text:
11institutetext:  Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la
Astronomía s/n, 18008-Granada, Spain, 11email<EMAIL_ADDRESS>22institutetext:
LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne
Université, Univ. Paris Diderot, Sorbonne Paris Cité, France 33institutetext:
Astronomical Institute of the Romanian Academy, 5 Cuţitul de Argint, 040557
Bucharest, Romania 44institutetext: Instituto de Astrofísica de Canarias
(IAC), C/Vía Láctea s/n, 38205 La Laguna, Tenerife, Spain 55institutetext:
Laboratório Interinstitucional de e-Astronomia – LIneA & INCT do e-Universo,
Rua Gal. José Cristino 77, Bairro Imperial de São Cristóvão, Rio de Janeiro
(RJ), Brazil 66institutetext: UNESP - São Paulo State University, Grupo de
Dinâmica Orbital e Planetologia, Guaratinguetá, SP, 12516-410, Brazil
77institutetext: Observatório Nacional/MCTI, Rua Gal. José Cristino 77, Bairro
Imperial de São Cristóvão, Rio de Janeiro (RJ), Brazil 88institutetext:
Universidade Federal do Rio de Janeiro - Observatório do Valongo, Ladeira
Pedro Antônio 43, CEP 20.080-090 Rio de Janeiro - RJ, Brazil 99institutetext:
Institut Polytechnique des Sciences Avancées IPSA, 63 boulevard de
Brandebourg, F-94200 Ivry-sur-Seine, France 1010institutetext: Institut de
Mécanique Céleste et de Calcul des Éphémérides, IMCCE, Observatoire de Paris,
PLS Research University, CNRS, Sorbonne Universités, UPMC Univ Paris 06, Univ.
Lille, 77 Av. Denfert-Rochereau, F-75014 Paris, France 1111institutetext:
Federal University of Technology–Paraná (UTFPR/Curitiba), Brazil
1212institutetext: Florida Space Institute, University of Central Florida,
Orlando, USA 1313institutetext: ISTEK Belde Observatory, Turkey
1414institutetext: Department of Astronomy and Space Sciences, University of
Ege, Turkey 1515institutetext: Faculty of Physics, University of Bucharest,
405, Atomistilor Street, 077125 Magurele, Ilfov, Romania 1616institutetext:
Ataturk University, Astrophysics Research & Application Center (ATASAM), 25240
Erzurum, Turkey 1717institutetext: Akdeniz University, Faculty of Sciences,
Department of Space Sciences and Technologies, 07058 Antalya, Turkey
1818institutetext: TÜBITAK National Observatory, Akdeniz University Campus,
07058 Antalya, Turkey 1919institutetext: School of Physics and Astronomy and
Wise Observatory, Tel Aviv University, Israel 2020institutetext: Department of
Astronomy and Space Sciences, Science Faculty, Erciyes University, 38030
Melikgazi, Kayseri, Turkey 2121institutetext: Particle Physics and
Astrophysics Department, Weizmann Institute of Science, Israel
2222institutetext: Astronomical Observatory “Amiral Vasile Urseanu” Bucharest,
Romania 2323institutetext: Space Sciences and Solar Energy Research and
Application Center (UZAYMER), Çukurova University, Adana, Turkey
2424institutetext: Space Observation and Research Center, Çağ University,
Mersin, Turkey 2525institutetext: Ege University, Faculty of Science,
Department of Physics, 35100, Bornova, Izmir, Turkey 2626institutetext:
Ataturk University, Science Faculty, Department of Astronomy & Space Sciences,
25240 Erzurum, Turkey 2727institutetext: Astronomical Observatory “Victor
Anestin” Bacau, Romania 2828institutetext: Astroclubul Bucureşti, Romania
2929institutetext: L13 Observatory, Romania 3030institutetext: L15
Observatory, Romania 3131institutetext: Ia cu Stele, Romania
3232institutetext: L16 Observatory, Romania 3333institutetext: L04
Observatory, Romania 3434institutetext: Galaţi Astronomical Observatory,
“Răsvan Angheluţă” Museum Complex of Natural Sciences, 6A, Regiment 11 Siret
Street, 800340, Galaţi, Romania 3535institutetext: Tiraspol State University,
5, Ghenadie Iablocikin Street, MD-2069, Chișinău, Republic of Moldova
3636institutetext: Asociatia Astroclubul Quasar, Romania

3737institutetext: Romanian Academy, Cluj-Napoca Branch, Astronomical
Observatory Cluj-Napoca, Str. Cireşilor, Nr. 19, 400487, Cluj-Napoca, Romania
3838institutetext: L22 Observatory, Romania 3939institutetext: Institute of
Astronomy, V.N. Karazin Kharkiv National University, Ukraine
4040institutetext: QOS Observatory, National Space Facilities Control and Test
Center, Ukraine 4141institutetext: Section of Astrophysics, Astronomy and
Mechanics, Department of Physics, National and Kapodistrian University of
Athens, GR-15784 Zografos, Athens, Greece 4242institutetext: Astronomical
Observatory of Odessa I.I. Mechnikov National University, Shevchenko Park,
Odessa, 65014, Ukraine 4343institutetext: Konkoly Observatory, Research Centre
for Astronomy and Earth Sciences, Eötvös Loránd Research Network (ELKH),
H-1121 Budapest, Konkoly Thege Miklós út 15-17, Hungary 4444institutetext:
ELTE Eötvös Loránd University, Institute of Physics, Budapest, Hungary
4545institutetext: Çanakkale Onsekiz Mart University, Faculty of Arts and
Sciences, Department of Physics, TR-17020, Çanakkale, Turkey
4646institutetext: Çanakkale Onsekiz Mart University, Astrophysics Research
Center and Ulupınar Observatory, TR-17020, Çanakkale, Turkey
4747institutetext: Northolt Branch Observatories, UK 4848institutetext: Sainte
Marie, La Reunion, France 4949institutetext: Agrupació Astronòmica de
Sabadell, Barcelona, Spain 5050institutetext: International Occultation Timing
Association–European Section (IOTA-ES), Germany 5151institutetext: Almalex
Observatory, Leeds, UK 5252institutetext: Les Makes, La Reunion, France
5353institutetext: Ellinogermaniki Agogi Observatory, Athens, Greece
5454institutetext: Ondokuz Mayis University Observatory, Space Research
Center, 55200, Kurupelit, Samsun, Turkey 5555institutetext: Laboratory of
Space Researches, Uzhhorod National University, Uzhhorod, Daleka Str., 2A,
88000, Ukraine 5656institutetext: Astronomical Observatory Institute, Faculty
of Physics, A. Mickiewicz University, Słoneczna 36, 60-286 Poznań, Poland
5757institutetext: Mt. Suhora Observatory, Pedagogical University, ul.
Podchorazych 2, PL-30-084 Krakow, Poland 5858institutetext: Department of
Physics, Faculty of Science and Arts, İnönü University, Malatya, Turkey
5959institutetext: Astronomical Observatory, Institute of Theoretical Physics
and Astronomy, Vilnius University, Sauletekio av. 3, 10257 Vilnius, Lithuania
6060institutetext: Janusz Gil Institute of Astronomy, University of Zielona
Góra, Prof. Szafrana 2, PL-65-516 Zielona Góra, Poland

# Physical properties of the trans-Neptunian object (38628) Huya from a multi-
chord stellar occultation

P. Santos-Sanz 11 J.L. Ortiz 11 B. Sicardy 22 M. Popescu 3344 G. Benedetti-
Rossi 225566 N. Morales 11 M. Vara-Lubiano 11 J.I.B. Camargo 7755 C.L. Pereira
7755 F.L. Rommel 7755 M. Assafin 8855 J. Desmars 991010 F. Braga-Ribas
1111225577 R. Duffard 11 J. Marques Oliveira 22 R. Vieira-Martins 5577 E.
Fernández-Valenzuela 1212 B.E. Morgado 225577 M. Acar 13131414 S. Anghel
3310101515 E. Atalay 1616 A. Ateş 1313 H. Bakış 1717 V. Bakış 1717 Z. Eker
1717 O. Erece 17171818 S. Kaspi 1919 C. Kayhan 13132020 S.E. Kilic 1818 Y.
Kilic 17171818 I. Manulis 2121 D.A. Nedelcu 33 M.S. Niaei 1616 G. Nir 2121 E.
Ofek 2121 T. Ozisik 1818 E. Petrescu 2222 O. Satir 1616 A. Solmaz 23232424 A.
Sonka 33 M. Tekes 2323 O. Unsalan 2525 C. Yesilyaprak 16162626 R. Anghel 2727
D. Berteşteanu 2828 L. Curelaru 2929 C. Danescu 3030 V. Dumitrescu 3131 R.
Gherase 28283232 L. Hudin 3333 A-M. Stoian 3434 J.O. Tercu 34343535 R. Truta
3636 V. Turcu 3737 C. Vantdevara 3838 I. Belskaya 3939 T.O. Dementiev 4040 K.
Gazeas 4141 S. Karampotsiou 4141 V. Kashuba 4242 Cs. Kiss 43434444 N. Koshkin
4242 O.M. Kozhukhov 4040 Y. Krugly 3939 J. Lecacheux 22 A. Pal 4343 Ç.
Püsküllü 45454646 R. Szakats 4343 V. Zhukov 4242 D. Bamberger 4747 B. Mondon
4848 C. Perelló 49495050 A. Pratt 51515050 C. Schnabel 49495050 A. Selva
49495050 J.P. Teng 5252 K. Tigani 5353 V. Tsamis 5353 C. Weber 5050 G. Wells
4747 S. Kalkan 5454 V. Kudak 5555 A. Marciniak 5656 W. Ogloza 5757 T. Ozdemir
5858 E. Pakstiene 5959 V. Perig 5555 M. Zejmo 6060

(Received / Accepted )

###### Abstract

Context. Within our international program to obtain accurate physical
properties of trans-Neptunian objects (TNOs) we predicted a stellar
occultation by the TNO (38628) Huya of the star Gaia DR2 4352760586390566400
(mG = 11.5 mag.) for March 18, 2019. After an extensive observational campaign
to obtain astrometric data we updated the prediction and it turned out to be
favorable to central Europe. Therefore, we mobilized half a hundred of
professional and amateur astronomers in this region and the occultation was
finally detected from 21 telescopes located at 18 sites in Europe and Asia.
This makes the Huya event one of the best ever observed stellar occultation by
a TNO in terms of the number of chords.

Aims. The aim of our work is to determine accurate size, shape and geometric
albedo of the TNO (38628) Huya by using the observations obtained from a
multi-chord stellar occultation. We also aim at providing constraints on the
density and other internal properties of this TNO.

Methods. The 21 positive detections of the occultation by Huya allowed us to
obtain well-separated chords which permitted us to fit an ellipse for the limb
of the body at the moment of the occultation (i.e., the instantaneous limb)
with kilometric accuracy.

Results. The projected semi-major and minor axes of the best ellipse fit
obtained using the occultation data are (a′, b′) = (217.6 $\pm$ 3.5 km , 194.1
$\pm$ 6.1 km) with a position angle of the minor axis P′ = 55.2${}^{\circ}\pm$
9.1. From this fit, the projected area-equivalent diameter is of 411.0 $\pm$
7.3 km. This diameter is compatible with the equivalent diameter for Huya
obtained from radiometric techniques (D = 406 $\pm$ 16 km). From this
instantaneous limb, we obtained the geometric albedo for Huya ($p_{V}=0.079\pm
0.004$) and we explored possible three-dimensional shapes and constraints to
the mass density for this TNO. We did not detect the satellite of Huya through
this occultation, but the presence of rings or debris around Huya is
constrained using the occultation data. We also derived an upper limit for a
putative Pluto-like global atmosphere of about $p_{\rm surf}$ = 10 nbar.

Conclusions.

