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| Light curves of the occultation. Light curves in the form of normalized flux versus time (at mid-exposure) were obtained from the different observatories that recorded the occultation (Table 1). The black points and lines represent the light curves extracted from the observations. The blue lines show the best square-well-model fits to the main body and the ring at Konkoly, with square-well models derived from the assumed ring width and opacity (W = 70 km and p′ = 0.5) at other sites. The red points and lines correspond to the optimal synthetic profile deduced from the squarewell model fitted at each data point (see Methods). The rectangular profile in green corresponds to the ring egress event at Skalnate Pleso, which fell in a readout time of the camera (see Fig. 3). The light curves have been shifted in steps of 1 vertically for better viewing. 'Munich' corresponds to the Bavarian Public Observatory. Error bars are 1σ.
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Haumea-one of the four known trans-Neptunian dwarf planets- is a very elongated and rapidly rotating body1-3. In contrast to other dwarf planets4-6, its size, shape, albedo and density are not well constrained. The Centaur Chariklo was the first body other than a giant planet known to have a ring system7, and the Centaur Chiron was later found to p...
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... Astrophysical Institute of the Hungarian Academy of Sciences, the 0.65-m telescope at Ondrejov Observatory, operated by the Astronomical Institute of the Czech Academy of Sciences, the 1.5-m telescope at Sierra Nevada Observatory, operated by the Instituto de Astrofisica de Andalucia-CSIC, the that best simultaneously fits the secondary events of Fig. 1. The ring fit provides an opening angle B ring = 13.8° ± 0.5° and a position angle for the apparent minor axis of the ring of P ring = − 74.3° ± 1.3°. This is aligned, to within error bars, with Haumea's apparent minor axis P limb = − 76.3° ± 1.2° (Fig. 2). Moreover, the orbital pole position of Hi'iaka 14 implies a sub-observer ...
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... Lomb periodogram 30 of the residuals in declination showed its strongest peak at a signifi- cant periodicity of 49.5 ± 0.9 days, which coincides with the known 20 orbital period of Hi'iaka (49.462 ± 0.083 days). A sinusoidal fit to the residuals (Extended Data Fig. 1) using the orbital period of Hi'iaka had a maximum when the theoretical position of Hi'iaka was at its northernmost position with respect to Haumea, and the minimum of the fit corresponded to the southernmost position of the satellite Hi'iaka. Hence we verified that the oscillation was indeed correlated with the the- oretical positions of Hi'iaka. ...
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... average. The main parameters of the star are shown in Extended Data Table 1. The brightness of the star was similar to that of Haumea, so at the time of the occultation we expected a brightness change of around 50% in the Haumea + star blended source. The resulting light curves (photon flux relative to the average value, versus time) are shown in Fig. ...
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... we use the best available dataset-the Asiago light curve-to derive Haumea's atmospheric upper limits (Fig. 1). From Haumea's mass of (4.006 ± 0.04) × 10 21 kg (ref. 20) and assuming that the body itself is in hydrostatic equilibrium we derive an average surface gravity of 0.39 m s −2 ...
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... body, the light curves reveal brief dimmings from most of the sites before and/or after the main event. The timings of these events (see Extended Data Table 2) were extracted by fitting square-well ring profiles to the short events, in the same way as for Chariklo (ref. 7). However, the only resolved profiles come from the Konkoly 1-m telescope ( Fig. 1). At that station, we derive a radial width (in the ring plane) of W ring ≈ 74 km at ingress and W ring ≈ 44 km at egress, with respective apparent opacities (along the line of sight) of p′ = 0.55 and p′ = 0.56. This implies so-called equivalent widths W equiv = W ring p′ of 41 km and 25 km, respectively, a measure of the radially ...
