# Stellar Loci. VII. Photometric Metallicities of 5 Million FGK Stars Based on
GALEX GR6+7 AIS and Gaia EDR3

Xue Lu Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal
University, Beijing 102206, China  Department of Astronomy, Beijing Normal
University No.19, Xinjiekouwai St, Haidian District, Beijing, 100875, China
Haibo Yuan Institute for Frontiers in Astronomy and Astrophysics, Beijing
Normal University, Beijing 102206, China  Department of Astronomy, Beijing
Normal University No.19, Xinjiekouwai St, Haidian District, Beijing, 100875,
China  Shuai Xu Institute for Frontiers in Astronomy and Astrophysics, Beijing
Normal University, Beijing 102206, China  Department of Astronomy, Beijing
Normal University No.19, Xinjiekouwai St, Haidian District, Beijing, 100875,
China  Ruoyi Zhang Institute for Frontiers in Astronomy and Astrophysics,
Beijing Normal University, Beijing 102206, China  Department of Astronomy,
Beijing Normal University No.19, Xinjiekouwai St, Haidian District, Beijing,
100875, China  Kai Xiao Institute for Frontiers in Astronomy and Astrophysics,
Beijing Normal University, Beijing 102206, China  Department of Astronomy,
Beijing Normal University No.19, Xinjiekouwai St, Haidian District, Beijing,
100875, China  School of Astronomy and Space Science, University of Chinese
Academy of Sciences, Beijing 100049, China  Yang Huang School of Astronomy and
Space Science, University of Chinese Academy of Sciences, Beijing 100049,
China  Timothy C. Beers Department of Physics and Astronomy, University of
Notre Dame, Notre Dame, IN 46556, USA  Joint Institute for Nuclear
Astrophysics – Center for the Evolution of the Elements (JINA-CEE), USA  Jihye
Hong Department of Physics and Astronomy, University of Notre Dame, Notre
Dame, IN 46556, USA  Joint Institute for Nuclear Astrophysics – Center for the
Evolution of the Elements (JINA-CEE), USA Haibo Yuan<EMAIL_ADDRESS>
(Received XXX; Revised YYY; Accepted ZZZ)

###### Abstract

We combine photometric data from GALEX GR6+7 AIS and Gaia EDR3 with stellar
parameters from the SAGA and PASTEL catalogs to construct high-quality
training samples for dwarfs ($\rm 0.4<BP-RP<1.6$) and giants ($\rm 0.6<BP-
RP<1.6$). We apply careful reddening corrections using empirical temperature-
and extinction-dependent extinction coefficients. Using the two samples, we
establish a relationship between stellar loci (NUV$-$BP vs. BP$-$RP colors),
metallicity, and $\rm M_{G}$. For a given BP$-$RP color, a 1 dex change in
[Fe/H] corresponds to an approximately 1 magnitude change in NUV$-$BP color
for solar-type stars. These relationships are employed to estimate
metallicities based on NUV$-$BP, BP$-$RP, and $\rm M_{G}$. Thanks to the
strong metallicity dependence in the GALEX NUV-band, our models enable a
typical photometric-metallicity precision of approximately
$\sigma_{\rm[Fe/H]}$ = 0.11 dex for dwarfs and $\sigma_{\rm[Fe/H]}$ = 0.17 dex
for giants, with an effective metallicity range extending down to [Fe/H]
$=-3.0$ for dwarfs and [Fe/H] $=-4.0$ for giants. We also find that the NUV-
band based photometric-metallicity estimate is not as strongly affected by
carbon enhancement as previous photometric techniques. With the Gaia and GALEX
data, we have estimated metallicities for about 5 million stars across almost
the entire sky, including approximately 4.5 million dwarfs and 0.5 million
giants. This work demonstrates the potential of the NUV-band for estimating
photometric metallicities, and sets the groundwork for utilizing the NUV data
from space telescopes such as the upcoming Chinese Space Station Telescope.

metallicity; stellar fundamental parameters; astronomy data analysis

##  1 Introduction

Metallicity (metal abundance; generally parametrized by [Fe/H]), is one of the
basic stellar parameters, and plays an important role in studying the
formation and evolution of not only stars and stellar populations, but also of
galaxies such as the Milky Way. Analyzing the stellar metallicity distribution
within the Milky Way provides valuable insights into its origin and evolution
through chemical and kinematic studies (e.g., Beers & Christlieb 2005;
Matteucci 2021).

There are two main methods to measure stellar metallicity for large samples of
stars utilized to date: spectroscopic and photometric. Spectroscopy has long
been the primary approach, and significant progress has been made with large-
scale spectroscopic surveys over the past two decades. Notable surveys include
the Sloan Digital Sky Survey and the Sloan Extension for Galactic
Understanding and Evolution (SDSS/SEGUE; York et al. 2000; Yanny et al. 2009;
Rockosi et al. 2022), the Radial Velocity Experiment (RAVE; Steinmetz et al.
2006), the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST;
Deng et al. 2012; Liu et al. 2014), the Apache Point Observatory Galactic
Evolution Experiment (APOGEE; Majewski et al. 2017), and the GALactic
Archaeology with HERMES (GALAH; Buder et al. 2018). Moderate ($R\sim 7,500$)-
to high ($R\gtrsim 20,000)$-resolution spectroscopy can achieve high-precision
metallicity estimates, typically around or below 0.1 dex, especially in cases
of high spectral signal-to-noise ratios. However, there are also disadvantages
to spectroscopy. For example, spectroscopic surveys are more time-consuming
and require complex data analysis compared to photometric surveys.
Consequently, the number of observed sources collected from the aforementioned
surveys represents only a tiny fraction of the estimated total number of stars
in the Milky Way. The resulting limited samples, coupled with typically
complex selection functions for the targets, poses challenges to obtaining a
more complete and unbiased set of metallicity estimates for stars in the Milky
Way.

Stellar metallicity can also be obtained by analyzing photometric data;
original efforts can be traced back to Schwarzschild et al. (1955), but steady
progress in this approach has been made over the intervening decades due to
improvements in technology and the use of optimized filters. Stellar colors
are not a pure function of the effective temperature; other stellar parameters
also have an impact, including the stellar metallicity. Though it has a
smaller effect on the stellar color than temperature, the metallicity of a
star can still be inferred photometrically. The dependence of stellar loci on
metallicity is more pronounced in bluer colors, as metallic absorption lines
in the optical region are primarily concentrated in the this wavelength range.

A typical procedure for obtaining photometric-metallicity estimates involves
several steps. First, cross-matches of photometric catalogs of stars with
available spectroscopic-metallicity estimates are performed. Data quality cuts
and careful reddening corrections are then applied for the stars in common.
Subsequently, various techniques such as metallicity-dependent stellar loci
fitting (e.g., Yuan et al. 2015a), principal component analysis (e.g.,
Casagrande et al. 2019), stellar isochrone fitting (e.g., An & Beers 2020),
neural networks (e.g., Whitten et al. 2021; Yang et al. 2022), and others are
employed to establish the relationship between stellar colors and
metallicities. This relationship is then further validated and tested using
other independent sets of data. Finally, the established relationship is
applied to all photometric data that satisfy certain conditions, enabling the
determination of photometric metallicities for those sources. Furthermore, it
is important to recognize that the relationship between stellar colors and
metallicities varies for stars of different luminosity classes.

Among these methods, the stellar loci fitting method stands out as one of the
earliest, and has been widely employed (e.g., Ivezić et al. 2008; Yuan et al.
2015a; Starkenburg et al. 2017; Huang et al. 2019, 2021). Ivezić et al. (2008)
used the SDSS colors $u-g$ and $g-r$ to provide photometric metallicities for
2 million dwarfs with a precision of 0.15 dex, down to a metallicity limit of
[Fe/H] $\sim-2.0$. In a later study, Yuan et al. (2015a) investigated the
metallicity dependence of the stellar loci from SDSS and their intrinsic
widths after considering effect of metallicity and photometric error, by using
re-calibrated photometric data from SDSS stripe 82 (Yuan et al. 2015c). It was
found that a 1 dex decrease in metallicity results in a decrease of about
0.20/0.02 mag in the $u-g/g-r$ colors and increase of about 0.02/0.02 mag in
the $r-i/i-z$ colors, respectively. Additionally, Yuan et al. (2015b)
estimated photometric metallicities for half a million FGK stars from SDSS
stripe 82 with a typical precision of 0.1 dex by simultaneously fitting de-
reddened $u-g$, $g-r$, $r-i$, and $i-z$ colors from SDSS to those predicted
for metallicity-dependent stellar loci. After that, Zhang et al. (2021)
studied metallicity-dependent SDSS stellar color loci for red giant stars, and
measured stellar metallicities in Stripe 82 using the same technique,
achieving a typical precision of 0.2 dex. Notably, they observed systematic
differences between the metallicity-dependent stellar loci of red giants and
main-sequence stars.

