11institutetext: Institut für Physik und Astronomie, Universität Potsdam, Haus
28, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany 22institutetext:
Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
33institutetext: Dr. Remeis-Sternwarte & ECAP, Astronomical Institute, FAU
Erlangen-Nürnberg, Sternwartstr. 7, 96049 Bamberg, Germany 44institutetext:
Astronomical Institute AS CR, Fričova 298, 251 65 Ondřejov, Czech Republic

# Probing the inner Galactic Halo with blue horizontal branch stars:

Gaia DR3 based catalogue with atmospheric and stellar parameters ††thanks: The
catalogue is only available in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-
bin/qcat?J/A+A/

R. Culpan 11 M. Dorsch 1133 S. Geier 11 I. Pelisoli 22 U. Heber 33 B. Kubátová
44 M. Cabezas 44<EMAIL_ADDRESS>
(Received 19/10/2023 Accepted xx/xx/2024)

###### Abstract

Context. Stars that are found on the blue horizontal-branch (BHB) have evolved
from low-mass stars that have completed their core hydrogen burning main
sequence stage and have undergone the helium flash at the end of their red-
giant phase. They are, hence, very old objects that can be used as markers in
studying galactic structure and formation history. The fact that their
luminosity is virtually constant at all effective temperatures also makes them
good standard candles.

Aims. We provide a catalogue of BHB stars with stellar parameters that have
been calculated from spectral energy distributions (SED), as constructed from
multiple large-scale photometric surveys. In addition, we update our previous,
Gaia Early Data Release 3 catalogue of BHB stars with parallax errors less
than 20% by using the SED results to define the selection criteria. The
purpose of these catalogues is to create a set of BHB star candidates with
reliable stellar parameters as well as providing a more complete full-sky
catalogue with candidate objects found along the whole BHB: from where RR-
Lyrae are found on the instability strip to the extreme horizontal branch.

Methods. We selected a large dataset of Gaia Data Release 3 (DR3) objects
based only on their position in the colour magnitude diagram, tangential
velocity and parallax errors. Spectral energy distributions were then used to
evaluate contamination levels in the dataset and derive optimised data quality
acceptance constraints. This allowed us to extend the Gaia DR3 colour and
absolute magnitude criteria further towards the extreme horizontal-branch. The
level of contamination found using SED analysis was confirmed by acquiring
spectra using the Ondřejov Echelle spectrograph attached to the Perek 2m
telescope at the Astronomical Institute of the Czech Academy of Sciences.

Results. We present a catalogue of 9,172 Galactic Halo BHB candidate stars
with atmospheric and stellar parameters calculated from synthetic SEDs. We
also present an extended Gaia DR3 based catalogue of 22,335 BHB candidate
stars with a wider range of effective temperatures and Gaia DR3 parallax
errors of less than 20%. This represents an increase of 33% compared to the
our 2021 catalogue, with a contamination level of 10%.

###### Key Words.:

stars: horizontal branch – catalogs – stars:Hertzsprung-Russel and C-M
diagrams

††offprints: R. Culpan,

##  1 Introduction

The term horizontal branch (HB) was coined to describe a horizontal structure
observed in the colour magnitude diagram (CMD) in globular clusters. The
horizontal branch extends from the red clump at the red end through the
instability strip where RR-Lyrae are found to the extreme horizontal-branch
(EHB) at the blue end (Catelan, 2009). HB stars are what remains of low-
metallicity ${\sim}0.8M_{\odot}$ to ${\sim}2.3\,M_{\odot}$ main-sequence stars
that have evolved past the helium flash at the end of the red-giant phase. The
extent of the HB varies from cluster to cluster which led to the distinction
of red HB stars redwards of the instability strip and blue HB stars bluewards.
As such these are early type stars that are already billions of years old when
they move to the BHB. A more detailed description of BHB stars, their
properties and their evolution from main-sequence stars can be found in
Moehler (2001); Catelan (2009) and references therein.

Observationally, the photometry of cooler, A-type, BHB stars places them in
the same colour-magnitude space as main-sequence A- and B-type stars. The
cooler A-type BHB fall on the bluer side of the instability strip where RR-
Lyrae are found (Montenegro et al., 2019). The hotter B-type BHB stars fall on
the redder side of the EHB stars, also called hot subdwarf stars (Heber,
2009). The spectra of BHB stars are similar to A-type subgiant or late B-type
main sequence stars. Because BHB stars rotate slowly (Behr, 2003; Xue et al.,
2008), their spectral lines are usually sharper than main-sequence A- and
B-type stars.

These classifications rely on an accurate and precise determination of colour
and absolute magnitude. Gaia has enabled immense progress to be made in this
field but even with Gaia DR3 the uncertainties in parallax, colour, apparent
magnitude, and proper motions still lead to a degree of misplacement of some
stars in the CMD causing contamination in catalogues that are based on Gaia
DR3 data alone. This presents the additional challenge of removing such
contaminants. The main categories of stars that plot closest to the BHB in the
colour-magnitude diagram, as illustrated in Figure 1, are hot subdwarfs (see
e.g. Culpan et al., 2022), extremely low mass (ELM) white-dwarfs and pre-ELM
(as compiled by Pelisoli & Vos, 2019), and RR-Lyrae (see Eyer et al., 2023).
Further contamination is caused by blue straggler stars, normal main-sequence
stars that have been rejuvenated through the accretion of additional hydrogen
(McCrea, 1964; Shara et al., 1997; Chen & Han, 2009; Ekanayake & Wilhelm,
2018). They follow the part of the main-sequence that is brighter and bluer
than the main-sequence turnoff of the Galactic Halo, i. e. where normal main-
sequence A-type and B-type would no longer be present in older stellar
populations. The brightest blue stragglers can be up to three magnitudes
brighter than the main-sequence turnoff (Rain et al., 2021).

Figure 1: The Gaia DR3 colour magnitude diagram for 30,000 randomly selected
objects with parallax errors less than 10% and tangential velocities greater
than 145 km s-1 (grey dots); BHB CMD selection region from Culpan et al.
(2021) (turquoise shading); a selection of RR-Lyrae from Gaia DR3 Clementini
et al. (2022) (red dots); hot-subdwarfs CMD selection region from Culpan et
al. (2022) (yellow shading); white dwarfs CMD selection region from Gentile
Fusillo et al. (2021) (pink shading); (pre-)ELM white dwarfs from Pelisoli &
Vos (2019) (blue circles).

Blue stragglers, because of their somewhat higher gravities, can be
distinguished from A-type BHB stars spectroscopically (Xue et al., 2008, and
references therein), while this is difficult for B-type stars because of their
similar gravities (Hunger & Heber, 1987; Raddi et al., 2021). Main-sequence
stars of spectral type A- and B- (see e.g. Silva & Napiwotzki, 2011; Raddi et
al., 2021; Liu et al., 2023) are also found in this region of the colour-
magnitude diagram but are not expected in the Galactic Halo because their
expected main-sequence lifetime is shorter than the age of this region.
However, low numbers of younger runaway main-sequence stars that have been
ejected from the Galactic Disc are found in this region.

Here we present a new release of the Gaia DR3 based catalogue of halo BHB
stars that is more complete than the original Gaia Early Data Release 3 (EDR3)
based version (Culpan et al., 2021) in crowded regions, particularly close to
the Galactic Plane, and at the bluer end of the HB where late B-type BHB stars
are expected. The catalogue of Galactic Halo BHB candidate stars with stellar
parameters derived from their spectral energy distributions (SEDs) is a subset
of the newly released Gaia DR3 based catalogue. The SEDs have been generated
using photometric data from multiple large-scale surveys. We have used the SED
results to modify the Gaia DR3 selection criteria to populate the catalogue.
They were further combined with newly acquired spectra to estimate the level
of contamination in the catalogue. As such, the process to define the BHB
selection criteria has been an iterative one. Only the final result shall be
described in this paper.

The contents of this paper are as follows: In Section 2 we explain the
generation of stellar parameters using SEDs and apply this method to the
16,794 BHB candidates in the parallax selection of Culpan et al. (2021) and
use the results to revise and extend the Gaia DR3 CMD selection criteria.
Section 3 describes how we selected and verified the applicability of various
astrometric, photometric, and blending quality criteria when applied to our
particular Gaia DR3 data set. In Section 4 we estimate the contamination
levels and completeness of the Gaia DR3 catalogue using the stellar parameters
from the SEDs as well as acquired spectra. Section 5 covers the apparent
magnitude range, distances and sky coverage of the Gaia DR3 catalogue. In
Section 6 we summarise our findings and draw our conclusions.

##  2 Spectral energy distribution analysis of BHB candidates

We used all of the 16,794 BHB star candidates with parallax errors ¡ 20% found
by Culpan et al. (2021) as the starting point for the SED analysis. The SED of
a star is defined as the observed spectral flux density as a function of
wavelength. This involved retrieving the photometric data from 66 surveys,
where available (see Appendix B). Photometric data have only been used in SED
generation if they had no error flags set and thus conformed to all the
quality criteria for the survey from which they came.

