Detectability of continuous gravitational waves from planetary-mass companions orbiting compact stars

Abdusattar Kurban; Ali Esamdin; Jianping Yuan; Na Wang; Rai Yuen; Wenming Yan; Xia Zhou; Yong-Feng Huang; Yu-Bin Wang; Zhigang Wen

arxiv: 2604.05425 · v1 · submitted 2026-04-07 · 🌌 astro-ph.HE

Detectability of continuous gravitational waves from planetary-mass companions orbiting compact stars

Abdusattar Kurban , Xia Zhou , Na Wang , Yong-Feng Huang , Wenming Yan , Jianping Yuan , Ali Esamdin , Yu-Bin Wang

show 2 more authors

Zhigang Wen Rai Yuen

This is my paper

Pith reviewed 2026-05-10 20:11 UTC · model grok-4.3

classification 🌌 astro-ph.HE

keywords continuous gravitational wavesplanetary-mass companionswhite dwarfspulsarsultrashort-period binariesspace-based detectorssignal-to-noise ratioDECIGO

0 comments

The pith

Fourteen known ultrashort binaries with planetary companions generate continuous gravitational waves strong enough for future detectors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calculates the continuous gravitational wave signals from planetary-mass companions orbiting pulsars and white dwarfs whose masses, distances, and orbital periods have already been measured. It compares the predicted strain amplitudes and frequencies to the noise curves of space-based detectors. Fourteen systems reach a signal-to-noise ratio of at least five after four years of observation, including three with pulsar primaries and eleven with white-dwarf primaries. These signals lie below the sensitivity of near-term missions such as LISA but fall inside the reach of more advanced future observatories such as DECIGO and BBO. The authors conclude that such detections would permit joint gravitational-wave and electromagnetic studies of the formation and evolution of these companions.

Core claim

Planetary-mass companions in ultrashort-period orbits around compact stars produce continuous gravitational waves whose amplitudes and frequencies are obtained from the standard quadrupole formula applied to the systems' measured orbital periods, component masses, and distances. For fourteen specific systems the resulting signals yield signal-to-noise ratios of at least five within four years of observation. Three of these systems have pulsar primaries and eleven have white-dwarf primaries. The signals remain undetectable by LISA, TianQin, or Taiji but enter the sensitivity band of DECIGO and BBO.

What carries the argument

The quadrupole gravitational-wave strain amplitude and frequency computed directly from the orbital motion of each planetary-mass companion around its measured compact primary.

If this is right

Three pulsar systems and eleven white-dwarf systems qualify as detectable candidates under the quadrupole approximation.
Detection would open the possibility of joint gravitational-wave and electromagnetic surveys of ultrashort-period planetary companions.
The signals require the sensitivity of future decahertz-scale interferometers rather than near-term missions.
The same parameter set that produces the gravitational-wave prediction also fixes the electromagnetic observables of the systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

A confirmed detection would supply an independent measurement of the orbital period through the gravitational-wave frequency.
Non-detection by DECIGO or BBO could tighten constraints on the masses or distances of these particular systems.
The same approach could be extended to other known ultracompact binaries whose parameters were not included in the present sample.

Load-bearing premise

The masses, orbital periods, and distances of the listed binary systems are known accurately enough that the derived gravitational-wave amplitudes and frequencies are reliable.

What would settle it

A measured gravitational-wave strain upper limit or detection from any one of the fourteen systems that differs from the calculated amplitude by an amount exceeding the combined uncertainties in the input orbital period, masses, and distance.

Figures

Figures reproduced from arXiv: 2604.05425 by Abdusattar Kurban, Ali Esamdin, Jianping Yuan, Na Wang, Rai Yuen, Wenming Yan, Xia Zhou, Yong-Feng Huang, Yu-Bin Wang, Zhigang Wen.

