Homework 6 Solutions

Evaluate 0 and plot the density on a logarithmic

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: e integral is simple power law for xα+1, which yields: MD 2 2π Σ 0 R 0 (Rout /R0 )α+2 − (Rin /R0 )α+2 = α+2 moving terms over and pulling out the (Rout/R0)α+2 factor in the brackets: Σ0 = MD (α + 2) 2 2π R 0 α+2 R0 Rout α+2 −1 Rin Rout 1− switching out two powers of R0/Rout will give you the expression above. (c) [10 pts] Combine these expressions to obtain a single expression for the density of the disk as a function of r and z: ρ(r, z ) = ρ0 r Rout α−β − e z2 H ( r )2 and derive an expression for the constant ρ0. This is just a matter of combining equations: MD (α + 2) ρ(r, 0) = 3/2 2 2 π R 0 H0 R0 Rout α+2 1− Rin Rout α+2 −1 r R0 α−β Putting this into the form above, it’s clear that MD (α + 2) ρ0 = 2 2 π 3 / 2 R 0 H0 R0 Rout α+2 1− Rin Rout α+2 −1 (d) [10 pts] Consider a disk with total mass 0.1 M¤, Rin = 0.1 AU, Rout = 300 AU, α =  ­1.5, β = 0.25 and H(Rout) = 300 AU (this is known as a “bow tie” disk) around a star of mass...
View Full Document

This document was uploaded on 02/26/2014 for the course PHYS 160 at UCSD.

Ask a homework question - tutors are online