无穷脉冲极限下观测红移与脉冲星计时调制的精确等价性
Exact Equivalence of the Observed Redshift and the Pulsar Timing Modulation in the Infinitesimal-Pulse Limit
AI总结：
本文研究脉冲星计时调制与观测红移的等价性，推导了无穷脉冲极限下两者完全相等的结论，还给出有限发射间隔下两者的精确关系，明确差异由发射间隔与观测红移变化特征时标的比值控制。
AI中文摘要：
脉冲星计时阵列（PTA）收集毫秒脉冲星射电信号的到达时间，引力波可调制这些到达时间。尽管PTA的可观测量涉及沿不同光程传播的连续射电脉冲，其在扰动线性阶下的标准理论描述与描述单条测地线上光子频率分数变化的观测红移的Sachs-Wolfe公式等价。这种等价性在线性阶下已为人熟知，但PTA文献中尚未系统探讨其在一阶之外的有效性。本文表明，在连续发射事件之间原时间隔趋于零的极限下，计时调制与观测红移完全相等，无需展开时空几何。对于有限发射间隔，本文推导了计时调制与观测红移之间的精确关系，并表明两者的差异由发射间隔与观测红移变化的特征时标之比控制。
英文摘要：
The pulsar timing arrays (PTA) collect the times of arrival of radio signals from the millisecond pulsars, and gravitational waves can modulate their arrival times. Although the PTA observable involves successive radio pulses propagating along different light paths, its standard theoretical description at linear order in perturbations is equivalent to the Sachs-Wolfe formula for the observed redshift, which describes the fractional change in photon frequency along a single geodesic. While this equivalence is well known at linear order, its validity beyond first order has not been systematically addressed in the PTA literature. Here we show that, in the limit of vanishing proper-time separation between successive emission events, the timing modulation is exactly equal to the observed redshift, without expanding the spacetime geometry. For a finite emission interval, we derive the exact relation between the timing modulation and the observed redshift, and show that their difference is controlled by the ratio between the emission interval and the characteristic timescale over which the observed redshift varies.