**Figure 1.** Figure 1: Comparison of the characteristic strain of our sample with p fgwS n(fgw) for Tobs = 4 yr of observations, where S n(fgw) represents the noise power spectral densities for TianQin (dotted line; Huang et al. 2020), LISA (dashed line; Robson et al. 2019), Taiji (densely dashdotted line; Liu et al. 2023), DECIGO (dot-dashed line), and BBO (solid line) (Yagi & Seto 2011; Sun & Li 2023; Sun et al. 2024). The st… view at source ↗

**Figure 2.** Figure 2: S/N values of the promising sources for various detectors and observation durations. The circles, squares, filled pluses, rhombuses, and pentagons represent the TianQin, LISA, Taiji, DECIGO, and BBO results, respectively. The data points situated on the horizontal gray line corresponding to each source signify the S/N values calculated for Tobs = 4 yr. The S/N values calculated for Tobs = 2 yr and Tobs = 8… view at source ↗

read the original abstract

Binary systems with ultrashort-period planetary-mass companions are expected to radiate continuous gravitational waves (GWs). However, earlier studies found that the detectability of such systems by the Laser Interferometer Space Antenna (LISA) is unlikely. In this study, we investigate the detectability of GWs from planetary-mass companions orbiting pulsars (PSRs) or white dwarfs (WDs) whose fundamental parameters, essential for calculating GW properties, have been measured. We compare the GW signals from our sample with the sensitivity curves of space-based GW detectors. We find that fourteen sources achieve a signal-to-noise ratio (\(\text{S/N}\)) of \(\gtrsim 5\) within four years of observations. Among these, three sources have PSR primaries (2S 0918-549 b, 4U 0513-40 b, and 4U 1543-62), and eleven systems possess WD primaries (BW Scl b, CP Eri b, CR Boo b, EF Eri b, GP Com b, GW Lib b, SDSS J0926+3624 b, SDSS J1507+5230 b, SMSS J1606-1000 b, SRGeJ0453 b, and WZ Sge b). We note that their detectability is less probable with near-term missions such as LISA, TianQin, and Taiji. Nevertheless, they could be detected by more advanced, future-generation observatories, such as the Deci-hertz Interferometer Gravitational wave Observatory (DECIGO) and the Big Bang Observer (BBO). This offers the potential to investigate the formation and evolution of ultrashort-period planetary-mass companions around compact stars through joint GW and electromagnetic surveys.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper lists fourteen specific observed binaries that could reach S/N ≳5 with DECIGO or BBO, but skips any propagation of the sizable distance and mass uncertainties that directly affect the strain amplitude.

read the letter

The main point is that the authors take real electromagnetic measurements of ultrashort-period planetary-mass companions around pulsars and white dwarfs, plug them into the standard quadrupole formula, and find fourteen systems that clear S/N of about 5 in four years of observation with future deci-hertz detectors. Three are pulsar systems and eleven are white-dwarf ones. They correctly note that LISA, TianQin, and Taiji are unlikely to see them, while DECIGO and BBO could in principle pick them up and enable multi-messenger work on planet formation around compact stars.

Referee Report

3 major / 2 minor

Summary. The manuscript examines continuous gravitational-wave emission from planetary-mass companions in ultrashort-period binaries with measured electromagnetic parameters (pulsar or white-dwarf primaries). Using the standard quadrupole formula, it computes GW amplitudes and frequencies for a sample of systems and compares them to the sensitivity curves of LISA, TianQin, Taiji, DECIGO, and BBO. The central claim is that exactly fourteen sources (three with PSR primaries and eleven with WD primaries) reach a matched-filter S/N ≳5 after four years of observation with DECIGO or BBO, while remaining undetectable by near-term missions.

