发表机构
ASTRON, Netherlands Institute for Radio Astronomy; SETI Institute; University of Durham; University of Amsterdam; University of Wisconsin-Milwaukee; University of North Carolina; Newcastle University; NASA Goddard Space Flight Center（荷兰射电天文研究所（ASTRON）; 搜寻地外文明研究所; 杜伦大学; 阿姆斯特丹大学; 威斯康星大学密尔沃基分校; 北卡罗来纳大学; 纽卡斯尔大学; 美国国家航空航天局戈达德太空飞行中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对脉冲星计时中轮廓演化延迟的建模问题，本文提出勒让德多项式展开（LIFD）替代传统FD模型，在模拟数据上减少85%残差偏移，并降低色散量估计偏差，支持其用于纳赫兹引力波探测。
AI 中文摘要
射电脉冲星表现出脉冲轮廓形状随频率变化的特性，这些变化在观测频带内引入了观测脉冲到达时间（TOA）的系统性延迟。北美纳赫兹引力波天文台（NANOGrav）使用频率相关（FD）的对数多项式函数对这些延迟进行建模，其系数通过对不同射电频率的TOA测量进行拟合得到。然而，FD参数容易吸收来自其他色散效应（如星际色散）的功率，导致拟合的FD值高估轮廓演化，并在不同数据集间显著变化。为了分离这些效应，我们引入了两种新的轮廓演化的数学表述：单项式展开（IFD）和勒让德多项式展开（LIFD）。我们在NANOGrav 15年数据集中11颗脉冲星的观测数据以及模拟数据上测试了这些模型，并将其性能与频率分辨脉冲模板进行了比较。我们发现，基于勒让德的模型通常预测的计时延迟更接近真实的轮廓演化，对于模拟数据，相对于FD的残差偏移最多减少了85%。此外，我们发现轮廓演化模型的选择可能使拟合的色散模型产生偏差，基于FD的模型将注入的色散量（DM）高估了0.013 pc cm^-3，而LIFD则为0.0002 pc cm^-3。这些结果支持使用勒让德基来减轻色散效应之间的协方差，直接有利于针对这些效应的计时研究以及为纳赫兹引力波探测开发先进的噪声建模技术。
英文摘要
Radio pulsars exhibit frequency-dependent variations in the shape of their pulse profiles that introduce systematic delays in the observed pulse times of arrival (TOA) across an observing band. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) models these delays using a frequency-dependent (FD) log-polynomial function whose coefficients are fit to TOA measurements at different radio frequencies. However, FD parameters are prone to absorbing power from other chromatic effects, such as interstellar dispersion, leading to fitted FD values that overestimate profile evolution and vary significantly across datasets. To separate these effects, we introduce two new mathematical formulations of profile evolution: a monomial expansion (IFD) and a Legendre polynomial expansion (LIFD). We test these models on observations of 11 pulsars in the NANOGrav 15-year dataset and on simulated data, and also compare their performance to that of frequency-resolved pulse templates. We find that Legendre-based models generally predict timing delays that more closely replicate the true profile evolution, reducing the residual offset relative to FD by as much as 85% for the simulated data. Additionally, we find that the choice of profile evolution model can bias the fitted dispersion model, with FD-based models overestimating the injected DM by 0.013 pc cm^-3 compared to 0.0002 pc cm^-3 for LIFD. These results support the use of Legendre bases to mitigate covariances between chromatic effects, directly benefiting targeted timing studies of these effects and the development of advanced noise-modeling techniques for nanohertz gravitational-wave detection.
CommentsSubmmited to The Astrophysical Journal on October 7th
