What the study found
The study found that self-gravitating bosonic configurations in the nonrelativistic regime have a critical central density and a maximum particle number beyond which no stationary solutions are found. It also found that radially excited configurations that satisfy the virial relation are expected to be metastable.
Why the authors say this matters
The authors state that the critical particle number can be used to estimate the maximum stable mass and radius. For axion-like bosons, the study indicates configurations with masses of tens of Earth masses and radii on the order of meters.
What the researchers tested
The researchers numerically solved the nonlinear Gross–Pitaevskii–Poisson (GPP) equations for self-gravitating bosonic configurations in the nonrelativistic regime. They used a coordinate transformation to write the equations in dimensionless form, computed sequences of stationary solutions including ground and radially excited states, and identified bifurcation points between them.
What worked and what didn't
The virial relation worked as a diagnostic condition for equilibrium and led to the determination of a critical central density and a maximum particle number. Excited configurations satisfying the virial relation were found to violate stability conditions from radial perturbation analyses, so they are expected to be metastable. No stationary solutions were found above the maximum particle number.
What to keep in mind
The abstract does not describe additional limitations beyond the nonrelativistic regime and the specific equations studied. The numerical results are presented for the model used here, and the axion-like boson mass example is given for 10−5 eV.
Key points
- A critical central density and a maximum particle number were identified for self-gravitating bosonic configurations.
- No stationary solutions were found above the maximum particle number.
- Radially excited configurations satisfying the virial relation are expected to be metastable.
- The virial relation was used as a diagnostic condition for equilibrium.
- For axion-like bosons with mass 10−5 eV, the estimated configurations have masses of tens of Earth masses and meter-scale radii.
Disclosure
- Research title:
- Self-gravitating bosonic configurations have a stability limit
- Authors:
- Gilbert Reinisch, J. A. de Freitas Pacheco
- Institutions:
- Observatoire de la Côte d’Azur
- Publication date:
- 2026-04-03
- OpenAlex record:
- View
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