Huang et al. (2019, 2022, 2023) apply a similar technique to the photometric
data of SkyMapper Southern Survey (SMSS; Onken et al. 2019) DR2 and the
Stellar Abundances and Galactic Evolution Survey (SAGES; Fan et al. 2023) DR1,
whose optimally designed narrow/medium-band u,v filters enabled photometric-
metallicity estimates down to [Fe/H] $\sim-3.5$ for a total of some 50 million
stars.

Broad-band photometry is generally believed to be unsuitable for photometric-
metallicity estimation, due to very weak sensitivity to changes in stellar
metallicity. However, by combining data from Gaia EDR3 (Brown et al. 2021) and
LAMOST DR7 (Luo et al. 2015) and using the stellar loci fitting technique, Xu
et al. (2022a) obtained metallicity estimates for about 27 million stars
(including over 20 million dwarfs and 6 million giants) with $\rm 10<G<16$
across almost the entire sky. They found that, for a given $\rm(BP-RP)$ color,
a 1 dex change in [Fe/H] results in a 5 mmag change in the $\rm(BP-G)$ color
for solar-type stars. Despite the very weak sensitivity, the exquisite data
quality of the Gaia colors, together with careful reddening corrections and
color calibrations, enable a typical precision of approximately $\delta[\rm
Fe/H]=0.2$ dex. Utilizing the extensive dataset of photometric metallicities
and considering additional criteria, Xu et al. (2022b) compile an updated
catalog of the Best and Brightest metal-poor stars. This catalog offers
valuable targets for subsequent high-resolution spectroscopic observations.

Based on previous work, bluer and narrower bands are more sensitive to
metallicity; the availability of high-precision photometric data is also
highly advantageous for accurate and precise estimates of photometric
metallicity. However, thus far, the capability of the near-ultraviolet (NUV)
band (with a bandwidth on the order of 1000 Å) data for estimation of
phometric metallicities has not yet been fully explored. In this study, we aim
to develop the utility of NUV data from the Galaxy Evolution Explorer (GALEX;
Martin et al. 2005) for this purpose.

The paper is organized as follows. In Sections 2 and 3, we introduce the data
and the method used in this work. The results and a discussion are described
in Section 4. The final sample is described in Section 5. Section 6 presents a
summary.

##  2 Data

###  2.1 GALEX GR6+7 AIS

GALEX was a NASA Explorer Mission, launched on April 28, 2003, with the
primary objective of conducting the first space-based sky survey in both the
near and far ultraviolet. GALEX surveys include an all-sky imaging survey, and
medium and deep imaging surveys covering specific areas, as well as
spectroscopic surveys utilizing grism technology. GALEX simultaneously
performs sky surveys in two bands through use of a dichroic beam splitter:
far-UV (FUV; $1344-1786\rm\AA$) and near-UV (NUV; $1771-2831\rm\AA$). The
field-of-view of GALEX is 1.28/1.24∘, and the spatial resolution is
$4.2/5.3^{\prime\prime}$ for the FUV/NUV, respectively (Morrissey et al.
2007). The GALEX GR6+7 AIS database (Bianchi et al. 2014) is a valuable
catalog derived from the mission, containing 214,449,551 source measurements.

###  2.2 Gaia Early Data Release 3

The Gaia Early Data Release 3 (EDR3; Brown et al. 2021) provides unprecedented
photometric data with milli-magnitude precision for over one billion stars in
the $G$, $G_{\rm BP}$ and $G_{\rm RP}$ bands111For simplicity of notation, we
refer to the $G_{\rm BP}$ and $G_{\rm RP}$ magnitudes as ‘BP’ and ‘RP’ in the
remainder of this paper.. It also provides trigonometric parallaxes and proper
motions for nearly 1.5 billion sources. This vast and high-quality dataset
serves as an excellent resource for estimating photometric metallicities for
an enormous number of stars.

Figure 1: HR diagram of the training samples, color-coded by [Fe/H]. The
dwarfs and giants are separated by the black dashed line (Xu et al. 2022a):
$\rm M_{G}=-{(BP-RP)}^{2}+6.5\times(BP-RP)-1.8$.

###  2.3 Construction of Training Samples

We obtain spectroscopic data for the training samples by combining metallicity
information from the Stellar Abundances for the Galactic Archeology (SAGA;
Suda et al. 2008, 2011; Yamada et al. 2013; Suda et al. 2017) and the PASTEL
(Soubiran et al. 2010, 2016) catalogs. After removing old and duplicate
sources, the number of stars in the combined dataset is 26,350. After
performing a cross-match with the GALEX GR6+7 AIS and Gaia EDR3 catalogs, we
obtain NUV/BP/RP-band information for 4,026 sources, which are used to
construct our final training samples. Considering that the stellar loci in the
NUV-band are highly sensitive to metallicity, and the sensitivity differs
between giants and dwarfs (Zhang et al. 2021), we divide the selected sources
into these two categories using an empirical cut (Xu et al. 2022a), as shown
in Figure 1. The cuts for the training samples are as follows:

  1. 1.

$\rm 0.4<(BP-RP)_{0}<1.6$ for dwarfs and $\rm 0.6<(BP-RP)_{0}<1.6$ for giants

  2. 2.

$-3.5<[\rm Fe/H]<+0.5$ for dwarfs (considering the metallicity dependency is
too weak to estimate metallicity for dwarf stars with $\rm[Fe/H]<-3.5$ using
the GALEX NUV data) and $\rm-5<[Fe/H]<+0.5$ for giants

  3. 3.

$\rm NUV>15$ to avoid saturation (Morrissey et al. 2007) and $\rm
error_{NUV}<0.1$ to ensure the data quality

  4. 4.

$\rm E(B-V)<0.15$. The $\rm E(B-V)$ used here is from the Schlegel et al.
(1998, hereafter SFD98) dust reddening map (note that the 14% systematic over-
estimated values have been corrected in the empirical reddening coefficients
described in Section 3.

Figure 2: Distributions of the dwarf (top panel) and giant (bottom panel)
training samples after cutting in the [Fe/H] vs. $\rm(BP-RP)_{0}$ plane,
color-coded by $\rm M_{G}$.

After applying these cuts, the dwarf and giant samples have a very limited
number of sources with $-2.5<[\rm Fe/H]<-0.3$. We thus add 200 high-quality
dwarfs and giants from LAMOST with $-2.5<[\rm Fe/H]<-0.3$, $\rm
SNRg\,(LAMOST)>40$, $\rm error_{NUV}<$ 0.05, E(B-V) $<0.05$, and $\rm NUV>15$
into the dwarf and giant training samples. There are small metallicity offsets
between the LAMOST and the previous training samples: $-$0.07 dex for dwarfs
and $-$0.06 dex for giants. Finally, a total of 1073 and 1107 sources are
selected as our dwarf and giant training samples, respectively. Their
distributions in the [Fe/H] vs. (BP$-$RP)0 plane are shown in Figure 2.

##  3 Method

###  3.1 Reddening Corrections

Due to the ultra-broad Gaia passbands, it is important to perform careful
reddening corrections. Zhang & Yuan (2023) consider the dependence of
reddening coefficients on $\rm T_{eff}$ and $\rm E(B-V)$, providing a better
description of empirical reddening coefficients than simply single-valued
coefficients. According to their results, the reddening coefficients exhibit a
stronger dependence on $\rm T_{eff}$ for broader filters (such as the Gaia
passbands) and bluer filters (such as the GALEX filters). In this work, we
utilize the python package provided by Zhang & Yuan (2023) to obtain $\rm
T_{eff}$\- and $\rm E(B-V)$-dependent reddening coefficients: $\rm
R(T_{eff},E(B-V))$ for the BP$-$RP and NUV$-$BP colors. The intrinsic colors
of stars are estimated as follows:

$color_{0}=color_{obs}-R_{color}(T_{\rm eff},E(B-V))\times E(B-V).$

All colors referred to hereafter are the intrinsic (de-reddened) colors unless
otherwise noted.

In the python package of Zhang & Yuan (2023), the input temperatures could be
replaced by $\rm BP-RP$ colors when unavailable, as adopted in this work.
During this process, we observe differences in the reddening coefficients
between dwarfs and giants. We randomly select 10,000 sources in common with
$\rm E(B-V)<0.5$ from LAMOST DR8 (Luo et al. 2015), Gaia EDR3 and GALEX GR6+7
to present the differences in the $\rm BP-RP$ vs. $\rm NUV-BP$ intrinsic color
loci between giants and dwarfs in Figure 3, which illustrates that BP$-$RP
colors differ between dwarfs and giants at the same NUV$-$BP color. This
results in a modest bias in the reddening coefficients obtained from Zhang &
Yuan (2023) for giants, mainly due to the lack of giants in their UV sample.
Therefore, we make an attempt to correct this bias by subtracting 0.3 mag from
BP$-$RP colors for giants when using the python package of Zhang & Yuan
(2023). The result is shown in Figure 4.

