Stellar size measurements
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Direct Measurement Techniques for Stellar Size
Measuring the sizes of stars is challenging because, except for the Sun, stars appear as point sources even in large telescopes due to atmospheric blurring. Early breakthroughs came from the use of two-slit interference, pioneered by Fizeau and implemented by Michelson, who made the first direct measurement of a star’s angular diameter using fringe visibility techniques. This method was later confirmed and became foundational for optical interferometry in astronomy, allowing for direct angular size measurements of stars like Betelgeuse 1.
Modern advancements include the use of stellar intensity interferometry, which can be applied to large telescope arrays such as Cherenkov telescopes. These systems can achieve high accuracy in reconstructing stellar sizes by fitting visibility curves, with optimal results obtained when the zero-baseline correlation is measured. Analytical expressions now exist to estimate the achievable accuracy in advance, aiding in observation planning 2. Additionally, the VERITAS Cherenkov telescopes have achieved unprecedented angular resolution (≤0.1 milliarcseconds) in direct measurements using stellar occultations, surpassing previous methods like lunar occultation 6.
Indirect Methods and Predictive Models for Stellar Angular Diameters
Because direct measurements are limited to a small number of stars, indirect methods are widely used. Predictive models based on broadband photometry (such as K, V, or B bands) can estimate angular diameters with high accuracy, especially for main-sequence stars (error ~2.2%), and somewhat larger errors for giants and evolved stars 3. More recent approaches use relationships between measured angular diameters and photometric data, introducing concepts like pseudomagnitude and differential surface brightness (DSB). These methods, combined with extensive catalogs of measured diameters, allow for statistical errors as low as 1% when the spectral type and photometry are known 4.
Catalogs and Large-Scale Surveys of Stellar Sizes
Direct measurements using optical interferometry and lunar occultations have yielded about 600 apparent star diameters, but new catalogs now provide estimated diameters for hundreds of thousands of stars using indirect methods 4. Historical intensity interferometry programs have also provided angular diameters for dozens of stars across a range of spectral types 5. Long-baseline optical interferometry, such as with the CHARA Array, continues to provide precise angular diameters for bright stars, which, when combined with parallax and other data, yield accurate linear radii and effective temperatures 10.
Specialized Measurements: Stellar Coronae and Galaxy Sizes
For stellar X-ray coronae, direct spatial measurements are not possible, but scaling laws and X-ray line diagnostics allow for estimates of coronal sizes based on temperature and density. These methods suggest that the emitting regions occupy a small fraction of the stellar surface, with filling factors up to 0.1 9.
In the context of galaxies, new physically motivated definitions of size based on stellar mass density contours have reduced the scatter in the mass–size relation, providing more precise measurements of galaxy sizes and insights into their growth and structure 8. For star-forming galaxies, size measurements across different wavelengths reveal that size growth is primarily governed by stellar mass, with little dependence on redshift or environment 7.
Conclusion
Stellar size measurements have evolved from pioneering direct techniques like optical interferometry to sophisticated indirect methods using photometric data and statistical modeling. Direct measurements remain limited to a select group of stars, but indirect methods and large catalogs now enable accurate size estimates for vast numbers of stars. Advances in instrumentation, data analysis, and theoretical modeling continue to improve the precision and scope of stellar size measurements, deepening our understanding of stellar and galactic structure and evolution 12345678+2 MORE.
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