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This article has an erratum: [https://doi.org/10.1051/0004-6361/202346365e]

Issue
A&A
Volume 673, May 2023
Article Number L4
Number of page(s) 14
Section Letters to the Editor
DOI https://doi.org/10.1051/0004-6361/202346365
Published online 05 May 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

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). However, the nature of this material, namely, whether it is a permanent or transient ring or a dust shell, is still a matter of debate.

Quaoar’s ring, referred to as Q1R hereafter, was detected during several stellar occultations observed between 2018 and 2021 (Morgado et al. 2023). Q1R has a radius of about 4100 km with significant azimuthal variations in the optical depth, ranging between 0.004 and 0.1–0.7, and in width, ranging from 5 km to 300 km. Like Chariklo’s and Haumea’s rings, Quaoar’s Q1R ring orbits close to the 1/3 spin-orbit resonance (SOR) with the central body, suggesting a link between this resonance and the ring (Salo et al. 2021; Sicardy et al. 2021; Morgado et al. 2023). Meanwhile, a unique property of Q1R is its location, which is far outside Quaoar’s classical Roche limit. This limit is estimated to be at 1780 km from the body center, assuming particles with a bulk density of ρ = 0.4 g cm−3. Outside the Roche limit, rings should accrete into satellites over timescales of less than 100 years (Kokubo et al. 2000; Takeda & Ida 2001). However, collisions more elastic than previously considered for Saturn’s ring may maintain a ring unaccreted at distances greater than the Roche limit (Morgado et al. 2023). The 6/1 mean-motion resonance (MMR) with Quaoar’s satellite, Weywot, may contribute to the confinement of the ring since the satellite’s eccentricity creates an equilibrium region capable of concentrating ring material in an arc over a longitude interval (Morgado et al. 2023). The confinement of the rings may also be due to the presence of putative “shepherd” satellites.

This Letter presents observations of a stellar occultation by Quaoar that occurred on August 9, 2022. This event was observed in Hawaii, the continental US, and Mexico. The high image acquisition rate and high signal-to-noise-ratios (S/Ns) obtained at Mauna Kea with the Alopeke camera at the Gemini North 8.1-m telescope and Wide-field InfraRed Camera (WIRCam) at the Canada-France-Hawaii 3.6-m Telescope (CFHT) allowed the dense part of Q1R to be radially resolved and its optical depth to be probed in the r′, z′ and Ks bands. Furthermore, this event revealed a new ring around Quaoar, hereafter called the Q2R (Quaoar’s second ring).

2. Prediction and observation

The occultation of August 9, 2022 was predicted within the framework of the European Research Council (ERC) Lucky Star project1. The campaign was managed by the Occultation Portal website2 described in Kilic et al. (2022). The occultation shadow crossed the continental United States, Mexico, and the Hawaiian archipelago with a geocentric shadow velocity of 17.6 km s−1. The shadow path and the sites involved in the observation campaign are shown in Appendix C.1. More details on the occulted star and Quaoar are provided in Table 1.

Table 1.

More details about the occulted star and Quaoar.

Table B.1 summarizes the observational circumstances. Among the stations, CFHT was equipped with the WIRCam (Puget et al. 2004) at 2.15 μm (Ks-band) with an 8.8 Hz acquisition rate. The nearby Gemini North telescope used the Alopeke instrument (Scott et al. 2021) to simultaneously record the event with the z′(947 nm) and r′(620 nm) bands at a 10 Hz cadence. The images at the Tohoku University Haleakala Observatory (TUHO) in Hawaii and at the Transneptunian Automated Occultation Survey (TAOS II) in Baja California (Mexico) were taken with no filter to maximize the S/N. Q2R was not detected in these observations, likely due to insufficient S/N values. At the University of California, Santa Cruz (UCSC – California, US), the Dunrhomin Observatory (Colorado, US), Sommers-Bausch Observatory (Colorado, US), Nederland (Colorado, US), and a mobile station in Bonny Doon Eco Reserve (California, US), only the main body was recorded due to a low S/N.

3. Data analysis

The data sets were analyzed using the standard photometry procedures of the Platform for Reduction of Astronomical Images Automatically (PRAIA, Assafin et al. 2011). The flux of the occulted star was corrected by the flux of nearby reference stars to account for sky transparency variations and was normalized to the total star+Quaoar flux outside the occultation.

The Stellar Occultation Reduction and Analysis package (SORA, Gomes-Júnior et al. 2022) was used to derive the ingress and egress instants of the occultation by the main body, assuming an opaque body without atmosphere. More details are presented in Appendix A. The extremities of the resulting chords were finally used to fit an elliptical model to Quaoar’s limb at the moment of the occultation.