Figure 3: The differences in $\rm BP-RP$ vs. $\rm NUV-BP$ color loci between
dwarfs (blue dots) and giants (red dots). Figure 4: RNUV-BP, as a function of
BP$-$RP, for dwarfs (dashed lines) and giants (solid lines) at different
extinction values.

###  3.2 $\rm[Fe/H]$\- and $\rm M_{G}$-dependent Stellar Loci

Similar to Yuan et al. (2015a), we conduct a polynomial fitting for stellar
loci, and employ a minimum $\chi^{2}$ technique to derive the metallicity for
dwarfs and giants, respectively. Unlike Yuan et al. (2015a), we consider the
effects of both metallicities and absolute magnitude on stellar loci rather
than metallicities alone (see APPENDIX A). A fourth-order three-dimensional
polynomial with thirty-one free parameters is adopted to fit the relationship
among NUV$-$BP, BP$-$RP color, [Fe/H], and $\rm M_{G}$ for both dwarfs and
giants:

$\displaystyle(NUV-BP)=$ $\displaystyle p0\cdot X^{4}+p1\cdot Y^{4}+p2\cdot
Z^{4}+p3\cdot X^{3}\cdot Y$ $\displaystyle{}+p4\cdot Y^{3}\cdot X+p5\cdot
X^{3}\cdot Z+p6\cdot Z^{3}\cdot X$ $\displaystyle{}+p7\cdot Z^{3}\cdot
Y+p8\cdot Y^{3}\cdot Z+p9\cdot X^{2}\cdot Y^{2}$ $\displaystyle{}+p10\cdot
X^{2}\cdot Z^{2}+p11\cdot Z^{2}\cdot Y^{2}+p12\cdot X^{3}$
$\displaystyle{}+p13\cdot Y^{3}+p14\cdot Z^{3}+p15\cdot X^{2}\cdot Y+p16\cdot
Y^{2}\cdot X$ $\displaystyle{}+p17\cdot X^{2}\cdot Z+p18\cdot Z^{2}\cdot
X+p19\cdot Z^{2}\cdot Y$ $\displaystyle{}+p20\cdot Y^{2}\cdot Z+p21\cdot
X^{2}+p22\cdot Y^{2}+p23\cdot Z^{2}$ $\displaystyle{}+p24\cdot X\cdot
Y+p25\cdot Y\cdot Z+p26\cdot X\cdot Z$ $\displaystyle{}+p27\cdot X+p28\cdot
Y+p29\cdot Z+p30,$ (1)

where $X,Y,Z$ represents the BP$-$RP color, [Fe/H], and $\rm M_{G}$,
respectively. The $\rm M_{G}$ here are calculated by:

$M_{G}=G-10-5\times\log_{10}{\frac{1}{parallax}}-R_{G}\times E(B-V),$

where the parallax values are the Gaia parallaxes corrected by Lindegren et
al. (2021), $\rm R_{G}$ values are from the python package of Zhang & Yuan
(2023), and $\rm E(B-V)$ values are from the SFD98 redenning map. During the
fitting process, a 3$\sigma$-clipping procedure is performed to reject
outliers. The fitting coefficients $p_{i}$ are provided in Table 1.

Table 1: Fitting Coefficients for the Dwarfs and Giants Coeff. | Giants | Dwarfs
---|---|---
p0 |  $-$0.7607 |  $+$5.8352
p1 |  $-$0.0207 |  $-$0.0231
p2 |  $-$0.0012 |  $-$0.0210
p3 |  $+$0.1987 |  $+$2.6037
p4 |  $-$0.0413 |  $+$0.0153
p5 |  $-$1.8229 |  $-$0.8798
p6 |  $-$0.0921 |  $+$0.4813
p7 |  $-$0.0068 |  $-$0.0089
p8 |  $-$0.0032 |  $-$0.0085
p9 |  $-$0.2876 |  $-$2.0478
p10 |  $-$0.9692 |  $-$1.3104
p11 |  $-$0.0000 |  $+$0.0198
p12 |  $-$5.9457 |  $-$11.2965
p13 |  $-$0.1228 |  $-$0.1001
p14 |  $+$0.1019 |  $+$0.0225
p15 |  $-$2.3209 |  $-$12.0546
p16 |  $+$0.3297 |  $+$2.8586
p17 |  $+$5.8758 |  $+$9.1233
p18 |  $+$2.1666 |  $-$3.7948
p19 |  $+$0.0044 |  $+$0.1869
p20 |  $+$0.0142 |  $-$0.1947
p21 |  $+$24.6050 |  $-$2.3854
p22 |  $-$0.3129 |  $-$0.5011
p23 |  $-$1.2202 |  $+$1.0914
p24 |  $+$3.8330 |  $+$13.9786
p25 |  $+$0.1420 |  $-$1.0543
p26 |  $-$6.2672 |  $+$10.1043
p27 |  $-$20.7169 |  $-$8.6359
p28 |  $-$0.9627 |  $-$1.7705
p29 |  $+$2.2438 |  $-$5.4122
p30 |  $+$9.5277 |  $+$8.6614

The fitting results for the dwarf training sample are shown in Figure 5. The
distribution of the dwarf training sample in the NUV$-$BP vs. BP$-$RP plane is
plotted in panel (a), color-coded by [Fe/H]. From inspection, there are clear
dividing lines between sources with different metallicities. Panel (b) shows
the variations of the stellar locus at $\rm M_{G}=4.5$ for different
metallicities relative to the one at [Fe/H] = $-$0.5. A 1 dex change in
metallicity corresponds to an approximately 1 mag change in (NUV$-$BP) color
for solar-type stars, which is about 2–3 times larger than the change in the
$\rm v-BP$ color (Huang et al. 2023), about 5 times larger than the change in
the $u-g$ color (Yuan et al. 2015b), and about 200 times larger than the
change in the BP$-$G color (Xu et al. 2022a). This can be attributed to the
prevalence of strong metal absorption lines in the NUV-band, leading to
heightened sensitivity to metallicity, as expected. The fitting residuals, as
a function of BP$-$RP, [Fe/H], $\rm M_{G}$, E(B$-$V), and NUV are plotted in
panels (c), (d), (e), (f), and (g), respectively. No trends are found. Panel
(h) plots the histogram distribution of the fitting residuals. A Gaussian
profile is fitted to the distribution, resulting in a narrow peak centered at
0.00 mag with a $\sigma$ of 0.13 mag. The fitting results of the giant
training sample are similar, and shown in Figure 6.

Figure 5: Panel (a): Distributions of the dwarf training sample in the
NUV$-$BP vs. BP$-$RP plane (stellar loci), color-coded by [Fe/H] as shown in
the right color bar. Panel (b): When $\rm M_{G}=4.5$, the variations of
stellar loci for different metallicities (as shown in the label) relative to
the one at [Fe/H] = $-$0.5. Panels (c–g): Fitting residuals as a function of
BP$-$RP color, [Fe/H], $\rm M_{G}$, E(B$-$V), and NUV, respectively. Panel
(h): Histogram distribution of the fitting residuals, with the Gaussian
fitting profile over-plotted in black.  Figure 6: Same as Figure 5, but for
the giant training sample.

Based on the [Fe/H]- and $\rm M_{G}$-dependent stellar loci, we employ a
minimum $\chi^{2}$ technique to estimate the photometric metallicities from
NUV$-$BP, BP$-$RP, and absolute magnitude $\rm M_{G}$. The $\chi^{2}$ is
defined as:

$\displaystyle\chi^{2}([\rm Fe/H])=$ $\displaystyle\frac{[\rm C^{int}_{NUV-
BP}-C^{int}_{NUV-BP}(BP-RP,[Fe/H],M_{G})]^{2}}{\sigma_{\rm
NUV}^{2}+\sigma_{\rm BP}^{2}},$ (2)

where $\rm C_{NUV-BP}^{int}$ is the intrinsic NUV$-$BP color, $\rm
C^{int}_{NUV-BP}(BP-RP,[Fe/H])$ represents the predicted intrinsic NUV$-$BP
color based on the metallicity- and $\rm M_{G}$-dependent stellar loci, and
$\sigma_{\rm NUV}^{2}$ and $\sigma_{\rm BP}^{2}$ represent the magnitude
uncertainties in NUV and BP, respectively. Indeed, $\sigma_{\rm BP}^{2}$ could
be safely ignored compared to $\sigma_{\rm NUV}^{2}$. We utilize a brute-force
algorithm to determine the optimal [Fe/H] value for each source. For a given
dwarf, the [Fe/H] value is varied from $-$4.0 to +1.0 with steps of 0.01 dex,
resulting in 501 $\chi^{2}$ values. For a given giant, the [Fe/H] value is
varied from $-$5.0 to +1.0 with steps of 0.01 dex. The minimum $\chi^{2}$
among these values corresponds to the optimal [Fe/H] value.

