11institutetext: Observatório Nacional, Coordenação de Astronomia e
Astrofísica, 20921-400 Rio de Janeiro, Brazil 22institutetext: Instituto
Universitario de Física Aplicada a las Ciencias y las Tecnologías, Universidad
de Alicante, San Vicent del Raspeig, E03080, Alicante, Spain 33institutetext:
Instituto de Astrofísica de Andalucía, CSIC, Apt 3004, E18080 Granada, Spain
44institutetext: Florida Space Institute, University of Central Florida,
Orlando, FL 32816, USA 55institutetext: Instituto de Astrofísica de Canarias
(IAC), C/Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain 66institutetext:
Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna,
Tenerife, Spain 77institutetext: Université Côte d’Azur, Observatoire de la
Côte d’Azur, CNRS, Laboratoire Lagrange, Bd. de l’Observatoire, CS 34229,
06304 Nice cedex 4, France 88institutetext: Departmento de Astrofísica, Centro
de Astrobiología (CSIC-INTA), ESAC Campus, Camino Bajo del Castillo s/n
Villanueva de la Cañada, E-28692 Madrid, Spain; Spanish Virtual Observatory,
Spain 99institutetext: Centro de Estudios de Física del Cosmos de Aragón
(CEFCA), Unidad Asociada al CSIC, Plaza San Juan 1, 44001 Teruel, Spain
1010institutetext: Instituto de Astronomia, Geofísica e Ciências Atmosféricas,
Universidade de São Paulo, 05508-090, São Paulo, Brazil 1111institutetext:
Donostia International Physics Centre (DIPC), Paseo Manuel de Lardizabal 4,
20018 Donostia-San Sebastian, Spain; IKERBASQUE, Basque Foundation for
Science, 48013, Bilbao, Spain 1212institutetext: Campus Duque de Caxias,
Universidade Federal do Rio de Janeiro, 25265-970, Duque de Caxias, RJ, Brazil

# J-PLUS: A first glimpse at spectrophotometry of asteroids - The MOOJa
catalog

David Morate 11 Jorge Marcio Carvano 11 Alvaro Alvarez-Candal 223311 Mário De
Prá 44 Javier Licandro 5566 Andrés Galarza 11 Max Mahlke 7788 Enrique Solano-
Márquez 88 Javier Cenarro 99 David Cristóbal-Hornillos 99 Carlos Hernández-
Monteagudo 99 Carlos López-Sanjuan 99 Antonio Marín-Franch 99 Mariano Moles 99
Jesús Varela 99 Héctor Vázquez Ramió 99 Jailson Alcaniz 11 Renato Dupke 11
Alessandro Ederoclite 1010 Claudia Mendes de Oliveira 1010 Laerte Sodré Jr
1010 Raul E. Angulo 1111 Francisco M. Jiménez-Esteban 88 Beatriz B. Siffert
1212 J-PLUS collaboration

###### Abstract

Context. The Javalambre Photometric Local Universe Survey (J-PLUS) is an
observational campaign that aims to obtain photometry in 12 ultraviolet-
visible filters (0.3–1 $\mu$m) of $\sim$8 500 deg2 of the sky observable from
Javalambre (Teruel, Spain). Due to its characteristics and strategy of
observation, this survey will let us analyze a great number of Solar System
small bodies, with improved spectrophotometric resolution with respect to
previous large-area photometric surveys in optical wavelengths.

Aims. The main goal of this work is to present here the first catalog of
magnitudes and colors of minor bodies of the Solar System compiled using the
first data release (DR1) of the J-PLUS observational campaign: the Moving
Objects Observed from Javalambre (MOOJa) catalog.

Methods. Using the compiled photometric data we obtained very-low-resolution
reflectance (photospectra) spectra of the asteroids. We first used a
$\sigma$-clipping algorithm in order to remove outliers and clean the data. We
then devised a method to select the optimal solar colors in the J-PLUS
photometric system. These solar colors were computed using two different
approaches: on one hand, we used different spectra of the Sun, convolved with
the filter transmissions of the J-PLUS system, and on the other, we selected a
group of solar-type stars in the J-PLUS DR1, according to their computed
stellar parameters. Finally, we used the solar colors to obtain the
reflectance spectra of the asteroids.

Results. We present photometric data in the J-PLUS filters for a total of 3
122 minor bodies (3 666 before outlier removal), and we discuss the main
issues of the data, as well as some guidelines to solve them.

###### Key Words.:

minor bodies, asteroids: general - methods: surveys - techniques:
spectrophotometry

##  1 Introduction

The minor bodies that populate the Solar System are considered to be one of
the most pristine materials within it, remnants of the processes that followed
the condensation of the pre-solar nebula and the formation of the planets.
Since then, these objects have undergone little or none geological and thermal
transformations. However, they have experienced intense collisional events
that affected their shape, size and surface composition, among other
properties; they have also been exposed to different dynamical mechanisms,
which transported these objects from their original locations to their current
orbits. Thus, the study of minor bodies would provide answers to questions
about the origin and evolution of the Solar System.

Figure 1: J-PLUS filter system. The solid magenta line represents the $uJAVA$
filter; the blue adjacent curves (dotted and solid) represent the $J0378$ and
$J0395$ filters, respectively; the following cyan curves (dotted and solid)
represent the $J0410$ and $J0430$ filters; the three solid red lines are the
narrow-band filters $J0515$, $J0660$, and $J0861$; these eight filters were
designed specifically for J-PLUS. The remaining dashed black lines are the
broad-band SDSS filters: from left to right, lines: $g$, $r$, $i$, $z$. For
comparison, the spectral templates of four taxonomical classes (source:
http://smass.mit.edu/busdemeoclass.html) have been included: C (solid, blue),
X (dotted, red), S (dashed, orange), and V (dash-dotted, green). The spectra
have been shifted for better graphical representation, and normalized at 0.515
microns, which, out of the central wavelengths of every filter, is the nearest
value to 0.55 microns, the most commonly used value for normalization of
reflectance spectra of asteroids in the visible wavelength range. Note that
the spectral templates do not cover the ultraviolet region (below 0.45
microns).

As pointed out by DeMeo & Carry (2014), the next step to improve our knowledge
on this matter is to obtain spectra for a large sample of minor bodies.
Spectroscopic observations of asteroids provide information on the surface
composition of these objects. However, due to the observational methods, the
number of spectra that are present in the literature is somehow limited: for
visible wavelengths there are spectra available for $\sim$3000 objects (e.g.
Bus & Binzel 2002a; Lazzaro et al. 2013; de León et al. 2018), while near-
infrared spectra are available for only $\sim$1000 (see DeMeo et al. 2009 and
Binzel et al. 2019).

Since the beginning of the 21st century, large-area surveys have become a
powerful and usual tool to respond unanswered questions in different
astronomic fields. Examples of these projects are SDSS (York et al. 2000) and
Pan-STARRS (Kaiser et al. 2010) at visible wavelengths, and WISE (Wright et
al. 2010), AKARI (Ishihara et al. 2010), 2MASS (Skrutskie et al. 2006), VISTA
(Sutherland et al. 2015), and UKIDSS (Lawrence et al. 2007) at different
infrared wavelengths. Given the vast fractions of the sky that these surveys
cover in their observations, they pose the opportunity to analyze a large
sample of Solar System objects (SSOs) which, although may not be the original
goal, lie scattered within the obtained data.

Several works have taken advantage of the aforementioned surveys to compile
large photometric datasets of minor bodies: Ivezić et al. (2001) extracted
data from the SDSS to create the SDSS Moving Object Catalog (MOC), whose last
version contains data for more than 450 000 objects111An updated version of
the MOC catalogue can be found at http://svo2.cab.inta-csic.es/vocats/svomoc;
Popescu et al. (2016), using data from the VISTA Hemisphere Survey (VHS),
created the Moving Objects from VISTA Survey (MOVIS) catalog with data for
more than 50 000 objects; Mainzer et al. (2011) obtained mid-infrared
photometry for more than 150 000 objects from the WISE survey, and produced
the largest database (so far) of sizes and albedos of asteroids. These
datasets have in common a limited number of filters (five in the SDSS and four
in VISTA and WISE). However, even with only four or five filters, the minor
bodies science production is extensive, due to the large number of observed
objects. Some of the most relevant works derived from each of the previously
mentioned surveys can be found in Ivezić et al. (2002); Parker et al. (2008);
Carvano et al. (2010); Hasselmann et al. (2011); Masiero et al. (2011); Rivkin
(2012); Masiero et al. (2013); Alí-Lagoa et al. (2013); Mainzer et al. (2014);
Masiero et al. (2014); Hasselmann et al. (2015); Licandro et al. (2017);
Popescu et al. (2018); Morate et al. (2018).

Figure 2: Graphical comparison of the transmissions of the ECAS filters (black
solid lines), and the J-PLUS filters (red dashdotted lines) in the ultraviolet
region. The numbers correspond to: 1-$u$, 2-$J0378$, 3-J3095, 4-$J0410$,
5-$J0430$. ECAS transmissions are normalized to unity at the maximum of the u
filter, and J-PLUS transmissions are normalized to unity at the maximum of the
$J0430$ filter.

### The Javalambre Photometric Local Universe Survey

J-PLUS is a photometric sky survey which aims to cover $\sim$8 500 deg2,
designed to observe and characterize galaxies and stars of the Milky Way halo,
with a wide range of astrophysical applications (Cenarro et al. 2019). See
also https://www.j-plus.es/.

Figure 3: J-PLUS DR1 skymap coverage, represented using the International
Celestial Reference System (ICRS). Source: J-PLUS website
(http://archive.cefca.es/catalogues/jplus-dr1/coverage_map.html).

J-PLUS observations are performed with the JAST/T80 0.8-m telescope, located
in the Observatorio Astronómico de Javalambre (OAJ, Teruel, Spain; Cenarro et
al. 2014), using the panoramic camera T80Cam (Marin-Franch et al. 2015), with
a 2 deg2 field of view (FoV), covering a wavelength region between 0.35 to 1
$\mu$m by means of a 12 filter system: five intermediate-band filters (four of
them equivalent to the SDSS g’, r’, i’, and z’ filters, the other one being a
modified version of the SDSS u’ filter), and seven narrow-band filters
designed specifically for J-PLUS (see Fig. 1). The observational strategy is
to obtain, sequentially, three exposures per filter, being the total time of
acquisition in the 12 filters for the same field approximately one hour.
Taking into account a) the large fraction of sky coverage, b) the spectral
resolution, better than previous visible large-area photometric surveys, and
c) the observational strategy, we expect to obtain improved spectrophotometry
(compared to existing datasets) for quite a large number of minor bodies in
the Solar System.

