The Astronomical Journal, 163:152 (13pp), 2022 April https://doi.org/10.3847/1538-3881/ac4de7
© 2022. The Author(s). Published by the American Astronomical Society.
APOGEE Net: An Expanded Spectral Model of Both Low-mass and High-mass Stars
Dani Sprague1 , Connor Culhane1, Marina Kounkel2 , Richard Olney1, K. R. Covey3 , Brian Hutchinson1,4 , Ryan Lingg1 ,
Keivan G. Stassun2 , Carlos G. Román-Zúñiga5 , Alexandre Roman-Lopes6 , David Nidever7 , Rachael L. Beaton8,9,17 ,
Jura Borissova10 , Amelia Stutz11 , Guy S. Stringfellow12 , Karla Peña Ramírez13 , Valeria Ramírez-Preciado14 ,
Jesús Hernández5 , Jinyoung Serena Kim15 , and Richard R. Lane16
1 Dept. of Computer Science, Western Washington University, 516 High Street, Bellingham, WA 98225-9165, USA; marina.kounkel@vanderbilt.edu
2 Department of Physics and Astronomy, Vanderbilt University, VU Station 1807, Nashville, TN 37235, USA
3 Dept. of Physics and Astronomy, Western Washington University, 516 High Street, Bellingham, WA 98225-9164, USA
4 Computing and Analytics Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, Richland, WA 99354-1793, USA
5 Universidad Nacional Autónoma de México, Instituto de Astronomía, AP 106, Ensenada 22800, BC, México
6 Departamento de Astronomia, Facultad de Ciencias, Universidad de La Serena. Av. Juan Cisternas 1200, La Serena, Chile
7 Department of Physics, Montana State University, P.O. Box 173840, Bozeman, MT 59717-3840, USA
8 Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton, NJ 08544, USA
9 The Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101, USA
10 Instituto de Física y Astronomía, Universidad de Valparaíso, Av. Gran Bretaña 1111, Playa Ancha, Casilla 5030, Chile
11 Departamento de Astronomía, Universidad de Concepción, Casilla 160-C, Concepción, Chile
12 Center for Astrophysics and Space Astronomy, Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA
13 Centro de Astronomía (CITEVA), Universidad de Antofagasta, Av. Angamos 601, Antofagasta, Chile
14 Universidad Nacional Autónoma de México, Instituto de Astronomía, AP 106, Ensenada 22800, BC, México
15 Steward Observatory, Department of Astronomy, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721, USA
16 Centro de Investigación en Astronomía, Universidad Bernardo O’Higgins, Avenida Viel 1497, Santiago, Chile
Received 2021 November 12; revised 2022 January 10; accepted 2022 January 13; published 2022 March 8
Abstract
We train a convolutional neural network, APOGEE Net, to predict Teff, log g, and, for some stars, [Fe/H], based on
the APOGEE spectra. This is the first pipeline adapted for these data that is capable of estimating these parameters
in a self-consistent manner not only for low-mass stars, (such as main-sequence dwarfs, pre-main-sequence stars,
and red giants), but also high-mass stars with Teff in excess of 50,000 K, including hot dwarfs and blue supergiants.
The catalog of ∼650,000 stars presented in this paper allows for a detailed investigation of the star-forming history
of not just the Milky Way, but also of the Magellanic clouds, as different type of objects tracing different parts of
these galaxies can be more cleanly selected through their distinct placement in Teff–log g parameter space than in
previous APOGEE catalogs produced through different pipelines.
Unified Astronomy Thesaurus concepts: Astroinformatics (78); Computational methods (1965); Stellar
classification (1589); Massive stars (732); Magellanic Clouds (990); Young stellar objects (1834)
Supporting material: machine-readable table
1. Introduction G3II, to which more can be added to further express features
Effective temperature (T pertaining to unique metallicity of a particular star, information oneff) and surface gravity (log g) are
among the most fundamental properties of a star. Determination of multiplicity, as well as ranges that would signify an uncertainty in
these parameters (or their proxy) has allowed for an understanding classification. In the era predating computers, this allowed to
of how stars form and how they evolve over time. immediately grasp the precise nature of a particular star of interest.
In the early days of spectroscopy, direct measurement of these Nowadays, however, given the diversity and complexity of the
parameters was challenging due to a lack of precise stellar models. encoded information, such a classification can be difficult and
However, it was possible to assign stars a particular spectral impractical to use when dealing with a large number of stars.
classi cation that can be used as a proxy for T . Spectral types, Over the years, the models of stellar atmospheres havefi eff
ranging from O to M, were determined through examining the improved, allowing to create grids of synthetic spectra with
type and the strength of various absorption lines. Each type can known Teff, log g, and other parameters, to which the spectra of
further be subdivided into subtypes, usually 0 9. Similarly, real stars could be compared (e.g., Kurucz 1979, 1993; Coelho–
through examining widths of certain lines, stars were assigned into et al. 2005; Husser et al. 2013). However, not all synthetic spectra
different luminosity classes that can be used as a proxy of the size are created equal due to inclusion of different physics, and they
of a star, ranging from supergiants (I) to dwarfs (V). Hundreds of may have substantial systematic differences in the derived stellar
thousands of stars were classi ed in such a manner (Gray & parameters when matched against real data. Careful considerationfi
Corbally 2009). This led to complex classi cations such as, e.g., of individual spectral features can help in fine-tuning the extractedfi
parameters, but, as these features are different across different
17 Hubble Fellow. spectral types, this is not always practical to do in a self-consistent
manner when analyzing spectra from large surveys.
