Measuring the Solar Radius

Measuring the Solar Radius during Total Solar Eclipses

Total solar eclipses offer unique opportunities to measure the value of the solar radius, a fundamental astronomical quantity, and to investigate its variability through time. Those moments when the Moon is about to fully cover the Sun provide an unparalleled view of the light emitted by the lowermost layers of the solar atmosphere, a light hidden by the Sun’s glare at all other time. By analysing its spectrum (the flash spectrum), the solar radius can be estimated.

Context

The solar radius is a fundamental astronomical quantity. However, determining its most suitable value for accurately predicting solar eclipses is not straightforward because the Sun is not a solid object. We are specifically interested in identifying the value of the solar radius that, when used in an accurate eclipse computational model, produces the most accurate predictions for second and third contact times – the moments when the Sun’s photosphere is fully covered and then begins to reappear

The widely used “standard” value of 959.63 arcseconds for the solar radius at one astronomical unit originates from a 1891 publication and has been used for over a century. However, recent research and observations suggest that other values might be more appropriate. Knowing the precise boundaries of the umbral shadow path is crucial, especially for observers located very near the edge, as small differences in predictions can significantly impact the visible eclipse phenomenon or the predicted duration of totality. The accuracy of local eclipse circumstances is a direct function of the accuracy of the inputs and the computational model used. While most other inputs for eclipse calculations are known with a high degree of accuracy, the specific value of the solar radius for eclipse computations is a key area of research. Total solar eclipses offer unique opportunities to make measurements related to this value

Method

Our approach to estimating the eclipse solar radius is based on observing total solar eclipses from locations very close to the edge of the path of totality. At these liminal sites, the relative motion between the solar and lunar limbs is almost tangential. This tangential motion makes the duration of totality (or coronality) extremely sensitive to the value of the solar radius used in calculations. Moving even a short distance from the edge can dramatically change the predicted duration of totality

A key technique involves observing the flash spectrum. The flash spectrum is visible for brief moments at the start and end of totality and allows us to geometrically separate light originating from different layers of the Sun’s atmosphere, such as the photosphere, chromosphere, and corona. We look for the vanishing and reappearance of the photospheric continuum in the flash spectrum, which defines second and third contact

We use timestamped video recordings of the flash spectrum, captured using a setup involving a diffraction grating and a camera, coupled with a source of accurate UTC time to time stamp each frame. By analysing these videos, we extract light curves that show the change in intensity from the last Baily’s beads before second contact and the first Baily’s beads after third contact. These experimental light curves are then compared to simulations that model the changing light intensity based on the relative movement of the solar and lunar limbs, accounting for the complex topography of the lunar limb and the solar limb darkening effect. Since the value of the solar radius value is intrinsically embedded into the simulation model, we can determine the best-fit solar radius by finding which simulation most closely matches our experimental light curves

Goal

Our primary goal is to determine the most accurate value for the solar radius that should be used in precise eclipse computational models for predicting eclipse contact times. By obtaining and analyzing observations, particularly flash spectrum videos from the edge of the totality path, we aim to refine this value

Based on observations we collected at past eclipses, we derived an eclipse solar radius equal to 959.95 ±0.05 arcseconds. This value is slightly larger than the canonical solar radius (i.e. 959.63 arcseconds). Adopting this optimised value in eclipse computations helps improving the accuracy of eclipse path maps and predictions

Our research strives for ongoing experimental validation to further refine the measurement. aiming to contribute to a more precise understanding and more informed solar eclipses observations.