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... of each event. Consequently, we used a simple model with a uniform ring of width of 70 km and apparent opacity of 0.5 that provides the typical average equivalent width observed at Konkoly. These fits account for the readout times between exposures and eventually provide the timings of the synthetic events. Note that in one case (Skalnate egress; Fig. 1) the ring is not detected because it should occur during a readout time. Note also that at several stations (Lajatico, San Marcello Pistoiese, Asiago and Wendelstein) the egress ring event is not recorded, not as a result of a lack of signal-to-noise ratio, but because our view of the ring is blocked by Haumea's body (Fig. ...
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Among the four known transneptunian dwarf planets, Haumea is an exotic, very elongated, and fast rotating body. In contrast to the other dwarf planets, its size, shape, albedo, and density are not well constrained. Here we report results of a multi-chord stellar occultation, observed on 2017 January 21. Secondary events observed around the main bod...
Citations
... In addition, the DCR effect can be minimized by restricting the target being close to the meridian when observed. Ortiz et al. (2017), Winters et al. (2017) and White et al. (2022) reduced the astrometric errors in this way. However, even if we observe close to the meridian, some systematic errors exist in declination. ...
The color of a star is a critical feature to reflect its physical property such as the temperature. The color index is usually obtained via absolute photometry, which is demanding for weather conditions and instruments. In this work, we present an astrometric method to measure the catalog-matched color index of an object based on the effect of differential color refraction (DCR). Specifically, we can observe an object using only one filter or alternately using two different filters. Through the difference of the DCR effect compared with reference stars, the catalog-matched color index of an object can be conveniently derived. Hence, we can perform DCR calibration and obtain its accurate and precise positions even if observed with Null filter during a large range of zenith distances, by which the limiting magnitude and observational efficiency of the telescope can be significantly improved. This method takes advantage of the DCR effect and builds a link between astrometry and photometry. In practice, we measure the color indices and positions of Himalia (the sixth satellite of Jupiter) using 857 CCD frames over 8 nights by two telescopes. Totally, the mean color index BP-RP (Gaia photometric system) of Himalia is 0.750 \pm 0.004 magnitude. Through the rotational phased color index analysis, we find two places with their color indices exceeding the mean \pm 3 \sigma.
... The first example of its kind was discovered around the Centaur 10199 Chariklo (Braga-Ribas et al. 2014) in 2013. In 2017, a somewhat similar structure was observed around the dwarf planet 136108 Haumea (Ortiz et al. 2017) and more recently around the trans-Neptunian object (TNO) 50000 Quaoar (Morgado et al. 2023). Besides those, a ring was also proposed around the Centaur 2060 Chiron (Ortiz et al. 2015;Sickafoose et al. 2020), but it is yet to be confirmed by better observational data. ...
Recently, it has been reported the discovery of a dense ring around the trans-Neptunian object 50000 Quaoar. The ring particles seem to be very close to the 6/1 mean motion resonance with Weywot, the only known satellite in the system. In this work we investigate the dynamical environment in the close vicinity of the 6/1 orbital resonance in the context of the restricted three body problem. We aim to analyze whether, in view of observational constraints, the ring could be effectively evolving in resonant motion with the satellite. Through the technique of dynamical maps we identify and characterize the 6/1 mean motion resonance, finding that the main location of the resonance deviates by only $29$ km from the central part of the ring. This difference lies within the 3$\sigma$ confidence level, considering the uncertainties in the observational parameters. We also show that the Weywot's eccentricity plays a significant role in the dynamical structure of the 6/1 resonance. The results show that the resonance width is smaller than the estimated ring's width. Under assumption of a ring with eccentricity smaller than 0.05, clumping of test particles appears at the position of the different resonant multiplets, considering the nominal value of Weywot's eccentricity. This is in agreement with observations, which indicate that the estimated resonance width ($\leq$ 10 km) is comparable with the narrow and dense arc of material within Quaoar's ring. Our results may be an indicative that the 6/1 resonance resonance plays a key role in confining the arc ring.
... Later, another ring system was unambiguously detected, this time around the large trans-Neptunian object (TNO) and dwarf planet Haumea (Ortiz et al. 2017). In addition, yet another ring system has just been announced around the large TNO Quaoar Pereira et al. 2023). ...
