Lineprofiles: better handling of initial guess in root finder about gradus.jl HOT 2 CLOSED

I am able to reproduce. These sorts of precision errors in the root finder normally mean the extrema of the bracketing interval which sets up the precision tracer missed the disc. This often happens when roughly $r_\text{e} \geq \frac{1}{2} r_\text{d}$.

A simple fix is to set, e.g.

d = GeometricThinDisc(0.0, 800.0, π / 2)

But I'll leave this issue open with the addition that

• This should either generate a more friendly error message; or
• Use a better heuristic when calculating the bracketing intervals for continuous discs / find appropriate behaviour when the disc is sparse.

For the latter, the offending line is

which could probably be safely set to d.outer_radius + Δ, where Δ is just a safety offset. In the past this had to scale to help the root finder converge, but we're using a better default algorithm now, so we might be able to get away with just using the same maximum offset for each emission radius.

from gradus.jl.

Fixed in #107

from gradus.jl.