Grids of synthetic SEDs were calculated with an amended version of the ATLAS12
(Kurucz, 1996; Irrgang et al., 2018) code. A detailed description of the SED
fit method used here can be found in Heber et al. (2018) and Latour et al.
(2023). An example is shown in Fig. 2 and Table LABEL:table:B1 lists
photometic data used for the full sample. Free parameters in this $\chi^{2}$
fit were the star’s effective temperature ($T_{\mathrm{eff}}$), surface
gravity ($\log g$), angular diameter ($\Theta$), as well as the colour excess
caused by interstellar extinction. The latter was treated using the extinction
law of Fitzpatrick et al. (2019) for a reddening parameter of $R_{55}=3.02$,
the mean value for the Milky Way. Because the metallicity could not be
determined from the SED alone, we assumed $\mathrm{[Fe/H]}=-1.7$, a standard
value for cool BHB stars in the Galactic field (Behr, 2003). Stars hotter than
the Grundahl jump (11500 K, Grundahl et al., 1999) were assigned solar
metallicity because their metal abundances are increased as a result of
diffusion.

Latour et al. (2023) successfully used this approach for BHB stars in globular
clusters, as shown in their fig. 7. The angular diameter allows a measurement
of the stellar radius $R$ when combined with a distance measurement:
$R=\Theta/(2\varpi)$, where $\varpi$ is the parallax. Here, we used the Gaia
DR3 parallax measurements, corrected for zero-point offsets following
Lindegren et al. (2020).

Figure 2: An example of the results of a spectral energy distribution
generated for the BHB candidate star Gaia DR3 6305433829332391168 with the
photometric data labelled. The grey line is the best-fit SED solution for the
available photometric data. The bottom panel showing the residuals between the
best fit solution and the photometric data.

We found that the SEDs for stars where photometric data were available over
the full range of wavelengths (from ultra-violet to infra-red) gave the most
reliable results on the $T_{\mathrm{eff}}$ versus $\log g$ and the
$T_{\mathrm{eff}}$ versus $R$ plots with the BHB candidates plotting close to
the BaSTI zero-age horizontal-branch (ZAHB) and the terminal-age horizontal-
branch (TAHB) lines as defined in Pietrinferni et al. (2004) and updated in
Hidalgo et al. (2018)(see our figure 3). The BHB candidate stars with full
range wavelength photometry available plotted in a well-defined cloud in the
BHB region of the Gaia DR3 colour-magnitude diagram, (see Figure 4). We
defined the full range of wavelengths as having data available from less than
2000 $\mathrm{\AA}$ to over 8000 $\mathrm{\AA}$.

Figure 3: The stellar parameters calculated by the synthetic SEDs from
photometric data. All SED results are shown as yellow circles, the SED results
for objects with full wavelength range photometric data available are shown as
turquoise triangles. The Red line is the BaSTI ZAHB line. The black line is
the BaSTI TAHB. Upper panel:$T_{\mathrm{eff}}$ versus $\log g$; Lower panel:
$T_{\mathrm{eff}}$ versus $R$.

In order to ensure that no selection effects were distorting our results we
verified that the BHB candidates with full range photometric data were not
clustered within a particular colour, parallax, or apparent magnitude range.
Full range photometric data was available for Galactic halo objects across all
of the sky including regions of high apparent stellar density (see Figure 5)
giving us confidence that our results from the SED analysis were applicable to
the entire BHB candidate catalogue.

Figure 4: The Gaia DR3 CMD showing a sample of stars with tangential
velocities greater than 145 km s-1(yellow dots), Culpan et al. (2021) objects
with full range SEDs (cyan dots), Culpan et al. (2021) objects with full range
SEDs and modelled reddening greater than 0.2 mag (magenta squares) and the
known BHB Feige 86 possessing $T_{\mathrm{eff}}$ around 15,000K (Németh, 2017)
(blue triangle) which lies outside the Gaia DR3 CMD BHB region from Culpan et
al. (2021). Figure 5: Sky distribution of Gaia DR3 BHB candidate stars (cyan
dots) and the catalogue of BHB stars with stellar parameters based on SEDs
using full photometric range data (magenta dots).

We plotted the SED results for $T_{\mathrm{eff}}$ versus $\log g$ and
$T_{\mathrm{eff}}$ versus stellar radius to identify which of the BHB
candidate stars with photometric data over a wide wavelength range plotted
between the ZAHB and the TAHB lines (see Figure 3). We found that the BHB
candidate CMD selection of Culpan et al. (2021) was largely restricting the
upper limit of the $T_{\mathrm{eff}}$, thus excluding hotter BHB stars with
B-type spectra. In particular we noted that the known BHB star Feige 86 with
$T_{\mathrm{eff}}$ around 15,000K (Németh, 2017) was not present in the Culpan
et al. (2021) catalogue (see Figure 4).

We found that the interstellar reddening that was calculated for the SED
generation was a critical issue. When we included the objects that had
reddening values greater than 0.2 mag in the candidate selection we found a
greatly increased scatter in the CMD plots (see Figure 4)

We also found that the main-sequence contamination levels increased where the
BHB candidates with high reddening overlapped with the main-sequence in the
CMD. In this way we used the reddening as calculated in the SED generation to
define the Gaia DR3 CMD selection criteria and the upper limit on absolute
magnitude was taken to be 0.2 mag extinction line when plotted on the Gaia DR3
CMD.

##  3 Revising the BHB star candidate catalogue from Gaia DR3 using the SED
results

In order to raise the upper limit on the $T_{\mathrm{eff}}$ we extended the
Gaia DR3 CMD search criteria towards the cluster of hot subdwarfs found in
Culpan et al. (2022). The resulting overlap (see Figure 6) means that 643 of
the BHB candidates found are also hot subdwarf candidates as found in Culpan
et al. (2022).

Figure 6: The Gaia DR3 colour magnitude diagram for 30,000 randomly selected
objects with parallax errors less than 10% and tangential velocities greater
than 145 km s-1 (grey dots); BHB CMD selection region from Culpan et al.
(2021) (turquoise outline); extended BHB CMD selection region (blue shading);
hot-subdwarfs CMD selection region from Culpan et al. (2022) (yellow shading);
white dwarfs CMD selection region from Gentile Fusillo et al. (2021) (pink
shading); Feige 86 (blue triangle).

Based on Gaia DR3 data we calculated the absolute $G$ magnitude
($G_{\mathrm{abs}}$), tangential velocity ($V_{T}$), proper motion error
($\sigma_{\mathrm{pm}}$), and tangential velocity error ($\sigma_{V_{T}}$) as:

$G_{\mathrm{abs}}=\verb!phot_g_mean_mag!+5+5\,\log_{10}(\verb!parallax!/1000),$
(1) $V_{T}=4.74\cdot\texttt{pm}/\texttt{parallax},$ (2)
$\sigma_{\mathrm{pm}}=\frac{\sqrt{(\sigma_{\mathrm{pmra}}\,\texttt{pmra})^{2}+(\sigma_{\mathrm{pmdec}}\,\texttt{pmdec})^{2}}}{\texttt{pm}},$
(3)
$\sigma_{V_{T}}=V_{T}\sqrt{\frac{\sigma_{\mathrm{pm}}}{\texttt{pm}}+\frac{\sigma_{\mathrm{parallax}}}{\texttt{parallax}}}.$
(4)

The Gaia DR3 CMD search criteria were also revised to follow the BaSTI
theoretical $G_{\mathrm{abs}}$ versus $(G_{\rm BP}-G_{\rm RP})$ lines relating
to the 0 mag and 0.2 mag reddening (Pietrinferni et al., 2004; Hidalgo et al.,
2018). The actual selection criteria used (see Table 1 and Appendix C) were
somewhat wider than the 0 mag and 0.2 mag reddening lines (see Figure 12) to
allow for errors in the calculated absolute magnitude arising from
uncertainties of up to 20% in the Gaia DR3 parallax measurements.

###  3.1 Determination of the Gaia DR3 data quality filtering criteria

Since the release of Gaia DR3 many studies were made using many different
quality selection criteria. We have used the stellar parameters generated
using SEDs to quantify the effect that different criteria have on the levels
of contamination found in this catalogue and thus support our own quality
criteria selection. We have defined contaminants as being stars that do not
plot in the BHB region of the $T_{\mathrm{eff}}$ versus $R$ and the
$T_{\mathrm{eff}}$ versus $\log g$ plots. It should be noted that our quality
criteria selection findings apply to our BHB star catalogue and may not
necessarily be transferable to other situations using Gaia DR3 data.

The selection of the parallax quality criterion was examined by looking at the
scatter observed in the CMD as the parallax error cutoff was varied. We
observed an increase in scatter in the cloud of BHB candidates on the CMD as
the parallax error cutoff was increased but there was no obvious point (e. g.
a sudden increase or drop) at which a best value could be justified. We have,
thus, continued to use the parallax error ¡ 20% as the parallax quality
criterion for the sake of consistency with the Culpan et al. (2021) and Culpan
et al. (2022) catalogues. Relaxing the parallax quality criterion will
consequently increase the possible errors of the absolute magnitude and the
tangential velocity calculations (see Equations 1 and 2) which will have the
effect of increasing contamination levels within the catalogue.