Being such a large survey, the photometric calibration of J-PLUS’ data follows
a complex procedure. The data presented here relies on a calibration that uses
the locus of the Main Sequence stars observed in the footprint of the survey,
anchoring the colors to Pan-STARSS’s, as described in detail in (López-Sanjuan
et al. 2019).

Another interesting feature of the J-PLUS survey is its powerful photometric
resolution in the ultraviolet region: five filters are covering the $0.3-0.45$
$\mu$m range. Compared to J-PLUS, the most prominent survey that offers
ultraviolet spectral information of minor bodies (for a total of 589 objects)
is the Eight Color Asteroid Survey (ECAS, Zellner et al. 1985), which has only
three filters in the same region: s, u, and b, centered at 0.337, 0.359, and
0.437 $\mu$m respectively (see Fig. 2). Note that, although the central
wavelength of the b ECAS filter is 0.437 $\mu$m, this filter covers a broad
wavelength range, i.e., it includes non-ultraviolet information, while all the
J-PLUS ultraviolet filters are narrow-band (except for the $u$ filter), giving
specific coverage for this region. As we will see in the next section, the
number of Solar System objects that we expect to recover from J-PLUS
observations in this spectral region is approximately one order of magnitude
higher than the number of available objects in the literature, which will
improve the present knowledge of minor bodies in an spectral region that has
not yet been deeply explored.

The present work is organized as follows: in Sect. 2 we give a brief summary
of the survey status, we present the catalog and its most remarkable
properties, and we also discuss the outlier removal. In Sect. 3 we present a
method to select the optimal solar colors in the J-PLUS photometric system,
needed to later compute the reflectance photospectra. In Sect. 4 we discuss
the data quality and the main issues that need to be addressed. Last, in
Section 5 we summarize the contents of the paper, proposing future analises
that should be done, as well as ways to improve the data extraction from the
survey observations.

Finally, we want to stress that the scope of the present work is to select
photometric data from minor bodies contained in the first data release (DR1)
of J-PLUS, providing a large sample of minor bodies colors, that can be used
to compute very-low-resolution spectra (or photospectra), rather than
performing in-depth analyses of the obtained data, also noting that the
present work is one in a list of articles presenting diverse aspects of J-PLUS
DR1 (e.g., Logroño-García et al. 2019; Whitten et al. 2019; Solano et al.
2019).

##  2 Observations and MOOJa (Moving Objects Observed from Javalambre) catalog

Solar System objects move over the sky background. This means that, depending
on the exposure time of the image, the proper motion of the object, and the
pixel scale of the detector, the object might appear as a trace, instead of a
point source, difficulting, or even making impossible the computation of its
photometry. Fortunately, the majority of SSOs have proper motions smaller than
1$\arcsec$/min (mainly objects located in the Main Belt and beyond), which,
combined with the mean exposure times in every filter (as we will point out in
the next paragraph) will be sufficient for most of the asteroids observed by
the survey to be detected as point sources, computing their photometry with no
issues.

Although the scientific aim of J-PLUS was not specifically oriented to the
observation of minor bodies, its observational strategy allows their detection
within the survey images. The observations follow a sky tiling: each tile has
the size of the T80Cam FoV, and in order to guarantee coverage continuity,
neighboring pointings overlap in the FoV limits. For each pointing of the
survey, all 12 filters are observed consecutively, following a predefined
sequence. Every J-PLUS pointing is made of 36 exposures (3 for each filter),
and the 3 exposures in a given filter are consecutive, with a small dithering
of $10^{\prime\prime}$ between them that allows the removal of bad pixels or
columns. The three exposures are then combined, resulting in 12 images per
field (one per filter). The mean exposure time per image in the broad-band
filters is $\sim$1 minute, and in the case of the narrow-band filters, is
$\sim$2-3 minutes. The complete filter sequence is the following: $i$, $u$,
$J0430$, $J0861$, $J0515$, $J0410$, $r$, $J0378$, $J0660$, $g$, $J0395$, and
$z$. This filter acquisition order has been defined in a way that observations
between filters with similar central wavelengths are performed within long
enough time intervals for non-sidereal movement detection, while, at the same
time, minimizing long filter wheel rotations.

### The MOOJa catalog

The J-PLUS DR1222http://archive.cefca.es/catalogues/jplus-dr1/ contains images
of 511 fields, collected from November 2015 to January 2018. Its sky coverage
is shown Fig. 3. The total non-overlapped area is $\sim$900 deg2, i.e.,
approximately $\sim$10% of the intended area has already been observed. This
is the dataset from which the minor bodies data has been extracted.

The asteroids present in the J-PLUS DR1 are recovered using the SSOS pipeline,
a versatile software developed to detect both known and unknown SSOs in
astronomical images.333https://ssos.readthedocs.io/ A detailed description of
the pipeline setup is given in Mahlke et al. (2019). SSOS is applied to each
J-PLUS field individually. We briefly summarize the pipeline in the following
steps: first, all sources present in the 12 images of each field are
catalogued using SExtractor (Bertin & Arnouts 1996). Next, the sources
detection in the individual images are associated to their corresponding
observation epochs using SCAMP (Bertin 2006). SSOs are then separated from the
stars, galaxies, and other sources within the sample primarily by evaluating
their apparent motion. Finally, using the SkyBoT service (Berthier et al.
2006), the output sample is cross-matched with the known population of
asteroids. The astrometry of both known and unknown objects is reported to the
Minor Planet Centre (MPC). However, the positions of the unknown objects are
not sufficient to determine the orbits on their own. They will be combined
with other isolated tracklets by the MPC, hopefully producing orbits of new
asteroids. Thus, the unknown objects have been left out of the catalog, since
none of them has been confirmed by the MPC as a new discovery. Magnitudes were
computed using SExtractor by fitting adaptive apertures to the source’s pixels
in the image. SExtractor automatically computes instrumental magnitudes from
the pixel values inside the aperture by relying on telescope and image
metadata present in the FITS headers of the files to calibrate to the AB
system.

The majority of the asteroids in the catalog were observed in a single
pointing during a complete filter sequence, or run. However, some of these
objects were not detected in all the filters, probably due to the target
brightness. In addition, there were some cases in which the asteroid was
observed in two consecutive runs during the same night (cases in which the run
had to be restarted), or even in different nights. Whenever an asteroid was
detected in more than one run in the same night, we divided the data into
blocks in which the elapsed time from the first to the last filter acquisition
is, at maximum, 60 min444See Section 4 for details on the 60 min limit.. Then,
we selected the block with the maximum number of different filters, and, when
there were more than one block which fulfilled this condition, we selected the
block corresponding to the data with the smallest mean errors. If the asteroid
was observed in different nights, in only one run each night, we selected the
data corresponding to the night with the maximum number of different filters,
and again, if this number was the same for the different nights, we selected
the data with the smallest errors.

The full catalog presents data for a total of 3 666 objects: 3 570 numbered
asteroids, plus 96 asteroids with only provisional designation. Out of them,
359 have been observed in all the 12 filters; 386 in, at least, the 5
ultraviolet filters; and 2 476 in, at least, the 7 non-ultraviolet filters. In
Fig. 4, we can see the distribution of the observed objects throughout the
main asteroid belt.

Figure 4: Asteroids within the MOOJa catalog which have proper elements
available (black) superimposed to all proper elements for minor bodies in the
Solar System (red). We represent their semimajor axis values vs the sine of
inclination of the orbit (left panel) and vs eccentricity (right panel). Data
available at the AstDyS-2 website
(https://newton.spacedys.com/~astdys2/propsynth/all.syn).

To remove outliers, we applied a $\sigma$-clipping algorithm in the color
space. We do not expect the color distributions to be completely gaussian-
like. However, despite this limitation, we proceed assuming that they are,
since this assumption does not appear to introduce unwanted features in the
data rejection process. We computed colors $m_{f}-m_{J0515}$555We chose
$m_{J0515}$ as the normalization filter, see below., and then we computed the
mean and standard deviation of the corresponding distributions. We selected
data satisfying $|x-\overline{x}|>2.5\sigma$666This threshold was established
based on a compromise between data completeness and cleanness: more
restrictive thresholds removed observations that were not really flawed,
while, by being less restrictive, we did not manage to remove data that were
obvious outliers, where $x$ is the color and $\sigma$ is the standard
deviation of the sample, discarding the $m_{f}$ observation of the
corresponding color. The process was iterated until no outliers were found.
The final color distributions are shown in Fig. 5. A total number of 460
objects were removed due to the $\sigma$-clipping procedure. In Fig. 6, we
show how many objects have data colors for each filter (referred to J0515),
before and after the outlier removal.

Figure 5: Histograms for the color distribution after the sigma clipping was
performed, in order to remove outliers. As mentioned in the main text, all the
colors are referred to mJ0515, which is the filter that we have used for
normalization. The bin size is 0.10 mags. Figure 6: Number of objects that
have been observed in an specific filter and in J0515.

We have to keep in mind two things: first, all the objects that do not have
observations on the J0515 filter, were removed, since we cannot use this
filter to normalize the corresponding photospectrum; second, and related to
the previous point, if the observation in the J0515 filter is considered an
outlier, that object will also be removed, since, again, even if the other
observations are valid, the photospectrum cannot be constructed due to the
lack of reliability of the reference observation. Due to this, another 84
entries were removed from the original dataset. Thus, we will provide two
catalogs: one, with all the recovered data, in case the reader wants to
perform their own analyses, and another, which we consider a robust enough
dataset, with the colors referred to the normalization filter
($m_{f}-m_{J0515}$), ready to compute the corresponding photospectra (see
Section 3).