In particular, although a good performance by various survey
Original content from this work may be used under the terms
of the Creative Commons Attribution 4.0 licence. Any further pipelines for programs such as APOGEE has been previously
distribution of this work must maintain attribution to the author(s) and the title achieved for low-mass stars with Teff< 7000 K, many such
of the work, journal citation and DOI. pipelines have lacked calibration to measure parameters of
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The Astronomical Journal, 163:152 (13pp), 2022 April Sprague et al.
hotter stars due to a sparsity of their spectral features (e.g., arose as a mismatch between a synthetic spectra and the data.
García Pérez et al. 2016). Its parameters are only limited to the red giants. The latest
Previously, we have developed a neural network, APOGEE value added catalog was released in DR14 (Abolfathi et al.
Net, which self-consistently measured Teff, log g, and [Fe/H] 2018). From DR16 onwards it has offered no improvements
for cool (Teff< 6500 K) stars, including more exotic and rare compared to ASPCAP.
18 There was an effort to extend The
objects, such as pre-main-sequence stars (Olney et al. 2020). In Cannon to also report Teff and [Fe/H] for the M dwarfs (Birky
this work, we extend its functionality to estimate these et al. 2020), but there was no unified model that could perform
parameters for all stellar objects, ranging from early O to late on the full APOGEE sample.
M types. The Payne (Ting et al. 2019) was another data-driven
approach that was trained on the Kurucz atmospheric models.
2. Data Unlike the Cannon they did not use ASPCAP parameters for
label transfer, and derived their own set of labels. Prior to
2.1. Data Products DR16, they were the first to produce a comprehensive set of
The APOGEE project (Blanton et al. 2017; Majewski et al. stellar parameters (including log g) for dwarfs with Teff< 8000
2017; S. Majewski et al. 2022, in preparation) uses two K. Although robust across much of the parameter space, there
spectrographs mounted at two 2.5 meter telescopes—one at the was a degeneracy between log g and metallicity among M
Apache Point Observatory (APO), and the other one at the Las dwarfs, confusing their parameters with pre-main-sequence
Campanas Observatory (LCO; Bowen & Vaughan 1973; Gunn stars. As such, they did not report parameters for sources with
et al. 2006). It is capable of observing up to 300 sources Teff< 4000 K and log g> 3.5 dex.
simultaneously in the H band (1.51–1.7 μm), with the APOGEE Net I (Olney et al. 2020) attempted to build on the
resolution of R∼ 22,500 with the field of view being 3° in efforts from the Payne, supplementing the available parameters
diameter at APO, and 2° in diameter at LCO (Wilson et al. for intermediate mass dwarfs and the red giants with Teff, log g,
2010, 2019). and [Fe/H] derived from photometric relations and the
The latest public data release is DR17 (Abdurro’uf et al. theoretical isochrones for the M dwarfs and the pre-main-
2021; J. Holtzman et al. 2022, in preparation). It consists of sequence stars. This combination of the parameters was used to
∼660,000 unique stars, many with multiple visit spectra. Due train a neural network that is capable of deriving stellar
to the targeting strategy of the survey (Zasowski et al. properties for APOGEE spectra for all stars with Teff< 6700 K
2013, 2017), a large fraction of the sources that have been in a homogeneous manner. However, a lack of a training
observed are red giants. However, a number of other targets sample of sources hotter than Teff> 8000 K resulted in all
have also been observed, such as provided by additional goal spectra that were dominated by the H lines to clump at the edge
and ancillary programs (Beaton et al. 2021; Santana et al. 2021) of the grid and, therefore, parameters for stars with Teff> 6700
—they include pre-main-sequence stars in several star-forming K were not reliable.
regions, and main-sequence and evolved stars of various There have been numerous efforts to derive spectral types for
spectral types. In particular A and F dwarfs are observed in OB stars toward a number of star-forming regions through
every field due to their use as telluric calibrators. cross-matching APOGEE observations to the optical spectra
with known types and deriving relations based on equivalent
widths of various H lines in the near-infrared (Roman-Lopes
2.2. Existing Pipelines
et al. 2018, 2019, 2020; Borissova et al. 2019; Ramírez-
The primary pipeline for the reduction and extraction of Preciado et al. 2020). For optimal performance, however, these
stellar parameters from the APOGEE spectra is ASPCAP efforts require initial separation of B and F stars (as they can
(García Pérez et al. 2016). It performs a global simultaneous fit have a comparable strength of the H lines, requiring other lines
for eight stellar parameters, which include Teff, log g, v sin i, to disentangle them). Furthermore, such a classification does
various metallicity metrics, and other parameters, through not currently bridge the gap of A and F stars to fully connect
performing a least-squares-fit between the data and a synthetic OB stars to the stellar parameters of all the other sources
spectral grid. In old data releases, full set of derived stellar observed by APOGEE.
parameters were made available only for red giants. For main-
sequence dwarfs or pre-main-sequence stars, while some Teff
were reported, neither metallicity nor log g were made 3. The APOGEE Net Model
available. DR16 has expanded the list of stars for which it 3.1. Training Labels
derived full parameters to all sources with Teff< 8000 K
(Ahumada et al. 2020). DR17 (SDSS-IV collaboration 2022, in To construct the training labels for the high-mass stars, we
preparation; J. Holtzman et al. 2022, in preparation) has added used SIMBAD (Wenger et al. 2000) to search for sources with
Teff and log g for hotter stars up to Teff< 20,000 K. However, existing literature measurements of their spectral parameters.
despite the increase in coverage, and improvement in Unfortunately, direct and accurate measurements of Teff and
parameters over different data releases, there are some log g for high-mass stars observed by APOGEE are rare;
systematic features that remain which make these parameters however, many more had a reported spectral type and a
not optimal for some types of stars, particularly those that are luminosity class (if both are available), which can be used as a
still young (Figure 1). proxy of Teff and log g.