... The ring of Haumea is located very close to its 3:1 spin-orbit resonance (Ortiz et al. 2017) and this also appears to be the case for Chariklo, although the rotation period of Chariklo is not as clearly determined as in the case of Haumea, and its central mass is not known. For Quaoar, the main ring is close to the 3:1 resonance Pereira et al. 2023). ...
We could accurately predict the shadow path and successfully observe an occultation of a bright star by Chiron on 2022 December 15. The Kottamia Astronomical Observatory in Egypt did not detect the occultation by the solid body, but we detected three extinction features in the light curve that had symmetrical counterparts with respect to the central time of the occultation. One of the features is broad and shallow, whereas the other two features are sharper with a maximum extinction of $\sim$25$\%$ at the achieved spatial resolution of 19 km per data point. From the Wise observatory in Israel, we detected the occultation caused by the main body and several extinction features surrounding the body. When all the secondary features are plotted in the sky plane we find that they can be caused by a broad $\sim$580 km disk with concentrations at radii of 325 \pm 16 km and 423 \pm 11 km surrounding Chiron. At least one of these structures appears to be outside the Roche limit. The ecliptic coordinates of the pole of the disk are $\lambda$ = 151$^\circ~\pm$ 8$^\circ$ and $\beta$ = 18$^\circ~\pm$ 11$^\circ$, in agreement with previous results. We also show our long-term photometry indicating that Chiron had suffered a brightness outburst of at least 0.6 mag between March and September 2021 and that Chiron was still somewhat brighter at the occultation date than at its nominal pre-outburst phase. The outermost extinction features might be consistent with a bound or temporarily bound structure associated with the brightness increase. However, the nature of the brightness outburst is unclear, and it is also unclear whether the dust or ice released in the outburst could be feeding a putative ring structure or if it emanated from it.
... Later photometric, and thermal flux measurements confirmed that Haumea was indeed a triaxial ellipsoid (Lockwood et al. 2014). The presently known most precise dimensions of Haumea come from the stellar occultation observations of Ortiz et al. 2017 with equatorial axes of a = 1161 ± 30 km and b = 852 ± 4 km, and a polar axis of c = 513 ± 16 km. ...
... This precludes the mass movement of glacial flows, as well as any substantial vapor pressure supported atmosphere, as has been observed on Pluto (Moore et al. 2016;Gladstone et al. 2016). 3 -50 nbar upper limits on atmospheric pressure, depending on composiiton, are also provided by Ortiz et al. 2017. ...
... We evaluate the gravitational potential to the 4th order. We use the coefficients C 20 through C 44 as calculated by Sanchez et al. 2020, who used Haumea's shape as determined by Ortiz et al. 2017, and the methodology of Balmino 1994 for calculating the coefficients. Balmino 1994 present a methodology for calculating the spherical harmonic gravity coefficients for a triaxial ellipsoid, assuming a homogeneous composition (i.e. ...
Haumea, thought to be the Kuiper Belt's 3rd most massive object, has a fast 3.92 hr rotational period, resulting in its shape as a triaxial ellipsoid. Here, we make the first detailed predictions of Haumea's surface morphology, considering in particular effects stemming from its unique shape. Given observations have indicated Haumea's surface to be predominantly inert water ice, we predict crater characteristics, with craters likely to be the predominant surface feature on Haumea. In calculating Haumea's surface gravity, we find that g varies by almost two orders of magnitude, from a minimum of 0.0126 m/s^2 at the location of the equatorial major axis, to 1.076 m/s^2 at the pole. We also find a non-monotonic decrease in g with latitude. The simple to complex crater transition diameter varies from 36.2 km at Haumea's location of minimum surface gravity to 6.1 km at the poles. Equatorial craters are expected to skew to larger volumes, have depths greater by a factor of > 2, and have thicker ejecta when compared with craters at high latitudes. Considering implications for escape of crater ejecta, we calculate that Haumea's escape velocity varies by 62% from equator to pole. Despite higher escape velocities at the poles, impacts there are expected to have a higher mass fraction of ejecta escape from Haumea's gravitational well. Haumea may be unique among planet-sized objects in the solar system in possessing dramatic variations in crater morphology across its surface, stemming solely from changes in the magnitude of its surface gravity.