The colors catalog provided consists of data for 3122 asteroids. In Appendix A
we show some color-color distributions, as a quick proof-of-concept for the
reader (since the main focus of this work is to obtain photospectra rather
than doing color analyses) that the data presented in the MOOJa catalog is
enough to provide an apparent differentiation between the C and S complexes.
Out of those 3122 objects, 278 have been observed in every filter, thus, we
will be able to construct their complete photospectra. In addition, another
2005 objects have data for, at least, 6 colors (i.e., observed in 7 filters,
including the normalization one, J0515). In Fig. 7 we show how many objects
have data available for a given total number of colors.

Figure 7: Number of objects per quantity of colors remaining after sigma-
clipping.

The limiting magnitude of the survey can be inferred by plotting the
photometric errors versus the predicted magnitude for the detected objects
(see Fig. 8). The limiting magnitude depends on the filter: photometric data
with magnitude errors smaller than 0.1 can be obtained, for the uJAVA, J0378,
and J0395 filters (UV region), for V magnitudes brighter than V$\sim$17.5; for
J0410 and J0430 (transition region from the UV to the visible) this limit goes
up to V$\sim$19; finally, for the visible filters (gSDSS, J0515, rSDSS, J0660,
iSDSS, J0861, and zSDSS) the limiting magnitude is V$\sim$20.5. This explains
why in the redder filters there are data for smaller objects, as opposed to
the bluer filters where only those objects which are big enough were detected
in the UV region (see Fig. 9).

Figure 8: Distribution of the errors associated to each observation (for the
sigma-clipped dataset), relative to the predicted apparent V magnitude, for
the 12 filters of J-PLUS. The horizontal black line corresponds to an error of
0.1 mag. Figure 9: Mean absolute magnitudes per color. Magnitudes extracted
from the JPL website.

Taking into account the area that the DR1 has already covered, a conservative
estimate of the total number of minor bodies that will be recovered after the
survey is completed is approximately 18 000 objects, out of which we expect
$\sim$1 800 observed in all the 12 filters, $\sim$2 000 in the 5 ultraviolet
filters, and $\sim$12 000 in the 7 non-ultraviolet filters.

The full catalog consists of a list of asteroids, labeled by their
identification number or provisional designation (first column of the
catalog). After the ID number, there are three columns regarding each of the
12 filters: the first column is the detected magnitude, the second is the
error in the magnitude measurement, and the third is the MJD at the middle of
the three exposures in the corresponding filter. Each asteroid has also
associated (in the case it has been computed) their corresponding taxonomic
classification, according to Carvano et al. (2010), computed using SDSS data,
in the second-to-last column of the catalog. The absolute magnitudes, H (from
the JPL website), for each object are in the next-to-last column. Finally, in
the last column, and for quick reference, it is shown the number of filters in
which the object has been observed.

The colors catalog presents the colors, as $m_{f}-m_{J0515}$. The catalog also
has the identification number of each entry in the first column. Then, it
provides 4 entries per color, with the color value, its corresponding error,
the elapsed time between the observation in both filters, and the MJD of the
observation in the $m_{f}$ filter. As it was the case for the full catalog,
the columns with taxonomy and absolute magnitude are included. In this case,
we also provide the predicted V magnitude at the moment of the observation
(extracted using the JPL Horizons service) in the next-to-last column. The
last column shows the number of colors for which each object has data
available (analogous to the last column of the full catalog).

Both datasets can be downloaded from the CDS repository [link will be inserted
here once the paper is accepted.].

##  3 The solar colors in the J-PLUS photometric system

Solar System objects reflect the light of the Sun at the wavelengths observed
by J-PLUS. It is, therefore, necessary to remove this signature to obtain
reflectance values. These reflectance values, the spectra of minor bodies, are
used to infer their surface composition, by comparison with meteoritic
samples.

In order to transform J-PLUS magnitudes into reflectances, we have followed a
simple equation, where the reflectance value for each filter, $R_{f}$, is
computed as

$R_{f}=10^{-0.4(C_{f,ast}-C_{f,\odot})}$ (1)

where $C_{f}=m_{f}-m_{J0515}$ is the color, or magnitude diference, between
filter $f$ and the normalization filter ($J0515$), for both the asteroid and
the Sun, at the nominal central wavelengths for each filter (see Table 1).

Table 1: Central wavelengths and bandwidths of the J-PLUS filters. Source: http://www.j-plus.es/survey/instrumentation. ID | Filter Name | Central $\lambda$ ($\mu$m) | Bandwidth ($\mu$m)
---|---|---|---
1 | $u$ | 0.3485 | 0.0508
2 | $J0378$ | 0.3785 | 0.0168
3 | $J0395$ | 0.3950 | 0.0100
4 | $J0410$ | 0.4100 | 0.0200
5 | $J0430$ | 0.4300 | 0.0200
6 | $g$ | 0.4803 | 0.1409
7 | $J0515$ | 0.5150 | 0.0200
8 | $r$ | 0.6254 | 0.1388
9 | $J0660$ | 0.6600 | 0.0145
10 | $i$ | 0.7668 | 0.1535
11 | $J0861$ | 0.8610 | 0.0400
12 | $z$ | 0.9114 | 0.1409

From Eq. 1 it is clear that solar colors ($C_{f,\odot}$) in the pertinent
filters are needed to obtain reflectances. Values of $C_{f,\odot}$ are not yet
determined by the collaboration, at least not for all filters involved.
Therefore, in order to obtain reliable $C_{f,\odot}$ we have used nine sets of
data, following two different approaches: one theoretical (four sets) based on
published spectra of the Sun, and one empirical (five sets) based on J-PLUS
colors of solar type stars.

In the next subsections we provide a more detailed description of the solar
spectra that we used, as well as the solar analog selection process. In the
last subsection, we will discuss which one would be the best solar colors
choice, and how do we select it.

###  3.1 Theoretical solar colors

There exist several solar spectra in the literature that have been and are
used by the community. These are all extraterrestrial solar irradiance
spectra, obtained at airmass zero, and are all based on data from satellites,
space shuttle missions, high-altitude aircrafts, rocket soundings, ground-
based solar telescopes, and (or) modeled spectral irradiance. Out of all the
available spectra, we arbitrarily chose four of them, in order to have enough
different sources and results. The ones used for this analysis were:

  * •

1985 Wehrli Standard Extraterrestrial Solar Irradiance Spectrum

  * •

2000 ASTM Standard Extraterrestrial Spectrum Reference E-490-00

  * •

MODTRAN ETR Thuillier Spectrum

  * •

PMOD/WRC Solar Reference Spectrum

Further references can be found in Wehrli (1985); Fröhlich & Lean (1997);
Thuillier et al. (2003, 2004); Chance & Kurucz (2010), and Haberreiter et al.
(2017). All four spectra are available online777The first three spectra are
available at https://rredc.nrel.gov/solar//spectra/, and the PMOD spectrum is
available at the public FTP of the PMOD/WRC
(ftp://ftp.pmodwrc.ch/pub/data/SolarReferenceSpectrum/).. To compute
$C_{f,\odot}$, we convolved the four spectra with the J-PLUS filters
transmission. The detector efficiency and atmospheric transmission information
are already included in the filter transmission curves. The computed solar
colors are shown in Table 2.

###  3.2 Empirical solar colors

The second approach to solve the problem of obtaining the solar colors in the
J-PLUS photometric system was to analyze the DR1 searching for a set of
possible Sun-like stars observed in the 12 filters. Solar-type stars, solar
analogs, and solar twins are stars that are particularly similar to the Sun,
the solar twin being most like the Sun followed by solar analogs and then
solar-types (Soderblom & King 1998). Solar twins should be indistinguishable
from the Sun, this means:

  1. 1.

Stellar parameters similar to those of the Sun

  2. 2.

Age within $\sim$1 Gyr, so that the evolutionary state is comparable.

  3. 3.

No known stellar companion, because the Sun has none.

We stress here that this type of stars are not particularly targeted by the
survey strategy and we have to rely on serendipitous observations. The most
commonly used stellar parameters are effective temperature, gravity, and
metallicity (represented as $T_{\textrm{eff}}$, $\log g$, and [Fe/H],
respectively). In the Sun’s case, these parameters are
$T_{\textrm{eff}}=5777\pm 10$K, $\log g=4.4374\pm 0.0005$, and zero
metallicity888The metallicity of a star is defined relative to the Sun.,
$[\textrm{Fe}/\textrm{H}]=0$ (see Smalley 2005 and references within).

Stellar parameters can be computed from J-PLUS data. We used a supervised
machine learning model discussed by Galarza et al. (in prep.), based on the
random forest algorithm (see Breiman 2001 and references within) to compute
them.

The model needs a subset of well-known data in order to be trained: this
training subset was obtained by cross-checking the J-PLUS DR1 catalog with the
SEGUE survey from the SDSS. It uses a set of multiple J-PLUS colors for a
given object as input parameters, and then returns estimated values of
effective temperature, surface gravity, and metallicity as output parameters.

Using this method, we managed to select a list of 8633 stars within J-PLUS,
with $5767\textrm{K}<T_{\textrm{eff}}<5787\textrm{K}$, thus meeting the first
criterion: we will refer to this dataset as the G1 set. The remaining
criteria, however, were not fully achievable due to the low spectral
resolution and the need of a thorough analysis of the data in the G1 set,
which is out of the scope of the present work. To compensate for this, we
selected several subsets of the G1, producing a total of five sets of Sun-like
stars, that we named G1–G5. These subsets were arbitrarily selected, filtered
using the following criteria (the number of objects in each group is shown
between parentheses):

  * •

G1: Stars with $5767\textrm{K}<T_{\textrm{eff}}<5787\textrm{K}$ (8633)

  * •

G2: Stars with $5772\textrm{K}<T_{\textrm{eff}}<5782\textrm{K}$ (4792)

  * •

G3: Stars with $5767\textrm{K}<T_{\textrm{eff}}<5787\textrm{K}$ and
photometric errors in every filter less than 0.01 magnitudes (691)

  * •

G4: Stars with $5772\textrm{K}<T_{\textrm{eff}}<5782\textrm{K}$ and
photometric errors in every filter less than 0.01 magnitudes (409)

  * •

G5: Stars with $5767\textrm{K}<T_{\textrm{eff}}<5787\textrm{K}$,
$-0.3<[\textrm{Fe}/\textrm{H}]<0.3$ and $4.1<\log g<4.7$ (71)

In Table 2 we can see $C_{f,\odot}$ derived for the G1 to G5 datasets.

