New Constraint on the Atmosphere of (50000) Quaoar from a Stellar Occultation

The occultation of a faint star (Gaia DR2 catalog source ID: 4145978492632029696, ICRS position at epoch J2000: α = 18^h08^m155, δ = −15°17'58'', Gaia Gmag = 15.73; Gaia Collaboration 2018) on 2019 June 28 was originally predicted by the European Research Council (ERC) Lucky Star project.²⁰ The project predicts stellar occultations by TNOs using Numerical Integration of the Motion of an Asteroid (NIMA) version 3 orbital elements (Camargo et al. 2014; Desmars et al. 2015). The prediction confirmed that Quaoar's shadow swept over the major islands of Japan at a relative velocity of v_rel = 24.6 km s⁻¹. This v_rel and Quaoar's radius (R_equi = 555 ± 2.5 km; Braga-Ribas et al. 2013) yielded a maximum possible duration of the occultation to be 45.1 s. At the geocentric distance of Quaoar, D = 41.85 au, the angular diameter of Quaoar during the occultation corresponds to ∼37 mas. The same occultation event was also predicted by the Research and Education Collaborative Occultation Network (RECON) project,²¹ which is a coordinated TNO occultation observation network (Buie & Keller 2016).

On 2019 June 28, we carried out observations of the occultation event at four stations distributed in Japan, as summarized in Table 1. However, only one out of the four stations, Kiso Observatory, could acquire data under a good weather condition. At Kiso, photometric data were obtained using the Tomo-e Gozen camera (Sako et al. 2018) mounted on a 1.05 m f/3.1 Schmidt telescope. Tomo-e is an optical wide-field camera developed for time-domain astronomy, equipped with 84 CMOS sensors developed by Canon Inc. The sensitive wavelength range of the CMOS sensor is 350–700 nm with a peak at ∼500 nm (Kojima et al. 2018). The field of view (FoV) for each CMOS sensor is 397 × 224 with an angular pixel scale of 119. This Tomo-e Gozen camera offers a sequential shooting mode at a maximum frame rate of 2 Hz (=0.5 s integration) with rolling shutter. According to the results of performance tests by Sako et al. (2018), the absolute timing uncertainty of the Tomo-e Gozen camera was less than 0.1 ms.

Table 1.  Circumstances of the 2019 June 28 Stellar Occultation Observations for Observing Stations

Observation Site	Longitude	Aperture	Obs. Status	Observers
	Latitude	Camera
	Altitude
Kiso Observatory	137°37'315 E	1.05 m	Positive	R. Ohsawa
	35°47'500 N	Tomo-e Gozen
	1132 m
Nishi-Harima Astronomical Observatory	134°20'080 E	2.0 m	Bad weather	K. Arimatsu
	35°01'310 N	ZWO ASI-1600 Cool		J. Takahash
	449 m			M. Tozuka
				Y. Itoh
Okayama University	133°55'214 E	0.35 m	Bad weather	G. L. Hashimoto
	34°41'191 N	SBIG STL-1001E		M. Yamashita
	42 m
Bisei Spaceguard Center	133°32'400 E	1.0 m	Bad weather	S. Urakawa
	34°40'191 N	mosaic CCD camera
	428 m

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The target star was observed with the Tomo-e Gozen camera in a 15 minute window centered on the predicted central time of the occultation (12 hr 37 m on 2019 June 28 UTC). The exposure time was 0.5 s for each frame corresponding to the frame rate of ∼2.0 Hz. The readout overhead time between exposures was less than 0.1 ms. At the relative velocity of Quaoar, v_rel = 24.6 km s⁻¹, the time resolution corresponds to a physical resolution of 12.3 km on Quaoar's surface. No filter was used in the present observation. A movie data set consisting of 180 frames were compiled into a FITS data cube by one capture procedure. The time interval between the individual data cubes' integrations was approximately 3.6 s. During the observation, 10 data cubes (corresponding to 1800 frames in total) were obtained by each sensor. In the following analyses, we used the data cubes obtained by a single sensor that detected the occulted star.

