arXiv subjects

D. Ehrenreich

Publications and source records attributed to D. Ehrenreich.

At least 163 records · Page 9Linked to original sources

arXiv2019

High-resolution confirmation of an extended helium atmosphere around WASP-107b

Probing the evaporation of exoplanet atmospheres is key to understanding the formation and evolution of exoplanetary systems. The main tracer of evaporation in the UV is the Lyman-alpha transition, which can reveal extended exospheres. Recently, NIR metastable helium triplet (1.08 microns) revealed extended thermospheres in several exoplanets, opening a new window into evaporation. We aim at spectrally resolving the first helium absorption signature detected in WASP-107b with HST/WFC3. We obtained one transit of WASP-107b with the high-resolution spectrograph CARMENES. We detect an excess helium absorption signature of 5.54+/-0.27 % in the planet rest frame during the transit. The detection is in agreement with the previous detection done with WFC3. The signature shows an excess absorption in the blue part of the lines suggesting that HeI atoms are escaping from the atmosphere of WASP-107b. We interpret the time-series absorption spectra using the 3D EVE code. Our observations can be explained by combining an extended thermosphere filling half the Roche lobe and a large exospheric tail sustained by an escape rate of metastable helium on the order of 10^6 g/s. In this scenario, however, the upper atmosphere needs to be subjected to a reduced photoionisation and radiation pressure from the star for the model to match the observations. The helium feature is detected from space and the ground. The ground-based high-resolution signal brings detailed information about the spatial and dynamical structure of the upper atmosphere, and simulations suggest that the HeI signature of WASP-107b probes both its thermosphere and exosphere establishing this signature as a robust probe of exoplanetary upper atmospheres. Surveys with NIR high-resolution spectrographs (e.g. CARMENES, SPIRou or NIRPS) will deliver a statistical understanding of exoplanet thermospheres and exospheres via the helium triplet.

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arXiv2018

Hubble PanCET: An extended upper atmosphere of neutral hydrogen around the warm Neptune GJ 3470 b

GJ 3470b is a warm Neptune transiting an M-dwarf star at the edge of the evaporation desert. It offers the possibility of investigating how low-mass, close-in exoplanets evolve under the irradiation from their host stars. We observed three transits of GJ 3470b in the Lyman-alpha line with the Hubble Space Telescope (HST) as part of the Panchromatic Comparative Exoplanet Treasury (PanCET) program. Absorption signatures are detected with similar properties in all three independent epochs, with absorption depths of 35+-7% in the blue wing of the line, and 23+-5% in the red wing. The repeatability of these signatures, their phasing with the planet transit, and the radial velocity of the absorbing gas allow us to conclude that there is an extended upper atmosphere of neutral hydrogen around GJ 3470 b. We determine from our observations the stellar radiation pressure and XUV irradiation from GJ 3470 and use them to perform numerical simulations of the upper atmosphere of GJ 3470b with the EVaporating Exoplanets (EVE) code. The unusual redshifted signature can be explained by the damping wings of dense layers of neutral hydrogen that extend beyond the Roche lobe and are elongated in the direction of the planet motion. This structure could correspond to a shocked layer of planetary material formed by the collision of the expanding thermosphere with the wind of the star. The blueshifted signature is well explained by neutral hydrogen atoms escaping at rates of about 1e10 g s-1 that are blown away from the star by its strong radiation pressure and are quickly photoionized, resulting in a smaller exosphere than that of the warm Neptune GJ 436b. The stronger escape from GJ 3470b, however, may have led to the loss of about 4-35% of its current mass over its 2 Gyr lifetime.

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arXiv2018

Spectrally resolved helium absorption from the extended atmosphere of a warm Neptune-mass exoplanet

Stellar heating causes atmospheres of close-in exoplanets to expand and escape. These extended atmospheres are difficult to observe because their main spectral signature - neutral hydrogen at ultraviolet wavelengths - is strongly absorbed by interstellar medium. We report the detection of the near-infrared triplet of neutral helium in the transiting warm Neptune-mass exoplanet HAT-P-11b using ground-based, high-resolution observations. The helium feature is repeatable over two independent transits, with an average absorption depth of 1.08+/-0.05%. Interpreting absorption spectra with 3D simulations of the planet's upper atmosphere suggests it extends beyond 5 planetary radii, with a large scale height and a helium mass loss rate =< 3x10^5 g/s. A net blue-shift of the absorption might be explained by high-altitude winds flowing at 3 km/s from day to night-side.