Table 2: Solar colors for each J-PLUS filter, computed from solar spectra (theoretical) and from Sun-like stars observed in J-PLUS in all 12 filters (empirical). All the colors are referred to the $J0515$ filter, the normalization filter that we have used for J-PLUS spectrophotometric data (i.e., mi \- mJ0515). Spectrum/ | $u$ | $J0378$ | $J0395$ | $J0410$ | $J0430$ | $g$ | $r$ | $J0660$ | $i$ | $J0861$ | $z$
---|---|---|---|---|---|---|---|---|---|---|---
Dataset |  |  |  |  |  |  |  |  |  |  |
Theoretical |  |  |  |  |  |  |  |  |  |  |
1985 Wehrli | 1.4913 | 1.2941 | 1.1518 | 0.5876 | 0.5118 | 0.1757 | -0.2877 | -0.3269 | -0.3979 | -0.4180 | -0.4202
2000 ASTM | 1.5110 | 1.3023 | 1.1455 | 0.5853 | 0.5097 | 0.1750 | -0.2879 | -0.3275 | -0.3985 | -0.4173 | -0.4338
Thuillier | 1.4325 | 1.2426 | 1.1240 | 0.5561 | 0.4993 | 0.1614 | -0.2777 | -0.3157 | -0.4048 | -0.4387 | -0.4251
PMOD/WRC | 1.4749 | 1.2665 | 1.1499 | 0.5707 | 0.4913 | 0.1605 | -0.2874 | -0.3156 | -0.4072 | -0.4154 | -0.4245
Empirical |  |  |  |  |  |  |  |  |  |  |
G1 | 1.4048 | 1.1210 | 1.0886 | 0.5541 | 0.5015 | 0.1456 | -0.3288 | -0.3752 | -0.4997 | -0.5330 | -0.5587
G2 | 1.4042 | 1.1195 | 1.0883 | 0.5537 | 0.5013 | 0.1455 | -0.3288 | -0.3753 | -0.4994 | -0.5328 | -0.5585
G3 | 1.4828 | 1.2037 | 1.1375 | 0.5778 | 0.5125 | 0.1489 | -0.3265 | -0.3742 | -0.4903 | -0.5169 | -0.5443
G4 | 1.4808 | 1.2014 | 1.1361 | 0.5768 | 0.5125 | 0.1483 | -0.3261 | -0.3746 | -0.4901 | -0.5169 | -0.5444
G5 | 1.5256 | 1.2784 | 1.1909 | 0.5853 | 0.5123 | 0.1579 | -0.3296 | -0.3728 | -0.4923 | -0.5167 | -0.5331

###  3.3 The optimal solar colors for MOOJa photospectra

In order to check for the quality of the determined solar colors and to select
the dataset that better reproduces the asteroid reflectances, we used a sample
of known spectra of minor bodies, and then compared it with the reflectances
that we retrieved from the MOOJa catalog using each set of solar colors.

The spectra of minor bodies were taken from the several dedicated surveys that
have observed, up to now, more than 3 000 spectra in the visible spectral
range. The most prominent ones, due to the number of observed objects, as well
as their spectral resolution, are SMASS (I and II, Xu et al. 1995; Bus &
Binzel 2002b), S3OS2 (Lazzaro et al. 2004), and PRIMASS (de Leon et al. 2018).
We have used these, together with other well-known datasets (ECAS, Zellner et
al. 1985; Sawyer, Sawyer 2005; 24 Color-Asteroid-Survey, Chapman et al. 2005)
for comparison with the J-PLUS spectrophotometry.

For each object present in the literature and in J-PLUS DR1 we first convolved
their spectra with the J-PLUS transmission filters to obtain the reflectances
in each fitler using

$R_{f}=\frac{\sum\limits_{\lambda}T_{f}S\lambda
d\lambda}{\sum\limits_{\lambda}T_{f}\lambda d\lambda},$ (2)

where $T_{f}$ is the filter transmission, $S$ is the spectrum reflectance, and
$\lambda$ and $d\lambda$ are, the wavelength of the spectrum and its step,
respectively. This means that, to convolve the spectra with the filters, we
needed to interpolate the filter transmissions at the corresponding spectral
wavelengths, in order to have one point of the filter transmission curve for
each reflectance and wavelength value.

In the cases where the error information associated to each point of the
literature spectra was available, the errors were propagated according to
uncertainty propagation theory (this is the case of SMASSII, S3OS2, ECAS, and
24CAS). When the spectra did not have error information available (SMASSI,
Sawyer, and PRIMASS), the errors were computed as the absolute value of the
difference, point to point, between the spectrum and its fourth-order
polynomial fit. The corresponding photospectra, together with the J-PLUS
observations, are shown in Appendix B.

There are a number of factors that may account for differences between spectra
observed by different surveys, ranging from actual spectral variation in the
asteroids to survey systematic factors and choices of solar analog stars.
Thus, we decided to parameterize this difference, taking into account the
differences in reflectance, as well as the errors associated to both spectrum
and photospectrum. This parameter, $Q$, roughly quantifies how similar is one
literature spectrum to its corresponding J-PLUS photospectrum. Its definition
is:

$\delta
Q_{i}=\sqrt{\frac{(R_{i,Lit.}-R_{i,JPLUS})^{2}}{\sigma_{i,Lit.}^{2}+\sigma_{i,JPLUS}^{2}}},\\\
Q=\frac{\sum\limits_{i=1}^{N}\delta Q_{i}}{N-1},$ (3)

where $R_{i,Lit.}$ is the reflectance value for the filter $i$ obtained after
the convolution of the literature spectrum with the J-PLUS filters,
$R_{i,JPLUS}$ is the reflectance value for the filter $i$ computed from the
J-PLUS magnitudes after removing the solar colors; $\sigma_{i,Lit.}$ and
$\sigma_{i,JPLUS}$ are their respective errors; and finally, $N$ is the number
of filters in which the asteroid has been observed in J-PLUS.

Each J-PLUS photospectrum has as many associated $Q$ indexes as available
spectra in the literature (see Table 3 for information of the analyzed
photospectra). Also, for each solar colors set, we thus have a $Q$
distribution. Due to the definition of the $Q$ index, we expect that, the
closer the value of $Q$ is to zero, the more similar a J-PLUS spectrum is to
its literature counterparts. Thus, we will consider the distribution with the
smallest mean value of $Q$ as the best approximation, and we will select the
solar colors that produced that distribution as the best suited to compute the
photospectra of the asteroids in the MOOJa catalog. The analysis of the
resulting distributions is discussed in the next paragraphs.

Table 3: List of asteroids within the MOOJa catalog that have published spectra or photospectra in different databases. The first column indicates the identification number of the asteroid, and the second column shows the survey(s) where the asteroid was observed. The numbers correspond to: 1-ECAS, 2-24CAS, 3-SMASSI, 4-SMASSII, 5-S3OS2. 6-Sawyer, 7-PRIMASS. The third and fourth columns show, respectively, the number of J-PLUS filters in which the asteroid has been observed, and the time elapsed (in minutes) from the exposure in the first filter to the exposure in the last one. Columns five and six are the date and the time at mid-observation. Asteroid | Survey | Nf | $t_{\rm{Total}}$ | Date | Time
---|---|---|---|---|---
90 | 1,2,4,5 | 10 | 35.2 | 2017-10-14 | 22:31:33
95 | 1,4,5,6 | 10 | 35.3 | 2017-10-13 | 21:15:57
122 | 2,4 | 10 | 36.0 | 2017-09-14 | 01:00:37
159 | 1,4 | 10 | 31.3 | 2017-11-21 | 21:34:23
184 | 4,5 | 12 | 38.0 | 2017-09-21 | 02:55:42
277 | 1 | 11 | 75.2 | 2017-08-14 | 02:19:06
413 | 2,4 | 9 | 36.3 | 2017-03-29 | 20:08:07
462 | 2,4 | 12 | 45.1 | 2017-11-26 | 20:10:27
712 | 1,2,4,6 | 9 | 31.2 | 2017-10-15 | 18:55:39
758 | 2 | 9 | 31.2 | 2017-11-21 | 23:13:51
784 | 4 | 12 | 39.4 | 2016-12-30 | 02:32:55
851 | 1,3 | 10 | 38.9 | 2017-09-28 | 22:13:18
1024 | 4,5 | 12 | 64.2 | 2017-01-08 | 01:43:09
1212 | 1,2,4 | 12 | 37.9 | 2018-01-16 | 19:24:56
1245 | 1 | 12 | 38.0 | 2017-11-19 | 23:51:23
1677 | 5 | 12 | 43.9 | 2017-10-29 | 02:19:01
1796 | 1,4,5 | 12 | 39.9 | 2017-08-22 | 01:47:24
1923 | 4,7 | 12 | 37.9 | 2017-09-20 | 00:00:53
2149 | 3 | 12 | 38.8 | 2017-02-20 | 23:08:27
2251 | 4 | 12 | 39.9 | 2017-08-22 | 02:57:29
2645 | 3 | 12 | 41.4 | 2017-10-27 | 04:20:00
2730 | 4 | 12 | 38.1 | 2017-09-21 | 00:10:14
2902 | 4 | 12 | 37.9 | 2017-09-19 | 23:11:23
3259 | 5 | 12 | 41.1 | 2017-10-13 | 18:48:10
3885 | 4 | 12 | 38.2 | 2017-11-21 | 22:22:45
4733 | 4 | 12 | 39.7 | 2017-02-17 | 23:55:11
4993 | 4 | 12 | 38.2 | 2017-10-17 | 00:49:08
6661 | 7 | 12 | 50.5 | 2017-08-15 | 03:09:08
6769 | 7 | 12 | 38.1 | 2017-10-15 | 00:04:47
7274 | 7 | 9 | 36.9 | 2016-12-07 | 02:16:50
34339 | 7 | 10 | 38.0 | 2017-09-24 | 03:18:31
85167 | 7 | 9 | 30.1 | 2017-01-07 | 00:43:29
113374 | 7 | 8 | 38.1 | 2017-09-23 | 22:48:49

The solar colors shown in Table 2 were used to construct the photospectra of
the asteroids in Table 3. Then, after comparing these with the literature
spectra, we obtained the $Q$ distribution associated to the use of each solar
colors set. In Fig. 10 we show the cumulative distribution functions (CDF) for
every $C_{f,\odot}$ set derived from a different solar spectrum. The mean
values of $Q$ for the four distributions are shown in Table 4. We find that
the CDF with the minimum mean value of $Q$ is the one associated to the 2000
ASTM E-490 spectrum; thus, we selected the corresponding solar colors as the
best choice derived from the theoretical approach.

