 Density positivity for an axisymmetric logarithmic potential

ID: density-positivity-for-an-axisymmetric-logarithmic-potential

ρ = \frac{V ^{2}}{4 π G q ^{2}} \frac{R ^{2} + ( 2 - q ^{- 2} ) z ^{2}}{( R ^{2} + q ^{- 2} z ^{2} ) ^{2}} .

For

V > 0

, nonnegative mass density away from the origin is equivalent to

q^{2} \geq 1/2

. Strict positivity requires

q^{2} > 1/2

. This condition does not by itself guarantee a nonnegative galactic distribution function.

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