scalefree 0.1.6

Scale-free DF velocity moments and VP calculations with a Fortran backend.

scalefree

Scale-free dynamical models (Fortran backend) with a small Python interface for computing intrinsic/projected velocity moments and (optionally) reconstructed velocity profiles (VPs) and Gauss–Hermite summaries.

The guiding principles are:

• Keep the user-facing API small and predictable
• Delegate heavy computation to a compiled backend
• Provide structured, parseable outputs for reproducible workflows

This code was developped in the context of the HSTPROMO collaboration.

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What this package provides

vprofile(...)

Runs the ScaleFree Fortran backend and returns intrinsic/projected velocity moments and (optionally) VP / Gauss–Hermite summaries.

Typical uses:

• Line-of-sight (LOS) kinematics
• Proper-motion (plane-of-sky) kinematics (POSr, POSt)
• VP reconstruction from moments (when enabled)

scalefree.hermite

Utilities to fit Gauss–Hermite coefficients to a velocity-profile file and to evaluate analytic Gauss–Hermite profiles.

mock(...)

A convenience routine for generating synthetic 6D samples (x, y, z, vx, vy, vz) from a chosen model configuration (internally uses vprofile() to obtain GH parameters across angular bins).

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Installation

From source (recommended for development)

poetry install

With pip

pip install scalefree

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Fortran requirement

vprofile() uses a Fortran executable. If you do not provide a precompiled binary, a local build requires gfortran.

Install gfortran:

• Debian/Ubuntu: sudo apt-get install gfortran
• Fedora: sudo dnf install gcc-gfortran
• macOS (Homebrew): brew install gcc

---

Quickstart

1) Run vprofile()

from scalefree import vprofile

res = vprofile(
    potential="logarithmic",  # or "kepler", 1, 2, or a callable returning 1/2
    gamma=2.0,
    q=0.8,
    df=1,
    beta=0.0,
    s=0.5,
    t=0.0,
    inclination=60.0,
    xi=0.0,
    theta=0.0,
    usevp=True,
    algorithm=3,
)

print(res.blocks.keys())
print(res.blocks["vp"]["by_iproj"][1])  # iproj=1 LOS, 2 POSr, 3 POSt

2) Fit Gauss–Hermite moments from a VP file

from scalefree import hermite  # module

gauss_info, gaussh_info, h_moments = hermite.hermite("my_vp.dat")
print(gaussh_info)
print(h_moments["h3"], h_moments["h4"])

3) Generate a simple mock

from scalefree import mock

X = mock(
    potential=lambda: 1,
    gamma=4.0,
    q=0.9,
    beta=0.0,
    inclination=90.0,
    nsamples=10_000,
    nbins=180,
    usevp=True,
)

print(X.shape)  # (N, 6): (x, y, z, vx, vy, vz)

---

Documentation

To keep this README short, more detailed guides are intended to live under docs/:

• docs/getting-started.md
• docs/api.md
• docs/vprofile.md
• docs/gauss-hermite.md
• docs/mock-generator.md
• docs/troubleshooting.md
• Theory notes:
  • docs/theory/rotation.md
  • docs/theory/vp-shapes.md
  • docs/theory/pos-velocity.md

---

References and citation guidance

If you use this code in research, please cite the foundational scale-free modelling reference and any additional methodological references relevant to your workflow.

Core scale-free models (foundational)

• de Bruijne, van der Marel & de Zeeuw (1996), MNRAS, 282, 909–925. arXiv: astro-ph/9601044

Plane of sight moments equations

• Vitral et al. (2024), ApJ, 970, 1. DOI: 10.3847/1538-4357/ad571c. aeXiv: astro-ph/2407.07769

BibTeX (copy/paste)

@ARTICLE{1996MNRAS.282..909D,
  author  = {de Bruijne, Jos H. J. and van der Marel, Roeland P. and de Zeeuw, P. Tim},
  title   = {Scale-free dynamical models for galaxies: flattened densities in spherical potentials},
  journal = {Monthly Notices of the Royal Astronomical Society},
  year    = {1996},
  volume  = {282},
  number  = {3},
  pages   = {909--925},
  doi     = {10.1093/mnras/282.3.909},
  eprint  = {astro-ph/9601044},
  archivePrefix = {arXiv}
}

@ARTICLE{2024ApJ...970....1V,
       author = {{Vitral}, Eduardo and {van der Marel}, Roeland P. and {Sohn}, Sangmo Tony and {Libralato}, Mattia and {del Pino}, Andr{\'e}s and {Watkins}, Laura L. and {Bellini}, Andrea and {Walker}, Matthew G. and {Besla}, Gurtina and {Pawlowski}, Marcel S. and {Mamon}, Gary A.},
        title = "{HSTPROMO Internal Proper-motion Kinematics of Dwarf Spheroidal Galaxies. I. Velocity Anisotropy and Dark Matter Cusp Slope of Draco}",
      journal = {\apj},
     keywords = {Dark matter, Dwarf spheroidal galaxies, Astronomy data analysis, Proper motions, Stellar kinematics, Stellar dynamics, Galaxy dynamics, Galaxy structure, 353, 420, 1858, 1295, 1608, 1596, 591, 622, Astrophysics - Astrophysics of Galaxies, Astrophysics - Cosmology and Nongalactic Astrophysics},
         year = 2024,
        month = jul,
       volume = {970},
        pages = {1},
          doi = {10.3847/1538-4357/ad571c},
       eprint = {2407.07769},
}

---

Authors:

• Roeland P. van der Marel,

  1994-1995 :
    development of code
  address : Space Telescope Science Institute
  Research Programs Office (RPO)
  3700 San Martin Drive
  Baltimore, MD 21218
  Tel : [phone]
  Fax : [phone]
  e-mail : [e-mail]
  homepage : https://www.stsci.edu/~marel/

• Jos H. J. de Bruijne,

  1994-1995 :
    testing and application of code
  address : Sterrewacht Leiden
  Postbus 9513
  2300 RA Leiden
  The Netherlands
  Tel : [phone]
  Fax : [phone]
  e-mail : [e-mail]
  homepage : http://www.strw.leidenuniv.nl/~debruyne/

• Eduardo Vitral,

  2023-present :
    development of the Python interface
    implementation of plane-of-sky routines
    testing and application of code
  address : Royal Observatory of Edinburgh
  Edinburgh, UK
  e-mail : [e-mail]
  homepage : https://eduardo-vitral.github.io