11institutetext: Department of Physics, University of Notre Dame, Notre Dame,
IN. 46556, USA
11email<EMAIL_ADDRESS>22institutetext: JINA Center for the Evolution of the
Elements (JINA-CEE), USA 33institutetext: Departamento de Astronomia,
Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre,
RS, Brazil 44institutetext: Centro de Estudios de Física del Cosmos de Aragón
(CEFCA) - Unidad Asociada al CSIC, Plaza San Juan, Planta 2, E-44001, Teruel,
Spain 55institutetext: Instituto de Astrofísica de Canarias, E-38205 La
Laguna, Tenerife,Spain 66institutetext: Departamento de Astrofísica,
Universidad de La Laguna, E-38206 La Laguna, Tenerife, Spain 77institutetext:
Department of Astronomy and Space Science, Chungnam National University,
Daejon 34134, Korea 88institutetext: Observatório Nacional - MCTIC (ON), Rua
Gal. José Cristino 77, São Cristóvão, 20921-400, Rio de Janeiro, Brazil
99institutetext: Centro de Astrobiología (CSIC-INTA), ESAC, Camino Bajo del
Castillo S/N, E-28692 Villanueva de la Cañada Madrid, Spain 1010institutetext:
Instituto de Astronomia, Geofísica e Ciências Atmosféricas (IAG), Universidade
de São Paulo (USP), Rua do Matão 1226, C. Universitária, São Paulo, 05508-090,
Brazil 1111institutetext: Departamento de Física, Universidade Federal de
Sergipe (UFS), Av. Marechal Rondon, S/N, 49000-000 São Cristóvão, SE, Brazil
1212institutetext: Centro de Estudios de Física del Cosmos de Aragón (CEFCA),
Plaza San Juan, 1, E-44001, Teruel, Spain 1313institutetext: University of
Michigan, Dept. Astronomy, 1085 S. University Ann Arbor, MI 48109, USA
1414institutetext: University of Alabama, Dept. of Phys. & Astronomy, Gallalee
Hall, Tuscaloosa, AL 35401, USA 1515institutetext: X-ray Astrophysics
Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
1616institutetext: Department of Physics, University of Maryland, Baltimore
County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

# J-PLUS: Identification of low-metallicity stars with
artificial neural networks using SPHINX

D. D. Whitten, 1122 V. M. Placco, 1122 T. C. Beers, 1122 A. L. Chies-Santos 33
C. Bonatto 33 J. Varela 44 D. Cristóbal-Hornillos 44 A. Ederoclite 44 T.
Masseron 5566 Y. S. Lee 77 S. Akras 88 M. Borges Fernandes 88 J. A. Caballero
99 A. J. Cenarro 44 P. Coelho 1010 M. V. Costa-Duarte 1010 S. Daflon 88 R. A.
Dupke 8813131414 R. Lopes de Oliveira 15151616 10 10 8 8 C. López-Sanjuan 44
A. Marín-Franch 44 C. Mendes de Oliveira 1010 M. Moles 1212 A. A. Orsi 1212 S.
Rossi 1010 L. Sodré 1010 H. Vázquez Ramió 1212

(Received 15 May 2018)

###### Abstract

Context. We present a new methodology for the estimation of stellar
atmospheric parameters from narrow- and intermediate-band photometry of the
Javalambre Photometric Local Universe Survey (J-PLUS), and propose a method
for target pre-selection of low-metallicity stars for follow-up spectroscopic
studies. Photometric metallicity estimates for stars in the globular cluster
M15 are determined using this method.

Aims. By development of a neural-network-based photometry pipeline, we aim to
produce estimates of effective temperature, $T_{\rm eff}$, and metallicity,
[Fe/H], for a large subset of stars in the J-PLUS footprint.

Methods. The Stellar Photometric Index Network Explorer, SPHINX, is developed
to produce estimates of $T_{\rm eff}$ and [Fe/H], after training on a
combination of J-PLUS photometric inputs and synthetic magnitudes computed for
medium-resolution ($R\sim$2000) spectra of the Sloan Digital Sky Survey. This
methodology is applied to J-PLUS photometry of the globular cluster M15.

Results. Effective temperature estimates made with J-PLUS Early Data Release
photometry exhibit low scatter, $\sigma(T_{\rm eff})$ = 91 K, over the
temperature range 4500 $<T_{\rm eff}$ (K) $<$ 8500\. For stars from the J-PLUS
First Data Release with 4500 $<T_{\rm eff}$ (K) $<$ 6200, $85\pm 3$ % of stars
known to have [Fe/H] $<-2.0$ are recovered by SPHINX. A mean metallicity of
[Fe/H]=$-2.32\pm 0.01$, with a residual spread of 0.3 dex, is determined for
M15 using J-PLUS photometry of 664 likely cluster members.

Conclusions. We confirm the performance of SPHINX within the ranges specified,
and verify its utility as a stand-alone tool for photometric estimation of
effective temperature and metallicity, and for pre-selection of metal-poor
spectroscopic targets.

###### Key Words.:

stars: chemically peculiar – stars: fundamental parameters – stars: abundances
– techniques: photometric – methods: data analysis

##  1 Introduction

The chemical properties of individual stars in the Milky Way are crucial in
order to develop an understanding of our Galaxy’s chemical evolution and
assembly history. In particular, the metallicity distribution function of
Galactic halo stars is among the most important observational constraints for
cosmological models (Beers & Christlieb 2005; Salvadori et al. 2010). The
comparatively rare stars with metallicity below 1% of the Solar value –
described in terms of their metal abundance, very metal-poor (VMP;
[Fe/H]111[A/B]$\equiv\log_{10}(N_{\rm A}/N_{\rm B})_{*}-\log_{10}(N_{\rm
A}/N_{\rm B})_{\odot}$ $<-2.0$), extremely metal-poor (EMP; [Fe/H] $<-3.0$),
and ultra metal-poor (UMP; [Fe/H] $<-4.0$) – are expected to include the
earliest generations of stars to have formed since the Big Bang. With the
exception of mass-transfer binaries and highly evolved late-type giants, these
ancient stars retain the chemical signature of their natal environments.
Measurement of the chemical abundances of the earliest stars thereby provides
a means to study the nucleosynthetic pathways and astrophysical mechanisms
that were in operation during the first generations of stars born in the early
Universe. One example is the most iron-poor star presently known, SMSS
J031300.36-670839.3 ([Fe/H] $\leq-7.1$), from which the carbon ([C/Fe]) and
[Mg/Ca] abundance ratios are believed to have originated from a single
explosion of a metal-free $\sim 60$ M☉-mass star (Keller et al. 2014).

Figure 1: Synthetic spectra of varying abundances are shown plotted over the
J-PLUS filters $J0395$, $J0410$, and $J0430$. The $J0395$ filter is optimally
centered on the Ca II H & K lines, which can be used as indicators of the
overall stellar metallicity. The temperature-sensitive H$\delta$ line is
apparent in the F410 filter. The $J0430$ filter captures the CH $G$-band,
which serves as a carbon indicator.

A substantial fraction of VMP stars exhibit large enhancements of their [C/Fe]
ratios, increasing rapidly with declining [Fe/H] (see Yoon et al. 2018 and
references therein); these are known collectively as carbon-enhanced metal-
poor (CEMP) stars (Beers & Christlieb 2005). Guided by the work of Spite et
al. (2013) and Bonifacio et al. (2015), Yoon et al. (2016) explored the
complex morphology of CEMP stars in the $A$(C)-[Fe/H] space222$A$(X) = log
$\epsilon$(X) = log(NX/NH) + 12, where $\rm X$ represents a given element..
The so-called Yoon-Beers diagram (Fig. 1 of Yoon et al.) provides evidence for
multiple progenitors and/or environments in which different sub-classes of
CEMP stars are found. The identification and study of significantly larger
samples of CEMP stars is crucial for future studies, as only $300+$ of these
stars with available high-resolution spectroscopy are currently known.

Obtaining chemical abundances and overall estimates of metallicity is a costly
endeavor, however, requiring pre-selection and follow-up spectroscopic
analysis for confirmation. While there are now tens of thousands of VMP stars
with well-measured (medium-resolution) spectroscopic metallicities, the
numbers of known EMP and UMP stars are considerably smaller; in particular,
$\sim$30 UMP stars have been discovered to date (the compilation as given in
Placco et al. 2015, 2016, and Abohalima & Frebel 2017; Starkenburg et al.
2018; Frebel et al. 2018; Aguado et al. 2018).

###  1.1 Photometric methods

Wide-field photometry offers an alternative means to probe the chemical
characteristics of stars, and presents a method for pre-selection of targets
based on their colors. Using broad-band photometry from the Sloan Digital Sky
Survey (SDSS; York et al. 2000), Ivezić et al. (2008) developed a methodology
for estimating metallicity for F- and G-type main-sequence stars ($5000<T_{\rm
eff}$ (K) $<7000$, $3<\log{g}<5$) using polynomial regressions based on de-
reddened $u-g$ and $g-r$ colors. This approach was found to be effective down
to [Fe/H] $\sim-2.0$.

Later, An et al. (2013) and An et al. (2015) used fiducial isochrone fits to
SDSS ugriz photometry to extend metallicity determinations for main-sequence
stars with broad-band photometry down to at least [Fe/H] $\sim$ $-2.5$. This
new threshold is below the peak in the metallicity distribution function of
outer-halo population stars ([Fe/H]$=-2.2$; Carollo et al. 2007, 2010),
leading them to conclude that $\sim$35–-55% of local halo stars belong to this
population. Other notable moderate- and narrow-band photometric metallicity
estimation techniques have existed for many years, for instance, the
Washington (Canterna 1976) and Strömgren (Strömgren 1963, 1964) systems.
However, no wide-field large sky-coverage surveys in these systems have been
carried out to date. The Canada-France Imaging Survey, which will cover 10,000
deg2 of the northern sky with a $u$-band, demonstrated metallicity sensitivity
of $\sigma$[Fe/H] = 0.2 dex down to [Fe/H] $\sim-2.5$ for dwarf stars (3 ¡
log$g$ ¡ 5) when combined with SDSS and PS1 photometry (Ibata et al. 2017a,
b).

Pre-selection of targets for spectroscopic follow-up can dramatically increase
the success rate for the identification of large numbers of metal-poor stars.
For example, using all-sky APASS optical, 2MASS near-infrared, and WISE mid-
infrared photometry, Schlaufman & Casey (2014) developed an efficient method
for selecting bright ($V<$ 14) metal-poor candidates based on their lack of
molecular absorption near 4.6 $\mu$m. This effect was demonstrated to be
present in atmospheres of all surface gravities in the effective temperature
range $4500\lesssim T_{\rm eff}$ (K) $\lesssim 5500$. Of these targets, 32.5%
were found to have $-3.0<$ [Fe/H] $<-2.0$. The identification of bright metal-
poor candidates is of great benefit to high-resolution follow-up observations,
for which the acquisition of high-resolution spectra with high signal-to-noise
can become prohibitively expensive in terms of telescope time.

New multi-band photometric surveys build upon previous broad-band photometric
metallicity determinations by implementation of one or more narrow-band
filters across the optical and near-infrared spectrum to target key stellar
absorption features. The SkyMapper Southern Survey (Keller et al. 2007) makes
use of a 310 Å $v$-band filter, which covers (but is not centered on) the Ca
II K line, along with SDSS-like $ugriz$ filters, to survey much of the entire
Southern Hemisphere sky. Other recent ongoing surveys, such as Pristine
(Starkenburg et al. 2017), are employing a narrow-band ($\sim$100 Å) filter
centered on the Ca II H & K lines, a technique pioneered by Anthony-Twarog et
al. (1991). When used in conjunction with pre-existing SDSS or Pan-STARRs
(Tonry et al. 2012) broad-band filter photometry, they obtain improved
photometric metallicity estimates for numerous stars over large swaths of sky.
As described by Starkenburg et al. (2017), Pristine’s resulting success rate
for recovering EMP stars is 26%, with 80% of the remaining candidates being
VMP stars. When combined with SDSS photometry, Pristine has demonstrated an
accuracy of $\sim$0.2 dex down to [Fe/H] $<-$3.0. The use of Ca II H & K
photometry from Pristine has already led to the discovery of a [Fe/H]$<-4.66$
star, Pristine_221.8781+9.7844 (Starkenburg et al. 2018).