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arXiv2018

Extrasolar planets and brown dwarfs around AF-type stars. X.The SOPHIE northern sample. Combining the SOPHIE and HARPS surveys to compute the close giant planet mass-period distribution around AF-type stars

The impact of the stellar mass on the giant planet properties is still to be fully understood. Main-Sequence (MS) stars more massive than the Sun remain relatively unexplored in radial velocity (RV) surveys, due to their characteristics that hinder classical RV measurements. Our aim is to characterize the close (up to 2.5 au) giant planet (GP) and brown dwarf (BD) population around AF MS stars and compare this population to stars with different masses. We used the SOPHIE spectrograph located on the 1.93m telescope at Observatoire de Haute-Provence to observe 125 northern, MS AF dwarfs. We used our dedicated SAFIR software to compute the RV and other spectroscopic observables. We characterized the detected sub-stellar companions and computed the GP and BD occurrence rates combining the present SOPHIE survey and a similar HARPS survey. We present new data on two known planetary systems around the F5-6V dwarfs HD16232 and HD113337. For the latter, we report an additional RV variation that might be induced by a second GP on a wider orbit. We also report the detection of fifteen binaries or massive sub-stellar companions with high-amplitude RV variations or long-term RV trends. Based on 225 targets observed with SOPHIE or HARPS, we constraint the BD frequency within 2-3 au around AF stars to be below 4 percents (1-sigma). For Jupiter-mass GP within 2-3 au (periods below 1000 days), we found the occurrence rate to be 3.7 (+3/-1) percents around AF stars with masses below 1.5 solar masses, and to be below 6 percents around AF stars with masses above 1.5 solar masses. For periods smaller than 10 days, we find the GP occurrence rate to be below 3 or 4.5 percents, respectively. Our results are compatible with the GP frequency reported around FGK dwarfs and are compatible with a possible increase of GP orbital periods with the stellar mass as predicted by formation models.

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arXiv2018

The 55 Cnc system reassessed

Orbiting a bright, nearby star the 55 Cnc system offers a rare opportunity to study a multiplanet system that has a wide range of planetary masses and orbital distances. Using two decades of photometry and spectroscopy data, we have measured the rotation of the host star and its solar-like magnetic cycle. Accounting for this cycle in our velocimetric analysis of the system allows us to revise the properties of the outermost giant planet and its four planetary companions. The innermost planet 55 Cnc e is an unusually close-in super-Earth, whose transits have allowed for detailed follow-up studies. Recent observations favor the presence of a substantial atmosphere yet its composition, and the nature of the planet, remain unknown. We combined our derived planet mass (Mp = 8.0+-0.3 Mearth) with refined measurement of its optical radius derived from HST/STIS observations (Rp = 1.88+-0.03 Rearth over 530-750nm) to revise the density of 55 Cnc e (rho = 6.7+-0.4 g cm-3). Based on these revised properties we have characterized possible interiors of 55 Cnc e using a generalized Bayesian model. We confirm that the planet is likely surrounded by a heavyweight atmosphere, contributing a few percents of the planet radius. While we cannot exclude the presence of a water layer underneath the atmosphere, this scenario is unlikely given the observations of the planet across the entire spectrum and its strong irradiation. Follow-up observations of the system in photometry and in spectroscopy over different time-scales are needed to further investigate the nature and origin of this iconic super-Earth.

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arXiv2018

The SOPHIE search for northern extrasolar planets XIII. Two planets around M-dwarfs Gl617A and Gl96

We report the detection of two exoplanets and a further tentative candidate around the M-dwarf stars Gl96 and Gl617A, based on radial velocity measurements obtained with the SOPHIE spectrograph at the Observatoire de Haute-Provence. Both stars were observed in the context of the SOPHIE exoplanet consortium's dedicated M-dwarf subprogramme, which aims to detect exoplanets around nearby M-dwarf stars through a systematic survey. For Gl96, we present the discovery of a new exoplanet at 73.9 d with a minimum mass of 19.66 earth masses. Gl96 b has an eccentricity of 0.44, placing it among the most eccentric planets orbiting M stars. For Gl617A we independently confirm a recently reported exoplanet at 86.7 d with a minimum mass of 31.29 earth masses. Both Gl96 b and Gl617A b are potentially within the habitable zone, though Gl96 b's high eccentricity may take it too close to the star at periapsis.