Aperture photometry for the occulted star (plus the occulting body) is performed using the data cube after bias and flat-field corrections. We should note that Quaoar itself was not detected from the obtained data during the occultation with a 3σ upper limit G-band magnitude of 18.8. A constant sky background value was estimated from the average value of the aperture fluxes obtained during the occultation and was subtracted from the light curve. Due to possible rapid changes in atmospheric conditions, the obtained flux values for individual data points can suffer time-dependent flux fluctuations. In order to correct the possible flux fluctuations and calibrate the flux value of the target star, we carry out differential photometry with 148 reference stars (Gaia DR2 G-band magnitudes of 12–15) simultaneously detected in the same sensor. The calibrated light curve is then normalized to the unocculted flux. Figure 1 shows the light curve of the target star after the calibration and the normalization. Except for the Quaoar's occultation, no stellar occultation candidate event by Quaoar's satellite Weywot or by other unknown satellites or rings was found in the light curve.

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As shown in Figure 1, the observed duration of the occultation is roughly ∼45 s, which is comparable to the maximum possible duration of the occultation (45.1 s, see Section 2.1). In order to measure the precise physical length of the observed chord, we fit to the ingress and egress part of the light curve with a sharp edge occultation model convolved by Fresnel diffraction, the angular diameter and the spectral energy distribution of the occulted star, and the efficiency and the finite integration time of the Tomo-e CMOS sensor.

A characteristic scale of the Fresnel diffraction effect is defined as the Fresnel scale, ${L}_{{\rm{F}}}=\sqrt{\lambda D/2}$, where λ is the wavelength of the observation and D is the distance between the observer and Quaoar. L_F of the observed occultation event thus varies from 1.0 to 1.5 km at the distance of Quaoar, D = 41.85 au, when λ varies from 350 to 700 nm. To estimate the effects of diffraction, we generate Fresnel diffraction profiles for a circular occulting disk using a numerical code originally developed for the simulation of the stellar occultation light curve by TNOs (Arimatsu et al. 2017, 2019). In this calculation, we assume that Kiso Observatory's chord sampled almost the central part of Quaoar and the observed occultation direction can be approximated to be perpendicular to Quaoar's limb as our baseline case. Since the Tomo-e Gozen camera was used in no filter mode, both the spectral efficiency of the camera and the stellar spectrum should be taken into account for producing synthetic light curves. Furthermore, the profiles should be convolved by the finite size of the occulted star. To estimate the spectrum and the angular diameter of the occulted star, we carry out a spectral model fit with the following flux catalog data: Gaia DR2 (Gaia Collaboration 2018) BP (m_BP = 17.35 ± 0.01) and RP (m_RP = 14.468 ± 0.004) bands and Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006) J (m_J = 12.18 ± 0.04), H (m_H = 11.09 ± 0.04), and Ks (m_K = 10.73 ± 0.03) bands. The comparison of these cataloged values with a stellar spectrum model (Castelli & Kurucz 2004) indicates that the cataloged fluxes are explained by spectral models with an effective temperature and $\mathrm{log}[g]$ of T_eff = 3750 K and $\mathrm{log}[g]=2.0$, respectively. We thus select a spectral model with T_eff = 3750 K, $\mathrm{log}[g]=2.0$, and [M/H] = 0 (solar metallicity) as the template stellar spectral energy distribution. T_eff for the selected model is consistent with that from the Gaia DR2 catalog (${T}_{\mathrm{eff}}={4027}_{-742}^{+582}\,{\rm{K}};$ Gaia Collaboration 2018). The best-fit parameters yield a stellar angular diameter of 0.0417 ± 0.0007 mas and an extinction value of $E(B-V)=1.88\pm 0.02$. At the geocentric distance of Quaoar (D = 41.85 au), the best-fit angular diameter corresponds to 1.3 km in the celestial plane. With the best-fit parameters, selected stellar spectral model, and system efficiency (Kojima et al. 2018) and the integration time of the Tomo-e Gozen camera, the diffraction profiles are convolved to generate a synthetic light curve directly comparable to the observed data points.

