Validating the Angular Sizes of Red Clump Stars with Intensity Interferometry

TL;DR

This work addresses validating the Red Clump SBC calibration used for precise distance measurements by applying intensity interferometry to measure limb-darkened angular diameters. It develops a framework that connects the stellar intensity profile to squared visibility via the van Cittert–Zernike relation and uses photon-cairing through g^(2) to infer angular sizes, with Fisher-information bounds guiding achievable precision. Applying the method to targets such as HD 360 and HD 17652 shows that in the H band at baselines near 100 m one can reach angular-diameter uncertainties of $<1\%$ in practical exposures, and that multi-band observations sampling the primary peak and secondary maxima provide robust model-insensitive cross-checks. The study highlights that multiplexed, multi-wavelength intensity interferometry with facilities like the Cherenkov Telescope Array Observatory can make these measurements time-efficient, thereby offering a principled cross-check that strengthens the Red Clump SBC calibration and the underlying distance ladder anchors.

Abstract

The surface-brightness-color (SBC) relationship for Red Clump stars provides a critical foundation for precision distance ladder measurements, including the 1\% distance determination to the Large Magellanic Cloud. Current SBC calibrations rely on angular diameter measurements of nearby Red Clump stars obtained through long-baseline optical interferometry using the Very Large Telescope Interferometer. We explore the application of intensity interferometry to measure limb-darkened angular diameters of Red Clump stars, offering a complementary approach to traditional amplitude interferometry. We describe the framework for extracting angular diameters from squared visibility measurements in intensity interferometry, accounting for limb darkening through the stellar atmosphere models. For the Red Clump star HD~17652, we show that intensity interferometry in the $H$ band at baselines matching PIONIER ($\sim$100~m) could achieve $<1$\% angular size uncertainties in 2-hour exposures by measuring the primary peak of the visibility function, enabling direct comparison with existing measurements. Critically, observations at shorter wavelengths probe the secondary visibility maximum, providing independent checks of both measurement and systematic errors that are largely insensitive to limb-darkening assumptions. Exploiting the multiplex advantage of simultaneous multi-bandpass observations and the large number of baselines available with telescope arrays such as the Cherenkov Telescope Array Observatory can reduce observing times to practical levels, making intensity interferometry a viable tool for validating the angular sizes for a subset of the Red Clump star calibration sample.

Figures (3)

• Figure 1: Left: Normalized $B$ and $H$-band intensity profiles $I(\theta)/I(0)$ computed by SATLAS and PHOENIX for $T=4800$K and $\log{g}=2.5$, which is the closest match to the Red Clump star HD 360. Right top: Squared visibility $|V|^2$ corresponding to the intensity profiles. Right bottom: Difference between the PHOENIX and SATLAS squared visibilities. The interferometric measurements of HD 360 by 2018AA...616A..68G lie within $u<0.5$.
• Figure 2: Squared visibilities $|\mathcal{V}|^2$ in $B$, $V$, $R$, $I$, $H$, and $K$ for the intensity profiles calculated by SATLAS.
• Figure 3: Estimated uncertainty in the scale factor parameter $s$. $\sigma_s$ for (Top) HD 360 and (Bottom) HD 17652 . The measurement noise is based on two 4-m telescopes separated by a baseline distance $B$, a photon detector detector with 42.4 ps FWHM timing jitter,an overall instrumental throughput of 0.3, and an exposure time is set to $T_{obs}=2$ h. The dashed horizontal line is the scale uncertainty for these stars as measured in the $H$-band using PIONIER 2018AA...616A..68G.