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arXiv2018

Helium in the eroding atmosphere of an exoplanet

Helium is the second-most abundant element in the Universe after hydrogen and is one of the main constituents of gas-giant planets in our Solar System. Early theoretical models predicted helium to be among the most readily detectable species in the atmospheres of exoplanets, especially in extended and escaping atmospheres. Searches for helium, however, have hitherto been unsuccessful. Here we report observations of helium on an exoplanet, at a confidence level of 4.5 standard deviations. We measured the near- infrared transmission spectrum of the warm gas giant WASP-107b and identified the narrow absorption feature of excited metastable helium at 10,833 angstroms. The amplitude of the feature, in transit depth, is 0.049 +/- 0.011 per cent in a bandpass of 98 angstroms, which is more than five times greater than what could be caused by nominal stellar chromospheric activity. This large absorption signal suggests that WASP-107b has an extended atmosphere that is eroding at a total rate of 10^10 to 3 x 10^11 grams per second (0.1-4 per cent of its total mass per billion years), and may have a comet-like tail of gas shaped by radiation pressure.

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arXiv2018

High-energy environment of super-Earth 55 Cnc e I: Far-UV chromospheric variability as a possible tracer of planet-induced coronal rain

The irradiation of close-in planets by their star influences their evolution and might be responsible for a population of ultra-short period planets eroded to their bare core. In orbit around a bright, nearby G-type star, the super-Earth 55 Cnc e offers the possibility to address these issues through UV transit observations. We used the Hubble Space Telescope to observe the transit in the FUV over 3 epochs in Apr. 2016, Jan. 2017, and Feb. 2017. These observations reveal significant short- and long-term variability in 55 Cnc chromospheric emission lines. In the last 2 epochs, we detected a larger flux in the C III, Si III, and Si IV lines after the planet passed the approaching quadrature, followed by a flux decrease in the Si IV doublet. In the second epoch these variations are contemporaneous with flux decreases in the Si II and C II doublet. All epochs show flux decreases in the N V doublet as well, albeit at different orbital phases. These flux decreases are consistent with absorption from optically thin clouds of gas, are mostly localized at low and redshifted radial velocities in the star rest frame, and occur preferentially before and during the transit. These 3 points make it unlikely that the variations are purely stellar, yet we show that the occulting material is also unlikely to originate from the planet. We tentatively propose that the motion of 55 Cnc e at the fringes of the stellar corona leads to the formation of a cool coronal rain. The inhomogeneity and temporal evolution of the stellar corona would be responsible for the differences between the visits. Additional variations are detected in the C II doublet in the first epoch and in the O I triplet in all epochs with a different behavior that points toward intrinsic stellar variability. Further observations at FUV wavelengths are required to disentangle between star-planet interactions and the activity of the star

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arXiv2017

Hubble PanCET: An isothermal day-side atmosphere for the bloated gas-giant HAT-P-32Ab

We present a thermal emission spectrum of the bloated hot Jupiter HAT-P-32Ab from a single eclipse observation made in spatial scan mode with the Wide Field Camera 3 (WFC3) aboard the Hubble Space Telescope (HST). The spectrum covers the wavelength regime from 1.123 to 1.644 microns which is binned into 14 eclipse depths measured to an averaged precision of 104 parts-per million. The spectrum is unaffected by a dilution from the close M-dwarf companion HAT-P-32B, which was fully resolved. We complemented our spectrum with literature results and performed a comparative forward and retrieval analysis with the 1D radiative-convective ATMO model. Assuming solar abundance of the planet atmosphere, we find that the measured spectrum can best be explained by the spectrum of a blackbody isothermal atmosphere with Tp = 1995 +/- 17K, but can equally-well be described by a spectrum with modest thermal inversion. The retrieved spectrum suggests emission from VO at the WFC3 wavelengths and no evidence of the 1.4 micron water feature. The emission models with temperature profiles decreasing with height are rejected at a high confidence. An isothermal or inverted spectrum can imply a clear atmosphere with an absorber, a dusty cloud deck or a combination of both. We find that the planet can have continuum of values for the albedo and recirculation, ranging from high albedo and poor recirculation to low albedo and efficient recirculation. Optical spectroscopy of the planet's day-side or thermal emission phase curves can potentially resolve the current albedo with recirculation degeneracy.