... The sizes of the satellites have not been measured directly, but with their low masses and surface spectra that resemble pure water ice (Barkume et al. 2006;Fraser & Brown 2009), it appears likely that the objects are icy fragments with densities of ≲ 1 g cm −3 , in marked contrast to the 1.8-2.0 g cm −3 density of Haumea (Ortiz et al. 2017;Dunham et al. 2019). ...
We have used the Atacama Large Millimeter Array (ALMA) to measure precise absolute astrometric positions and detect the astrometric wobble of dwarf planet Orcus and its satellite Vanth over a complete orbit. We also place upper limits to the astrometric wobble induced by Dysnomia on dwarf planet Eris around its orbit. From the Vanth-Orcus barycentric motion, we find a Vanth-Orcus mass ratio of 0.16$\pm$0.02 -- the highest of any known planet or dwarf planet. This large ratio is consistent with the hypothesis that Vanth is a largely-intact impactor from a giant collision in the system, and that the system has likely evolved to a double synchronous state. We find only an upper limit of the barycenter motion of Eris, which implies a one sigma upper limit to the Dysnomia-Eris mass ratio of 0.0085, close to the modeled transition region between giant impact generated satellites which are largely intact remnants of the original impactor and those which form out of reaccreted disk material left over post-impact. The low albedo of Dysnomia leads us to marginally favor the intact impactor scenario. We find that Dysnomia has density of <1.2 g cm$^{-3}$, significantly lower than the 2.4 g cm$^{-3}$ of Eris.
... The simplest and still useful models are the uniform-density and uniformly rotating spheroids and ellipsoids, which enable analytic expressions of physical characteristics (see Lyttleton 1953;Chandrasekhar 1987 for the classical results). These simple results are still useful in, for instance, studying the equilibrium figure of a dwarf planet, Haumea, which is thought to have a triaxial ellipsoidal shape (Ortiz et al, 2017;Dunham et al, 2019;Noviello et al, 2022). In a completely different context of compact star physics, the models have been utilized to mimic the rapidly rotating compact stars, which may assume time-dependent triaxial ellipsoid. ...
We examine the effects of a massive concentric ring around a spheroid or an ellipsoid with uniform density and uniform rotation. Equilibrium sequences of axisymmetric Maclaurin-like spheroid and triaxial Jacobi-like ellipsoids are obtained. Due to the gravitational field of the ring, Maclaurin-like spheroid does not have a spherical limit when the object's angular frequency vanishes. At a critical value of the eccentricity of the spheroid's meridional section, a triaxial Jacobi-like ellipsoid bifurcates. When a parameter characterizing the gravitational field of the ring is smaller than a threshold, the bifurcation points of Maclaurin-like and Jacobi-like ellipsoids exist and the critical eccentricity is slightly larger than that of the classical Maclaurin-to-Jacobi bifurcation. When the parameter exceeds the threshold, the Maclaurin-like spheroid does not have the bifurcation point and the Jacobi-like ellipsoid appears at the lower eccentricity than the Maclaurin-like spheroid. By comparisons of the energy of the ellipsoids with the same angular momentum, it is shown that the critical point of bifurcation does not correspond to the onset of the secular instability of Maclaurin-like spheroid. It is concluded that the gravitational field of a massive ring surrounding a uniformly rotating spheroid stabilizes it against a bar-shaped deformation due to viscous dissipations.
