Snow White

Snow White is the white dwarf analysis pipeline in Astra. It classifies white dwarf spectra into spectral subtypes and fits effective temperature (Teff) and surface gravity (log g) for DA-type white dwarfs using an emulator-based Balmer line fitting method.

Snow White runs on BOSS combined spectra for sources in the mwm_wd carton program.

Overview

The pipeline has two stages:

1. Classification – A random forest classifier assigns a white dwarf spectral type (DA, DB, DC, DQ, DZ, and many subtypes) based on spectral line features.

2. DA fitting – If the source is classified as DA (or DA:), the pipeline fits Teff and log g by fitting Balmer absorption lines with a PCA-based spectral emulator.

Classification

Snow White extracts a set of spectral line features from the input spectrum and feeds them into a pre-trained random forest classifier. The feature extraction (get_line_info_v3.line_info) works as follows:

1. The spectrum is scaled so that the total flux sums to the number of pixels (a simple normalization).

2. The flux is binned by pairs of pixels and interpolated onto a standard wavelength grid (3850–8300 Angstroms, 1 Angstrom spacing).

3. A pseudo-continuum is estimated using a spline fit through predefined anchor points.

4. For each white dwarf subtype (DA, DB, DQ, DZ, WD+MS, peculiar, hot DQ), the ratio of the observed flux to the pseudo-continuum (or to a blackbody fit for WD+MS and peculiar types) is computed in diagnostic wavelength windows defined by feature files.

5. H-alpha emission features are measured separately.

6. All features are concatenated into a single feature vector.

The random forest outputs class probabilities for 24 white dwarf subtypes (see Output fields below). The classification is assigned as:

• The most probable class, if its probability is at least 0.5.

• A dual classification (e.g., DA/DB) if the second-most-probable class has a probability ratio greater than 0.6 relative to the top class.

• An uncertain classification (e.g., DA:) otherwise.

DA fitting

For spectra classified as DA or DA:, Snow White fits Teff and log g by fitting the profiles of the Balmer hydrogen absorption lines.

Spectral emulator

The fitting uses a PCA-based spectral emulator (Emulator_DA) trained on a grid of DA white dwarf model atmospheres. The emulator performs PCA decomposition on the model grid and uses linear interpolation in (log10(Teff), log g) space to predict PCA weights at arbitrary parameter values. This allows rapid generation of model spectra without repeatedly reading from the full grid.

Fitting procedure

1. Grid search – The normalized spectrum is compared against a pre-computed grid of DA models (da_flux_cube.npy) to find a coarse best-fit Teff. If a photometric Teff and log g solution exists in a reference table (matched by Gaia DR3 source ID), that is used as the starting point instead.

2. Line selection – Different sets of Balmer lines are used depending on the temperature regime:

   • Hot (Teff > 40,000 K): a dedicated hot line list

   • Warm (16,000–40,000 K): the standard line list

   • Cool (8,000–16,000 K): a cool line list

   • Very cool (Teff < 8,000 K): a very-cool line list

3. Balmer line fitting – Each Balmer line is individually normalized by fitting a linear pseudo-continuum to the line wings. The emulator generates a model spectrum at trial (Teff, log g, wavelength shift) values, the model lines are normalized the same way, and residuals are computed. The fit uses lmfit.minimize with least_squares (soft L1 loss) to find the best parameters. The parameter bounds are:

   • Teff: 4,000–120,000 K

   • log g: 6.01–9.49 dex (internally stored as 601–949, divided by 100)

   • Wavelength shift: -80 to +80 Angstroms

4. Uncertainty estimation – After convergence, the fit is repeated using leastsq (Levenberg-Marquardt) starting from the best-fit values to estimate formal parameter uncertainties. A noise model is applied to the formal uncertainties to produce the reported values:

   • e_teff = 1.5 * raw_e_teff + 100 K

   • e_logg = 2 * raw_e_logg + 0.05 dex

Hot/cold solution disambiguation

Because the strength of hydrogen Balmer lines peaks near Teff ~ 13,000 K, a given set of line profiles can be consistent with both a hotter and a cooler temperature solution. Snow White handles this ambiguity as follows:

• If a photometric starting point was available (from the Gaia-matched reference table), only the single fit from that starting point is used.

• Otherwise, the pipeline fits the spectrum twice: once starting from the best grid temperature, and once starting from the opposite side of the 13,000 K Balmer maximum. The correct solution is chosen by comparing the predicted Gaia BP-RP color from each model against the observed BP-RP color. The solution whose synthetic color is closest to the observed value is adopted.

