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

Author(s)

Sharma, Abhishek, Tahelyani, Divya, Sengupta, Anand S., Mitra, Sanjit

Abstract

We study IndIGO-D, a decihertz gravitational-wave mission concept, focusing on a specific configuration in which three spacecraft fly in formation to form an L-shaped interferometer in a heliocentric orbit. The two orthogonal arms share a common vertex, providing a space-based analogue of terrestrial Michelson detectors, while operating in an optimised configuration that yields ppm-level arm-length stability. Assuming 1000 km arm length, we analyse the orbital motion and antenna response, and assess sensitivity across the [0.1 - 10] Hz band bridging LISA and next-generation ground-based interferometers. Using fiducial sensitivity curves provided by the IndIGO-D collaboration, we compute horizon distances for different source classes. Intermediate-mass black-hole binaries with masses $10^{2}$ - $10^{3} \, M_\odot$ are detectable to redshifts $z \sim 10^{3}$, complementing the reach of LISA and terrestrial detectors. Binary neutron star systems are observable to a horizon distance of $z \lesssim 0.3$, allowing continuous multi-band coverage with Voyager-class interferometers from the decihertz regime to merger. A Bayesian parameter-estimation study of a GW170817-like binary shows that the sky localization area improves from $\sim 21 \,\mathrm{deg}^2$ at one month to $0.3 \,\mathrm{deg}^2$ at six hours pre-merger! These sky areas are readily tiled by wide-field time-domain telescopes such as the Rubin Observatory, whose $9.6 \,\mathrm{deg}^2$ field of view and r-band depth enable high-cadence, repeated coverage of GW170817-like kilonovae at this distance and beyond. IndIGO-D exploits the rapid evolution of binaries in the decihertz band to bridge the gap between millihertz and terrestrial observations, enabling early warnings on timescales from months to hours and enhancing the prospects for multi-band and multi-messenger discoveries.

Figures

Caption

The orbits of the three spacecraft constituting IndIGO-D. The spacecraft 1 at the vertex orbits the Sun in ecliptic plane at a distance of 1 AU, while the orbits of spacecraft 2 and 3 are inclined by $60^\circ$ with respect to ecliptic which results in the most stable flight configuration such that the inter spacecraft separation remain nearly constant throughout the motion.

Caption

Flexing of the arms: fractional variation of the inter-spacecraft separation (computed using the approximated orbits described by \cref{Eq:anomaly_relation_approximated}) along the two arms over one orbital period of the constellation. The separation varies by ${\sim 7.5\,\mathrm{m}}$ over a drift timescale ${t_{\rm drift} \sim \mathcal{O}(\mathrm{months})}$ within a single orbital period.

Caption

Variation in the magnitude of the antenna pattern functions across the whole sky in nearly one orbital period of the spacecraft constellation, assuming long-wavelength limit. Grids in the sky-map correspond to the ecliptic longitude and ecliptic latitude that marks the position in the sky in the SSB frame. Note that at any instant there exists 4 blind and 2 bright spots where the magnitude of antenna patterns are 0 and 1, respectively. The 4 blind spots lie in the detector's plane along the lines making an angle of $45^\circ$ with the detector's arms. The 2 bright spots lie perpendicular to the detector's plane, above and below the detector.

Caption

: Noise amplitude spectral density : Horizon distance

Caption

: Comparison of detector sensitivities and horizon distances. Note that IndIGO-D is sensitive to binary neutron star systems out to a horizon distance of $\sim 1000$ Mpc, similar to LIGO-Voyager~\cite{Adhikari2018Voyager}. \\ (a) Noise sensitivities: Detector noise amplitude spectral densities (ASD) for various detectors, along with the ASD of the GW170817- and GW150914-like GW signals, given by $2\sqrt{f}\tilde h(f)$. The red-filled circles represent the time before the merger at a specific GW frequency.\\ (b) Horizon distance (right axis) and corresponding redshift (left axis) as functions of source-frame total mass for equal-mass compact binaries. Detection distances are evaluated for 48 uniformly distributed sky positions, with the inclination angle fixed to zero (face-on). The upper solid line indicates the horizon distance, while the dark and light shaded bands indicate the distances enclosing $50\%$ and $90\%$ of sky locations, respectively. : Caption not extracted

Caption

Detection fractions (SNR $\geq 8$) for simulated merging binary neutron star systems with component masses $(1.4, 1.4)\, \msun$, isotropic orientations, and a population distributed uniformly in comoving volume out to ${z = 0.33}$. IndIGO-D and Voyager detect 17.72\% and 26.04\% of the sources, respectively. All sources detected by IndIGO-D will also be detected by Voyager. The overlap illustrates the multi-band science potential, in which IndIGO-D provides long-duration tracking and pre-merger localisation in the dHz band for events later observed in the Voyager band.

Caption

Sky-localization area (90\% credible interval) for a GW170817-like binary neutron star at different pre-merger epochs in simulated IndIGO-D data: one month, one week, one day, and six hours before merger. For comparison, we also show the localization obtained with ET at six hours before merger and the post-merger localization with the AHLV network at design sensitivity. For reference, the localization patch for the real GW170817 event observed by the HLV network during the O3 run is included. The ET sky posterior is bimodal; only the dominant mode is shown, with the secondary mode located on the opposite side of the sky. The corresponding epochs are indicated on the time–frequency track of the binary, which is colored by the accumulated signal-to-noise ratio over the three-month in-band evolution in IndIGO-D up to $30\,\si{\hertz}$.

Caption

Comparison of two-dimensional marginalized posterior distributions in chirp mass and mass ratio for a GW170817-like system, obtained from simulated IndIGO-D data at different epochs before merger, as indicated in the legend. The contours show the 90\% credible regions, with colours matching those of the IndIGO-D early-warning skymaps in~\cref{fig:skymaps}. As expected, parameter inference becomes progressively more accurate as the signal accumulates in-band. These results can be directly compared with the corresponding sky-localization performance shown in \cref{fig:skymaps}.

Caption

Comparison of the antenna pattern functions corresponding to the two polarizations, with and without assuming the LWL, evaluated in the frequency domain for a GW170817 like system as a function of frequency. Consideration of finite detector size effects results in complex valued $F_{+,\times}$. The top and bottom panels correspond to the real and imaginary parts of $F_{+,\times}$. The modulation in the lower end of the frequency spectrum corresponds to the changing orientation and position of the detector as the binary radiates for a longer period of time in the lower frequency regime. As the inspiral rate increases, the time-dependent effects get suppressed and the antenna pattern functions become nearly constant in LWL (dashed dark blue curve). However, consideration of finite detector size effects results in modulated $F_{+,\times}$ at the higher end of the frequency spectrum (solid light blue curve).