CLAM

CLAM (Constrained Linear Absorption Model) fits stellar spectra from APOGEE using grid interpolation combined with a sinusoidal continuum model. It operates in log-flux space and uses NMF-based spectral decomposition.

What it does

CLAM determines:

• Effective temperature (teff)

• Surface gravity (logg)

• Overall metallicity (m_h)

• Carbon abundance (c_m)

• Nitrogen abundance (n_m)

• Microturbulent velocity (v_micro)

• Projected rotational velocity (v_sini)

How it works

1. Grid preparation: A pre-computed grid of NMF spectral weights (W) and components (H) is loaded. The grid is parameterized by v_sini, [N/M], [C/M], [M/H], v_micro, log(g), and Teff (in log10 space for Teff).

2. Continuum model: The continuum is modeled using a sinusoidal design matrix with 7 modes per APOGEE detector region. Three detector regions are used:

   • 15120–15820 A (green chip)

   • 15840–16440 A (red chip, blue half)

   • 16450–16960 A (red chip, red half)

   This gives 21 continuum coefficients total.

3. Forward model: The forward model combines:

   • Rectified flux from the NMF decomposition: exp(W * (-H))

   • Continuum from the sinusoidal basis: exp(A_continuum * theta)

   Everything is computed in log-flux space for numerical stability.

4. Initial guess: An iterative grid search steps through the parameter grid at progressively finer resolution to find a good starting point. The continuum coefficients are solved analytically (via LU decomposition) at each grid point while the NMF weights are evaluated from the grid.

5. Optimization: Starting from the initial guess, scipy.optimize.curve_fit is used to refine all parameters simultaneously (stellar labels + continuum coefficients). The Jacobian is computed analytically using the grid interpolator’s derivative.

6. Custom grid interpolator: CLAM uses a custom RegularGridInterpolator that is approximately 5x faster than SciPy’s implementation for slinear interpolation.

Output fields

Field	Description
teff	Effective temperature (K)
e_teff	Uncertainty on Teff
logg	Surface gravity (log cm/s^2)
e_logg	Uncertainty on log(g)
m_h	Overall metallicity [M/H] (dex)
e_m_h	Uncertainty on [M/H]
n_m	Nitrogen abundance [N/M] (dex)
e_n_m	Uncertainty on [N/M]
c_m	Carbon abundance [C/M] (dex)
e_c_m	Uncertainty on [C/M]
v_micro	Microturbulent velocity (km/s)
e_v_micro	Uncertainty on v_micro
v_sini	Projected rotational velocity (km/s)
e_v_sini	Uncertainty on v sin i
initial_*	Initial guess values for each label
rchi2	Reduced chi-squared of the fit
result_flags	Bitfield describing result quality

Flags

Flag	Bit	Meaning
flag_spectrum_io_error	2^0	Could not read the spectrum (I/O error)
flag_runtime_error	2^1	A runtime error occurred during fitting

Key caveats

• CLAM operates in log-flux space. Pixels with zero or negative flux are problematic and will be masked.

• The grid has finite boundaries in all dimensions. The optimizer is bounded by the grid limits, so results at the edges may be truncated.

• Model scatter (an empirical estimate of systematic model uncertainties) is added in quadrature to the observational uncertainties. The first and last 50 pixels of the APOGEE wavelength grid are masked by setting their model variance to infinity.

• The sinusoidal continuum model with 7 modes per region is flexible enough to capture typical APOGEE continuum shapes but may struggle with unusual continua (e.g., heavily reddened or emission-line objects).

• Uncertainties are derived from the covariance matrix of curve_fit and may underestimate the true uncertainties, particularly when the model is a poor fit.

• CLAM is under active development and some features (such as the initial guess routine) may evolve between versions.