In the case of rings, the events were fitted using the square box model described in Appendix E and pipelines based on the SORA package. This provides the radial width of the ring Wr (assuming a circular ring), its normal opacity, pN, and normal optical depth, τN, from which the equivalent width, Ep = WrpN, and equivalent depth, Aτ = WrτN, are derived.

In the case of the CFHT and Gemini data, the acquisition rate and S/N were high enough to provide resolved profiles of the dense part of Q1R. Then, Ep and Aτ can be obtained directly from the numerical calculations of the integrals Aτ = ∫Wr(vrτN)dt and Ep = ∫Wr(vrpN)dt (i.e., without using the square model described above), vr is the star velocity perpendicular to the ring, measured in the ring plane.

The dense part of Q1R has a radial profile reminiscent of the Saturnian F-ring core (Bosh et al. 2002). More precisely, it is consistent with a Lorentzian shape used here to provide the full width at half maximum (FWHM) of the profile and the event’s timing, from which its location relative to Quaoar is obtained.

4. Results

4.1. Main body

The event on August 9, 2022 provided ten chords across Quaoar’s main body. However, Gemini used a dual camera at two wavelengths, resulting in nine effective chords across the body, that is, N = 18 chord extremities with the timings listed in Table A.1.

We used the SORA package to fit an ellipse to those extremities projected in the sky plane. This ellipse is defined by M = 5 parameters and the fit has N − M = 13 degrees of freedom. The fitted parameters are the ephemeris offsets fc and gc to apply to Quaoar’s center in right ascension and declination, respectively, the apparent semi-major axis a′ of the limb, its apparent oblateness ϵ′ = (a′−b′)/a′, where b′ is the apparent semi-minor axis of the limb, and P is the position angle of b′. The elliptical fit also considers a σmodel, which is the uncertainty of the ellipse associated with the existence of putative topographic features on the surface of Quaoar. From the methodology presented by (Johnson & McGetchin 1973), we estimated that Quaoar might support topographic features of about 5 km, given Quaoar’s density ρ = 1.99 g cm−3 and strength S = 0.0303 × 109 dynes cm−2, consistent with an ice-rich composition. The standard deviation of the observed radial residuals is ∼8 km, providing an upper limit for topographic features consistent with this prediction. Considering the equivalent radius in area as 542 km, this corresponds to 1.5%. The fit results are listed in Table 2. The chords and the best-fitting elliptical limb are plotted in Fig. 1, with more details given in Fig. A.2.

Table 2.

Retrieved parameters of Quaoar’s body and its rings.

thumbnail Fig. 1.

Representation of our results on Quaoar’s shape (center) and the detection of the two rings Q1R (outer ring) and Q2R (inner ring). The red segments correspond to the 1-σ error bars on the particular events. The orbit of Q1R is determined from a simultaneous fit using the present work and previous detections of 2018, 2019, 2020, and 2021 reported by Morgado et al. (2023) (see Sect. 4.2). The solution for the orbit of the new Q2R ring assumes that this ring is co-planar and concentric with Q1R. The central part of the plot (occultation by the solid body) is enlarged in Fig. A.2. In yellow, we show the 1/3 SOR resonance with Quaoar, and in teal is the 5/7 SOR resonance (considering the double-peaked rotation period). The purple ellipse represents 6/1 MMR with Weywot, and the green ellipse presents the expected Roche limit, considering particles with a bulk density of ρ = 0.4 g cm−3. The arrow shows the star’s motion relative to Quaoar. Note: the orbital radius of Weywot is about three times larger than that of Q1R, and thus it is not shown in this representation.

4.2. Ring Q1R

The Q1R ring was detected on both sides of the main body in the Gemini and CFHT light curves, and their physical properties were determined as described in Sect. 3. Although the detections of the dense part of the Q1R in the Gemini and CFHT light curves indicate the presence of diffuse material around the ring, the quality of the TAOS II and TUHO light curves only allows for the narrow and dense part of the ring to be detected. Therefore, the parameters Ep and Aτ were determined by the square box model for these data.

Due to the low optical depth of the Q1R segment intercepted before the closest approach, only the light curves obtained at Gemini and CFHT have sufficient S/N for detection (see an example in Fig. 2 and more details in Figs. 3, D.1, E.1, and E.2). The Gemini detection in the r′ bandpass seems more sharply defined than its counterpart in z′, but this effect remains marginal considering the S/N. The CFHT light curve shows a drop simultaneously, but it may be affected by a seeing deterioration that compromises an accurate determination of the ring boundaries. Even so, the central times of the Gemini and CFHT detections are all consistent at the 1-σ level. The parameters of Q1R for all the detections are presented in Table E.1.

thumbnail Fig. 2.