... Ó òàáë. 1 íà âå äå íî ä³àìåò ðè òà ñå -ðåäí³ ù³ëüíîñò³ ò³ë ãà ðÿ ÷î¿ ñêëà äî âî¿ ÏÊ, äëÿ ÿêèõ ä³àïà çî íè ïî õè áîê ìåíø³ â³ä 50 %. Òóò äàí³ äëÿ Õà ó ìåà â³äïîâ³äà þòü îö³íêàì â ðî áîò³ [15]. Çã³äíî ç äà íè ìè [9] ñå ðåä íÿ ù³ëüí³ñòü Õà ó ìåà ñòà íî âèòü 2.55 ã/ñì 3 ç ïî õèá êîþ ìåíø í³ae 4 % ïðè åêâ³âà ëåí òíî ìó ä³àìåòð³ 1240 êì. ...
... Òà êèé ðîçì³ð Õà ó ìåà áó ëî îò ðè ìà íî â ðî áîò³ [6]. ϳçí³øå ðîçì³ð Õà ó ìåà áó ëî óòî÷ íå íî, ³ â³í âè ÿ âèâ ñÿ ïîì³òíî á³ëüøèì [15]. Çã³äíî ç äà íè ìè [15] ìàê ñè ìàëü íà ñå ðåä íÿ ù³ëüí³ñòü Õà ó ìåà ñòà íîâèòü 1.885 ã/ñì 3 ïðè åêâ³âà ëåí òíî ìó ä³àìåòð³ ïðè áëèç íî 1600 êì. ...
... ϳçí³øå ðîçì³ð Õà ó ìåà áó ëî óòî÷ íå íî, ³ â³í âè ÿ âèâ ñÿ ïîì³òíî á³ëüøèì [15]. Çã³äíî ç äà íè ìè [15] ìàê ñè ìàëü íà ñå ðåä íÿ ù³ëüí³ñòü Õà ó ìåà ñòà íîâèòü 1.885 ã/ñì 3 ïðè åêâ³âà ëåí òíî ìó ä³àìåòð³ ïðè áëèç íî 1600 êì. Äàí³ äëÿ Ïëó òî íà âçÿò³ ç ðî áî òè [14]. ...
... In the last decade, three ring systems have been discovered around minor bodies in the outer Solar System: the Centaur Chariklo (Braga-Ribas et al. 2014), the dwarf planet Haumea (Ortiz et al. 2017), and the Trans-Neptunian Object (TNO) (50000) Quaoar (Morgado et al. 2023). Dense material has also been detected around the Centaur Chiron (Ruprecht et al. 2015;Ortiz et al. 2015;Sickafoose et al. 2020). ...
Context. Quaoar is a classical trans-Neptunian object (TNO) with an area-equivalent diameter of 1100 km and an orbital semi-major axis of 43.3 astronomical units. Based on stellar occultations observed between 2018 and 2021, an inhomogeneous ring (Q1R, i.e., Quaoar’s first ring) has been detected around this body.
Aims. A new stellar occultation by Quaoar was observed on August 9, 2022, with the aim of improving Quaoar’s shape models and the physical parameters of Q1R, while searching for additional material around the body.
Methods. The occultation provided nine effective chords across Quaoar, pinning down its size, shape, and astrometric position. Large facilities, such as Gemini North and the Canada-France-Hawaii Telescope (CFHT), were used to obtain high acquisition rates and signal-to-noise ratios. The light curves were also used to characterize the Q1R ring (radial profiles and orbital elements).
Results. Quaoar’s elliptical fit to the occultation chords yields the limb with an apparent semi-major axis of 579.5 ± 4.0 km, apparent oblateness of 0.12 ± 0.01, and area-equivalent radius of 543 ± 2 km. Quaoar’s limb orientation is consistent with Q1R and Weywot orbiting in Quaoar’s equatorial plane. The orbital radius of Q1R is refined to a value of 4057 ± 6 km. The radial opacity profile of the more opaque ring profile follows a Lorentzian shape that extends over 60 km, with a full width at half maximum (FWHM) of ∼5 km and a peak normal optical depth of 0.4. Besides the secondary events related to the already reported rings, new secondary events detected during the August 2022 occultation in three different data sets are consistent with another ring around Quaoar with a radius of 2520 ± 20 km, assuming the ring is circular and co-planar with Q1R. This new ring has a typical width of 10 km and a normal optical depth of ∼0.004. Just as Q1R, it also lies outside Quaoar’s classical Roche limit.
