Reaching diffraction-limited localization with coherent PTAs
用相干脉冲星计时阵列实现衍射极限定位
Current pulsar timing array (PTA) analyses are phase incoherent and thus to not take full advantage of pulsar distance information, thereby missing out on improved angular resolution and on a potential factor-of-two gain in detection sensitivity for individual gravitational-wave (GW) sources. In this work, we investigate the impact of precise pulsar distance measurements on angular resolution as an extension to previous work measuring the angular resolution of a dense isotropic PTA [D. L. Jow , How many pixels are there in a polarized pulsar timing array map?, Phys. Rev. D 113, 043034 (2026)PRVDAQ2470-001010.1103/zvb6-7ggb]. We present a coherent map-making technique that utilizes precise pulsar distance measurements to reach a diffraction-limited resolution of an individual source: <inline-formula><mml:math><mml:mi>δ</mml:mi><mml:msub><mml:mi>θ</mml:mi><mml:mrow><mml:mi>diff</mml:mi></mml:mrow></mml:msub><mml:mo>×</mml:mo><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>SNR</mml:mi><mml:mo>)</mml:mo><mml:mo>≍</mml:mo><mml:mn>1</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>arcmin</mml:mi></mml:math></inline-formula>, where <inline-formula><mml:math><mml:mi>δ</mml:mi><mml:msub><mml:mi>θ</mml:mi><mml:mrow><mml:mi>diff</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>λ</mml:mi><mml:mi>GW</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>r</mml:mi></mml:math></inline-formula> is the diffractive angle and SNR refers to the detection strength of the source. With this level of angular resolution, identifying an electromagnetic counterpart may become feasible, enabling multimessenger follow-up. We show that for SNR = 10, which may be the current sensitivity level using a coherent analysis, the diffraction limit is reached with approximately ten equidistant pulsars with distances of about 300 parsecs. Moreover, angular resolution scales sharply with the number of known pulsar distances as <inline-formula><mml:math><mml:mo>∼</mml:mo><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>SNR</mml:mi><mml:msup><mml:mo>)</mml:mo><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>dist</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. Thus, each additional pulsar with high signal-to-noise timing and precise distance measurement can improve PTA resolution by an order of magnitude. The distance to the best-timed millisecond pulsar (PSR <inline-formula><mml:math><mml:mi>J</mml:mi><mml:mn>0437</mml:mn><mml:mo>-</mml:mo><mml:mn>4715</mml:mn></mml:math></inline-formula>) is already constrained to sub-parsec levels. We argue, therefore, that a coherent analysis of PTA data, fully incorporating pulsar distance information, is timely.
展开 ▾展示相干分析可将单个引力波源定位到约1角分,每增加一个精确距离测量可提升近一个数量级的分辨率,且已有脉冲星达到亚秒差距精度,方法具有现实可行性。
既往PTA分析常将背景视为各向同性随机信号,未充分利用脉冲星距离信息。近期,Jow+ 2025提出利用地球项进行匹配滤波成图,但分辨率受限。本文进一步引入脉冲星项,首次实现相干匹配滤波成图,达到Boyle+ 2012提出的衍射极限角分辨率(~1角分),有望实现多信使证认。随着脉冲星距离测量技术进步(如VLBI、闪烁干涉),更多脉冲星将具备亚秒差距精度,相干PTA分析将成为解析纳米赫兹引力波天空、区分天体物理与宇宙学起源的关键工具。
预印本 2025-12-11 · 刊出 2026-07-09 · 收录 2026-07-22