无挠Palatini时空中剪切模的脉冲星计时响应与空间关联
Pulsar Timing Response and Spatial Correlations of Shear Modes in Torsionless Palatini Spacetime
- Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究无挠Palatini时空中剪切模的脉冲星计时响应，推导出短波长极限下归一化重叠缩减函数呈纯偶极形式cosζ，并指出其与太阳系历表误差的空间简并性。
AI中文摘要：
在纳赫兹频段，脉冲星计时残差之间的空间关联为表征随机引力波背景及其偏振内容提供了关键观测量。在无挠Palatini时空（一种将度规与联络视为独立变量的引力理论框架）中，非度规性可以产生两个额外的剪切模，分别称为剪切-x模和剪切-y模。本文研究了由发射脉冲星和接收地球的剪切诱导运动所产生的脉冲星计时响应。假设电磁场与物理度规最小耦合，且地球和脉冲星具有不可忽略的有效超动量（hypermomentum）响应，我们推导了单脉冲星红移、频域两点关联函数以及相应的空间关联。对于平稳且各向同性的随机剪切背景，在短波长极限下，不同脉冲星之间的归一化重叠缩减函数（ORF）退化为纯偶极形式Γ_ab^sh(ζ)=cosζ，其中ζ为两颗脉冲星之间的角间距。相同的偶极关联也可由各向同性的太阳系历表误差产生，导致两种信号之间存在空间简并。这种简并凸显了除角关联之外的信息对于在脉冲星计时阵列（PTA）数据中识别Palatini剪切特征的重要性。
英文摘要：
In the nanohertz band, spatial correlations between pulsar timing residuals provide a key observable for characterizing stochastic gravitational-wave backgrounds and probing their polarization content. In torsionless Palatini spacetime, nonmetricity can generate two additional shear modes, referred to as the shear-$x$ and shear-$y$ modes. In this work, we investigate the pulsar timing response produced by the shear-induced motions of the emitting pulsar and the receiving Earth. Assuming that the electromagnetic field is minimally coupled to the physical metric and that the Earth and pulsar possess non-negligible effective hypermomentum responses, we derive the single-pulsar redshift, the frequency-domain two-point correlation function, and the corresponding spatial correlation. For a stationary and isotropic stochastic shear background, the normalized overlap reduction function (ORF) for distinct pulsars reduces in the short-wavelength limit to the pure dipolar form $Γ_{ab}^{\mathrm{sh}}(ζ)=\cosζ$, where $ζ$ is the angular separation between the two pulsars. The same dipolar correlation can also be produced by isotropic Solar System ephemeris errors, leading to a spatial degeneracy between the two signals. This degeneracy highlights the importance of information beyond the angular correlation for identifying Palatini shear signatures in PTA data.
