Burst-with-memory events are potential transient gravitational wave (GW) sources for the maturing pulsar timing array (PTA) efforts. We provide a computationally efficient prescription to model pulsar timing residuals induced by supermassive black hole pairs in general relativistic hyperbolic trajectories employing a Keplerian-type parametric solution. Injection studies have been pursued on the resulting bursts with linear GW memory (LGWM) events with simulated datasets to test the performance of our pipeline, followed by its application to the publicly available NANOGrav 12.5-year (NG12.5) dataset. Given the absence of any evidence of LGWM events within the real NG12.5 dataset, we impose 95% upper limits on the PTA signal amplitude as a function of the sky location of the source and certain characteristic frequency ($n$) of the signal. The upper limits are computed using a signal model that takes into account the presence of intrinsic timing noise specific to each pulsar, as well as a common, spatially uncorrelated red noise, alongside the LGWM signal. Our investigations reveal that the 95% upper limits on LGWM amplitude, marginalized over all other parameters, is $3.48\pm 0.51\mathrm{\mu }\mathrm{s}$ for $n>3.16\mathrm{nHz}$. This effort should be relevant for constraining both burst and memory events in the upcoming International Pulsar Timing Array data releases.

中文翻译：

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从双曲黑洞相遇中搜索线性引力波记忆的有效方法及其在 NANOGrav 12.5 年数据集中的应用

记忆爆发事件是成熟脉冲星计时阵列（PTA）工作的潜在瞬态引力波（GW）源。我们提供了一种计算有效的方法，使用开普勒型参数解对一般相对论双曲轨迹中超大质量黑洞对引起的脉冲星计时残差进行建模。我们利用模拟数据集对线性 GW 内存 (LGWM) 事件产生的突发进行了注入研究，以测试我们的管道的性能，然后将其应用于公开的 NANOGrav 12.5 年 (NG12.5) 数据集。鉴于真实 NG12.5 数据集中没有任何 LGWM 事件的证据，我们对 PTA 信号幅度施加 95% 的上限，作为源的天空位置和某些特征频率的函数（$n$）的信号。上限是使用信号模型计算的，该模型考虑了每个脉冲星特有的固有定时噪声的存在，以及常见的、空间不相关的红噪声以及 LGWM 信号。我们的调查表明，LGWM 幅度的 95% 上限（相对于所有其他参数而言被边缘化）为$3.48\pm 0.51\mathrm{\mu }\mathrm{s}$为了$n>3.16\mathrm{赫兹}$。这项工作应该与即将发布的国际脉冲星定时阵列数据发布中的突发事件和内存事件相关。