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What DOROTHY does

DOROTHY predicts the labels of a star from a low-resolution spectrum. This page explains the idea in four parts, one figure each.

Labels from spectra

A star’s spectrum encodes its atmospheric parameters and its composition. These are the effective temperature (Teff), the surface gravity (log g), the iron abundance [Fe/H] and the abundances of other elements. Each of these numbers is one label of the star.

High-resolution surveys measure labels precisely. APOGEE observes the H band (1.51 to 1.70 µm) at a resolving power of about 22,500 (Majewski et al. 2017), and its pipeline fits synthetic spectra to each observation (García Pérez et al. 2016). GALAH observes four optical bands at a resolving power of about 28,000 (Buder et al. 2021).

Low-resolution surveys observe many more stars. DESI (DESI Collaboration et al. 2022), BOSS (Dawson et al. 2013) and LAMOST (Cui et al. 2012) have resolving powers between about 1500 and 7500. At these resolutions, neighbouring absorption lines blend, so a pipeline cannot fit each line on its own.

The same stellar spectrum at high and low resolution: at high resolution each absorption line is resolved; at low resolution neighbouring lines blend into broad, shallow features. Illustrative. High resolution: APOGEE, GALAH Each line is resolved, so a pipeline fits the labels to the lines. Low resolution: DESI, BOSS, LAMOST The lines blend, so DOROTHY learns the labels from the whole spectrum. wavelength (illustrative)
The same stellar spectrum at high and low resolution: at high resolution each absorption line is resolved; at low resolution neighbouring lines blend into broad, shallow features. Illustrative. High resolution: APOGEE, GALAH Each line is resolved, so a pipeline fits the labels to the lines. Low resolution: DESI, BOSS, LAMOST The lines blend, so DOROTHY learns the labels from the whole spectrum. wavelength (illustrative)

A low-resolution spectrum blends the absorption lines that a high-resolution spectrum resolves; the spectra are illustrative.

The blended spectrum still holds the information. DOROTHY uses a neural network to read the labels from the whole spectrum. This approach follows The Cannon (Ness et al. 2015), The Payne (Ting et al. 2019) and astroNN (Leung and Bovy 2019).

Stars in common

Thousands of stars have both a low-resolution spectrum and high-resolution labels. On these stars, the network learns to predict the labels from the spectrum. It then predicts labels for the stars that have only a low-resolution spectrum. This is label transfer.

Stars in common: a survey observes many stars and a label source fewer; the network trains on the stars that have both a spectrum and labels, and predicts labels for the stars that have only a spectrum. Proportions are illustrative. Spectra from a survey Labels from a label source Labels only not used Both the network trains here Spectrum only the network predicts the labels here
Stars in common: a survey observes many stars and a label source fewer; the network trains on the stars that have both a spectrum and labels, and predicts labels for the stars that have only a spectrum. Proportions are illustrative. Spectra from a survey Labels from a label source Labels only not used Both the network trains here Spectrum only the network predicts the labels here

The network trains on the stars with both a spectrum and labels, and predicts labels for the rest; the proportions are illustrative.

DOROTHY matches stars across surveys by their Gaia DR3 source ID (Gaia Collaboration and Vallenari et al. 2023). It keeps every star in one file, the super-catalogue, with one row per star (What is in the super-catalogue).

One model for several surveys

Each survey samples the spectrum on its own wavelength grid, so one input layer cannot read every survey. The multi-head model gives each survey its own encoder. An encoder maps the survey’s spectrum to a vector of fixed length. A shared trunk combines the vectors of the surveys that observed the star. One output head per label source then predicts that source’s labels.

The multi-head model: each survey's spectrum goes through its own encoder to a vector of fixed length; the vectors of the surveys a star has are concatenated or averaged, passed through shared layers, and one head per label source predicts the value and log-scatter of every parameter. Spectra Encoders Combine Trunk Heads Outputs BOSS3 × 4506 DESI3 × 7650 LAMOST MRSnot observed zeros (concat)or skipped (mean) concator mean sharedlayers APOGEEhead μ, ln sper parameter GALAHhead μ, ln sper parameter

The multi-head model: one encoder per survey, a shared trunk, and one head per label source.

A star needs a spectrum from only one of the surveys of the model. APOGEE and GALAH measure the same quantities with different methods, so their labels differ systematically. Separate heads keep the two scales apart (The model).

Uncertainties

For every label, the network predicts two numbers: the prediction μ and the predicted scatter s. Together they describe a normal distribution. The predicted scatter is the expected spread of the measured labels around μ. It is large when the spectrum constrains the label poorly, or when the label source’s own measurements are noisy.

A prediction is a normal distribution: its centre mu is the prediction and its width s is the predicted scatter; a measured label y falls somewhere under it. Illustrative. μ s y μ: the prediction s: the predicted scatter, the expected spread of measured labels around μ y: a measured label label value (illustrative)
A prediction is a normal distribution: its centre mu is the prediction and its width s is the predicted scatter; a measured label y falls somewhere under it. Illustrative. μ s y μ: the prediction s: the predicted scatter y: a measured label label value

A prediction is a normal distribution with centre μ and width s; the values are illustrative.

After training, DOROTHY checks the predicted scatter on stars that the network did not train on. It fits one calibration factor c per label source and label, and reports the uncertainty c s (Uncertainties).