###  1.2 The Javalambre Photometric Local Universe Survey

Located at the Observatorio Astrofísico de Javalambre (OAJ, Teruel, Spain),
the Javalambre Auxiliary Survey Telescope (JAST/T80) is a 83 cm telescope that
is currently carrying out the Javalambre Photometric Local Universe Survey
(J-PLUS; Cenarro et al. 2018). A twin of JAST/T80, based at the Cerro Tololo
InterAmerican Observatory (CTIO, Chile), is executing the Southern Photometric
Local Universe Survey (S-PLUS; Mendes de Oliveira et al. 2018), a Southern
Hemisphere counterpart of J-PLUS.

J-PLUS is the first large-sky survey conducted at the OAJ, and was initially
conceived to aid with photometric calibration of the upcoming Javalambre
Physics of the Accelerating Universe Survey (J-PAS; Benitez et al. 2014), to
be executed as well at the OAJ. While J-PAS is motivated by cosmological goals
and, hence, has formally stronger requirements than J-PLUS in terms of
photometric depth and number of narrow-band filters (see Benitez et al. (2014)
for details), J-PLUS has scientific goals that are largely (but not
exclusively) related to the science of the Milky Way Halo and local Universe
studies. The seven narrow-band ($\sim$100 Å) filters of J-PLUS ($J0378$,
$J0395$, $J0410$, $J0430$, $J0450$, $J0515$, $J0660$, $J0861$) are
specifically designed to detect a variety of absorption features across the
optical spectrum (Cenarro et al. (2018) for details). The filter system also
hosts traditional $ugriz$ bands, similar to those of SDSS, but with a more
stable $u$-band response (Cenarro et al. 2018). Fig. 1 depicts the location of
some filters of special interest – $J0395$, $J0410$, and $J0430$, from left to
right – along with the corresponding spectral features, illustrated with
synthetic spectra.

These filters provide the sensitivity necessary to detect absorption features
such as the Ca II H & K lines, and the CH $G$-band, but mapping their behavior
to estimate metallicity, [Fe/H], and the carbon-to-iron abundance ratio,
[C/Fe], presents a highly degenerate problem. At temperatures above $\sim
5750$ K, the CH molecule begins to dissociate, while the H$\gamma$ line
broadens to the extent of disrupting the feature. The Ca II H & K lines also
exhibit a strong temperature dependence. In addition, many lines respond to
varying surface gravity due to Stark pressure broadening. A robust technique
capable of unraveling the complex behavior of the parameter space explored by
these filters for estimates of stellar parameters is thus required.

###  1.3 Artificial Neural Networks

Machine learning tools – and in particular, Artificial Neural Networks (ANN) –
have a long history (Rosenblatt 1958), but have found success in data-driven
astronomical applications. Once adequately trained, these networks are
powerful statistical pattern recognition tools capable of modeling highly
complex behavior, through implementation of non-linear activation functions
according to a user-specified architecture. Fabbro et al. (2018) applied their
deep convolutional neural network, StarNet, to SDSS-III APOGEE (Eisenstein et
al. 2011) spectra for determination of effective temperature, surface gravity,
and metallicity, with precision and accuracy similar to that of the APOGEE
pipeline. Using APOGEE DR14 for validation, Ting et al. (2018) applied a
neural network function in their method, The Payne, to interpolate training
sets of physical ab initio spectral models, and produced estimates of stellar
parameters and 15 element abundances.

Deep convolutional networks have also been used to determine the evolutionary
states of red giants from astroseismology (Hon et al. 2017). Using frequency
power spectra from the Kepler mission (Borucki et al. 2010), Hon et al. (2018)
classified 426 red giants as red giant branch or helium-core burning stars.
Neural networks have been employed for classification-based problems in
astronomy as well, such as star-galaxy classification (Kim & Brunner 2017) and
spectral classification (Kheirdastan & Bazarghan 2016).

In this paper, the utility of ANNs for estimates of effective temperature and
metallicity is explored. We present the Stellar Photometric Index Network
Explorer (SPHINX333https://github.com/DevinWhitten/SPHINX), a software package
based on ANN estimation of stellar parameters ($T_{\rm eff}$ and [Fe/H]) from
the J-PLUS mixed-bandwidth photometry. All training catalogs and parameter
determination routines used in the text are provided. The databases and ANN
used in the development and operation of SPHINX are described in Sections 2
and 3. The basic structure is outlined in Section 4. In Section 5, the
training process and results of effective temperature determinations are
described, followed by the results of the metallicity determinations in
Section 6. An application of SPHINX to a case study of the metal-poor globular
cluster M15 is conducted in Section 7. A preliminary investigation of carbon
sensitivity within the J-PLUS filter system is described in Section 8, and a
concluding discussion of results and future applications is given in Section
9.

##  2 Databases

Figure 2: Left: Hess diagram of the SDSS Reservoir available for training of
the photometric ANN pipeline. Top Right: Metallicity distribution of the SDSS
Reservoir and the subset with J-PLUS DR1 photometry. Bottom Right:
Distribution of effective temperatures for the subset of the SDSS Reservoir
with [Fe/H] ¡ -2.5.

###  2.1 The J-PLUS Early and First Data Releases

Calibration and testing of the network’s inputs are performed in part with the
J-PLUS data set. The J-PLUS First Data
Release444j-plus.es/datareleases/data_release_dr1 (hereafter DR1) consists of
511 pointings collected from November 2015 to January 2018 with JAST/T80 in
all twelve optical bands described above, and covers approximately 1022 deg2.
The reduction and photometric calibration of the J-PLUS DR1, as well as the
limiting magnitudes in the twelve bands, are presented in Cenarro et al.
(2018). A representative subset of the DR1, the J-PLUS Early Data Release
(EDR), comprises 18 pointings (36 deg2), and is publicly
available555j-plus.es/datareleases/early_data_release. In addition to the
present paper, the J-PLUS EDR and science verification data have been used to
refine the membership in the nearby galaxy clusters Abell 2589 and Abell 2593
(Molino et al. 2018), analyze the globular cluster M15 (Bonatto et al. 2018),
study the H$\alpha$ emission (Logroño-García et al. 2018) and the stellar
populations (San Roman et al. 2018) of several local galaxies, and compute the
stellar and galaxy number counts up to $r=21$ (López-Sanjuan et al. 2018).

Selections of the 6 arcsec aperture photometry are made from the MagABDualObj
catalogs for each release. To limit contamination from non-stellar type
objects, we remove extended sources using the stellarity index given by
SExtractor, CLASS_STAR $\geq$ 0.92 (Bertin & Arnouts 1996; López-Sanjuan et
al. 2018). This morphological classifier is itself based on a neural network,
taking into account the pixel scale of the image and full width at half
maximum.

From these selections, we obtained 3,132,543 and 78,329 sources for DR1 and
EDR, respectively. Minor variations in the 6 arcsec aperture photometry were
present, tile by tile, in EDR. Corrections were made, based on a stellar-locus
regression technique provided by Cristóbal-Hornillos et al. (priv. comm.). For
training and validation of SPHINX, these catalogs were cross-matched, using a
1.0 arcsec search radius, with stars from the SDSS Reservoir (described in
Section 2.2) with available stellar atmospheric-parameter estimates. This
search radius was varied to 3.0 arcsec, and no new stars were obtained.

Interstellar extinction is expected to be small in EDR and DR1. However,
application of extinction corrections is still expected to improve the
performance of the photometric ANNs. One method to determine reddening
coefficients for J-PLUS photometry is to convolve the filter-response
functions corresponding to each of the J-PLUS filters with the reddening law
from Fitzpatrick (1999). The result is a transmission-weighted sum of the
wavelength-dependent extinction contribution within the filter bandpass. These
values are provided in Table 1. The effective wavelength, $\lambda_{\rm eff}$,
is determined from a transmission-weighted average of the wavelength for each
filter.

Table 1: Reddening coefficients for the J-PLUS photometric system. Filter | $\lambda_{\rm eff}$ | A($\lambda$)/$E(B-V)$
---|---|---
(name) | (Å) |
u | 3536 | 4.295
J0378 | 3782 | 4.013
J0395 | 3939 | 3.849
J0410 | 4108 | 3.685
J0430 | 4303 | 3.506
g | 4810 | 3.120
J0515 | 5141 | 2.864
r | 6271 | 2.235
J0660 | 6604 | 2.070
i | 7669 | 1.668
J0861 | 8611 | 1.377
z | 8979 | 1.290

To estimate the line-of-sight reddening, $E(B-V)$, for our sources, we use
Schlafly & Finkbeiner (2011). Corrections for reddening estimates for the
J-PLUS photometry indeed improve the synthetic magnitude calibrations (Section
2.3). However, these corrections are subject to some limitations, particularly
in that this extinction map is only two-dimensional. In future work, we will
utilize three-dimensional estimates of dust extinction (e.g., Green et al.
2018), based on parallaxes from Gaia Data Release 2 (Gaia Collaboration et al.
2016). In this work, we implement a hard extinction selection, corresponding
to $E(B-V)$ ¡ 0.05 dex, so that more reddened sources are not admitted to our
samples.

###  2.2 The SDSS Reservoir

Three separate spectroscopic campaigns comprise the training databases for
SPHINX, hereafter called the SDSS Reservoir. The first, SDSS’s Baryon
Oscillation Spectroscopic Survey (BOSS; Dawson et al. 2013), obtained over
500,000 stellar spectra (including repeated stars) across a wavelength of
3,600 - 10,000 Å (R $\approx$ 2,000) over approximately 10,000 deg2 of the
sky. Our database includes 80,221 stars from this survey, selected for high
signal-to-noise and low metallicity ([Fe/H] $<-0.5$). The Sloan Extension for
Galactic Understanding and Exploration (SEGUE; Yanny et al. 2009) took place
in two phases, SEGUE-1 and SEGUE-2, and covered a combined area of 2,755 deg2.
We make use of 147,811 of the $\sim$350,000 spectra from this sample. Finally,
we include 74,572 spectra from the component of SDSS-I known as the Legacy
Survey, provided by SDSS DR7 (Abazajian et al. 2009). This survey covered
primarily $\sim$7,500 deg2 of the North Galactic Cap, with additional stripes
in the South Galactic Cap amounting to $\sim$740 deg2.

Stellar parameters for these databases were derived using the SEGUE Stellar
Parameter Pipeline (SSPP; Lee et al. 2008a, b). This pipeline made robust
determinations of effective temperature ($T_{\rm eff}$), surface gravity
($\log{g}$), metallicity ([Fe/H]), and carbonicity ([C/Fe]) over a temperature
range $4000<T_{\rm eff}$ (K) $<8000$. Typical random uncertainties in the
effective temperature and metallicity estimates for F- and G-type stars were
determined empirically, $\sigma(T_{\rm eff})\sim$ 130 K, and
$\sigma$([Fe/H])$\sim$ 0.21 dex (Allende Prieto et al. 2008). The color-
magnitude diagram of stars available for training from the SDSS Reservoir is
shown in Fig. 2, along with the effective temperature and metallicity
distributions of source matches with J-PLUS DR1. In all three plots, stars
were limited to those with $\sigma(T_{\rm eff})<250$ K, $\sigma$[Fe/H] $<0.3$
dex, and $S/N>25$, as dictated by the SSPP (where $S/N$ is the signal-to-noise
ratio).

Figure 3: Synthetic magnitudes determined with SDSS Reservoir and J-PLUS
filter-response functions are compared with photometry from the J-PLUS First
Data Release. Scatter in the calibrations increases for bluer filters, as the
uncertainty in the interstellar extinction correction is larger. The colors
are indicative of the photometric tile from which the data were obtained, for
which no biases are seen.

