Analytical approaches to the study of the phase of the visibility function

TL;DR

This work analyzes how the phase of the visibility function in space-based radio interferometry depends on baseline projection and source geometry. It develops a Fourier-based framework, expressing the azimuthal brightness as a Fourier series and deriving an analytic decomposition of V(u,φ_u) into radial integrals with Bessel functions; for small baselines, a universal phase relation tan φ_V ≈ J1(2π u r0)/J0(2π u r0) emerges for ring-like sources. The theory is validated against 3D MHD simulations of black hole accretion and is qualitatively consistent with GMVA observations of M87*, supporting phase-closure approaches and interpretation of high-resolution visibility data in space VLBI. Collectively, the results provide practical tools for linking measured visibility phases to source structure and improving imaging of supermassive black holes.

Abstract

In radio interferometric observations, the main source of information is the complex visibility function, which includes amplitude and phase. In this paper, the dependence of the phase of the visibility function on the base projection is investigated when used in radio interferometry with space bases up to six Earth diameters. The dependence of the phase of the visibility function on the projection of the base and direction is obtained. It is shown that for small values of the base projections, this dependence has a universal character and is consistent with the results of numerical magnetohydrodynamic models.

Figures (6)

• Figure 1: The figure shows examples of images for cases when a) - $a_0=2$, $a_1=a_2=0$, b) - $a_0=2$, $a_1=1$, $a_2=0$ and c) - $a_0=2$, $a_1=0$, $a_2=1$.
• Figure 2: The figure shows the dependence of the phase of the visibility function in degrees on the projection of the base in units of the Earth's diameter for thin and thick ring models with a uniform brightness distribution.
• Figure 3: The figure shows the dependence of the phase of the visibility function on the projection of the base in units of the Earth's diameter for the mhd model at $t=0$ and the corresponding analytical models of thin and thick disks.
• Figure 4: The figure shows the dependence of the phase of the visibility function on the projection of the base in units of the Earth's diameter for the mhd model at $t=1000$ and the corresponding analytical models of thin and thick disks.
• Figure 5: The figure shows the dependence of the phase of the visibility function on the projection of the base in units of the Earth's diameter for the mhd model at $t=2000$ and the corresponding analytical models of thin and thick disks.