The effect of applying the astrometric quality selection criterion used in
Culpan et al. (2021), `astrometric_sigma5d_max` ¡ 1.5, which was taken from
Lindegren et al. (2020) was compared to the `fidelity_v2` criterion from
Rybizki et al. (2021). We found that Rybizki et al. (2021) removed an
additional 92 sources from the parallax error ¡ 20% candidates compared to
Lindegren et al. (2020). This represents less than 1% of the candidates.
Examination of the SEDs for these 92 objects showed no benefit in their
removal in terms of reduction of contamination levels. We have retained the
use of the Lindegren et al. (2020) criterion.

We applied the photometry quality criterion from Riello et al. (2021, section
9.4) that calculates the `astrometric_excess_noise_corrected` = $C^{*}$ and
suggests a fitted scatter line

$|C^{*}|<N\cdot\sigma_{C^{*}}$ (5)

Varying the value of $N$ in Equation 5 between 1 and 5 merely changes the
number of sources selected by 25 (in a population of over 13,000) and was, as
such, deemed to be of negligible significance. We have retained the value of 5
as recommended in Riello et al. (2021, section 9.4).

We compared the crowded region filter from Culpan et al. (2022) to the
blending criterion from Riello et al. (2021, section 9.3). The Culpan et al.
(2022) criterion requires that the BHB candidate’s $G$ flux must make up at
least 70% of the $G$ flux detected within a 5 arcsec radius around that
candidate. The blending criterion from Riello et al. (2021) is defined as the
number of transits where the $G_{BP}$ or $G_{RP}$ photometry is likely blended
with nearby sources, compared to the total number of transits used for the
photometry measurements. We found that the (`beta` ¡ 0.1) criterion from
Riello et al. (2021) removed an additional 8,639 BHB candidates compared to
the Culpan et al. (2022) criterion. Once again, the contamination level found
from the SED analysis was not reduced by applying the more restrictive
criterion. Thus, we retained the crowded region filter from Culpan et al.
(2022).

The application of the data quality filters as described above to the Gaia DR3
data set resulted in 23,415 BHB candidates (see Table 1).

###  3.2 Sources of catalogue contamination

There is a compromise to be met between completeness and contamination in our
Gaia DR3 based catalogue of BHB stars. The contamination levels found may be
reduced by placing tighter quality and selection criteria but this will also
reduce the number of candidate stars found. We considered two types of
contaminants to our catalogue.

The first type of contaminant is given by stars that should not plot in the
same Gaia DR3 colour magnitude space as BHB stars but do so because of
erroneous Gaia DR3 measurements. The main contaminants in this category will
be those objects that plot closest to the BHB in Gaia DR3 colour magnitude
space. The main contaminants of this type are hot subdwarfs, pre-ELM white
dwarfs, and RR-Lyrae stars. The closer the true proximity of these objects to
the BHB region and the larger the population the greater the expected
contamination.

The most common contaminants of this type are RR-Lyrae stars. The low
temperature end of the BHB meets the instability strip where RR-Lyrae are
found on the CMD (see Figure 1). Our aim is to generate a catalogue of non-
intrinsically variable stars that lie between the instability strip and the
EHB, making these variable stars a significant contaminant in the catalogue.
We cross-matched our BHB candidate stars with the SIMBAD database and the Gaia
DR3 variability RR-Lyrae catalogue (Eyer et al., 2023; Clementini et al.,
2022) to find known RR-Lyrae. Of our BHB candidates we found 1,004 known RR-
Lyrae from the SIMBAD database and 1,136 in the Gaia catalogue. It should be
noted that only a small fraction of the Clementini et al. (2022) RR-Lyrae that
satisfy the parallax quality criterion, the tangential velocity selection
criterion and the BHB CMD selection criteria. We then calculated the excess
flux error as defined in Gentile Fusillo et al. (2021) and Culpan et al.
(2022) for all BHB candidates. The excess flux error is calculated by
comparing the `phot_g_flux_error` of each candidate object to the median $G$
flux error of 500 similar objects in terms of colour (`bp_rp`), $G$ flux
($\log_{10}$ `phot_g_mean_flux`), and the number of observations
(`phot_g_n_obs`) taken from the full Gaia DR3 catalogue. The flux error method
is sensitive to any variable stars within the limits of the Gaia exposure time
and the timescale of repeat observations. We found that over 90% of the known
RR-Lyrae had an excess flux error greater than 6.0 (see Figure 7). This was
then used as a criterion for the removal of a further 189 candidate variable
stars that are not found among those that are known in SIMBAD or in the Gaia
DR3 variability RR-Lyrae catalogue.

The fact that the remaining BHB candidates that were not identified as being
variable have an average excess flux error of 0.4 demonstrates that excess
flux error is an effective differentiator for variability.

Figure 7: The distribution of excess flux error for known SIMBAD and Gaia DR3
RR Lyrae that are found within our catalogue of BHB candidates. A best-fit
Gaussian distribution (cyan line) as been superimposed.

The second type of contaminant is stars that are not BHB stars but correctly
plot in the same region in Gaia DR3 colour magnitude space. This category
includes young A-type and B-type main-sequence stars and blue stragglers. We
have, as previously stated, focussed on the Galactic Halo to remove
contamination from main-sequence A- and B-type stars by setting a lower limit
on the tangential velocity. This criterion will, however, not filter out high
proper motion disk objects. Furthermore, a 20% error on parallax will lead to
a scatter in tangential velocities of up to 40 km s-1 around a mean value
allowing further contamination from main-sequence disk objects with higher
errors on their parallax measurement. It should be noted that the tangential
velocity that is calculated from pmra and pmdec is calculated in the
heliocentric reference frame and not the Galaxy centered reference frame.
Stars in the Galactic Halo may have a high radial velocity along the line of
sight and hence a low tangential velocity in the heliocentric reference frame.
Such stars may, thus, not be selected. This effect is more prevalent in the
direction of motion of the heliocentric system.

We applied the extended Gaia DR3 CMD selection criteria for BHB stars while
applying the astrometric, photometric, crowded region, and RR-Lyrae rejection
criteria given above (see Table 1). This resulted in 22,335 BHB candidate
stars.

Table 1: Table of criteria to select the BHB candidate stars. 1\. Gaia DR3 CMD
selection (see Appendix C): 30,228 objects
---
$\verb!parallax!>0$
$\verb!parallax_over_error!>5$
$-0.4<(G_{\rm BP}-G_{\rm RP})<0.5$
$G_{\rm abs}<138.07(G_{\rm BP}-G_{\rm RP})^{6}-153.85(G_{\rm BP}-G_{\rm
RP})^{5}-40.727(G_{\rm BP}-G_{\rm RP})^{4}+73.368(G_{\rm BP}-G_{\rm RP})^{3}$
$-7.4054(G_{\rm BP}-G_{\rm RP})^{2})-9.5575G_{\rm BP}-G_{\rm RP}+3.8459$
$G_{\rm abs}>-3.2382(G_{\rm BP}-G_{\rm RP})^{3}+7.1259(G_{\rm BP}-G_{\rm
RP})^{2}-3.583(G_{\rm BP}-G_{\rm RP})-0.2$
$v_{t}>=145km/s$
2\. Photometric quality selection criteria: 30,088 objects
$|C^{*}|<5.\sigma_{c^{*}}$
3\. Blended object rejection criterion: 23,619 objects
BHB candidate flux fraction from 5 arcsec radius ¿ 0.7
4\. RR-Lyrae removal criterion: 22,335 objects
Objects listed as RR-Lyrae in Simbad
Objects considered RR-Lyra candidates in Gaia DR3
$\verb!excess_flux_error!>6.0$
5\. BHB candidates with wide wavelength range photometric data: 10,604 objects
from 2000 Å to 8000 Å
6\. SEDs calculated without error flags: 10,222 objects
At least 5 photometry measurements used for the fit
Maximum 20% uncertainty in radius
Maximum 0.3dex uncertainty in log(L)
5\. SED generated effective temperature and surface gravity plot within BHB
region of Kiel diagram: 9,172 objects
$\log_{10}(g)<4.4157\log_{10}(T_{\mathrm{eff}})-13.720$
$\log_{10}(g)>4.0150\log_{10}(T_{\mathrm{eff}})-12.742$

##  4 Catalogue contamination estimation

In order to estimate the levels of contamination in the Gaia DR3 catalogue of
BHB stars we used two independent methods that both were not dependent on Gaia
DR3 data: the SED method as described in Section 3 as well as the analysis of
spectra acquired specifically for this project using the Astronomical
Institute of the Czech Academy of Sciences’ Perek 2m telescope located at
Ondřejov in the Czech Republic.

###  4.1 Contamination estimation using SED results

As previously stated in Section 2, the BHB candidate stars with a full
wavelength range of photometric data available give the most reliable SEDs.
Full range photometric data were used in generating the SED for 10,604 of the
22,335 (53%) BHB candidates found (see Table 1). As we found no apparent
selection effects with regard to Gaia DR3 colour, parallax, or apparent
magnitude we consider the BHB candidates with full range photometric data to
be representative of the catalogue as a whole.