##  4 Results and discussion

We employed the above model and technique to determine the photometric-
metallicity estimates, denoted as $[\rm Fe/H]_{GALEX}$, based on the NUV$-$BP,
BP$-$RP, and absolute magnitude $\rm M_{G}$ obtained from Gaia EDR3 and GALEX
GR6+7 AIS datasets. In this section, we test and verify the accuracy and
precision of our approach.

###  4.1 Results for the Training Sample

The photometric metallicities for the dwarf and giant training samples are
presented in Figures 7 and 8, respectively. The residuals $\Delta$[Fe/H],
defined as $\Delta[\rm Fe/H]=[\rm Fe/H]_{GALEX}-[\rm Fe/H]_{\rm HR}$, is used
to assess the precision of our results here, where $[\rm Fe/H]_{\rm HR}$ is
[Fe/H] from high-resolution spectroscopy (PASTEL and SAGA). Panel (a) shows a
histogram distribution of the $\Delta[\rm Fe/H]$. The standard deviation of
$\Delta$[Fe/H] for the dwarf training sample is 0.16 dex, with a mean value of
0.01 dex. For the giant training sample, the standard deviation is 0.21 dex,
with a mean value of 0.01 dex. Panel (b) shows the correlation between $[\rm
Fe/H]_{\rm GALEX}$ and $[\rm Fe/H]_{\rm HR}$. Strong correlations are found
for [Fe/H] down to [Fe/H] $\sim-3.0$ for the dwarfs and to [Fe/H] $\sim-4.0$
for the giants. Panels (c), (d), (e), (f), (g) show the distributions of
$\Delta$[Fe/H] as a function of BP$-$RP color, $[\rm Fe/H]_{\rm HR}$, $\rm
M_{G}$, E(B$-$V) and NUV, respectively. No discernible trends are found.

In panel (b) of Figure 7, at $\rm[Fe/H]<-2.0$, the dispersion for dwarfs
between $[\rm Fe/H]_{\rm GALEX}$ and $[\rm Fe/H]_{HR}$ increases,
corresponding to the sources in panel (h), whose color slightly deviates from
$\Delta[\rm Fe/H]=0.0$. This is due to the fact that lower metallicity
corresponds to a lower sensitivity of the stellar locus. Consequently,
estimating precise photometric metallicities for very metal-poor (VMP; [Fe/H]
$\leq-2.0$) and extremely metal-poor (EMP; [Fe/H] $\leq-3.0$) stars becomes
challenging. This challenge is also evident for giants, though with slightly
improved performance, as seen in panel (b) of Figure 8.

Panel (h) of Figure 7 and Figure 8 plots $\Delta$[Fe/H] in the color-magnitude
diagram. For dwarfs, most $\Delta[\rm Fe/H]$ values are very close to zero. A
small region with slight deviations from $\Delta[\rm Fe/H]=0$ is derived from
the larger dispersion in the most metal-poor stars. Overall, $\Delta[\rm
Fe/H]$ has no significant structure associated with $\rm M_{G}$, which is
attributed to our consideration of $\rm M_{G}$ of our model. There is also no
significant structure associated with $\rm M_{G}$ for giants. For some
individual outliers, it is not meaningful to consider them due to the scarcity
of these sources. We consider the outliers in our comparison with the test
sample below.

Figure 7: Photometric metallicities for the dwarf training sample. Panel (a):
Histogram distribution of the residuals $\Delta[\rm Fe/H]$, with the Gaussian
fitting profile over-plotted in black. Panel (b): Comparison of photometric-
metallicity estimates from GALEX and Gaia data with high-resolution
spectroscopic metallicities from SAGA or PASTEL. Panels (c–g): $\Delta[\rm
Fe/H]$ as a function of BP$-$RP color, $\rm[Fe/H]_{HR}$, $\rm M_{G}$,
E(B$-$V), and NUV, respectively. Panel (h): The color-magnitude diagram,
color-coded by $\Delta[\rm Fe/H]$. Figure 8: Same as Figure 7, but for the
giant training sample. Figure 9: Test results for 633,807 dwarfs. Panel (a):
Histogram distribution of the residuals $\Delta[\rm Fe/H]$, with the mean and
standard deviation values labeled. Panel (b): $[\rm Fe/H]_{GALEX}$ as a
function of $[\rm Fe/H]_{LAMOST}$, color-coded by number density. Panel (c),
(d), (e), (f), (g): $\Delta[\rm Fe/H]$ as a function of BP$-$RP color, $[\rm
Fe/H]_{LAMOST}$, $\rm M_{G}$, E(B$-$V), and NUV, respectively. The black-solid
lines indicate the median values and standard deviations. The black-dashed
line indicates the zero level. Panel (h): Distributions of the dwarfs in the
(NUV $-$ BP) vs. (BP $-$ RP) plane, color-coded by [Fe/H] values from LAMOST,
as indicated by the right color bar. The expression for the black-dashed line
is: $(\rm NUV-BP)<-1.56\times(BP-RP)^{2}+10.87\times(BP-RP)-4.78$ for dwarfs.
Figure 10: Same as Figure 9, but for 72,911 giants. The expression for the
black-dashed line is: $\rm(NUV-BP)<-7.20\times(BP-RP)^{2}+27.69\times(BP-
RP)-16.63$.  Figure 11: The spatial distribution (RA and Dec) of the residuals
$\Delta$[Fe/H]. The top row of panels are for the test-with-LAMOST sample of
633,807 dwarfs and 72,911 giants, respectively. The bottom row of panels are
the sub-sample of these stars with $|Z|>300$ pc (441,141 dwarfs and 64,696
giants, respectively.)

###  4.2 External Tests with LAMOST DR8

In order to verify the accuracy of our model, some external checks are
performed in this section by comparing with spectroscopic-metallicity
measurements from LAMOST DR8. First, we cross-match the LAMOST DR8 data with
GALEX GR6+7 AIS and Gaia EDR3. After application of the following cuts:

  1. 1.

Signal-to-noise ratio for the g-band of the LAMOST spectra $\rm SNR_{g}>20$

  2. 2.

Galactic latitude $|b|>10^{\circ}$ and $\rm E(B-V)\leq 0.5$

  3. 3.

Sources with $\rm 10<G\leq 16$ and within the limits of BP$-$RP color and $\rm
phot\\_bp\\_rp\\_excess\\_factor$ (the same as Xu et al. 2022a),

we retain a sample with 633,807 dwarfs and 72,911 giants. The comparison
results are displayed in Figures 9, 10, and 11. Note that there are small
metallicity offsets between the LAMOST and training sample: $-0.07$ dex for
dwarfs, and $-0.06$ dex for giants. The residual $\Delta[\rm Fe/H]$ is defined
as: $\Delta[\rm Fe/H]=[\rm Fe/H]_{GALEX}-[\rm Fe/H]_{LAMOST}$.

For the dwarfs in Figure 9, we fit the histogram distribution of the residuals
$\Delta[\rm Fe/H]$ with a Gaussian profile, and obtain a small standard
deviation of only 0.11 dex, centered at $-$0.06 dex, as shown in panel (a).
Panel (b) shows the relationship between $[\rm Fe/H]_{GALEX}$ and $[\rm
Fe/H]_{LAMOST}$. Most sources exhibit good agreement between
$\rm[Fe/H]_{GALEX}$ and $\rm[Fe/H]_{LAMOST}$, except for a tiny fraction of
sources located at the bottom right, which could be due to stellar activity in
the NUV-band. From inspection of panels (c–g), we conclude that the
$\Delta[\rm Fe/H]$ values exhibit no discernible trends with BP$-$RP color,
$[\rm Fe/H]_{LAMOST}$, $\rm M_{G}$, E(B$-$V), and NUV. Panel (h) shows the
distributions of the 633,807 dwarfs in the NUV$-$BP vs. BP$-$RP plane, color-
coded by $\rm[Fe/H]_{LAMOST}$. The black-dashed line is used to separate the
outliers. From inspection, there are some cooler metal-rich stars located
below the black-dashed line, we assume due to stellar activity. These sources
would be miss-classified as metal-poor stars in our model.