###### Key Words.:

Kuiper belt objects: individual: Huya – Methods: observational – Techniques:
photometric

††offprints: P. Santos-Sanz<EMAIL_ADDRESS>
##  1 Introduction

The stellar occultation technique is a very direct way to obtain highly
accurate sizes, derive albedos, and, in some cases, even densities and 3D
shapes for TNOs (e.g. Sicardy et al. 2011; Ortiz et al. 2012, 2017).
Atmospheres and satellites can also be detected and characterized by means of
stellar occultations (Sicardy et al. 2006; Meza et al. 2019). Very fine
details, undetectable by any other ground-based technique, can also be
detected using stellar occultations, such as the rings detected around the
centaurs Chariklo (Braga-Ribas et al. 2014) and Chiron (Ortiz et al. 2015;
Ruprecht et al. 2015) and around the dwarf planet Haumea (Ortiz et al. 2017).
These discoveries have opened a new way of research within the planetary
sciences of the distant solar system bodies (Sicardy et al. 2019a, b). All of
the above points out that the stellar occultation technique is a very powerful
means to obtain information about the physical properties of TNOs.

From October 2009, when the first stellar occultation by a TNO, apart from
Pluto, was recorded (Elliot et al. 2010), to date, about 77 stellar
occultations produced by 33 different TNOs, excluding the one presented here,
have been detected. About 50 of these occultations have been detected from
only one or two different locations which did not allow us to obtain the
projected shape and size of the body. In these cases, it is always possible to
derive astrometric positions with very low uncertainties for the TNO that can
be used to improve their ephemerides (Rommel et al. 2020). To be able to fit
the five parameters of an ellipse, at least three different observations are
needed, otherwise, the problem is degenerate. The remaining 22 occultations
(produced by 15 different TNOs) of the total of 77, were detected from more
than two locations (i.e., multi-chord occultations) which allowed us to
properly characterize their shapes and to derive very interesting and accurate
physical properties. This means that we have only obtained a good physical
characterization using stellar occultations of about 15 TNOs, excluding Huya
(see e.g. Elliot et al. 2010; Sicardy et al. 2011; Ortiz et al. 2012, 2017,
2020a; Braga-Ribas et al. 2013; Benedetti-Rossi et al. 2016, 2019; Dias-
Oliveira et al. 2017; Souami et al. 2020, and references therein).

The stellar occultation by the TNO (38628) Huya presented here is the best
ever stellar occultation by a TNO in terms of the number of chords obtained so
far, excluding Pluto and the recent occultation by the TNO (307261) 2002 MS4
on August 8, 2020 (Rommel et al. in prep). It is also the first multi-chord
occultation reported for Huya.

The TNO (38628) Huya was discovered on March 10, 2000 from the ‘Llano del Hato
National Astronomical Observatory’ in Mérida (Venezuela) by astronomers of the
Quasar Equatorial Survey Team (QUEST, Ferrin et al. 2001). Huya is classified
as a plutino (i.e. it is in the 2:3 mean motion orbital resonance, MMR, with
Neptune) and it is among the group of the $\sim$ 100 largest known TNOs, in
fact, it is one of the biggest plutinos together with (119951) 2002 KX14,
(84922) 2003 VS2, and (208996) 2003 AZ84.

Infrared spectra of Huya appears moderately red and featureless with a lack of
signatures of water ice and other volatiles (Jewitt & Luu 2001; de Bergh et
al. 2004; Fornasier et al. 2013), however other infrared spectra show faint
signs of water ice (Barucci et al. 2011; Merlin et al. 2017). This points out
to a surface covered with a thick and red layer of dark organic compounds
which would be homogeneously covered with trace amounts of water ice.
Aqueously altered silicate minerals have also been proposed to explain some
absorption features observed in the near-infrared spectra of Huya (Licandro et
al. 2001; de Bergh et al. 2004). Besides spectra, colors from Spitzer Space
Telescope at 3.6 and 4.5 $\mu$m, have been modeled indicating a surface
composition of 40 $\pm$ 20% H2O, 30 $\pm$ 10% silicates, and 30 $\pm$ 10%
organics (Fernández-Valenzuela et al. 2021).

The rotational period of Huya is not well-determined due to the small peak-to-
peak amplitude of its light curve, but a period of 6.75 $\pm$ 0.01 h was
proposed by Ortiz et al. (2003) based on observations taken in February and
March 2002. According to more recent work by Thirouin et al. (2014), the
period of 6.75 h could be an alias of Huya’s rotation period that they propose
(5.28 h) based on observations obtained from 2010 to 2013. Other alternative
periods cannot be totally ruled out.

Huya has a known satellite provisionally designated as S/2012 (38628) 1,
discovered by a team led by K. Noll in 2012 using images from Hubble Space
Telescope (HST) (Noll et al. 2012). The satellite’s separation distance from
the primary is estimated to be at least 1740 km.

The thermal emission from the Huya’s system has been measured with
Spitzer/MIPS in 2004 and with Herschel/PACS and SPIRE in 2010. From these
thermal data, using HV = 5.04 $\pm$ 0.03 mag, Fornasier et al. (2013) obtained
an area-equivalent diameter for the system of D$\rm{}_{eq}=458\pm 9$ km and a
geometric albedo at V-band of p$\rm{}_{V}=0.083\pm 0.004$. The area-equivalent
diameter of Huya itself (DHuya = 406 $\pm$ 16 km) and its satellite
(D$\rm{}_{Satellite}\sim$ 213 km), assuming the same albedo as Huya, were also
obtained in that work. A summary of the orbital elements and most relevant
physical characteristics of Huya from the literature is shown in Table 1.

In the present work, we analyzed the 21 chords obtained from the stellar
occultation of the star Gaia DR2 4352760586390566400 (mG = 11.5 mag.) produced
on March 18, 2019 by the TNO Huya. This paper is organized as follows. In
Section 2 we describe the observations carried out to predict the occultation
and the observations of the occultation itself. In Section 3 we detail the
analysis of the Huya’s occultation data. In Section 5 the observations
performed to refine the rotational period of Huya in order to determine the
rotational phase at the moment of the occultation are presented. In Section 5
the results obtained from the analysis of the occultation are given and
discussed (i.e. the instantaneous limb fit, the projected diameter, the 3D
shapes, the albedo, the density and the search for material orbiting Huya,
etc). Lastly, our conclusions are presented in Section 6.

Table 1: Orbital and physical parameters of Huya from literature.

Object | a | q | i | e | HV | P |  $\Delta$m | Class. | DHuya | pV | DSatellite
---|---|---|---|---|---|---|---|---|---|---|---
| [AU] | [AU] | [deg] |  | [mag] | [h] | [mag] |  | [km] | [%] |
(38628) Huya | 39.69 | 28.55 | 15.47 | 0.28 | 5.04 $\pm$ 0.03a | 6.75 $\pm$ 0.01b / 5.28 $\pm$ 0.01c |  $<$ 0.1b / 0.02 $\pm$ 0.01c | Plutino | 406 $\pm$ 16a | 0.083 $\pm$ 0.004a |  $\sim$ 213 kma

a: semi-major axis in Astronomical Units (AU), q: perihelion distance in AU,
i: orbital inclination in degrees, and e: eccentricity, from Minor Planet
Center (MPC-IAU) database, May 2021. HV [mag]: absolute magnitude at V-band. P
[h]: preferred single-peaked rotational periods. $\Delta$m [mag]: peak-to-peak
amplitude of the rotational light curves shown in the previous column. Class.:
dynamical classification following Gladman et al. (2008) scheme. DHuya: area-
equivalent diameter of Huya from radiometric technique, pV: geometric albedo
at V-band from radiometric technique, DSatellite: estimated diameter of the
Huya’s satellite from radiometric technique. References: a) Fornasier et al.
(2013); b) Ortiz et al. (2003); c) Thirouin et al. (2014).

##  2 Observations

###  2.1 Predictions

Due to the wealth of information that can be obtained from stellar
occultations by TNOs (e.g. Sicardy et al. 2011; Ortiz et al. 2012, 2017,
2020b, 2020a, and references therein), we have been performing intensive
astrometric and photometric observing campaigns since 2010 with the aim to
predict these events. This observing strategy allows us to derive accurate
predictions (see Ortiz et al. 2020b, for a recent review).

Huya’s orbit and ephemerides were derived using the Numerical Integration of
the Motion of an Asteroid, NIMA (Desmars et al. 2015), a tool developed within
the ERC Lucky Star project111https://lesia.obspm.fr/lucky-star/. Part of the
astrometric data of Huya used to feed NIMA were obtained with the 1.6-m
telescope at Observatório Pico dos Dias (OPD) in Brazil on June 3, 2017 and
July 8, 17, 2018. This telescope was equipped with an Andor IKon-L camera
(2048 $\times$ 2048 pixels, field of view -FOV- = 6.1 $\times$ 6.1 arcmin,
Resolution = 0.18 arcsec/pixel) and I-Johnson filter. In the course of these
campaigns we found that the TNO (38628) Huya would occult a V = 11.7 mag star
(Gaia DR2 4352760586390566400, mG = 11.5 mag) on March 18, 2019.

Around five months before the event, we refined the original NIMA’s prediction
using more astrometric data, as well as data available in the Minor Planet
Center database222https://www.minorplanetcenter.net/db-search. Near the
occultation date, we refined again the prediction using images of Huya
acquired with the 1.5-m telescope in Sierra Nevada Observatory (OSN) in
Granada, Spain. This observing run was performed on March 2, 3, 8, 10, and 11,
2019, around two weeks before the occultation event, with the 2k $\times$ 2k
Andor IKON-L camera. 109 images were obtained in 2 $\times$ 2 binning mode at
moon illumination $<20\%$. The detailed setup of these observations, including
weather conditions and other related information, is shown in Table 2. Bias
and sky flat-field frames were taken each night to calibrate the images.

Table 2: Summary of the ‘last minute’ astrometric observing campaign.

Telescope | Date | CCD | Scale | FOV | Filter | Exp. | N | Seeing | SNR | 1$\sigma$(RA) | 1$\sigma$(Dec) | Offset(RA) | Offset(Dec)
---|---|---|---|---|---|---|---|---|---|---|---|---|---
OSN 1.5-m | March 2,3,8,10,11, 2019 | 2k $\times$ 2k | 0.46′′/pix | 7.5′ $\times$ 7.5′ | R-Johnson | 400 s | 109 | 1.6” | 45 | 8 mas | 8 mas | 149 mas | -92 mas

Telescope is the telescope used during the observing run. Date are the
observing dates. CCD is the size of the Andor IKON-L detector. Scale is the
binned image scale of the instrument. FOV is the field of view of the
instrument. Filter is the filter used. Exp. is the exposure time of the
individual images. N is the total number of images. Seeing is the average
seeing during the observing runs. SNR is the signal to noise ratio of the
object. 1$\sigma$(RA) is the average 1$\sigma$ uncertainty in right ascension
(RA) of the astrometry in milliarcseconds (mas). 1$\sigma$(Dec) is the average
1$\sigma$ uncertainty in declination (Dec) of the astrometry in mas. The
Offset(RA) and Offset(DEC) are the offsets for right ascension and declination
with respect to the JPL#28 orbit expressed in mas.

The images obtained during the OSN observing campaign were astrometrically
solved using Gaia DR2 (Gaia Collaboration et al. 2016, 2018), which was the
most precise astrometric catalog available when this occultation happened. The
prediction was obtained using the coordinates of the occulted star (Gaia DR2
4352760586390566400) propagated to the occultation epoch using the Gaia DR2
proper motions and parallax, and the relative astrometry (offsets) of Huya
with respect to the Jet Propulsion Laboratory orbit JPL#28. The average
1$\sigma$ astrometric uncertainties obtained and the offsets with respect to
the orbit JPL#28 are shown in Table 2. These uncertainties translate to
1$\sigma$ uncertainties of 165 km projected on Earth surface (cross-track) and
20 s in time (along-track). The final prediction map obtained is shown in
Figure 1. Note that the center line of the shadow path of this final
prediction is $\sim$ 3000 km east of the prediction based only on the JPL#28
orbit of Huya and the Gaia DR2 position of the star, and $\sim$ 1900 km west
of the prediction obtained about five months before the event. The width of
the shadow path in this Figure is assumed to be the diameter of Huya derived
from Herschel and Spitzer thermal data (D = 406 km, according to Fornasier et
al. 2013). The real shadow path of the occultation was $\sim$ 78 km west of
the final prediction (see Figure 3) but within the estimated uncertainties.

