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= (V2)1/2 K πGOO ' Consider the dispersion relation of a linear spiral density wave perturbation (equation 4.45 in Chapter 3 of the lecture notes). The Toomre's parameter is defined as Q where (V2) 1/2 is the root-mean-square turbulent plus thermal velocity, к the epicyclic frequency, σ the unperturbed surface density of the disc and G the gravitational constant. For Q = 1/√2, show that the spiral pattern is unstable if К (√2-1) (V²² ) 1/2 < |k| < (√√2+1) where k is the wavenumber of the perturbation. К (V+2)1/2

= (V2)1/2 K πGOO ' Consider the dispersion relation of a linear spiral density wave perturbation (equation 4.45 in Chapter 3 of the lecture notes). The Toomre's parameter is defined as Q where (V2) 1/2 is the root-mean-square turbulent plus thermal velocity, к the epicyclic frequency, σ the unperturbed surface density of the disc and G the gravitational constant. For Q = 1/√2, show that the spiral pattern is unstable if К (√2-1) (V²² ) 1/2 < |k| < (√√2+1) where k is the wavenumber of the perturbation. К (V+2)1/2

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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= (V2)1/2 K πGOO ' Consider the dispersion relation of a linear spiral density wave perturbation (equation 4.45 in Chapter 3 of the lecture notes). The Toomre's parameter is defined as Q where (V2) 1/2 is the root-mean-square turbulent plus thermal velocity, к the epicyclic frequency, σ the unperturbed surface density of the disc and G the gravitational constant. For Q = 1/√2, show that the spiral pattern is unstable if К (√2-1) (V²² ) 1/2 < |k| < (√√2+1) where k is the wavenumber of the perturbation. К (V+2)1/2
Transcribed Image Text:= (V2)1/2 K πGOO ' Consider the dispersion relation of a linear spiral density wave perturbation (equation 4.45 in Chapter 3 of the lecture notes). The Toomre's parameter is defined as Q where (V2) 1/2 is the root-mean-square turbulent plus thermal velocity, к the epicyclic frequency, σ the unperturbed surface density of the disc and G the gravitational constant. For Q = 1/√2, show that the spiral pattern is unstable if К (√2-1) (V²² ) 1/2 < |k| < (√√2+1) where k is the wavenumber of the perturbation. К (V+2)1/2
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