘要
混淆极限以下的亚毫米星系计数形状是宇宙恒星形成的关键记录，但只能通过地图表面亮度的一维分布P(D)进行统计访问。经典的P(D)分析将计数压缩为通量积分约束，并需要完整的仪器前向模型。我们引入了对混淆P(D)尾部的极值理论分析：峰值超过阈值形式，其中超过阈值u的超出量遵循广义帕累托分布（GPD）。GPD形状参数ξ(u)是计数局部对数斜率的通量分辨、归一化无关的读数，其引力透镜调制Δξ(u)探测计数的局部曲率。我们推导了两者的解析关系，用端到端模拟验证，并将该方法应用于Planck 857 GHz地图和GAMA-09的Herschel/SPIRE 350 μm地图。在Planck的5角分分辨率下，尾部反映明亮、成团的天空而非暗弱计数，尽管背景单独排除了单幂律计数模型。在SPIRE分辨率下，ξ随阈值显著上升，与强透镜明亮族群一致（首次在P(D)尾部探测到透镜效应），且明亮掩蔽地图支持Schechter模型。在星系团后方，我们设置了Δξ(u)的首个校准上限。CCAT/FYST应能直接区分计数模型，但星系团透镜探测需要的10^15太阳质量团数量超过天空所含。因此，GPD尾部统计量在阈值通量量级、低于探测极限处区分计数的函数形式，对地图均值、增益和计数归一化不变，且对成团稳健；透镜为计数特征提供校准标尺，其探测有待对巨质量团的深、高分辨率巡天。
英文摘要
The shape of the submillimeter galaxy number counts below the confusion limit is a key record of cosmic star formation but is accessible only statistically, through the one-point distribution of map surface brightness, $P(D)$. Classical $P(D)$ analysis compresses the counts into flux-integrated constraints and requires a full instrument forward model. We introduce an extreme-value-theory analysis of the confusion $P(D)$ tail: the peaks-over-threshold formalism, in which exceedances above a threshold $u$ follow a generalized Pareto distribution (GPD). The GPD shape parameter $ξ(u)$ is a flux-resolved, normalization-free readout of the local logarithmic slope of the counts, and its gravitational-lensing modulation $Δξ(u)$ probes their local curvature. We derive analytic relations for both, validate them with end-to-end simulations, and apply the method to Planck 857 GHz maps and the Herschel/SPIRE 350 $μ$m map of GAMA-09. At Planck's 5' resolution the tail reflects the bright, clustered sky rather than the faint counts, though the background alone excludes the single power-law count model. At SPIRE resolution $ξ$ rises markedly with threshold, consistent with the strongly lensed bright population (a first detection of lensing in a $P(D)$ tail), and the bright-masked map favors the Schechter model. Behind galaxy clusters we set the first calibrated upper limits on $Δξ(u)$. CCAT/FYST should separate the count models directly, but a cluster-lensing detection needs more $10^{15}\,M_\odot$ clusters than the sky contains. The GPD tail statistic thus discriminates the functional form of the counts at fluxes of order the threshold, below the detection limit, invariant to map mean, gain and count normalization, and robust to clustering; lensing supplies a calibrated ruler for count features, whose detection awaits deep, high-resolution surveys of massive clusters.
Comments33 pages, 16 figures. Version submitted to A&A: revised Herschel forward model (App. D.5) and text revisions, conclusions unchanged. Code at https://github.com/kmbasu/GPD-Analysis-of-CIB