Figure 10: Empirical cumulative distribution functions of the $Q$ index
obtained after the comparison of the J-PLUS spectrophotometric data with the
literature spectra, for the four different solar colors choice.

In the case of the empirical colors, we note that the colors produced by sets
G1 and G2 are very similar, as well as those related to G3 and G4. This is
confirmed by the CDFs (shown in Fig. 11) of the $Q$ index associated to the
use of these sets of $C_{f,\odot}$, where the dark green and cyan curves are
mainly overlapped by the light green and blue distributions, respectively. The
mean values of the $Q$ distribution for these cases are shown in Table 4. The
smallest mean corresponds to the solar colors derived from the G5 set,
something that, in principle, we might expect, since the stars contained in
this group are, according to their stellar parameters, the most similar to the
Sun.

Figure 11: Empirical cumulative distribution functions of the $Q$ index obtained after the comparison of the J-PLUS spectrophotometric data with the literature spectra, for the five different solar colors choice. Table 4: Mean values and their corresponding sigmas for the $Q$ distributions derived from the use of solar colors computed from Sun spectra (theoretical) and also from the ones obtained after computing the mean colors of different datasets of J-PLUS Sun-like stars (empirical). Spectrum/ |  |
---|---|---
Dataset | $\overline{Q}$ | $\sigma_{Q}$
Theoretical |  |
1985 Wehrli | 1.31 | 0.81
2000 ASTM E-490 | 1.27 | 0.80
Thuillier | 1.36 | 0.83
PMOD/WRC | 1.33 | 0.83
Empirical |  |
G1 | 1.27 | 0.77
G2 | 1.28 | 0.77
G3 | 1.28 | 0.82
G4 | 1.28 | 0.82
G5 | 1.16 | 0.73

Taking into account the previous discussion, we adopt $C_{f,\odot}$ derived
from the stars in the G5 group as our solar colors because this is the set
that produces the smallest $Q$ index mean, i.e., the smallest differences
between the photospectra in J-PLUS and their spectroscopy counterparts in the
literature. In Fig. 19 (see Appendix C) we show a sample of 74 photospectra of
asteroids in the MOOJa catalog, computed using our adopted colors. The quality
of the photospectra and the improved resolution with respect to previous
photometric surveys will let us perform taxonomical classifications for a
large number of minor bodies.

However, we note that there exists a systematic reddening in the visible
region of the resulting reflectance photospectra when using the theoretical
solar colors. Although this has been investigated, we did not find any
satisfactory explanation for this effect. The mean reflectance variations that
are induced, depending on which solar colors are used to compute the
photospectra (2000 ASTM E-490 as the best theoretical choice, G5 stellar group
as the empirical equivalent) are as follows: gSDSS, 0.0153$\pm$0.0013; rSDSS,
0.042$\pm$0.003; J0660, 0.047$\pm$0.005; iSDSS, 0.099$\pm$0.012; J0861,
0.102$\pm$0.011; zSDSS, 0.101$\pm$0.015 (all in magnitude units).

Given these mean variations, we should have in mind that the solar colors
choice might induce changes in the slope of some spectra, enough to modify a
future taxonomical classification. In order to assess how would this affect
taxonomical comparisons, we have selected a subset of photospectra from
Appendix C that visually match the templates of an S- (24 objects) and a
V-type (4 objects), since these are the easier ones to classify through means
of visual inspection.999The objects that are unambiguosly matched by visual
inspection to S-types are 473, 1608, 1677, 1736, 2149, 2498, 2902, 2963, 3259,
3338, 3446, 3863, 4028, 4109, 4703, 5293, 5795, 15419, 18960, 25046, 27082,
46304, 67611, and 102120; V-types are 1709, 2557, 9755, and 18195. Then, we
computed the mean reflectance photospectra for both cases, using the 2000 ASTM
E-490 and the G5 solar colors, and compared them to the corresponding
taxonomic class templates (S- and V-types). In Figure 12 we can see this
systematic difference. Judging by the excesive reddening produced in both
cases when using the theoretical colors, compared to the corresponding
taxonomic template, we are prone to suggest the empirical colors derived from
the G5 set as the optimal choice, as already mentioned.

Figure 12: Mean photospectra for a subset of S-types (left) and V-types
(right) from Appendix C (see main text). The blue dots and curves represent
the photospectra (reflectance points and a cubic spline fit to these points,
respectively) computed using the empirical solar colors (G5 set). In red, the
results corresponding to the use of theoretical solar colors (2000 ASTM E-490
set). The black curves represent the Bus-DeMeo template for an S-type (left)
and a V-type (right).

Nevertheless, we stress that this selection was based in the analysis shown in
the present work, and that the perfect choice of the solar colors for the
J-PLUS filter system does not exist. Because of this, all the solar colors
that we computed in this work are presented in Table 2, leaving the final
choice to the users of the catalog. In addition, future data releases might
provide larger datasets of solar type stars and better statistics, and
thorough searches for solar analogs might remove the need of statistical
analyses. Thus, we encourage the reader and the catalog users to test other
paths and, if possible, improve the solar color computation.

##  4 Caveats, issues, and possible solutions

Figure 13: Histogram showing the distribution of the exposure times, in
minutes, for the asteroids observed in five or more filters. Bin size is 5
minutes. Note that, in some cases, the total exposure time is higher than 60
min. This is due to the choice of the optimal subset of observations for every
asteroid (see Section 2). However, the majority of the cases are concentrated
around the mean value Figure 14: Normalized histograms showing the
distribution of elapsed times, in minutes, between contiguous filters.
Usually, observations in filters at longer wavelengths come (although not
immediately) after those at shorter wavelengths, except for the cases of
filters $J0410$–$J0395$, $J0430$–$J0410$, $J0515$–$g$, and $i$–$J0660$ (see
the filter sequence in Section 2). Histograms have been overplotted and
separated according to their mean times for a better visual representation.
Bin size is 1 minute. Figure 15: Simulated light curve for an spheroid with
axial ratio of 0.7, as observed by J-PLUS. Sets of points with the same color
represent the central instant of observations with the 12 J-PLUS filters.

(a)

(b)

Figure 16: (a) Resulting photospectra for the lightcurve in Fig.15 using the
optical constants of the HED meteorite Allan Hill A76005, with the reflectance
spectra of the meteorite shown as a continuous black line. (b) Same as the
previous figure, for the optical constants of the Taggish Lake meteorite.

We stress that the spectrophotometry that can be generated using the MOOJa
catalog is not exactly equivalent to the spectra that the observed asteroids
would present if observed by a spectrograph. Usually, when observing a fixed
object in the sky, e.g., a star, obtaining its spectrum or its photospectrum
is essentially equivalent, since observations are often carried out on time
scales which are significantly shorter than the typical variability time scale
of most stars. The same does not hold true for asteroids: minor bodies are
normally non-spherical objects, and might present different surface
compositions from one region of the asteroid to another. Because of this, and
due to their rotation, which is generally in the scale of a few hours, the
reflected sunlight varies its intensity along the observation time. If we
obtain the spectrum (or photospectrum) of an asteroid using a short enough
total exposure time, these fluctuations can be neglected. However, for long
exposure times, and depending on the rotation period, shape, and pole
orientation of the specific object, the induced reflectance variations might
need to be taken into account.

Usually, we refer to exposure times as the total time elapsed since the
opening of the shutter of the camera until the moment that the shutter closes,
this is, the duration of one exposition. However, because in the case of the
MOOJa catalog we are dealing with photometric spectra, we are referring to
exposure times as the total time elapsed from the first filter observation to
the last, whether the asteroid was observed in the 12 filters or not. In Fig.
13, we show the total exposure times for all the asteroids observed within the
MOOJa catalog. Although some asteroids present more than one hour of total
exposure time (given the constraints that we imposed to obtain the
spectrophotometry), in the majority of the cases the exposure time is around
40 min, due to the filter observation sequence and to the survey strategy.

The magnitude variation during this interval can be estimated by considering
the lightcurves reported by the Asteroid Lightcurve
Database101010http://www.minorplanet.info/lightcurvedatabase.html. The median
rotation period for more than 18 000 asteroids is $\sim$6.3 h, and the median
of the lightcurve amplitudes is $\sim$0.38 magnitudes. Thus, for a lightcurve
amplitude of 0.38 magnitudes with a 6.3 h period, and a 40 min interval
between the first and last filter measurement, we could estimate a mean
uncertainty of $\sim$0.16 magnitudes, which might induce errors around
$\sim$15% when translated to reflectance.

Also, the fact that the filter measurements were not ordered according to the
central wavelengths of the filters, as explained in Section 2, might introduce
non-negligible uncertainties between adjacent points, depending on the time
intervals between these contiguous spectrophotometric points (see Fig. 14). In
Table 5 we show the estimated mean magnitude variations that might be induced
by these time separations. Note that the higher estimated variations are those
related to the ’jump’ from filters $J0861$ to $z$, and from filters $J0660$ to
$i$. This is evident by looking at Fig. 18, e.g. for asteroids 462, 1245,
1677, or 2251, where the points corresponding to the $z$ filter are shifted
upwards with respect to the $J0861$ points, or the $i$ point is shifted
downwards with respect to the $J0660$ point.

It is worth to mention that, in some of the presented plots in Appendixes B
and C, there seems to persist a number of low-quality observations: asteroid
851, which shows a very red slope; 2730, where there is a point which seems
very out of the overall trend; or 6661, 6769, and 9688, which seem to have a
very low SNR. In these cases, when the sigma-clipping algorithm was not enough
to eliminate these datapoints, some additional procedures that could be used
are, for example, filtering data that are highly discrepant with respect to
the others (for instance, with respect to adjacent values, preceding and
following) or highly discrepant with respect to the overall spectral shape
(for instance by fitting the spectra with an appropriate function and
identifying outliers with respect to the trend). These options are left
unexplored, open for future versions of the catalog.

