# Linear limb darkening coefficient, u

I was wondering if anyone knew of any resources to understand the linear limb darkening coefficient, $u$. That is to say, how the $\theta$-dependent coefficient $u$ (or sometimes $b_{\nu}$) varies with wavelength and with stellar effective temperature.

I've looked at a number of sources, such as Schwarzschild (1906), Milne (1921) and my own lecture notes and others, but nothing on this coefficient? Does anyone know where to even start looking for information of the properties of $u$?

• Could you be a bit more specific? I'm not familiar with this coefficient, but if you properly define u or b_{\nu} I may be able to help. Commented Nov 1, 2015 at 13:28
• Have you had any exposure to radiative transfer? Commented Nov 1, 2015 at 14:02
• Yes, of course. But it has been a while, but the books that exposed me to it say nothing about this coefficient - though I'm sure it's defined implicitly. Commented Nov 1, 2015 at 17:03
• Have you seen this link astro.keele.ac.uk/jkt/codes/jktld.html Commented Nov 2, 2015 at 19:02
• @JamesKilfiger I've asked a related question
– uhoh
Commented May 20, 2016 at 10:39

A limb darkening law is specified in terms of the cosine of an angle $$\theta$$ between the line of sight to the observer and a line from the centre of the star to the point on the stellar surface considered.
The simplest limb darkening law is where one assumes that the dependence on $$\cos \theta$$ is linear - the so-called linear limb darkening law. It is usually written as $$\frac{I_\theta}{I_0} = 1 - u\left(1 - \cos\theta\right)\ ,$$ where $$I_\theta$$ is the observed intensity at (a circle of) points defined by the angle $$\theta$$, $$I_0$$ is the intensity at the centre of the disc and $$u$$ is the linear limb darkening coefficient.