The synthetic light curve is fitted to the data points obtained in 6.6 s windows centered on the apparent ingress/egress time of the occultation by minimizing χ²,

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}\displaystyle \frac{{({\phi }_{i,\mathrm{obs}}-{\phi }_{i,\mathrm{syn}})}^{2}}{{\sigma }_{i}^{2}},\end{eqnarray} \tag{ 1 }$$

where ${\phi }_{i,\mathrm{obs}}$, ${\phi }_{i,\mathrm{syn}}$, and σ_i are the observed and synthetic stellar fluxes, and the 1σ error at a data point i, respectively. The best-fit results are shown in Figure 2. From the light curve fitting, we obtained an event duration of 45.50 ± 0.05 seconds. Considering a velocity of ${v}_{\mathrm{rel}}=24.6\,\mathrm{km}\,{{\rm{s}}}^{-1}$, it is equivalent to a chord length of 1121.0 ± 1.2 km. The best-fit χ² corresponds to 37.0 with 25 degrees of freedom. The center-to-edge distance of the occultation (corresponding to one half of the best-fit chord length; 560.5 ± 0.6 km) is slightly larger than the equivalent radius R_equi = 555 ± 2.5 km and comparable to the equatorial radius ${R}_{\mathrm{equa}}={569}_{-17}^{+24}\,\mathrm{km}$ estimated by the previous occultation study (Braga-Ribas et al. 2013). This result is thus consistent with our baseline assumption that the observed chord sampled the central part. However, this single chord does not bring further constraints on the Quaoar's shape. The central time of the occultation derived from the fit is 12:37:17.79 ± 0.02 on 2019 June 28 UTC. We should note that the effect of the diffraction and the selection of the stellar parameters do not significantly affect the fit results because the resultant synthetic light curve is largely dominated by the finite integration time.

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In order to make constrains on Quaoar's atmosphere from the light curve data, synthetic light curves are calculated with an atmospheric refraction model based on a ray trace technique described by Sicardy et al. (1999). The atmospheric refraction model requires an assumption on its composition. Although the previous occultation studies by Braga-Ribas et al. (2013) and Fraser et al. (2013b) ruled out the existence of Quaoar's isothermal N₂ or CO atmosphere due to the lack of corresponding refraction features in the observed light curves, they cannot rule out the possibility of a tenuous CH₄ atmosphere since its refraction feature in sublimation equilibrium is expected to be much fainter. The possibility of a CH₄ atmosphere is also consistent with the existence of a CH₄ ice feature on the near-infrared spectrum of Quaoar's surface (Schaller & Brown 2007a). We thus consider a pure CH₄ atmosphere. For a vertical temperature profile of Quaoar's pure CH₄ atmosphere, we assume a Pluto-like profile, based on the previous study by Braga-Ribas et al. (2013). Heating of CH₄ molecules by their absorption of solar near-infrared radiation should increase the temperature at the stratosphere. We thus adopt a temperature profile increasing from an equilibrium surface temperature (altitude z = 0 km) to z ∼ 10 km with a gradient of dT/dz = 5.7 K km⁻¹ and isothermal stratosphere of T = 102 K, as proposed in Braga-Ribas et al. (2013). For the surface temperature, we adopt T = 44 K, which is the mean surface temperature measured from mid- to far-infrared observations (Fornasier et al. 2013) and is comparable to the upper limit temperature obtained by the previous occultation study (44.3 K; Fraser et al. 2013b). On the other hand, Fraser et al. (2013b) pointed out that a slight uncertainty of the assumed surface temperature could cause a large variation in the observational constraint on the surface pressure. Thus we also adopt T = 42 K, corresponding to the equilibrium surface temperature assumed by Braga-Ribas et al. (2013), as a reference.

Since we assume a pure molecular ${\mathrm{CH}}_{4}$ atmosphere, the atmospheric refractivity ν(z) at an altitude z is given by

$$\begin{eqnarray}&&\nu (z)=n(z)\times {K}_{{\mathrm{CH}}_{4}},\end{eqnarray} \tag{ 2 }$$

where n and ${K}_{{\mathrm{CH}}_{4}}$ are the number density at z and the molecular refractivity of CH₄, respectively. We take ${K}_{{\mathrm{CH}}_{4}}=1.629\times {10}^{-23}$ cm³ molecular⁻¹ given by Bose et al. (1972). The number density n(z) is calculated by integrating the hydrostatic equation from the surface upwards, assuming that the surface pressure is p_s and it is an ideal gas,