Detection of Q1R, Q2R, and the main body in the Gemini (z′) light curve. The normalized flux is plotted in black vs. time (UTC), while the best-fitting models are over-plotted in red. The shallow events caused by Q1R (ingress) and Q2R (ingress and egress) are fitted by a square model. A Lorentzian function fits the dense part of Q1R at egress; see Sect. 3. The spikes observed during the disappearance and the re-appearance of the star behind Quaoar stem from the diffraction by the sharp opaque limb of the body. Note: there is a variation in the flux close to −110 and 290 s, caused by sudden variations in the seeing, and they can be neglected. More detailed views of Q1R and Q2R obtained at other telescopes are displayed in Figs. 3, D.1, E.1, and E.2.

thumbnail Fig. 3.

Detection of the Q2R ring in the Gemini and CFHT light curves. The data points are plotted in black, and the red lines are the square box model fits derived from the quantities listed in Table E.1. An arbitrary offset was applied in the vertical direction for clarity. The time axis is relative to August 9, 2022 at 06:34:49.26 UTC, the time of the closest approach of Mauna Kea to Quaoar’s shadow center.

We have combined the data from this work and the previous observations to improve the Q1R orbital parameters, assuming a fixed ring pole orientation between 2018 and 2022, as per Morgado et al. (2023). We tested a range of pole orientations and ring radii using a χ2 statistic, resulting in two complementary solutions presented in Table 2. The preferred solution has a χ2 per degree of freedom and shows a better agreement with observations than the mirror solution with . Moreover, the preferred solution is co-planar with Weywot’s orbit to within 5 ± 7 deg, as expected from a primordial disk surrounding Quaoar that evolved into a ring and formed its satellite, while the mirror solution is inclined by 45 ± 7 deg with respect to Weywot’s orbit.

The position angles of Quaoar’s projected pole (345.2 ± 1.2 deg) and Q1R (350.2 ± 0.2 deg) are misaligned by ∼5 deg (Table 2). Thus, our results are consistent with Q1R orbiting close to Quaoar’s equatorial plane, assuming that the body is an oblate spheroid. Part of this misalignment could stem from the fact that Quaoar is a triaxial ellipsoid (or a body with a more complex shape). Hence, the position angle of Quaoar’s limb does not necessarily coincide with the position angle of Quaoar’s pole.

4.3. The discovery of a new ring around Quaoar

The unique photometric quality of the Gemini and CFHT data allowed for the detection of additional material around Quaoar (Fig. 2). These data sets reveal additional secondary events symmetrically located with respect to Quaoar (Fig. 3). Two such events are simultaneously detected in the Gemini z′-band and CFHT Ks-band light curves before the closest approach, with detections reaching around 5.5σ and 5.2σ, respectively. Conversely, the light curves display simultaneous events after the closest approach with significant detections, standing at 5.7σ, 3.7σ, and 4.7σ for the Gemini z′, Gemini r′, and CFHT data sets, respectively. Assuming that the light curves have a normal distribution, the probability that individual points of equivalent width Ep(3σ)> 12 km occur randomly in each light curve is p ≈ 1.4 × 10−3, with p approaching zero for values larger than Ep. While the two light curves of the Gemini instrument may be correlated as they were taken at the same telescope, the Gemini and CFHT data are independent in terms of fast-seeing fluctuations. Using Poisson statistics, we estimate that the probability that the simultaneous events in the Gemini and CFHT data occur randomly due to the seeing fluctuations is very low, with p ≈ 10−6.

Some dips in flux were observed in the vicinity of Q2R detection in the region after the closest approach (Fig. 3). These detections are at the detection limit of our data, so we cannot say whether these are due to seeing variations or additional structures. Furthermore, we do not observe counterparts of these dips in the region before the closest approach.

All these detections are consistent with a new circular ring (Q2R) co-planar and concentric with Q1R, orbiting at 2520 ± 20 km from Quaoar (Table 2). The radial width, optical depth, equivalent width, and equivalent depth of Q2R are listed in Table E.1. They were obtained as described in Appendix E.

