GFH-v2 Pipeline for Searches of Long-Transient Gravitational Waves from Newborn Magnetars

TL;DR

GFH-v2 provides an improved, astrophysically informed semi-coherent search framework for long-transient gravitational waves from newborn magnetars by reformulating the spin-down evolution with a power-law model ($f_{\rm gw}(t)$) into a linear GFH space via $x=1/f^{n-1}$, enabling efficient clustering of signal tracks. It introduces substantial methodological and computational upgrades over the original GFH, including optimized parameter-space constraints, adaptive coherence/observation times, and a GPU-friendly implementation that increases speed by up to an order of magnitude. Theoretical sensitivity analyses are complemented by empirical injections into real O4a data, showing overall agreement with predictions and highlighting frequency-dependent deviations due to instrumental features. The results demonstrate GFH-v2 as a robust, scalable directed-search tool for current and future GW runs, with potential extensions to broader magnetar spin-down models and hybrid ML-assisted pipelines for long-duration GW astronomy.

Abstract

This paper presents an enhanced methodology for searching long transient gravitational waves associated with a newborn magnetar using a strongly improved version of the generalized Frequency Hough Transform algorithm, called GFH-v2. We describe the main developments introduced relative to the original implementation and outline the optimized parameter-space selection used in the search. We then compute the theoretical sensitivity of the method and compare it with an empirical sensitivity estimate obtained by injecting simulated signals into LIGO-Virgo-KAGRA O4a data. The updated framework achieves improved sensitivity and computational performance. These results provide a robust basis for future directed searches for long-transient gravitational-wave signals from core-collapse supernovae and other transient events in current and upcoming observing runs.

Figures (11)

• Figure 1: Gravitational wave signal strain amplitude as a function of initial spin frequency $f_{\rm gw}(t=0)\equiv f_0$ and ellipticity $\epsilon$. We have fixed the source distance to be 1 Mpc for illustration purposes.
• Figure 2: Workflow of the GFH transform. Top left: Raw strain data with injected signals. Top right: Original time–frequency peakmap. Bottom left: Coordinate-transformed peakmap, where signal trajectories become linear. Bottom right: Resulting Hough map, corresponding to 5 simulated signals injected in O4a LIGO Livingston data with $f_0 = 900$–$1000$ Hz, $\epsilon = (2.5$–$3)\times10^{-3}$, at a distance of 0.1 Mpc and sky location of SN2023ixf.
• Figure 3: Left: FFT duration $T_{\rm FFT}$ versus $f_0$ for different ellipticities. Right: Definition of the observation time $T_{\rm obs}$ from the decay of the signal amplitude for a fixed reduction factor $\alpha_{\rm h}$ shown for $\epsilon = 0.002$ and $f_0 = 900$ Hz.
• Figure 4: Left: Sensitivity $h_{\rm 0,min}$ as a function of $\alpha_{\rm h}$ for different initial frequencies $f_0$ and fixed ellipticity $\epsilon = 0.001$. Right: Dependence of $h_{\rm 0,min}$ on $\alpha_{\rm h}$ for different ellipticities $\epsilon$ at a representative $f_0= 1000 Hz$.
• Figure 5: Observation time $T_{\rm obs}$ as a function of $f_0$ for different ellipticities, corresponding to the optimal $\alpha_{\rm h}$ derived from Fig. \ref{['fig:Alpha']}.