As the ‘last minute’ prediction from the OSN telescope (see Table 2) was
favorable to many countries in Europe and involved a bright star, we alerted
our (previously notified) European collaborators emphasizing the importance of
observing this occultation. 21 positive detections from 18 sites
longitudinally distributed and 16 misses were obtained.

Figure 1: Last minute prediction of the occultation using Gaia DR2 star
catalog (Gaia Collaboration et al. 2016, 2018) and relative astrometry of Huya
regarding the occulted star obtained from the 1.5-m telescope in Sierra Nevada
Observatory, Granada, Spain. The green line indicates the centrality of the
shadow path and the blue lines the limits of the shadow assuming an area-
equivalent diameter for Huya of 406 km (Fornasier et al. 2013). The 1$\sigma$
precision along the path is 165 km and the 1$\sigma$ precision in time is 20
s. The arrow in the right bottom shows the direction of the shadow motion. Map
credit: https://www.gpsvisualizer.com/ and Australian Topography
(©Commonwealth of Australia –Geoscience Australia– 2016. Creative Commons
Attribution 4.0 International License).

###  2.2 Stellar Occultation

On March 18, 2019, a total of 49 telescopes located in Europe and Asia
(Israel) were ready to observe the occultation by the TNO Huya. Some of them
were located far from the nominal prediction (e.g. Spain, UK, Eastern Turkey)
to allow the detection of the Huya satellite, possible rings, and also because
we alerted the community of amateur occultation observers through the
‘planoccult’ list. Time series of images or video observations were acquired
with 37 of these telescopes (from the other 12, 8 had bad weather, and 4
suffered technical problems). Video observations were converted to FITS images
prior to their analysis using same procedures and precautions adopted in
Benedetti-Rossi et al. (2016). From 21 of the 37 telescopes, located at 18
different sites, we recorded the occultation of the star produced by Huya.
From 16 of the 37 telescopes the occultation was not detected. All stations
and telescopes that recorded a positive detection plus two very close stations
which missed the occultation (QOS Observatory in Ukraine and Çukurova
University Observatory in Turkey) are listed in Table 4. Basic information
about the 49 telescopes that participated in this campaign and their locations
is shown in the online Table LABEL:SummaryObserv.

Aperture photometry for each data set was obtained, from which we derived the
light curves (flux of the star normalized to the mean value before the
occultation, versus time). The light curves from the 21 positive observations
at 18 sites (see Table 4) showed drops in flux caused by the occultation.
Light curves from the other 16 telescopes that did not detect the occultation
were also obtained and carefully analyzed. We analyzed with special care the
negative detection at QOS Observatory in Zalistci (Ukraine), which was the
closest to the shadow path. This closer non detection can notably constrain
the projected shape edge of Huya (see Figure 3 and Table 4).

Figure 2: One of the images of the occultation obtained from the Astronomical
Observatory Cluj-Napoca in Romania (see Table 4 for details). The source
marked with 1 corresponds to the occulted star plus Huya before the beginning
of the occultation. The other marked sources were used as reference stars. The
FOV of the image is 20 $\times$ 13 arcmin, north is up and east is to the
left.

The time in all the observing sites was synchronized via Network Time Protocol
servers (NTP) or GPS-based Video Time inserters (VTI). Each image header
includes the acquisition time. Most of the series of images were obtained with
around 10-15 minutes before the predicted occultation time up to around 10-15
minutes after the event. This strategy allows us to have a good
characterization of the photometric baseline and to probe the surroundings of
the object (i.e. the presence or not of satellites, rings or other orbiting
material). No filters were used in any of the telescopes in order to maximize
the signal to noise ratio (SNR) of the occulted star with the aim to obtain
the best possible photometric data.

The light curves of the occultation were obtained using our own IDL
(Interactive Data Language) codes based on DAOPHOT routines and using the
PRAIA photometry tool (Assafin et al. 2011), after the usual dark, bias, and
flat-field corrections when calibration images were available. Then, the
relative photometry of the occulted star was obtained on the images using the
stars present in the FOV as comparison stars with the aim of minimizing flux
variations due to atmospheric transparency fluctuations and to different
seeing conditions. We used as many reference stars as possible from 3 to
$\sim$ 25 depending on the FOV (see Fig. 2). In some cases, the observers only
read a Region of Interest (RoI) of the detector to minimize the readout time,
in these cases, the FOV was smaller (i.e., a less number of reference stars)
than the FOV from other telescopes. We did not use the same reference stars
for different data sets, as the number of stars within the FOV was different
from telescope to telescope. In the end, the flux of the occulted star is
compared to an ensemble mean of all the selected reference stars. The chosen
aperture diameters, starting with diameters around the full width at half
maximum (FWHM), minimized the flux dispersion of the occulted star before and
after the occultation.

It is important to note that the flux of the occulted star obtained during the
occultation is the combination of the flux of the star and the flux of Huya,
although in this case, the flux of Huya has a very small contribution ($\sim$
0.07 %) to the total flux due to the brightness of the occulted star. Finally,
the light curve (i.e. the combined flux of the occulted star and Huya versus
time) was obtained for each data set. The light curves obtained from the 21
telescopes that detected the occultation show deep dimmings in flux at the
expected occultation times (Figure 4). Detailed information about the sites,
telescopes, detectors, exposure times, observers, and light curves dispersion,
from which the occultation was detected is shown in Table 4. This Table also
includes information about the two stations closest to the shadow path that
reported a negative detection (QOS Observatory in Ukraine and Çukurova
University Observatory in Turkey). More details and complementary information
on the analysis of these occultation light curves are given in Section 3.

Figure 3: Map of post-occultation shadow path of the stellar occultation by
Huya, the path width (limited by the blue lines) is the area-equivalent
diameter obtained from the reconstructed ellipse fit (D = 411.3 km, see
Section 5.1). The site positions from where the occultation was recorded are
shown with green marks, the negative detections with red marks, and the sites
that did not observe due to bad weather or to technical problems are indicated
with white marks. The green line indicates the centrality of the shadow path
and the blue lines the limits of the shadow. The arrow in the right bottom
shows the direction of the shadow motion. Map credit:
https://www.gpsvisualizer.com/ and Australian Topography (©Commonwealth of
Australia –Geoscience Australia– 2016. Creative Commons Attribution 4.0
International License).

##  3 Analysis of the Stellar Occultation by Huya

The TNO (38628) Huya occulted the mG= 11.5 mag star Gaia DR2
4352760586390566400 on March 18, 2019 at $\sim$ 00:53 UTC. The typical
sampling times were greater than 0.2 seconds (i.e., $\geq$ 1.61 km in the body
plane of Huya), this means that our data are dominated by the exposure times
rather than by the Fresnel diffraction effects ($\simeq$ 1.13 km) or the
stellar diameter ($\simeq$ 0.70 km at Huya’s distance). The Fresnel scale
value of F = $\sqrt{\lambda d/2}$ = 1.13 km is obtained from the geocentric
distance of Huya during the occultation (d = 28.3500 AU) and the average
central wavelength of the observations ($\lambda$ = 600 nm). To estimate the
angular diameter of the occulted star we use its V (11.751 mag) and K (10.294
mag) apparent magnitudes from the NOMAD catalog (Zacharias et al. 2004) and
the van Belle (1999) equation for main sequence stars, obtaining a diameter of
$\simeq$ 0.0342 mas ($\simeq$ 0.70 km at Huya’s distance). Table 3 summarizes
the occulted star details and other related information.

Table 3: Details of the occulted star and other occultation related
information.

Designation |  Gaia DR2 4352760586390566400
---|---
Coordinates DR2a |  $\alpha$ = 16h 41m 06s.4260, $\delta$ = -06∘ 43’ 34”.5756
Star position errorsb | errRA = 0.1474 mas, errDec = 0.1143 mas
Proper motions & Parallaxc | pmRA = -4.506 $\pm$ 0.090 mas yr-1, pmDec = -14.340 $\pm$ 0.055 mas yr-1, Plx = 1.5717 $\pm$ 0.0478 mas
Magnitudesd | B = 12.296, V = 11.751, R = 11.380, J = 10.541, H = 10.384, K = 10.294, G= 11.538
Star Diametere |  $\sim$ 0.0342 $\pm$ 0.0014 mas ($\sim$ 0.70 $\pm$ 0.03 km at Huya’s distance)
Fresnelf | 1.13 km
Exposure time effectg | 1.61 km
Velocityh | 8.07 km/s

  * aGaia DR2 coordinates propagated to the occultation epoch (2019.211) using the proper motions and parallax.

  * b errRA and errDEc are the errors in RA and Dec from the Gaia DR2 catalog propagated to the occultation epoch using the formalism by Butkevich & Lindegren (2014). This formalism has been applied using the SORA tool (Gomes-Júnior et al. 2022)

  * c pmRA and pmDec are the proper motions in RA and Dec and respective errors, Plx is the absolute stellar parallax with error.

  * dB, V, R, J, H and K from the NOMAD catalog (Zacharias et al. 2004). G from the Gaia DR2 catalog (Gaia Collaboration et al. 2018).

  * eSize estimated using V and K magnitudes and the van Belle (1999) equation for a main sequence star.

  * fFresnel diffraction effect: F = $\sqrt{\lambda d/2}$, with d = 28.3500 AU at the occultation moment and $\lambda$ = 600 nm.

  * gSmallest exposure time from the positive detections multiplied by the event shadow velocity.

  * hVelocity of Huya with respect to the star as seen from Earth.

The light curves obtained from the stellar occultation (see Figure 4) are used
to derive the times of disappearance (‘ingress’ time) and reappearance
(‘egress’ time) of the star behind the Huya’s limb. These ingress and egress
times can be directly translated to distances in the plane of the sky using
the apparent motion of Huya relative to the occulted star, which is 8.07 km/s
for this occultation (see Table 3). The derived segments in the plane of the
sky are known as ‘chords’. From these chords we can obtain the physical
properties described in Section 5. The times of disappearance and reappearance
and their uncertainties at each site are obtained creating a synthetic light
curve by using a square-well model convolved with the Fresnel scale, the star
apparent size and the exposure time (Elliot et al. 1984; Roques et al. 1987).
The parameters fitted are the ingress and egress times and the depth of the
occultation. The difference between the data and the synthetic light curve is
iteratively minimized using a $\chi^{2}$ metric. This technique is described
in detail in Ortiz et al. (2017) and Benedetti-Rossi et al. (2019) and
references therein.

The ingress and egress times and their associated uncertainties obtained in
this way are shown in Table 6. These times determined 20 chords of different
sizes in the plane of the sky also included in Table 6. Due to a CCD camera
failure the ROASTERR-1 Observatory (Romania) missed the ingress. As a
consequence only the egress time is considered for this observatory (see light
curve #4 in Figure 4). At the end, 19 chords obtained from the 21 telescopes
that detected the occultation in Table 4 were used to obtain the results
described in Section 5:

  * •

The chord from the Amateur Observatory-3 in Romania (AO-3) is not used because
the absolute time information of this chord was missed, there was no timestamp
in images and no time in image headers, this means that we only have relative
timing. We used reference time for the first frame as 00:00:00.0 UTC and
derive the chord size with its associated error bars.

  * •

The light curves obtained from Galați Observatory-1 and Galați Observatory-2
in Romania were obtained at the same site with the same integration time, so
we merged the two data sets in order to have a single light curve and chord
(#18) with more data with the star occulted.

Figure 4: Stellar occultation light curves (normalized flux versus time) from
the 21 positive detections, as presented in Table 4. Each individual
measurement is indicated with a dot, these measurements have been connected
with a solid line for clarity. The light curves are shifted in flux for a
better viewing and are presented from top to bottom with respect to their
distance to the center of the predicted shadow path, West to East. Flux
uncertainties are not shown in order to avoid an unreadable plot (the standard
deviation of the measurements are indicated in Table 4). The chord #18 is the
combination of 2 light curves obtained from the same site (Galați Observatory,
Romania) with 2 telescopes of 40-cm and 20-cm, respectively. The light curve
in red (AO-3) was not used to obtain the limb fit, it has been shifted in time
to properly appear in this plot because the time information of this chord was
missed.