5. Discussion and conclusions

The stellar occultation of August 9th, 2022 provided nine effective occultation chords obtained in Hawaii, Mexico, and the continental United States. They constrained Quaoar’s shape, providing an apparent semi-major axis of a′=579.5 ± 4.0 km, an apparent oblateness ϵ′=0.12 ± 0.01, and an area-equivalent radius of km. Using an absolute magnitude of HV = 2.73 ± 0.06 (Fornasier et al. 2013), this yields a geometric albedo of pV = 0.124 ± 0.006. Our value of Requiv differs from that of Braga-Ribas et al. (2013), 555.0 ± 2.5 km, by about 12 km, that is, at the 4-σ level. This difference could be evidence that Quaoar is not an oblate spheroid, but rather a triaxial ellipsoid or a body with a more complex shape; alternatively, it may be caused by a change in the aspect-angle since 2011, as observed from Earth.

The continuous region and the dense part of Q1R were detected during this event. The dense part was radially resolved and showed a Lorentzian profile reminiscent of Saturn’s F ring (Bosh et al. 2002) or Neptune’s ring arcs (Nicholson et al. 1990; Sicardy et al. 1991). This contrasts with the sharp edges observed for Chariklo’s main ring C1R (Bérard et al. 2017; Morgado et al. 2021). The dense part of Q1R is detected over a radial width of ∼60 km with a peak optical depth of τN ≈ 0.4, an FWHM Lorentzian width of 5 km and an equivalent width Ep of around 2 km (see Table E.1). The values presented here are more precise than (but consistent with) those published by Morgado et al. (2023).

The detections of the dense part of Q1R in 2021 imply a minimum arc length of 365 km, corresponding to an azimuthal extension of about 5.1 deg (Morgado et al. 2023). The detections from CFHT, Gemini, TUHO, and TAOS II in 2022 (Figs. E.1, E.2) suggest a minimum arc-length of 226 km or ∼3.2 deg. Since 2011, we have obtained 19 cuts of the Q1R with a sufficient S/N to detect the densest region. The limited azimuthal extent of the two detections of the dense regions means that they could both be parts of the same arc-like structure. If this structure was detected two times among the 19 cuts, then its extent can be estimated using Poisson statistics. This analysis yields an arc length with a 70% chance of falling between 18 and 72 deg. In this case, all of the detections in either 2021 or 2022 would each be correlated samples of one part of this arc.

The more tenuous component of Q1R is radially resolved and shows no marked structures, being consistent with a square model within our S/N limits. The best light curves (Gemini and CFHT) provide a typical width of 80–100 km and a typical normal optical depth of 0.003 (and, thus, an equivalent width of ∼0.3 km) for that component at the longitude where it was detected (Table E.1).

Our detections, combined with those reported by Morgado et al. (2023), improved the orbital elements of Q1R. They are consistent with a circular ring of radius 4057.2 ± 5.8 km (Table 2) corresponding to about 7.5 × Quaoar’s area-equivalent radius Requiv. This value coincides with the 6/1 MMR with Weywot (4020 ± 60 km) and within 3-σ of the 1/3 SOR with Quaoar (4200 ± 60 km), considering the double-peaked rotation period of 17.6788 ± 0.0004 h (Ortiz et al. 2003).

Our preferred solution for Q1R’s orbital pole is consistent with this ring being co-planar with Weywot’s orbit. Moreover, the apparent semi-major axes of Quaoar’s limb and Q1R’s orbit are aligned at the 4-σ level, suggesting that Q1R lies in Quaoar’s equatorial plane, as expected from a colliding ring system (Kokubo et al. 2000).

Our data reveal a new ring (Q2R) around Quaoar. The detections are consistent with a circular ring of radius 2520 ± 20 km co-planar with Q1R (Table 2, Figs. 3 and 1). It has a typical width of 10 km, an optical depth of about 0.004, and an equivalent depth of about 0.04 km (see accurate values in Table E.1). Although closer to Quaoar than Q1R, Q2R is at 4.6× Quaoar’s radius, also outside Quaoar’s Roche limit, which is estimated to be around 1780 km, assuming the ring particle density as ρ = 0.4 g cm−3 (Morgado et al. 2023).

Using previously determined values for Quaoar’s mass and rotation period (Table 1), we derived a 5/7 SOR radius of 2525 ± 35 km. This coincides with Q2R’s radius, 2520 ± 20 km, to within the 1-σ error bars. Like the 1/3 SOR, the 5/7 SOR is a second-order resonance and, as such, may play an essential role in the confinement of Q2R. However, more solid determinations of Q2R’s orbit and Quaoar’s shape are required.