For the giants in Figure 10, the dispersion of the residuals $\Delta[\rm
Fe/H]$ is 0.17 dex, with a mean value of $-$0.06 dex, as shown in panel (a).
As indicated by the relationship between $[\rm Fe/H]_{GALEX}$ and $[\rm
Fe/H]_{LAMOST}$ in panel (b), the majority of sources also exhibit good
agreement between $\rm[Fe/H]_{GALEX}$ and $\rm[Fe/H]_{LAMOST}$. However, there
are more outliers located at the bottom right compared to the dwarfs. This
could be due to more stellar activity in cool giants, leading to a decrease in
the NUV magnitude and lower $[\rm Fe/H]_{GALEX}$ values. In panels (c–g),
there are some subtle trends in the residuals worth discussing. In panel (c),
the median value of $\Delta[\rm Fe/H]$ is slightly smaller at bluer and redder
BP$-$RP colors, which is mainly attributed to the scarcity of bluer and redder
$\rm BP-RP$ sources in our training sample. The result of panel (d) is similar
to that shown in panel (b). Panel (e) shows that the errors are larger for
intrinsically brighter stars. Panel (f) shows that both the median differences
and errors increase as $\rm E(B-V)$ increases. While the errors display very
weak dependence on NUV magnitude, as shown in panel (g), and also seen in the
dwarfs. Panel (h) shows the distributions of the 72,911 giants in the NUV$-$BP
vs. BP$-$RP plane, color-coded by $\rm[Fe/H]_{LAMOST}$. The black-dashed line
is used to separate the outliers.

Figure 11 shows the spatial distribution of the residuals $\Delta$[Fe/H]. Due
to the over-estimation of extinction values in the SFD98 reddening map close
to the Galactic plane, there is an over-estimation of [Fe/H] in our model for
the stars in this region, as shown in the top row of panels (especially in
dwarfs). We can eliminate this over-estimation from SFD98 by applying a
$|Z|>300$ pc cut, as shown in the bottom row of panels.

###  4.3 Additional Tests

Comparisons with other independent stellar-metallicity measurements (spanning
a wide range of [Fe/H] values) are presented in this section. Four catalogs
are used here: the value-added catalog of LAMOST DR8 (Wang et al. 2022), the
SEGUE DR12 (Alam et al. 2015) catalog, the catalog of 10,000 VMP stars from
LAMOST DR3 (Li et al. 2018), and the 400 VMP metal-poor stars studied with
LAMOST and Subaru (Li et al. 2022). To perform the comparisons, we cross-match
these catalogs with the Gaia EDR3 and GALEX GR6+7 AIS catalogs, respectively.
We retain the sources after applying the criteria similar to those used for
the LAMOST DR8 test sample. The results are presented in Figure 12, with the
top panels for dwarfs and the bottom panels for giants.

In the left column of panels, we show the comparison with the LAMOST DR8
value-added catalog. $[\rm Fe/H]_{PASTEL\&VMP}$ represents $[\rm
Fe/H]_{PASTEL}$ (for $[\rm Fe/H]>-1.5$) and $[\rm Fe/H]_{VMP}$ (for $[\rm
Fe/H]<-1.5$) from Wang et al. (2022). The residuals between the $[\rm
Fe/H]_{GALEX}$ and $[\rm Fe/H]_{PASTEL\&VMP}$ were fitted with a Gaussian
profile. For dwarfs, we obtain a dispersion of 0.15 dex centered at $-$0.08
dex. For giants, a dispersion of 0.21 dex centered at $-$0.06 dex is obtained.
The middle column of panels displays the comparison with SEGUE DR12. For
dwarfs, we obtain a dispersion of 0.16 dex centered at $-$0.11 dex. For
giants, a dispersion of 0.25 dex centered at $-$0.07 dex is obtained. The
right column of panels displays the comparison with the catalogs of Li et al.
(2018, 2022). For dwarfs, we obtain a dispersion of 0.25 dex centered at +0.29
dex. For giants, the dispersion is 0.26 dex centered at +0.19 dex. From
inspection, our [Fe/H] measurements exhibit good consistency with other
catalogs for most sources, both for metal-rich stars and VMP stars.

There are a few sources with $\rm[Fe/H]_{GALEX}$ values larger than
$\rm[Fe/H]_{obs}$ located in the upper part of the right panels of Figure 12.
Their locations in the color-color diagram are close to the metal-rich stellar
loci, probably due to their large photometric errors. In addition, there is an
under-estimation of [Fe/H] in our model for a portion of sources with $[\rm
Fe/H]_{GALEX}$ values lower than $-$3.0, as can be mainly seen in the bottom
middle panel of Figure 12. This is because the metallicity dependence
decreases monotonically as NUV$-$BP color decreases at the same BP$-$RP color.
Thus, between the over-estimates or under-estimates of NUV$-$BP colors caused
by photometric errors, the under-estimates lead to a larger under-estimation
in the calculation of photometric metallicities. Overall, from these tests,
[Fe/H] estimates from our model are reliable even for metallicity down to
[Fe/H] $\sim-$3.5.

Figure 12: From left to right, the columns of panels represent comparisons
with the LAMOST DR8 value-added catalog of Wang et al. (2022), the SEGUE DR12
(Alam et al. 2015) catalog, and the VMP catalog of Li et al. (2018) & Li et
al. (2022), respectively. The left column of panels is color-coded by the
source number density. In the right column of panels, the red and gray dots
are from Li et al. (2022) and Li et al. (2018), respectively. The dwarfs are
plotted in the top fow of panels and the giants in the bottom row of panels.
The mean and standard deviation values of the residuals $\Delta[\rm Fe/H]$ are
labeled in the lower-right of each panel.

###  4.4 The Influence of Carbon Enhancement

Photometric-metallicitymeasurements are often over-estimated for VMP/EMP stars
due to contamination of the blue narrow/medium-band filters by molecular
carbon bands such as CN (e.g., Hong et al. 2023, Huang et al. 2023). In this
subsection, we check whether the strong molecular carbon bands strongly
influence the photometric-metallicity estimates found by use of the NUV-band.
We cross-match the medium- and high-resolution spectroscopic catalog of
VMP/EMP stars with available [Fe/H] and [C/Fe] measurements compiled by Hong
et al. (2023) with our Gaia EDR3 and GALEX GR6+7 AIS catalog. After applying
metallicity cuts of $\rm-4<[Fe/H]_{spec}\leq-2,[Fe/H]_{GALEX}>-4$, and $\rm
flag=0$, we obtain a sample of 231 stars in common.

Figure 13 shows comparisons of the photometric-metallicity estimates we obtain
with the spectroscopic determinations, color-coded by [C/Fe]. The
$\rm[Fe/H]_{spec}$ and [C/Fe] values are originally from Yoon et al. (2016),
Li et al. (2022), Placco et al. (2022), and Zepeda et al. (2023). Figure 14 is
a color-magnitude diagram for the VMP/EMP samples of stars with [C/Fe] $\leq$
+0.7 and [C/Fe] $>$ +0.7, indicated by red and blue symbols, respectively.

From inspection of Figure 13, all three samples exhibit a good correlation
between $\rm[Fe/H]_{GALEX}$ and $\rm[Fe/H]_{spec}$, with small offsets. Note
that the dispersion value is larger for the sub-sample of stars with [C/Fe]
$>$ +0.7 than for the sub-sample with [C/Fe] $<$ +0.7. This is likely due to
1) the fact that the sub-sample of stars with [C/Fe] $>$ +0.7 are bluer (and
less sensitive to [Fe/H]) and fainter (larger photometric errors), and thus
have larger uncertainties in the $\rm[Fe/H]_{GALEX}$ estimates and, 2) the
effects of carbon enhancement on our estimates, primarily for the cooler
giants in our sample. However, we point out that, for all three samples, there
are stars with photometric-metallicity estimates that straddle the one-to-one
line, which is superior to the behavior seen by Hong et al. (2023) when
comparing to photometric-metallicity estimates obtained using the u- and
v-band filters from the SAGES and SMSS samples (see their Figure A1, where the
carbon-enhanced stars often result in higher-metallicity estimates than their
spectroscopic values). A similar problem is encountered in the analysis of
Martin et al. (2023), which used the Gaia XP spectra in combination with
synthetic photometry of the Pristine survey CaHK magnitudes (see Martin et al.
2023).

Thus, we conclude that the addition of the NUV-band can provide for improved
estimates of photometric metallicity for stars with strong carbon
enhancements. Clearly, having an independent estimate of [C/Fe], as is
possible with the filter sets used by J-PLUS and S-PLUS, would provide an even
better alternative.