##  4 Rotational light curve of Huya

To obtain the rotational phase of Huya at the moment of the occultation, we
used the already published photometry of 299 images acquired in 2010-2013 with
the 1.5-m OSN telescope in Granada (Spain) and with the 1.23-m telescope at
Calar Alto Observatory in Almería (Spain), see Thirouin et al. (2014) for
further details about these observations. We merged these data with 116 new
images of Huya acquired on 8 nights on July 1-4 and August 1-4 ($\sim$ 3-4 h
of observation each night), 2019 with the 1.5-m OSN telescope with integration
times of 400 seconds, binning 2 $\times$ 2 and no filter in order to achieve
the highest SNR.

Standard bias and flat field corrections were applied on all the images before
the extraction of the fluxes of the object and of the selected comparison
stars by means of aperture photometry technique. To perform this task we used
specific routines coded in IDL, trying different values for the apertures
(starting with apertures around the FWHM) and sky ring annulus for the object
and the same values for the comparison stars in order to maximize the SNR of
the object and to minimize the dispersion of the photometry. When possible, we
choose the same set of comparison stars for all nights within the observing
run to minimize systematic photometric errors. The data processing used was
the same as that described in detail in e.g. Fernández-Valenzuela et al.
(2016).

The final product obtained is the flux of Huya respect to the comparison stars
versus time (corrected for light travel times). A Lomb-Scargle technique (Lomb
1976) is applied to these time series data in order to obtain the rotational
period of Huya. The rotation period with the highest spectral power obtained
from the Lomb-Scargle periodogram is 6.725 $\pm$ 0.006 h (Figure 5), which is
compatible with other published rotation periods (e.g. Ortiz et al. 2003;
Thirouin et al. 2014). Aliases of this period, like e.g. $\sim$ 5.2 h or
$\sim$ 4.3 h, cannot be excluded as is shown in the bottom panel of Figure 5.

This updated rotational light curve allows us to determine the rotational
phase at the moment of the occultation and it turns out that Huya was near one
of its absolute brightness minima at the time of the March 18, 2019
occultation. This means that the TNO occulted the star when its apparent
surface area was near its minimum. The rotational light curve in the upper
panel of Figure 5 is fitted with a Fourier function in order to derive the
peak-to-peak amplitude of the light curve, which results to be of 0.031 $\pm$
0.005 mag. This amplitude is slightly larger than the previously published
amplitudes (Ortiz et al. 2003; Thirouin et al. 2014). The zero rotational
phase in the upper panel of Figure 5 was chosen to be the moment of the
stellar occultation (i.e. March 18, 2019 00:54:00 UTC).

Alternatively, the very shallow rotational light curve obtained could be
directly related to the rotation of the satellite of Huya, as it is suspected
to be the case for the TNO 2002 TC302 (Ortiz et al. 2020a). If Huya’s
satellite has a very irregular shape, it could cause a shape-driven light
curve which would dominate the rotational light curve of the system, this
would also be consistent with a very round shape for Huya (Maclaurin
spheroid). On the other hand, a rotational period of 6.725 h would indeed be a
weird period for a satellite, because a rotation period synchronized with its
orbital period is expected, which would be of days, not of hours. However, we
know that Haumea’s largest satellite, Hi’iaka, has a much faster rotation
period ($\sim$ 9.8 h) than its orbital period ($\sim$ 49.5 days) according to
Hastings et al. (2016). A binary system with a mass ratio of the satellite to
the main body similar to the Huya system is Varda-Ilmarë (mass ratio $\sim$
9%). In this system, it is likely that the rotation of the main body, Varda,
is not synchronized with the mutual orbital period. This can be explained by
the fact that the estimated time scale for synchronization is longer than the
age of the solar system (Grundy et al. 2015). Similar calculations can be
performed when the orbit of the Huya’s satellite becomes available, which will
shed light on whether or not its rotation is synchronized with its orbital
period, and whether this potential lack of synchronization is common in TNO
satellites.

Figure 5: Top panel: Rotational light curve (relative magnitude vs. rotational
phase) of Huya obtained from the data described in Section 4. The data have
been folded with a rotational period of 6.725 h. The zero rotational phase in
the plot is fixed close to the moment of the occultation (March 18, 2019
00:54:00 UTC). Bottom panel: Lomb periodogram showing the rotational period P
= 6.725 h, which corresponds to the peak with the highest spectral power. The
two other aliases at high spectral power correspond to other possible
rotational periods of Huya: P $\sim$ 5.2 h and P $\sim$ 4.3 h.

##  5 Results

The obtained physical properties of Huya, namely, its projected shape, the
size, the geometric albedo, and the 3D shape are shown in sections 5.1 and
5.2. These were determined from the chords presented in the previous section.
In Section 5.3 the environment around Huya is characterized and possible rings
or debris orbiting this plutino are constrained. Finally, in Section 5.4 we
constrain a putative Huya’s atmosphere.

###  5.1 Projected shape, diameter and albedo of Huya

From the 19 chords numbered in Table 6, we have 37 chord extremities that can
be used to obtain the projected shape (i.e. the instantaneous limb) of Huya at
the moment of the occultation. These extremities give the position ($f$, $g$)
of the star projected in the sky plane of the body and relative to the center
of the object. $f$ and $g$ are counted positively toward local celestial east
and celestial north, respectively, and are measured in kilometers (see, e.g.,
Benedetti-Rossi et al. 2019). Note that we have 37 instead of 38 extremities
because we discard the ingress time of the ROASTERR-1 Observatory in Romania
(chord #4), which was missed due to a CCD camera failure. The closest negative
chord from QOS Observatory in Ukraine is also used to constrain the limb. We
fitted an ellipse to these 37 points as described below.

The best-fitting ellipse was obtained through a $\chi^{2}$ minimization method
applied to the 37 chord extremities. The function to minimize is
$\chi^{2}=\sum_{i=1}^{37}(r_{i,\rm obs}-r_{i,\rm com})^{2}/\sigma^{2}_{i,\rm
r}$, where r is the radius from the center of the ellipse ($f_{\rm c}$ ,
$g_{\rm c}$), the subscripts “obs” and “com” means observed and computed
respectively and $\sigma_{i,\rm r}$ are the errors on the extremities
determination. What we finally obtain from this fit are the apparent or
projected semi-axes of the ellipse (a′ , b′), the center of the ellipse
($f_{\rm c}$ , $g_{\rm c}$) and the position angle of the minor axis of the
ellipse (P′), i.e. the apparent position angle of the pole measured eastward
from celestial north. Since the ellipse fit is not linear in the parameters,
an estimate of the error in the parameters using a $\chi^{2}$ minimization
technique may result in an underestimation of the errors. Therefore, we
estimated the uncertainties in the five parameters of the fitted ellipse using
a Monte Carlo approach, as done in Santos-Sanz et al. (2021). We randomly
generated the 37 chord extremities $10^{4}$ times, meeting the requirements
provided by their corresponding uncertainties. For each one of these sets of
randomly generated extremities, we obtained the best-fitting ellipse in terms
of a minimization of the sum of squared residuals $\sum_{i=1}^{37}(r_{i,\rm
obs}-r_{i,\rm com})^{2}$, where $r_{i,\rm obs}$ and $r_{i,\rm com}$ are the
same as described above. In the end, we had $10^{4}$ best-fitting ellipses to
the 37 randomly obtained extremities (i.e. $10^{4}$ possible values of the
five parameters that determine an ellipse: a′, b′, $f_{\rm c}$, $g_{\rm c}$,
and P′). From these parameter distributions, we obtained the 1$\sigma$
uncertainty in each parameter as the standard deviation of the corresponding
distribution (see Table 7 and Figure 6).

The parameters and uncertainties obtained for the best-fitting ellipse as
explained above were ($f_{\rm c}$ , $g_{\rm c}$) = (2984.7 $\pm$ 3.2 km ,
-1850.9 $\pm$ 1.7 km), (a′ , b′) = (217.6 $\pm$ 3.5 km , 194.1 $\pm$ 6.1 km)
and P′ = 55.2${}^{\circ}\pm$ 9.1. The axes ratio of this ellipse is small and
close to 1.0 (a′/b′ = 1.12 $\pm$ 0.05) which indicates that Huya is a very
round object, as is shown in Figure 6 where the 19 chords (only egress for
chord #4) and their uncertainties obtained from the occultation are plotted in
the plane of the sky together with the best-fitting ellipse to their
extremities. Note that the center obtained from the elliptical fit ($f_{\rm
c}$ , $g_{\rm c}$) provides the offsets with respect to the positions of Huya
obtained using the Jet Propulsion Laboratory orbit JPL#28 + Development
Ephemeris model DE431, assuming that the Gaia DR2 occulted star position is
correct. As shown in Figure 6, the centers of the chords were not well aligned
and their extremities were not always well fitted by the best-fitting ellipse.
On the other hand, an ellipse would be the expected projected shape for Huya
considering that an icy body with its size should have adopted a regular
equilibrium figure with only minor irregularities due to topography (see
discussion in Section 5.2). If this is true, the chords centers must be
aligned (see, e.g. Braga-Ribas et al. 2013; Santos-Sanz et al. 2021). For
completeness, and to check if this solution is very different from the
original one we slightly shift the chords by performing a linear fit to the
centers of the chords and looking for the ellipse that best fits these chords.
The semi-axes obtained for the best-fitting ellipse to the shifted chords were
(a′ , b′) = (220.2 $\pm$ 4.3 km , 197.4 $\pm$ 6.1 km), which differ by less
than 2% concerning the unshifted solution. Since both solutions, the original
and the shifted one, are virtually the same, we decided to use the best-
fitting ellipse to the original (unshifted) chords as the best solution since
in the latter no a priori assumption is made about the centers of the chords.

From the limb fit to the original chords we derived an area-equivalent
diameter of Huya at the moment of the occultation of $D_{eq}$ = 411.0 $\pm$
7.3 km. If Huya is a triaxial body this diameter is a lower limit of the total
area-equivalent diameter of this plutino because, as shown in Section 4, Huya
was very close to its absolute brightness minimum at the moment of the
occultation, i.e. its projected area was very close to its minimum. If Huya is
an oblate Maclaurin-like body this diameter will be the real projected
diameter, and the rotational light curve should be due, in this case, to
albedo variations in the surface. Anyway, this diameter is smaller than the
radiometric area-equivalent diameter obtained using Herschel (PACS and SPIRE)
and Spitzer (MIPS) measurements: $D_{eq}$ = 458 $\pm$ 9.2 km (Fornasier et al.
2013).

However, to do a proper comparison of the occultation and radiometric
diameters we have to take into account that the radiometric diameter includes
the thermal flux of Huya and its satellite since neither Herschel Space
Observatory nor Spitzer Space Telescope can resolve the Huya’s system.
Fornasier et al. (2013) did an estimation of the equivalent size of the main
body and the satellite from radiometric models (assuming same geometric albedo
for both bodies) obtaining $D_{\rm Main}$ = 406 $\pm$ 16 km and $D_{\rm
Satellite}$ = 213 $\pm$ 30 km. This means that the area-equivalent diameter of
Huya obtained from the occultation is slightly bigger (411.0 km) than the
radiometric-derived one (406 km), but both diameters are fully compatible
within their error bars. This underestimation in the radiometric diameters has
been noted for other TNOs when properly comparing occultation diameters with
radiometric ones (Ortiz et al. 2020a, b).

Figure 6: Best-fitting ellipse (in black) to the 19 chords presented in Table
6 (for chord #4 only egress time is used). The fitted ellipse determines the
projected shape of Huya at the moment of the occultation and has axes of 435.2
$\pm$ 7.0 km $\times$ 388.2 $\pm$ 12.2 km. The gray ellipses are the best-
fitting ellipses to the $10^{4}$ randomly generated chord extremities (see
Section 5.1 for details). The black dots are the centers of the chords, and
the gray line crossing all the chords is a weighted linear fit to these dots.
The black solid lines in the extremities of the chords are the 1$\sigma$
uncertainties of the ingress/egress times. The red arrow shows the direction
of the shadow motion. The chord numbers are the same as those used in Tables 4
and 6 and Figure 4. The negative detection at QOS Observatory in Ukraine
(light gray line at the left of the ellipse) helps to constrain the limb fit.