The first alternative to a direct grid fitting performed by To perform a transformation, we have compiled a list of
ASPCAP was a data-driven approach, The Cannon (Ness et al. high-mass stars, independent of the APOGEE footprint, for
2015; Casey et al. 2016). It was trained on a population of which there exist independent measurement for both spectral
select stars with the parameters from ASPCAP from DR10 in
an attempt to improve on some of the systematic features that 18 https://www.sdss.org/dr16/irspec/the-cannon/
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Figure 1. Stellar parameters derived from APOGEE spectra from various pipeline+data set combinations (listed clockwise from upper left): Synspec version of
ASPCAP, DR17 (J. Holtzman et al. 2022, in preparation; [Fe/H] is not available for cool and hot dwarfs); The Cannon (Ness et al. 2015), DR14; The Payne (Ting
et al. 2019), DR14; and APOGEE Net I (Olney et al. 2020), DR17.
Figure 2. Distribution of Teff and log g color coded by luminosity class (left panel) and spectral type (right panel) for sources in the literature in which both sets of
these parameters are measured independently. Diamonds are the data, crosses are the computed grid.
type and luminosity class, as well as a separate measurement of (2004), Lyubimkov et al. (2005), Crowther et al. (2006),
Teff and log g. In total, we have collated 851 measurements Kudritzki et al. (2008), Martayan et al. (2008), Fraser et al.
from Lyubimkov et al. (2002), Adelman (2004), Repolust et al. (2010), Lyubimkov et al. (2010), Lyubimkov et al. (2012),
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metallicity of the stars with Teff> 6500 K to compensate for the
inclusion of these spurious values in training.
3.2. Model Training
3.2.1. Initial Experiment Setup
The original trained model from Paper I saw only Teff in the
range of 3000–6700 K; including sources with Teff> 50,000 K
substantially skewed the weights within the network, and led to
both to a decreased performance on cooler stars (<6000 K), as
well as a lack of generalization among high-mass stars.
Therefore, we instead trained a new model from scratch, using
a similar model architecture and the PyTorch library Paszke
et al. (2017). In our new model, we converted Teff into log
space, and renormalized logTeff , log g, and [Fe/H] through
z-score standardization. That is, given a value x, it is
standardized as z = x- x¯ , where x̄ denotes the mean value of
S
our training set, and S the standard deviation. The actual mean
Figure 3. Distribution of Teff and log g in the training sample classes. Yellow and standard deviation values are reported in Table 2.
dots are the sources from APOGEE Net I, red circles are sources with Teff and
log g from SIMBAD for hot stars in a parameter space inaccessible to The limited number of OB stars in the the training data (and
APOGEE Net I. Blue squares show the sources for which Teff and log g were even greater scarcity of blue giants and supergiants) poses
transformed from the corresponding spectral type and luminosity class challenges for training; specifically, there is a risk that the model
combination. will prioritize maximizing performance among stars in the dense
regions of the Teff–log g space, even if it means sacrificing
Nieva (2013), Bianchi & Garcia (2014), David & Hillenbrand performance on these relatively rare stars. To penalize the model
(2015), Mahy et al. (2015), Cazorla et al. (2017), Martins & for ignoring these rare stars, we apply a nonuniform weighting to
Palacios (2017), Molina (2018), and Heuser (2018). each star in our training objective. We explored various weighting
We find that among OBAF stars, there is usually an schemes for our objective function, including gridding the Teff–
unambiguous correlation between the two sets of parameters log g parameter space and weighting stars in each grid cell
(Figure 2). We note that among the cooler stars (<6000 K), the inversely proportional to the number of stars in the grid cell.
luminosity class and log g tend to be rather inconsistent Ultimately, we settled upon a weighting scheme using Kernel
(Morgan 1937)—e.g., it is relatively common for giants found Density Estimation (KDE; Scott 1992). We used KDE to
in the red clump to have a luminosity class of III, IV, or V, despite approximate the density of stars in the 2D standardized Teff–
having very similar Teff and log g. However, as reliable Teff and log g space, and weight each star inversely proportional to its
log g are available for cool stars, in their case, such an exercise of density. If di is the density estimate for a star i, we weight the loss
converting these log g from luminosity classes is unnecessary. on star i with max ( c , 5). The 1/di term accomplishes theWe have encoded all spectral types to a numeric value: di
O= 00, B= 10, A= 20, F= 30, such that a star with a class of inversely proportional weighting; the max function puts a cap on
B2.5 would have a numeric label of 12.5. Similarly luminosity how much we weight any given star; and c is a constant chosen
classes I–V were transformed to numeric labels 1 5. If a star such that the average weight across stars is 1.–
had a range of luminosity classes listed, an average was taken Training a neural network relies on particular design
e.g., IV V would be labeled as 4.5. We then used a simple decisions and hyperparameters (such as the learning rate,— –
convolutional neural network to perform an interpolation expression for loss, architecture of the model itself, etc.). To
improve the performance we tuned our model by performing a
between the two sets of parameters for the OBAF stars to hyperparameter sweep with Weights and Biases (Table 3), a
construct a transformation grid. developer tool for machine learning (wandb; Biewald 2020).
