scalefree 0.3.1

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.

---

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)

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). Keep in mind that the underlying formalism is scale-free, so please refer to this link for scaling it back to physical values.

---

Installation

From source (recommended for development)

poetry install

With pip

pip install scalefree --upgrade

---

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

# Minimal projected (point) run + VP/Gauss–Hermite reconstruction
res = vprofile(
    potential="log",   # "log"/"logarithmic" or "kepler" (or 2 / 1)
    gamma=2.0,
    q=0.8,
    df=1,
    beta=0.0,
    s=0.0,
    t=0.0,
    inclination=60.0,  # degrees
    xi=0.0,            # degrees on projected plane (0 = major axis)
    theta=0.0,         # degrees (used only for intrinsic runs; safe to keep)
    usevp=True,        # set False if you only want moments
)

# Projected velocity moments (iproj: 1=LOS, 2=POSr, 3=POSt)
proj_los = res.blocks["projected_point"]["by_iproj"][1]
mu = proj_los["v1"]
sigma = (proj_los["v2"] - mu**2) ** 0.5
print(f"LOS: mean={mu:.6g}, sigma={sigma:.6g}")

# Optional: VP / Gauss–Hermite summary (only present when usevp=True)
vp_los = res.blocks["vp"]["by_iproj"][1]
print(f"LOS GH: h3={vp_los['h3']:.6g}, h4={vp_los['h4']:.6g}")

2) Fit Gauss–Hermite moments from a VP file

from pathlib import Path
import tempfile
import numpy as np

from scalefree import vprofile, hermite

res = vprofile(
    potential="log",
    gamma=2.0,
    q=0.8,
    beta=0.0,
    s=0.0,
    t=0.0,
    inclination=60.0,
    xi=0.0,
    theta=0.0,
    usevp=True,
)

iproj = 1  # 1=LOS, 2=POSr, 3=POSt
vp_data = res.blocks["vp_table"][iproj]["data"]  # (N,2): [v, vp]

# Write to a writable temp location
vp_path = Path(tempfile.gettempdir()) / "my_vp.dat"
np.savetxt(vp_path, vp_data, header="v vp")

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

3) Generate a simple mock

from scalefree import mock

X = mock(
    potential=2,
    gamma=2.0,
    q=0.9,
    df=2,
    beta=-0.1,
    s=0.2,
    t=0.0,
    nsamples=10_000,
    nbins=180,
)

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/vmoments.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