GitHub

Notation & outputs

This page explains the most common outputs produced by the solver and how to interpret them.

Throughout the docs we use the term model to refer to the object returned by solve_structure(...) (or produced by the simulation helpers). That model stores derived results in two places:

  • model.quantities: scalar “headline” results (mass, radius, etc.)
  • model.derivatives: scalar sensitivities / response coefficients (useful for parameter estimation and post-processing)

The exact set of keys can depend on the gravity regime/model. The lists below describe the current DEFp implementation (see DEFpGravity).

Conventions

  • Units:
    • Internal integration is done in CGS-like units for microphysics, with standard conversions for plotting/reporting.
    • Unless stated otherwise, masses are in grams (or in solar masses when explicitly converted), radii are in cm (or km when explicitly converted), frequencies are in 1/s.
  • The symbol φ denotes the scalar field in scalar–tensor gravity. φc is its central value.
  • The subscript A denotes the star (object) evaluated at the surface / asymptotic matching.

Most results are stored with Symbol keys (some of them use Unicode). You can always inspect what your particular run produced:

sort!(collect(keys(model.quantities)))
sort!(collect(keys(model.derivatives)))

model.quantities

The DEFp model currently defines the following keys.

Global star properties

  • :R

    • Stellar radius (surface where pressure drops to ~0).
    • Typical range: ~10–15 km for neutron stars.

  • :mA

    • Gravitational (ADM) mass of the star.
    • Typical range: ~1–2 solar masses.

  • :m̃A

    • “Jordan-frame” mass (a frame-dependent mass used in scalar–tensor conventions).
    • Useful for comparisons depending on which frame your observable is defined in.

  • :φ∞

    • Asymptotic value of the scalar field far from the star.

  • :αA

    • Effective scalar coupling of the star (sometimes called the scalar charge per unit mass, depending on conventions).
    • Interpreted as how strongly the star sources / responds to the scalar field.

  • :bc_φ∞

    • A boundary-condition residual for φ∞.
    • Near zero indicates the shooting/matching for the asymptotic scalar field has converged.

  • :Ω

    • Rotation angular frequency used for slow-rotation quantities.

  • :JA

    • Angular momentum.

  • :IA

    • Moment of inertia.

Log-transformed quantities

Some logs are stored to make derivatives and interpolation more stable:

  • :lnIA — log(IA)
  • :lnmA — log(mA)
  • :lnm̃A — log(m̃A)

  • :pc

    • Central pressure.

  • :φc

    • Central scalar field.

  • :cs_c

    • Speed of sound at the center (as returned by the EoS).

model.derivatives

The DEFp model also provides a small set of response coefficients.

  • :dφ∞_dφc

    • Sensitivity of the asymptotic scalar φ∞ to the central scalar φc.

  • :αA, :βA, :kA

    • Scalarization-related response coefficients.
    • These are typically defined from derivatives of mass / scalar charge w.r.t. φ∞ (exact conventions depend on the model).

Sanity checks

A few quick checks that often catch configuration/unit mistakes early:

  • :R is of order 1e6 cm (10 km) for neutron stars.
  • :mA is of order 1e33 g (1 solar mass).
  • :bc_φ∞ should be close to 0 for converged solutions.
  • If you enable slow rotation, :IA should be positive and scale roughly like mA * R^2.

Where these are defined

  • DEFp quantities and derivatives are assembled in the DEFp gravity implementation.
  • If you want the authoritative list for your current version, inspect the quantities_names and derivative rules in the source.