Probing Compact Binary Coalescences in the Decihertz GW Band with IndIGO-D

The gist The study analyzes IndIGO-D, a decihertz gravitational-wave mission concept, focusing on an L-shaped interferometer in a heliocentric orbit to probe compact binary coalescences across the 0.1 – 10 Hz band, bridging the gap between LISA and terrestrial detectors.

Detector Geometry and Orbital Configuration

The IndIGO-D detector consists of three spacecraft forming an L-shaped interferometer with 1000 km arms, operating in a heliocentric orbit to achieve ppm-level arm-length stability. The vertex spacecraft follows a circular trajectory in the ecliptic plane, and the orbits of the other two spacecraft must be eccentric and inclined by 60◦ with respect to the ecliptic plane to result in a fixed arm-length configuration up to first order in α=l/2R. The orbital inclination is given by tanϵ = √3α / (1 + α).

Antenna Pattern Functions

The antenna pattern functions describe the directional sensitivity of the detector towards the two polarizations of the GWs, and they are time and frequency dependent. The phase shift recorded at the output port is given by Eq. (9), which involves a detector tensor Dij. In the long wavelength limit (LWL), when the wavelength of the observed GW signal is very large in comparison to the length of the detector arms, the transfer functions given by Eq. (A5) approaches unity, and the antenna patterns become only time-dependent.

Science Capabilities

IndIGO-D is designed to target a low-frequency gap between mHz and terrestrial bands, with a fiducial noise power spectral density (PSD) spanning 0.1 to 30 Hz. The sensitivity curve suggests that a GW170817-like BNS system would be detectable for several years prior to coalescence, enabling continuous monitoring throughout the slow early inspiral.

Horizon Distances for Coalescing Compact Binary Sources

The sensitivity of a GW detector to compact binaries is characterized by the horizon distance, defined as the farthest luminosity distance at which a source produces a signal-to-noise ratio (SNR) of 8. IndIGO-D attains a horizon redshift of z ∼0.3 for binary neutron star systems, and it is sensitive to IMBHs with total masses in the 102–104 M⊙ range out to redshifts exceeding z ∼ O(102) for equal mass ratios.

Multiband Access to BNS Sources

A population of simulated BNS systems with component source-frame masses of 1.4 M⊙ was used to determine the fraction of sources that satisfy ρ ≥ 8 in both IndIGO-D and Voyager. Approximately 18% of the sources are detectable by IndIGO-D and 26% by Voyager, demonstrating a significant fraction of BNS systems within z ≤ 0.33 remain jointly detectable in dHz and ground-based detector bands.

Observational Reach for Intermediate-Mass Black-Hole Systems

For intermediate-mass black hole systems with total masses in the range 102–105 M⊙, IndIGO-D fills the observational gap precisely. The coalescence of an equal-mass binary with a source-frame total mass of 103 M⊙ remains detectable up to redshift z ∼ 600 as shown in Fig. (4b).

Probing Environmental Effects and Orbital Eccentricity

Observations in the dHz band offer a unique opportunity to probe the dark matter (DM) environments surrounding compact binaries. The sensitivity in this regime allows it to detect or place strong constraints on the presence of DM spikes surrounding IMBHs. Furthermore, the dHz band may retain measurable residual eccentricity from their formation channel, which is difficult to constrain with ground-based detectors.

Early Warning Capabilities

IndIGO-D can localize a binary-neutronstar source to an area of ∼ 21 deg2 one month before merger, and this improves to ∼ 0.3 deg2 at six hours before coalescence. This capability is well matched to the field of view and depth of modern wide-field optical telescopes, enabling pre-merger electromagnetic follow-up. The dHz band provides substantially earlier directional information than existing or 3G high-frequency detector networks, indicating the potential of IndIGO-D for actionable pre-merger alerts and coordinated electromagnetic follow-up.

Conclusion

IndIGO-D will observe the early inspirals of BNS systems out to a redshift of 0.3, that will later be observed by the LIGO Voyager or future 3G detectors such as the ET or CE, enabling multi-band observations. At higher masses, IndIGO-D is sensitive to IMBHBs with total masses in the 102 − 104 M⊙ range out to redshifts exceeding z ∼ O(102) for equal mass ratios. Such a distance reach far surpasses that of both LISA and ground-based observatories and opens a new observational window onto the formation pathways of IMBHs. By filling the spectral gap between LISA and terrestrial detectors, IndIGO-D will enable practical multi-band observations possible where, many systems observable in the dHz regime will reappear in the high-frequency band within days or hours, rather than the decade-long delay characteristic of LISA-to-terrestrial detector transitions.

How it works

The study outlines several key aspects of the IndIGO-D concept. The detector configuration involves three spacecraft flying in formation to form an L-shaped interferometer in a heliocentric orbit. The orbital motion is designed such that the inter-spacecraft separation remains fixed to first order in the small dimensionless parameter α=l/2R.

Key Scientific Opportunities

The scientific opportunities offered by GW observations in the dHz band have motivated several detector concepts, including DECIGO [22–24], TianGO [18], Lunar Gravitational-Wave Antenna (LGWA) [25–27] and Laser Interferometer Lunar Antenna (LILA) [28, 29]. These include uncovering the progenitors of Type Ia supernovae, probing dynamical signatures of the environments in which compact binaries merge, exploring the population and growth of intermediate-mass black holes, tracing the evolutionary pathways of stellar-mass compact objects, and investigating the formation of light-seed black holes.

Early Warning Performance

The analysis quantifies early warning capability using Bayesian parameter estimation studies of simulated signals from a GW170817-like BNS system. IndIGO-D can localize such sources within O(10) deg2 one month, and O(1) deg2, one week before merger with accurate chirp mass measurement with uncertainties O(10−5)! The resulting sky areas are ideally suited for EM follow-up with wide-field telescopes enabling the discovery of short GRB afterglows, kilonovae, and other transient signatures with unprecedented temporal lead time.

Chirp Mass Measurement

The dHz band enables an early and precise measurement of the chirp mass, with fractional uncertainties of O(10−6 − 10−5) achievable weeks to months prior to merger for a GW170817-like system.

1. Bold Header: Early Warning Localization Precision Improvement

The improved AI system can perform precise tracking of signals by leveraging IndIGO-D's early warning capabilities, which localize a binary-neutronstar source to an area of ∼ 21, deg2 one month before merger. This allows for actionable early-warning alerts and coordinated observations.

2. Bold Header: Multi-Messenger Prioritization

The system can enable efficient and targeted multi-messenger campaigns by using the precision measurement of chirp mass, which provides fractional uncertainties of O(10−6 − 10−5) achievable weeks to months prior to merger. This allows for identifying systems with chirp masses indicative of long-lived remnants or enhanced mass ejection as high-priority targets.

3. Bold Header: Multi-Band Source Characterization

The AI system can facilitate coherent multiband measurements by bridging the gap between LISA and terrestrial detectors, which is achieved because IndIGO-D allows for multi-band observations possible where, many systems observable in the dHz regime will reappear in the high-frequency band within days or hours.

4. Bold Header: Dark Matter Environment Probing

The improved system can constrain dark matter distributions by utilizing the sensitivity of IndIGO-D to detect or place strong constraints on the presence of DM spikes surrounding IMBHs, which is relevant for studying the distribution and nature of particle DM in the vicinity of compact objects.

5. Bold Header: Orbital Eccentricity Measurement

The AI system can measure binary orbital eccentricity, a parameter that is difficult to constrain with ground-based detectors, which helps differentiate between the formation processes of BBHs, especially those formed in dense stellar environments.