###  2.3 Synthetic magnitudes

Figure 4: Top panel: Temperature sensitivity of the H$\delta$ feature. Over an
effective temperature range of 5250 $<T_{\rm eff}$ (K) $<8000$, we expect an
increase in absorption of 31% for a star of $\log{g}=2.50$, [Fe/H] $=-2.50$,
and [C/Fe] $=0.0$. Middle panel: The variation in Ca II H & K line strengths
with increasing metallicity for a star of $T_{\rm eff}=5000$ K, $\log{g}=1.0$,
and [C/Fe] $=0.0$. Bottom panel: The Ca II H & K line response to increasing
effective temperature. The Ca II H line is nearly superposed with H$\epsilon$.

Synthetic photometry was computed for all spectra in the databases described
above. This was done initially to provide the photometric inputs required for
network training before J-PLUS had accumulated an adequate number of source
photometry with EDR and DR1. First, filter intensities were computed by taking
the inner product of the flux-calibrated spectrum and the J-PLUS filter-
response functions. These filter intensities were converted to synthetic
magnitudes using the following form of the asinh magnitude, or luptitude
(Lupton et al. 1999):

$m=(-2.5/\ln{10})\cdot[\sinh^{-1}{\frac{f}{2bf_{0}}}+\ln{b}].$ (1)

Here, $f$ is the integrated flux through the filter. Appropriate values for
the classical zero-point, $f_{0}$, and the softening parameter, $b$, were
determined by calibrating the synthetic intensities to known J-PLUS magnitudes
from a cross-match of EDR and DR1 with synthetic magnitudes derived from the
flux-calibrated spectra for stars in common with the SDSS Reservoir. This was
done using the orthogonal distance regression technique (Boggs & Rogers 1990),
taking into account error estimates in the native photometry as well as the
variances in the flux reported in the medium-resolution SDSS spectra.

The resulting synthetic magnitude calibrations for stars in the SDSS Reservoir
are shown in Fig. 3. In addition, minor offsets ($\pm 0.2$ mag) were found and
removed in a few J-PLUS tiles during the calibration. Residuals in the
synthetic magnitude calibrations are moderately dependent on the $S/N$ of the
underlying SDSS spectra, particularly for the $J0395$ and $J0410$ filters.
Sources with $S/N<25$ and magnitude uncertainties larger than 0.1 mag were
thus excluded for each calibration. This $S/N$ cut has the effect of
preferentially removing calibration stars at fainter magnitudes, where we find
that the scatter for each calibration tends to increase. Considering again a
critical limit in the scatter of 0.1 mag, we find limiting magnitude values
for each filter, provided in Table 2 along with the standard deviation,
$\sigma_{m}$, of the corresponding calibration. Use of synthetic magnitudes
beyond these limits is not recommended, as the calibrations are less reliable.
Both uncertainties in the underlying SDSS spectra and the native J-PLUS
photometry contribute to the scatter seen in the Fig. 3, but if synthetic
magnitudes are limited to those with $S/N>25$, the critical residual value of
0.1 mag is reached at characteristically brighter values in the native
photometric system.

Table 2: Limiting magnitudes for synthetic calibrations. Filter | mlim | $\sigma_{m}$
---|---|---
(name) | (mag) | (mag)
J0395 | 18.46 | 0.11
J0410 | 18.52 | 0.09
J0430 | 18.69 | 0.08
g | 18.68 | 0.07
J0515 | 18.79 | 0.05
r | 18.90 | 0.04
J0660 | 18.80 | 0.04
i | 18.75 | 0.04
J0861 | 18.48 | 0.05

As expected, the scatter in the photometric calibration was seen to increase
for bluer filters, where CCD response and atmospheric absorption become more
problematic. This calibration ensured that synthetic magnitudes were on the
same scale as the J-PLUS photometric system, thus both synthetic and native
photometry could be used interchangeably within the magnitude and S/N limits
specified.

The blue cutoff of the SEGUE spectra ($\sim$ 3700 Å) preclude determination of
synthetic magnitudes for the $J0378$ and $u$-band filters. The same is true
for the $z$-band filter, for which the response curve extends beyond the range
of the SEGUE spectra. Consequently, these filters are excluded from the
methodology. Once photometry is available for a sufficient number of these
stars, construction of synthetic magnitudes for training of the ANNs will not
be necessary, and these filters should certainly be included, as they each
capture important information about the stellar atmospheres.

###  2.4 The synthetic library

For exploratory and training purposes, we make use of a library of synthetic
spectra. To build the synthetic spectra library, we proceed similarly to the
approach described by Lee et al. (2013). In short, we use a specific grid of
model atmospheres computed with the MARCS code (Gustafsson et al. 2008), which
takes into account the impact of the carbon enhancement in the atmosphere.
From those model atmospheres we generate the synthetic spectra using the
Turbospectrum routine (Álvarez & Plez 1998; Plez 2012). Compared to Lee et al.
(2013), we improve the procedure in several aspects. First, we extend the
wavelength range, now covering the entire optical region from 3000 Å to 10,000
Å. In addition, we update the linelists, which now include CN, CH, NH, C2,
MgH, TiO, ZrO, CaH, VO, and SiH for the molecules, and the ultimate version of
VALD3 (Ryabchikova et al. 2015) for the atoms. Finally, we extend the grid to
a much larger space of parameters, $3500\leq T_{\rm eff}$ (K) $\leq 8000$ in
increments of 250 K, $0.0\leq$ $\log{g}$ $\leq 5.0$ in increments of 0.5 dex,
$-4.5\leq$ [Fe/H] $\leq+0.5$ in increments of 0.25 dex, and $-1.5\leq$ [C/Fe]
$\leq+4.5$ in increments of 0.25 dex.

Due to the finite resolution of this library, we interpolate when necessary
using a 4D cubic spline interpolation routine (Lee, Y.S., priv. comm.).
Training sets can then be generated with stellar parameters distributed
anywhere within the parameter regions of interest. A crude flux-calibration is
performed on these spectra by convolving each normalized spectrum with a
blackbody function corresponding to its effective temperature. This library is
primarily used for investigation of the photometric carbon sensitivity,
discussed in Section 8.

###  2.5 Narrow-band parameter response

In addition to sampling the overall blackbody function of the spectral-energy
distribution (SED), we expect response to a number of temperature-sensitive
features present in the narrow-band filters. For example, the $J0410$ filter
hosts a particularly temperature-dependent feature, the H$\delta$ line (4102
Å); see Fig. 4. In the upper left panel, we consider the strength of H$\delta$
over the temperature range 5250 $<T_{\rm eff}$ (K) $<8000$ for a star of
log$g$ = 2.5, [Fe/H] $=-2.50$, and [C/Fe] = 0.0. As seen in the upper right
panel, this temperature range corresponds to a 31% increase in the equivalent
width of H$\delta$, from 18.4 Å to 24.2 Å. Thus, we anticipate success using
networks in which training parameters include photometric colors and
magnitudes incorporating the $J0410$ filter.

The Ca II H & K lines (3969 Å and 3934 Å, respectively) display similar
behavior with increasing metallicity. In the middle-left panel, we vary the
metallicity of a $T_{\rm eff}$ = 5000 K star over the range $-$4.00 $<$ [Fe/H]
$<$ 0.0. From inspection of the middle-right panel, for a star of solar
metallicity, the equivalent widths of the Ca II H & K lines are 42% and 64%
stronger than for a [Fe/H] = $-2.0$ star of the same temperature. However, the
Ca II H & K lines also exhibit an asymmetric temperature dependence. In the
same range of effective temperature, the Ca II H line strength can increase by
as much as 50% for a star with [Fe/H] = $-$2.50, due to the increasing
influence of H$\epsilon$ at $\lambda$ = 3970 Å. Meanwhile, the Ca II K line
nearly vanishes by $T_{\rm eff}$ = 7500 K. We therefore expect to obtain a
keen sensitivity to metallicity by incorporation of the $J0395$ filter in our
methodology, and anticipate the necessity to unravel a degeneracy with
effective temperature.

##  3 Artificial Neural Network

###  3.1 Architecture

In the development of SPHINX, we generalize the use of the core ANN element
with what amounts to a three-layered system. The motivations for this
structure are discussed in Section 4. Here, we consider the basic function of
an ANN.

For the core implementation of the ANN, we make use of the multi-layered
perceptron class, MLPRegressor, from scikit-learn (Pedregosa et al. 2011). We
choose a feed-forward algorithm with one hidden layer of neurons. As an
example, Fig. 5 shows a schematic of this network. Each node computes a non-
linear function of the scalar product of the input vector and a weight vector.
For N nodes, the functional form can be expressed as follows:

$y(\mathbf{x})=\tilde{g}\Big{[}\sum_{i=1}^{N}\omega_{i2}\cdot
g(\bm{\omega}_{i1}^{\rm T}\mathbf{x})\Big{]}.$ (2)

Here, x denotes the input vector, in our case, the pre-scaled magnitudes from
a subset of the J-PLUS filter set. Each neuron, $i$ of $N$, in the hidden
layer receives the sum of the input vector with the weight vector
corresponding to the first layer, $\bm{\omega_{i1}}$, represented for
simplicity by the inner product, where T denotes the transpose. For each
hidden layer, we implement a bias neuron, the corresponding weight of which is
included in $\bm{\omega_{i1}}$. These bias neurons produce a constant output
of 1, and thus are not connected to the previous layer. Bias neurons help to
shape the output of the activation function, where they shift the inner
product in a way analogous to the y-intercept of a linear equation.

The node then applies an activation function, g, and the output is provided to
the output layer. A similar sum is then performed with the outputs of each
neuron in the hidden layer and the weights of the second layer where, in
general, the output activation function, $\tilde{g}$, is not required to be
the same function used in previous layers.

A hyperbolic tangent activation function was implemented in SPHINX, in part
because it resulted in faster convergence times, but also because the function
maps the input vectors to ($-$1,1), while the logistic sigmoid produces values
in an asymmetric range (0,1). It has been empirically shown that symmetric
activation functions produce faster convergence times (Le Cun et al. 1991).
This is the case for the application of effective temperature and metallicity
estimates.

Optimal weights for the network are determined using a stochastic gradient
descent algorithm. With traditional back-propagation, partial derivatives are
computed for each weight with respect to a specified error function, E, to
determine the influence of small perturbations of each weight’s value. In this
manner, new values of the $i$th weight in the $j$th layer can be determined as
follows (Riedmiller 1994):

$\omega_{ij}(t+1)=\omega_{ij}(t)-\epsilon\frac{\partial
E}{\partial\omega_{ij}}(t).$ (3)

Here, $\epsilon$ is the learning rate, which scales the update correction.
Fixed values of this parameter were found to introduce oscillations, where the
updated value over-corrects with each iteration, and so never converges to the
optimal weight. To overcome this, a stochastic gradient-based optimizer known
as Adam was implemented, in which an adaptive-learning rate is computed from
first-order moments of the gradient in the scalar error function (Kingma & Ba
2014).

Figure 5: An example network element used in the SPHINX ANN pipeline. The base
ANN utilizes a feed-forward algorithm and consists of a single hidden layer.
The inputs are scaled combinations of J-PLUS colors and/or magnitudes. Figure
6: Example schematic of the Stellar Photometric Index Network Explorer
(SPHINX). The architecture consists of a scalable three-layered neural
network. The hidden layer performs the hyperbolic tangent activation function
on the neuron-specific weighted inputs. The following layer represents each
sub-networks best estimate of the stellar parameter. The final layer performs
a validation weighted sum of the estimates verified to have resulted from the
interpolating networks.

###  3.2 Pre-scaling/Normalization

Prior to using the magnitudes of our training set to converge the network, a
form of pre-scaling must be applied, whereby all input variables are set to
the same scale. The most common technique is simply a linear rescaling, in
which we subtract the sample mean and divide by the standard deviation,
leaving each input vector with a mean of zero and variance of one. A more
robust method of pre-scaling is included as an option in SPHINX, in which the
center of the distribution is taken as the median, and the spread is
determined by some specified percentile range. This provides the option to
control the fraction of inputs between [$-$1, 1], or the optimal domain of the
activation function’s response.