We have performed some simulations of the theoretical photospectra that would
be obtained, as function of asteroid shape, aspect angle, rotational period
and superficial composition, in order to assess how rotation could affect the
obtained reflectance spectra of asteroids observed by J-PLUS. We consider
asteroid shape models as sets of triangular facets. The bidirectional
reflectance of each facet is obtained using Hapke’s IMSA equation (Hapke 2005)
using a double-lobed Henyey-Greenstein phase function, with the single scatter
albedo and phase parameters calculated using geometrical optics from sets of
optical constants that vary with wavelength. The integrated reflectance of all
facets that are visible and illuminated at a given observational geometry are
then calculated for an array of wavelengths, which are then convolved with the
band pass of each J-PLUS filter according to the filter sequence and using
exposure times that are consistent with the observations.

Figure 15 shows the simulated lightcurve for an asteroid with spheroidal
shape, an axis ratio of 0.7, a rotation period of 6 hours, and an amplitude of
$\leavevmode\nobreak\ 0.15\,mag$. Using optical constants for the HED
meteorite Allan Hills A76005 (Davalos et al. 2017) and the Taggish Lake
meteorite (Roush 2003), we simulated a V- and a D-type asteroid, respectively.
The measured photospectrum would vary depending on the portion of the
lightcurve that is observed (see Fig.16).

As expected, the changes induced by rotation in the photospectrum are a
function of the amplitude of the portion of the light curve sampled during the
observations. The simulated lightcurve has a moderate amplitude ($\sim$0.15);
if the amplitude was wider (i.e., the object had a more elongated shape) this
variation would be greater, enough to modify spectral points even with small
errors (as we see in Figs. 18 and 19). In addition, given that these
simulations were performed for two extreme taxonomical classes, such as a V-
and a D-type, we expect this effect to induce changes enough to blur the
limits between closer classes such as C-, B-, X-, or even S-type asteroids.

The approach that we propose to solve this issue is to take into account the
three individual expositions for each filter, using the slopes of the
variations in time as some sort of ’partial’ lightcurve, in order to correct
these rotation-induced magnitude shifts.

Table 5: Mean values and their corresponding errors, in minutes, for the elapsed time between observations corresponding to contiguous filters. The next-to-last column corresponds to the mean magnitude variations estimated using the median values of the lightcurve amplitudes and periods in the Asteroid Lightcurve Database (see main text). The final column represents the percentage of error induced in the reflectance by the variations in magnitude. Contiguous filters |  $t_{cont}$ (min) |  $\Delta$ Mag. | Rerr (%)
---|---|---|---
$J0378$-$u$ | 20.7 $\pm$ 2.4 | 0.08 | 7
$J0395$-$J0378$ | 12.3 $\pm$ 2.1 | 0.05 | 5
$J0410$-$J0395$ | 19 $\pm$ 3 | 0.08 | 7
$J0430$-$J0410$ | 10.4 $\pm$ 1.3 | 0.04 | 4
$g$-$J0430$ | 26 $\pm$ 3 | 0.10 | 9
$J0515$-$g$ | 19 $\pm$ 3 | 0.08 | 7
$r$-$J0515$ | 6.6 $\pm$ 1.2 | 0.03 | 3
$J0660$-$r$ | 8.8 $\pm$ 2.1 | 0.04 | 4
$i$-$J0660$ | 29 $\pm$ 4 | 0.12 | 11
$J0861$-$i$ | 10.3 $\pm$ 1.4 | 0.04 | 4
$z$-$J0861$ | 30 $\pm$ 4 | 0.12 | 11

There are also situations in which the reflectance variations between adjacent
points are extremely large. These cases probably arise from the fact that the
asteroid is passing over, or near, a star in the field at the moment of one of
the exposures, or that one of the frames (or all of them) present low data
quality. The sigma-clipping algorithm removed some of these outliers. However,
even after processing the data, some extreme reflectance variations remain: in
order to deal with this issue, the best approach would be to examine the three
individual frames obtained for each filter, and discard those in which the
asteroid is located too close to a star in the background, or those in which
the photometric quality is below some previously imposed threshold.
Unfortunately, these individual frames were not available for the first data
release, thus, this issue will need to be addressed on a future version of the
catalog.

##  5 Summary and future work

This work focused in presenting to the scientific community the Moving Objects
Observed from Javalambre (MOOJa) catalog, a compilation of spectrophotometric
data of asteroids observed within the Javalambre Photometric Local Universe
Survey in 12 filters covering wavelengths from 0.3 up to 1 $\mu$m. A total of
3 666 different asteroids were detected. We applied a sigma-clipping algorithm
to this initial collection of observations, on the colors that are used to
compute spectrophotometry, to clean and remove outliers, and to obtain a more
robust dataset. The eventual colors catalog that we provide consists of 3 122
objects, of which 278 are observed in the 12 filters, i.e., with a complete
spectrum. The catalog has been compiled using data only from the first data
release of J-PLUS, which covers $\sim$10% of the sky region intended to be
observed. We expect to recover around 18 000 objects in the full duration of
the survey, as well as to discover new ones, obtaining spectrophotometry for
these bodies at the same time of the discovery.

We present a new method to select a suitable set of solar colors in the J-PLUS
photometric system (out of several options, computed both theoretically and
empirically) that will be used in order to compute the photospectra of the
asteroids within the MOOJa catalog. This method makes use of those asteroids
that have been previously observed by past surveys, and have also been
observed by J-PLUS.

We also have introduced the most relevant issues that might prevent us from
maximizing the science outcome of the use of the catalog: the most important
one, the time interval between observations in contiguous filters; and
secondly, flawed observations that cannot be removed with the sigma-clipping
algorithm. We propose that the best course of action in order to remove both
sources of error is to examine each of the three individual images in every
filter: in the first case, correcting the magnitude variation induced by the
lightcurve, and in the second, simply removing suboptimal exposures from the
computations. Unfortunately, these data were not available as part of the DR1,
but are available within the DR2. At the moment there is an ongoing effort to
further extend the catalog, which will be updated once all the minor bodies
data within the DR2 are recovered and processed.

In addition, we would like to address some interesting points that might serve
as a checklist for future works:

  * •

The first and most immediate analysis should focus on the taxonomic
classification of the asteroids observed within the catalog. The fact that the
observations are done using 12 filters will provide a huge number of asteroid
classifications, and will exponentially increase our knowledge of distribution
of different materials throughout the Solar System.

  * •

Since the number of ultraviolet filters in which asteroids are observed is
higher than any previous survey in the field, this might provide new insights
into this wavelength region. A novel taxonomic system in the UV should be
probed, to enhance our knowledge of minor bodies science within this spectral
domain.

  * •

Given the spectral resolution and the distribution of the filters’ central
wavelengths, the information on the MOOJa catalog will allow for a more robust
definition of the 0.7 $\mu$m absorption band (related to aqueous altered
minerals on the surface of the asteroid), than using SDSS data.

We would like to mention that there exists another ongoing survey, S-PLUS
(Southern Photometric Local Universe Survey, see Mendes de Oliveira et al.
2019) that is carried out using an identical duplicate of the telescope used
in Javalambre, the T80, located near the summit of Cerro Tololo in central
Chile. The aim of this survey is basically the same as J-PLUS, but instead of
covering the sky of the northern hemisphere, will cover the southern side.
This will provide a similar number of spectrophotometric data of asteroids.

Along these lines, another important survey that might benefit from J-PLUS
operations (and viceversa) is the Gaia mission (see Mignard et al. 2007;
Delbo’ et al. 2012; Tanga & Mignard 2012), since its spectrophotometric system
covers basically the same region as J-PLUS. Specifically, the Gaia-BP
spectrophotometer covers the UV region, where J-PLUS also offers a total of
seven narrow-band and two broad-band filters. Thus, J-PLUS data might be used,
for example, to test and calibrate Gaia spectra for minor bodies in the
ultraviolet range. The synergies that might arise from combining both datasets
are very interesting and should be taken into account.

To summarize, the vast number of minor bodies photospectra that this catalog,
and its future versions, will provide, might be the first step into a new era
in which large-area surveys will be key to solve unanswered questions in the
area of minor bodies of the Solar System, due to the wealth of data (and its
quality) that will be available to the community.

###### Acknowledgements.

DM acknowledges the CNPq for the support in form of a PCI grant, and also the
FAPERJ for the support in the form of a Pós-Doutorado Nota 10 grant. JMC
acknowledges CPNq for support through a research fellowship. AAC acknowledges
support from FAPERJ (grant E26/203.186/2016) and CNPq (grants 304971/2016-2
and 401669/2016-5), from the Universidad de Alicante under contract
UATALENTO18-02, and from the State Agency for Research of the Spanish MCIU
through the ”Center of Excellence Severo Ochoa” award to the Instituto de
Astrofísica de Andalucía (SEV-2017-0709)” MDP ackowledges funding by the
Preeminent Postdoctoral Program (P3) at the University of Central Florida. JL
acknowledges support from the project AYA2015-67772-R (MINECO). AG
acknowledges CAPES for the support in the form of a Phd. grant. MM
acknowledges funding by the European Space Agency under the research contract
C4000122918. ESM and FJE acknowledges funding by the Spanish State Research
Agency (AEI) Projects AYA2017-84089 and MDM-2017-0737 at Centro de
Astrobiología (CSIC-INTA), Unidad de Excelencia María de Maeztu. The present
work is based on observations made with the JAST/T80 telescope for the J-PLUS
project at the Observatorio Astrofísico de Javalambre in Teruel, a Spanish
Infraestructura Cientifico-Técnica Singular (ICTS) owned, managed and operated
by the Centro de Estudios de Física del Cosmos de Aragón (CEFCA). Data has
been processed and provided by CEFCA’s Unit of Processing and Archiving Data
(UPAD). Funding for the J-PLUS Project has been provided by the Governments of
Spain and Aragón through the Fondo de Inversiones de Teruel; the Aragón
Government through the Research Groups E96, E103, and E16_17R; the Spanish
Ministry of Science, Innovation and Universities (MCIU/AEI/FEDER, UE) with
grants PGC2018-097585-B-C21 and PGC2018-097585-B-C22; the Spanish Ministry of
Economy and Competitiveness (MINECO) under AYA2015-66211-C2-1-P,
AYA2015-66211-C2-2, AYA2012-30789, and ICTS-2009-14; and European FEDER
funding (FCDD10-4E-867, FCDD13-4E-2685). The Brazilian agencies FAPESP and the
National Observatory of Brazil have also contributed to this project.

