The Payne

The Payne is a neural network-based spectral emulator that estimates stellar labels by fitting a forward model to observed APOGEE spectra. Unlike pipelines that directly predict labels from spectra, The Payne uses a trained neural network as a fast spectral emulator and optimizes labels to best match the observed spectrum.

What it does

The Payne estimates a comprehensive set of stellar labels from APOGEE spectra:

• Stellar parameters: Teff, log g, microturbulence (v_turb), macroturbulence (v_macro)

• Chemical abundances: [C/H], [N/H], [O/H], [Na/H], [Mg/H], [Al/H], [Si/H], [P/H], [S/H], [K/H], [Ca/H], [Ti/H], [V/H], [Cr/H], [Mn/H], [Fe/H], [Co/H], [Ni/H], [Cu/H], [Ge/H]

• Isotope ratio: 12C/13C

• Radial velocity: v_rel (if enabled via v_rad_tolerance)

• Fit quality: chi-squared and reduced chi-squared

How it works

Neural network emulator

The Payne uses a simple feedforward neural network with two hidden layers and leaky ReLU activations to emulate stellar spectra. Given a set of stellar labels, the network rapidly predicts the corresponding spectrum:

input labels -> Dense + Leaky ReLU -> Dense + Leaky ReLU -> Dense -> predicted spectrum

The network weights and biases are loaded from a pre-trained model (payne_apogee_nn.pkl). The labels are internally scaled to a [0, 1] range using pre-computed x_min and x_max values.

Fitting procedure

For each observed spectrum, The Payne:

1. Continuum-normalizes the observed spectrum using a Chebyshev polynomial (degree 4 by default) fit across three APOGEE detector regions:

   • 15,100 – 15,793 Angstroms

   • 15,880 – 16,417 Angstroms

   • 16,499 – 17,000 Angstroms

2. Interpolates the observed spectrum onto the model wavelength grid.

3. Optimizes the stellar labels using scipy.optimize.curve_fit with the Trust Region Reflective (TRF) method, minimizing the chi-squared difference between the model and observed spectrum.

4. Estimates uncertainties from the covariance matrix of the fit. Correlation coefficients between all pairs of labels are also computed and stored.

Radial velocity

Radial velocity fitting is controlled by the v_rad_tolerance parameter (default: 0, meaning disabled). When enabled, an additional label representing the radial velocity is optimized simultaneously with the stellar labels, and the model spectrum is Doppler-shifted accordingly.

Pixel masking

A mask (payne_apogee_mask.npy) can be applied to exclude certain spectral pixels from the fit. Masked pixels have their inverse variance set to zero.

Noise model

A post-hoc noise model is applied to adjust formal uncertainties. The raw (formal) uncertainties from the fit covariance matrix are stored as raw_e_* fields, while the corrected uncertainties (using empirical calibration from ThePayne_corrections.pkl) are stored as e_* fields.

Output fields

Stellar parameters

Field	Type	Description
teff	float	Effective temperature (K)
e_teff	float	Uncertainty in Teff
logg	float	Surface gravity (log10(cm/s^2))
e_logg	float	Uncertainty in log g
v_turb	float	Microturbulent velocity (km/s)
e_v_turb	float	Uncertainty in v_turb
v_macro	float	Macroturbulent velocity (km/s)
e_v_macro	float	Uncertainty in v_macro
v_rel	float	Relative radial velocity (km/s)

Chemical abundances

Each abundance is reported as [X/H] in dex:

Fields	Element
c_h, e_c_h	Carbon
n_h, e_n_h	Nitrogen
o_h, e_o_h	Oxygen
na_h, e_na_h	Sodium
mg_h, e_mg_h	Magnesium
al_h, e_al_h	Aluminum
si_h, e_si_h	Silicon
p_h, e_p_h	Phosphorus
s_h, e_s_h	Sulfur
k_h, e_k_h	Potassium
ca_h, e_ca_h	Calcium
ti_h, e_ti_h	Titanium
v_h, e_v_h	Vanadium
cr_h, e_cr_h	Chromium
mn_h, e_mn_h	Manganese
fe_h, e_fe_h	Iron
co_h, e_co_h	Cobalt
ni_h, e_ni_h	Nickel
cu_h, e_cu_h	Copper
ge_h, e_ge_h	Germanium
c12_c13, e_c12_c13	Carbon isotope ratio (12C/13C)

All labels also have raw_e_* counterparts storing the formal uncertainties before noise model correction.

Fit quality and metadata

Field	Type	Description
chi2	float	Chi-squared of the best fit
reduced_chi2	float	Reduced chi-squared
result_flags	bitmask	Bitfield encoding quality flags

Correlation coefficients

Pairwise correlation coefficients between all labels are stored as rho_<label1>_<label2> fields (e.g., rho_teff_logg, rho_teff_fe_h). These are derived from the covariance matrix of the fit.

Spectral data

Field	Type	Description
wavelength	array	Wavelength array (log-lambda spaced, 8575 pixels)
model_flux	array	Best-fit model flux (continuum x rectified model)
continuum	array	Fitted continuum

These spectral data arrays are stored in intermediate pickle files and loaded on demand.

Flags

Flag	Bit	Description
flag_fitting_failure	2^0	The fitting procedure failed
flag_warn_teff	2^1	Teff < 3,100 K or Teff > 7,900 K
flag_warn_logg	2^2	log g < 0.1 or log g > 5.2
flag_warn_fe_h	2^3	[Fe/H] > 0.4 or [Fe/H] < -1.4
flag_low_snr	2^4	S/N < 70

Summary flags

• flag_warn: Set when any flag bit is non-zero (i.e., result_flags > 0).

• flag_bad: Set only when flag_fitting_failure is set.

Caveats

• The Payne is a forward-modeling approach: it uses a neural network to emulate spectra and optimizes labels to fit the data. This is fundamentally different from pipelines like AstroNN or APOGEENet, which directly predict labels from spectra.

• The effective training range is approximately 3,100 – 7,900 K in Teff, 0.1 – 5.2 in log g, and -1.4 to +0.4 in [Fe/H]. Results outside these ranges are flagged.

• The optimization uses bounded parameters (labels are internally constrained to [0, 1] in normalized space). This means the optimizer cannot extrapolate far beyond the training grid.

• Continuum normalization uses a 4th-order Chebyshev polynomial fit with a fixed pixel mask. Poor continuum fits (e.g., for emission-line stars or heavily reddened spectra) can propagate into biased label estimates.

• The model and continuum spectral arrays are stored as intermediate pickle files, not in the database directly. These files are loaded lazily when the model_flux or continuum attributes are accessed.

• The formal uncertainties from the covariance matrix tend to underestimate true uncertainties, which is why a post-hoc noise model correction is applied.