In total, in constructing the training sample, we retained all of Tuning involves a guided search of the hyperparameter space,
the sources from APOGEE Net I if they had Teff< 6700 K or if
( ) repeatedly training models with different hyperparameters andthey had log g <11.3 ´ log10 Teff - 40 (Figure 3), to poten- evaluating their resulting performance on a held out valida-
tially improve on the parameters on the supergiants, as their tion set.
previously estimated Teff and log g might have been artificially
compressed due to a relative rarity of such objects. They were
supplemented with Teff and log g either transformed from the 3.2.2. Colors
spectral type, or from independently available measurements. Although the model architecture from Olney et al. (2020)
They are listed in Table 1. that operated only on the spectra could perform well on the full
In addition to these parameters, APOGEE Net I has also data sample, here we explore adding metadata for each star to
included [Fe/H] as a parameter it predicts. To retain this further improve the performance. This metadata consists of
functionality, we have preserved Fe/H input for low-mass stars, 2MASS and Gaia EDR3 broadband photometry (G, BP, RP, J,
and included it if an independent measurement exists. However, H, K), as well as parallax (Cutri et al. 2003; Gaia Collaboration
as a spectrum of high-mass stars does not have prominent metal et al. 2021). Temperature-sensitive features can be robustly
lines, requiring this feature would substantially limit the training recovered directly from the spectra itself, and, as the APOGEE
sample. Thus, we have forced [Fe/H]= 0 for all the hot stars spectra cover the H band, the effects of reddening are not as
where it was unavailable, and we do not report on the predicted significant in comparison to the optical light. Nonetheless, the
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Table 1
Stellar Parameters for Sources Observed by APOGEE
APOGEE α δ logT aeff log g
a [Fe/H]a SNR
ID (J2000) (J2000) (dex) (dex) (dex)
2M00000019-1924498 0.000832 −19.413851 3.7351 ± 0.0027 4.238 ± 0.038 −0.293 ± 0.013 229.8
2M00004819-1939595 0.200805 −19.666548 3.6667 ± 0.0024 1.674 ± 0.058 −1.308 ± 0.031 311.7
2M00011569+6314329 0.315407 63.242489 4.137 ± 0.020 3.684 ± 0.074 238.7
2M00032713+5533033 0.863082 55.550926 4.183 ± 0.028 3.81 ± 0.10 263.2
T b b b ceff,train log gg,train [Fe/H],train Reference Reference Spec
c
(dex) (dex) (dex) Type
3.734 4.224 −0.311 Paper I
3.670 0.88 Teff, Kordopatis et al. (2013)
4.306 4.04 SpT, Martin (1972) B2V
Note. Only a portion shown here. Full table is available in electronic form.
a Parameters predicted in this work.
b Parameters used to train the network.
c Reference for the parameters used in training; SpT shows that the spectral type and luminosity class were available, Teff shows that Teff, log g, and occasionally [Fe/
H] measurements were available.
(This table is available in its entirety in machine-readable form.)
Table 2 tensor is subsequently passed through another DNN to generate
Parameters for Standardization the final output (Figure 4).
Parameter Average Standard Deviation When tuning the hyperparameters of this model, we also
included the number of hidden layers in the DNN (from 0 to
logTeff 3.67057 0.09177 10, where 0 meant there was no color feature branch) and the
log g 2.92578 1.18907 number of hidden units in each layer. There are alternative
Fe/H −0.13088 0.25669 mechanisms one could use to inject the color feature
information; we leave an investigation of their relative merits
Table 3 to future work. The final model is presented in
Classifier Hyperparameter Tuning Values Appendix appendix.
Hyperparameter Values
Optimizer SGD, ASGD, Adam, Adamw, Adamax (Best: 3.2.3. Uncertainties
Adamax)
Learning Rate 0.005–0.000005 (Best: 0.00075) We generate the uncertainties in the parameters in a manner
Dropout 1%–80% (Best: 0.07646) similar as that described in Olney et al. (2020). We used the
Minibatch Size 128 (Best: 128) uncertainties in the spectral flux that is reported in the DR17
Loss Weighter KDE, Grid, Linear on Teff, Exponential on Teff(Best: apStar file, and created multiple realization of the same
KDE) spectrum. This was done through generating zero-mean, unit-
KDE Bandwidth 0.08–1 (Best: 0.7671) variance random Gaussian noise for each wavelength, multi-
Kernel Size 3, 5, 7, 11 (Best: 3) plying it by the spectral uncertainties, and adding the resulting
Double Conv Channel True, False (Best: False)
Disable Conv Layers Combination from { 2, 4, 6, 8, 10, 12 } or None noise to the spectrum. If the uncertainties in the spectral flux
(Best: None) were larger than five times the median uncertainty across all
Color Model Depth 0–10 Î (Best: 5) wavelengths, they were clipped to that limit. This was done to
Color Model Width 8, 16, 32, 64, 128, 256, 512, Varied (Best: Varied) prevent bad portions of a spectrum (such as in particularly
noisy regions, e.g., near the telluric lines) from skewing the
weights of the model. Although apStar files contain a pixel
spectra cover only a narrow ∼0.2μm band. As such, providing mask to identify bad pixels, it was not used, so as to allow the
colors to the network allows it to infer the shape of the entire network to recognize the noise on its own and down-weight it
SED. Through having access to additional data, it allows the when the model was training. The metadata (colors and
network to more finely tune its predictions. A similar approach parallaxes) were passed as is without adding variance.