Figure 13: Comparisons of $[\rm Fe/H]_{GALEX}$ with spectroscopic measurements
for VMP/EMP stars (taken from the compilation of Hong et al. 2023), color-
coded by [C/Fe]. From left to right the panels show the full sample, the sub-
sample of stars with [C/Fe] $>$ +0.7, and the sub-sample of stars with [C/Fe]
$\leq$ +0.7, respectively. The mean and standard deviation values of residuals
$\Delta[\rm Fe/H]$ are labeled in the upper-left of each panel. Note that, in
all three panels, there are stars with $[\rm Fe/H]_{GALEX}$ that straddle the
black-solid one-to-one lines; they are not uniformly biased high due to the
effect of carbon, as has been seen to occur for several previous photometric-
metallicity techniques (see text). Figure 14: Color-magnitude (observed color
and apparent magnitude) diagram for sub-samples of the VMP/EMP stars shown in
Figure 13, represented by the red ([C/Fe] $\leq$ +0.7) and blue ([C/Fe] $>$
+0.7) symbols, respectively. The squares and circles represent dwarfs and
giants, respectively.

##  5 The Final Sample

In this section, we cross-match the entire Gaia EDR3 data and GALEX GR6+7 AIS
data to create our (nearly) all-sky sample. After imposing the following
selection criteria:

  1. 1.

GALEX: error${}_{\rm NUV}<$ 0.15 and NUV $>$ 15 to avoid saturation

  2. 2.

Gaia (same as Xu et al. 2022a except that we extend the bright G magnitude
limit to 6): sources of $|b|>10^{\circ}$, $\rm E(B-V)\leq 0.5$, $\rm 6<G<16$,
and limit on phot_bp_rp_excess_factor and BP$-$RP color,

4,468,105 dwarfs and 503,700 giants remain in our final sample (4,971,805
stars in all). The color–magnitude diagram for this sample is shown in Figure
15. The G-magnitude distributions of the final sample (with flag=0) are shown
in Figure 16.

We apply our model to this final sample. The [Fe/H] (with flag=0)
distributions are shown in Figure 17. The increase in the numbers of stars at
the minimum [Fe/H] values is due to 1) the metallicities in our model can only
be reliably determined in a range of $-4.0<$ [Fe/H] $\leq+1.0$ for dwarfs and
$-4.5<$ [Fe/H] $\leq+1.0$ for giants, respectively, which resulting in an
accumulation at the boundary of the range and, 2) there still remain stars
with stellar activity, although we have applied a flag in an attempt to filter
them out. For dwarfs, there are 14,528 VMP and 2,972 EMP and stars,
respectively. For giants, there are 18,747 VMP and 3,656 EMP stars,
respectively.

The spatial distributions in the Z-R plane are shown in Figure 18, where Z is
the distance to the Galactic plane, and R is the Galactocentric distance. The
spatial distributions, color-coded by [Fe/H], are shown in Figure 19. The
evident vertical gradients in metallicity within the disk-system stars are
observable in both panels.

The columns contained in the final sample catalog are listed in Table 2.
Similar to Huang et al. (2023), the radial-velocity values in the catalog are
collected from five spectroscopic surveys: GALAH DR3+ (Buder et al. 2021),
SDSS/ APOGEE DR17 (Abdurro’uf et al. 2022), Gaia DR3 (Katz et al. 2023),
LAMOST DR9222http://www.lamost.org/dr9/v1.0/ (medium resolution catalog and
low resolution catalog)  and SDSS/SEGUE DR16 (Ahumada et al. 2020). In total,
over 4,702,675 stars in our final sample have radial-velocity measurements.
When a star has two more radial-velocity measurements, we adopt the results
from the highest spectral resolution survey. Note that we calibrated all of
the radial-velocity offsets based on the APOGEE radial-velocity values. The
catalog is publicly available at xxxx.

Figure 15: Color-magnitude diagram of the final sample, color-coded by source number density. Figure 16: The G-magnitude distribution of the final sample (with flag=0). The left and right panels are for the dwarfs and giants, respectively. Figure 17: The [Fe/H] distribution of the final sample (with flag=0). The left and right panels are for the dwarfs and giants, respectively. For dwarfs, there are 14,522 VMP and 2,962 EMP stars, respectively. For giants, there are 18,245 VMP and 3,582 EMP stars, respectively. Note that the increase in the numbers of stars at the lowest metallicities are due to limitations of our model and the likely presence of stellar activity (see text). Figure 18: The spatial distributions in the Z–R plane of the final sample, color-coded by number densities. The left and right panels are for the dwarfs and giants, respectively. The Sun is located at (R, Z) = (8.178, 0.0) kpc.  Figure 19: The spatial distributions in the Z–R plane of the final sample, color-coded by $[\rm Fe/H]_{GALEX}$. The left and right panels are for the dwarfs and giants, respectively. The Sun is located at (R, Z) = (8.178, 0.0) kpc.  Table 2: Description of the Final Sample Field | Description | Unit
---|---|---
source_id | Unique source identifier for Gaia EDR3 (unique with a particular Data Release) | –
ra | Right ascension from Gaia | deg
dec | Declination from Gaia | deg
parallax | Parallax | mas
parallax_error | Standard error of parallax | mas
parallax_corrected |  Parallax corrected by Lindegren et al. (2021) | mas
pmra | Proper motion in right ascension direction | mas/year
pmra_error | Standard error of proper motion in right ascension direction | mas/year
pmdec | Proper motion in declination direction | mas/year
pmdec_error | Standard error of proper motion in declination direction | mas/year
ruwe | Renormalised unit weight error | –
phot_bp_rp_excess_factor | BP/RP excess factor | –
phot_bp_mean_mag | Integrated BP-band mean magnitude | –
phot_rp_mean_mag | Integrated RP-band mean magnitude | –
phot_g_mean_mag | G-band mean magnitude | –
l | Galactic longitude | deg
b | Galactic latitude | deg
feh_gaia |  Photometric metallicity from Xu et al. (2022a) | –
feh_Gaia_error |  Formal error of feh_gaia from Xu et al. (2022a) | dex
ebv |  Value of $\rm E(B-V)_{SFD}$ | –
type |  Flag to classify stars (Xu et al. 2022a); 0 for dwarfs and 1 for giants | –
NUVmag | NUV calibrated magnitude | –
e_NUVmag | NUV calibrated magnitude error | mag
BP_RP0 |  Intrinsic BP$-$RP color after color correction | –
NUV_BP0 |  Intrinsic NUV$-$BP color after color correction | –
feh_GALEX_old |  Photometric metallicity derived from previous model without consideration of $\rm M_{G}$ | –
feh_GALEX |  Photometric metallicity derived from New Model with consideration of $\rm M_{G}$ | –
M_G | Absolute Magnitude of G-band, calculated by: |
| $\rm M_{G}=G-10-5\times\log_{10}{\frac{1}{parallax\\_corrected}}-R_{G}\times E(B-V)$ | –
flag1 | The quality flag | –
rpgeo |  Median of the photogeometric distance posterior (r_med_photogeo) from Bailer-Jones et al. (2021) | pc
b_rpgeo |  16th percentile of the photogeometric distance posterior (r_lo_photogeo) from Bailer-Jones et al. (2021) | pc
B_rpgeo |  84th percentile of the photogeometric distance posterior (r_lo_photogeo) from Bailer-Jones et al. (2021) | pc
rv | Radial velocity | km/s
e_rv | Error of radial velocity | km/s
flag_rv | Flag to indicate the source of radial velocity, which takes the values “GALAH,” “APOGEE,” “Gaia,” |
| “LAMOST_MRS,” “LAMOST_LRS,” “SEGUE” | –

##  6 Summary

In this work, we combine the SAGA and PASTEL catalogs with Gaia EDR3 and GALEX
GR6+7 AIS data as our training sample to construct a relational model from
stellar loci that incorporate $\rm M_{G}$ to estimate photometric
metallicitities for dwarfs and giants. We construct an all-sky sample from
Gaia EDR3 and GALEX GR6+7 AIS data as our final sample (4,468,105 dwarfs and
503,700 giants), employing a precise reddening correction using empirical
temperature- and extinction-dependent extinction coefficients.

We first obtain the [Fe/H]- and $\rm M_{G}$-dependent stellar loci for the
NUV$-$BP and BP$-$RP colors. For a given $\rm BP-RP$ color, a 1 dex change in
[Fe/H] causes an approximate 1 mag change in $\rm NUV-BP$ color for solar-type
stars. The [Fe/H]- and $\rm M_{G}$-dependent stellar loci are then used to
estimate stellar photometric metallicities from $\rm NUV-BP$, BP$-$RP, and
$\rm M_{G}$. As a result of the very strong metallicity dependence in the NUV-
band and the precise reddening corrections, we have obtained a typical
precision of 0.11 dex for dwarfs and 0.17 dex for giants, with an effective
metallicity range from $-3.0<$ [Fe/H] $\leq+0.5$ for dwarfs and $-4.0<$ [Fe/H]
$\leq+0.5$ for giants. We also demonstrate that the NUV-band based
photometric-metallicity estimate is not as strongly affected by carbon
enhancement as previous photometric techniques. Moreover, our tests confirm
that incorporating absolute magnitude ($\rm M_{G}$) in the stellar loci serves
to further improve the accuracy of the photometric-metallicity estimates.