Table E.1 shows that differences in the equivalent widths of Q1R and Q2R are observed between the z′, r′, and Ks filters. The significance and interpretation of these differences require more analysis and will be discussed in a forthcoming publication. Moreover, the high S/N obtained at Gemini and CFHT will be used to detect or put a stringent upper limit on a putative atmosphere. Finally, the comparison of past (and possibly future) results derived from multi-chord occultations by Quaoar’s main body will be used to constrain its shape better. This will be important for better understanding the dynamics of Quaoar’s ring system, particularly under the effect of spin-orbit resonances with the body.

Acknowledgments

C.L.P is thankful for the support of the CAPES and FAPERJ/DSC-10 (E26/204.141/2022). This work was carried out within the “Lucky Star” umbrella that agglomerates the efforts of the Paris, Granada, and Rio teams, funded by the European Research Council under the European Community’s H2020 (ERC Grant Agreement No. 669416). This study was financed in part by the National Institute of Science and Technology of the e-Universe project (INCT do e-Universo, CNPq grant 465376/2014-2). This study was financed in part by CAPES – Finance Code 001. The following authors acknowledge the respective CNPq grants: B.E.M. 150612/2020-6; F.B.R. 314772/2020-0; R.V.M. 307368/2021-1; M.A. 427700/2018-3, 310683/2017-3, 473002/2013-2; J.I.B.C. 308150/2016-3, 305917/2019-6. R.C.B acknowledges the FAPERJ grant E26/202.125/2020. E.F.-V. acknowledges financial support from the Florida Space Institute and the Space Research Initiative. J.L.O., P.S.-S., M.V-L, and M.K. acknowledge financial support from the grant CEX2021-001131-S funded by MCIN/AEI/ 10.13039/501100011033, they also acknowledge the financial support by the Spanish grants PID2020-112789GB-I00 from AEI and Proyecto de Excelencia de la Junta de Andalucía PY20-01309. Funding for RECON was provided by grants from USA: NSF AST-1413287, AST-1413072, AST-1848621, and AST-1212159. We thank RECON observers Doug Thompson, Ken Conway, Dorey Conway, Terry Miller, David Schulz, Michael von Schalscha, and Matt Christensen for their efforts in collecting data. Based on observations obtained with WIRCam, a joint project of CFHT, Taiwan, Korea, Canada, France, at the Canada-France-Hawaii Telescope (CFHT) which is operated from the summit of Maunakea by the National Research Council of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. The observations at the Canada-France-Hawaii Telescope were performed with care and respect from the summit of Maunakea which is a significant cultural and historic site. We thank Marc Baril and Tom Vermeulen for their time dedicated to the observation performed at Canada-France-Hawaii Telescope (CFHT). Based on observations obtained at the international Gemini Observatory, a program of NSF’s NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). This work made use of data from GN-2022B-DD-101 observing program and were obtained with the High-Resolution Imaging instrument(s) ‘Alopeke (and/or Zorro). ‘Alopeke (and/or Zorro) was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley. ‘Alopeke (and/or Zorro) was mounted on the Gemini North (and/or South) telescope of the international Gemini Observatory, a program of NSF’s NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. This work was enabled by observations made from the Gemini North telescope, located within the Maunakea Science Reserve and adjacent to the summit of Maunakea. We are grateful for the privilege of observing the Universe from a place that is unique in both its astronomical quality and its cultural significance. This research used SORA, a python package for stellar occultations reduction and analysis, developed with the support of ERC Lucky Star and LIneA/Brazil, within the collaboration of Rio-Paris-Granada teams. This work profited from unpublished occultations by Quaoar made at SOAR (SO2019A-003) and the Pico dos Dias Observatory (OP2019A-004) to improve the accuracy of the ephemeris NIMAv16.

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Appendix A: Main body occultation and elliptical fit

The light curves obtained with the Gemini and CFHT telescopes present prominent diffraction signatures in the main body occultation mainly due to the high acquisition rate, the large wavelength, and high S/N of the light curves. During the occultation, Quaoar was at a geocentric distance of 41.983157 au, implying a Fresnel scale, , from 1.5 to 2.6 km, for visible to near-infrared (CFHT Ks-band) wavelengths, respectively. Considering the apparent velocity of the event as 17.57 km s−1 and the acquisition rate of the Gemini and CFHT instruments, we obtained a spatial resolution of these light curves of ∼1.8 km. These high-S/N light curves have a Fresnel diffraction effect on the same order of magnitude as the instrumental response (e.g., the integration time).

