Phase closure nulling. Application to the spectroscopy of faint companions

We provide a complete theory of the phase closure of a binary system in which a small, feeble, and unresolved companion acts as a perturbing parameter on the spatial frequency spectrum of a dominant, bright, resolved source. We demonstrate that the influence of the companion can be measured with precision by measuring the phase closure of the system near the nulls of the primary visibility function. In these regions of phase closure nulling, frequency intervals always exist where the phase closure signature of the companion is larger than any systematic error and can then be measured.We show that this technique allows retrieval of many astrophysically relevant properties of faint and close companions such as flux, position, and in favorable cases, spectrum. We conclude by a rapid study of the potentialities of phase closure nulling observations with current interferometers and explore the requirements for a new type of dedicated instrument.

💡 Research Summary

The paper presents a comprehensive theoretical framework for exploiting closure phase nulling (CPN) to detect and characterize faint, unresolved companions orbiting bright, resolved primary stars in optical/infrared interferometry. The authors start by describing the visibility function of a resolved primary star, which for a uniform disk follows a Bessel‑type pattern that reaches zero (a null) at specific spatial frequencies determined by the baseline length and observing wavelength. At these nulls the primary’s complex visibility amplitude vanishes while its phase undergoes a rapid 180° transition. Because the primary contribution is essentially removed, any secondary source—even with a contrast as low as 10⁻⁴–10⁻⁵—imposes a measurable perturbation on the closure phase of a three‑baseline triangle.

Mathematically, the total complex visibility is expressed as V(u)=V₁(u)+V₂(u), where V₁(u)=J₁(πθu)/(πθu) represents the primary’s visibility (θ being the angular diameter) and V₂(u)=c·exp