Although synthetic magnitudes are calibrated to the J-PLUS photometric system,
it is highly desirable to train the ANN with inputs for which the
distributions match that of the validation, or science set. Otherwise, pre-
scaling the input colors could push these inputs to a region that requires the
ANN to extrapolate from the inputs, or operate near the asymptotic region of
the activation function.

This ANN structure serves as the basis for the architecture of SPHINX, where
we generalize the use of the ANN in a larger, three-layered structure in an
attempt to maximize the capability of the ANN, while including the variety of
input combinations available. We describe the detailed design of SPHINX in
Section 4.3.

##  4 Parameter determination and optimization with SPHINX

###  4.1 Training set assembly

In contrast to an ANN’s capability for modeling patterns in high-
dimensionality space, their ability to extrapolate beyond the boundaries of
their underlying training set is quite limited. One consequence of this
limitation is the need to be aware of the distribution of the validation set
prior to training of the network. While we have no a-priori knowledge of the
chemical abundance and atmospheric-parameter distributions in EDR and DR1, we
have all of the necessary information regarding the magnitude distributions,
which can be used to construct an ideal training set.

At present, SPHINX allows for selection of training stars from a variety of
catalogs, including the subset of EDR and DR1 sources with available SSPP-
estimated parameters, as well as SDSS Reservoir sources with synthetic
magnitudes calibrated to the J-PLUS photometric system. SPHINX then performs a
signal-to-noise, photometric error, and $E(B-V)$ rejection according to the
specified thresholds, in addition to the faint/bright limits, all of which are
set in the input parameter file. With the appropriate parameter bounds and
rejections determined, the training set can be uniformly sampled across the
target variable, in this case $T_{\rm eff}$ or [Fe/H]. This routine is
optional, but is designed to protect against overemphasis by the network on a
particular region of the parameter space.

Once all desired processing of a training set is complete, we define a scale
frame, which describes each input distribution in the target set. This
includes the center location and spread estimates that SPHINX uses to linearly
scale and unscale all inputs to the networks for training and parameter
estimation. If the number of target sources is large, it may be desirable to
set the scales according to the target photometry. However, if the target list
consists of only a few sources, this is not advised; the scales should be set
based on the training set’s photometric distributions. The default manner of
determining the center and spread of each distribution is to fit a Gaussian to
each input. A more robust method utilizing the median and fourth-spread, or
$f$ spread (i.e., the interquartile range), is also available, although it was
found that alternative estimates of the scales did not significantly influence
the network’s performance.

###  4.2 Approximating input distributions

While the SDSS Reservoir and DR1 catalogs are sufficiently large that we can
construct training sets across a reasonably wide range of stellar parameters
and magnitudes, an effective method to accommodate a variety of target (or
testing) distributions is required. For instance, our selection from the
J-PLUS M15 photometry (details in Section 7) comprises stars of 14 $<g<18$,
well within the SDSS Reservoir distribution. However, the SDSS Reservoir
distribution peaks at $g=18.3$, with a standard deviation of 1.2 mag, while
the M15 distribution mean and standard deviation are $g=16.3$ and 1.1 mag,
respectively. Training stars naively sampled from the SDSS Reservoir catalog
would introduce a bias towards the fainter stars in the M15 cluster, which is
not ideal.

We include the option to force the training set input distributions to best
approximate those of the target or science set. For a certain magnitude or
color input, it is assumed that the center and spread of the target
distribution have previously been set. The following error function is
minimized for $\gamma$, the scale of the Gaussian distribution in the training
set corresponding to the center and scale of the target distribution:

$\Phi(\gamma|\bar{x},\sigma)=\sum_{i}^{N}\left|y_{i}-\gamma\cdot\rm{exp}\left[\frac{-(x-\bar{x})^{2}}{2\sigma^{2}}\right]\right|^{-\alpha},$
(4)

where the scale $\gamma$ sets the maximum number of stars with input value
$x\pm\delta x$ that can be drawn from the training distribution, such that the
resulting input distribution conforms to a Gaussian described by $\bar{x}$ and
$\sigma$. We leave $\alpha$ as a free parameter (default $\alpha=1/2$) to tune
the level with which the algorithm penalizes non-conformities to the desired
distribution.

###  4.3 Network optimization with SPHINX

In general, the proper combination of inputs for the network – or, for that
matter, their quantity – is not known. We anticipate the use of temperature-
sensitive filters such as $J0410$ and $J0660$, and metallicity-sensitive
filters such as $J0395$, $J0515$, and $J0861$. Beyond these, however, it is
not directly apparent what additional combinations facilitate the capabilities
of the network. Further, for networks operating with different combinations of
photometric inputs, one network may be forced to extrapolate, but not another.

To address these concerns and ensure resilience against potentially faulty
inputs in both the training and science case data, we enable a system of
networks, or ANN units, each with a distinct combination of the available
inputs. SPHINX determines all combinations of the specified filters and their
corresponding colors, assigning and training a network for a specified number
of these combinations. Throughout the operation and analysis of SPHINX, the
number of inputs to each ANN unit is small ($N=6$), to maximize the ANN’s
dependence on the each input in the subset, and also to mitigate the
convergence time of each ANN in the array.

The basic schematic of SPHINX is shown in Fig. 6. For simplicity of this
illustration, only a sub-sample of available colors is shown, and the number
of ANN units is limited to three. As can be seen, SPHINX amounts to a three-
layered neural network, consisting of a layer of subordinate ANN units that we
call the network array. This array is of scalable size; we evaluate the
performance of SPHINX as a function of array size in Section 6. For every
network estimate made, SPHINX notes when that network is extrapolating outside
of its training domain. This is accomplished with a structure that we refer to
as an interpolation frame, which stores the domains of all inputs in the
training set. All estimates made in the network array layer are subject to an
interpolation check, flagging any/all estimates where extrapolation was
necessary.

During training, the performance of each ANN unit in the network array is
evaluated and recorded using a validation set, and this analysis is used to
assign each ANN unit a score for future reference and for computing final
estimates. We define a score for the network, which we base on a modified
median absolute deviation (MAD) of the verification set:

$\xi_{N}=\rm{median}(|\mathbf{E_{N}}-\rm{median}(\mathbf{E_{N}})|)^{-\beta},$
(5)

where EN represents the error in network N’s estimate of the target variable
in the verification set. Here, $\beta$ is left as a free parameter (default
$\beta=2$) to control the degree to which we penalize ANN units with poorer
performance in the final parameter estimate. We then assert that the proper
science estimate is the weighted sum of each network estimate and its
corresponding score, $\xi_{N}$.

Figure 7: Effective-temperature estimates, $T_{\rm eff}$, from SPHINX, as a
function of the adopted value from the SSPP for a testing catalog consisting
of J-PLUS EDR photometry (left panels). For comparison, $g-r$ calibrations
from Fukugita et al. (2011) (middle panels) and Lee et al. (2008a) (right
panels) were applied to the sample. The residuals for each temperature
calibration are shown against the accepted temperature in the bottom panel,
where the green region depicts the standard deviation from a Gaussian maximum-
likelihood fit.

A system of twelve filters corresponds to $\binom{12}{2}$ = 66 possible
colors. With a network array size of six ANN units, the resulting number of
unique color combinations is $\binom{66}{6}$ = 90,858,768, an infeasible
number of networks to train in a finite time. To address this, we allow for a
specified number of input combinations to be utilized, whereby a subsample of
networks from the underlying ensemble is selected. This can be done at random,
or if any specific filters or colors are desired, SPHINX can be restricted to
employ combinations of colors in which at least one input is comprised of
these specifications. We make use of this feature for effective temperature
and metallicity estimates, where SPHINX is forced to use of $J0410$ and
$J0395$, respectively, in combination with the other available filters.

Before consideration of the final parameter estimates, each ANN unit estimate
is verified by the interpolation check described above. The number of
contributing ANN units is recorded for future consideration via the
NET_ARRAY_FLAG, and the final estimate is simply a weighted sum of the
contributing ANN unit estimates and corresponding validation scores,
$\xi_{N}$. With the ensemble of contributing ANN units, we compute the MAD of
the estimates, as well as the standard deviation, which is also weighted by
the validation scores. These serve as the uncertainty in the parameter
estimate reported by SPHINX. This procedure can also be used to determine the
most optimal networks achieved in the network array. If specified, SPHINX
considers only networks with the highest scores, $\xi_{N}$, and excludes all
other estimates from the final parameter estimation.

##  5 Effective temperature determination with SPHINX

For effective-temperature training, we restricted the range of interest to
4500 ¡ $T_{\rm eff}$ (K) $<8500$. We selected stars with DR1 photometry from
the SDSS Reservoir, and reserved all EDR sources for testing purposes. For
simplicity, stars for which metallicities exceed Solar were excluded,
anticipating the influence of high metal abundance on the underlying continua.
A limit of 0.1 mag in the error reported for the observed photometry, with a
faint limit of 20 on all magnitudes was applied to the training set, in
addition to the extinction limit of $E(B-V)<0.05$ mag stated previously.

It was possible that, even with excellent synthetic photometric errors and an
optimal $S/N$ in the underlying spectrum, the temperature assigned to the
training star by the SSPP was incorrect, or at least imprecise. We therefore
implemented a $\pm$ 120 K cut on the adopted $T_{\rm eff}$ error estimate, and
insisted that the individual estimates from the SSPP – in this case the
adopted estimate and estimates derived from the H$\alpha$ & H$\delta$ Balmer-
line strengths666T1 and T2 as described in Lee et al. (2008a) – not differ
from by more than 75 K.

With the optimally cleaned stars selected, training sets were constructed by
uniformly sampling temperatures between the maximum and minimum temperature
thresholds. The act of sorting and partitioning the catalog into 15 bins prior
to randomly sampling 200 stars from each bin ensured that a roughly even
distribution of temperatures was obtained. The final DR1 training batch
consisted of 1152 stars. Both the training and testing sets included stars
with surface gravities in the range $1.0<\log{g}<5.0$. The median $\log{g}$ in
both sets was 4.1, with a standard deviation of 0.5 dex. Both sets were
dominated by main-sequence stars, but $\sim$5 % of stars had surface gravities
consistant with giants ($\log{g}<3.0$).

SPHINX was applied to 1015 stars with EDR photometry. For analysis of the
network performance, we excluded testing sources with spectral $S/N<$ 20,
and/or a larger uncertainty in the SSPP $T_{\rm eff}$ estimate ($\sigma(T_{\rm
eff})>150$ K). For comparison, effective temperature estimates were made with
two broad-band calibrations, Eq. 1 of Fukugita et al. (2011), and $T_{l}$ of
Lee et al. (2008a). Fukugita et al. (2011) determined an empirical temperature
range for their calibration of $3850<T_{\rm eff}$ (K) $<8000$, and noted the
smallest scatter of $\sigma(T_{\rm eff})=93$ K when using $g-r$ compared to
other broad-band colors. The $T_{l}$ estimate was derived to be effective for
a wide range of temperatures, beyond $4500<T_{\rm eff}$ (K) $<7500$, making it
ideal as a comparison for our calibration with SPHINX.

We made use of a number of robust estimators of central location and scale,
and adopted the suggested nomenclature from Beers et al. (1990). For measures
of central location, in addition to the median $C_{\rm M}$, we used the
trimean $C_{\rm TRI}$ – based on the sample median and upper and lower fourths
of the distribution(s) – the biweight location $C_{\rm BI}$, and the mean
$C_{\mu}$. For estimates of scale, we made use of a normalized median absolute
deviation, $S_{\rm MAD}$, which is particularly suited for heavy-tailed
distributions (Beers et al. 1990). In addition, a scale estimate based on the
fourth spread, the $f$ pseudosigma, $S_{f}$, was used, along with the biweight
scale estimate $S_{\rm BI}$ and standard deviation $S_{\sigma}$.