With the limb-darkened angular diameter of the star estimated and considering the observation band pass and its FWHM, we also fit the local normal velocity (v⊥). By minimizing the χ2 statistic, we found the velocity and the ingress (egress) time that best explained the observed light curve. This was applied to the Gemini z’-band data since this was our best light curve. The radial velocities obtained are v⊥ = 10.2 km s−1 and v⊥ = 16.6 km s−1 for ingress and egress instants, respectively. The separation between the chords obtained from the Gemini and CFHT when projected onto the sky plane was about 160 meters, a value smaller than the star’s apparent diameter. Therefore, the velocities were considered the same at both sites. This procedure resulted in an optimal fit for both diffraction spikes and the baseline occultation by the main body. Figure A.1 presents an example of this fit with the Gemini z’ light curve plotted with the modeled curve.

thumbnail Fig. A.1.

Gemini z’ light curve (black dots) and the modeled light curve (red) considering the local normal star velocity, the wavelength and apparent star size. The geometric model is in blue. The normalized flux is plotted as a function of the seconds before and after the local closest approach (2022-08-09 06:34:49.26 UT).

Ingress and egress times for the main body occultation are presented in Table A.1. The instant uncertainties of the Gemini and CFHT light curves are limited by occultation modeling, not data quality. The elliptical fit parameters to the chord extremities are presented in Fig. A.2.

Table A.1.

Ingress and egress times for Quaoar’s main body.

thumbnail Fig. A.2.

Close-up view of Fig. 1 shows the best elliptical fit (black ellipse) and ellipses within 1-σ region (grey) to the ten chords derived from the timings in Table A.1. The grey 1-σ fits differ only slightly from the black best-fit. The red segments represent the 1-σ error bars in the ingress and egress times. At this scale, the Gemini and CFHT chords are superimposed, and their error bars would be too small to be seen (i.e., they are here represented by red squares, much bigger than their actual sizes).

Appendix B: Observational circumstances

The observational circumstances for this occultation campaign are presented in Table B.1. We present in this work the analysis of ten data sets with positive detections for the main body, of which four are detections of the Q1R ring and three are detections of both the Q1R and Q2R rings. In addition, we have more eighteen sites that participated in the observation campaign, but reported cloudy skies. The target star was too faint for the setup in Woodside (CA, US) and Summerland BC, CA, even with 4 and 3 seconds of exposure, respectively; in addition, the Summerland data was acquired while clouds were drifting through the field.

Table B.1.

Observational circumstances.

Appendix C: Occultation map

Figure C.1 presents the stellar occultation map with all the sites involved in this campaign. The green dots mark the positive detections and orange dots are stations that reported cloudy weather. The white dot represents the Woodside observation with the eVscope where the event was not detected due to the low S/N of the data set. The continuous line represents the limit of the Quaoar’s shadow projected over the Earth. The dashed-lines represent the Q1R and Q2R projections, as annotated in the image.

thumbnail Fig. C.1.

Occultation map with positive detections (black dots) and sites that reported cloudy weather (orange dots). The white dot represents no data due to the instrumental limits. In red we display a site with data but no occultation detected. The black solid lines mark Quaoar’s shadow limits and the black dashed lines mark the Q1R and Q2R projections. The black arrow in the bottom right indicates the direction of motion of the shadow.

Appendix D: Light curves

Figure D.1 displays all the normalized light curves obtained during the stellar occultation by (50000) Quaoar of August 9, 2022. The stellar flux has been corrected for sky transparency fluctuations using reference stars. The time scale is relative to the closest approach time at each site. Besides the occultation by Quaoar and Q1R, the Gemini and CFHT light curves revealed the new Q2R ring. The Tohoku (TUHO) and TAOS II data allowed for the detection of the densest region of the Q1R ring. Due to the S/N limitations, the Nederland, Dunrhomin, Sommers-Bausch, UCSC, and Bonny Doon stations detected only the occultation by the main body. Some data sets presented dropped frames during the photometric process, such as the Durhomin and Nederland. This occurred due to the degradation of the sky quality shortly after the occultation of the main body, in addition to clouds crossing the field of view of the telescope.

We noticed that the Gemini and CFHT light curves were misaligned in time, probably caused by an offset in the Gemini data. As we have a reliable time source for the CFHT data, we aligned the centers of these chords by applying an offset of + 0.27 seconds on the Gemini chord, obtaining values of closer to 1. Although very close, this result is slightly better than applying an offset to the CFHT chord.

thumbnail Fig. D.1.