When plotting the $T_{\mathrm{eff}}$ against the $\log g$ (see Figure 8) we
found that 9,172 of the 10,604 objects with full photometric range data
plotted within the horizontal branch region, defined by the cut-off lines

$\mathrm{cut_{lower}}=4.4157\log_{10}(T_{\mathrm{eff}})-13.720,$ (6)
$\mathrm{cut_{upper}}=4.0150\log_{10}(T_{\mathrm{eff}})-12.742.$ (7)

These lines are based on the ZAHB and TAHB isochrones from BaSTI models given
in Pietrinferni et al. (2004), but somewhat widened to include the coherent
cloud of BHBs. This gave an estimated contamination level of 14%. We confirmed
these selection criteria by plotting the same BHB candidates in
$T_{\mathrm{eff}}$ versus $R$ space, as well as the $T_{\mathrm{eff}}$ versus
$L$ space where they also occupy a coherent region around the ZAHB and TAHB
isochrones (see Figure 8).

Figure 8: Upper panel: $T_{\mathrm{eff}}$ versus $\log g$ as calculated from
the 22,335 BHB candidate objects where an SED calculation was made (yellow
dots), 10,604 SEDs where the full frequency range is available (cyan dots) of
which 9,172 (magenta dots) lie within the horizontal branch region as marked
by the green lines defined by Eq. 6 and 7. The BaSTI ZAHB (blue line) and TAHB
(black line) are also shown. Middle panel: $T_{\mathrm{eff}}$ versus $R$.
Lower Panel: $T_{\mathrm{eff}}$ versus $L$ for the same subsets.

###  4.2 Contamination estimation from spectral analysis

Spectra were acquired for BHB candidates with a Gaia DR3 apparent $G$
magnitude of brighter than 11.0 mag at the Ondřejov Observatory in the Czech
Republic over a 18 month period. The spectra were acquired using the Perek 2m
telescope through an Echelle spectrograph with a resolving power of $R$ =
51,600 around H$\alpha$. The resulting spectra were reduced using the
IRAF111IRAF is distributed by the National Optical Astronomy Observatories,
which are operated by the Association of Universities for Research in
Astronomy, Inc., under cooperative agreement with the National Science
Foundation. (Tody, 1986, 1993) package and a dedicated semi-automatic pipeline
Cabezas (2023) which incorporates a full range of standard procedures for
echelle spectra reduction, including bias correction, flat-fielding,
wavelength calibration, heliocentric calibration, and continuum normalization.

The criteria used to differentiate between spectra from BHB stars and from
main-sequence stars were the width and the depth of the Balmer series hydrogen
spectral lines in a similar fashion to Xue et al. (2008). Examples of BHB and
main-sequence spectra are shown in Figure 9. Over an 18 month period we
acquired spectra for 69 BHB candidates of which 6 were found to be main-
sequence stars giving a $9\pm 3$ % contamination level, similar to that found
with the SED analyses (Section 4.1) albeit with a far smaller sample.

(a) TYC 1738-745-1 (H$\alpha$)

(b) TYC 3655-1179-1 (H$\alpha$)

(c) TYC 1738-745-1 (H$\beta$)

(d) TYC 3655-1179-1 (H$\beta$)

Figure 9: Reduced spectra for a BHB star TYC 1738-745-1 (left panels) and a
high proper motion main-sequence star TYC 3655-1179-1 (right panels) for
H$\alpha$ (upper panels) and H$\beta$ (lower panels).

##  5 Sky Coverage, magnitude, and distance

The extended catalogue of BHB candidate stars presented here covers a similar
apparent magnitude range and hence a similar distance range as the Culpan et
al. (2021) predecessor but contains 32% more BHB candidates. Thus, the level
of completeness of the catalogue has been improved (see Figure 10).

Figure 10: Comparison of the Culpan et al. (2021) Gaia DR3 apparent magnitude
distribution of the BHB candidate objects from the SED based catalogue
(magenta) and the Gaia DR3 based catalogue (cyan). The peak values of these 2
histograms are found at similar values indicating that both catalogues are
investigating similar volumes. Finding additional BHB candidates in the same
volume indicates increased completeness of the new catalogue. Figure 11:
Histogram of the geometric distance (Bailer-Jones et al., 2021) to BHB
candidates from the Gaia DR3 based catalogue (blue) and the SED based
catalogue of BHB candidates with stellar parameters (green).

The catalogue of BHB candidates with stellar parameters calculated from SEDs
using full photometry range data contains 9,172 stars with a sky coverage as
shown in Figure 5, a distance range of 235 pc to 7,435 pc as shown in Figure
11 calculated from the zero-point corrected parallax (Bailer-Jones et al.,
2021) and an apparent magnitude range of 7.6 mag to 15.5 mag as shown in
Figure 10.

##  6 Summary and Conclusions

The Gaia DR3 catalogue of BHB star candidates is an update to the parallax
selected catalogue presented in Culpan et al. (2021). This latest version of
the catalogue has improved coverage at the hotter end of the BHB at
$T_{\mathrm{eff}}$ greater than 10,500 K. The data quality of Gaia DR3 permits
less restrictive criteria being applied in regions of high apparent stellar
density allowing more BHB candidates to be found. The Final Parallax Selection
in the Culpan et al. (2021) catalogue had 16,794 candidate objects. The
extended catalogue presented here (see Figure 5 and Appendix A) contains
22,335 BHB candidates. This represents an increase of 32%.

We have used photometric data from 66 large scale surveys to generate
synthetic SEDs and associated stellar parameters for a large number of BHB
candidates where no spectra are available. The use of such a rich dataset has
allowed reliable stellar parameters to be computed. The modelled SEDs have
then been used to refine the Gaia DR3 CMD selection criteria and to
demonstrate contamination levels of less than 12% in the catalogue.

This contamination level has also been observationally confirmed using spectra
acquired in the Ondřejov Observatory in the Czech Republic (see Figure 12).

We have demonstrated that the use of theoretically interpolated SEDs is a
powerful tool in constructing a richer, more complete and less contaminated
catalogue than was done in the past.

This increase of 32% in the number of BHB candidate stars compared to Culpan
et al. (2021) but within the same volume and apparent magnitude range,
represents another step in generating a more complete full-sky catalogue of
BHB stars in the inner Galactic Halo.

Figure 12: The SED based catalogue of Galactic Halo BHB candidate stars. Gaia
DR3 CMD showing objects with a tangential velocity greater than 145 km s-1
(grey dots). The Gaia DR3 based catalogue of BHB stars (magenta dots), the SED
confirmed BHB stars (green dots), spectrally confirmed BHB stars (yellow
triangles), spectrally confirmed main-sequence stars (red squares). Zero mag
extinction (black line) and 0.2 mag extinction (cyan line) theoretical tracks
are superimposed.

We then generated the SEDs as described above and used the results to
extinction correct the Gaia DR3 $(G_{BP}-G_{RP})$ and $G_{\mathrm{abs}}$
values. This was then used to define the lower absolute magnitude limit of the
Gaia DR3 CMD BHB candidate selection region.

A further iteration was made using these newly defined Gaia DR3 CMD selection
criteria and 22,335 BHB candidates (see Figure 12) were found. Of these
candidates 10,222 (46%) had photometric data available that supported the
generation of stellar- and atmospheric parameters from SEDs. The stellar- and
atmospheric parameters generated indicate that 9,172 (41%) of these objects
lie in the parameter space expected for BHBs.

###### Acknowledgements.

We thank Andreas Irrgang (University of Erlangen-Nüenberg) for amending the
ATLAS12 code and developing the SED fitting tool. I.P. acknowledges funding by
the UK’s Science and Technology Facilities Council (STFC), grant ST/T000406/1,
and from a Warwick Astrophysics prize post-doctoral fellowship made possible
thanks to a generous philanthropic donation. B.K, and M.C. acknowledge the
support from the Grant Agency of the Czech Republic (GAČR 22-34467S) and
RVO:67985815 and the Stellar Department of the Astronomical Institute of the
Czech Academy of Science. This research made use of TOPCAT, an interactive
graphical viewer and editor for tabular data Taylor (Taylor (2005)). This
research made use of the SIMBAD database, operated at CDS, Strasbourg, France;
the VizieR catalogue access tool, CDS, Strasbourg, France. Some of the data
presented in this paper were obtained from the Mikulski Archive for Space
Telescopes (MAST). STScI is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST
for non-HST data is provided by the NASA Office of Space Science via grant
NNX13AC07G and by other grants and contracts. This research has made use of
the services of the ESO Science Archive Facility. 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. This work has made use of
BaSTI web tools.