Significance. If the numerical results survive error propagation, the work supplies a concrete list of multi-messenger targets for future deci-Hz observatories. It demonstrates that systems already characterized electromagnetically can be prioritized for GW searches, potentially constraining formation channels of planetary-mass companions around compact objects. The reliance on observationally determined parameters rather than population synthesis is a methodological strength.

major comments (3)

[Abstract] Abstract: The claim that fourteen specific sources achieve S/N ≳5 is presented without any displayed formula for h_0, integration time, or noise-weighted inner product. The quadrupole scaling h_0 ∝ M_chirp^{5/3} f^{2/3}/D is standard, yet the manuscript must show the explicit expression used for the four-year integrated S/N against the DECIGO/BBO curve and confirm that the listed systems were evaluated with that expression.
[Abstract] Abstract and parameter discussion: No Monte-Carlo or analytic propagation of uncertainties is reported. Literature distances (often Gaia-based with 20–40 % fractional errors) and companion masses (frequently lower limits) enter linearly into h_0 and therefore into S/N. A table or figure showing the range of S/N obtained when each of the fourteen systems is drawn from its published 1σ posteriors is required to substantiate that the count of fourteen remains stable.
[Abstract] Abstract: The assumption that all orbits are circular and that spin-orbit or higher-order post-Newtonian corrections are negligible is stated implicitly. For the shortest-period WD systems (e.g., WZ Sge b, GP Com b), even modest eccentricity or spin-induced quadrupole moments could alter the frequency evolution and matched-filter S/N; a brief justification or bound on these effects should be added.

minor comments (2)

The abstract lists the fourteen systems but does not indicate the source catalog or reference for each measured parameter set; a supplementary table with references, adopted values, and uncertainties would improve traceability.
The phrase “within four years of observations” should specify whether this assumes continuous data taking or accounts for duty cycle and data gaps typical of space-based interferometers.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us improve the clarity and robustness of the manuscript. We address each major comment below and will incorporate revisions as noted.

read point-by-point responses

Referee: [Abstract] Abstract: The claim that fourteen specific sources achieve S/N ≳5 is presented without any displayed formula for h_0, integration time, or noise-weighted inner product. The quadrupole scaling h_0 ∝ M_chirp^{5/3} f^{2/3}/D is standard, yet the manuscript must show the explicit expression used for the four-year integrated S/N against the DECIGO/BBO curve and confirm that the listed systems were evaluated with that expression.

Authors: We agree that the explicit formula should be more prominently displayed. Section 2 of the manuscript derives the characteristic strain h_0 from the quadrupole formula and defines the matched-filter SNR as the square root of the noise-weighted inner product integrated over T_obs = 4 years against the detector noise spectral density. All fourteen systems were evaluated with this expression. In the revision we will add the key SNR formula as an equation in the abstract (or immediately following it) and restate that the listed sources use this standard four-year integration. revision: yes
Referee: [Abstract] Abstract and parameter discussion: No Monte-Carlo or analytic propagation of uncertainties is reported. Literature distances (often Gaia-based with 20–40 % fractional errors) and companion masses (frequently lower limits) enter linearly into h_0 and therefore into S/N. A table or figure showing the range of S/N obtained when each of the fourteen systems is drawn from its published 1σ posteriors is required to substantiate that the count of fourteen remains stable.

Authors: We acknowledge the absence of formal error propagation. In the revised manuscript we will add a new appendix (or subsection) that performs a Monte-Carlo sampling of the fourteen systems using the published 1σ uncertainties on distance and the reported mass values (treating lower limits by sampling from the minimum value upward). The resulting S/N distributions will be summarized in a table or figure, and we will show that the conclusion of S/N ≳5 for these sources remains stable under the quoted errors. revision: yes
Referee: [Abstract] Abstract: The assumption that all orbits are circular and that spin-orbit or higher-order post-Newtonian corrections are negligible is stated implicitly. For the shortest-period WD systems (e.g., WZ Sge b, GP Com b), even modest eccentricity or spin-induced quadrupole moments could alter the frequency evolution and matched-filter S/N; a brief justification or bound on these effects should be added.

