Search for planetary-mass ultra-compact binaries using data from the first part of the LIGO--Virgo--KAGRA fourth observing run

TL;DR

This work conducts a semi-coherent search for gravitational waves from inspiraling planetary-mass ultra-compact binaries in LIGO–Virgo–KAGRA O4a data using the Generalized frequency-Hough transform on time-frequency peakmaps, targeting chirp masses $\mathcal{M}\in[10^{-5},10^{-2}]\,M_\odot$. No detections are found, enabling model-independent constraints on the distance reach $d_{\mathrm{max,95\%}}$ and on merger-rate densities for equal-mass and asymmetric systems; the distance reach scales as $d_{\mathrm{max,95\%}} \propto \mathcal{M}^{1.24}$, consistent with a $\mathcal{M}^{5/4}$ expectation. The analysis also provides model-dependent constraints on PBHs by translating rate limits into bounds on the PBH abundance and mass-function parameters, focusing on asymmetric-mass PBHs and employing a DM-density-based galactic-rate rescaling. These results complement microlensing and prior GW sub-solar-mass searches and are attentive to eccentricity effects, offering a complementary path to probe planetary-mass PBH binaries and their role in dark matter.

Abstract

We present a search for gravitational waves from inspiraling, planetary-mass ultra-compact binaries using data from the first part of the fourth observing run of LIGO, Virgo and KAGRA. Finding no evidence of such systems, we determine the maximum distance reach for such objects and their merger rate densities, independently of how they could have formed. Then, we identify classes of primordial black-hole mass distributions for which these rate limits can be translated into relevant constraints on the mass distribution of primordial black holes, assuming that they compose all of dark matter, in the mass range $[10^{-6},10^{-3}]M_\odot$. Our constraints are consistent with existing microlensing results in the planetary-mass range, and provide a complementary probe to sub-solar mass objects.

Figures (8)

• Figure 1: Model-independent distance reach constraints for equal-mass inspiraling compact objects. We show the distance reach at which 95% of signals would be recovered for equal-mass systems. The green shaded region denotes one standard deviation uncertainty on the distance reach, while the gray-shaded region indicates excluded distances. These constraints follow the expected power-law of $d_{\text{max,95\%}}\propto \mathcal{M}^{5/4}$.
• Figure 2: Model-independent constraints on rate density at the 90% confidence-level for equal-mass (left) and asymmetric mass-ratio inspiraling compact objects (right). These constraints are derived following the procedure outlined in \ref{['subsec:comp-lim-rate']}, and obey the expected power law of $\mathcal{R}\propto\mathcal{M}^{-15/4}$.
• Figure 3: Model-dependent constraints on asymmetric mass-ratio inspiraling PBHs. We interpret the rate densities in \ref{['fig:asymm-rate']} as arising from PBHs, and constrain the effective parameter $\tilde{f}$ as a function of asymmetric mass-ratio PBHs using \ref{['eqn:rate_asymm']}. We restrict the plot only to masses for which $\tilde{f}<1$, and note that we were unable to constrain $\tilde{f}<1$ for equal-mass systems.
• Figure 4: Constraints on PBHs from this search, in red, and other GW and electromagnetic analyses. Our limits on the mass function $f(m_2)$ (shorthand for $f(\ln m_2)$) are valid for mass distributions respecting the conditions mentioned in the text for asymmetric mass ratio binaries, assuming $f_\text{PBH}=1$. No curve is shown for equal-mass systems, as $\tilde{f} < 1$ is not constrained. We assume $f(\ln m_1)\Delta\ln m_1\sim 1$ and use the corresponding values of $\tilde{f}$ in \ref{['fig:model-dep-constraints']} at $m_1=2.5\,M_\odot\xspace$ to obtain the red line on this plot. We emphasize that these constraints are valid only for the classes of mass functions discussed in \ref{['subsec:robust']}. If one wishes to produce our constraints for different choices of $f_\text{PBH}$, the red curve will be scaled upwards by $f_\text{PBH}^{-53/37}$. Constraints from other probes (microlensing and GWs) are also presented for comparison on $f_\text{PBH}$, and are implicitly valid for monochromatic mass functions and subject to astrophysical uncertainties. Purple curves correspond to constraints from previous GW searches Kavanagh:2018ggoLIGOScientific:2019kanLIGOScientific:2021jobLVK:2022ydqNitz:2022ltlWang:2023qgwBoybeyi:2024mhpLIGOScientific:2025kry, while dashed blue curves indicate microlensing constraints EROS-2:2006ryyCroon:2020oukMroz:2024wiaMroz:2024mse that could weaken significantly due to PBH clustering Gorton:2022fybGreen:2025dut. Our constraints on the mass function in red should be referenced to the red left $y-$axis, while all other constraints are directly on $f_\text{PBH}$ and should be referenced to the right $y-$axis.
• Figure 5: Comparison of upper limits on distance reach calculated through injections and with the formula given in \ref{['eqn:dmax']}. The blue line indicates the theoretical expectation for the distance reach at 95% confidence, adjusted by the source-specific factor $\mathcal{C}$ (see text for details). The shaded region denotes the $\pm1\sigma$ uncertainty on the distance reach based on the range of source-specific $\mathcal{C}_s$ values. The magenta points indicate the derived distance reach at which 95% of injections are recovered in our simulations. The green line indicates the upper limit that we would actually quote based on the Feldman-Cousins procedure. Our results show that the injection studies agree well with the theoretical blue and green curves and fall well within the shaded region. For each set of fifty injections, at each chirp mass, performed at different distance reaches to derive these results, we analyze different frequency bands and different times across the O4a dataset.