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##  Appendix A Gaia DR3 catalogues of BHB candidate stars

Table 2:  Catalogue columns.  Column | Format | Description | Unit
---|---|---|---
source_id | I19 | Gaia EDR3 source identifier | -
ra | F10.6 | Gaia EDR3 Right ascension | deg
dec | F10.6 | Gaia EDR3 Declination | deg
l | F10.6 | Galactic longitude | deg
b | F10.6 | Galactic latitude | deg
parallax | F8.4 | Gaia parallax $\bar{\omega}$ | mas
parallax_error | F8.4 | Error on parallax | mas
abs_g_mag | F8.4 | Absolute magnitude in G-band | mag
abs_g_mag_zpc | F8.4 | Absolute magnitude in G-band from zpc parallax | mag
phot_g_mean_mag | F6.3 | Gaia apparent G magnitude | mag
bp_rp | F6.3 | Gaia $G_{BP}$ \- $G_{RP}$ magnitude | mag
phot_bp_rp_excess_factor_corrected | F6.3 | Corrected Gaia $G_{BP}$ \- $G_{RP}$ excess factor | -
phot_bp_rp_excess_factor_corrected_error | F6.3 | Error on corrected Gaia $G_{BP}$ \- $G_{RP}$ excess factor | -
pmra | F7.3 | Gaia proper motion $\mu_{\rm\alpha}\cos{\rm\delta}$ | ${\rm mas\,yr^{-1}}$
pmra_error | F7.3 | Error on pmra | ${\rm mas\,yr^{-1}}$
pmdec | F7.3 | Gaia proper motion $\mu_{\rm\delta}$ | ${\rm mas\,yr^{-1}}$
pmdec_error | F7.3 | Error on pmdec | ${\rm mas\,yr^{-1}}$
pm | F7.3 | Gaia proper motion $\mu$ | ${\rm mas\,yr^{-1}}$
pm_error | F7.3 | Error on proper motion | ${\rm mas\,yr^{-1}}$
vt | F7.3 | Tangential velocity | $(km.s^{-1})$
vt_error | F7.3 | Error on tangential velocity | $(km.s^{-1})$
excess_flux_error | F7.3 | Excess flux error | -
zeropoint | F7.3 | parallax zero point | mas
parallax_zpc | F8.4 | zero point corrected parallax | mas
within_5_arcsec | F8.4 | Gaia objects within 5 arcsec of BHB candidate | -
5_arcsec_flux | F8.4 | Total G flux from within 5 arcsec radius of BHB candidate | counts
candidate_flux_fraction | F8.4 | Fraction of 5 arcsec flux that comes from BHB candidate | -
SED_flag | Boolean | Flag for SED calculation | -
SED_logtheta | f8.4 | Angular diameter $log(\Theta)$ | -
SED_logtheta_minus_error | f8.4 | Angular diameter minus error $log(\Theta)_{min}$ | -
SED_logtheta_plus_error | f8.4 | Angular diameter plus error $log(\Theta)_{max}$ | -
SED_e_44m55 | f8.4 | Reddening | mag
SED_e_44m55_minus_error | f8.4 | Reddening minus error | mag
SED_e_44m55_plus_error | f8.4 | Reddening plus error | mag
SED_teff | f8.4 | Effective temperature $T_{eff}$ | K
SED_teff_minus_error | f8.4 | Effective temperature minus error $(T_{eff})_{min}$ | K
SED_teff_plus_error | f8.4 | Effective temperature plus error $(T_{eff})_{max}$ | K
SED_logg | f8.4 | Surface gravity $log(g)$ | $log(cm/sec^{2})$
SED_logg_minus_error | f8.4 | Surface gravity minus error $log(g)_{min}$ | $log(cm/sec^{2})$
SED_logg_plus_error | f8.4 | Surface gravity plus error $log(g)_{max}$ | $log(cm/sec^{2})$
SED_z | f8.4 | Metallicity | -
SED_r | f8.4 | Median stellar radius from SED calculation | $R_{\odot}$
SED_r_minus_error | f8.4 | Stellar radius minus error from SED calculation | $R_{\odot}$
SED_r_plus_error | f8.4 | Stellar radius plus error from SED calculation | $R_{\odot}$
SED_m | f8.4 | Median stellar mass from SED calculation | $M_{\odot}$
SED_m_minus_error | f8.4 | Stellar mass minus error from SED calculation | $M_{\odot}$
SED_m_plus_error | f8.4 | Stellar mass plus error from SED calculation | $M_{\odot}$
SED_l | f8.4 | Median stellar luminosity from SED calculation | $L_{\odot}$
SED_l_minus_error | f8.4 | Stellar luminosity minus error from SED calculation | $L_{\odot}$
SED_l_plus_error | f8.4 | Stellar luminosity plus error from SED calculation | $L_{\odot}$

##  Appendix B Photometric surveys used for synthetic SED generation

Table 3:  66 Surveys used in SED calculations.  Survey | Data count | Citation
---|---|---
The DENIS Database | 42502 | DENIS Consortium (2005)
Dark Energy Camera Plane Survey (DECaPS) DR1 | 8762 | Schlafly et al. (2018)
DECam Local Volume Exploration Survey (DELVE) DR2 | 29080 | Drlica-Wagner et al. (2022)
Dark Energy Survey (DES) DR2 | 6201 | Abbott et al. (2021)
Far Ultraviolet Spectroscopic Explorer (FUSE) | 39 | Dixon et al. (2009)
Gaia Data Release 3 BP/RP low-resolution spectral data | 329732 | De Angeli et al. (2023)
Hubble Source Catalog (V1 and V2) | 16 | Whitmore et al. (2016)
Tycho-2 Catalogue | 2509 | Høg et al. (2000)
Hipparcos Catalogue | 38 | van Leeuwen (2007)
Yale/San Juan Southern Proper Motion (SPM) Catalog 4 | 35970 | Girard et al. (2011)
Gaia EDR3 | 92827 | Riello et al. (2021)
Homogeneous Means in the UBV System | 104 | Mermilliod (2006)
The Geneva Photometry Catalogue | 47 | Rufener (1999)
uvby-beta Catalogue | 233 | Hauck & Merlilliod (1998)
Stellar Photometry in Johnson’s 11-color system | 1 | Ducati (2002)
2 Micron All-Sky Survey - Catalog of Point Sources | 90454 | Skrutskie et al. (2006)
Beijing-Arizona-Taiwan-Connecticut (BATC) Large Field Multi-Color Sky Survey | 186 | Xu & Zahaoji (2005)
IRSF Magellanic Clouds Point Source Catalog | 135 | Kato et al. (2008)
Galactic Legacy Infrared Mid-Plane Survey Extraordinaire (GLIMPSE) | 102 | Spitzer Science Center (2009)
Spitzer Survey of the Large Magellanic Cloud | 250 | Meixner et al. (2006)
UKIDSS-DR6 Galactic Plane Survey | 282 | UKIDSS Consortium (2012)
UKIDSS-DR9 LAS, GCS and DXS Surveys | 6421 | Lawrence et al. (2013)
AllWISE Data Release | 58617 | Cutri et al. (2013)
Revised catalog of GALEX UV sources | 29991 | Bianchi et al. (2017)
AAVSO Photometric All Sky Survey (APASS) DR9 | 114422 | Henden et al. (2015)
Swift/UVOT Serendipitous Source Catalog | 799 | Yershov (2014)
KiDS-ESO-DR3 multi-band source catalog | 194 | de Jong et al. (2015)
Pan-STARRS release 1 (PS1) Survey | 70115 | Chambers et al. (2016)
VLT Survey Telescope ATLAS | 7680 | Shanks et al. (2015)
XMM-OM Serendipitous Source Survey Catalogue | 608 | Page et al. (2012)
The Dark Energy Survey (DES): Data Release 1 | 5387 | Abbott et al. (2018)
The band-merged unWISE Catalog | 60584 | Schlafly et al. (2019)
CatWISE2020 catalog | 59057 | Marocco et al. (2021)
Catalogue of stellar UV fluxes | 12 | Thompson et al. (1978)
UBVRIJKLMNH Photoelectric Catalogue | 11 | Morel & Magnenat (1978)
Spectroscopically Identified Hot Subdwarf Stars | 23 | Kilkenny et al. (1988)
UBV(RI)cHalpha photometry in omega Cen | 588 | Bellini et al. (2009)
South Galactic cap MCT blue objects | 1 | Lamontagne et al. (2000)
Magellanic Clouds Photometric Survey: The LMC | 182 | Zaritsky et al. (2004)
UBVRI Standard Stars | 1 | Landolt (2007)
Omega Centauri Spitzer photometry | 491 | Boyer et al. (2008)
Extended Kepler-INT Survey | 1522 | Greiss et al. (2012)
JK photometry of 12 galactic globular clusters | 6 | Cohen et al. (2015)
OGLE LMC BVI photometry | 12 | Udalski et al. (2000)
UBVI photometry in NGC 6752 | 9 | Kravtsov et al. (2016)
UBV photometry of metal-weak candidates | 15 | Norris, et al. (1999)
The ZTF catalog of periodic variable stars | 152 | Chen et al. (2020)
Spitzer Kepler Survey (SpiKeS) catalog | 200 | Werner et al. (2021)
Edinburgh-Cape Blue Object Survey. Zone 1 | 30 | Kilkenny et al. (1997)
Edinburgh-Cape Blue Object Survey. III. | 42 | O’Donoghue et al. (2013)
Edinburgh-Cape Blue Object survey. IV | 28 | Kilkenny et al. (2015)
Edinburgh-Cape Blue Object survey. V | 15 | Kilkenny et al. (2016)
UBVRI photometry in 48 globular clusters | 1917 | Stetson et al. (2019)
Javalambre Photometric Local Universe Survey Data Release DR3 | 16533 | von Marttens et al. (2024)
Pan-STARRS Data Release 2 | 67667 | Flewelling (2018)
Survey of the Magellanic Stellar History (SMASH) DR2 | 2182 | Nidever et al. (2017)
Southern Photometric Local Universe (S-PLUS) Survey DR3 | 12934 | Mendes de Oliveira (2019)
SkyMapper Southern Survey: DR2 | 124543 | Onken et al. (2019)
SDSS Photometric Catalogue, Release 12 | 30601 | Alam et al. (2015)
IGAPS. merged IPHAS and UVEX of northern Galactic plane | 1562 | Monguió, et al. (2020)
Visible and Infrared Survey Telescope for Astronomy DR6 | 41589 | McMahon et al. (2021)
Final Merged Log of International Ultraviolet Explorer Observations | 1636 | NASA (1985)
VISTA Deep Extragalactic Observations (VIDEO) Survey DR5 | 33 | Jarvis (2013)
VISTA Kilo-degree Infrared Galaxy Public Survey (VIKING) DR4 | 1384 | Edge et al. (2013)
VISTA Magellanic Survey (VMC) catalog DR4 | 98 | Cioni et al. (2011)
VISTA Variable in the Via Lactea Survey (VVV) DR4 | 1539 | Minniti et al. (2023)