Authors: We thank the referee for highlighting this implicit assumption. Ultrashort-period binaries are expected to be fully circularized by tidal dissipation on timescales much shorter than the system ages; any residual eccentricity would be negligible. We will add a short paragraph in the methods section providing an order-of-magnitude bound showing that spin-induced quadrupole and higher-order post-Newtonian corrections contribute negligibly to the frequency evolution and matched-filter SNR over a four-year observation for the relevant masses and frequencies of the cited WD systems. revision: yes

Circularity Check

0 steps flagged

No circularity: calculations use external EM parameters and standard quadrupole formula

full rationale

The paper selects binary systems whose masses, periods, and distances are taken from independent electromagnetic observations in the literature. It applies the standard quadrupole radiation formula for circular orbits to compute h0 and then integrates against published DECIGO/BBO noise curves to obtain S/N. No parameters are fitted to GW data, no self-citation supplies a uniqueness theorem or ansatz that forces the result, and the central claim (14 sources above S/N ≳5) is a direct numerical evaluation rather than a renaming or self-referential definition. Uncertainties in input parameters affect the numerical values but do not create a circular derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the accuracy of previously published electromagnetic measurements of binary parameters and on the applicability of the standard general-relativity quadrupole formula for continuous waves from circular binaries.

axioms (1)

standard math Gravitational waves from binary systems are emitted according to the quadrupole approximation for circular orbits
This is invoked to translate measured orbital periods and masses into gravitational-wave strain amplitude and frequency.

pith-pipeline@v0.9.0 · 5655 in / 1480 out tokens · 85678 ms · 2026-05-10T20:11:29.261451+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

h0 = 8√5 (G Mc)^{5/3} / (c^4 D_L) (2π f_orb)^{2/3} and S/N = hc / √(f_gw S_n(f_gw)) with T_obs=4 yr
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

stationarity check ˙f_gw < 1/T_obs² and circular-orbit assumption

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

(2014); [22] Fiore et al

Stovall et al. (2014); [22] Fiore et al. (2023); [23] Kandel & Romani (2023); [24] in’t Zand et al. (2007); [25] Markwardt et al. (2002); [26] Papitto et al. (2008); [27] Falanga et al. (2005); [28] Burdge et al. (2022); [29] Pala et al. (2022); [30] Knigge (2006); [31] Wild et al. (2022)

work page 2014
[2]

(2018); [33] Neustroev & Mäntynen (2023); [34] Kupfer et al

Gaia Collaboration et al. (2018); [33] Neustroev & Mäntynen (2023); [34] Kupfer et al. (2024); [35] Groot et al. (2001); [36] Roelofs et al. (2007); [37] Gentile Fusillo et al. (2021); [38] Muñoz-Giraldo et al. (2024); [39] Breedt et al. (2012); [40] Pala et al. (2020); [41] Zorotovic & Schreiber (2022); [42] Chen et al. (2024); [43] Amantayeva et al. (20...

work page 2018

[1] [1]

(2014); [22] Fiore et al

Stovall et al. (2014); [22] Fiore et al. (2023); [23] Kandel & Romani (2023); [24] in’t Zand et al. (2007); [25] Markwardt et al. (2002); [26] Papitto et al. (2008); [27] Falanga et al. (2005); [28] Burdge et al. (2022); [29] Pala et al. (2022); [30] Knigge (2006); [31] Wild et al. (2022)

work page 2014

[2] [2]

(2018); [33] Neustroev & Mäntynen (2023); [34] Kupfer et al

Gaia Collaboration et al. (2018); [33] Neustroev & Mäntynen (2023); [34] Kupfer et al. (2024); [35] Groot et al. (2001); [36] Roelofs et al. (2007); [37] Gentile Fusillo et al. (2021); [38] Muñoz-Giraldo et al. (2024); [39] Breedt et al. (2012); [40] Pala et al. (2020); [41] Zorotovic & Schreiber (2022); [42] Chen et al. (2024); [43] Amantayeva et al. (20...

work page 2018