Towards measuring astrophysical third order correlation functions with the H.E.S.S. optical intensity interferometer

TL;DR

This study targets the extraction of the interferometric closure phase in intensity interferometry by measuring third-order correlations, focusing on the cosine of the closure phase $cos φ$ in a triangle of telescopes. The authors develop and apply a concrete analysis framework to compute the third-order correlation $g^{(3)}$ from H.E.S.S. data on Nunki and Dschubba, isolating the three-photon contribution via a two-photon model and Gaussian-tube fits, but find no astrophysical $cos φ$ signal within current sensitivity. They validate their approach through a laboratory experiment with a rotating ground-glass disk that yields a measured $cos φ$ consistent with unity, confirming the method’s viability. The work also quantifies the substantial sensitivity gains required and discusses how next-generation facilities (e.g., CTA Large-Sized Telescopes or dedicated SIITAR-like arrays) could make closure-phase measurements feasible, thereby enriching high-angular-resolution imaging with intensity interferometry.

Abstract

The closure phase, the sum of the three Fourier phases in a telescope triangle, is an important tool in astronomical interferometry, helping to reconstruct the geometries of the observed objects. While already established in amplitude interferometry, for the recently expanding field of intensity interferometers the closure phase enables recovering information of the interferometric phases that are otherwise inaccessible with this technique. To extract the (cosine of) the closure phase ($\cos φ$) in intensity interferometry, third-order correlations between three simultaneously measuring telescopes have to be computed. As the signal-to-noise of such three-photon correlations is too small for current generation intensity interferometers, no third-order correlations of astrophysical targets have been recorded so far. In this paper we present the first measurements of third order correlation functions of two stellar systems, Nunki ($σ$ Sgr) and Dschubba ($δ$ Sco), observed with the H.E.S.S. intensity interferometer in 2023. We show how to isolate the three-photon contribution term from the two-photon contributions, in order to access $\cos φ$. For the observed stellar targets the sensitivity is not high enough to extract closure phase information. To demonstrate that the analysis works well we further extract $\cos φ$ in a laboratory experiment, using the H.E.S.S. intensity interferometer and a pseudo-thermal light source.

Figures (11)

• Figure 1: Second-order temporal correlation measurements of both stars at a wavelength of $470\,$nm. The full $g^{(2)}$ analysis of these datasets, including the determination of the data point at a projected baseline of $0$, can be found in vogel2025simultaneous.
• Figure 2: Third-order temporal correlation measurement of both stars at a wavelength of $470\,$nm. Both cases are integrated over the entire measurement time.
• Figure 3: Analysis of the $g^{(3)}$ data for extracting the non-trivial three-photon contribution of Nunki. Left: original $g^{(3)}$ data. The dashed orange rectangle indicates the region that is excluded for the 2-dimensional fitting of the $g^{(2)}$ contributions. Center: The two-photon model, constructed from the results of the 2-dimensional fit of three gaussian functions along the $g^{(2)}$ axes. Right: The difference between the original data and the 2-d fits.
• Figure 4: Analysis of the $g^{(3)}$ data for extracting the non-trivial three-photon contribution of Dschubba. Left: original $g^{(3)}$ data. The dashed orange rectangle indicates the region that is excluded for the 2-dimensional fitting of the $g^{(2)}$ contributions. Center: The two-photon model, constructed from the results of the 2-dimensional fit of three gaussian functions along the $g^{(2)}$ axes. Right: The difference between the original data and the 2-d fits.
• Figure 5: Reconstructed parameters for Nunki according to the single star limb-darkened model from vogel2025simultaneous. From left to right: the intensity profile of the star, squared visibility map on earth, Fourier phase map on earth. In the latter two maps, the uv tracks of the H.E.S.S. measurements are also shown