has been previously considered before by Guiglion et al. (2020) Different realization of the same spectrum were all
in deriving stellar parameters for RAVE spectra. independently passed through to the model, resulting in
We feed color information as a seven-dimensional vector slightly different predictions of Teff, log g, and [Fe/H]. The
into a fully connected deep neural network (DNN) with final reported parameters for each star are a median of 20 such
rectified linear unit element-wise nonlinearities after each predictions, which was deemed representative compared to an
hidden layer as the activation function to achieve a nonlinear arbitrarily large number of scatterings for a few stars. The
transformation of the data. Afterwards, the output of this DNN uncertainties in these parameters are estimated through a
together with the output of convolutional layers used for the standard deviation, to measure a scatter in the outputs between
spectra is concatenated to form a single tensor. This combined different realizations.
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the model. Different parts of the parameter space had different
means of deriving their initial set of labels. Some of those
labels were based on synthetic spectra matching to the data,
some of them were based on theoretical isochrones, and some
of them were based on empirical photometric relations. Such a
stitching together of various sets of labels may have caused
discontinuities in the parameter space that the model has
learned to interpolate across. The physics included in
computing the original set of synthetic spectra from which
some of the labels were derived may be incomplete—this may
introduce systematic offsets in the predicted parameters that are
difficult to quantify. This is generally the case with most
pipelines deriving parameters for data from large spectroscopic
surveys. Nonetheless, the accuracy that can be inferred from
the overall parameter distribution is sufficient for a wide variety
of applications.
4.2. High-mass Stars
In general, as APOGEE Net II matches the performance of
APOGEE Net I for low-mass stars; the primary improvement in
the pipeline is in its new ability to generalize the parameters of
high-mass stars. Indeed, the derived Teff are strongly correlated
to the previously measured spectral types for the same stars
(Figure 7), particularly among the main-sequence stars. There
is some scatter; for the high-mass stars this scatter is in part
driven by multiplicity. As almost all O stars tend to be
multiples (Preibisch et al. 2001; Duchêne & Kraus 2013), it is
not uncommon for spectral features of both stars to be detected
in the same spectrum. Although spectral types can contain
information on both stars (e.g., O5+O9.5), such information is
Figure 4. Architecture of the neural net model used in this paper. See also
Appendix appendix for code. difficult to encode, as such, a comparison is done for only one
star in the pair, but the derived Teff may favor a second star.
4. Results Different wavelength regimes may also be more or less
sensitive to the presence of a companion, as such, optical
4.1. Low-mass Stars spectra, from which most spectral types have been derived may
The training and initial testing on a withheld sample was not offer a perfect match to the H-band APOGEE spectra. As
performed on the APOGEE data reduced with the DR16 such, the correlation between spectral type and the measured
version of the pipeline. We then apply the trained model to the Teff is particularly strong among B stars that had spectral types
derived directly from the APOGEE spectra (Ramírez-Preciado
APOGEE DR17 data in full. The two sets of parameters et al. 2020) rather than those measured from other data sets.
between DR16 and DR17 reductions are typically consistent The hot main-sequence stars (Teff> 10
4 K, log g> 3.7) are
with each other within the ∼1.2–1.5σ. relatively numerous in the sample and they tend to have a set
The resulting distribution of Teff and log g is shown in log g as a function of their Teff and their Teff (and the spectralFigure 5. Although [Fe/H] are predicted for all stars, we do not features that correspond to it) vary smoothly as a function of
report it for sources with Teff> 6500 K, as the training labels the mass of the star. However, this is not the case for blue
for them are unreliable. giants and blue supergiants. Only a few hundred of these stars
The typical reported uncertainties are 0.03 dex in log g, with luminosity classes from the literature have been observed.
0.002 dex in logTeff (30 for a 6000 K star), and 0.01 dex in There is also a large gap in log g between the blue giants and
[Fe/H], which is largely consistent with the typical uncertain- blue supergiants (e.g., Figure 2, the difference between red and
ties in APOGEE Net I. On average the reported uncertainties green lines); this gap is difficult for a CNN to fully reproduce,
are also comparable to those reported by ASPCAP DR17 for especially given a limited sample size owing to the rarity of
these parameters. such objects, resulting in log g of supergiants being over-
Overall, the parameters for cool stars show a good agreement estimated and placing them closer to log g distribution of other
with APOGEE Net I (Figure 6). Examining the difference in stars. Finally, luminosity classes at Teff< 8000 K become less
the parameters between two versions of the pipeline relative to precisely defined relative to log g (e.g., Figure 2). Combined,
the reported uncertainties, the scatter is typically within 1.5–2σ these effects make it difficult to achieve optimal performance in
(Figure 6, right panel). As such, this is likely a factor that extracting stellar parameters of these type of stars. The
should be considered regarding a systematic uncertainty in the mismatch in log g for the supergiants between the training
absolute calibration of the spectral parameters between two labels and those predicted by the model is partially apparent in
separate models. While the derived parameters with APOGEE Figure 6, but these objects are extremely rare.