All the positive light curves obtained during the August 9, 2022 stellar occultation by Quaoar. The black dots represent the data points. These light curves are plotted as a function of the time in seconds relative to the closest approach for each site. The green and gray vertical lines stand for Q2R and Q1R, respectively. When detected, these lines stand for calculated detection times. For light curves where these secondary structures were not detected, the green and gray lines mark theoretical times expected from our best-fit solution for a circular ring. The horizontal gray dashed lines represent the baseline and minima of the stellar fluxes.

Appendix E: Modeled ring detections

The ring events were fit using the models described in Elliot et al. (1984) and Bérard et al. (2017), that is, square boxes with uniform opacity and sharp edges. As with the main body occultation modeling, the modeled curve was convolved with observation bandpass, apparent star diameter, and instrumental response, but now fitting an opacity for the square box. The outputs of a given fit are the width, W, of the event, its apparent opacity, p′ (corresponding to the depth of the observed stellar flux drop), and its apparent optical depth, τ′= − ln(1 − p′). The geometry of the ring (assumed here to be circular) is defined by its opening angle, B, and the position angle, P, of its apparent semi-minor axis, counted positively from local celestial north to the celestial east direction. This provides the radial width, Wr, the normal opacity, , and the normal optical depth, τN = τ′ |sinB|/2, of the ring from each event. The factor of 2 in the formula for τN is due to the fact that Airy diffraction by individual ring particles results in a loss of light, resulting in an observed optical depth to be twice as large as would be measured at the ring level; see more details in Cuzzi (1985), Roques et al. (1987). We note that the formulae for pN and τN are valid only for mono-layer and poly-layer rings, respectively. The equivalent width (respectively, depth) Ep = WrpN (respectively, Aτ = WrτN) measures the amount of ring material that blocked the stellar rays in the mono-layer (resp. poly-layer) case.

A Lorentzian function is fitted to the dense part of the Q1R in the Gemini and CFHT light curves, converted from flux to normal optical depth as a function of radial distance in the ring plane. The area under the curve equals the equivalent width, Aτ, of the ring, and the full-width half minimum (FWHM) gives us the approximate width of the ring’s core. The position of the function’s valley gives us the average radial distance between the ring and Quaoar’s center. The Ep value was obtained from the integral of the ring profile in the curve of the normal opacity, pN, as a function of the radial distance in the sky plane. This modeling considers the stellar apparent diameter of 1.33 km, which has negligible influence on the ring profile.

Figs. E.1 and E.2 present all light curves in which the Q1R and Q2R rings were detected. The TAOS II light curve, used for detecting of the densest region of the Q1R ring, was obtained by applying aperture photometry to stacked images in order to increase the S/N. Stacking was performed using Python routines built from the astropy library as described in Morgado et al. (2019), where each new image is the average of six original images, resulting in a temporal resolution of 1.2 seconds for each stacked image.

Table E.1.

Physical parameters of rings Q1R and Q2R.

thumbnail Fig. E.1.

Fits to the Q1R and Q2R light curve data taken with Gemini (z’), Gemini (r’), and CFHT (Ks) (the corresponding filters are indicated in parentheses). These light curves are plotted as a function of the time in seconds relative to the local closest approach (C/A). The blue dots represent residuals with an arbitrary vertical offset for clarity. Note: the y-axis scale is different in the rightmost panel in each row (dense part of Q1R).

thumbnail Fig. E.2.

Fits to the Q1R dense ring in light curve data taken with TUHO and TAOS II telescopes, from top to bottom. TAOS II data are stacked every six images. These light curves are plotted as a function of the time in seconds relative to the local closest approach (C/A), with a different y-axis scale in the rightmost panel in each row (dense part of Q1R). The green vertical dashed lines represent the theoretical times for the Q1R and Q2R rings. Note: although marginal, the two data points that detect the Q1R ring in the TAOS II light curve are statistically significant at the 4.2-σ level.

All Tables

Table 1.

More details about the occulted star and Quaoar.

In the text
Table 2.

Retrieved parameters of Quaoar’s body and its rings.

In the text
Table A.1.

Ingress and egress times for Quaoar’s main body.

In the text
Table B.1.

Observational circumstances.

In the text
Table E.1.

Physical parameters of rings Q1R and Q2R.

In the text

All Figures

thumbnail Fig. 1.