$$\begin{eqnarray}&&\displaystyle \frac{{dp}(z)}{{dz}}=-\mu \,n(z)g,\end{eqnarray} \tag{ 3 }$$

where μ is the mean molecular mass and g is the gravitational acceleration. In Equation (3), we assume g = 0.4 m s⁻² given by Braga-Ribas et al. (2013). p(z) is the pressure at z and p(0) = p_s. For a stellar ray with an impact parameter from Quaoar's shadow center r, its bending angle ω(r) is calculated by

$$\begin{eqnarray}&&\omega (r)={\int }_{-\infty }^{+\infty }\displaystyle \frac{r}{x}\displaystyle \frac{\partial \nu }{\partial r}\,{dx},\end{eqnarray} \tag{ 4 }$$

where x is the trajectory of the ray. For simplicity, we assume a spherical shape of Quaoar in the model. The apparent distance of the ray from the shadow center is thus r + ω(r) × D, where D is the distance of Quaoar (D = 41.85 au). Since ω(r) tends to be less than zero, the atmospheric refraction could cause a reduction of the apparent radius of the occulting object. We thus generate synthetic light curves for different radii and calculated their χ² values derived by Equation (1). In order to derive the synthetic light curve, each atmospheric refraction profile is convolved by the stellar angular diameter and the finite integration time. Figure 3 shows the distribution of the obtained χ² values for different radius models against the surface pressure p_s. The χ² values for individual radii show local minimums at different radii. However, the envelope of these χ² curves reaches its minimum value at p_s = 0 nbar. According to the χ² envelope for the T = 44 K models, we find that then1σ and 3σ detection upper limits are p_s = 6 and p_s = 16 nbar, respectively. On the other hand, the T = 42 K models give 1σ and 3σ upper limits of p_s = 5 and p_s = 15 nbar, respectively. In the present analysis, the obtained upper limit does not significantly depend on the uncertainty of the assumed surface temperature since the synthetic light curve is predominantly determined by p_s in the assumed CH₄ atmosphere model. Figure 4 shows the observed ingress and egress profiles overlaid with the synthetic light curves of the T = 44 K models with 1σ and 3σ upper limit p_s values.

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As already described in Section 1, the existence of Quaoar's atmosphere has been discussed in the previous occultation studies. The upper limit on p_s of Quaoar is significantly lower than the previous measurements by Braga-Ribas et al. (2013; 1σ and 3σ upper limits of p_s = 21 and 56 nbar, respectively, assuming T = 42 K) and Fraser et al. (2013b; a 3σ upper limit surface pressure and temperature of p_s = 138 nbar and T = 44.3 K, respectively). Since the saturation vapor pressure of CH₄ at T = 44 K and T = 42 K are 120 and 33 nbar, respectively (Fray & Schmitt 2009), the obtained upper limit pressure is smaller than the expected surface pressure of a possible global atmosphere equilibrated with CH₄ ice. However, the saturation vapor pressure is highly dependent on the surface temperature. A p_s = 6 nbar CH₄ atmosphere would imply an equilibrium temperature of 39.6 K (Fray & Schmitt 2009), which is lower than but not significantly different from the mean surface temperature (T = 44 K; Fornasier et al. 2013). If the surface temperature is lower than 39.6 K, the presence of an extremely tenuous atmosphere in equilibrium with CH₄ ice is consistent with our nondetection at the obtained upper limits. Finally, our single-chord data cannot rule out the possibility of a local atmosphere suggested by Braga-Ribas et al. (2013). According to the previous study of local atmospheres on TNOs (Ortiz et al. 2012), a focusing effect of a local atmosphere with a surface pressure greater than ∼microbars could cause a central flash, a short-timescale brightening of an occulted star that occurs in the middle of an occultation. We should note that, however, any signature of the central flash candidate is found in our 2 Hz cadence light curve during the occultation with a 2σ upper limit of 11% of the total stellar flux. Since thermophysical properties of Quaoar are uncertain, it is difficult to put a limit on a local atmosphere in the present study. Further multi-chord occultation observations, as well as investigations of the surface thermal properties, will provide valuable information on the atmospheric conditions of Quaoar.