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arXiv2017

Fe I in the β Pictoris circumstellar gas disk I. Physical properties of the neutral iron gas

The young planetary system β Pictoris is surrounded by a circumstellar disk of dust and gas. Because both dust and gas have a lifetime shorter than the system age, they need to be replenished continuously. The gas composition is partly known, but its location and its origin are still a puzzle. The gas source could be the exocomets (or so-called falling and evaporating bodies, FEBs), which are observed as transient features in absorption lines of refractory elements (Mg, Ca, and Fe) when they transit in front of the star at several tens of stellar radii. Nearly 1700 high-resolution spectra of β Pictoris have been obtained from 2003 to 2015 using the HARPS spectrograph. In these spectra, the circumstellar disk is always detected as a stable component among the numerous variable absorption signatures of transiting exocomets. Summing all the 1700 spectra allowed us to reach a signal-to-noise ratio higher than 1000, which is an unprecedentedly high number for a β Pictoris spectrum. It revealed many weak Fe I absorption lines of the circumstellar gas in more than ten excited states. These weak lines bring new information on the physical properties of the neutral iron gas in the circumstellar disk. The population of the first excited levels follows a Boltzmann distribution with a slope consistent with a gas temperature of about 1300 K; this temperature corresponds to a distance to the star of ~ 38 RStar and implies a turbulence of ξ ~ 0.8 km/s.

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arXiv2017

The long egress of GJ~436b's giant exosphere

The M dwarf GJ 436 hosts a transiting warm Neptune known to experience atmospheric escape. Previous observations revealed the presence of a giant hydrogen exosphere transiting the star for more than 5 h, and absorbing up to 56% of the flux in the blue wing of the stellar Lyman-α line of neutral hydrogen (H i Lyα). The unexpected size of this comet-like exosphere prevented observing the full transit of its tail. In this Letter, we present new Lyα observations of GJ 436 obtained with the Space Telescope Imaging Spectrograph (STIS) instrument onboard the Hubble Space Telescope. The stability of the Lyα line over six years allowed us to combine these new observations with archival data sets, substantially expanding the coverage of the exospheric transit. Hydrogen atoms in the tail of the exospheric cloud keep occulting the star for 10-25 h after the transit of the planet, remarkably confirming a previous prediction based on 3D numerical simulations with the EVaporating Exoplanet code (EVE). This result strengthens the interpretation that the exosphere of GJ 436b is shaped by both radiative braking and charge exchanges with the stellar wind. We further report flux decreases of 15 +/- 2% and 47 +/- 10% in the red wing of the Lyα line and in the line of ionised silicon (Si iii). Despite some temporal variability possibly linked with stellar activity, these two signals occur during the exospheric transit and could be of planetary origin. Follow-up observations will be required to assess the possibility that the redshifted Lyα and Si iii absorption signatures arise from interactions between the exospheric flow and the magnetic field of the star.

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arXiv2017

Precise masses for the transiting planetary system HD 106315 with HARPS

The multi-planetary system HD 106315 was recently found in K2 data . The planets have periods of $P_b \sim9.55$ and $P_c \sim 21.06\,$days, and radii of $ r_b = 2.44 \pm 0.17\, $ and $r_c = 4.35 \pm 0.23\, $ $R_{\oplus}$. The brightness of the host star (V=9.0 mag) makes it an excellent target for transmission spectroscopy. However, to interpret transmission spectra it is crucial to measure the planetary masses. We obtained high precision radial velocities for HD~106315 to determine the mass of the two transiting planets discovered with Kepler K2. Our successful observation strategy was carefully tailored to mitigate the effect of stellar variability. We modelled the new radial velocity data together with the K2 transit photometry and a new ground-based partial transit of HD 106315c to derive system parameters. We estimate the mass of HD 106315b to be 12.6 $\pm$ 3.2 $M_{\oplus}$ and the density to be $4.7 \pm 1.7\, g\,cm^{-3}$, while for HD 106315c we estimate a mass of 15.2 $\pm$ 3.7 $M_{\oplus}$ and a density of $1.01 \pm 0.29\, $g\,cm$^{-3}$. Hence, despite planet c having a radius almost twice as large as planet b, their masses are consistent with one another. We conclude that HD 106315c has a thick hydrogen-helium gaseous envelope. A detailed investigation of HD 106315b using a planetary interior model constrains the core mass fraction to be 5-29\%, and the water mass fraction to be 10-50\%. An alternative, not considered by our model, is that HD 106315b is composed of a large rocky core with a thick H-He envelope. Transmission spectroscopy of these planets will give insight into their atmospheric compositions and also help constrain their core compositions.