From the best-fitting ellipse we derived the geometric albedo at V-band of the
Huya’s surface at the moment of the occultation by means of the equation
(Sicardy et al. 2011):

$p_{V}=10^{0.4(V_{sun}-H_{\rm V})}/(A/\pi)$ (1)

, where $V_{sun}$ is the V-magnitude of the Sun ($V_{sun}$ = -26.74 mag),
$H_{\rm V}$ is the absolute magnitude of Huya at V-band, and $A$ is the
projected area of the TNO (expressed in AU2) directly obtained from the
occultation limb fit.

It is important to highlight that the absolute magnitude provided for Huya in
the literature is that of the Huya’s system (i.e., the combined magnitude of
Huya and its satellite). To obtain the absolute magnitude of Huya itself we
used the difference in optical magnitude between Huya and its satellite
measured by Noll et al. (2012) which is of $\sim$ 1.4 mag. Using this
difference, and assuming $H_{\rm V}$ = 5.04 $\pm$ 0.03 mag for the Huya’s
system from Fornasier et al. (2013), we obtained an absolute magnitude of
$H_{\rm V}$ = 5.31 mag for Huya. Finally, to obtain the albedo, we have to
correct this $H_{\rm V}$ taking into account the rotational phase at the
moment of the occultation. The object was close to its minimum projected area
during the occultation (Section 4) this means that we should add $\Delta m/2$
= 0.031/2 mag = 0.016 mag to $H_{\rm V}$ to derive the absolute magnitude of
Huya at the moment of the occultation, obtaining $H_{\rm V}$ = 5.326 mag.
Using the latter $H_{\rm V}$ we obtained a geometric albedo of $p_{\rm V}$ =
0.079 $\pm$ 0.004 for Huya. This albedo is smaller than the albedo derived
from the radiometric method using Herschel and Spitzer thermal data ($p_{\rm
V}=0.083\pm 0.004$, from Fornasier et al. 2013), but the radiometric albedo
was computed for the Huya’s system.

###  5.2 Three-dimensional shape models for Huya

In what follows, we have assumed fluid-like behavior for Huya, as is commonly
done for TNOs (see, e.g., Thirouin et al. 2010; Duffard et al. 2009), and have
used the Chandrasekhar formalism (Chandrasekhar 1987) to obtain possible
Maclaurin or Jacobi equilibrium shapes for this TNO.

In general, TNOs with shallow rotational light curves ($\Delta$m $\leq$ 0.15
mag) are associated with Maclaurin-like shapes (Sheppard & Jewitt 2002; Ortiz
et al. 2003; Duffard et al. 2009). In this case, the variability is produced
by albedo marks on the surface of the object, and the rotational light curves
will be single-peaked. For larger peak-to-peak amplitudes ($\Delta$m $>$ 0.15
mag) a Jacobi ellipsoid shape is expected. In this case, the rotational light
curve is shape-driven, presenting a double-peaked shape. We believe that most
($\sim$ 75%) of the large TNOs (D $>$ 300 km) have Maclaurin spheroid shapes,
rather than triaxial ellipsoid shapes (Duffard et al. 2009).

According to Tancredi & Favre (2008), Huya has enough size to reach
hydrostatic equilibrium. We also know from the statistics of rotational
periods and amplitudes of TNOs, most of which are the size of Huya or even
smaller, that hydrostatic equilibrium shapes reproduce that statistic well
(see, e.g, Duffard et al. 2009). This is a clear indication that not only Huya
but also other smaller TNOs seem to be compatible with hydrostatic
equilibrium. One of the reasons could be that the mechanical properties of the
internal material are probably weaker than those of water ice, perhaps due to
porosity or other effects (see, e.g, Thirouin et al. 2010). Then, under this
equilibrium assumption, a Maclaurin spheroid with semi-axes a, b, and c (a = b
$>$ c, where c is the rotation axis) is the most likely three-dimensional
shape for this TNO, taking into account the single-peaked and shallow
($\Delta$m = 0.031 mag) rotational light curve presented by this body (see
Section 4 and Figure 5). Therefore, we explore possible Maclaurin shapes
compatible with the rotational light curve and with the results obtained from
the occultation. According to Bierson & Nimmo (2019) and from Figure 3 in
Grundy et al. (2019) the expected density for a TNO with D $\sim$ 410 km is
$\rho$ $<$ 800 kg/m3. A Maclaurin spheroid with this density rotating with a
period of 6.725 h (i.e., the preferred one discussed in Section 4) would have
semi-axis ratios a/c = b/c = 1.87. The aspect angle333We consider that the
aspect angle is 0∘ if the object is in a pole-on geometry and 90∘ for an
equator-on geometry. needed to obtain, from this Maclaurin, the projected
axial ratio obtained from the occultation (a′/b′ = 1.12) is 32∘, which is a
very small aspect angle. Note that for a random distribution of spin axes, the
most likely aspect angle is 60∘ and the typical probability density
distribution goes with the sine of the aspect angle. The likelihood of aspect
angles 32∘ or smaller is $\sim$ 15%. This probability is not too small, but it
means it is not very likely.

If Huya’s satellite is in the equatorial plane, the tilt angle of the orbit
will allow us to determine the aspect angle. Huya’s satellite orbit is not
available yet although it should be ready soon (Grundy private communication).
However, with the data we currently have, a Maclaurin spheroid with $\rho\sim$
800 kg/m3 compatible with the occultation and with the preferred rotational
period (P = 6.725 h) would have axes: 2a = 435 km, 2b = 435 km, 2c = 233 km,
for an aspect angle of 32∘. For the other possible and shorter rotation
periods (P $\sim$ 5.2 h and P $\sim$ 4.3 h) the aspect angle should be even
smaller ($<30^{\circ}$), which is more unlikely (probability $\sim$ 13%).

Alternatively, we can assume that the rotational light curve of Huya is
produced by a rotating triaxial ellipsoid (i.e. a Jacobi ellipsoid) with semi-
axes a, b and c (a $>$ b $>$ c, with c the axis of rotation). The minimum
density expected for a Jacobi ellipsoid rotating with P = 6.725 h is $\rho$ =
859 kg/m3. The aspect angles compatible with the occultation (a′/b′ = 1.12)
and with the rotational light curve ($\Delta$m $<$ 0.031 mag) span from 31∘ to
43∘. For these aspect angles, a family of Jacobi solutions rotating at 6.725 h
with $\rho_{\rm min}$ = 859 kg/m3 is possible: 2a = [440-455] km, 2b =
[428-442] km, 2c = [253-261] km. On the other hand, the minimum density
required for a Jacobi rotating with P $\sim$ 5.2 h is $\rho$ = 1440 kg/m3, a
very large density for a body of the Huya’s size. A Jacobi ellipsoid rotating
with P $\sim$ 4.3 h would require an even larger and unlikely minimum density
($\rho$ = 2100 kg/m3).

An alternative three-dimensional shape solution to a Maclaurin (close to pole-
on) or Jacobi (with too high densities) shapes invokes non-hydrostatic
equilibrium shapes, via granular media or differentiation (the latter unlikely
for Huya’s size) which would not need so high densities. The exploration of
these non-hydrostatic solutions is out of the scope of this paper.

###  5.3 Probing Huya’s environment

We did not detect secondary drops below the 3$\sigma$ level of noise in the
positive occultation light curves related to the satellite or possible rings
around Huya (Figure 4). Secondary drops below the 3$\sigma$ level were also
not detected in the negative light curves. We can constrain the presence of
rings (or debris) around Huya using the light curves obtained during the
occultation (e.g. Braga-Ribas et al. 2014; Ortiz et al. 2017; Sickafoose et
al. 2019; Santos-Sanz et al. 2021).

For a given exposure time in seconds (texp), and a measured photometric
uncertainty ($\sigma$), for event velocity v (v = 8.07 km/s for the
occultation by Huya), at a significance of 3$\sigma$, the minimum detectable
ring width is w = texp v. Opacity variations can be detected at the 3$\sigma$
level, where op = 3$\sigma$. For other opacities (op) the minimum width (w) of
a ring detectable at 3$\sigma$ can be obtained as w = 3$\sigma$ texp v / op.

The best positive occultation light curve, in terms of flux dispersion, was
obtained from the C18 telescope at the Wise Observatory data (see Table 4)
with $\sigma_{flux}$ = 0.009. The minimum opacity of a putative ring
detectable at 3$\sigma$ using this light curve is 2.7% for a ring width of
24.2 km. In other words, a ring with a width $\geq$ 24.2 km and an opacity
$\geq$ 2.7% would produce a drop in the light curve easily detectable below
the 3$\sigma$ level of noise. If the opacity of the ring were 50% we could
have detected rings with a width $\geq$ 1.3 km at 3$\sigma$. For an opacity of
100% a ring with a width $\geq$ 0.7 km could have been detected below the
3$\sigma$ level (see Table 8). The latter constraints on the ring’s width were
obtained without take into account the dead-time during the data acquisition,
which was of 1.46 s for the C18 at Wise Observatory. This means that rings
with widths $\leq$ 11.8 km could have been lost during the dead-times. The
other positive occultation light curve obtained at the same observatory with
the W-FAST telescope (Nir et al. 2021) has a very short dead-time of only
0.007 s (maximum ring width during dead-time = 0.06 km) with also a small
dispersion in flux ($\sigma_{flux}$ = 0.015). Therefore, from this data we
could have detected rings at the 3$\sigma$ level of noise with widths $\geq$
0.7 km for an opacity of 50% and with widths $\geq$ 0.4 km for an opacity of
100%, in both cases, with negligible ring width losses during the dead-times
($\leq$ 0.06 km).

We obtained constraints at the 3$\sigma$ level on the ring sizes for the other
positive light curves and the closest negative one for the minimum opacity and
for opacities of 50% and 100%. The derived constraints are shown in Table 8.
The best constraint, in terms of ring width, was obtained from the Amateur
Observatory-3 in Romania, with integration times of 0.0333 s (without dead-
times) and $\sigma_{flux}$ = 0.074, from where rings with widths $\geq$ 0.1 km
for an opacity of 50% could have been detected at the 3$\sigma$ level of
noise.

From all the above, we can conclude that no debris or rings of the type found
in the dwarf planet Haumea (opacity $\sim$ 50%, Ortiz et al. 2017) have been
detected around Huya through this stellar occultation. However, narrow ($\leq$
0.1 km) and optically thin rings (opacity $\leq$ 50%) at different geometries,
not probed by the occultation light curves, cannot be ruled out. Note also
that diffraction effects will be important for rings with a width $<$ 1.13 km
(the Fresnel scale value) and high opacity.

###  5.4 Constraints to a putative atmosphere

Assuming that Huya is a predominantly icy body, we attempt to place
constraints on a possible atmosphere. The sublimation rate of water ice is
extremely low at Huya’s distance from the Sun. Only very volatile ices can
sublimate there, but volatile retention models such as those by Schaller &
Brown (2007) indicate that a body of Huya’s size cannot have retained those
ices. So the most likely scenario is that Huya does not have an atmosphere of
any sort. The ingress and egress data can shed light on an upper limit for a
potential atmosphere, but not a very tight one. In any case, we estimate here
the upper limit of an atmosphere around Huya, and more precisely, its surface
pressure $p_{\rm surf}$. To do so, we have to assume a composition and a
temperature profile for this putative atmosphere, which are both unknown.

We may derive some orders of magnitude by assuming that Huya’s atmosphere has
the same composition (mainly N2 with traces of CH4), and same temperature
profile as Pluto’s atmosphere. This results in a surface temperature of about
36 K, with a rapid increase up to $\sim$110 K at 30 km altitude due to CH4
heating, followed by a roughly isothermal upper branch near 100 K.

A ray-tracing scheme (see Dias-Oliveira et al. 2015) then allows us to compare
the W-FAST at Wise Observatory data (which is the best data set in terms of
temporal sampling and flux dispersion) with models using various values of
$p_{\rm surf}$. The results are displayed in Fig. 7. It indicates that an
upper limit of about $p_{\rm surf}=10$ nbar can be placed for a Pluto-like
Huya’s atmosphere.

