IMF sampling - progenax — differentiable initial conditions for N-body simulations

progenax provides four canonical IMF parameterisations, each appropriate to a different use case. This page samples from all four, plots them, and explains when to use each.

Setup¶

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
from progenax.imf import PowerLawIMF, Maschberger, ChabrierIMF

key = jax.random.PRNGKey(0)
key_salp, key_kroupa, key_chab, key_masch = jax.random.split(key, 4)
N = 100_000   # Large enough for smooth histograms
m_grid = jnp.logspace(-1.5, 2.0, 100)   # 0.03 - 100 M_sun

The four IMFs¶

Salpeter (single power law)¶

salpeter = PowerLawIMF(
    exponents=[2.35],
    breakpoints=[],
    m_min=0.1,
    m_max=100.0,
)
masses_salp = salpeter.sample(key_salp, N)

Kroupa (multi-segment broken power law)¶

kroupa = PowerLawIMF.kroupa()
masses_kroupa = kroupa.sample(key_kroupa, N)

Chabrier (lognormal + power law)¶

chabrier = ChabrierIMF(m_c=0.22, sigma=0.57, alpha=2.3)
masses_chab = chabrier.sample(key_chab, N)

Maschberger (smooth, default)¶

maschberger = Maschberger(alpha=2.3, beta=1.4, mu=0.2)
masses_masch = maschberger.sample(key_masch, N)

Plotting¶

fig, ax = plt.subplots(figsize=(8, 5))
for name, masses in [
    ("Salpeter", masses_salp),
    ("Kroupa", masses_kroupa),
    ("Chabrier", masses_chab),
    ("Maschberger", masses_masch),
]:
    log_masses = jnp.log10(masses)
    ax.hist(log_masses, bins=50, density=True, alpha=0.5, label=name)
ax.set_xlabel("log₁₀(M / M☉)"); ax.set_ylabel("dN/dlogM")
ax.set_yscale("log"); ax.legend()
plt.savefig("imf_comparison.png", dpi=120)

Expected: all four IMFs agree closely above $\sim 1\,\Msun$ (the Salpeter regime) and differ in the low-mass turnover. Salpeter has no turnover; Kroupa breaks at 0.5 $\Msun$ ; Chabrier and Maschberger are smooth.

Choosing the right IMF¶

Choose	When
Maschberger	Default for new code. Closed-form inverse-CDF, smooth, HMC-friendly. progenax production default
Salpeter	High-mass-only studies; comparison with classical work
Kroupa	Backwards compatibility with prior cluster modelling
Chabrier	Unresolved-population integrated colours

For binary-aware inference, the IMF combines with the Moe & Di Stefano (2017) multiplicity statistics — see Binary-aware IMF recovery.

For environment-dependent IMF (top-heavy in dense / metal-poor populations), see Environment-dependent IMFs.

Next step¶

Glossary defines every term you’ve seen in the tutorial path. After that, drop into Theory & methods for the full theory section, Architecture & design for design rationale, or API reference for the full API reference.

References¶

Moe, M., & Di Stefano, R. (2017). Mind your Ps and Qs: The interrelation between period (P) and mass-ratio (Q) distributions of binary stars. The Astrophysical Journal Supplement Series, 230, 15. 10.3847/1538-4365/aa6fb6