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Measurement of the photosphere oblateness of $γ$ Cassiopeiae via Stellar Intensity Interferometry with the VERITAS Observatory

This paper presents the first measurement of an oblate stellar photosphere using intensity interferometry with the VERITAS Observatory, determining the size, shape, and rotational orientation of the rapid rotator $\gamma$ Cassiopeiae.

Original authors: A. Archer, J. P. Aufdenberg, P. Bangale, J. T. Bartkoske, W. Benbow, J. H. Buckley, Y. Chen, N. B. Y. Chin, J. L. Christiansen, A. J. Chromey, A. Duerr, M. Escobar Godoy, S. Feldman, Q. Feng, S. Filbe

Published 2026-05-28

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CC BY 4.0

Original authors: A. Archer, J. P. Aufdenberg, P. Bangale, J. T. Bartkoske, W. Benbow, J. H. Buckley, Y. Chen, N. B. Y. Chin, J. L. Christiansen, A. J. Chromey, A. Duerr, M. Escobar Godoy, S. Feldman, Q. Feng, S. Filbert, L. Fortson, A. Furniss, W. Hanlon, O. Hervet, C. E. Hinrichs, J. Holder, Z. Hughes, T. B. Humensky, W. Jin, M. N. Johnson, M. Kertzman, M. Kherlakian, D. Kieda, N. Korzoun, T. LeBohec, M. A. Lisa, M. Lundy, G. Maier, N. Matthews, P. Moriarty, R. Mukherjee, W. Ning, R. A. Ong, A. Pandey, M. Pohl, E. Pueschel, J. Quinn, P. L. Rabinowitz, K. Ragan, P. T. Reynolds, D. Ribeiro, E. Roache, J. G. Rose, I. Sadeh, L. Saha, M. Santander, J. Scott, G. H. Sembroski, R. Shang, D. Tak, J. V. Tucci, J. Valverde, V. V. Vassiliev, D. A. Williams, S. L. Wong, The VERITAS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to measure the exact shape of a spinning top from miles away, using only a camera that is too blurry to see the top’s details. That is essentially the challenge astronomers faced with the star Gamma Cassiopeiae ( $\gamma$ Cas).

This star is a "rapid rotator"—it spins so fast that it bulges at its equator, much like how the Earth is slightly wider at the middle than at the poles, but on steroids. Because it spins near its breaking point, it’s not a perfect sphere; it’s an oblate spheroid (a squashed ball).

Here is how the researchers in this paper solved the problem, explained in everyday terms:

1. The Problem: The "Blurry Photo"

Traditional telescopes act like single eyes. Even the best ones struggle to see the fine details of a star’s surface because the star is so far away and so small in our sky. Previous measurements using infrared light could see the dusty disk of gas surrounding the star, but they couldn’t see the star’s actual surface (the photosphere) clearly enough to tell if it was round or squashed.

2. The Solution: A New Kind of "Ruler"

The team used an instrument called VERITAS (Very Energetic Radiation Imaging Telescope Array System). Usually, VERITAS is used to look for high-energy gamma rays from space. But for this study, they repurposed it as a Stellar Intensity Interferometer.

Think of it this way:

Traditional Interferometry (Michelson): Imagine two people holding mirrors and trying to combine the light waves perfectly. If the wind shakes the mirrors even a tiny bit, the image breaks. This is hard to do with visible light because the atmosphere is turbulent.
Intensity Interferometry (What they used): Instead of combining the light waves themselves, they measured the brightness fluctuations (the intensity) at two different telescopes and looked for a statistical correlation. It’s like two people listening to the same distant drumbeat. Even if the wind messes up the sound waves individually, if they both hear the rhythm at the same time, they know they are listening to the same source. This method is robust against atmospheric turbulence.

3. The Measurement: Taking a "3D Scan"

By using six different pairs of telescopes spaced up to 170 meters apart, they created a "baseline" (a ruler) that could measure the star’s size from different angles.

As the Earth rotated, the angle between the telescopes and the star changed. This allowed them to take measurements from many different directions, effectively creating a "shadow map" or a Fourier transform of the star’s shape.

4. The Results: The Star is Squashed

By fitting their data to mathematical models, they found:

It’s Not Round: The star is definitely oblate. The ratio of its width (equator) to its height (pole) is about 1.28. In other words, it’s roughly 28% wider than it is tall.
The Size: The "minor axis" (the shortest way across the star) has an angular diameter of 0.43 milliarcseconds. To put that in perspective, that’s incredibly small.
The Orientation: They determined the angle of the star’s rotation axis in the sky is about 116 degrees (measured from North). This matches previous observations of the star’s surrounding gas disk, confirming that the disk and the star’s bulge are aligned.

5. The "Physics Model" Fit

They didn’t just measure the shape; they also tested a complex physics model called the Roche-von Zeipel model. This model accounts for:

Gravity Darkening: The poles of a fast-spinning star are hotter and brighter, while the equator is cooler and darker (because gravity is weaker there due to the spin).
Limb Darkening: The edges of the star look darker than the center.

Their data fit this model perfectly. The results suggest:

The star is spinning at 97.7% of its breakup speed (the speed at which it would fly apart).
The equatorial radius is about 10.9 times the radius of our Sun.
The mass is about 15 times the mass of our Sun.