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## Appendices

##  Appendix A Color vs. color examples

Here we show four color-color distributions of asteroids observed within the
MOOJa catalog. In grey, all the observed objects within the colors catalog
(that are observed in the corresponding filters). Overplotted, the asteroids
(only C-, S-, V-, and X-types) that were previously classified according to
their SDSS colors (see Carvano et al. 2010): C-types, in red; S-types, in
black; V-types, in blue; X-types, in green. Top panels are a combination of
broad-band-filters-only (left) and narrow-band-filters-only (right). Bottom
panels are combinations of both broad and narrow-band filters. It is easy to
separate between, at least, C- and S-types using the combinations in the top-
and bottom-left panels.

Figure 17: Color-color distributions for some filter combinations.

##  Appendix B J-PLUS spectra vs. literature spectra

Photospectra in the 0.3-1.0 $\mu$m region of the 33 asteroids within the MOOJa
catalog which are also available in the literature. The J-PLUS
spectrophotometry (computed using the G5 solar colors, see Sect.3) is
represented in blue, and the literature spectra, overplotted, are represented
as follows: ECAS, orange right-pointing triangles, $\vartriangleright$;
SMASSI, green circles, $\circ$; SMASSII, black squares, $\Box$; S3OS2, magenta
left-pointing triangles $\vartriangleleft$; 24CAS, gray down-pointing arrows
$v$; Sawyer, cyan diamonds, $\Diamond$; PRIMASS, red crosses, $\times$. All
photospectra are normalized at 0.515 $\mu$m, which is the central wavelength
of the $J0515$ filter, which, among the central wavelengths of all the
filters, is the nearest one to 0.55 $\mu$m, the most widely used value to
normalize visible asteroid’s spectra.

Figure 18: Comparison between photospectra of J-PLUS asteroids and visible
literature spectra.

##  Appendix C J-PLUS photospectra collection

Photospectra in the 0.3-1.0 $\mu$m region of 74 asteroids within the MOOJa
catalog. These objects have been detected by J-PLUS in all the 12 filters and
with $(m_{f}-m_{J0515})_{err}<0.1$ magnitude units. The dots represent the
J-PLUS data, and the solid curve is a cubic polynomial fit, for a better
visualization of the overall spectral shape.

Figure 19: Photospectra of asteroids detected in the MOOJa catalog. Figure 20:
Photospectra of asteroids detected in the MOOJa catalog (continued). Figure
21: Photospectra of asteroids detected in the MOOJa catalog (continued).


# Cross-Lingual Training with Dense Retrieval for Document Retrieval

Peng Shi1, Rui Zhang2, He Bai1, and Jimmy Lin1
1 David R. Cheriton School of Computer Science, University of Waterloo
2 Department of Computer Science and Engineering, Penn State University
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Dense retrieval has shown great success in passage ranking in English.
However, its effectiveness in document retrieval for non-English languages
remains unexplored due to the limitation in training resources. In this work,
we explore different transfer techniques for document ranking from English
annotations to multiple non-English languages. Our experiments on the test
collections in six languages (Chinese, Arabic, French, Hindi, Bengali,
Spanish) from diverse language families reveal that zero-shot model-based
transfer using mBERT improves the search quality in non-English mono-lingual
retrieval. Also, we find that weakly-supervised target language transfer
yields competitive performances against the generation-based target language
transfer that requires external translators and query generators.

##  1 Introduction

Dense retrieval uses dense vector representations for semantic encoding and
matching. It has shown its effectiveness in open-domain question answering and
passage ranking Nogueira and Cho (2019); Yang et al. (2019); Karpukhin et al.
(2020). However, most of the existing work focus on high-resource languages
such as English, where large-scale annotations are readily accessible. Widely
available large-scale datasets such as Natural Questions (NQ) Kwiatkowski et
al. (2019) and MS MARCO Nguyen et al. (2016) are used for training dense
retrieval encoder to achieve state-of-the-art performances in English. Such
data is especially hard to obtain for low-resource languages, considering that
large amounts of annotations are required for training dense retrieval
encoders.

More recently, Shi et al. (2020) proposed several cross-lingual transfer
techniques for bridging the language gaps between high-resource languages and
low-resource languages for document reranking. However, unlike dense
retrieval, document reranking affects the efficiency of the document retrieval
because reranking is the second stage inference based on the results of first-
stage term-matching based retrieval.

In this work, we focus on improving the traditional term-matching based
retrieval without losing the efficiency of the retriever. Our model combines
term-matching scores and dense retrieval similarity in a single step,
overcoming the efficiency issue of two-stage document reranking and exploiting
the representation ability of neural models at the same time. More
specifically, we explore techniques for leveraging the relevance judgments in
a source language, usually a high-resource language such as English, to train
dense retrievers for mono-lingual document retrieval in multiple target (non-
English) languages. Note that this setting is different from cross-lingual
information retrieval (CLIR), where queries and documents are in different
languages Shi and Lin (2019); Yu and Allan (2020); Jiang et al. (2020);
Litschko et al. (2021); Yu et al. (2021); Chen et al. (2021). Following the
idea of cross-lingual training Shi et al. (2020), we examine low-resource
techniques including zero-shot model-based transfer and weakly-supervised
target language transfer; we also explored the technique by leveraging public
translators, such as Google Translate, to improve the language transfer of the
dense retriever.

We train our retrieval models using Natural Questions and MS MARCO in English,
and we evaluate our transfer approaches on diverse text collections for
document retrieval in six target languages including NTCIR 8 in Chinese
Mitamura et al. (2008), TREC 2002 in Arabic Oard and Gey (2002), CLEF 2006 in
French Di Nunzio et al. (2006), FIRE 2012 in Hindi, FIRE 2012 in Bengali Yadav
and Robins Yadav , TREC 3 in Spanish Harman (1995). Our experimental results
show that while the dense retriever itself cannot obtain performances as
competitive as traditional exact term matching methods such as BM25 or
BM25+RM3 query expansion, combining them can obtain effectiveness improvements
without losing the efficiency. Especially, the weakly-supervised target
language transfer yields competitive performances compared with the
generation-based target language transfer that requires external translators.

##  2 Related Work

Dense retrieval showed its superiority over the traditional term matching
based methods such as BM25 or BM25+RM3 query expansion on passage retrieval
task Dai and Callan (2019b, a); Karpukhin et al. (2020); Zhang et al. (2019);
Chang et al. (2020); MacAvaney et al. (2020). A bi-encoder architecture is
used for the dense retrievers, where the queries and documents are mapped into
hidden vectors independently without any interaction between them. Compared
with term-based sparse retrieval using TF-IDF or BM25, it can capture synonyms
or paraphrases by incorporating contexts and provide additional flexibility to
learn task-specific representations Lin et al. (2020).

Document reranking is another topic in document retrieval. With pretrained
language models, the reranking effectiveness has been improved significantly
Nogueira and Cho (2019); Yilmaz et al. (2019). A cross-encoder architecture is
often used for document reranking, where the tokens of query and the document
can have full interactions in the encoder and the matching signals can be
easily captured by the models.

The multilingual BERT Devlin et al. (2018) has shown its language transfer
abilities over different tasks Wu and Dredze (2019). Shi et al. (2020) were
the one of the first to build IR re-rankers based on the mBERT for non-English
corpus by leveraging the relevance judgments in English.

##  3 Preliminaries

We explore different strategies for the cross-lingual transfer of dense
passage retriever (DPR) to improve traditional retrieval methods such as BM25
or BM25+RM3. DPR uses a dense encoder $E_{P}(\cdot)$ that encodes passages to
a $d$-dimension vectors and builds an index for document collections that are
used for retrieval. For the query, a different encoder $E_{Q}(\cdot)$ is used
for mapping the query into $d$-dimension vector. Based on the query vector,
the closest top $k$ passages are retrieved from the pre-built index based on
the pre-defined distance function. Following Karpukhin et al. (2020), we
define the distance function as $sim(q,p)=E_{Q}(q)^{\top}E_{P}(p)$. We use
pretrained mBERT as the start point and the hidden state of [CLS] token is
regarded as the representation of the encoded text. During inference, we apply
both bag-of-words exact term matching such as BM25 or BM25+RM3 and dense
retrieval. The relevance score of each document combines the term-matching
scores with dense retrieval similarity $S_{doc}=\alpha\cdot
S_{term}+(1-\alpha)\cdot S_{dense}$ where $\alpha$ is tuned via cross-
validation. All candidate documents are sorted by the above score $S_{doc}$ to
produce the final output.

##  4 Cross-Lingual Relevance Transfer

To perform cross-lingual transfer of DPR from a high-resource source language
to low-resource target languages, we investigate two groups of strategies. The
first strategy, model-based transfer, directly applies the retrieving model
trained on the source language to other target languages in a zero-shot
manner. The second strategy explores two data augmentation techniques to build
the training data on target languages for finetuning.

###  4.1 Model-based Transfer

By exploiting the zero-shot cross-lingual transfer ability of pre-trained
transformers such as mBERT Devlin et al. (2018) and XLM-Roberta Conneau et al.
(2019), we train the dense retriever encoder in the source language and apply
inference directly on target languages. These pre-trained transformers only
require raw text in different languages, e.g. Wikipedia, and are trained in a
self-supervised manner, so we characterize this approach as “low resource”.

###  4.2 Target Language Transfer

To bridge the language gap between the training and the inference, a direct
solution is target language data augmentation. In this work, we explore two
techniques for creating a target language transfer set, including generation-
based query synthesis and weakly supervised query synthesis.

#### Generation-based Query Synthesis.

The goal of the generation-based query synthesis is to leverage powerful
generation models to predict reasonable queries given documents in the target
language. We choose the multilingual version of BART (mBART) Liu et al.
(2020), a pretrained sequence-to-sequence transformers, as our query
generation model. The input of the model is the passage and its learning
target is the corresponding query. We use the translate-train technique to
obtain the generation models. More specifically, we leverage Google Translate
to translate the query-document pairs in English to target languages. In the
inference stage, we use the passages in the target language collections as the
input and generate corresponding queries in the same language. In our
preliminary experiments, we also tried zero-shot transfer that model is
trained on English query-document pairs and directly applied to target
languages for query inference. However, the generated queries are of low
quality, and this observation is also confirmed by Chi et al. (2020).