Acknowledgements: This project used public archival data from the Dark Energy
Survey (DES). Funding for the DES Projects has been provided by the U.S.
Department of Energy, the U.S. National Science Foundation, the Ministry of
Science and Education of Spain, the Science and Technology FacilitiesCouncil
of the United Kingdom, the Higher Education Funding Council for England, the
National Center for Supercomputing Applications at the University of Illinois
at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the
University of Chicago, the Center for Cosmology and Astro-Particle Physics at
the Ohio State University, the Mitchell Institute for Fundamental Physics and
Astronomy at Texas A&M University, Financiadora de Estudos e Projetos,
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro,
Conselho Nacional de Desenvolvimento Científico e Tecnológico and the
Ministério da Ciência, Tecnologia e Inovação, the Deutsche
Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy
Survey. The Collaborating Institutions are Argonne National Laboratory, the
University of California at Santa Cruz, the University of Cambridge, Centro de
Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the
University of Chicago, University College London, the DES-Brazil Consortium,
the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH)
Zürich, Fermi National Accelerator Laboratory, the University of Illinois at
Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the
Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory,
the Ludwig-Maximilians Universität München and the associated Excellence
Cluster Universe, the University of Michigan, the National Optical Astronomy
Observatory, the University of Nottingham, The Ohio State University, the
OzDES Membership Consortium, the University of Pennsylvania, the University of
Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the
University of Sussex, and Texas A&M University. Based in part on observations
at Cerro Tololo Inter-American Observatory, National Optical Astronomy
Observatory, which is operated by the Association of Universities for Research
in Astronomy (AURA) under a cooperative agreement with the National Science
Foundation.

This work presents results from the European Space Agency (ESA) space mission
Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis
Consortium (DPAC). Funding for the DPAC is provided by national institutions,
in particular the institutions participating in the Gaia MultiLateral
Agreement (MLA).

Based on observations made with the NASA/ESA Hubble Space Telescope, and
obtained from the Hubble Legacy Archive, which is a collaboration between the
Space Telescope Science Institute (STScI/NASA), the Space Telescope European
Coordinating Facility (ST-ECF/ESAC/ESA) and the Canadian Astronomy Data Centre
(CADC/NRC/CSA).

The UKIDSS project is defined in Lawrence et al (2007). UKIDSS uses the UKIRT
Wide Field Camera (WFCAM; Casali et al, 2007). The photometric system is
described in Hewett et al (2006), and the calibration is described in Hodgkin
et al. (2009). The pipeline processing and science archive are described in
Irwin et al (2009, in prep) and Hambly et al (2008).

This publication makes use of data products from the Wide-field Infrared
Survey Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration.

Based on data products from observations made with ESO Telescopes at the La
Silla Paranal Observatory under programme IDs 177.A-3016, 177.A-3017 and
177.A-3018, and on data products produced by Target/OmegaCEN, INAF-OACN, INAF-
OAPD and the KiDS production team, on behalf of the KiDS consortium. OmegaCEN
and the KiDS production team acknowledge support by NOVA and NWO-M grants.
Members of INAF-OAPD and INAF-OACN also acknowledge the support from the
Department of Physics & Astronomy of the University of Padova, and of the
Department of Physics of Univ. Federico II (Naples).

Based on observations obtained as part of the VISTA Hemisphere Survey, ESO
Progam, 179.A-2010.

This publication has made use of data from the VIKING survey from VISTA at the
ESO Paranal Observatory, programme ID 179.A-2004. Data processing has been
contributed by the VISTA Data Flow System at CASU, Cambridge and WFAU,
Edinburgh.

##  Appendix C ADQL query for BHB candidates

The following query can be used in the https://gea.esac.esa.int/archive/
website to get a file containing 30,228 BHB candidates from the Gaia DR3 data
set:

$\verb!SELECT *!$
---
$\verb!FROM gaiadr3.gaia_source!$
$\verb!WHERE parallax_over_error >= 5!$
$\verb!AND parallax > 0!$
$\verb!AND (4.74 / parallax * pm) >= 145!$
$\verb!AND phot_g_mean_mag + 5 + 5*log10(parallax/1000) <
138.07*power(bp_rp,6) - 153.85*power(bp_rp,5)!$
$\verb! - 40.727*power(bp_rp,4) + 73.368*power(bp_rp,3) -
7.4054*power(bp_rp,2) - 9.5575*bp_rp + 3.8459!$
$\verb!AND phot_g_mean_mag + 5 + 5*log10(parallax/1000) >
-3.2382*power(bp_rp,3) + 7.1259*power(bp_rp,2)!$
$\verb! - 3.583*bp_rp - 0.2!$
$\verb!AND bp_rp < 0.5 AND bp_rp > -0.4!$


11institutetext: University of Amsterdam, Science park 904, 1012 WX Amsterdam,
The Netherlands 22institutetext: Elsevier BV, Radarweg 29, 1043 NX Amsterdam,
The Netherlands 22email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
# Document Embedding for Scientific Articles:
Efficacy of Word Embeddings vs TFIDF

H.J. Meijer 1122 0000-0003-2901-8119 J. Truong 22 R. Karimi 22
0000-0002-2534-1907

###### Abstract

Over the last few years, neural network derived word embeddings became popular
in the natural language processing literature. Studies conducted have mostly
focused on the quality and application of word embeddings trained on public
available corpuses such as Wikipedia or other news and social media sources.
However, these studies are limited to generic text and thus lack technical and
scientific nuances such as domain specific vocabulary, abbreviations, or
scientific formulas which are commonly used in academic context. This research
focuses on the performance of word embeddings applied to a large scale
academic corpus. More specifically, we compare quality and efficiency of
trained word embeddings to TFIDF representations in modeling content of
scientific articles. We use a word2vec skip-gram model trained on titles and
abstracts of about 70 million scientific articles. Furthermore, we have
developed a benchmark to evaluate content models in a scientific context. The
benchmark is based on a categorization task that matches articles to journals
for about 1.3 million articles published in 2017. Our results show that
content models based on word embeddings are better for titles (short text)
while TFIDF works better for abstracts (longer text). However, the slight
improvement of TFIDF for larger text comes at the expense of 3.7 times more
memory requirement as well as up to 184 times higher computation times which
may make it inefficient for online applications. In addition, we have created
a 2-dimensional visualization of the journals modeled via embeddings to
qualitatively inspect embedding model. This graph shows useful insights and
can be used to find competitive journals or gaps to propose new journals.

###### Keywords:

Word Embedding Document Embedding Journal Embedding Academic Corpus TFIDF
Embedding Validation Content Modeling

##  1 Introduction

Neural network derived word embeddings are dense numerical representations of
words that are able to capture semantic and syntactic information[21]. Word
embedding models are calculated by capturing word relatedness[11] in a corpus
as derived from contextual co-occurrences. They have proven to be a powerful
tool and have attracted the attention of many researchers over the last few
years. The usage of word embeddings has improved various natural language
processing (NLP) areas including named entity recognition[5], part-of-speech
tagging[27], and semantic role labelling[9, 16]. Word embeddings have also
given promising results on machine translation[8], search[7] and
recommendation[22, 23].
Similarly, there are many potential applications of the embeddings in the
academic domain such as improving search engines, enhancing NLP tasks for
academic texts, or journal recommendations for manuscripts. Published studies
have mostly focused on generic text like Wikipedia[15, 24], or informal text
like reviews[26, 13] and tweets[19, 33]. We aim to validate word embedding
models for academic texts containing technical, scientific or domain specific
nuances such as exact definitions, abbreviations, or chemical/mathematical
formulas. We will evaluate the embeddings by matching articles to their
journals. To quantify the match, we use the ranks derived by sorting
similarity of embeddings between each article and all journals. Furthermore,
we plot the journal embeddings as a 2-dimensional representation of journal
relatedness. Our 2-dimensional plot of embeddings visualizes relatedness in a
scatter plot[4, 10].

##  2 Data and environment

In this study, we compare content models based on TFIDF, embeddings, and
various combinations of both. This section describes the training environment
and parameters as well as other model specifications to create our content
models.

###  2.1 Dataset:

Previous studies have highlighted the benefits of learning embeddings in a
similar context as they are later used in[12, 30]. Thus, we trained our models
on title and abstracts of approximately 70 million scientific articles from 30
thousand distinct sources such as journals and conferences. All articles are
derived from Scopus abstract and citation database [1]. After tokenizing,
removal of stopwords and stemming the dataset contains a total of ca. 5.6
billion tokens (ca. 0.64 million unique tokens). The word occurrences in this
training set follow a Pareto-like distribution as described by Wiegand et
al[32]. This distribution indicates that our original data has similar
properties as standard English texts.

