Beyond Plane Waves: Coherent Network Response to Collimated Gravitational-Wave Wavepackets

Author(s)

Campos, S.D.

Abstract

We present a paraxial wavepacket model for collimated gravitational-wave bursts and derive the coherent response of detector networks to these structured signals. For current LIGO-Virgo baselines, analytic mismatch estimates and overlaps show that PWM waveforms are effectively indistinguishable from standard sine-Gaussian bursts, validating the plane-wave approximation. We then identify a regime relevant to third-generation networks in which finite transverse structure produces non-negligible geometric phase shifts. A toy event-level Monte Carlo compares a standard burst-search ranking with a paraxial wavepacket model-constrained statistic that penalizes geometric inconsistencies across detectors; in this controlled setup, the PWM prior yields a factor of $\sim3$-$4$ gain in detection efficiency at a fixed false-alarm rate, while maintaining performance on plane-wave-like signals.

Figures

Strain in a single detector for a highly collimated GW (solid) and a reference sine-Gaussian burst (dotted), both with carrier frequency $f_0 = 100~\mathrm{Hz}$ and temporal width $\sigma_t = 5~\mathrm{ms}$. With a phase offset $\Delta\phi = 0.05$~rad, the single-detector overlap is $\mathcal{O}_I \simeq 0.9988$. The near coincidence of the curves shows that, in the plane-wave limit, the PWM is effectively indistinguishable from a suitably chosen elliptically polarized sine-Gaussian for a single detector.
Caption Strain in a single detector for a highly collimated GW (solid) and a reference sine-Gaussian burst (dotted), both with carrier frequency $f_0 = 100~\mathrm{Hz}$ and temporal width $\sigma_t = 5~\mathrm{ms}$. With a phase offset $\Delta\phi = 0.05$~rad, the single-detector overlap is $\mathcal{O}_I \simeq 0.9988$. The near coincidence of the curves shows that, in the plane-wave limit, the PWM is effectively indistinguishable from a suitably chosen elliptically polarized sine-Gaussian for a single detector.
Strain in two interferometric detectors from the same collimated Gaussian GW packet. Left: realistic case with beam width $w = 10^9\,\mathrm{m}$ and transverse separation $|\Delta x_\perp| = 3\times 10^6\,\mathrm{m}$, giving $A_2/A_1 \simeq 0.999995$ so the traces are nearly identical. Right: illustrative case with $w = 5\times 10^6\,\mathrm{m}$ and the same separation, giving a clearly different response with $A_2/A_1 \simeq 0.84$.
Caption Strain in two interferometric detectors from the same collimated Gaussian GW packet. Left: realistic case with beam width $w = 10^9\,\mathrm{m}$ and transverse separation $|\Delta x_\perp| = 3\times 10^6\,\mathrm{m}$, giving $A_2/A_1 \simeq 0.999995$ so the traces are nearly identical. Right: illustrative case with $w = 5\times 10^6\,\mathrm{m}$ and the same separation, giving a clearly different response with $A_2/A_1 \simeq 0.84$.
Strain in two interferometric detectors from the same collimated Gaussian GW packet. Left: realistic case with beam width $w = 10^9\,\mathrm{m}$ and transverse separation $|\Delta x_\perp| = 3\times 10^6\,\mathrm{m}$, giving $A_2/A_1 \simeq 0.999995$ so the traces are nearly identical. Right: illustrative case with $w = 5\times 10^6\,\mathrm{m}$ and the same separation, giving a clearly different response with $A_2/A_1 \simeq 0.84$.
Caption Strain in two interferometric detectors from the same collimated Gaussian GW packet. Left: realistic case with beam width $w = 10^9\,\mathrm{m}$ and transverse separation $|\Delta x_\perp| = 3\times 10^6\,\mathrm{m}$, giving $A_2/A_1 \simeq 0.999995$ so the traces are nearly identical. Right: illustrative case with $w = 5\times 10^6\,\mathrm{m}$ and the same separation, giving a clearly different response with $A_2/A_1 \simeq 0.84$.
Wave–plane breakdown horizon versus network baseline $B$ and GW frequency $f$. Contours show the analytical mismatch ($1 - \mathcal{O}$) between a structured PWM and an SBS template. The red circle indicates the current terrestrial baseline regime (LIGO–Virgo), where SBS templates remain highly accurate. The orange cross indicates the future 3G regime, in which longer baselines and higher sensitivity enter the PWM, requiring structured templates to avoid systematic parameter biases.
Caption Wave–plane breakdown horizon versus network baseline $B$ and GW frequency $f$. Contours show the analytical mismatch ($1 - \mathcal{O}$) between a structured PWM and an SBS template. The red circle indicates the current terrestrial baseline regime (LIGO–Virgo), where SBS templates remain highly accurate. The orange cross indicates the future 3G regime, in which longer baselines and higher sensitivity enter the PWM, requiring structured templates to avoid systematic parameter biases.
Distributions of $\chi^2_{\rm geom}$ for the three toy-MC background classes: incoherent, semi-coherent, and coherent-like glitches. Incoherent glitches occupy the highest $\chi^2_{\rm geom}$ values, semi-coherent glitches lie at intermediate values, and coherent-like glitches form a lower-$\chi^2$ tail that partially overlaps the signal region.
Caption Distributions of $\chi^2_{\rm geom}$ for the three toy-MC background classes: incoherent, semi-coherent, and coherent-like glitches. Incoherent glitches occupy the highest $\chi^2_{\rm geom}$ values, semi-coherent glitches lie at intermediate values, and coherent-like glitches form a lower-$\chi^2$ tail that partially overlaps the signal region.
Toy-MC comparison between the SBS ranking statistic and the PWM-constrained statistic. Left: probability density functions of the background ranking statistics for SBS (black) and PWM (blue). Right: detection efficiency as a function of matched FAR for the same experiment. Solid curves show efficiencies for the full signal population, dashed curves for the paraxial-like subpopulation. For thresholds chosen to match the FAR of the corresponding SBS background distribution, the PWM statistic recovers a factor of $\sim 3$--$4$ more signals at FAR levels between $10^{-2}$ and $10^{-4}$ in this controlled toy-MC, while the efficiencies for the paraxial-like subpopulation remain very similar for the two rankings.
Caption Toy-MC comparison between the SBS ranking statistic and the PWM-constrained statistic. Left: probability density functions of the background ranking statistics for SBS (black) and PWM (blue). Right: detection efficiency as a function of matched FAR for the same experiment. Solid curves show efficiencies for the full signal population, dashed curves for the paraxial-like subpopulation. For thresholds chosen to match the FAR of the corresponding SBS background distribution, the PWM statistic recovers a factor of $\sim 3$--$4$ more signals at FAR levels between $10^{-2}$ and $10^{-4}$ in this controlled toy-MC, while the efficiencies for the paraxial-like subpopulation remain very similar for the two rankings.
ROC curves for the SBS and PWM ranking statistics from the toy-MC study are shown for both the full combined signal population and the paraxial-like subsample. Over a broad range of FPR values, the PWM curves systematically lie above the SBS curves, indicating superior discrimination and ranking performance.
Caption ROC curves for the SBS and PWM ranking statistics from the toy-MC study are shown for both the full combined signal population and the paraxial-like subsample. Over a broad range of FPR values, the PWM curves systematically lie above the SBS curves, indicating superior discrimination and ranking performance.
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