Our work demonstrates the feasibility and great potential of photometric-
metallicity estimates using the NUV-band photometry, due to its very strong
sensitivity to [Fe/H]. A number of lessons have been learned in this
exploration, including:

  1. 1.

The NUV-band photometry also exhibits a strong dependence on surface gravity,
therefore, the absolute magnitude ($\rm M_{G}$ in this work) has to be taken
into account in the modeling

  2. 2.

The reddening correction in the NUV-band is essential and challenging. In
addition to the effect of surface gravity, even the effect of metallicity on
the extinction coefficient needs to be considered

  3. 3.

Stellar activity in cool dwarf and giant stars could cause a significant
under-estimation of metallicity, thus should be considered when hunting for
VMP/EMP stars

  4. 4.

Future improvement in the calibration precision of the NUV-band photometry is
very important

  5. 5.

With future improvement in the calibration precision in the NUV-band
photometry, it may be possible to identify likely carbon-enhanced VMP/EMP
stars by a comparison of photometric-metallicity estimates based on the NUV-
band with other bands, such as the u- and v-bands.

Our final sample, encompassing a wide range of [Fe/H] values, is expected to
be valuable for numerous research studies. For instance, it can provide
candidate metal-poor candidate stars for subsequent high-resolution
spectroscopic follow-up, and also for chemo-dynamical studies of MW stellar
populations. This work lays the foundation for using NUV-band data from space
telescopes such as the upcoming Chinese Space Station Telescope (CSST; Zhan
2011).

This work is supported by the National Natural Science Foundation of China
through the project NSFC 12222301, 12173007 and 11603002, the National Key
Basic R&D Program of China via 2019YFA0405503 and Beijing Normal University
grant No. 310232102. We acknowledge the science research grants from the China
Manned Space Project with NO. CMS-CSST-2021-A08 and CMS-CSST-2021-A09. T.C.B.
acknowledges partial support from grant PHY 14-30152, Physics Frontier
Center/JINA Center for the Evolution of the Elements (JINA-CEE), and from
OISE-1927130: The International Research Network for Nuclear Astrophysics
(IReNA), awarded by the US National Science Foundation. His participation in
this work was initiated by conversations that took place during a visit to
China in 2019, supported by a PIFI Distinguished Scientist award from the
Chinese Academy of Science. This work has made use of data from the European
Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed
by the Gaia Data Processing and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular, the institutions
participating in the Gaia Multilateral Agreement. Guoshoujing Telescope (the
Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a
National Major Scientific Project built by the Chinese Academy of Sciences.
Funding for the project has been provided by the National Development and
Reform Commission. LAMOST is operated and managed by the National Astronomical
Observatories, Chinese Academy of Sciences. We acknowledge the invaluable
contribution of GALEX (NASA’s Galaxy Evolution Explorer) in providing the
dataset used in this research.

## References

  * Abdurro’uf et al. (2022) Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35, doi: 10.3847/1538-4365/ac4414
  * Ahumada et al. (2020) Ahumada, R., Allende Prieto, C., Almeida, A., et al. 2020, ApJS, 249, 3, doi: 10.3847/1538-4365/ab929e
  * Alam et al. (2015) Alam, S., Albareti, F. D., Allende Prieto, C., et al. 2015, ApJS, 219, 12, doi: 10.1088/0067-0049/219/1/12
  * An & Beers (2020) An, D., & Beers, T. C. 2020, ApJ, 897, 39, doi: 10.3847/1538-4357/ab8d39
  * Bailer-Jones et al. (2021) Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Demleitner, M., & Andrae, R. 2021, AJ, 161, 147, doi: 10.3847/1538-3881/abd806
  * Beers & Christlieb (2005) Beers, T. C., & Christlieb, N. 2005, ARA&A, 43, 531, doi: 10.1146/annurev.astro.42.053102.134057
  * Bianchi et al. (2014) Bianchi, L., Conti, A., & Shiao, B. 2014, VizieR Online Data Catalog, II/335
  * Brown et al. (2021) Brown, A. G. A., Vallenari, A., Prusti, T., et al. 2021, Astronomy & Astrophysics, 650, C3, doi: 10.1051/0004-6361/202039657e
  * Buder et al. (2018) Buder, S., Asplund, M., Duong, L., et al. 2018, Monthly Notices of the Royal Astronomical Society, 478, 4513, doi: 10.1093/mnras/sty1281
  * Buder et al. (2021) Buder, S., Sharma, S., Kos, J., et al. 2021, Monthly Notices of the Royal Astronomical Society, 506, 150, doi: 10.1093/mnras/stab1242
  * Casagrande et al. (2019) Casagrande, L., Wolf, C., Mackey, A. D., et al. 2019, MNRAS, 482, 2770, doi: 10.1093/mnras/sty2878
  * Deng et al. (2012) Deng, L.-C., Newberg, H. J., Liu, C., et al. 2012, Research in Astronomy and Astrophysics, 12, 735, doi: 10.1088/1674-4527/12/7/003
  * Fan et al. (2023) Fan, Z., Zhao, G., Wang, W., et al. 2023, ApJS, 268, 9, doi: 10.3847/1538-4365/ace04a
  * Hong et al. (2023) Hong, J., Beers, T. C., Lee, Y. S., et al. 2023, arXiv e-prints, arXiv:2311.02297.  https://arxiv.org/abs/2311.02297
  * Huang et al. (2019) Huang, Y., Chen, B. Q., Yuan, H. B., et al. 2019, ApJS, 243, 7, doi: 10.3847/1538-4365/ab1f72
  * Huang et al. (2021) Huang, Y., Beers, T. C., Wolf, C., et al. 2021, arXiv e-prints, arXiv:2104.14154.  https://arxiv.org/abs/2104.14154
  * Huang et al. (2022) —. 2022, ApJ, 925, 164, doi: 10.3847/1538-4357/ac21cb
  * Huang et al. (2023) Huang, Y., Beers, T. C., Yuan, H.-B., et al. 2023, arXiv e-prints, arXiv:2307.04469, doi: 10.48550/arXiv.2307.04469
  * Ivezić et al. (2008) Ivezić, Ž., Sesar, B., Jurić, M., et al. 2008, ApJ, 684, 287, doi: 10.1086/589678
  * Katz et al. (2023) Katz, D., Sartoretti, P., Guerrier, A., et al. 2023, A&A, 674, A5, doi: 10.1051/0004-6361/202244220
  * Li et al. (2018) Li, H., Tan, K., & Zhao, G. 2018, The Astrophysical Journal Supplement Series, 238, 16, doi: 10.3847/1538-4365/aada4a
  * Li et al. (2022) Li, H., Aoki, W., Matsuno, T., et al. 2022, The Astrophysical Journal, 931, 147, doi: 10.3847/1538-4357/ac6514
  * Lindegren et al. (2021) Lindegren, L., Bastian, U., Biermann, M., et al. 2021, A&A, 649, A4, doi: 10.1051/0004-6361/202039653
  * Liu et al. (2014) Liu, X. W., Yuan, H. B., Huo, Z. Y., et al. 2014, in Setting the scene for Gaia and LAMOST, ed. S. Feltzing, G. Zhao, N. A. Walton, & P. Whitelock, Vol. 298, 310–321, doi: 10.1017/S1743921313006510
  * Luo et al. (2015) Luo, A. L., Zhao, Y.-H., Zhao, G., et al. 2015, Research in Astronomy and Astrophysics, 15, 1095, doi: 10.1088/1674-4527/15/8/002
  * Majewski et al. (2017) Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784d
  * Martin et al. (2005) Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJ, 619, L1, doi: 10.1086/426387
  * Martin et al. (2023) Martin, N. F., Starkenburg, E., Yuan, Z., et al. 2023, arXiv e-prints, arXiv:2308.01344, doi: 10.48550/arXiv.2308.01344
  * Matteucci (2021) Matteucci, F. 2021, A&A Rev., 29, 5, doi: 10.1007/s00159-021-00133-8
  * Morrissey et al. (2007) Morrissey, P., Conrow, T., Barlow, T. A., et al. 2007, The Astrophysical Journal Supplement Series, 173, 682, doi: 10.1086/520512
  * Morrissey et al. (2007) Morrissey, P., Conrow, T., Barlow, T. A., et al. 2007, ApJS, 173, 682, doi: 10.1086/520512
  * Onken et al. (2019) Onken, C. A., Wolf, C., Bessell, M. S., et al. 2019, PASA, 36, e033, doi: 10.1017/pasa.2019.27
  * Placco et al. (2022) Placco, V. M., Almeida-Fernandes, F., Arentsen, A., et al. 2022, The Astrophysical Journal Supplement Series, 262, 8, doi: 10.3847/1538-4365/ac7ab0
  * Rockosi et al. (2022) Rockosi, C. M., Lee, Y. S., Morrison, H. L., et al. 2022, ApJS, 259, 60, doi: 10.3847/1538-4365/ac5323
  * Schlegel et al. (1998) Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525, doi: 10.1086/305772
  * Schwarzschild et al. (1955) Schwarzschild, M., Searle, L., & Howard, R. 1955, ApJ, 122, 353, doi: 10.1086/146094
  * Soubiran et al. (2016) Soubiran, C., Le Campion, J.-F., Brouillet, N., & Chemin, L. 2016, A&A, 591, A118, doi: 10.1051/0004-6361/201628497
  * Soubiran et al. (2010) Soubiran, C., Le Campion, J. F., Cayrel de Strobel, G., & Caillo, A. 2010, A&A, 515, A111, doi: 10.1051/0004-6361/201014247
  * Starkenburg et al. (2017) Starkenburg, E., Martin, N., Youakim, K., et al. 2017, MNRAS, 471, 2587, doi: 10.1093/mnras/stx1068
  * Steinmetz et al. (2006) Steinmetz, M., Zwitter, T., Siebert, A., et al. 2006, AJ, 132, 1645, doi: 10.1086/506564
  * Suda et al. (2011) Suda, T., Yamada, S., Katsuta, Y., et al. 2011, MNRAS, 412, 843, doi: 10.1111/j.1365-2966.2011.17943.x
  * Suda et al. (2008) Suda, T., Katsuta, Y., Yamada, S., et al. 2008, PASJ, 60, 1159, doi: 10.1093/pasj/60.5.1159
  * Suda et al. (2017) Suda, T., Hidaka, J., Aoki, W., et al. 2017, PASJ, 69, 76, doi: 10.1093/pasj/psx059
  * Wang et al. (2022) Wang, C., Huang, Y., Yuan, H., et al. 2022, The Astrophysical Journal Supplement Series, 259, 51, doi: 10.3847/1538-4365/ac4df7
  * Whitten et al. (2021) Whitten, D. D., Placco, V. M., Beers, T. C., et al. 2021, ApJ, 912, 147, doi: 10.3847/1538-4357/abee7e
  * Xu et al. (2022a) Xu, S., Yuan, H., Niu, Z., et al. 2022a, ApJS, 258, 44, doi: 10.3847/1538-4365/ac3df6
  * Xu et al. (2022b) Xu, S., Yuan, H., Zhang, R., et al. 2022b, ApJS, 263, 29, doi: 10.3847/1538-4365/ac9908
  * Yamada et al. (2013) Yamada, S., Suda, T., Komiya, Y., Aoki, W., & Fujimoto, M. Y. 2013, MNRAS, 436, 1362, doi: 10.1093/mnras/stt1652
  * Yang et al. (2022) Yang, L., Yuan, H., Xiang, M., et al. 2022, A&A, 659, A181, doi: 10.1051/0004-6361/202142724
  * Yanny et al. (2009) Yanny, B., Rockosi, C., Newberg, H. J., et al. 2009, AJ, 137, 4377, doi: 10.1088/0004-6256/137/5/4377
  * Yoon et al. (2016) Yoon, J., Beers, T. C., Placco, V. M., et al. 2016, The Astrophysical Journal, 833, 20, doi: 10.3847/0004-637X/833/1/20
  * York et al. (2000) York, D. G., Adelman, J., John E. Anderson, J., et al. 2000, The Astronomical Journal, 120, 1579, doi: 10.1086/301513
  * Yuan et al. (2015a) Yuan, H., Liu, X., Xiang, M., Huang, Y., & Chen, B. 2015a, ApJ, 799, 134, doi: 10.1088/0004-637X/799/2/134
  * Yuan et al. (2015b) —. 2015b, ApJ, 803, 13, doi: 10.1088/0004-637X/803/1/13
  * Yuan et al. (2015c) Yuan, H., Liu, X., Xiang, M., et al. 2015c, ApJ, 799, 133, doi: 10.1088/0004-637X/799/2/133
  * Zepeda et al. (2023) Zepeda, J., Beers, T. C., Placco, V. M., et al. 2023, The Astrophysical Journal, 947, 23, doi: 10.3847/1538-4357/acbbcc
  * Zhan (2011) Zhan, H. 2011, Scientia Sinica Physica, Mechanica & Astronomica, 41, 1441, doi: 10.1360/132011-961
  * Zhang & Yuan (2023) Zhang, R., & Yuan, H. 2023, ApJS, 264, 14, doi: 10.3847/1538-4365/ac9dfa
  * Zhang et al. (2021) Zhang, R.-Y., Yuan, H.-B., Liu, X.-W., et al. 2021, Research in Astronomy and Astrophysics, 21, 319, doi: 10.1088/1674-4527/21/12/319

