Boson Star Mass–Radius Calculator

Boson-star physical background

Boson stars are hypothetical compact objects made of bosons occupying a single macroscopic quantum state, similar in spirit to a Bose–Einstein condensate. They arise in models of dark matter, including ultralight axion-like particles and scalar-field dark matter. Gravity tends to compress a boson-star configuration, while quantum or interaction-induced pressure can provide support.

Boson-star structure is often studied with Einstein–Klein–Gordon equations; dilute weak-field treatments can instead use a coupled Gross–Pitaevskii–Poisson description. This page does not solve either system numerically. It applies fixed scaling expressions to provide a rapid, branch-dependent mass–radius estimate from the values entered in the form.

Boson-star formulas used in the calculator

Noninteracting boson-star branch

For the calculator’s noninteracting boson-star branch, the maximum stable mass scales with the Planck mass M_Pl and particle mass m as

and the corresponding radius is represented as

In the JavaScript implementation, the entered mass is multiplied by 1.78266192 × 10⁻³⁶ before it appears in the denominators, while M_Pl is set to 2.176 × 10⁻⁸. The displayed mass is then divided by the solar-mass constant and the displayed radius by 1,000. Thus, on this branch, reducing the entered boson mass raises both outputs produced by the code.

Repulsively self-interacting boson-star branch

For a positive scattering length, this boson-star calculator switches to a self-interacting expression in which a computed interaction factor λ multiplies the mass scaling:

and the radius scaling is

In this page’s code, λ is formed directly from the entered values as

with a_s first converted from femtometers to metres and m retained as the entered numerical value in eV. The code then uses the square root of that quantity and the squared mass conversion in its self-interacting denominators. A positive scattering length can therefore change the displayed values sharply, but the result should be read as this implementation’s scaling output rather than as a unit-complete field-theory prediction.

Interpreting boson-star calculator outputs

When you enter a boson mass and scattering length, this boson-star calculator converts the scattering length to metres and then selects its branch:

• a_s = 0: uses the noninteracting expressions to return the maximum-mass and radius outputs.
• a_s > 0: computes λ from the scattering length and entered mass, then applies the self-interacting expressions.

The boson-star mass output is presented in M_☉ (solar masses) and the radius in km. The scientific notation is especially important here: changing the mass input by several orders of magnitude, or changing from zero to a positive scattering length, can move the displayed result by many orders of magnitude.

• Compare like with like: hold the boson mass fixed when isolating the effect of a positive scattering length.
• Use a zero scattering length when you specifically want the noninteracting code path.
• Treat extreme radii or masses as a prompt to inspect the input units and the limits of the implemented scaling, not as a standalone compact-object classification.

Worked example: the calculator’s default boson-star inputs

This boson-star worked example uses the form’s default noninteracting inputs:

• Boson mass: m = 1 × 10⁻¹⁰ eV
• Scattering length: a_s = 0 fm

Entering those values follows the noninteracting branch. From the constants and conversions in the JavaScript, it produces approximately 8.45 × 10⁻¹ M_☉ and 7.36 × 10³⁵ km. The exceptionally large radius is a direct consequence of the expression implemented on this page, so it should not be relabeled as a neutron-star-scale prediction.

To examine the other boson-star branch, keep the mass fixed and enter a positive scattering length. The calculation will form λ using the converted metre value of the scattering length and the entered mass, then use the self-interacting equations. Compare the two outputs as a sensitivity check on the code paths, while remembering that this form does not establish stability, formation history, or observational viability.

Boson-star comparison with astrophysical object classes

This comparison places the boson-star calculator’s output units beside familiar astrophysical categories, but it does not convert a scaling result into an identification of an actual object. Check both reported quantities, the selected interaction branch, and the assumptions behind the input parameters before making such a comparison.

Boson-star scaling assumptions and limitations

The boson-star scaling relations implemented here are intentionally simple and should be read as order-of-magnitude code outputs, not precision predictions. Key limitations include:

• Idealized, isolated, spherically symmetric configurations: rotation, magnetic fields, and environmental effects such as surrounding baryons or tidal fields are neglected.
• Single bosonic species: the calculation uses one scalar-field mass m and one contact-interaction input, the scattering length a_s.
• Two hard branches: zero scattering length selects the noninteracting expression, while every positive scattering length selects the self-interacting expression; the page does not model a smooth crossover.
• Implementation-level units: the positive-scattering-length branch combines a scattering length converted to metres with the numerical mass entered in eV when forming λ. Consequently, numerical output alone should not be treated as a unit-consistent physical prediction.
• No stability or formation history: the calculator does not test dynamical stability, formation channels, cosmological evolution, or compatibility with observations.

For quantitative boson-star work, especially in relativistic or strongly self-gravitating regimes, use a unit-consistent model and solve the relevant field equations numerically for the chosen potential. This page is best used to inspect the stated mass–radius scaling branches and to build intuition about how its two form inputs affect them.

How to use: practical boson-star form tips

To use this boson-star mass–radius form, enter a positive boson mass in eV and choose the scattering length that selects the branch you want to inspect.

• Use the boson mass field to compare how the calculator’s displayed scalings respond to different candidate masses.
• Set the scattering length to 0 to use the noninteracting branch; use a positive value to activate the self-interacting branch.
• If the calculator returns extremely large or small values, verify the eV and fm inputs and treat the result as an indicative implementation trend rather than a precise astrophysical measurement.

Intuitive picture: boson-star mass and radius trends

For this boson-star calculator, the clearest way to read the parameter trends is to follow the two code branches:

• Lower entered boson masses increase both outputs on the noninteracting branch because the mass conversion appears in the denominator of both expressions.
• Positive scattering lengths activate the self-interacting branch, where the square root of λ contributes to both displayed values.
• Branch selection matters: moving from exactly zero to any positive scattering length changes the formula, so it is more informative to compare calculations within a branch before drawing broader conclusions.