• If the observed Gaia BP and RP magnitudes are not available, the pipeline cannot disambiguate and sets flag_missing_bp_rp_mag.

Output fields

Classification probabilities

Field	Description
classification	Assigned spectral type string (e.g., DA, DB, DA/DB, DA:)
p_cv	Probability of CV (cataclysmic variable)
p_da	Probability of DA
p_dab	Probability of DAB
p_dabz	Probability of DABZ
p_dah	Probability of DAH (magnetic DA)
p_dahe	Probability of DAHe
p_dao	Probability of DAO
p_daz	Probability of DAZ
p_da_ms	Probability of DA+MS (DA with main-sequence companion)
p_db	Probability of DB
p_dba	Probability of DBA
p_dbaz	Probability of DBAZ
p_dbh	Probability of DBH
p_dbz	Probability of DBZ
p_db_ms	Probability of DB+MS (DB with main-sequence companion)
p_dc	Probability of DC (featureless)
p_dc_ms	Probability of DC+MS
p_do	Probability of DO
p_dq	Probability of DQ
p_dqz	Probability of DQZ
p_dqpec	Probability of DQpec (peculiar DQ)
p_dz	Probability of DZ
p_dza	Probability of DZA
p_dzb	Probability of DZB
p_dzba	Probability of DZBA
p_mwd	Probability of magnetic white dwarf
p_hotdq	Probability of hot DQ

Stellar parameters (DA only)

Field	Description
teff	Effective temperature (K)
e_teff	Uncertainty in Teff (K), after noise model
logg	Surface gravity (log g, dex)
e_logg	Uncertainty in log g (dex), after noise model
raw_e_teff	Formal (pre-noise-model) uncertainty in Teff
raw_e_logg	Formal (pre-noise-model) uncertainty in log g
v_rel	Relative velocity used in the fit (km/s)

Spectral data

Field	Description
wavelength	Wavelength array (log-lambda spaced, 4648 pixels starting at log10(lambda) = 3.5523)
model_flux	Best-fit DA model flux, resampled to the wavelength grid (DA fits only)

Flags

Snow White uses a result_flags bit field. The individual flags are:

Flag	Bit	Description
flag_low_snr	2^0	Signal-to-noise ratio is 8 or below. Results may be unreliable.
flag_unconverged	2^1	The fit did not converge.
flag_teff_grid_edge_bad	2^2	Teff is at the edge of the model grid.
flag_logg_grid_edge_bad	2^3	log g is at the edge of the model grid.
flag_no_flux	2^4	The spectrum has no flux (all zeros or invalid). No results are produced.
flag_not_mwm_wd	2^5	The source is not in the mwm_wd program. No analysis is performed.
flag_missing_bp_rp_mag	2^6	Gaia BP or RP magnitude is missing, so the hot/cold solution could not be disambiguated. No stellar parameters are reported.

Things to know

• Only DA white dwarfs get stellar parameters. Other subtypes (DB, DC, DQ, DZ, etc.) receive a classification and class probabilities, but no Teff or log g.

• The noise model inflates formal uncertainties. The reported e_teff and e_logg include an empirical correction applied to the formal fitting uncertainties. If you need the raw formal errors, use raw_e_teff and raw_e_logg.

• Hot/cold ambiguity requires Gaia photometry. Without BP and RP magnitudes, the pipeline cannot choose between the hot and cold solutions and will set flag_missing_bp_rp_mag without reporting stellar parameters.

• Low S/N results are flagged but still reported. When the spectrum has S/N <= 8, flag_low_snr is set. The fitted parameters are still present in the output, but should be treated with caution.

• Classification notation:

  • A plain type like DA means the classifier is confident (probability >= 0.5).

  • A type with a colon like DA: means the top class had probability < 0.5, and the second class was not close enough to warrant a dual classification.

  • A dual type like DA/DB means the top two classes had similar probabilities (ratio > 0.6).

• Input spectra. Snow White operates on BOSS combined spectra (BossCombinedSpectrum). Only sources assigned to the mwm_wd carton program are analyzed; all others are immediately flagged with flag_not_mwm_wd.

• Grid boundaries. The emulator covers Teff from 4,000 to 120,000 K and log g from 6.01 to 9.49. Fits that land on these boundaries should be interpreted carefully.