A synthetic photosphere model for γCas. See figure 13 below for more details.
Reference: A. Archer et al. (The VERITAS Collaboration), ApJ. 995, 191 (2025)
Full text version
ArXiv: ArXiV: 2506.15027
Contacts: Dave Kieda
We use the stellar intensity interferometry system implemented with the Very Energetic Radiation Imaging Telescope Array System (VERITAS) at Fred Lawrence Whipple Observatory (FLWO) as a light collector to obtain measurements of the rapid rotator star γ Cassiopeiae, at a wavelength of 416 nm. Using data from baselines sampling different position angles, we extract the size, oblateness, and projected orientation of the photosphere. Fitting the data with a uniform ellipse model yields a minor-axis angular diameter of 0.43±0.02 mas, a major-to-minor-radius ratio of 1.28±0.04, and a position angle of 116◦ ± 5 ◦ for the axis of rotation. A rapidly-rotating stellar atmosphere model that includes limb and gravity darkening describes the data well with a fitted angular diameter of 0.604+0.041−0.034 mas corresponding to an equatorial radius of 10.9+0.8−0.6 R⊙, a rotational velocity with a 1 σ lower limit at 97.7% that of breakup velocity, and a position angle of 114.7+6.4−5.7 degrees. These parameters are consistent with Hα line spectroscopy and infrared-wavelength Michelson interferometric measurements of the star’s decretion disk. This is the first measurement of an oblate photosphere using intensity interferometry.
FITS files: N/A
Figures from paper (click to get full size image):
Figure 1: Baseline coverage of the six telescope pairs in the u−v plane for the data tabulated in Table B1. Points reflect the weighted-mean position of each ∼hour-long run. The curves are point-reflected about the origin.
Figure 2: The correlation function as a function of relative time and time-in-run, for a typical 2 hour run. While the correlogram is constructed every 2 seconds, the vertical axis has been binned more coarsely in this figure, to reduce statistical noise and make the correlation more visible. The diagonal feature is the correlation peak proportional to the squared visibility that changes during the run due to the variation in the optical path delay between the two telescopes. This correlation function is from pair T2T4, taken at 03:37 on UTC 2023-12-26.
Figure 3: An example of a tracking correction in T2. A large negative ADC (analog-to-digital converter) value corresponds to intense light incident on the PMT. Due to tracking limitations of the array, at about 200 sec into the run, the star’s image becomes slightly less centered on the PMT. At 400 sec into the run, the operator adjusted the tracking, causing the telescope to briefly stop tracking the star altogether, and the current drops sharply. When the tracking is corrected, the current is stronger. The frames around the spike are removed from the correlogram before processing further.
Figure 4: A portion of the power spectrum for T1, as a function of frequency and time in run. Short, sporadic bursts from the on-site radio repeater produce strong signals at 79.4 MHz (an alias of the 171 MHz radio signal). Frames containing these bursts are removed from the correlogram before further processing.
Figure 5: The OPD-corrected projection of the correlation function as a function of relative time, defined in equation 3. The correlation is quantified by the integral of a Gaussian peak fitted near relative time ≈ 0. This correlation function is from pair T2T3, taken at 02:31 on UTC 2024-02-19. Before further analysis, the uncertainty on the area of the Gaussian fit (A) is replaced as discussed in section 3.5.
Figure 6: Distribution of areas from fits to background noise in the region of relative time far from the peak, for all runs. The gray band on fig. 7 corresponds to the red lines at ±3.58 fs, which are ±2σ from the mean of this distribution. This measures the spread of areas that may be found when fitting to background noise alone, and includes 95% of the data in the distribution.
Figure 7: The area of the fitted correlation peak, proportional to the squared visibility, as a function of the magnitude of the baseline. The curve represents the best fit with a uniform disk model. Points in gray, excluded from the fit, are below the threshold where the signal/noise is too low to reliably detect peaks, as discussed in section 3.6. This threshold is marked with a gray shaded box.
Figure 8: The center panel shows the u − v midpoint of all runs and telescope pairs, with different color shaded regions indicating angular slices in the u − v plane. For data within each of the individual slices, the surrounding panels of corresponding colors show the squared visibility as a function of the length of the baseline. Each slice is fit with a uniform disk model, to extract the effective 1-dimensional radius of a given angular projection. The zero-baseline squared visibility is constrained to be the same for all slices, with a value from the uniform ellipse fit of figure 10. Identical light shaded regions in each panel show the range of fits between the most extreme values of the 8 individual slices; these are drawn to guide the eye, making small differences between panels more apparent. A datapoint at large baseline in slice 5 is drawn in red and discussed in the text.
Figure 9: The uniform-disk radius from fitting A versus baseline to datapoints in different slices in the u − v plane (see figure 8), as a function of the average angle of the slice.
Figure 10: For each telescope pair, the normalized visibility is shown as a function of local hour angle. Curves represent the best fit with a uniform ellipse model. The singular T1T4 data point is shown as a red square, because it passes all quality cuts yet we suspect it may be a fit to random background fluctuations, like those discussed in section 3.6. It is included in the fit shown. Fits are reported with and without this point in table 2.
Figure 11: Using the same data shown in figure 10, the best fit using a Roche-von Zepiel models for a rapidly rotating star.
Figure 12: Best fit parameter distributions for the Roche-von Zeipel stellar model from fitting 1000 bootstrap samples with replacement from Table B1. The dashed lines show the 1σ lower bound error and the 1σ upper bound of each parameter: θeq, the equatorial angular diameter; Ω/Ωc, fraction of the critical angular rotation rate; ϕ ∗ position angle of the visible rotation axis; and CRvZ, the proportionality constant between the model squared visibilities and measured correlation peak integrals.
Figure 13: A synthetic photosphere for γ Cas with θeq=0.60 mas, Ω/Ωcrit =0.9888 and ϕ∗ = 114◦ consistent with the best fit values to the VERITAS interferometry.
Figure 14: A comparison of two Roche-von Zeipel synthetic spectral energy distributions (SEDs) to archival absolute spectrophotometry of γ Cas between 1200 ˚A and 8170 ˚A. Data for wavelengths beyond 3200 ˚A are from Burnashev (1985). International Ultraviolet Explorer (IUE) data have been rebinned from high dispersion to low dispersion (González-Riestra et al. 2000) and extracted from the IUE Newly-Extracted Spectra (INES) data archive. The faster spinning model (Ω/Ωc = 0.9999) is more gravity darkened and requires a larger polar temperature at the same equatorial angular diameter to match the spectrophotometry.
Figure 15: A normalized, high-resolution spectrum of γ Cas in the VSII bandpass from the ELODIE archive (Moultaka et al. 2004, observation 20030816/0030, in black) and a normalized model spectrum (in blue) from the same model Roche-von Zeipel that best fits the VERITAS data in Table B1. The rotationally broadened Hδ line at 4100 ˚A is filled in the emission from the disk surrounding γ Cas. The disk is not included in our model.
