I always wonder when do they stop considering the outer layers part of the star and not relatively dense solar wind soup. Nobody says Earth has 7000km radius, even tho there's traces of exosphere past 500km.
I always wonder when do they stop considering the outer layers part of the star and not relatively dense solar wind soup. Nobody says Earth has 7000km radius, even tho there's traces of exosphere past 500km.
The outer boundary is the point where a photon has a ~50% chance of escaping without encountering another particle.
Do you have a source? I'd love to read more. :)
Amateur stargazer's understanding:
Depending what kind of reading material you're looking for (e.g. high level details or mathematically/jargon dense papers) look for things discussing "Rosseland optical depth" and "grey atmosphere approximation".
At a high level, the common convention is to define the radius by finding where the optical depth is 2/3 when using Rosselands clever way of calculating a weighted mean of the opacity from that layer in the star to space across different wavelengths of light. 2/3 being a clever derivation from Eddington where, in an idealized model of a star, that's when the actual temperature of the star should equal its blackbody equivalent temperature.
Pedantically, this distance to the point of equality is an ever so slightly different value than the "distance from the center where there is a 50% chance a photon traveling directly outward will escape the star without another interaction" rule of thumb (in the same idealized grey model). Practically, that the difference is so small is why it's a fantastic rule of thumb explanation.
I'd recommend Carroll & Ostlie's Introduction to Modern Astrophysics, though it requires some basic calculus and physics.
The radius is based on visual observation. We have good theories and models about what's happening inside the star. We are quite sure that it's mostly empty space inside the radius. But that's not a good enough reason to say that the star's radius is anything other than what we see through our telescope.
Importantly, this works for stars relatively close to us (the farthest I can find is 16,000 light years for one hyper giant) but the majority of the stars catalogued in even our own galaxy have only been assigned a radius via taking the temperature (via color) and luminosity.