The Alternate View
Measuring the Bulge of a Spinning Star
by John G. Cramer
Stars, all of which originally coalesced from orbiting in-spiraling gases, have some amount of angular rotation, but some stars rotate much faster than others. On the low end of rotational speed, consider our own Sun. Because it is a sphere of hot plasma rather than a solid body, its various regions can rotate at different speeds. Its equatorial region makes one complete rotation every 25.7 days, while the regions near the solar poles rotate more slowly, only about one rotation every 33 days. The spin axis of the Sun is not quite perpendicular to the plane of the ecliptic in which the planets orbit, with a slight tilt of 7.25° off perpendicular. The relatively small spin of the Sun gives it a very slight equatorial bulge, adding only a few parts per million to its equatorial diameter.
On the high end of rotational speed, consider the bright star γ Cassiopeiae, which is about 550 light years from Earth. It is the hot blue subgiant of stellar type B0.5 IVe that is the central tip of the northern constellation Cassiopeia’s “W” shape. It rotates so rapidly that it should have a significant equatorial bulge, and it is known to have a surrounding hot disk of spun off material. It is one of the brightest variable stars in our night sky, with light output that fluctuates between stellar magnitudes 1.6 and 3.0.
It is rotating so fast that it is very close to the star’s upper rotational speed limit, beyond which the star will break up. Until recently, its rotational speed and the size of its equatorial bulge had not been measured or accurately estimated, but both were thought to be very large. Now, an innovative astronomical measurement technique, stellar intensity interferometry (SII), has become available that can provide information on the size, shape, and orientation of bright rotating stars like γ Cassiopeiae, allowing astrophysicists to estimate their rotational speeds and equatorial bulges with good accuracy.
The old/new technique of SII was first introduced in 1954, over 70 years ago, by University of Sidney astronomer Robert Hanbury Brown (1916-2002) and his colleagues Richard Q. Twiss (1920-2005) and John Davis (1932-2010) and was first used for astronomical measurements in the late 1950s. The group constructed pairs of radio-wave or optical detectors mounted on rail cars, varied the separation and orientation of these, and electronically multiplied their detector output signals, producing in real time a composite signal “bump” that fell off with increasing detector separation. (Note that electronic signal multiplication is the rough equivalent of requiring coincident photon events from both detectors.) The measured composite bump width was inversely proportional to the angular width of the observed object along the axis defined by the detector-pair separation, allowing measurement of the star’s diameter along that axis.
SII is based on the quantum Hanbury-Brown-Twiss effect, in which wave intensities (e.g., photon detection events) rather than wave amplitudes can be made to interfere. Because the photons of light are fundamental spin-1 particles, they are “bosons” constrained by Bose-Einstein quantum statistics. Because of their bosonic behavior, photons of similar wavelength tend to cluster together in time-momentum space and attempt to pile into and occupy the same quantum states. In stars emitting these photons, the width of the clustering, in arrival angle and time, reflects the inverse width of the emitting star. Accurate measurement of the clustering of such photons from two or more detectors that record angular direction and arrival time of coincident photons therefore provides otherwise inaccessible information on the angular width, shape, and orientation of the target star.
At the peak of this observational work with SII in the 1960s, Hanbury Brown’s group constructed the Narrabri Stellar Intensity Interferometer in north-central New South Wales, Australia. With this optical instrument they measured the angular diameters of 32 stars in the spectral range O5 to F8 that had a brightness greater than about magnitude 2.6. However, the quality and precision of these SII measurements was limited by the use of the very basic electronic, optical, and data storage technology of the time, which was rather crude by contemporary standards. The rival technique of Michelson amplitude interferometry (making two waves interfere to show phase differences) was found to give similar but more accurate results on stellar sizes and could be used at much lower light levels. For such reasons, after actively operating in the 1960s and early 1970s, the astronomical observations with SII at Narrabri were halted. The Narrabri Facility came to the end of its operating life and was dismantled in 1974.
Since that time some 50 years ago, electronic and optical technologies have progressively improved, and by around 2008, astronomers began to have second thoughts about the potential use and value of intensity interferometry. Of particular interest in this context was the planned gamma-ray astronomy instrument VERITAS (Very Energetic Radiation Imaging Telescope Array System), which would use telescopes similar to those of the old Narrabri facility. VERITAS was to consist of four 12-meter (39-foot) segmented-mirror optical telescopes. Its construction began in 2000-2003 at the Whipple Observatory on Mt. Hopkins in Arizona, selected for its clear, dark skies through much of the year. The first of the four VERITAS telescopes began operation in 2004, and the full four-instrument array began observations in 2007.
The telescope complex was designed to explore the very high energy (VHE) gamma-ray sky at energies above about 100 GeV by detecting flashes of Cherenkov light, focused by the four telescopes on low-noise photomultiplier detectors. The instrument produced detectable electrical signals from a small number of Cherenkov photons that would be too faint for ordinary telescope cameras to detect. The telescopes were placed about 100 meters (328 feet) apart in a rectangular configuration, allowing reconstruction by triangulation of the shape and direction of a shower of Cherenkov photons from cosmic gamma rays interacting with gas atoms in the upper atmosphere.