The results of the temperature estimates made with SPHINX and the comparison
calibrations on the EDR photometry are shown in Fig. 7 and summarized in Table
3, where we compare as well the statistics of high temperature stars ($T_{\rm
eff}>7000$ K). For estimates made with SPHINX, shown in the leftmost panel of
Fig. 7, central location estimates of the residuals $C_{\mu}=+21$ K and
$C_{\rm TRI}=+20$ K indicated a slight bias towards over-estimation for the
EDR sample. This behavior was in contrast to the under-estimation seen for
temperatures above $T_{\rm eff}>7000$ K, where the $C_{\rm M}$ and $C_{\rm
TRI}$ of the residuals were $-14$ K and $-28$ K, respectively. The scatter in
the region, where $S_{f}$ increased from 93 K to 171 K. Similarly, the $S_{\rm
MAD}$ increased from 93 K to 172 K. We attributed this behavior both to edge
effects emerging near the limit of the network interpolation range.
Interestingly, it was found that inclusion of the $J0410$ filter did not
significantly improve the performance of effective temperature estimates made
with SPHINX. We conclude that the quality of these estimates is more likely a
matter of J-PLUS filters tracing the overall SED, as well as the capability of
SPHINX to interpret the behavior of the SED over a wide temperature range.

Table 3: Central location and scale estimates of photometric temperature calibration residuals. | SPHINX | Fukugita et al. 2011 | Lee et al. 2008a
---|---|---|---
| (K) | (K) | (K)
$C_{\rm M}$ | $+20$ | $+60$ | $+57$
$C_{\rm TRI}$ | $+20$ | $+56$ | $+56$
$C_{\rm BI}$ | $+20$ | $+57$ | $+56$
$C_{\mu}$ | $+21$ | $+66$ | $+64$
$S_{\rm MAD}$ | 93 | 157 | 143
$S_{f}$ | 93 | 156 | 144
$S_{\rm BI}$ | 106 | 171 | 156
$S_{\sigma}$ | 91 | 146 | 138
$T_{\rm eff}>7000$ K
$C_{\rm M}$ | $-14$ | $-230$ | $-10$
$C_{\rm TRI}$ | $-28$ | $-233$ | $-15$
$C_{\rm BI}$ | $-26$ | $-230$ | $-19$
$C_{\mu}$ | $-5$ | $-201$ | $+13$
$S_{\rm MAD}$ | 172 | 218 | 199
$S_{f}$ | 171 | 213 | 195
$S_{\rm BI}$ | 161 | 195 | 208
$S_{\sigma}$ | 188 | 196 | 196

Using the $g-r$ calibration given in Eq. 1 of Fukugita et al. (2011), we
computed an $S_{f}$ of 156 K. This calibration, shown in the middle panels,
was biased as well towards over-estimation, indicated by the mean of the
residuals, $+$66 K, and $C_{\rm TRI}$ of $+$55 K. Similar to the estimates
made with SPHINX, we found under-estimation of effective temperature beyond
$T_{\rm eff}>7000$ K, where the median of the residuals was $-$230 K, with a
$C_{\rm TRI}$ of $-$233 K. Estimates in this regime became increasingly
uncertain, with $S_{f}$ of 213 K, and a $S_{\rm MAD}$ of 218 K.

In the right panel we compare the network temperature estimates to a
polynomial calibration of $g-r$ from the SSPP, $T_{I}$ (see Lee et al. 2008a,
for details). For this calibration, the median in the residuals of $+$57 K and
$C_{\rm TRI}$ of $+$56 K again indicated a systematic over-estimation. The
standard deviation of the Gaussian maximum-likelihood fit of 138 K increased
to 196 K in the high temperature range, $T_{\rm eff}>7000$ K. A number of
outliers were apparent around $T_{\rm eff}\sim 6200$ K for each calibration,
particularly in the Lee et al. (2008a) calibration, which was expected if
variable stars such as RR Lyrae stars are present in the EDR sample. Offsets
such as these would occur for stars of which spectroscopic and photometric
temperature estimates were made at disparate phases of the pulsation cycle.

We concluded that the use of SPHINX with J-PLUS photometry provides effective
temperatures with a bias reduced by a factor of three and a dispersion reduced
by $\sim$40% with respect to the previous broad-band calibrations. In,
addition SPHINX is less prone to under-estimation in the high-temperature
regime beyond 6500 K. No significant influence by surface gravity on the
effective temperature was seen in the range $2.0<\log{g}<5.0$, however for
lower values ($\log{g}<2.0$) determinations tended to be over-estimated by
$\sim 70$ K.

Figure 8: Metallicity estimates, [Fe/H], from SPHINX, as a function of the biweight estimate from the SSPP, for stars of effective temperature $4500<$ $T_{\rm eff}$ (K) $<$ 6200\. The gray region corresponds to the standard deviation of the residuals, determined from a maximum-likelihood Gaussian fit. Results from SPHINX using synthetic magnitudes from the SDSS Reservoir (left panels) are shown with the results from native J-PLUS DR1 photometry (right panels) for comparison. Table 4: Central location and scale estimates of photometric metallicity determinations. Trial | $C_{\mu}$ | $C_{\rm M}$ | $C_{\rm TRI}$ | $C_{\rm BI}$ | $S_{\sigma}$ | $S_{\rm MAD}$ | $S_{f}$ | $S_{\rm BI}$
---|---|---|---|---|---|---|---|---
| (dex) | (dex) | (dex) | (dex) | (dex) | (dex) | (dex) | (dex)
SDSS Reservoir | +0.02 | +0.03 | $+0.03$ | $+0.02$ | 0.22 | 0.22 | 0.22 | 0.23
J-PLUS DR1 | $-0.06$ | $-0.06$ | $-0.05$ | $-0.06$ | 0.25 | 0.25 | 0.25 | 0.27

##  6 Metallicity determination with SPHINX

Two separate trials were conducted for validation of the metallicity routine
in SPHINX. The maximum error on the biweight estimate of [Fe/H] from the SSPP
was set to $\pm 0.20$ dex. Similar to the temperature training, we insisted
that the adopted and biweight estimates of metallicity from the SSPP did not
differ by more than $\pm$0.20 dex. We refer the interested reader to Lee et
al. (2008a) for an in-depth description of the biweight and adopted estimators
from the SSPP. In short, the biweight is simply the robust average of all
accepted estimates from the pipeline, while the adopted estimate takes into
account an average of the biweight and a refined estimate that considers the
reduced $\chi^{2}$ of a synthetic spectrum match. In the event that the
refined and biweight estimates do not differ significantly ($<$ 0.15 dex), the
adopted value is set to the biweight estimate. The reliability of the
metallicity estimates from the SSPP was somewhat dependent on the $S/N$. We
therefore set the minimum $S/N$ to 40. The faint limit for all magnitudes was
set to 18.5 to insure reliability in the synthetic magnitude calibrations.

For both trials, an array of 100 ANN units was constructed, where SPHINX was
set to consider the five highest performing networks in each array.
Anticipating the utility of the $J0395$ filter sensitivity to the Ca II H & K
feature, we insisted on the use of $J0395$ photometry in each of the ANN
units. The results of the metallicity estimates for both samples are shown in
Fig. 8. Estimates of spread and central location in the residuals are provided
in Table. 4.

###  6.1 J-PLUS DR1 trial

The first trial implemented a testing set consisting entirely of J-PLUS DR1
photometry for stars in the range of $4500<$ $T_{\rm eff}$ (K) $<6200$. The
subset of the SDSS Reservoir with DR1 photometry in this range, after the
error criteria described previously, was limited to 935 stars, which included
only 28 stars with [Fe/H] $<-2.5$, of which five had [Fe/H]$<-3.0$. Therefore,
all DR1 stars with [Fe/H] $<-2.5$ were reserved for the testing set, and we
supplemented the DR1 training photometry with 500 stars with [Fe/H] $<-2.5$
and synthetic magnitudes from the SDSS Reservoir, of which 250 had [Fe/H]
$<-3.0$. By doing so, the testing set consisted entirely of native J-PLUS
photometry, while the training set maximized the number of low-metallicity
stars in the sample. The surface gravity range for the testing set was
$1.3<\log{g}<4.8$, with a median of 4.2 and standard deviation of 0.7 dex.

The median, $C_{\rm M}$, and biweight central location, $C_{\rm BI}$, of the
residuals were both found to be $-0.06$ dex for the DR1 trial, so the
predictions were prone to slight under-estimation when compared to the SSPP
values. The Gaussian fit to the residuals revealed a standard deviation of
$S_{\sigma}=0.25$ dex. The largest estimate of scale for the DR1 trial was the
biweight estimate, $S_{\rm BI}=0.27$ dex. The scatter in the metallicity was
independent of surface gravity in the range of $1.75<\log{g}<4.5$. SPHINX
tended to over-estimate the metallicity for low surface gravity stars
($\log{g}<1.75$), for which the residual median increased to $C_{\rm M}=+0.14$
dex. However, these stars are correspondingly cool ($T_{\rm eff}\lesssim 4750$
K), and it was found that stars in the range $4500<T_{\rm eff}$ (K) $<4850$
tended to produce over-estimations regardless of the surface gravity.

For both the classification and recovery fractions of VMP stars with SPHINX,
errors were expressed using the Wilson score approximation of the binomial
confidence interval (Wilson 1927; Brown et al. 2001). Of the 81 VMP stars in
the DR1 sample, $85\pm 3$ % were recovered by the [Fe/H] estimate from SPHINX.
SPHINX classified 109 stars in the DR1 sample as VMP, in which $63\pm 4$ %
were confirmed by the biweight estimate from the SSPP.

###  6.2 Synthetic SDSS trial

To explore the extent of current metallicity sensitivity with SPHINX, the
second trial consisted of training and testing sets constructed from the SDSS
Reservoir, using synthetic magnitudes. Effective temperature for both training
and testing sets was again restricted to $4500<$ $T_{\rm eff}$ (K) $<6200$,
with a surface gravity range of $1.0<\log{g}<4.8$. We included a wider
distribution of surface gravities in the synthetic SDSS trial, with a median
$\log{g}$ of 3.8 and standard deviation of 0.78 dex, to further explore the
potential influence on the final determinations. The training set consisted of
1986 stars, 590 of which had [Fe/H] $<-2.5$, with 269 having [Fe/H] $<-3.0$.

A slight over-estimation was seen in the residuals of the synthetic SDSS
trial, where the median and trimean estimates were both $+0.03$ dex.
Sensitivity was found to diminish below [Fe/H]$<-3.0$, where the residual
median, $C_{\rm M}$, increased to 0.17 dex. The standard deviation of the
residuals was $S_{\sigma}=0.22$ dex, somewhat improved from the DR1 trial. As
seen in Table 4, all estimates of scale were found to be smaller for the
synthetic SDSS trial. Similar to the DR1 trial, scatter in the residuals was
independent of surface gravity in the range $1.5<\log{g}<5.0$. Over-estimation
was also seen for cooler stars in SDSS trial, where the median residual
increased to $C_{\rm M}=+0.32$ dex for stars of $T_{\rm eff}<4750$ K. The
synthetic SDSS trial was repeated while excluding the use of the $J0395$
filter, resulting in a significant increase in scatter, where
$S_{\sigma}=0.41$ dex and $S_{\rm MAD}=0.43$ dex. We concluded that the
$J0395$ photometry is indeed a crucial component for metallicity sensitivity
with SPHINX.

Of the 214 VMP stars in the synthetic SDSS trial, $91\pm 2$ % were recovered,
while $93\pm 2$ % of the 209 stars classified as VMP by SPHINX were confirmed
the SSPP estimate. While there is an insufficient number of EMP stars in the
DR1 sample at present, we can investigate the classification and recovery
fractions of EMP using the synthetic SDSS sample. Of the 43 stars determined
to be [Fe/H] $<-3.0$ by the SSPP, SPHINX recovered $53\pm 6$ %. Of the 33
stars classified as EMP by SPHINX, $70\pm 6$ % were confirmed by the SSPP
estimate, while all remaining stars were VMP. These results are comparable to
those obtained by the Pristine survey (Starkenburg et al. 2017).