Figure 7: Comparison of various models assuming a Pluto-like atmosphere (see
text for details) with the data obtained at the Wise station with the W-FAST
instrument. The data points have been reprojected in the radial direction,
merging the ingress and egress part of the light curve. The surface pressures
used in each model are indicated next to each curve. The red model ($p_{\rm
surf}=100$ nbar) can clearly be discarded, considering its discrepancy with
the observations. The green model ($p_{\rm surf}=10$ nbar) could marginally
accommodate the last point just outside the occultation and the rapid drop
inside Huya’s shadow. The blue model ($p_{\rm surf}=1$ nbar) indicates that a
1 nbar atmosphere would go completely unnoticed in the data. We thus estimate
that a conservative upper limit of $p_{\rm surf}=10$ nbar of a Pluto-like
atmosphere is provided by this light curve.

##  6 Conclusions

  * •

This is the best ever stellar occultation produced by a TNO in terms of the
number of chords, excluding Pluto and the August 8, 2020 occultation by the
TNO 2002 MS4 (Rommel et al. in prep.). Such a large number of chords, together
with a relative small velocity of Huya with respect to the star as seen from
Earth (8.07 km/s), has allowed to obtain the instantaneous limb of Huya with
high precision.

  * •

An accurate area-equivalent diameter of 411.0 $\pm$ 7.3 km is determined from
this stellar occultation. This diameter is larger than the radiometric area-
equivalent diameter obtained for Huya using Herschel and Spitzer thermal data
when the existence of the satellite is taken into account (D = 406 $\pm$ 16
km; Fornasier et al. 2013), but still compatible within error bars.

  * •

After a careful correction of the absolute magnitude of Huya by the rotational
phase at the moment of the occultation and by the contribution of the
satellite to the total flux of the system, an accurate geometric albedo at
V-band is obtained: $p_{\rm V}$ = 0.079 $\pm$ 0.004. This albedo is smaller
than the radiometric albedo derived from Herschel and Spitzer measurements
($p_{\rm V}$ = 0.083 $\pm$ 0.004; Fornasier et al. 2013), but note that the
latter is the albedo of the Huya’s system, without subtracting the satellite
contribution.

  * •

From the occultation results it is not clear what the three-dimensional shape
of Huya is. The most likely shape is an oblate spheroid (Maclaurin), but a
triaxial ellipsoid cannot be totally discarded. In any case, using the
occultation results and the information on the rotational light curve (i.e.,
Ppreferred = 6.725 h and $\Delta$m = 0.031 mag) we can constrain possible 3D
solutions for Huya:

    * –

If Huya’s shape is a Maclaurin spheroid our preferred solution has axes: 2a =
435 km, 2b = 435 km, 2c = 233 km for an aspect angle of 32∘ and a density of
$\sim$ 800 kg/m3. The aspect angles for the other possible rotation periods (P
$\sim$ 5.2 h and P $\sim$ 4.3 h) are smaller, which is very unlikely.

    * –

If Huya’s shape is a Jacobi ellipsoid a family of solutions is possible: 2a =
[440-455] km, 2b = [428-442] km, 2c = [253-261] km for aspect angles spanning
from 31∘ to 43∘ and a minimum density of 859 kg/m3. The minimum densities
required for a Jacobi rotating with the other rotational periods are larger
and very unlikely for a body of the Huya’s size.

  * •

If hydrostatic equilibrium for a homogeneous body is used to explain the
occultation results and the rotational light curve, the densities appear to be
too high (Jacobi solutions), or the aspect angle is too small (Maclaurin
solutions). Alternative 3D shape solutions should invoke non-hydrostatic
equilibrium shapes, which would not need so high densities.

  * •

We did not detect evidence of the Huya’s satellite in any of the light curves
(positive or negative) of this occultation.

  * •

No dense rings similar to the structures seen around the dwarf planet Haumea
were detected orbiting Huya by means of this occultation, but very narrow
($\leq$ 0.1 km) and/or optically thin rings (opacity $\leq$ 50%) at different
geometries cannot be totally discarded.

  * •

We obtained an upper limit of about $p_{\rm surf}$ = 10 nbar for a putative
Pluto-like global atmosphere in Huya.

###### Acknowledgements.

P.S-S. acknowledges financial support by the Spanish grant AYA-
RTI2018-098657-J-I00 “LEO-SBNAF” (MCIU/AEI/FEDER, UE). P.S-S., J.L.O., N.M.,
M.V-L. and R.D. acknowledge financial support from the State Agency for
Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa”
award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709), they also
acknowledge the financial support by the Spanish grants AYA-2017-84637-R and
PID2020-112789GB-I00, and the Proyectos de Excelencia de la Junta de Andalucía
2012-FQM1776 and PY20-01309. The research leading to these results has
received funding from the European Union’s Horizon 2020 Research and
Innovation Programme, under Grant Agreement no. 687378, as part of the project
“Small Bodies Near and Far” (SBNAF). Part of the research leading to these
results has received funding from the European Research Council under the
European Community’s H2020 (2014-2020/ERC Grant Agreement no. 669416 “LUCKY
STAR”). Part of the work of M.P. was financed by a grant of the Romanian
National Authority for Scientific Research and Innovation, CNCS - UEFISCDI,
PN-III-P1-1.1-TE-2019-1504. This study was financed in part by the Coordenação
de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance
Code 001 and the National Institute of Science and Technology of the
e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). The
following authors acknowledge the respective CNPq grants: F.B-R 309578/2017-5;
RV-M 304544/2017-5, 401903/2016-8; J.I.B.C. 308150/2016-3 and 305917/2019-6;
M.A 427700/2018-3, 310683/2017-3 and 473002/2013-2; B.E.M. 150612/2020-6.
G.B.R. thanks the support of CAPES and FAPERJ/PAPDRJ (E26/203.173/2016) grant.
J.M.O. acknowledges financial support from the Portuguese Foundation for
Science and Technology (FCT) and the European Social Fund (ESF) through the
PhD grant SFRH/BD/131700/2017. E.F-V. acknowledges funding through the
Preeminant Postdoctoral Program of the University of Central Florida. C.K.,
A.P. and R.S. have been supported by the grants K-125015 and K-138962 of the
National Research, Development and Innovation Office (NKFIH, Hungary). E.P.
acknowledges the Europlanet 2024 RI project funded by the European Union’s
Horizon 2020 Research and Innovation Programme (Grant agreement No. 871149).
We are grateful to the CAHA and OSN staffs. This research is partially based
on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at
Calar Alto, operated jointly by Junta de Andalucía and Consejo Superior de
Investigaciones Científicas (IAA-CSIC). This research was also partially based
on observation carried out at the Observatorio de Sierra Nevada (OSN) operated
by Instituto de Astrofísica de Andalucía (CSIC). This article is also based on
observations made in the Observatorios de Canarias del IAC with the Liverpool
Telescope operated on the island of La Palma by the Instituto de Astrofísica
de Canarias in the Observatorio del Roque de los Muchachos. Part of the
results were based on observations taken at Pico dos Dias Observatory of the
National Laboratory of Astrophysics (LNA/Brazil). Part of the data were
collected during the photometric monitoring observations with the robotic and
remotely controlled observatory at the University of Athens Observatory - UOAO
(Gazeas 2016). We thank the Adiyaman University Astrophysics Application and
Research Center for their support in the acquisition of data with the ADYU60
telescope. 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.

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##  Appendix A Additional tables

Table 4: Observation details of the stellar occultation by the TNO Huya.

Chord | Observatory | Latitude (N) | Telescope diameter (m) | Exposure time | Observer(s) | Detection
---|---|---|---|---|---|---
number | (Country) | Longitude (E) | Detector | Cycle time |  | $\sigma_{flux}$
| IAU code | Altitude (m) |  | (seconds) |  |
1 | TÜBITAK National Observatory-1 | 36∘ 49’ 17.1” | 1.0 | 2.0 | Y. Kilic, T. Ozisik | Positive
| (Turkey) | 30∘ 20’ 08.0” | SI 1100 Cryo | 7.44 | O. Erece, S.E. Kilic | 0.021
| A84 | 2470 |  |  |  |
2 | TÜBITAK National Observatory-2 | 36∘ 49’ 29.1” | 0.60 | 15.0 | Y. Kilic, T. Ozisik | Positive
| (Turkey) | 30∘ 20’ 08.2” | FLI Proline 3041 | 20.0 | O. Erece, S.E. Kilic | 0.048
| A84 | 2455 |  |  |  |
3 | Romanian Academy, Astron. Obs. Cluj, Feleacu Station | 46∘ 42’ 37.6” | 0.30 | 4.0 |  | Positive
| (Romania) | 23∘ 35’ 35.7” | SBIG STT-1603ME | 4.5 | V. Turcu | 0.038
| — | 783 |  |  |  |
4 | ROASTERR-1 Observatory | 46∘ 49’ 15.6” | 0.30 | 0.2 |  | Positive
| (Romania) | 23∘ 35’ 47.0” | ASI 120MM | 0.5 | L. Hudin | 0.093
| L04 | 390 |  |  |  |
5 | W-FAST at Wise Observatory | 30∘ 35’ 48.0” | 0.57 | 1.0 |  | Positive
| (Israel) | 34∘ 45’ 48.0” | Andor Zyla | 1.007 | G. Nir | 0.015
| 097 | 900 |  |  |  |
6 | C18 at Wise Observatory | 30∘ 35’ 48.0” | 0.45 | 3.0 |  | Positive
| (Israel) | 34∘ 45’ 48.0” | QSI 683 | 4.46 | S. Kaspi | 0.009
| 097 | 900 |  |  |  |
7 | Astronomical Inst. of Romanian Academy-1 | 44∘ 24’ 43.2” | 0.50 | 2.0 | A. Sonka | Positive
| (Romania) | 26∘ 05’ 38.2” | FLI PL16803 | 4.2 | S. Anghel | 0.047
| 073 | 83 |  |  |  |
8 | Astronomical Inst. of Romanian Academy-2 | 44∘ 24’ 48.0” | 0.50 | 1.0 |  | Positive
| (Romania) | 26∘ 05’ 48.0” | Andor Zyla | 1.025 | D.A. Nedelcu | 0.041
| 073 | 81 |  |  |  |
9 | ISTEK Belde Observatory | 41∘ 01’ 49.3” | 0.40 | 0.8 | M. Acar | Positive
| (Turkey) | 29∘ 02’ 33.6” | Sony IMX236LQJ CMOS | 0.8 | A. Ateş | 0.088
| — | 150 |  |  | C. Kayhan |
10 | Amateur Observatory-1 | 44∘ 55’ 05.0” | 0.15 | 4.0 |  | Positive
| (Romania) | 25∘ 58’ 12.1” | QHY6 CCD | 6.0 | E. Petrescu | 0.030
| — | 167 |  |  |  |
11 | St. George Observatory | 45∘ 00’ 25.2” | 0.18 | 3.0 |  | Positive
| (Romania) | 25∘ 58’ 42.2” | ATIK 460EX | 4.0 | C. Danescu | 0.026
| L15 | 242 |  |  |  |
12 | Amateur Observatory-2 | 44∘ 26’ 36.5” | 0.20 | 0.20 |  | Positive
| (Romania) | 26∘ 31’ 12.5” | ASI 1600MM | 0.25 | V. Dumitrescu | 0.053
| — | 65 |  |  |  |
13 | Stardust Observatory | 45∘ 38’ 30.0” | 0.20 | 8.0 |  | Positive
| (Romania) | 25∘ 37’ 19.0” | CCD Atik 383L+mono (KAF8300) | 12.0 | L. Curelaru | 0.016
| L13 | 597 |  |  |  |
14 | Stardreams Observatory | 45∘ 12’ 13.3” | 0.20 | 1.0 |  | Positive
| (Romania) | 26∘ 02’ 44.2” | ZWO ASI120MM-S | 1.01 | R. Gherase | 0.074
| L16 | 379 |  |  |  |
15 | Martin S. Kraar Obs. / Weizmann Inst. | 31∘ 54’ 29.0” | 0.40 | 1.0 |  | Positive
| (Israel) | 34∘ 48’ 45.0” | QHY 367C | 3.83 | I. Manulis | 0.056
| C78 | 107 |  |  |  |
$\star$ | Amateur Observatory-3 | 47∘ 05’ 02.3” | 0.40 | 0.0333 |  | Positive
| (Romania) | 24∘ 23’ 30.9” | Watec 902H2 Ultimate | 0.0333 | R. Truta | 0.074
| — | 331 |  |  |  |
16 | Amateur Observatory-4 | 44∘ 45’ 41.5” | 0.20 | 0.20 |  | Positive
| (Romania) | 27∘ 20’ 25.1” | QHY 163M-CMOS | 0.25 | D. Berteşteanu | 0.093
| — | 41 |  |  |  |
17 | Bacau Observatory | 46∘ 33’ 56.3” | 0.35 | 2.0 |  | Positive
| (Romania) | 26∘ 54’ 15.0” | SBIG STL 6303E | 9.0 | R. Anghel | 0.026
| L57 | 170 |  |  |  |
18 | Galați Observatory-1 | 45∘ 25’ 07.9” | 0.40 | 20.0 | J.O. Tercu | Positive
| (Romania) | 28∘ 01’ 57.0” | CCD SBIG STL-6303E | 24.8 | A.-M. Stoian | 0.011
| C73 | 31 |  |  |  |
18 | Galați Observatory-2 | 45∘ 25’ 07.9” | 0.20 | 20.0 | J.O. Tercu | Positive
| (Romania) | 28∘ 01’ 57.0” | CCD Atik 383L+Mono | 31.3 | A.-M. Stoian | 0.031
| C73 | 31 |  |  |  |
19 | Barlad Observatory | 46∘ 13’ 54.1” | 0.20 | 0.50 |  | Positive
| (Romania) | 27∘ 40’ 10.2” | ASI 1600 | 0.82 | C. Vantdevara | 0.068
| L22 | 70 |  |  |  |
| QOS Observatory | 48∘ 50’ 54.0” | 0.30 | 0.2 | T. O. Dementiev | Negative
| (Ukraine) | 26∘ 43’ 12.0” | ZWO ASI 174MM | 0.200016 | O. M. Kozhukhov | 0.106
| L18 | 352 |  |  |  |
| Çukurova University | 37∘ 03’ 23.0” | 0.50 | 90 | A. Solmaz | Negative
| (Turkey) | 35∘ 21’ 04.0” | Orion Parsec 8300M | 108 | M. Tekes | 0.027
| — | 130 |  |  |  |