###  2.2 TFIDF

We used 3 TFIDF alternatives all created by the TFIDF and the hasher from the
pySpark mllib[2]. We controlled TFIDF alternatives in two ways, (a) adjusting
vocabulary size and (b) adjusting the number of hash buckets. We label the
TFIDF alternatives as follows:“vocabulary-size / number-of-hash-buckets”.
Thus, we label the TFIDF configuration that has a vocabulary size of 10,000
and 10,000 hash buckets as TFIDF 10K/10K. To select the TFIDF sets, we
measured memory footprint of multiple TFIDF configurations vs our accuracy
metric (see section 3 for detailed definition). As seen in Table 1, the
performance on both title and abstract stagnates; the same is true for the
memory usage. Given these results, we selected the 10K/10K, 10K/5K and 5K/5K
configurations for our research as reasonable compromises between memory
footprint and accuracy. We also do not expect significantly better performance
for higher vocabulary sizes such as 20K.

Table 1: TFIDF accuracy and memory usage vs variable hash-bucket and vocabulary size |  Memory | Median Rank
---|---|---
Vocabulary Size and Number of Hash Buckets | (GB) |  Title |  Abstract
1k (1k/1k) |  5.13 |  183 |  44
4k (4k/4k) |  9.29 |  59 |  20
7k (7k/7k) |  10.85 |  42 |  16
10k (10k/10k) |  11.61 |  35 |  14

###  2.3 Embeddings

Our word embeddings are obtained using a spark implementation[2] of the
word2vec skip-gram model with hierarchical softmax as introduced by Mikolov et
al[20]. In this shallow neural network architecture, the word representations
are the weights learned during a simple prediction task. To be precise, given
a word the training objective is to maximize the mean log-likelihood of its
context. We have optimized model parameters by means of a word similarity task
using external evaluation sets[6, 3, 17] and consequently used the best
performing model (see 4.1) as reference embedding model in this entire article
(referred to as embedding). Additionally, we created 4 variants of TFIDF
combined with embedding. All embedding models are listed below:

\- embedding: |  unweighted mean embedding of all tokens
---|---
\- TFIDF_embedding: |  tfidf-weighted mean embedding of all tokens
\- 10K_embedding: |  tfidf-weighted mean of the top 10,000 most occurring tokens
\- 5K_embedding: |  tfidf-weighted mean embedding of the top 5,000 most occurring tokens
-1K_6K_embedding: |  tfidf-weighted mean embedding of the top 6,000 most occurring tokens excluding the 1,000 most occurring tokens.

##  3 Methodology

To measure the quality of embeddings, we calculate a ranking between each
article and its corresponding journal. This ranking, calculated by comparing
embedding of the article with the embedding of all journals, will resemble the
performance of embeddings in a categorization task. Articles in 2017 are split
into 80%-20% training and test sets. Within training set, we average
embeddings per journal and define it as the embedding per journal. This study
is limited to journals with at least 150 publications in 2017 and those who
had papers in both test and training sets (roughly 3700 journals and 1.3
millions articles). We calculate the similarity of embeddings between each
article in the test set and all journals in the training set. We order
similarity scores such that rank one corresponds to the journal with the most
similar embedding. We record the rank of the source journal of each article
for evaluations. We do this for both title and abstract separately. We
calculate the performance per set, therefore we combine the ranking results of
all articles for a set into one score. We use the median and average for that:
the average rank takes the total average of all ranks, while the median is the
point at which 50% of all the ranks are higher and 50% of all the ranks are
lower. We keep track of the following results when ranking: source journal
rank, score as well as name of the best matching journal for both abstract and
title. We furthermore monitor the memory usage and computation time. To plot
the journal embeddings, we use PCA (Principal Component Analysis)-based tSNE.
tSNE (t-Stochastic Neighbor Embedding) is a vector reduction method introduced
by Maaten et al[18].

##  4 Results

In this section, the results of our research are presented; the detailed
discussion on the meaning and implications of these results are presented in
section 5, Discussion.

###  4.1 Model Optimization

During optimization, we tested the effect of several learning parameters on
training time and quality using three benchmark sets for evaluating word
relatedness, i.e. the WordSimilarity-353 [6], MEN [3] and the Rare Word [16]
test collection that contain generic and rare English word pairs along with
human-assigned similarity judgments. Only few parameters, i.e. number of
iterations, vector size and the minimum word count for a token to be included
in the vocabulary had significant effect on the quality. The learning rate was
0.025 and the minimum word count was 25. Our scores were close to external
benchmarks from above studies. We manually investigated the differences and
they were mostly due to word choice differences between academic context vs
non-academic. Indeed, the biggest difference was between television and show
pairs (because in academic context show would rarely relate to television).
Table 2.3 contains the average scores and training times when tuning the
parameters while fixing the remaining one. Our final and reference model is
based on 300-dimensional vectors, a context window of 5 tokens, 1 iteration
and 160 partitions.

Table 2: average accuracy scores and computation times during training.

|  value |  average score |  training time
---|---|---|---
vector size |  100 |  0.447 |  3.2 h
|  200 |  0.46 |  -a
|  300 |  0.51 |  -a
no. of iteration |  1 |  0.446 |  2.94 h
|  3 |  0.457 |  4.48 h
|  6 |  0.46 |  7.1 h
min. word count |  15 |  0.467 |  -b
|  25 |  0.473 |  -b
|  50 |  0.447 |  -b

  * a

ran in different cluster due to memory issues.

  * b

not significant.

###  4.2 Ranking

Figures 2 and 2 show the result of the categorization task via ranking
measures for titles and abstracts. The rank indicates the position of the
correct journal in the sorted list of all journals. These graphs show both the
average and the median ranks, based on the cosine-similarity between the
article and journal embeddings. These embedding vectors, whether calculated by
word2vec, TFIDF or their combinations can be considered as the feature vectors
used elsewhere for machine-learning tasks.

Figure 1: Median and average title rankings

Figure 2: Median and average abstract rankings Figure 3: Rank distribution for
the title and the abstract: Y-axis shows the fraction of articles.

###  4.3 Rank Distribution

Figure 3 shows the distributions of the ranks for our default embeddings,
TFIDF weighted embedding and the 10K/10K TFIDF. The figure plots the
cumulative percentage of articles as a function of rank. The plot gives a
detailed view of the ranks presented in Figures 2 and 2.

###  4.4 Memory Usage and Computation Time

Table 3 shows the total memory usage of each test set in gigabytes. Moreover,
it provides the absolute hit percentage of the title and the abstracts, i.e.
the percentage of articles that have their source journal as the first result
in the ranking. The table furthermore lists the median rank and the median
abstract rank, as visualized in Figures 2 and 2. Thus, this table gives an
overview of the memory usage of the sets, combined with their accuracy on the
ranking task.
We furthermore investigated compute efficiency for different content models.
To simulate what can happen during an online application, we selected 1000
random articles and then measured time needed for dot products between all
pairs. Time recorded excluded input/output time and all calculations started
from cached data with optimized numpy matrix/vector calculations. Table 4
shows computation time in seconds as well as ratios. Generally dot products
can be faster for dense vectors as opposed to sparse vectors. Generally TFIDF
vectors are stored as sparse vectors while embeddings are dense vectors.
Hence, we also created a dense vector version of TFIDF sets to isolate the
effect of sparse vs dense representation.

Table 3: memory usage and performance for various content models |  Memory | Absolute Hit | Median Rank
---|---|---|---
| (GB) |  Title |  Abstract |  Title |  Abstract
tfidf 5k 5K |  $9.82$ |  5.42% |  10.18% |  50 |  27
tfidf 5K 10K |  $11.47$ |  6.49% |  11.08% |  38 |  15
tfidf 10K 10K |  11.61 |  6.79% |  11.32% |  35 |  14
embedding |  $3.13$ |  7.92% |  9.24% |  27 |  23
5k embedding |  $3.13$ |  6.34% |  8.36% |  42 |  27
10k embedding |  $3.13$ |  7.03% |  8.76% |  34 |  25
tfidf embedding |  3.13 |  7.89% |  9.33% |  27 |  22
1k 6k embedding |  3.06 |  5.16% |  7.86% |  64 |  31
Table 4: comparing computation time between embeddings and TFIDF models | Seconds | Ratio vs Embedding
---|---|---
|  Title |  Abstract |  Title |  Abstract
TFIDF (sparse vector) |  154.95 |  169.89 |  231.25 |  184.36
TFIDF (dense vector) |  35.67 |  35.18 |  53.23 |  39.59
Embedding |  0.67 |  0.89 |  1 |  1

###  4.5 Journal Plot

Figure 4 shows the 2-dimensional visualization of the (default) journal
embeddings based on the abstracts. This plot is color coded to visualize
publishers. Some journal names have been added to the plot to indicate
research areas.

Figure 4: Journal plot of abstract embeddings after tSNE transformation. Red,
green, blue, and gray represent respectively Wiley, Elsevier, Springer-Nature,
and other/unknown publishers.