Figure 9: Metallicity estimates from SPHINX for three example stars with DR1
photometry, as a function of the number of ANN units employed. The scale
estimate, $S_{\rm MAD}$, is represented by the orange band. In all three cases
the scale is within the uncertainty in the spectroscopic value determined by
the SSPP, shown in gray.

Figure 10: Left panel: Color-magnitude diagram of the J-PLUS M15 stars. The
population is over-plotted with a PARSEC isochrone corresponding to an age of
10.5 Gyr, and metallicity of $Z=0.0001$ (Bressan et al. 2012), with an assumed
extinction of $E(B-V)=0.11$ mag. Of the 1437 stars in the sample, the 15 with
SEGUE-1 medium-resolution spectra are denoted by green triangles. Right panel:
Distribution of photometric metallicity estimates from M15. A Gaussian
distribution was fit to the photometric distribution, with the $\sigma$=0.33
dex region shaded. A stripe density plot is shown for the 66 confirmed M15
members with medium-resolution parameters from the SSPP. The shaded region in
the density plot depicts the $S_{f}$ of 0.13 dex.

To evaluate the performance of SPHINX as a function of the number of ANN units
employed in the network array, another series of trials were run on the DR1
photometric set. We made use of the DR1 training catalog supplemented with
synthetic VMP magnitudes, as described above. The number of ANN units was
varied from three to 500, and the classification and recovery fractions for
all cases was evaluated. We noted a small but consistent increase in the
classification fraction, from 49% to 51% over the range of three to 100 ANN
units. We found large oscillations in the recovery fractions over the full
range of employed ANN units, but a general increase of a few percent. In the
case of individual estimates, we found generally better convergence to a
limiting value as the array size was increased. In many cases, estimates
varied over 0.20 dex with smaller array size. This behavior is shown for three
example stars with different metallicities in Fig. 9. In all cases, the
variation in the estimates was seen to stabilized after array sizes $N>$ 50\.
For all three cases considered, the variation in the estimates of the
photometric metallicities, determined from the MAD, was well within the
uncertainty reported from the SSPP estimate.

##  7 A case study with M15

Photometric sources from the globular cluster M15 (Messier~15, NGC 7078)
provide an opportunity to test both the accuracy and precision of metallicity
estimates from SPHINX. Located at $\sim$10.4 kpc from the Sun, M15 is a
particularly bright globular cluster with a horizontal-branch magnitude of
$V=15.8$ and tidal radius of 21.5 arcmin (Harris 1996). M15 has a well-defined
spectroscopically determined age of 10.56 $\pm$ 0.47 Gyr (Koleva et al. 2008)
and metallicity of [Fe/H] = $-2.33\pm 0.02$ (Harris 1996; Carretta et al.
2009). Furthermore, with an intrinsic scatter in the metallicity of
$\sigma$([Fe/H])$<0.05$ dex, we regard this cluster as essentially mono-
metallic (Carretta et al. 2009). The accuracy of SPHINX determinations is
thereby investigated by considering the central location of the photometric
metallicity estimates for the cluster, while the spread is reflective of the
precision.

For this analysis, we made use of a stellar sample from Bonatto et al. (2018).
Data were obtained as a science verification set prior to the J-PLUS Early
Data Release. The 1.4 $\times$ 1.4 deg2 field of the J-PLUS T80Cam was
sufficiently large to contain the projected area of M15 in a single pointing.
Photometry extended to a limiting magnitude of $g\sim 21.5$ for over 40,000
stars. The photometric uncertainty at $g\sim 21.5$ was estimated to be
$\sigma_{m}\sim 0.2$, however typical uncertainties for magnitudes within the
calibration limit for SPHINX ($g\sim 18.79$) were less than 0.05 mag. Contrary
to the standard procedure of SExtractor used by OAJ, DAOPHOT PSF (Stetson
1987) was used to extract photometry of stars for M15, as the standard
pipeline is not currently able to cope with the level of stellar crowding
typical of GCs, and DAOPHOT PSF can typically reach deeper photometric limits
than SExtractor (Bonatto et al. 2018). Bonatto et al. (2018) applied a
decontamination algorithm using color-magnitude diagrams, based on the work of
Bonatto & Bica (2007), resulting in 1437 candidate member stars.

Our analysis included 98 stars with medium-resolution spectra from SEGUE-1.
Stellar parameters and radial velocities for these stars were determined from
the SSPP. For stars with high-quality estimates from the adopted and biweight
procedures, effective temperatures and metallicities were taken to be the
average of the two. Otherwise, a star was assigned the best of the two
estimates, evaluated on the basis of a visual comparison with model synthetic
spectra. Typical uncertainties in the radial velocity estimates were $\pm$7.0
km s-1. These stars were originally selected as candidates of M15 on the basis
of their proximity to the center of the cluster and thus required a check for
foreground/background contamination.

We rejected non-member SEGUE-1 stars on the basis of radial velocity. First,
we computed the biweight location and scale for the distribution of radial
velocities in the sample. With the tuning constant of the biweight estimator
set at 6.0, the central location was found to be $C_{\rm BI}=-108.0$ km s-1,
commensurate with a $C_{\rm TRI}$ = $-107.9$ km s-1. For estimates of scale,
we computed $S_{\rm BI}$ = 11.5 km s-1, $S_{f}$ = 11.5 km s-1. We rejected as
outliers stars with radial velocities outside of the range $C_{\rm BI}\pm
2\leavevmode\nobreak\ S_{\rm BI}$. This process was repeated until no new
stars were rejected; 66 stars remained. We recomputed the $C_{\rm BI}$ and
$S_{\rm BI}$ again, and found $-108.0$ km s-1 and 6.9 km s-1, respectively.
Finally, we compared these results with those determined by Pryor & Meylan
(1993), on the basis of high-dispersion spectroscopy. They measured a mean
velocity of $-107.09\pm 0.82$ km s-1, and a velocity dispersion of $8.95\pm
0.59$ km s-1, very similar to our values.

Of the 66 SEGUE-1 stars selected on the basis of radial velocity, a cross-
match with the J-PLUS M15 catalog using a 3 ″search radius identified 15 stars
in common. These stars are shown in the left panel of Fig. 10, along with 1083
J-PLUS stars and a $Z$=$10^{-4}$, 10.5 Gyr isochrone generated with the Padova
and Trieste Stellar Evolution Code (PARSEC; Bressan et al. 2012). Here, the
distance modulus for the cluster was taken to be 15.4 mag (Harris 1996). A
correction of 0.3 mag was applied to the $(J0410-J0861)_{0}$ color prediction
from PARSEC to align the isochrone with the giant branch seen in the M15
photometry. These spectroscopic targets largely occupied the giant branch,
with one possible horizontal-branch star.

SPHINX was applied to J-PLUS photometry of the 1437 M15 stars with a limiting
magnitude of $g\sim 18.0$ using an array of 50 ANN units, and resulted in
parameter estimates for 1041 sources (96% of the initial sample). The
remaining 396 were rejected by the pipeline due to restrictions on the
photometric errors, or extrapolation of all contributing networks. We excluded
estimates produced with less than 25 of the available ANN units, after which
664 (61% of the initial sample) stars remained. The right panel in Fig. 10
compares the distribution of photometric [Fe/H] estimates to both the 66 SSPP
medium-resolution parameters, as well as to the external spectroscopic value
of [Fe/H]$=-2.33\pm 0.02$ for the cluster (Carretta et al. 2009). A central
metallicity of [Fe/H] $=-2.32\pm 0.01$ was found from a Gaussian maximum-
likelihood fit to the distribution of metallicities from SPHINX. The error
estimate of the central metallicity, $\pm 0.01$ dex, was determined from a
bootstrap procedure, for which the 664 stars were randomly sampled with
replacement for 1000 trials. The standard deviation of the residuals for the
photometric estimates was determined to be 0.29 dex. We compared this to the
median value of [Fe/H] $=-2.31\pm 0.02$ for the 66 SEGUE-1 stars with SSPP
parameters, for which the error in the median was determined from the
bootstrap procedure. The $f$ spread of the SSPP metallicity distribution was
0.17 dex, corresponding to $S_{f}=0.13$ dex.

Table 5: Spectroscopic stellar parameters of 13 SEGUE-1 + J-PLUS stars in M15.

RA | DEC | $T_{\rm SP}$ | $\sigma(T_{\rm SP})$ | $T_{\rm SS}$ | $\sigma(T_{\rm SS})$ |  [Fe/H]SP |  $\sigma$([Fe/H]${}_{\rm SP})$ |  [Fe/H]SS |  $\sigma($[Fe/H]SS)
---|---|---|---|---|---|---|---|---|---
(hh:mm:ss) | (dd:mm:ss) | (K) | (K) | (K) | (K) |  | (dex) |  | (dex)
21:29:37.1 | 12:13:41 | 5570 | 93 | 5447 | 75 | -2.44 | 0.24 | -2.47 | 0.24
21:29:39.4 | 12:18:21 | 5411 | 84 | 5299 | 44 | -2.34 | 0.26 | -2.38 | 0.10
21:29:43.1 | 12:00:18 | 5690 | 55 | 5521 | 60 | -2.21 | 0.17 | -2.25 | 0.13
21:29:48.5 | 12:20:20 | 5510 | 81 | 5315 | 37 | -2.37 | 0.28 | -2.27 | 0.16
21:29:49.9 | 12:18:12 | 5288 | 93 | 5206 | 48 | -2.42 | 0.25 | -2.34 | 0.17
21:29:52.3 | 12:19:40 | 5128 | 108 | 5215 | 48 | -2.24 | 0.63 | -2.27 | 0.20
21:30:00.7 | 12:22:32 | 5568 | 136 | 5320 | 33 | -2.35 | 0.27 | -2.27 | 0.16
21:30:13.5 | 12:00:38 | 5523 | 91 | 5390 | 36 | -2.42 | 0.22 | -2.33 | 0.18
21:30:15.2 | 12:19:46 | 5352 | 114 | 5269 | 50 | -2.21 | 0.26 | -2.33 | 0.18
21:30:24.5 | 12:02:38 | 5592 | 130 | 5420 | 33 | -2.95 | 0.79 | -2.35 | 0.18
21:30:35.2 | 12:18:10 | 5626 | 117 | 5314 | 32 | -2.36 | 0.26 | -2.49 | 0.17
21:30:49.3 | 12:07:31 | 5532 | 114 | 5344 | 31 | -2.52 | 0.26 | -2.32 | 0.14
21:30:54.4 | 12:07:11 | 5569 | 121 | 5419 | 45 | -2.39 | 0.22 | -2.23 | 0.21
Figure 11: Metallicity estimates for 13 stars in the M15 cluster with both
SEGUE-1 spectra and J-PLUS photometry. Estimates are shown above the 1$\sigma$
and 2$\sigma$ regions corresponding to the standard deviation of SPHINX
estimates for the entire cluster, and the median error estimate from the SSPP.
The small red ellipse in the center represents the intrinsic scatter of the
M15 cluster, [Fe/H] = $-2.33\pm$ 0.02 (Carretta et al. 2009).

We consider the accuracy of the photometric metallicity estimates for the
cluster in Fig. 11. With the $\sigma$ estimate from the Gaussian distribution
of 0.30 dex and the uncertainty from the SSPP of 0.13 dex, we depict the
individual estimates for 13 stars of the original 15 with both photometric and
spectroscopic estimates. The elliptical regions of Fig. 11 corresponding to
0.5, 1.0, 1.5, and 2$\sigma$ from the center value of [Fe/H] $=-2.33$ for the
cluster were vertically scaled to a circular region for simplicity. We
excluded one star from this sample due to a large error estimate from SPHINX
([Fe/H]${}_{\rm SP}=-2.94\pm 0.79$). Another star, thought originally to
occupy the horizontal branch, was found to have a large deviation between the
photometric and spectroscopic estimates. We therefore excluded this estimate
on the basis of potential error in the photometry. Of the 13 stars considered
with SSPP and SPHINX metallicity estimates, 11 (85%) fall within the 1$\sigma$
region. The remaining two stars each lie within the 1.5$\sigma$ region. Both
the median and $C_{\rm BI}$ computed for the residuals were found to be
$-0.02$ dex. These 13 sources with spectroscopic parameters are provided in
Table 7. We use the SP subscript to denote values determined by SPHINX, while
SS refers to spectroscopically determined estimates from the SSPP.