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arXiv2017

Temporal evolution of the high-energy irradiation and water content of TRAPPIST-1 exoplanets

The ultracool dwarf star TRAPPIST-1 hosts seven Earth-size transiting planets, some of which could harbour liquid water on their surfaces. UV observations are essential to measure their high-energy irradiation, and to search for photodissociated water escaping from their putative atmospheres. Our new observations of TRAPPIST-1 Ly-$α$ line during the transit of TRAPPIST-1c show an evolution of the star emission over three months, preventing us from assessing the presence of an extended hydrogen exosphere. Based on the current knowledge of the stellar irradiation, we investigated the likely history of water loss in the system. Planets b to d might still be in a runaway phase, and planets within the orbit of TRAPPIST-1g could have lost more than 20 Earth oceans after 8 Gyr of hydrodynamic escape. However, TRAPPIST-1e to h might have lost less than 3 Earth oceans if hydrodynamic escape stopped once they entered the habitable zone. We caution that these estimates remain limited by the large uncertainty on the planet masses. They likely represent upper limits on the actual water loss because our assumptions maximize the XUV-driven escape, while photodissociation in the upper atmospheres should be the limiting process. Late-stage outgassing could also have contributed significant amounts of water for the outer, more massive planets after they entered the habitable zone. While our results suggest that the outer planets are the best candidates to search for water with the JWST, they also highlight the need for theoretical studies and complementary observations in all wavelength domains to determine the nature of the TRAPPIST-1 planets, and their potential habitability.

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arXiv2017

Ground-based photometry of the 21-day Neptune HD106315c

Space-based transit surveys such as K2 and TESS allow the detection of small transiting planets with orbital periods beyond 10 days. Few of these warm Neptunes are currently known around stars bright enough to allow for detailed follow-up observations dedicated to their atmospheric characterization. The 21-day period and 3.95 $R_\oplus$ planet HD106315c has been discovered based on the observation of two of its transits by K2. We have observed HD106315 using the 1.2m Euler telescope equipped with the EulerCam camera on two instances to confirm the transit using broad band photometry and refine the planetary period. Based on two observed transits of HD106315c, we detect its $\sim$1 mmag transit and obtain a precise measurement of the planetary ephemerids, which are critical for planning further follow-up observations. We have used the attained precision together with the predicted yield from the TESS mission to evaluate the potential for ground-based confirmation of Neptune-sized planets found by TESS. We find that 1-meter-class telescopes on the ground equipped with precise photometers could substantially contribute to the follow-up of 162 TESS candidates orbiting stars with magnitudes of $V \leq 14$. Out of these, 74 planets orbit stars with $V \leq 12$ and 12 planets orbit $V \leq 10$, which makes these candidates high-priority objects for atmospheric characterization with high-end instrumentation.

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arXiv2017

Characterization of the K2-18 multi-planetary system with HARPS: A habitable zone super-Earth and discovery of a second, warm super-Earth on a non-coplanar orbit

The bright M dwarf K2-18 at 34 pc is known to host a transiting super-Earth-sized planet orbiting within the star's habitable zone; K2-18b. Given the superlative nature of this system for studying an exoplanetary atmosphere receiving similar levels of insolation as the Earth, we aim to characterize the planet's mass which is required to interpret atmospheric properties and infer the planet's bulk composition. We obtain precision radial velocity measurements with the HARPS spectrograph and couple those measurements with the K2 photometry to jointly model the observed radial velocity variation with planetary signals and a radial velocity jitter model based on Gaussian process regression. We measure the mass of K2-18b to be $8.0 \pm 1.9$ M$_{\oplus}$ with a bulk density of $3.7 \pm 0.9$ g/cm$^3$ which may correspond to a predominantly rocky planet with a significant gaseous envelope or an ocean planet with a water mass fraction $\gtrsim 50$%. We also find strong evidence for a second, warm super-Earth K2-18c at $\sim 9$ days with a semi-major axis 2.4 times smaller than the transiting K2-18b. After re-analyzing the available light curves of K2-18 we conclude that K2-18c is not detected in transit and therefore likely has an orbit that is non-coplanar with K2-18b. A suite of dynamical integrations with varying simulated orbital eccentricities of the two planets are used to further constrain each planet's eccentricity posterior from which we measure $e_b < 0.43$ and $e_c < 0.47$ at 99% confidence. The discovery of the inner planet K2-18c further emphasizes the prevalence of multi-planet systems around M dwarfs. The characterization of the density of K2-18b reveals that the planet likely has a thick gaseous envelope which along with its proximity to the Solar system makes the K2-18 planetary system an interesting target for the atmospheric study of an exoplanet receiving Earth-like insolation.