##  5 Discussion

###  5.1 Results Analysis

####  5.1.1 Highest Accuracy

The data, as presented in Figures 2 and 2 shows that the 10k/10k set performs
better than all other TFIDF sets, although the difference with the 5k/10k is
low (a median rank difference of 1 on the abstracts and 3 on the titles). For
the embeddings, the TFIDF weighted embedding outperforms other embedding
models by a narrow margin: 1 median rank higher on the abstracts, and equal on
the titles.

####  5.1.2 Dataset and Model Optimization

The determinants for choosing the final model parameters were constrained by
their computational costs. Hence, even if increasing the number of iterations
could have led to better performing word embeddings we chose 1 training
iteration due to the increased training time. Similarly, we decided to stem
tokens prior to training in order to decrease the vocabulary size. This might
have led to a loss of syntactical information or caused ambiguous tokens.

####  5.1.3 TFIDF

The TFIDF feature vectors outperform the embeddings on abstracts, while the
embeddings outperform the TFIDF on titles. The main difference between
abstract and title is the number of tokens. Hence, embeddings which enhance
tokens by their semantic meaning outperform TFIDF on the title. On the other
hand, the TFIDF model outperforms on the abstract likely due to additional
specification by additional tokens. In other words, longer text provides a
better context and hence requires a less accurate semantic model for
individual tokens.
Furthermore, none of our various vocabulary size cut-offs improved TFIDF ranks
and indeed increasing the vocabulary size monotonically increased the
performance of the TFIDF. In other words, we could not find a cut-off strategy
to reduce noise and enhance TFIDF results. Although, it could still be
possible that at even higher vocabulary sizes the cut-off would result in a
sharper signal. However, since we noticed performance stagnation we did not
investigate larger vocabulary sizes beyond 10k (presented in Table 1).

####  5.1.4 Combination of TFIDF and embeddings

The limited TFIDF embeddings all fall short of full TFIDF embedding. We did
not find a vocabulary size cut-off strategy to increase accuracy by reducing
noise from rare or highly frequent words or their combinations. In other
words, it is best not to miss any word. This is in line with what we found
with the TFIDF results: larger vocabulary sizes enhances models.
Rank distribution; Although the limited TFIDF embeddings underperform, we
found that their rank distribution is different from the other embeddings. The
rank distribution of the limited TFIDF embeddings shows the following pattern:
a high/average performance on the top-rankings, a below average performance on
the middle rankings and an increased ratio of articles with worsened higher
ranks. The rank distribution seems to indicate that the cut-offs marginalize
ranks. The cut-off moved the “middle-ranked” articles to either the higher end
or the lower end with a net effect to deteriorate median ranks. However, the
articles that matched with limited TFIDF embedding had higher accuracy scores.
The reduction in vocabulary size did not reduce the storage size for the
embeddings, except for the 1K-6K case. This indicated that only the 1K-6K cuts
removed all tokens from some abstract and titles resulting in null records and
hence lower memory.

####  5.1.5 TFIDF & embeddings

Our hypothesis on the difference between the TFIDF and the standard embedding
is as follows:
The embeddings seem to outperform the TFIDF feature vectors in situations
where there is little information available (titles). This indicates that the
embeddings store some word meaning that enables them to perform relatively
well on the titles. The abstracts, on the other hand, contain much more
information. Our data seems to indicate that the amount of information
available in the abstracts enables the TFIDF to cope with the lack of an
explicit semantic model. If this is the case, we could expect that there would
be little performance increase on the title when we compare the embeddings to
the weighted TFIDF embeddings, because the TFIDF lacks the information to
perform well. This can be seen in our data, only the average rank increased by
3, indicating that there is a difference between the two embeddings, but not a
significant one. We would also expect on the abstract an increase in
performance since the TFIDF has more information in this context. We would
expect that the weighting applied by the TFIDF model, an importance weighting,
will improves the performance of the embedding. Our data shows a minor
improvement in performance: 1 median rank and 10 average ranks. While these
improvements cannot be seen as significant, our data at least indicates that
weighting the embeddings with TFIDF values has a positive effect on the
embeddings.

####  5.1.6 Memory usage & Calculation time

TFIDF outperforms the embeddings on the abstracts, but requires more memory.
Embedding uses 3.13 GB RAM, while the top performing TFIDF, 10K/10K, uses
11.61 GB (3.7 times more RAM footprint). This indicates that the embeddings
are able to store the relatedness information more densely than the TFIDF. The
embeddings furthermore need less calculation time for online calculations as
shown in Table 4. In average, embeddings are 200 times faster than sparse
TFIDF. When the vectors are transformed to dense vectors this is reduced to 46
times. The difference between the sparse and dense vectors is due to dense
vectors being processed more efficiently by low level vector operations. The
difference between the embedding and TFIDF dense vectors is mainly due to the
vector size. Embeddings use a 300 dimensional vector, while TFIDF uses a 10000
dimensional vector. Hence a time ratio of 33 is just normal and indeed close
to measured values of 40 and 53 in Table 4. Note that even though dense
representation is roughly 4-5 times faster, it requires 33 times more RAM
which can be prohibitive.

###  5.2 Improvements

This research demonstrates that even though the embeddings can capture and
preserve relatedness, TFIDF is able to outperform the embeddings on the
abstracts. We used basic word2vec but earlier research already shows
additional improvement potential for word2vec. Dai et al[4] showed that using
paragraph vectors improves the accuracy of word embeddings with 4.4% on
triplet creation with the Wikipedia corpus and a 3.9% improvement on the same
task based on the arXiv articles. Furthermore, Le et al[14] show that the
usage of paragraph vectors decrease the error rate (positive/negative) with
7.7% compared to averaging the word embeddings on categorizing text as either
positive or negative. While the improvement looks promising, we have to keep
in mind that our task differs from earlier research. We do not categorize on
two categories but about 3700 journals. Since the classification task is
fundamentally the same, still we would expect an improvement by using
paragraph vectors. However, the larger scale here complicates the task due to
the “grey areas” between categories. These are the areas in which the
classification algorithm is “in doubt” and could reasonably assign the article
to both journals. There are many similar journals and hence we cannot expect a
rank 1 for most of articles. Indeed our classes here are not exactly mutually
exclusive. Indeed in general, the number of these grey areas increase with
increased target class size.
Pennington et al[25] showed that the GloVe model outperforms the continuous-
bag-of-words (CBOW) model, which is used in this research, on a word analogy
task. Wang et al[31] introduced the linked document embedding method (LDE)
method, which makes use of additional information about a document, such as
citations. Their research specifically focused on categorizing documents,
showed a 5.89% increase of the micro-F1 score on LDE compared to CBOW, and a
9.11% increase of the macro-F1 score. We would expect that applying this
technique to our dataset would improve our scores, given earlier results on
comparable tasks. Although our results seem to indicate that the embeddings
work for academic texts, Schnabel et al[28] found that the quality of the
embeddings are depended on the validation task. Therefore, conservatively we
can only state that our research shows that embeddings work on academic texts
for journal classifications.
Despite immense existing researches, we have not been able to find published
results which are directly comparable to ours. This is due to our large target
class size (3700 journals) that requires a ranking measure. Earlier research
limited themselves to small number of groups such as binary classes or 3
classes [29]. We have opted median rank as our key measure, but like existing
research we have also reported absolute hit [31]. Our conclusions, were
indifferent to exact metric used (median vs average rank vs absolute hit).

##  6 Conclusion

Our research, based on academic corpus, indicates that embeddings provide a
better content model for shorter text such as title and fall short of TFIDF
for larger texts such as abstracts. The higher accuracy of TFIDF may not be
worth it, as it requires 3.7 more RAM and is roughly 200 times slower for
online applications. The performance of the embeddings have been improved by
weighing them with the TFIDF values on the word level, although this
improvement cannot be seen as significant on our dataset. The visualization of
the journal embedding shows that similar journals are grouped together,
indicating a preservation of relatedness between the journal embeddings.

##  7 Future work

####  7.0.1 Intelligent cutting

A better way of cutting could improve the quality of the embeddings. This
improvement might be achieved by cutting the center of the vector space out
before normalization. All words which are generic are in the center of the
spectrum, removing these words prevents the larger texts to be pulled towards
the middle of the vector space, where they lose the parts of their meaning
which set them apart from the other texts. We expect that this way of cutting,
instead of word-occurrence cutting, can enhance embeddings especially for
longer texts.

####  7.0.2 TFIDFs performance point

In our research, TFIDF performed better on the abstracts than on the titles,
which we think is caused by the difference in text size. Consequently, there
could be a critical length of text where the best performing model switches
from embedding to TFIDF. If this length is found, one could skip the TFIDF
calculations in certain situations, and skip the embedding training in other
scenario’s, reducing costs.

####  7.0.3 Reversed word pairs

At this point, there are no domain-specific word pair sets available. However,
as we demonstrated, we can still test the quality of word embeddings. Once one
has established that the word vectors are of high quality, could one create
word pairs from these embeddings? If this is the case we could create word
pair sets using the embeddings and then reverse engineer domain specific word
pairs for future use.

##  8 Acknowledgement

We would like to thank Bob JA Schijvenaars for his support, advice and
comments during this project.

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