##  Appendix A Motivation and Impact of Absolute Magnitude

In our initial work, we used the relationship between stellar loci (NUV$-$BP
and BP$-$RP colors) and metallicity to establish a model for estimation of
photometric metallicities, as shown in Figure A1. The residuals $\Delta[\rm
Fe/H]_{old}$ in Figure A2 is calculated from this initial model as
$\rm[Fe/H]_{GALEX_{old}}-[Fe/H]_{HR}$. This relationship is represented by the
colored lines in this figure. Apparently, $\Delta[\rm Fe/H]_{old}$ exhibits
some correlation with $\rm M_{G}$, which means that $\rm M_{G}$ has an effect
on our photometric metallicities, and a incorporation of $\rm M_{G}$ is
essential. Consequently, we refine our model by factoring in the impact of
$\rm M_{G}$ and indeed obtain better results than before.

The $\Delta[\rm Fe/H]_{old}$ in the middle column of panels of Figure A3 is
also calculated from our initial model as
$\rm[Fe/H]_{GALEX_{old}}-[Fe/H]_{LAMOST}$. Figure A3, which shows the
comparison with LAMOST DR8, is an effective illustration of the difference
(depicted by $\Delta[\rm Fe/H]$) between the photometric metallicities and
LAMOST metallicities. In the middle column of panels in Figure A3, we observe
a distinct pattern in the distribution of $\Delta[\rm Fe/H]_{old}$ with
respect to $\rm M_{G}$. As $\rm M_{G}$ increases, $\Delta[\rm Fe/H]_{old}$
shows a structured variation, especially among metal-poor giants.

Based on these observations, we decided to incorporate absolute magnitude
($\rm M_{G}$) into our model. The residuals $\Delta[\rm Fe/H]_{new}$ in the
right column of panels of Figure A3 is calculated from our new model as
$\rm[Fe/H]_{GALEX_{new}}-[Fe/H]_{LAMOST}$. This diagram demonstrates the
changes in $\Delta[\rm Fe/H]_{new}$ on the color-magnitude diagram, with black
contours representing star density. We could consider the $\Delta[\rm Fe/H]$
values of the majority of stars as being close to 0, indicating that our model
is well-suited for the majority of giants. Furthermore, it is evident that the
previously observed variation pattern is much weaker after considering $\rm
M_{G}$ in our new model. Additionally, the typical deviations from $\Delta[\rm
Fe/H]=0$ have been reduced, as indicated by the legends in each panel.
However, there are a minority of $\Delta[\rm Fe/H]$ values that display
deviations from zero among the bluer $\rm BP-RP$ colors, shown in the shaded
region in the bottom-middle panel. These stars could be interpreted as blue
horizontal-branch stars and stars situated near the boundary between dwarfs
and giants. Their properties slightly differ from those of most FGK giants in
our sample. In any case, as illustrated here, this new version performs better
compared with the old test result, successfully resolving the previously
discernible trends related to $\rm M_{G}$.

Figure A1: Distribution of the training sample in the ($\rm NUV-BP$) vs. ($\rm
BP-RP$) plane, color-coded by [Fe/H], with dwarfs in the left panel and giants
in the right panel. The colored lines represent different [Fe/H] values,
ranging from $+$0.5 to $-$3.5 in steps of 0.5 dex.

Figure A2: Distribution of the $\Delta[\rm Fe/H]$ (calculated from the model
without $\rm M_{G}$) as a function of $\rm M_{G}$ for dwarf (left) and giant
(right) stars, respectively. The red-solid line indicates the median values.
Figure A3: Color-magnitude diagram of the LAMOST DR8 test sample. Dwarfs are
shown in the upper row of panels and giants are shown in the lower row of
panels. The plots are color-coded by $[\rm Fe/H]_{LAMOST}$ (left column of
panels), $\Delta[\rm Fe/H]$ (old model without $\rm M_{G}$) (middle column of
panels), and $\Delta[\rm Fe/H]$ (new model with $\rm M_{G}$ considered) (right
column of panels). In the lower middle panel, the shaded region indicates
possible blue horizontal-branch stars or stars situated near the boundary
between dwarfs and giants.