Net I and II are largely self-consistent, there may be further However, we note that qualitatively, examining the distribu-
systematic features that may not necessarily be accounted by tion of hot stars in the right panel of Figure 7 color coded by
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Figure 5. Derived Teff and log g distribution for all ∼630,000 stars in the Milky Way in the APOGEE DR17 data.
Figure 6. Comparison of parameters between the training labels and the model predictions, using the reserved test sample that was not used in training the model. Left:
comparison of log g, color coded by Teff. Middle: comparison of Teff, color coded by log g. Right: difference between the training labels derived from APOGEE Net I
for cool stars with Teff < 6500 K and the model predictions for the same stars in this work, divided by the uncertainties measured both by APOGEE Net I and II added
in quadrature, to demonstrate the typical magnitude of residuals, in σ.
their luminosity types does show a preference for assigning APOGEE spectrum, combined with various atomic features
more luminous types to the sources with lower log g at a given (for Teff< 10,000 K), as well as He II absorption (for
Teff. Thus, although their log g may be overestimated, it can Teff> 25,000 K), are effective at determining Teff. Similarly,
nonetheless be used to separate stars of different luminosity surface gravity broadening is imprinted on the H lines: while
classes. log g is more difficult to measure, dwarfs do appear to have
Examining the spectra directly, they can be sorted based on somewhat wider lines than the giants (Figure 8, bottom).
their Teff measurements into a sequence (Figure 8, top). While Another method of evaluation is via HR diagram. Figure 9
hot stars lack the number of spectral features that are present in shows that the bluer stars are preferentially hotter as well, and
cooler stars, equivalent widths of H lines that fall into the that the more luminous stars tend to have lower log g. It should
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Figure 7. Left: comparison between spectral types in literature and the Teff measured for the stars in the sample, color coded by the luminosity class. Yellow circles
show the sources with spectral types measured directly from the APOGEE spectra, from Roman-Lopes et al. (2019, 2020) and Ramírez-Preciado et al. (2020). Spectral
types are formatted to range as O = 0–10, B = 10–20, A = 20–30, etc. Right: distribution of Teff and log g color coded by the literature luminosity class. Note that the
concentration of the supergiants at Teff ∼ 6000 K and log g = 3.5 is primarily from the Magellanic clouds (Section 4.3).
be noted that nearby OB stars are too bright to be targeted for conditions result in particularly informative region to evaluate
the spectroscopic observations with the current targeting the performance of the network.
strategy, as such hot stars tend to be more distant and more We select the MC members based on the parallax (<0.05
susceptible to be reddened due to extinction. Indeed, the mas) and radial velocity (>100 km s−1). Examining the
gradient of constant Teff or log g color coded on the HR distribution of Teff and log g of these stars does show some
diagram does appear to follow the reddening law, and it is surprising features: the red giant branch (RGB) appears to be
possible to deredden the hottest OB stars (logTeff > 4.2) to the trifurcated, in a manner that is not seen in the APOGEE sample
tip of the main sequence. of the Milky Way (Figure 11). However, there are physical
The final method of evaluation of the accuracy in the interpretations for this segmentation: the stars within each
determination of Teff and log g of high-mass stars with respect overdensity in the spectroscopic parameter space do trace
to the other sources is through examining the distribution of the different spatial regions in the MCs, and some of them have a
sources within the Galaxy. As high-mass stars have short particular targeting flag. Furthermore, the relative placement of
lifetimes, they are not expected to be located far from their these segments is mostly consistent with the parameters derived
regions of birth. Indeed, the hottest stars (Teff> 20,000 K) have from ASPCAP. However, in ASPCAP the sequences are
a very clumpy spatial distribution that almost exclusively trace somewhat closer together, partially overlapping, producing a
known star-forming regions. Similarly, somewhat cooler stars more continuous gradient. This could be due to the fact that in
(10,000< Teff< 20,000 K) are located primarily within the producing a fit, ASPCAP is considering all stellar parameters
Galactic disk, with the disk scale height increasing with (including Teff, log g, and all of the elemental abundances)
decreasing Teff (Figure 10), as the disk scale height also independent variables, and Teff could be skewed by the
depends on the age of the stellar population tracer being influence of opacity contributed by the C and O abundances.
employed. Along the RGB, the middle of the three overdensities
Similar distribution of sources is observed among the blue (Figure 11, yellow) are the common RGB stars and RSGs; the
and yellow supergiants. Although their Teff is lower than for the location of this branch is consistent with what is observed in
main-sequence counterparts of the same mass, selecting the Milky Way.
sources with, e.g., Teff> 8000 K and log g< 3.5 also The hotter branch (Figure 11, dark blue) is somewhat more
preferentially traces younger parts of the Galaxy. peculiar. Though there are stars in the Milky Way that do fall
into that parameter space, they do so solely due to being regular
RGB stars with low metallicity, there is not a concentration of
4.3. Magellanic Clouds them at Teff∼ 5000 K log g∼ 1.8 as there is in MCs. Their
The APOGEE-2 survey has primarily observed the stars of placement on 2MASS color–magnitude diagrams suggests that
the Milky Way; as such, APOGEE Net has been trained in the they are likely to be carbon-rich AGB-C stars (Boyer et al.
