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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We provide an approximate analytical expression of the mass-radius relationof a Newtonian self-gravitating Bose-Einstein condensate (BEC) with short-rangeinteractions described by the Gross-Pitaevskii-Poisson system. These equationsmodel astrophysical objects such as boson stars and, presumably, dark mattergalactic halos. Our study connects the non-interacting case studied by Ruffini& Bonazzola (1969) to the Thomas-Fermi limit studied by B\"ohmer & Harko(2007). For repulsive short-range interactions (positive scattering lengths),there exists configurations of arbitrary mass but their radius is always largerthan a minimum value. For attractive short-range interactions (negativescattering lengths), equilibrium configurations only exist below a maximummass. Above that mass, the system is expected to collapse and form a blackhole. We also study the radius versus scattering length relation for a givenmass. We find that stable configurations only exist above a (negative) minimumscattering length. Our approximate analytical solution, based on a Gaussianansatz, provides a very good agreement with the exact solution obtained bynumerically solving a nonlinear differential equation representing hydrostaticequilibrium. Our treatment is, however, easier to handle and permits to studythe stability problem, and derive an analytical expression of the pulsationperiod, by developing an analogy with a simple mechanical problem.

Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: I. Analytical results