This Table includes the sites from where the occultation was detected and the
closest negatives used to constrain the instantaneous shape of the object.
$\sigma_{flux}$ is the flux dispersion, i.e. the standard deviation of the
normalized flux (outside of the occultation in the case of positive
detections). Sites are sorted by their distance to the center of the predicted
shadow path, from West to East. The data from the site marked with $\star$ was
not used in the final analysis of the occultation (see Section 3 for a
detailed explanation).

Table 5: Summary table of the observing campaign. Observatory | Latitude (N) | Telescope | Observer(s) | Observation
---|---|---|---|---
(Country) | Longitude (E) | aperture |  |
IAU code | Altitude (m) | (m) |  |
Sant Esteve Sesrovires | 41∘ 29’ 37.5” | 0.40 | C. Schnabel | Negative
(Spain) | 01∘ 52’ 21.1” |  |  |
– | 180 |  |  |
Sabadell Observatory | 41∘ 33’ 00.2” | 0.50 | C. Perello | Negative
(Spain) | 02∘ 05’ 24.6” |  | A. Selva |
619 | 224 |  |  |
Normandy | 49∘ 36’ 26.4” | 0.14 | J. Lecacheux | Negative
(France) | 358∘ 46’ 03.3” |  |  |
– | 12 |  |  |
Northolt Branch Observatories | 51∘ 33’ 16.8” | 0.25 | G. Wells | Negative
(UK) | 359∘ 37’ 41.1” |  | D. Bamberger |
Z80 | 55 |  |  |
Almalex Observatory | 53∘ 50’ 15.4” | 0.28 | A. Pratt | Negative
(UK) | 358∘ 23’ 32.0” |  |  |
Z92 | 114 |  |  |
NOAK Observatory | 39∘ 39’ 08.8” | 0.25 | N. Sioulas | Bad
(Greece) | 20∘ 48’ 59.7” |  |  | weather
L02 | 546 |  |  |
Univ. of Athens Observatory - UOAO | 37∘ 58’ 06.8” | 0.40 | K. Gazeas | Negative
(Greece) | 23∘ 47’ 00.1” |  | E. Karampotsiou |
– | 250 |  |  |
Ellinogermaniki Agogi Observatory | 37∘ 59’ 52.3” | 0.40 | V. Tsamis | Negative
(Greece) | 23∘ 53’ 36.1” |  | K. Tigani |
C68 | 162 |  |  |
Konkoly Observatory Budapest | 47∘ 29’ 59.3” | 0.60 | A. Pal | Bad
(Hungary) | 18∘ 57’ 51.1” |  | R. Szakats | weather
053 | 469 |  |  |
Ulupınar Observatory | 40∘ 06’ 01.0” | 0.40 | C. Puskullu | Negative
(Turkey) | 26∘ 28’ 32.0” |  |  |
– | 410 |  |  |
Berlin | 52∘ 30’ 58.0” | 0.20 | C. Weber | Negative
(Germany) | 13∘ 25’ 40.0” |  |  |
– | 37 |  |  |
Konkoly Observatory Piszkestető | 47∘ 55’ 06.0” | 1.00 | A. Pal | Negative
(Hungary) | 19∘ 53’ 41.7” |  | R. Szakats |
561 | 944 |  |  |
TÜBITAK National Observatory-1 | 36∘ 49’ 17.1” | 1.00 | Y. Kilic, T. Ozisik | Positive
(Turkey) | 30∘ 20’ 08.0” |  | O. Erece, S.E. Kilic |
A84 | 2472 |  |  |
TÜBITAK National Observatory-2 | 36∘ 49’ 29.1” | 0.60 | Y. Kilic, T. Ozisik | Positive
(Turkey) | 30∘ 20’ 08.2” |  | O. Erece, S.E. Kilic |
A84 | 2472 |  |  |
Akdeniz University Observatory | 36∘ 49’ 27.0” | 0.25 | V. Bakış | Technical
(Turkey) | 30∘ 20’ 08.0” |  | H. Bakış | problems
– | 2490 |  | Z. Eker |
Mt. Suhora Observatory | 49∘ 34’ 09.0” | 0.60 | W. Ogłoza | Bad
(Poland) | 20∘ 04’ 03.0” |  |  | weather
– | 1009 |  |  |
Borowiec Observatory | 52∘ 16’ 37.2” | 0.40 | A. Marciniak | Bad
(Poland) | 17∘ 04’ 28.6” |  |  | weather
187 | 123 |  |  |
Romanian Acad., Astron. Obs. Cluj, Feleacu Station | 46∘ 42’ 37.6” | 0.30 |  | Positive
(Romania) | 23∘ 35’ 35.7” |  | V. Turcu |
– | 783 |  |  |
ROASTERR-1 Observatory | 46∘ 49’ 15.6” | 0.30 |  | Positive
(Romania) | 23∘ 35’ 47.0” |  | L. Hudin |
L04 | 390 |  |  |
W-FAST at Wise Observatory | 30∘ 35’ 48.0” | 0.57 |  | Positive
(Israel) | 34∘ 45’ 48.0” |  | G. Nir |
097 | 900 |  |  |
C18 at Wise Observatory | 30∘ 35’ 48.0” | 0.45 |  | Positive
(Israel) | 34∘ 45’ 48.0” |  | S. Kaspi |
097 | 900 |  |  |
Astronomical Inst. of Romanian Academy-1 | 44∘ 24’ 43.2” | 0.50 | A. Sonka | Positive
(Romania) | 26∘ 05’ 38.2” |  | S. Anghel |
073 | 83 |  |  |
Astronomical Inst. of Romanian Academy-2 | 44∘ 24’ 48.0” | 0.50 |  | Positive
(Romania) | 26∘ 05’ 48.0” |  | D.A. Nedelcu |
073 | 81 |  |  |
Astroclubul Bucureşti | 44∘ 24’ 49.0” | 0.40 | Z. Deak | Technical
(Romania) | 26∘ 05’ 48.1” |  |  | problems
– | 69 |  |  |
ISTEK Belde Observatory | 41∘ 01’ 49.3” | 0.40 | M. Acar | Positive
(Turkey) | 29∘ 02’ 33.6” |  | A. Ateş |
– | 150 |  | C. Kayhan |
ISTEK Belde Observatory | 41∘ 01’ 49.3” | 0.35 | M. Acar | Technical
(Turkey) | 29∘ 02’ 33.6” |  | A. Ateş | problems
– | 150 |  | C. Kayhan |
ISON-Uzhgorod Observatory “Derenivka” | 48∘ 33’ 48.2” | 0.40 | V. Kudak | Bad
(Ukraine) | 22∘ 27’ 12.6” |  | V. Perig | weather
K99 | 213 |  |  |
Amateur Observatory-1 | 44∘ 55’ 05.0” | 0.15 |  | Positive
(Romania) | 25∘ 58’ 12.1” |  | E. Petrescu |
– | 167 |  |  |
St. George Observatory | 45∘ 00’ 25.2” | 0.18 |  | Positive
(Romania) | 25∘ 58’ 42.2” |  | C. Danescu |
L15 | 242 |  |  |
Amateur Observatory-2 | 44∘ 26’ 36.5” | 0.20 |  | Positive
(Romania) | 26∘ 31’ 12.5” |  | V. Dumitrescu |
– | 65 |  |  |
Stardust Observatory | 45∘ 38’ 30.0” | 0.20 |  | Positive
(Romania) | 25∘ 37’ 19.0” |  | L. Curelaru |
L13 | 597 |  |  |
Stardreams Observatory | 45∘ 12’ 13.3” | 0.20 |  | Positive
(Romania) | 26∘ 02’ 44.2” |  | R. Gherase |
L16 | 379 |  |  |
Martin S. Kraar Obs./ Weizmann Inst. | 31∘ 54’ 29.0” | 0.40 |  | Positive
(Israel) | 34∘ 48’ 45.0” |  | I. Manulis |
C78 | 107 |  |  |
Amateur Observatory-3 | 47∘ 05’ 02.3” | 0.40 |  | Positive
(Romania) | 24∘ 23’ 30.9” |  | R. Truta |
– | 331 |  |  |
Amateur Observatory-4 | 44∘ 45’ 41.5” | 0.20 |  | Positive
(Romania) | 27∘ 20’ 25.1” |  | D. Berteşteanu |
– | 41 |  |  |
Bacau Observatory | 46∘ 33’ 56.3” | 0.35 |  | Positive
(Romania) | 26∘ 54’ 15.0” |  | R. Anghel |
L57 | 170 |  |  |
Galați Observatory-1 | 45∘ 25’ 07.9” | 0.40 | J.O. Tercu | Positive
(Romania) | 28∘ 01’ 57.0” |  | A.-M. Stoian |
C73 | 31 |  |  |
Galați Observatory-2 | 45∘ 25’ 07.9” | 0.20 | J.O. Tercu | Positive
(Romania) | 28∘ 01’ 57.0” |  | A.-M. Stoian |
C73 | 31 |  |  |
Barlad Observatory | 46∘ 13’ 54.1” | 0.20 |  | Positive
(Romania) | 27∘ 40’ 10.2” |  | C. Vantdevara |
L22 | 70 |  |  |
QOS Observatory | 48∘ 50’ 54.0” | 0.30 | T. O. Dementiev | Negative
(Ukraine) | 26∘ 43’ 12.0” |  | O. M. Kozhukhov |
L18 | 352 |  |  |
Çukurova University | 37∘ 03’ 23.0” | 0.50 | A. Solmaz | Negative
(Turkey) | 35∘ 21’ 04.0” |  | M. Tekes |
– | 130 |  |  |
Odessa Astronomical Observatory, Mayaky | 46∘ 23’ 49.1” | 0.80 | V. Kashuba | Negative
(Ukraine) | 30∘ 16’ 16.6” |  | V. Zhukov |
583 | 18 |  |  |
Adiyaman | 38∘ 13’ 31.2” | 0.60 | M. Żejmo | Bad
(Turkey) | 37∘ 45’ 06.1” |  |  | weather
– | 690 |  |  |
Ondokuz Mayıs University | 41∘ 22’ 04.0” | 0.35 | S. Kalkan | Technical
(Turkey) | 36∘ 12’ 06.0” |  |  | problems
– | 151 |  |  |
Moletai | 55∘ 18’ 57.5” | 0.35 | E. Pakštienė | Bad
(Lithuania) | 25∘ 33’ 48.0” |  |  | weather
– | 200 |  |  |
İnönü University Observatory | 38∘ 19’ 24.0” | 0.35 | T. Ozdemir | Bad
(Turkey) | 38∘ 26’ 13.0” |  |  | weather
– | 130 |  |  |
Makes Observatory-La Reunion | -21∘ 11’ 56.1” | 0.18 | J.P. Teng | Negative
(France) | 55∘ 24’ 36.3” |  |  |
– | 997 |  |  |
Sainte Marie-La Reunion | -20∘ 53’ 48.5” | 0.20 | B. Mondon | Negative
(France) | 55∘ 34’ 00.1” |  |  |
– | 54 |  |  |
Ataturk University | 39∘ 54’ 17.1” | 0.50 | C. Yesilyaprak | Negative
(Turkey) | 41∘ 14’ 40.1” |  | O. Satir, M.S. Niaei |
– | 1857 |  | E. Atalay |

