Fitting [α/Fe]

The α-enhanced grid (FSPS v4.0, aMIST isochrones + C3K spectra, [α/Fe] ∈ {−0.2, 0.0, +0.2, +0.4, +0.6}) adds α-element enhancement as a sampled stellar axis: a chemical clock for the formation timescale, measured jointly with, and degenerate with, the total metallicity. SSPDataAfe and CSPBasis_afe are subclasses of SSPData and CSPBasis. The [α/Fe] axis and its interpolation are the only additions, the nebular arguments are dropped, and everything else (SFH weights, dust, projection, flux factor, cosmology) is inherited.

The grid

Download it by name (612 MB, cached and SHA-256 verified like every published grid). Building it yourself needs python-fsps compiled from source with AFE_FLAG=1 against the FSPS v4.0 data tree, which is easy to get silently wrong.

import jax.numpy as jnp
from ceridwen.ssps import fetch_grid, SSPDataAfe
from ceridwen.csp import CSPBasis_afe
from ceridwen import Cosmology

ssp = SSPDataAfe.load(fetch_grid("amist_c3k_hr_krou_afe"))
ssp.display()                       # (n_afe, n_Z, n_age, n_wave) = (5, 13, 107, 10992)

csp = CSPBasis_afe(ssp, lookback_time=jnp.linspace(0.0, 12.0, 9),
                   cosmo=Cosmology.planck18(), zh_const=True, verbose=False)

theta = {
    "lookback_time":      jnp.linspace(0.0, 12.0, 9),
    "sfh":                jnp.exp(-jnp.linspace(0.0, 12.0, 9) / 1.0),
    "logzsol":            jnp.array([-0.3]),   # = [Fe/H] on an aMIST grid
    "afe":                jnp.array([0.4]),    # [α/Fe]: re-partitions that Z
    "tau_pow":            jnp.array([0.3]),
    "alpha_pow":          jnp.array([-1.0]),
    "diffuse_tau_kc":     jnp.array([0.2]),
    "diffuse_dust_index": jnp.array([0.0]),
}
wave, fnu = csp.wave, csp.get_spectrum(theta)   # rest-frame Lsun/Hz per Msun
print(csp)                                      # grids, [Fe/H] axis, Z_sun, parameters
i = int(jnp.argmin(jnp.abs(wave - 5500.0)))
print(f"{fnu.shape[0]} pixels, L_nu(5500 A) = {float(fnu[i]):.3e} Lsun/Hz per Msun")

amist_c3k_hr_krou_afe is built from the alpha-MC C3K high-resolution SSPs (MIST v2.5 + C3K v2.3) of M. J. Park, with a Kroupa IMF. The C3K spectra are resampled onto pixels of λ/Δλ = 6000 between 3000 and 9000 Å, so the file resolves R ≈ 3000 at the two-pixel floor there; ssp.display() reports the floor. Its native axis is the FSPS label log10 Z = [Fe/H] + log10(0.0185), i.e. logzsol = [Fe/H].

What differs from CSPBasis

• theta["afe"] is interpolated linearly between the two bracketing grid planes, so it works under jit, grad and vmap and in every sampler.
• logzsol is [Fe/H]: every [α/Fe] plane shares one [Fe/H] axis (FSPS AFE_FLAG=1). The total metallicity [Z/H] is the derived logzsol_total = logzsol + log10(1 - x + x 10^[α/Fe]), x = 0.687490 (MIST v2.5, GS98).
• There is no nebular model (no α-enhanced CLOUDY grids exist): Lines observations are refused, and the basis reads nothing from $SPS_HOME unless add_dust_emission=True.
• CSPBasis_afe accepts only α-aware 4-D grids; a solar-scaled 3-D grid raises a TypeError that points to CSPBasis. ssp_afe= is keyword-only when you construct a grid by hand.
• logzsol above +0.25 together with [α/Fe] above +0.4 is refused: FSPS ships the same isochrone file for [α/Fe] = +0.4 and +0.6 at [Fe/H] = +0.5, and display() lists the cell. A prior that reaches it raises at construction.
• The grid does not carry a surviving-mass table yet, so fit it with fitSED(..., mfrac=False) and quote the formed mass.
• Memory: a sampled afe enters the contraction as interpolation weights over the [α/Fe] axis, so no interpolated flux plane is built per sample and vectorised evaluation (jax.vmap, as nested sampling does over its live points) costs about as much memory as without afe. XLA's temporary memory for jit(vmap(csp.get_spectrum)) on amist_c3k_hr_krou_afe (CPU, compile-time memory_analysis): 0.005 GB at W = 1, 0.002 GB at W = 80, 0.011 GB at W = 400. The basis keeps two copies of the flux cube (2 × 306 MB for this grid, float32).

A full fit of a quiescent galaxy with [α/Fe], including a fitted spectrophotometric normalisation, is examples/demo_afe_quiescent.py.