English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We revisit the Polish doughnut model of accretion disks providing acomprehensive analytical description of the Polish doughnut structure. Wedescribe a perfect fluid circularly orbiting around a Schwarzschild black hole,source of the gravitational field, by the effective potential approach for theexact gravitational and centrifugal effects. This analysis leads to a detailed,analytical description of the accretion disk, its toroidal surface, thethickness, the distance from the source. We determine the variation of thesefeatures with the effective potential and the fluid angular momentum. Manyanalytical formulas are given. In particular it turns out that the distancefrom the source of the inner surface of the torus increases with increasingfluid angular momentum but decreases with increasing energy function defined asthe value of the effective potential for that momentum. The location of torusmaximum thickness moves towards the external regions of the surface withincreasing angular momentum, until it reaches a maximum an then decreases.Assuming a polytropic equation of state we investigate some specific cases.

On the Polish doughnut accretion disk via the effective potential approach