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arXiv2017

MOVES I. The evolving magnetic field of the planet-hosting star HD189733

HD189733 is an active K dwarf that is, with its transiting hot Jupiter, among the most studied exoplanetary systems. In this first paper of the Multiwavelength Observations of an eVaporating Exoplanet and its Star (MOVES) program, we present a 2-year monitoring of the large-scale magnetic field of HD189733. The magnetic maps are reconstructed for five epochs of observations, namely June-July 2013, August 2013, September 2013, September 2014, and July 2015, using Zeeman-Doppler Imaging. We show that the field evolves along the five epochs, with mean values of the total magnetic field of 36, 41, 42, 32 and 37 G, respectively. All epochs show a toroidally-dominated field. Using previously published data of Moutou et al. 2007 and Fares et al. 2010, we are able to study the evolution of the magnetic field over 9 years, one of the longest monitoring campaign for a given star. While the field evolved during the observed epochs, no polarity switch of the poles was observed. We calculate the stellar magnetic field value at the position of the planet using the Potential Field Source Surface extrapolation technique. We show that the planetary magnetic environment is not homogeneous over the orbit, and that it varies between observing epochs, due to the evolution of the stellar magnetic field. This result underlines the importance of contemporaneous multi-wavelength observations to characterise exoplanetary systems. Our reconstructed maps are a crucial input for the interpretation and modelling of our MOVES multi-wavelength observations.

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arXiv2017

Search for water vapor in the high-resolution transmission spectrum of HD189733b in the visible

Ground-based telescopes equipped with state-of-the-art spectrographs are able to obtain high-resolution transmission and emission spectra of exoplanets that probe the structure and composition of their atmospheres. Various atomic and molecular species, such as Na, CO, H2O have been already detected. Molecular species have been observed only in the near-infrared while atomic species have been observed in the visible. In particular, the detection and abundance determination of water vapor bring important constraints to the planet formation process. We search for water vapor in the atmosphere of the exoplanet HD189733b using a high-resolution transmission spectrum in the visible obtained with HARPS. We use Molecfit to correct for telluric absorption features. Then we compute the high-resolution transmission spectrum of the planet using 3 transit datasets. We finally search for water vapor absorption using a cross-correlation technique that combines the signal of 800 individual lines. Telluric features are corrected to the noise level. We place a 5-sigma upper limit of 100 ppm on the strength of the 6500 A water vapor band. The 1-sigma precision of 20 ppm on the transmission spectrum demonstrates that space-like sensitivity can be achieved from the ground. This approach opens new perspectives to detect various atomic and molecular species with future instruments such as ESPRESSO at the VLT. Extrapolating from our results, we show that only 1 transit with ESPRESSO would be sufficient to detect water vapor on HD189733b-like hot Jupiter with a cloud-free atmosphere. Upcoming near-IR spectrographs will be even more efficient and sensitive to a wider range of molecular species. Moreover, the detection of the same molecular species in different bands (e.g. visible and IR) is key to constrain the structure and composition of the atmosphere, such as the presence of Rayleigh scattering or aerosols.

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arXiv2017

Search for rings and satellites around the exoplanet CoRoT-9b using Spitzer photometry

Using Spitzer photometry at 4.5 microns, we search for rings and satellites around the long period transiting planet CoRoT-9b. We observed two transits in 2010 and 2011. From their non-detection, we derive upper limits on the plausible physical characteristics of these objects in the planet environment. We show that a satellite larger than about 2.5 Earth radii is excluded at 3-$σ$ for a wide range of elongations at the two epochs of observations. Combining the two observations, we conclude that rings are excluded for a wide variety of sizes and inclination. We find that for a ring extending up to the Roche limit, its inclination angle from the edge-on configuration as seen from the Earth must be lower than 13° in the case of silicate composition and lower than 3° in the case of material with water ice density.

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