Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 316 / 2 / vi

Table of contents
- Solution vi

Solution

In a steady axisymmetric outflow, mass conservation makes

2 π r Σ (r) v_{r} (r)

independent of

r

. The steady radial dust outflow therefore has

Σ (r) \propto \frac{1}{r v _{r}} \propto \frac{1}{( x - 1 ) [( 2 β - 1 ) x + 1 ]}, x = \frac{r}{a _{p}} .

It has an integrable

(r - a_{p})^{- 1/2}

pile-up just outside the source ring, where the radial speed starts from zero, and approaches

S i g ma \propto r^{- 1}

at large radius.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version