This table includes all the telescopes and observers that supported the Huya
occultation campaign. Sites are sorted by their distance to the center of the
predicted shadow path, from West to East.

Table 6: Ingress and egress times derived from the Huya occultation light
curves.

#chord | Observatory, Country | Ingress (UT) | Egress (UT) | Chord size (km)
---|---|---|---|---
1 | TÜBITAK National Observatory-1, Turkey | 00:52:34.387$\pm$2.592 | 00:53:00.703$\pm$0.142 | 212.4$\pm$22.1
2 | TÜBITAK National Observatory-2, Turkey | 00:52:30.407$\pm$5.500 | 00:52:52.439$\pm$5.500 | 177.8$\pm$88.8
3 | Romanian Acad., Astron. Obs. Cluj, Feleacu Sta., Romania | 00:53:51.515$\pm$0.115 | 00:54:37.293$\pm$0.089 | 369.4$\pm$1.7
4 | ROASTERR-1 Observatory, Romania | No data | 00:54:38.748$\pm$0.030 | —
5 | W-FAST-Wise Observatory, Israel | 00:51:21.416$\pm$0.016 | 00:52:07.918$\pm$0.023 | 375.3$\pm$0.3
6 | C18 at Wise Observatory, Israel | 00:51:21.110$\pm$0.040 | 00:52:07.851$\pm$0.040 | 377.2$\pm$0.7
7 | Astronomical Inst. Romanian Academy-1, Romania | 00:53:30.014$\pm$0.998 | 00:54:18.863$\pm$0.098 | 394.2$\pm$8.8
8 | Astronomical Inst. Romanian Academy-2, Romania | 00:53:31.111$\pm$0.041 | 00:54:18.814$\pm$0.041 | 385.0$\pm$0.7
9 | ISTEK Belde Observatory, Turkey | 00:52:59.908$\pm$0.062 | 00:53:50.451$\pm$0.083 | 407.9$\pm$1.2
10 | Amateur Observatory-1, Romania | 00:53:33.562$\pm$0.444 | 00:54:23.630$\pm$0.174 | 404.1$\pm$5.0
11 | St. George Observatory, Romania | 00:53:34.446$\pm$0.083 | 00:54:24.868$\pm$0.077 | 406.9$\pm$1.3
12 | Amateur Observatory-2, Romania | 00:53:30.484$\pm$0.020 | 00:54:21.217$\pm$0.200 | 409.4$\pm$1.8
13 | Stardust Observatory, Romania | 00:53:38.100$\pm$0.150 | 00:54:29.800$\pm$1.850 | 417.2$\pm$16.1
14 | Stardreams Observatory, Romania | 00:53:37.111$\pm$0.098 | 00:54:29.122$\pm$0.099 | 419.7$\pm$1.6
15 | Martin S. Kraar Obs., Israel | 00:51:30.046$\pm$0.100 | 00:52:23.578$\pm$1.148 | 432.0$\pm$10.1
$\star$ | Amateur Observatory-3, Romania | 00:00:00.000$\pm$0.007 | 00:00:43.218$\pm$0.007 | 348.8$\pm$0.1
16 | Amateur Observatory-4, Romania | 00:53:33.840$\pm$0.027 | 00:54:25.060$\pm$0.027 | 413.4$\pm$0.4
17 | Bacau Observatory, Romania | 00:53:46.520$\pm$3.400 | 00:54:33.919$\pm$0.083 | 382.5$\pm$28.1
18 | Galați Observatory-1 and 2, Romania | 00:53:40.500$\pm$0.440 | 00:54:25.420$\pm$0.440 | 362.5$\pm$7.1
19 | Barlad Observatory, Romania | 00:53:51.192$\pm$0.047 | 00:54:31.753$\pm$0.073 | 327.3$\pm$1.0

Sites are sorted by their distance to the center of the predicted shadow path,
from West to East. The chord marked with $\star$ was not used in the final
analysis of the occultation (see Section 3).

Table 7: Parameters of the best-fitting ellipse.

(a′ , b′) | (217.6 $\pm$ 3.5 km , 194.1 $\pm$ 6.1 km)
---|---
($f_{\rm c}$ , $g_{\rm c}$) | (2984.7 $\pm$ 3.2 km , -1850.9 $\pm$ 1.7 km)
P′ | 55.2${}^{\circ}\pm$ 9.1
$D_{\rm eq}$ | 411.0 $\pm$ 7.3 km
$p_{\rm V}$ | 0.079 $\pm$ 0.004

Parameters of the best-fitting ellipse obtained from the occultation chords
plus the closest non-detection constraint (Figure 6). The area-equivalent
diameter ($D_{\rm eq}$ ) and geometric albedo ($p_{\rm V}$) derived from this
limb fit are also included (see Section 5.1 for details).

Table 8: Ring constraints not accounting for dead-times.

Observatory | w | opmin | w(op=50%) | w(op=100%)
---|---|---|---|---
(Telesc., Country) | (km) |  | (km) | (km)
TÜBITAK National Observatory-1 | 16.1 | 6.3% | 2.0 | 1.0
(1.00 m, Turkey) |  |  |  |
TÜBITAK National Observatory-2 | 121.1 | 14.4% | 34.9 | 17.4
(0.60 m, Turkey) |  |  |  |
Romanian Academy, Astronomical Observatory Cluj, Feleacu Station | 32.3 | 11.4% | 7.4 | 3.7
(0.30 m, Romania) |  |  |  |
ROASTERR-1 Observatory | 1.6 | 27.9% | 0.9 | 0.5
(0.30 m, Romania) |  |  |  |
W-FAST at Wise Observatory | 8.1 | 4.5% | 0.7 | 0.4
(0.57 m, Israel) |  |  |  |
C18 at Wise Observatory | 24.2 | 2.7% | 1.3 | 0.7
(0.45 m, Israel) |  |  |  |
Astronomical Inst. of Romanian Academy-1 | 16.1 | 14.1% | 4.6 | 2.3
(0.50 m, Romania) |  |  |  |
Astronomical Inst. of Romanian Academy-2 | 8.1 |

license: Creative Commons - Attribution - https://creativecommons.org/licenses/by/4.0/

authors:
P. Santos-Sanz, J.L. Ortiz, B. Sicardy, M. Popescu, G.
  Benedetti-Rossi, N. Morales, M. Vara-Lubiano, J.I.B. Camargo, C.L. Pereira,
  F.L. Rommel, M. Assafin, J. Desmars, F. Braga-Ribas, R. Duffard, J. Marques
  Oliveira, R. Vieira-Martins, E. Fern\'andez-Valenzuela, B.E. Morgado, M.
  Acar, S. Anghel, E. Atalay, A. Ate\c{s}, H. Bak{\i}\c{s}, V. Bak{\i}\c{s}, Z.
  Eker, O. Erece, S. Kaspi, C. Kayhan, S.E. Kilic, Y. Kilic, I. Manulis, D.A.
  Nedelcu, M.S. Niaei, G. Nir, E. Ofek, T. Ozisik, E. Petrescu, O. Satir, A.
  Solmaz, A. Sonka, M. Tekes, O. Unsalan, C. Yesilyaprak, R. Anghel, D.
  Berte\c{s}teanu, L. Curelaru, C. Danescu, V. Dumitrescu, R. Gherase, L.
  Hudin, A-M. Stoian, J.O. Tercu, R. Truta, V. Turcu, C. Vantdevara, I.
  Belskaya, T.O. Dementiev, K. Gazeas, S. Karampotsiou, V. Kashuba, Cs. Kiss,
  N. Koshkin, O.M. Kozhukhov, Y. Krugly, J. Lecacheux, A. Pal, \c{C}.
  P\"usk\"ull\"u, R. Szakats, V. Zhukov, D. Bamberger, B. Mondon, C. Perell\'o,
  A. Pratt, C. Schnabel, A. Selva, J.P. Teng, K. Tigani, V. Tsamis, C. Weber,
  G. Wells, S. Kalkan, V. Kudak, A. Marciniak, W. Ogloza, T. Ozdemir, E.
  Pakstiene, V. Perig, and M. Zejmo

submitter: Pablo Santos-Sanz


text:
12.3% | 2.0 | 1.0
(0.50 m, Romania) |  |  |  |
ISTEK Belde Observatory | 6.5 | 26.4% | 3.4 | 1.7
(0.40 m, Turkey) |  |  |  |
Amateur Observatory-1 | 32.3 | 9.0% | 5.8 | 2.9
(0.15 m, Romania) |  |  |  |
St. George Observatory | 24.2 | 7.8% | 3.8 | 1.9
(0.18 m, Romania) |  |  |  |
Amateur Observatory-2 | 1.6 | 15.9% | 0.5 | 0.3
(0.20 m, Romania) |  |  |  |
Stardust Observatory | 64.6 | 4.8% | 6.2 | 3.1
(0.20 m, Romania) |  |  |  |
Stardreams Observatory | 8.1 | 22.2% | 3.6 | 1.8
(0.20 m, Romania) |  |  |  |
Martin S. Kraar Obs./Weizmann Inst. | 8.1 | 16.8% | 2.7 | 1.4
(0.40 m, Israel) |  |  |  |
Amateur Observatory-3 | 0.3 | 22.2% | 0.1 | 0.1
(0.40 m, Romania) |  |  |  |
Amateur Observatory-4 | 1.6 | 27.9% | 0.9 | 0.5
(0.20 m, Romania) |  |  |  |
Bacau Observatory | 16.1 | 7.8% | 2.5 | 1.3
(0.35 m, Romania) |  |  |  |
Galați Observatory-1 | 161.4 | 3.3% | 10.7 | 5.3
(0.40 m, Romania) |  |  |  |
Galați Observatory-2 | 161.4 | 9.3% | 30.0 | 15.0
(0.20 m, Romania) |  |  |  |
Barlad Observatory | 4.0 | 20.4% | 1.6 | 0.8
(0.20 m, Romania) |  |  |  |
QOS Observatory (NEGATIVE) | 1.6 | 31.8% | 1.0 | 0.5
(0.30 m, Ukraine) |  |  |  |

Ring width (w) and minimum opacity (opmin) for a 3$\sigma$ detection, obtained
from all the telescopes that detected the occultation and the closest negative
one. In the third and fourth column we estimate the ring width detectable at
3$\sigma$ level for opacities of 50% and 100% (completely opaque ring),
respectively.