Why This Matters

This is the first time ever that intensity interferometry has been used to measure the shape (oblateness) of a star, not just its size. It proves that this technique can provide detailed geometric information about stars, complementing other methods like spectroscopy (analyzing light colors) and infrared interferometry.

In short: They used a clever statistical trick with gamma-ray telescopes to prove that Gamma Cassiopeiae is a squashed, rapidly spinning star, and they measured exactly how squashed it is.

Technical Summary: Measurement of the Photosphere Oblateness of γ Cassiopeiae via Stellar Intensity Interferometry with the VERITAS Observatory

Problem and Motivation
The subgiant star γ Cassiopeiae (γ Cas) is a Be-type star rotating at nearly its breakup velocity, with its rotation axis inclined by approximately $60^\circ$ to the line of sight. This rapid rotation is expected to produce a pronounced equatorial bulge and anisotropic gravitational darkening. While previous Michelson interferometric measurements at infrared wavelengths have successfully characterized the star’s extended decretion disk—constraining the position angle of the rotational axis to $122^\circ$ —these methods are insensitive to the photosphere itself. Conversely, prior stellar intensity interferometry (SII) measurements at optical wavelengths have been limited to determining the overall angular size of the photosphere, lacking the baseline coverage necessary to resolve its shape. This paper addresses the gap by presenting the first SII measurement sensitive to the geometric shape (oblateness) and orientation of a stellar photosphere.

Methodology
The study utilizes the VERITAS Stellar Intensity Interferometer (VSII), implemented on the Very Energetic Radiation Imaging Telescope Array System (VERITAS) at the Fred Lawrence Whipple Observatory. The system employs four 12-meter imaging atmospheric Cherenkov telescopes as light collectors.

Data Acquisition: Observations were conducted at a wavelength of 416 nm using a narrow-band filter (10 nm bandwidth) to isolate photospheric light. Data were collected over 160 pair-hours between January 2023 and December 2024 during bright-moon periods. The six possible telescope pairs provided baseline coverage in the Fourier $u-v$ plane, with projected baselines ranging from 35 to 170 meters.
Correlation and Noise Reduction: The intensity correlation function was measured by correlating the digitized current signals (250 MHz sampling rate) from pairs of photomultiplier tubes. The analysis involved rigorous data cleaning:
1. Background Subtraction: Uncorrelated night-sky background light was removed by measuring off-star currents before and after each run.
2. Artifact Removal: Frames affected by telescope tracking corrections (which cause sharp drops in current) and radio-frequency interference (specifically a 79.4 MHz alias from an on-site repeater) were identified and excluded.
3. Peak Selection: A Gaussian fit was applied to the correlation peak near zero time lag. A threshold based on the distribution of background noise integrals was established to distinguish true signal peaks from statistical fluctuations.
Modeling: The squared visibilities were extracted from the integrated Gaussian peaks. Two modeling approaches were employed:
1. Geometric Models: The data were fitted with uniform disk and uniform ellipse models to extract effective angular sizes, axis ratios, and position angles.
2. Physical Model: A Roche–von Zeipel model for a rapidly rotating star was used, incorporating limb darkening, gravity darkening (with parameter $\beta = 0.20$ ), and temperature gradients. Synthetic visibilities were generated using the PHOENIX atmosphere code and compared to the data.

Key Contributions
The primary contribution of this work is the demonstration that stellar intensity interferometry can resolve the non-circular geometry of a star. By utilizing the varying orientation of baselines in the $u-v$ plane, the authors extracted the oblateness and rotational axis orientation of the photosphere, a capability not previously achieved with SII. The paper also details improved data processing techniques, including better uncertainty estimation via false-peak injection and the mitigation of radio interference artifacts.

Results

Uniform Ellipse Fit: Fitting the data with a uniform ellipse model yielded a minor-axis angular diameter of $0.43 \pm 0.02$ mas, a major-to-minor radius ratio of $1.28 \pm 0.04$ , and a position angle of the rotation axis of $116^\circ \pm 5^\circ$ .
Roche–von Zeipel Model: A more comprehensive physical model provided the following constraints:
- Equatorial angular diameter: $0.604^{+0.041}_{-0.034}$ mas.
- Equatorial radius: $10.9^{+0.8}_{-0.6} R_\odot$ .
- Position angle: $114.7^{+6.4}_{-5.7}$ degrees.
- Rotational velocity: The fit indicates the star is rotating at a rate very close to the breakup limit, with a $1\sigma$ lower limit of $97.7\%$ of the critical velocity ( $\Omega/\Omega_c \ge 0.977$ ).
- Mass and Temperature: The model implies a stellar mass of $15 \pm 2 M_\odot$ and a polar effective temperature of $\approx 26,500$ K.
Consistency: The derived position angle is consistent with previous infrared measurements of the decretion disk, suggesting the disk is aligned with the equatorial bulge of the photosphere. The projected rotation velocity ( $v \sin i = 389 \pm 20$ km s $^{-1}$ ) is consistent with spectroscopic estimates.

Significance
The authors claim this is the first measurement of an oblate photosphere using intensity interferometry. The results validate the capability of SII to provide high-angular-resolution constraints on stellar shape and orientation, complementing spectroscopic and Michelson interferometric data. The tight constraints on the rotation rate and geometry provide valuable input for stellar models of rapid rotators, requiring them to match both spectral and geometrical consequences of extreme rotation. The study also highlights the importance of systematic error control, particularly regarding radio interference and tracking artifacts, in achieving precision measurements with SII.