Milky Way stars almost exclusively—however, there have 2011; Nidever et al. 2020).
been several dedicated programs targeting stars in the The cooler branch (Figure 11, green) is particularly unusual,
Magellanic clouds (MCs; Zasowski et al. 2017; Nidever et al. as there are no counterparts to these stars in the APOGEE
2020; Santana et al. 2021). These galaxies are significantly sample in the Milky Way. However, all of these sources share
more metal-poor (Nidever et al. 2020; Hasselquist et al. 2021); the same targeting flag of APOGEE2_WASH_GIANT, which
as such, the unfamiliar chemistry and other features unique to is a classification that predates the release of Gaia DR2,
MCs may skew some of the weights within the APOGEE Net performed using Washington filter system to separate likely
model, particularly as abundances also affect Teff and log g due dwarfs and giants. Though sources with WASH_GIANT flag
to various elements playing a significant role in the energy have been observed from both northern and southern hemi-
transport in the outer structure of a star. As such, these extreme sphere, the peculiar concentration is limited only among the
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The Astronomical Journal, 163:152 (13pp), 2022 April Sprague et al.
Figure 8. Top: example APOGEE spectra for sources with logTeff ranging from 4.5 (blue) to 3.6 (red), with a step of 0.1 dex. The spectra are arbitrarily scaled in flux.
Some of the temperature-sensitive lines that can be used to infer parameters of hot stars are shown in gray, such as Brackett H lines and He II lines. The gaps in the
spectra correspond to the chip gap. Bottom: spectra with similar logTeff ∼ 4.1, but with three different log g.
Figure 9. HR diagram of the APOGEE sample of higher-mass stars, color coded by the predicted Teff (left) and log g (right). Black arrows show the reddening vector
corresponding to 1 AV.
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The Astronomical Journal, 163:152 (13pp), 2022 April Sprague et al.
Figure 10. Top: distribution of sources in the APOGEE DR17 data in galactic coordinates, color coded by the maximum Teff of a source along a line of sight. Note that
sources with Teff > 10,000 K tend to be concentrated in the plane, and sources with Teff > 20,000 K tend to primarily trace young star-forming regions. Bottom:
distribution of the sources, but limited to only sources with Teff > 8000 K, with the symbol size representative of log g < 3.5, to highlight the position of blue and
yellow giants and supergiants.
members of the Magellanic clouds. This clump also matches closer toward solar. Most of these sources have been
well to the variable stars identified by OGLE, usually as long specifically targeted for being Cepheid variables.
period variables with the subtype of small amplitude red giants
(Soszyński et al. 2009, 2011). The placement of these stars
along the color–magnitude diagram suggests they are oxygen- 5. Conclusions
rich AGB-O stars (Boyer et al. 2011). We present stellar parameters from the APOGEE spectra
Stars with Teff> 6000 K and log g> 2 (Figure 11, red) derived via a neural network, APOGEE Net. This is the first
appear to be young blue and yellow supergiants, and they pipeline for analyzing these data that is capable of extracting
appear to be spatially concentrated in the regions of active star stellar parameters for all stars, regardless of their temperature
formation. (from ∼3000 K to 50,000 K, which surpasses the hot limit of
Sources with log g∼ 2 and Teff∼ 6000 K (Figure 11, light 20,000 K reported by ASPCAP in DR17) or surface gravity
blue) have different metallicity from the supergiants that is (from ∼0 to ∼5 dex), in a self-consistent manner. This includes
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The Astronomical Journal, 163:152 (13pp), 2022 April Sprague et al.
Figure 11. Stars observed by APOGEE toward the Magellanic clouds. Top left: distribution of Teff and log g of the likely members (red), superimposed on the Milky
Way stars in grayscale background. Top middle: same as before, only with stars color coded by their estimated [Fe/H]. Top right: same as before, but separating the
stars into five categories based on the parameter space: red giant branch/red supergiant (RGB/RSG), carbon-rich AGB stars (C-AGB), oxygen-rich AGB stars (O-
AGB), blue and yellow supergiants (BSG/YSG), and the Cepheid variables. Second row left: 2MASS color–magnitude diagram of the stars that fall into this
parameter space. Second row right: ASPCAP parameters for the stars in this parameter space. Although three sequences of RGB/AGB stars overlap, they are
nonetheless distinct from one another in this data set as well. Other panels show the spatial distribution of the stars in these categories.
pre-main-sequence stars, main-sequence dwarfs, red giants, overestimated (closer to the main sequence) than the
massive-main-sequence stars, and blue supergiants. parameters in the training set may imply. Nonetheless, the
These parameters do have some dependence on the trained network does appear to place stars along a representative
neural network model: although this is less of an issue for sequence in both Teff and log g as such these types of stars can
common objects, the rarer classes of objects may not fully nonetheless be identified and selected.
reach the precise parameter space these objects are supposed to In addition to the stars observed in the Milky Way,
inhabit, e.g., blue supergiants may have their log g somewhat APOGEE Net appears to achieve adequate performance in
11
The Astronomical Journal, 163:152 (13pp), 2022 April Sprague et al.
regions with less familiar (to the neural network) chemistry, Appendix A
such as the Magellanic clouds. Although it does produce some Model Code
surprising features in the Teff and log g parameter space (which
are also present in other pipelines, such as ASPCAP, but to a class Model():
lesser degree, possibly due to allowing for independent class MetadataNet(nn.Module):
, ’’’’’’A simple feed-forward network for
parameters for C and O in the fitting process), these features metadata.’’’’’’
do appear to be physically motivated, identifying distinct def_ _init_ _(self):
classes of objects. ’’’’’’Initializes Metadata Net as a 5-layer deep
APOGEE DR17 is the final data release produced under network.’’’’’’