... In the last decade, three ring systems have been discovered around minor bodies in the outer Solar System: the Centaur Chariklo (Braga-Ribas et al. 2014), the dwarf planet Haumea (Ortiz et al. 2017), and the Trans-Neptunian Object (TNO) (50000) Quaoar (Morgado et al. 2023). Dense material has also been detected around the Centaur Chiron (Ruprecht et al. 2015;Ortiz et al. 2015;Sickafoose et al. 2020). ...
Quaoar is a classical Trans-Neptunian Object (TNO) with an area equivalent diameter of 1,100 km and an orbital semi-major axis of 43.3 astronomical units. Based on stellar occultations observed between 2018 and 2021, an inhomogeneous ring (Q1R, Quaoar's first ring) was detected around this body. Aims. A new stellar occultation by Quaoar was observed on August 9th, 2022 aiming to improve Quaoar's shape models and the physical parameters of Q1R while searching for additional material around the body. Methods. The occultation provided nine effective chords across Quaoar, pinning down its size, shape, and astrometric position. Large facilities, such as Gemini North and the Canada-France-Hawaii Telescope (CFHT), were used to obtain high acquisition rates and signal-to-noise ratios. The light curves were also used to characterize the Q1R ring (radial profiles and orbital elements). Results. Quaoar's elliptical fit to the occultation chords yields the limb with an apparent semi-major axis of $579.5\pm4.0$ km, apparent oblateness of $0.12\pm0.01$, and area-equivalent radius of $543\pm2$ km. Quaoar's limb orientation is consistent with Q1R and Weywot orbiting in Quaoar's equatorial plane. The orbital radius of Q1R is refined to a value of $4,057\pm6$ km. The radial opacity profile of the more opaque ring profile follows a Lorentzian shape that extends over 60 km, with a full width at half maximum (FWHM) of $\sim5$ km and a peak normal optical depth of 0.4. Besides the secondary events related to the already reported rings, new secondary events detected during the August 2022 occultation in three different data sets are consistent with another ring around Quaoar with a radius of $2,520\pm20$ km, assuming the ring is circular and co-planar with Q1R. This new ring has a typical width of 10 km and a normal optical depth of $\sim$0.004. Like Q1R, it also lies outside Quaoar's classical Roche limit.
... Similarly, for Haumea we have a 1/3 = 2,285 ± 8 km, whereas the ring orbits at 2, 287 −45 +75 km (ref. 3 ). ...
Planetary rings are observed not only around giant planets¹, but also around small bodies such as the Centaur Chariklo² and the dwarf planet Haumea³. Up to now, all known dense rings were located close enough to their parent bodies, being inside the Roche limit, where tidal forces prevent material with reasonable densities from aggregating into a satellite. Here we report observations of an inhomogeneous ring around the trans-Neptunian body (50000) Quaoar. This trans-Neptunian object has an estimated radius⁴ of 555 km and possesses a roughly 80-km satellite⁵ (Weywot) that orbits at 24 Quaoar radii6,7. The detected ring orbits at 7.4 radii from the central body, which is well outside Quaoar’s classical Roche limit, thus indicating that this limit does not always determine where ring material can survive. Our local collisional simulations show that elastic collisions, based on laboratory experiments⁸, can maintain a ring far away from the body. Moreover, Quaoar’s ring orbits close to the 1/3 spin–orbit resonance⁹ with Quaoar, a property shared by Chariklo’s2,10,11 and Haumea’s³ rings, suggesting that this resonance plays a key role in ring confinement for small bodies.
