\frac{d p}{d z} = - ρ Ω_{z}^{2} z .

Define vertically integrated pressure and the density-weighted disk scale height by

P = \int_{- \infty}^{\infty} p d z, H^{2} = \frac{1}{Σ} \int_{- \infty}^{\infty} ρ z^{2} d z .

Multiply the hydrostatic equation by

z

and integrate. Since

z p \to 0

at both boundaries, integration by parts gives

- P = - Ω_{z}^{2} Σ H^{2} .

Therefore

P = Σ H^{2} Ω_{z}^{2} .

 Ancestors (10)

 Discussion (0)

There are no discussions about this article yet.

There are currently no matching articles.