SDSS-IV. The next generation of the survey, SDSS-V, intends super(Model.MetadataNet, self)._ _init_ _()
to obtain spectra of >6 million stars, providing a much more self.l1=nn.Linear(7, 8)
homogeneous spectroscopic coverage of the Milky Way self.l2=nn.Linear(8, 16)
self.l3=nn.Linear(16, 32)
(Kollmeier et al. 2017), including young stars along the self.l4=nn.Linear(32, 32)
Galactic disk, both low-mass and high-mass. APOGEE Net and self.l5=nn.Linear(32, 64)
its subsequent iterations provide the means to uniformly infer self.activation=F.relu
stellar parameters in these spectra, which in turn allows to def forward(self, x):
analyze the star-forming history of the Galaxy. ’’’’’’Feeds some metadata through the network.
As more and more spectra are observed, and the census of Args:
x: A minibatch of metadata.
stars in rarer classes grows, it may be possible to retrain the Returns:
network to achieve an even better generalization across the An encoding of the metadata to feed into APOGEE Net.
entirety of the parameter space. However, the catalog presented ’’’’’’
here is a substantial step forward in characterizing spectro- x=self.activation(self.l1(x))
scopic stellar properties for all stars. x=self.activation(self.l2(x))
x=self.activation(self.l3(x))
The authors thank the Nvidia Corporation for their donation x=self.activation(self.l4(x))
x=self.activation(self.l5(x))
of GPUs used in this work. K.P.R. acknowledges support from return x
ANID FONDECYT Iniciación 11201161. A.S. gratefully class APOGEENet(nn.Module):
acknowledges funding support through Fondecyt Regular def_ _init_ _(self, num_layers: int=1, num_targets:
(project code 1180350) and from the ANID BASAL project int=3, drop_p: float=0.0) −> None:
FB210003. Funding for the Sloan Digital Sky Survey IV has super(Model.APOGEENet, self)._ _init_ _()
been provided by the Alfred P. Sloan Foundation, the U.S. # 3 input channels, 6 output channels, convolution
self.conv1=nn.Conv1d(num_layers, 8, 3, padding=1)
Department of Energy Office of Science, and the Participating
self.conv2=nn.Conv1d(8, 8, 3, padding=1)
Institutions. SDSS acknowledges support and resources from self.conv3=nn.Conv1d(8, 16, 3, padding=1)
the Center for High-Performance Computing at the University self.conv4=nn.Conv1d(16, 16, 3, padding=1)
of Utah. The SDSS website is www.sdss.org. self.conv5=nn.Conv1d(16, 16, 3, padding=1)
SDSS is managed by the Astrophysical Research Con- self.conv6=nn.Conv1d(16, 16, 3, padding=1)
sortium for the Participating Institutions of the SDSS self.conv7=nn.Conv1d(16, 32, 3, padding=1)
Collaboration including the Brazilian Participation Group, the self.conv8=nn.Conv1d(32, 32, 3, padding=1)
self.conv9=nn.Conv1d(32, 32, 3, padding=1)
Carnegie Institution for Science, Carnegie Mellon University, self.conv10=nn.Conv1d(32, 32, 3, padding=1)
Center for Astrophysics | Harvard and Smithsonian (CfA), the self.conv11=nn.Conv1d(32, 64, 3, padding=1)
Chilean Participation Group, the French Participation Group, self.conv12=nn.Conv1d(64, 64, 3, padding=1)
Instituto de Astrofísica de Canarias, The Johns Hopkins self.metadata=Model.MetadataNet()
University, Kavli Institute for the Physics and Mathematics #an affine operation: y=Wx + b
* *
of the Universe (IPMU)/University of Tokyo, the Korean self.fc1=nn.Linear(64 133 1 + 64, 512)
self.fc1_dropout=nn.Dropout(p=drop_p)
Participation Group, Lawrence Berkeley National Laboratory, self.fc2=nn.Linear(512, 512)
Leibniz Institut fr Astrophysik Potsdam (AIP), Max-Planck- self.fc3=nn.Linear(512, num_targets)
Institut fr Astronomie (MPIA Heidelberg), Max-Planck-Institut def forward(self, x: torch.Tensor, m: torch.Tensor)
fr Astrophysik (MPA Garching), Max-Planck-Institut fr Extra- −> torch.Tensor:
terrestrische Physik (MPE), National Astronomical Observa- ’’’’’’Feeds data through the network.
tories of China, New Mexico State University, New York Args:
University, University of Notre Dame, Observatrio Nacional/ x (Tensor): A spectra minibatch.
m (Tensor): A metadata minibatch corresponding to x.
MCTI, The Ohio State University, Pennsylvania State Returns:
University, Shanghai Astronomical Observatory, United King- A prediction from the network.
dom Participation Group, Universidad Nacional Autnoma de ”””
Mxico, University of Arizona, University of Colorado Boulder, # Max pooling over a (2) window
University of Oxford, University of Portsmouth, University of x = F.max_pool1d(F.relu(self.conv2(F.relu(self.
Utah, University of Virginia, University of Washington, conv1(x)))), 2)
x = F.max_pool1d(F.relu(self.conv4(F.relu(self.
University of Wisconsin, Vanderbilt University, and Yale conv3(x)))), 2)
University. x = F.max_pool1d(F.relu(self.conv6(F.relu(self.
Software: TOPCAT (Taylor 2005), APOGEE Net II conv5(x)))), 2)
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