When astrophysicists first began making plans for construction of the VERITAS instrument, its similarity to the old Narrabri Stellar Intensity Interferometer in Australia was noticed. The possibility of also using VERITAS for SII was investigated, revealing that it had the potential to become a very powerful instrument for that purpose.
In its current operation, for about 5-6 days in any lunar month the Moon reaches its brightest phase, and scattered moonlight creates a photon background that is too intense to permit VERITAS to carry out its main mission of detecting the faint light from cosmic gamma rays. During these periods, the VERITAS system can be pointed at a bright star and used to produce an information-rich pattern of photon-photon correlations through SII.
(We note as an aside that in the very different research area of ultra-relativistic heavy ion physics at CERN and Brookhaven, intensity interferometry is done with pi mesons, which are spin-0 bosons also subject to Bose-Einstein quantum statistics. This technique has been used by the author and others to study the geometry and evolution of the quark-gluon fireball that is produced in very high energy nucleus-nucleus collisions.)
This brings us to the recently reported SII measurements performed with VERITAS and targeting γ Cassiopeiae. In 2023 and 2024, on fourteen nights when the moonlight background was too bright to permit use of VERITAS for cosmic gamma ray measurements, the four telescopes were aimed at γ Cassiopeiae, which, because of its spin and equatorial bulge, appears in the sky as an infinitesimal ellipse that is much too small for even the best optical telescopes to resolve. But VERITAS can “see” that elliptical shape.
Between one and six selected pairs of the four telescopes, chosen for lowest noise, provided an average per day of about three hours of observation time, for a total of 38.26 hours of SII observations recording 2-detector correlated detections. As the nights progressed and the target star moved across the dark sky, the line of observation of the telescope pairs rotated over the target, sampling its width in varying directions. This allowed the measurement not only of the average angular width of the target, but its shape profile and ellipticity, reflecting the expected equatorial bulge. Further, the systematic relative intensities of the coincident wavelengths of light permitted the extraction of the surface temperatures at the equator and at the poles of the star.
When the profile of γ Cassiopeiae was modeled as a uniform ellipse, the VERITAS analysis found that the angular width of the ellipse at its equator was 0.60 milli-arc-seconds, the pole-to-pole angular width was 78% of that value, and that the system was rotating at about 97.7% of the critical spin velocity for stellar breakup.
These results were used with standard solar modeling to describe in detail the characteristics of γ Cassiopeiae. It has a mass of 15 ± 2 solar masses, an equatorial radius of 10.9 ± 0.7 solar radii, and a polar radius of 8.5 ± 0.4 solar radii. The effective temperature (temperature of an ideal black body with the same light emission) at the poles is about 27,250 K, and the effective temperature at its equator is about 16,650 K. (For comparison, the effective temperature of our Sun is 5,778 K.) The linear velocity of matter on γ Cassiopeiae’s equator is 450 ± 20 kilometers per second, implying that the star makes one complete rotation about every 0.89 days.
These are the very first astronomical SII measurements of the detailed shape of an oblate spinning star and of its temperature profile. It demonstrates a new kind of astronomical probing of stellar structure with unprecedented resolution. The data from such observation scan be digitally recorded as “events”, with photon energy and arrival time recorded for each individual telescope, and then combined later by pairing recorded events from individual telescope/detector systems. This allows the use of remote supercomputers for the complex data analysis and modeling.
The participant detectors may be close or widely separated (as long as they share the same master timing clock). This freedom makes possible a variety of detector configurations, including interferometry with three or more detectors, very wide baseline interferometry, and heuristic after-the-fact analysis of a star of new interest, using data stored some time ago. This technology for probing the detailed shapes of bright objects suggests the possibility of new wonders coming from stellar intensity interferometry.
Watch this AV column for future SII developments.
References:
R. Hanbury Brown and R. Q. Twiss, “A new type of interferometer for use in radio astronomy,” Phil. Mag. 45, 663 (1954); doi10.1080/14786440708520475.
M. Daniel, W. J. de Wit, D. Dravins, D. Kieda, S. LeBohec, P. Nunez, and E. Ribak, “Towards the Intensity Interferometry Stellar Imaging System,” preprint (2009); arXiv:0906.3276 [astro-ph.IM].
A. Archer, et al., “Measurement of the Photosphere Oblateness of γ Cassiopeiae via Stellar Intensity Interferometry with the VERITAS Observatory,” The Astrophysical Journal, 995:2, 191-206 (2025); doi10.3847/1538-4357/ae0744.
Hard SF Novels: John’s new 3rd hard SF novel, Fermi’s Question, and its prequel, Einstein’s Bridge, are available as eBooks from Baen Books at: https://www.baen.com/einstein-s-bridge.html. His first hard SF novel Twistor is available online from Amazon.
Non-Fiction Books: John’s new book How to Live Much Longer: The Mitochondrial DNA Connection (Springer Copernicus, May 2026) can be ordered online from Amazon or Springer. His book on his transactional interpretation of QM, The Quantum Handshake: Entanglement, Nonlocality, and Transactions, (Springer, January 2016) is also available from Amazon or Springer.
Alternate View Columns Online: Electronic reprints of 243 or more of “The Alternate View” columns written by John G. Cramer and previously published in Analog are currently available online at: http://www.npl.washington.edu/av.