[Paper Review] Detecting circumbinary exoplanets and hierarchical stellar triples with the LISA gravitational radiation mission

Jason H. Steffen, Dong-Hong Wu+1 more|arXiv (Cornell University)|Dec 9, 2018

Stellar, planetary, and galactic studies4 citations

TL;DR

This paper proposes detecting circumbinary exoplanets and hierarchical stellar triples via gravitational wave (GW) modulations in the LISA mission's data, primarily through Doppler shifts induced by the barycentric motion of double white dwarf (DWD) binaries due to orbiting third bodies. With a four-year mission, LISA could detect ~10 giant planets (M > 2 M_J), rising to ~100 with a ten-year mission, assuming planet occurrence rates similar to those around isolated stars.

ABSTRACT

We investigate the possibility of detecting planetary or stellar companions orbiting white dwarf binaries using the LISA gravitational radiation detector. Specifically, we consider the acceleration of the barycenter of the white dwarf binary due to the orbiting third body as well as the effect of changes in the tidal field across the binary due to the perturber's eccentric orbit. We find that the movement of the barycenter is detectable for both stellar and planetary mass objects. If circumbinary planets occur with frequencies similar to gas giant planets around isolated main sequence stars, then we expect to find of order 10 such planets in four years of LISA observations. For a longer, ten-year mission the accessible parameter space for planetary mass, orbital period, and binary orbital period grows and LISA's associated yield increases to ~100 expected detections.

Motivation & Objective

• To assess the detectability of circumbinary planets and hierarchical stellar triples using gravitational wave signals from the LISA mission.
• To evaluate two distinct GW modulation mechanisms: barycentric acceleration (Doppler shift) and tidal field-induced orbital period variation.
• To estimate the number of detectable circumbinary planets under realistic assumptions about planet occurrence rates and DWD population distributions.
• To determine the sensitivity of LISA to planetary companions based on orbital parameters and signal-to-noise thresholds.
• To compare the detectability of planetary vs. stellar-mass companions and identify the dominant detection mechanism.

Proposed method

• Model the Doppler shift in the gravitational wave frequency caused by the barycentric motion of a DWD binary due to a third-body companion, using radial velocity and orbital parameters.
• Derive the frequency shift amplitude using the relativistic Doppler formula and orbital mechanics, incorporating mass ratio, semi-major axis, and inclination.
• Assess the tidal field modulation effect from an eccentric orbiting third body, calculating its impact on the GW signal's orbital period variation.
• Use a galactic model of DWDs to estimate the number of resolvable DWDs with suitable orbital frequencies for planet detection.
• Apply planet occurrence rate models from Kepler data (Cumming et al. 2008) to estimate detectable planet populations, assuming similar rates around DWDs.
• Compute signal-to-noise ratios (S/N) for detection, using a threshold of S/N > 5, and integrate over mass and orbital period ranges to estimate expected detections.

Experimental results

Research questions

• RQ1 Can LISA detect circumbinary exoplanets through gravitational wave signals modulated by the barycentric motion of double white dwarf binaries?
• RQ2 Which of the two proposed GW modulation mechanisms—barycentric Doppler shift or tidal field-induced period variation—provides the dominant detection signature for LISA?
• RQ3 What is the expected number of detectable circumbinary planets over a 4-year and 10-year LISA mission, assuming planet occurrence rates similar to those around isolated main-sequence stars?
• RQ4 How does the detectability of planets depend on their mass and orbital period relative to the DWD binary's orbital frequency?
• RQ5 What fraction of resolvable DWDs would host detectable planetary companions, and where in the sky would such detections be most likely?

Key findings

• The Doppler shift mechanism due to barycentric motion is the dominant and most detectable signal, while tidal field modulation is generally outside LISA’s sensitivity range.
• With a four-year LISA mission, approximately 10 circumbinary giant planets (M > 2 M_J) are expected to be detected, assuming planet occurrence rates similar to those around isolated F, G, and K stars.
• Extending the mission to ten years increases the expected yield to around 100 detections, including tens of planets with orbital periods <100 days.
• Planets with masses >10 M_J and orbital periods <100 days would be detectable around nearly all resolvable DWDs.
• The detection rate is highest near the galactic center due to the higher density of DWDs and stronger GW signals.
• The method offers a more straightforward detection strategy than transit surveys, as the GW signal is stable and analyzable via standard time-domain techniques.