Weakly-supervised Query Synthesis. Wikipedia has documents in varies
languages, and it is a good transfer set in the cross-lingual training. We can
automatically build the target language transfer set without manual annotation
effort, by treating the titles of Wikipedia articles as queries and the
corresponding documents as positive candidates. We also retrieve top 1000
documents with BM25 for each query, and the documents except the positive
candidate are labeled as negative candidates. Queries whose positive document
is not in the retrieved set are removed. In this way, we can obtain query-
document pairs in target languages.

#### Two-stage Training.

We apply two-stage training to train the dense retriever encoders. The dense
retriever encoders are firstly trained on source language annotated data which
are available in a large scale; then the models are finetuned on the
synthesized query-document pairs in the target language.

Doc Language | Source | # Topics | # Docs
---|---|---|---
Chinese | NTCIR 8 | 73 | 308,832
Arabic | TREC 2002 | 50 | 383,872
French | CLEF 2006 | 49 | 171,109
Hindi | FIRE 2012 | 50 | 331,599
Bengali | FIRE 2012 | 50 | 500,122
Spanish | TREC 3 | 25 | 57,868

Table 1: Dataset statistics for test collections.

| AP | P@20 | nDCG | AP | P@20 | nDCG | AP | P@20 | nDCG
---|---|---|---|---|---|---|---|---|---
Model | NTCIR8-zh | TREC2002-ar | CLEF2006-fr
${\bf(0)}~{}\textrm{BM25}$ | $0.4014$ | $0.3849$ | $0.4757$ | $0.2932$ | $0.3610$ | $0.4056$ | $0.3111$ | $0.3184$ | $0.4458$
${\bf(1)}~{}\textrm{BM25+RM3}$ | $0.3384$ | $0.3616$ | $0.4490$ | $0.2783$ | $0.3490$ | $0.3969$ | $0.3421$ | $0.3408$ | $0.4658$
${\bf(2)}~{}\textrm{NQ zero-shot}$ | $0.4221^{\blacktriangleup}$ | $0.4164^{\blacktriangleup}$ | $0.5235^{\blacktriangleup}$ | $0.2943$ | $0.3560$ | $0.4012$ | $0.3470$ | $0.3469$ | $0.4726$
${\bf(3)}~{}\textrm{MS zero-shot}$ | $0.4167^{\blacktriangleup}$ | $0.4164^{\blacktriangleup}$ | $0.5095^{\blacktriangleup}$ | $0.3024$ | $0.3810^{\blacktriangleup}$ | $0.4285$ | $0.3332$ | $0.3418$ | $0.4573$
${\bf(4)}~{}\textrm{MS}\rightarrow\textrm{QGen}$ | $0.4258^{\blacktriangleup}$ | $0.4336^{\blacktriangleup}$ | $0.5308^{\blacktriangleup}$ | $0.2988$ | $0.3800$ | $0.4276$ | $0.3331$ | $0.3429$ | $0.4564$
${\bf(5)}~{}\textrm{MS}\rightarrow\textrm{Wiki}$ | $0.4135$ | $0.4123^{\blacktriangleup}$ | $0.5055^{\blacktriangleup}$ | $0.3060^{\blacktriangleup}$ | $0.3750$ | $0.4293$ | $0.3456$ | $0.3480$ | $0.4743$
| FIRE2012-hi | FIRE2012-bn | TREC3-es
${\bf(0)}~{}\textrm{BM25}$ | $0.3867$ | $0.4470$ | $0.5310$ | $0.2881$ | $0.3740$ | $0.4261$ | $0.4197$ | $0.6660$ | $0.6851$
${\bf(1)}~{}\textrm{+RM3}$ | $0.3660$ | $0.4430$ | $0.5277$ | $0.2833$ | $0.3830$ | $0.4351$ | $0.4912$ | $0.7040$ | $0.7079$
${\bf(2)}~{}\textrm{NQ zero-shot}$ | $0.3939$ | $0.4560$ | $0.5408$ | $0.2898$ | $0.3980$ | $0.4495^{\blacktriangleup}$ | $0.4910$ | $0.6980$ | $0.7007$
${\bf(3)}~{}\textrm{MS zero-shot}$ | $0.3944$ | $0.4580$ | $0.5461$ | $0.2896^{\blacktriangleup}$ | $0.3900$ | $0.4449$ | $0.4950$ | $0.7080$ | $0.7171$
${\bf(4)}~{}\textrm{MS}\rightarrow\textrm{QGen}$ | $0.3941$ | $0.4660$ | $0.5527$ | $0.2887$ | $0.3980$ | $0.4486$ | $0.4958^{\blacktriangleup}$ | $0.7180$ | $0.7239$
${\bf(5)}~{}\textrm{MS}\rightarrow\textrm{Wiki}$ | $0.3950$ | $0.4630$ | $0.5497$ | $0.2898^{\blacktriangleup}$ | $0.4050$ | $0.4549$ | $0.4972^{\blacktriangleup}$ | $0.7180$ | $0.7329$

Table 2: Experimental results on the baselines and our cross-lingual transfer
methods. Model (0) and (1) are term matching baselines. Model (2) NQ zero-
shot: zero-shot transfer of models trained on Natural Questions. Model (3) MS
zero-shot: zero-shot transfer of models trained on MS MARCO. Model (4)
$\textrm{MS}\rightarrow\textrm{QGen}$: trained on MS MARCO and then finetuned
on query generation data requiring external translators. Model (5)
$\textrm{MS}\rightarrow\textrm{Wiki}$: trained on MS MARCO and then finetuned
on query synthesis data from Wikipedia. For nDCG, we report nDCG@20.
Significant gains against the baselines are denoted with $\blacktriangleup$.

##  5 Experimental Setup

#### Evaluation.

We conduct experiments on six test collections in diverse languages (Chinese,
Arabic, French, Hindi, Bengali, Spanish). Data statistics are shown in Table
1. For the evaluation metrics, we adopt the average precision (AP) up to rank
1000, precision at rank 20 (P@20) and nDCG at rank 20 (nDCG), computed with
the trec_eval toolkit. The query was used to retrieve the top 1000 hits from
the corpus using BM25 or BM25+RM3 query expansion; the default Anserini Yang
et al. (2017) settings were used. For the dense retrieval, the top 100 hits
are retrieved from the index and the similarity scores are combined with the
term-matching scores. For the documents that are not in the retrieved set,
either from term-matching methods or dense retrieval, 0 score is assigned.
Fisher’s two-sided, paired randomization test Smucker et al. (2007) at
$p<0.05$ was applied to test for statistical significance.

#### Training.

For the model-based transfer, we explore two training datasets in the source
language, English in our case, including the Natural Question and MS MARCO.
Note that Natural Question is an open-domain question answering dataset, where
the queries are usually long questions instead of a bag of keywords in the
document ranking datasets. This introduces a new gap in query style besides
language in the transfer process. For training the query generator in target
languages, we obtain the training data by sampling 2000 query-passage pairs
from MS MARCO and translate them into target languages same as target
benchmarks. For two-stage training, we first train the dense encoders on the
MS MARCO dataset and then further tune them on the transfer set.

#### Inference.

For dense retrieval, documents are often too long to fit into BERT models for
encoding. A common approach to address this issue is to split the long
document into segments within fixed length (e.g. 512 tokens), and build an
index based on the segments. In this work, we segmented the documents using a
sliding window of 5 sentences and a stride of 1 sentence. For each query, the
score of document $S_{dense}$ is obtained by averaging the top-3 scores of the
retrieved segments. We applied five-fold cross-validation on all datasets,
choosing parameter $\alpha$ that yielded the highest AP.

##  6 Results and Discussions

Our results are shown in Table 2. Models (0) and Models (1) show the
effectiveness of BM25 and BM25 with RM3 query expansion. For each language, we
select the higher P@20 of the two models as the term-based matching baselines.
That is, for the French, Bengali and Spanish collections, we use the BM25+RM3
as the term-based matching baseline and for others, we use the BM25.

#### Finding #1: Zero-shot model-based transfer improves term-based matching.

The results of zero-shot model-based transfer are shown in Models (2) and
Models (3). Comparing with the corresponding baselines, we observe that the
model-based transfer, either NQ zero-shot or MS zero-shot, can improve the
retrieval effectiveness on P@20 for all collections, except the NQ zero-shot
on TREC3-es dataset. We do not observe a clear winner between NQ and MS,
though. For example, Models (2) perform better on Chinese and French
collections; while Models (3) yield better retrieval effectiveness on Arabic
and Spanish collections. Since mBERT is widely available, mono-lingual
retrieval improvements can be obtained “for free” with annotated data in
English. These results indicate that mBERT-based DPR effectively transfers
relevance matching across languages.

#### Finding #2: Target language transfer benefits certain collections, and
Wiki query synthesis is better than query generation.

Target language transfer results are shown in Models (4) and Models (5).
$\textrm{MS}\rightarrow\textrm{QGen}$ and
$\textrm{MS}\rightarrow\textrm{Wiki}$ denote two-stage training strategy with
different transfer sets, where QGen denotes generation-based query synthesis
and Wiki denotes weakly supervised query synthesis from Wikipedia. By
comparing the Models (4) with Models (3), we observe the second stage training
with generation-based query-document pairs can improve the effectiveness of
P@20 over the zero-shot model-based transfer on Chinese, French, Hindi,
Bengali and Spanish collections. However, there is no difference over AP for
all collections. By comparing the Models (5) with Models (3), we find that the
second stage training with weakly-supervised training data can improve the
P@20 over the zero-shot baselines on French, Hindi, Bengali and Spanish
collections.

Furthermore, by comparing these two transfer sets, we observe that, except for
the Chinese collection, the Wiki obtains better retrieval effectiveness than
QGen, which requires external translators and training query generators on
different languages.

##  7 Conclusion

We investigate the effectiveness of three transfer techniques for document
ranking from English training data to low-resource target languages. Our
experiments in six languages demonstrate that zero-shot transfer of mBERT-
based dense retrieval models improves traditional term-based matching method,
and finetuning on augmented data in target languages can further benefit
certain collections.

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