Representation of our results on Quaoar’s shape (center) and the detection of the two rings Q1R (outer ring) and Q2R (inner ring). The red segments correspond to the 1-σ error bars on the particular events. The orbit of Q1R is determined from a simultaneous fit using the present work and previous detections of 2018, 2019, 2020, and 2021 reported by Morgado et al. (2023) (see Sect. 4.2). The solution for the orbit of the new Q2R ring assumes that this ring is co-planar and concentric with Q1R. The central part of the plot (occultation by the solid body) is enlarged in Fig. A.2. In yellow, we show the 1/3 SOR resonance with Quaoar, and in teal is the 5/7 SOR resonance (considering the double-peaked rotation period). The purple ellipse represents 6/1 MMR with Weywot, and the green ellipse presents the expected Roche limit, considering particles with a bulk density of ρ = 0.4 g cm−3. The arrow shows the star’s motion relative to Quaoar. Note: the orbital radius of Weywot is about three times larger than that of Q1R, and thus it is not shown in this representation.
In the text
thumbnail Fig. 2.

Detection of Q1R, Q2R, and the main body in the Gemini (z′) light curve. The normalized flux is plotted in black vs. time (UTC), while the best-fitting models are over-plotted in red. The shallow events caused by Q1R (ingress) and Q2R (ingress and egress) are fitted by a square model. A Lorentzian function fits the dense part of Q1R at egress; see Sect. 3. The spikes observed during the disappearance and the re-appearance of the star behind Quaoar stem from the diffraction by the sharp opaque limb of the body. Note: there is a variation in the flux close to −110 and 290 s, caused by sudden variations in the seeing, and they can be neglected. More detailed views of Q1R and Q2R obtained at other telescopes are displayed in Figs. 3, D.1, E.1, and E.2.
In the text
thumbnail Fig. 3.

Detection of the Q2R ring in the Gemini and CFHT light curves. The data points are plotted in black, and the red lines are the square box model fits derived from the quantities listed in Table E.1. An arbitrary offset was applied in the vertical direction for clarity. The time axis is relative to August 9, 2022 at 06:34:49.26 UTC, the time of the closest approach of Mauna Kea to Quaoar’s shadow center.
In the text
thumbnail Fig. A.1.

Gemini z’ light curve (black dots) and the modeled light curve (red) considering the local normal star velocity, the wavelength and apparent star size. The geometric model is in blue. The normalized flux is plotted as a function of the seconds before and after the local closest approach (2022-08-09 06:34:49.26 UT).
In the text
thumbnail Fig. A.2.

Close-up view of Fig. 1 shows the best elliptical fit (black ellipse) and ellipses within 1-σ region (grey) to the ten chords derived from the timings in Table A.1. The grey 1-σ fits differ only slightly from the black best-fit. The red segments represent the 1-σ error bars in the ingress and egress times. At this scale, the Gemini and CFHT chords are superimposed, and their error bars would be too small to be seen (i.e., they are here represented by red squares, much bigger than their actual sizes).
In the text
thumbnail Fig. C.1.

Occultation map with positive detections (black dots) and sites that reported cloudy weather (orange dots). The white dot represents no data due to the instrumental limits. In red we display a site with data but no occultation detected. The black solid lines mark Quaoar’s shadow limits and the black dashed lines mark the Q1R and Q2R projections. The black arrow in the bottom right indicates the direction of motion of the shadow.
In the text
thumbnail Fig. D.1.

All the positive light curves obtained during the August 9, 2022 stellar occultation by Quaoar. The black dots represent the data points. These light curves are plotted as a function of the time in seconds relative to the closest approach for each site. The green and gray vertical lines stand for Q2R and Q1R, respectively. When detected, these lines stand for calculated detection times. For light curves where these secondary structures were not detected, the green and gray lines mark theoretical times expected from our best-fit solution for a circular ring. The horizontal gray dashed lines represent the baseline and minima of the stellar fluxes.
In the text
thumbnail Fig. E.1.

Fits to the Q1R and Q2R light curve data taken with Gemini (z’), Gemini (r’), and CFHT (Ks) (the corresponding filters are indicated in parentheses). These light curves are plotted as a function of the time in seconds relative to the local closest approach (C/A). The blue dots represent residuals with an arbitrary vertical offset for clarity. Note: the y-axis scale is different in the rightmost panel in each row (dense part of Q1R).
In the text
thumbnail Fig. E.2.

Fits to the Q1R dense ring in light curve data taken with TUHO and TAOS II telescopes, from top to bottom. TAOS II data are stacked every six images. These light curves are plotted as a function of the time in seconds relative to the local closest approach (C/A), with a different y-axis scale in the rightmost panel in each row (dense part of Q1R). The green vertical dashed lines represent the theoretical times for the Q1R and Q2R rings. Note: although marginal, the two data points that detect the Q1R ring in the TAOS II light curve are statistically significant at the 4.2-σ level.
In the text

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