Figure 12: Left panel: [C/Fe] estimates from the network trained on $S/N$ =
122 inputs; the color of the estimates are proportional to the signal-to-noise
of the validation photometry, where red indicates lower $S/N$. Middle panel:
[C/Fe] residuals for networks of various signal-to-noise are shown, as a
function of the $S/N$ for the validation sets employed. Right panel: Median
residuals for three tiers of validation sets, $S/N<28$, $S/N<36$, and
$S/N<65$, are shown, as a function of the network $S/N$.

J-PLUS photometry of M15 provides an opportunity to validate the effective
temperature and metallicity routines on a single stellar population. While
determinations of metallicity made with SPHINX exhibit a scatter of $\sim$0.26
dex, we are able to make estimations of central metallicity for M15 to
remarkably high accuracy, in addition to estimates of photometric effective
temperature that are commensurate with estimates from the SSPP. In fact, the
uncertainty in the mean of the metallicity distribution generated from
estimates using J-PLUS photometry is within the uncertainty in the value
determined from high-resolution spectra. While the capability of SPHINX is
currently limited with respect to individual precision measurements, SPHINX
enables studies of stellar populations as well.

##  8 Preliminary results on carbonicity

While SPHINX is presently limited to obtaining effective temperature and
metallicity determinations, we anticipate the addition of carbonicity ([C/Fe])
and surface gravity ($\log{g}$) estimates in the near future. This will
require more stars with J-PLUS photometry for proper training on their carbon
features. However, with our library of synthetic spectra, we are able to
explore the validity of a neural network approach to carbon detection. The
application of the synthetic library also permits an in-depth study of the
influence of underlying signal-to-noise on network training and estimation.

To isolate the carbon dependence on our synthetic spectra, we restricted our
analysis to synthetic spectra corresponding to a giant VMP star, $T_{\rm eff}$
= 5000 K, $\log{g}$ = 1.00, [Fe/H] = $-$2.50. Next, 100 spectra were generated
by way of cubic spline interpolation across the interval $-$1.0 $<$ [C/Fe] $<$
+2.5. These normalized spectra were convolved with a blackbody to best
approximate a flux-calibrated spectrum.

The flux of each spectrum was randomly rescaled from 50% to 150% to best
emulate a random distribution of distance moduli, then injected with Gaussian
noise, resulting in 66 batches of the original 100 spectra from 10 $<$ $S/N$
$<$ 122, each batch consisting of a unique global signal-to-noise. Synthetic
magnitudes for the narrow-band J-PLUS filters were computed in the same manner
as for the SDSS Reservoir, by convolving the noise-injected, blackbody-
calibrated synthetic spectrum with the appropriate filter-response function.
Linear scaling was then performed to center each input magnitude distribution.

For simplicity, SPHINX was limited to a single ANN unit for each trial
described below. For each trial, one of the 66 synthetic spectra batches was
used to train the ANN unit, consisting of six narrow-band inputs – $J0378$,
$J0395$, $J0430$, $J0515$, $J0660$, and $J0861$ – with a single hidden layer
of five hyperbolic tangent neurons and a stochastic gradient-descent
optimization. The result was an array of identical networks, each trained on a
set of inputs with a specific signal-to-noise, which we refer to as the
network $S/N$. These networks of unique $S/N$ were then tested on each batch
of noise-injected synthetic spectra, in order to evaluate the performance of
each version of the network with an approximation of photometry of varying
quality. In doing so, we assigned a median residual to each network and its
constituent 66 verification batch runs. The result of this analysis is shown
in Fig. 12.

The left panel of Fig. 12 shows the results of the $S/N$ = 122 network for all
batches of synthetic spectra. We find a characteristic behavior, namely, that
photometry of lower signal-to-noise results in a greater dispersion of the
predicted [C/Fe] about the true value. The dispersion is more prevalent in the
lower carbonicity regime ([C/Fe] $<$ 0.0), as might be expected, since the
carbon-sensitive features at low [C/Fe] are weaker, and so are generally more
influenced by the $S/N$ across the spectrum.

The middle panel of Fig. 12 shows the behavior of each network, as a function
of the $S/N$ in the photometry in the validation set. First, there is a
general trend of a reduction in the spread of the residuals as the signal-to-
noise of the validation photometry increases. Interestingly, in the input
range of $S/N<20$, networks trained on $S/N$ = 10 and $S/N$ = 20 outperform
those trained on higher-quality photometry, for which residuals exceeded a
standard deviation of 0.30 dex. We conclude that, in general, a network
trained on poor photometry will exhibit better performance on poor photometry.

The right panel of Fig. 12 tracks the performance of the network for different
regions of the validation signal-to-noise, as a function of the network’s S/N.
For sources of low quality ($S/N<28$), the median residual is worse overall
for all values of the network $S/N$. The low-quality source residuals tend to
increase as the networks are trained on higher-quality photometry. In the
region of 20 $\leq$ $S/N$ $\leq$ 30, we observe no significant increase in the
median residual of the low-quality source set (median residual $\sim$ 0.13
dex), while the high-quality set relaxes to a roughly consistent value of
$\sim$ 0.08 dex. This suggests an optimal region of $S/N$ for network
training, approximately $30<S/N<40$, to ensure high-confidence performance for
sources of both high and low quality, for network applications of this nature.

##  9 Discussion and conclusion

The Stellar Photometric Index Network Explorer, SPHINX, is designed to
estimate the effective temperature and metallicity of stellar atmospheres
using broad- and intermediate-band optical J-PLUS photometry, with a
particular emphasis on the capacity to identify low-metallicity stars. This
pipeline attempts to optimize training databases provided to converge its
constituent artifical neural network units, as well as the relative weight
assigned to these subordinate ANN units for use in science estimates. By doing
so, SPHINX has the potential to be quite flexible in its ability to
accommodate a variety of photometric data.

Estimates of effective temperature made using J-PLUS Early Data Release were
found to be successful across a temperature range of 4500 $<T_{\rm eff}$ (K)
$<8500$, with an uncertainty of $\pm$ 91 K. Comparisons were made to previous
calibrations by Lee et al. (2008a) and Fukugita et al. (2011), and in all
cases estimates by SPHINX with J-PLUS photometry proved superior to the broad-
band performance. For the application of both broad-band photometric methods,
the J-PLUS analogs to SDSS photometry were used. We emphasize the success of
temperature estimates made with SPHINX without the use of a-priori knowledge
of surface gravity, for which we find no significant influence on temperature
determinations within $2.0<\log{g}<5.0$.

Photometric estimates of metallicity for stars in the J-PLUS First Data
Release within 4500 $<T_{\rm eff}$ (K) $<$ 6200 indicate sensitivity down to
[Fe/H] $\sim$ $-$3.0, with a scatter of $\sigma$([Fe/H]) =0.25 dex. However,
verification of this sensitivity is limited by the lack of numerous [Fe/H]
$<-$3.0 stars in the footprint of J-PLUS at present. We find that metallicity
determinations made with J-PLUS DR1 photometry are not influenced by surface
gravity within the range $1.75<\log{g}<5.0$. SPHINX is a very effective as a
means for recovering and correctly identifying significant fractions of low-
metallicity stars. SPHINX recovers $85\pm 3$ % of very metal-poor (VMP)
targets in the DR1 testing set used, with $63\pm 4$ % of VMP candidates
correctly classified. For the trial consisting of synthetic magnitudes from
the SDSS Reservoir, $70\pm 6$ % of stars designated as [Fe/H]$<-3$ were
confirmed by the SSPP, while all remaining stars were VMP. Of the 43 EMP stars
in the synthetic SDSS trial, $53\pm 6$ % were recovered by SPHINX.

Photometric metallicity estimates were made using J-PLUS photometry of 664
sources associated with globular cluster M15 (NGC 7078). The central value
obtained, [Fe/H]$=-2.32\pm 0.01$, with a residual spread of 0.29 dex, was
commensurate with the value determined from SEGUE-1 medium-resolution spectra
of $-2.32\pm 0.02$ for the cluster. These estimates essentially match the
accepted value from the literature, $-2.33\pm 0.02$ (Harris 1996; Carretta et
al. 2009). The accuracy of estimates made by SPHINX was, in part, due to the
level of optimization made possible by way of adjustable neural network
architecture and the ability to tailor the training set used to converge the
subordinate ANN units. This enables SPHINX to make parameter estimates for
science cases involving stars of a single evolutionary stage, or to generalize
to accommodate field stars in a variety of evolutionary stages across large
regions of sky.

The development of SPHINX is at present limited to effective temperature and
metallicity estimates, but we anticipate the addition of carbon abundance
estimates, at least for some portion of the stellar parameter space. With
carbon-abundance estimates from SPHINX, the primary sub-classes of carbon-
enhanced metal-poor (CEMP) stars, the CEMP-$s$ and CEMP-no stars, describing
the nature of their neutron-capture element abundance ratios (Beers &
Christlieb 2005), could be discerned from photometry alone (Yoon et al. 2016),
avoiding the requirement for obtaining far-more time-consuming high-resolution
spectroscopic follow-up. In addition, with accurate parallaxes from Gaia DR2
(Gaia Collaboration et al. 2016), improved photometric maps of carbon
abundances for the inner- and outer-halo regions of the Milky Way are readily
obtainable (see spectroscopic-based maps in Lee et al. 2013).

In the future, we plan to provide photometric parameters for a substantial
portion of stars in the J-PLUS footprint. However, at present, a pure catalog
of stellar sources from J-PLUS is not yet available – present catalogs are
contaminated by quasars at faint magnitudes. Low-redshift quasars can be
identified and removed by straightforward PSF analysis and the use of color-
color diagrams (Caballero et al. 2008). However, high-redshift quasars remain
a challenge, as they are optically similar to ultracool dwarfs.

The artificial neural network methodology of SPHINX, in conjunction with
J-PLUS photometry, is an ideal tool for selecting low-metallicity targets for
spectroscopic follow-up. In addition, reasonable sensitivity has been
demonstrated for individual estimates of metallicity down to [Fe/H] $\sim-3.0$
for stars in the range $4500<T_{\rm eff}$ (K) $<6200$. We anticipate that
future data releases from J-PLUS will enable an expanded sensitivity to low-
metallicity stars. Ultimately, we expect to substantially increase the number
of known VMP, EMP, UMP, and CEMP stars in the coming years on the basis of
such studies.

###### Acknowledgements.

D.D.W., V.M.P., and T.C.B. acknowledge partial support from Grant No.
PHY-1430152 (Physics Frontier Center/JINA Center for the Evolution of the
Elements), awarded by the U.S. National Science Foundation. Based on
observations made with the (JAST/T80 and/or JST/T250) telescope/s at the
Observatorio Astrofísico de Javalambre, in Teruel, owned, managed, and
operated by the Centro de Estudios de Física del Cosmos de Aragón. We thank
the OAJ Data Processing and Archiving Unit (UPAD) for reducing and calibrating
the OAJ data used in this work. Funding for the J-PLUS Project has been
provided by the Governments of Spain and Aragon through the Fondo de
Inversiones de Teruel, the Spanish Ministry of Economy and Competitiveness
(MINECO; under grants AYA2016-79425-C3-2-P, AYA2015-66211-C2-1-P,
AYA2015-66211-C2-2, AYA2012-30789 and ICTS-2009-14), and European FEDER
funding (FCDD10-4E-867, FCDD13-4E-2685). The Brazilian agencies FAPESP and the
National Observatory of Brazil have also contributed to this project. S.A.
acknowledges support of CNPq, through postdoctoral fellowship (project
300336/2016-0). MVCD thanks the FAPESP scholarship process number
2014/18632-6. S.R. acknowledge financial support from CAPES, CNPq, and FAPESP.
T.M. acknowledges support provided by the Spanish Ministry of Economy and
Competitiveness (MINECO), under grant AYA-2017-88254-P. R.L.O. was partially
supported by the Brazilian agency CNPq (Universal Grants 459553/2014-3, PQ
302037/2015-2, and PDE 200289/2017-9). CMO and LSJ acknowledge the support
from FAPESP and CNPq. Y.S.L.acknowledges support from the National Research
Foundation (NFR) of Korea grant funded by the Ministry of Science and ICT
(No.2017R1A5A1070354 and NRF-2018R1A2B6003961). RAD acknowledges support from
CNPq through BP grant 312307/2015-2, CSIC through grant COOPB20263, FINEP
grants REF. 1217/13 - 01.13.0279.00 and REF 0859/10 - 01.10.0663.00 for
partial hardware support for the J-PLUS project through the National
Observatory of Brazil. PC acknowledges support from CNPq 305066/2015-3.
Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS-IV acknowledges support and resources from
the Center for High-Performance Computing at the University of Utah. The SDSS
web site is www.sdss.org. SDSS-IV is managed by the Astrophysical Research
Consortium for the Participating Institutions of the SDSS Collaboration
including the Brazilian Participation Group, the Carnegie Institution for
Science, Carnegie Mellon University, the Chilean Participation Group, the
French Participation Group, Harvard-Smithsonian Center for Astrophysics,
Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli
Institute for the Physics and Mathematics of the Universe (IPMU) / University
of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für
Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA
Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-
Institut für Extraterrestrische Physik (MPE), National Astronomical
Observatories of China, New Mexico State University, New York University,
University of Notre Dame, Observatário Nacional / MCTI, The Ohio State
University, Pennsylvania State University, Shanghai Astronomical Observatory,
United Kingdom Participation Group, Universidad Nacional Autónoma de México,
University of Arizona, University of Colorado Boulder, University of Oxford,
University of Portsmouth, University of Utah, University of Virginia,
University of Washington, University of Wisconsin, Vanderbilt University, and
Yale University.

## References

  * Abazajian et al. (2009) Abazajian, K. N., Adelman-McCarthy, J. K., Agüeros, M. A., et al. 2009, ApJS, 182, 543
  * Abohalima & Frebel (2017) Abohalima, A. & Frebel, A. 2017, ArXiv e-prints [arXiv:1711.04410]
  * Aguado et al. (2018) Aguado, D. S., Allende Prieto, C., González Hernández, J. I., & Rebolo, R. 2018, ApJ, 854, L34
  * Allende Prieto et al. (2008) Allende Prieto, C., Sivarani, T., Beers, T. C., et al. 2008, AJ, 136, 2070
  * Álvarez & Plez (1998) Álvarez, R. & Plez, B. 1998, A&A, 330, 1109
  * An et al. (2013) An, D., Beers, T. C., Johnson, J. A., et al. 2013, ApJ, 763, 65
  * An et al. (2015) An, D., Beers, T. C., Santucci, R. M., et al. 2015, ApJ, 813, L28
  * Anthony-Twarog et al. (1991) Anthony-Twarog, B. J., Twarog, B. A., Laird, J. B., & Payne, D. 1991, AJ, 101, 1902
  * Beers & Christlieb (2005) Beers, T. C. & Christlieb, N. 2005, Annu. Rev. Astron. Astrophys
  * Beers et al. (1990) Beers, T. C., Flynn, K., & Gebhardt, K. 1990, AJ, 100, 32
  * Benitez et al. (2014) Benitez, N., Dupke, R., Moles, M., et al. 2014, ArXiv e-prints [arXiv:1403.5237]
  * Bertin & Arnouts (1996) Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393
  * Boggs & Rogers (1990) Boggs, P. & Rogers, J. 1990, Contemporary Mathematics, 112, 186
  * Bonatto & Bica (2007) Bonatto, C. & Bica, E. 2007, MNRAS, 377, 1301
  * Bonatto et al. (2018) Bonatto, C., Chies-Santos, A. L., Coelho, P. R. T., et al. 2018, A&A
  * Bonifacio et al. (2015) Bonifacio, P., Caffau, E., Spite, M., et al. 2015, A&A, 579, A28
  * Borucki et al. (2010) Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, 327, 977
  * Bressan et al. (2012) Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127
  * Brown et al. (2001) Brown, L. D., Cai, T. T., & DasGupta, A. 2001, Statistical Science, 16, 101
  * Caballero et al. (2008) Caballero, J. A., Burgasser, A. J., & Klement, R. 2008, A&A, 488, 181
  * Canterna (1976) Canterna, R. 1976, AJ, 81, 228
  * Carollo et al. (2010) Carollo, D., Beers, T. C., Chiba, M., et al. 2010, ApJ, 712, 692
  * Carollo et al. (2007) Carollo, D., Beers, T. C., Lee, Y. S., et al. 2007, Nature, 450, 1020
  * Carretta et al. (2009) Carretta, E., Bragaglia, A., Gratton, R., D’Orazi, V., & Lucatello, S. 2009, A&A, 508, 695
  * Cenarro et al. (2018) Cenarro, A. J., Moles, M., Cristóbal-Hornillos, D., et al. 2018, ArXiv e-prints [arXiv:1804.02667]
  * Dawson et al. (2013) Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2013, AJ, 145, 10
  * Eisenstein et al. (2011) Eisenstein, D. J., Weinberg, D. H., Agol, E., et al. 2011, AJ, 142, 72
  * Fabbro et al. (2018) Fabbro, S., Venn, K. A., O’Briain, T., et al. 2018, MNRAS, 475, 2978
  * Fitzpatrick (1999) Fitzpatrick, E. L. 1999, PASP, 111, 63
  * Frebel et al. (2018) Frebel, A., Ji, A. P., Ezzeddine, R., et al. 2018, ArXiv e-prints [arXiv:1810.01228]
  * Fukugita et al. (2011) Fukugita, M., Yasuda, N., Doi, M., Gunn, J. E., & York, D. G. 2011, AJ, 141, 47
  * Gaia Collaboration et al. (2016) Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1
  * Green et al. (2018) Green, G. M., Schlafly, E. F., Finkbeiner, D., et al. 2018, ArXiv e-prints [arXiv:1801.03555]
  * Gustafsson et al. (2008) Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A&A, 486, 951
  * Harris (1996) Harris, W. E. 1996, AJ, 112, 1487
  * Hon et al. (2017) Hon, M., Stello, D., & Yu, J. 2017, MNRAS, 469, 4578
  * Hon et al. (2018) Hon, M., Stello, D., & Yu, J. 2018, MNRAS, 476, 3233
  * Ibata et al. (2017a) Ibata, R. A., McConnachie, A., Cuillandre, J.-C., et al. 2017a, ApJ, 848, 128
  * Ibata et al. (2017b) Ibata, R. A., McConnachie, A., Cuillandre, J.-C., et al. 2017b, ApJ, 848, 129
  * Ivezić et al. (2008) Ivezić, Z., Sesar, B., Jurić, M., et al. 2008, The Astrophysical Journal, 684, 287
  * Keller et al. (2014) Keller, S. C., Bessell, M. S., Frebel, A., et al. 2014, Nature, 506, 463
  * Keller et al. (2007) Keller, S. C., Schmidt, B. P., Bessell, M. S., et al. 2007, Publications of the Astronomical Society of Australia, 24, 1–12
  * Kheirdastan & Bazarghan (2016) Kheirdastan, S. & Bazarghan, M. 2016, Ap&SS, 361, 304
  * Kim & Brunner (2017) Kim, E. J. & Brunner, R. J. 2017, MNRAS, 464, 4463
  * Kingma & Ba (2014) Kingma, D. P. & Ba, J. 2014, CoRR, abs/1412.6980 [arXiv:1412.6980]
  * Koleva et al. (2008) Koleva, M., Prugniel, P., Ocvirk, P., Le Borgne, D., & Soubiran, C. 2008, MNRAS, 385, 1998
  * Le Cun et al. (1991) Le Cun, Y., Kanter, I., & Solla, S. 1991, Adv Neural Inform Process Syst, 3, 918
  * Lee et al. (2013) Lee, Y. S., Beers, T. C., Masseron, T., et al. 2013, AJ, 146, 132
  * Lee et al. (2008a) Lee, Y. S., Beers, T. C., Sivarani, T., et al. 2008a, AJ, 136, 2022
  * Lee et al. (2008b) Lee, Y. S., Beers, T. C., Sivarani, T., et al. 2008b, AJ, 136, 2050
  * Logroño-García et al. (2018) Logroño-García, R., Vilella-Rojo, G., López-Sanjuan, C., et al. 2018, A&A, submitted [arXiv:1804.04039]
  * López-Sanjuan et al. (2018) López-Sanjuan, C., Vázquez Ramió, H., Varela, J., et al. 2018, A&A, in press
  * Lupton et al. (1999) Lupton, R. H., Gunn, J. E., & Szalay, A. S. 1999, AJ, 118, 1406
  * Molino et al. (2018) Molino, A., Costa-Duarte, M. V., Mendes de Oliveira, C., et al. 2018, A&A, in press [arXiv:1804.03640]
  * Pedregosa et al. (2011) Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, Journal of Machine Learning Research, 12, 2825
  * Placco et al. (2016) Placco, V. M., Frebel, A., Beers, T. C., et al. 2016, ApJ, 833, 21
  * Placco et al. (2015) Placco, V. M., Frebel, A., Lee, Y. S., et al. 2015, ApJ, 809, 136
  * Plez (2012) Plez, B. 2012, Turbospectrum: Code for spectral synthesis, Astrophysics Source Code Library
  * Pryor & Meylan (1993) Pryor, C. & Meylan, G. 1993, in Astronomical Society of the Pacific Conference Series, Vol. 50, Structure and Dynamics of Globular Clusters, ed. S. G. Djorgovski & G. Meylan, 357
  * Riedmiller (1994) Riedmiller, M. 1994, Computer Standards & Interfaces
  * Rosenblatt (1958) Rosenblatt, F. 1958, Psychological Review, 65
  * Ryabchikova et al. (2015) Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, Phys. Scr, 90, 054005
  * Salvadori et al. (2010) Salvadori, S., Ferrara, A., Schneider, R., Scannapieco, E., & Kawata, D. 2010, MNRAS, 401, L5
  * San Roman et al. (2018) San Roman, I., Sánchez-Blázquez, P., Cenarro, A. J., et al. 2018, A&A, submitted [arXiv:1804.03727]
  * Schlafly & Finkbeiner (2011) Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103
  * Schlaufman & Casey (2014) Schlaufman, K. C. & Casey, A. R. 2014, ApJ, 797, 13
  * Spite et al. (2013) Spite, M., Caffau, E., Bonifacio, P., et al. 2013, A&A, 552, A107
  * Starkenburg et al. (2018) Starkenburg, E., Aguado, D. S., Bonifacio, P., et al. 2018, MNRAS[arXiv:1807.04292]
  * Starkenburg et al. (2017) Starkenburg, E., Martin, N., Youakim, K., et al. 2017, MNRAS, 471, 2587
  * Stetson (1987) Stetson, P. B. 1987, PASP, 99, 191
  * Strömgren (1963) Strömgren, B. 1963, QJRAS, 4, 8
  * Strömgren (1964) Strömgren, B. 1964, Astrophysica Norvegica, 9, 333
  * Ting et al. (2018) Ting, Y.-S., Conroy, C., Rix, H.-W., & Cargile, P. 2018, ArXiv e-prints [arXiv:1804.01530]
  * Tonry et al. (2012) Tonry, J. L., Stubbs, C. W., Lykke, K. R., et al. 2012, ApJ, 750, 99
  * Wilson (1927) Wilson, E. B. 1927, Journal of the American Statistical Association, 22, 209
  * Yanny et al. (2009) Yanny, B., Rockosi, C., Newberg, H. J., et al. 2009, AJ, 137, 4377
  * Yoon et al. (2016) Yoon, J., Beers, T. C., Placco, V. M., et al. 2016, ApJ, 833, 20
  * York et al. (2000) York, D. G., Adelman, J., Anderson, Jr., J. E., et al. 2000, AJ, 120, 1579