© J. Desmars et al. 2019

1. Introduction

Stellar occultation is a unique technique to obtain the physical parameters of distant objects or to probe their atmosphere and surroundings. For instance, Meza et al. (2019) have used 11 stellar occultations by Pluto from 2002 to 2016 to study the evolution of Pluto’s atmosphere. Meanwhile, occultations allow an accurate determination of the relative position of the centre of the body compared to the position of the occulted star, leading to an accurate astrometric position of Pluto at the time of occultation if the star position is also known accurately.

The accuracy of the position of the body mainly depends on the knowledge of the shape and size of the body, modelling of the atmosphere, precision of the timing system, velocity of the occultation, exposure time of the camera, precision of the stellar position, and magnitude of the occulted star. Since the publication of the Gaia catalogues in September 2016 for the first release (Gaia Collaboration 2016) and moreover with the second release in April 2018 (Gaia Collaboration 2018) including proper motions and trigonometric parallaxes of the stars, the precision of the stellar catalogues can now reach a tenth of a milliarcsecond. For comparison, before Gaia catalogues, the precision of stellar catalogues such as UCAC2 (Zacharias et al. 2004) or UCAC4 (Zacharias et al. 2013), was about 50−100 mas per star including zonal errors. With Gaia, the precision of positions deduced from occultations is expected to be around few milliarcseconds, taking into account the systematic errors. Thanks to the accuracy of the Gaia DR2 catalogue, occultations can provide the most accurate astrometric measurement of a body in the outer solar system.

In this paper, we present the astrometric positions we derived from occultations presented in Meza et al. (2019; Sect. 2.1) and in other publications (Sect. 2.2). We detail a method to derive astrometric positions from other publications, knowing the circumstances of occultations: timing and impact parameter (Appendix). Finally, in Sect. 3 we present a refined ephemeris of Pluto’s system barycentre and we discuss the improvement in the predictions of future occultations by Pluto at a milliarcsecond level accuracy as well as the geometry of past events (Sect. 4).

2. Astrometric positions from occultations

2.1. Astrometric positions from occultations in Meza et al. (2019)

Meza et al. (2019) provide 11 occultations by Pluto from 2002 to 2016. Beyond the parameters related to Pluto’s atmosphere, another product of the occultations is the astrometric position of the body. From the geometry of the event, we determine the position of Pluto’s centre of figure (α_c, δ_c). This position corresponds to the observed position of the object at the time of the occultation for a given star position (α_s, δ_s). In particular, the position of the body we derive only depends on the star position. Before Gaia catalogues, we determined the star position with our own astrometry. Table 1 gives the position of Pluto’s centre and its precision we derived from the geometry of the occultation and the corresponding star position from our astrometry. With Gaia, the astrometric position of Pluto’s centre can be refined by correcting the star position with the Gaia DR2 star position with the relations

(1)

(2)

This refined position only depends on the Gaia DR2 position, which is much more accurate than previous catalogues or our own astrometry. The associated position of the occulted stars in Gaia DR2 catalogue (α_GDR2, δ_GDR2) are listed in Table 2. The positions take into account the proper motions and parallax from Gaia DR2. The table also presents the Gaia source identifier and the estimated precision of the star position in right ascension and declination at the time of the occultation, taking into account precision of the stellar position and the proper motions as given in Gaia DR2, for all the occultations studied in this paper.

Finally, Table 3 provides the absolute position in right ascension and declination of Pluto’s centre derived from the geometry and stellar positions of Gaia DR2. The residuals related to JPL ephemeris¹ DE436/PLU055 are also indicated as well as the differential positions between Pluto and Pluto’s system barycentre used to refine the orbit (see Sect. 3). A flag indicates if the position is used in the NIMAv8 ephemeris determination. Finally, the reconstructed paths of the occultations are presented in Fig. 6.

2.2. Astrometric positions from other publications

Several authors have published circumstances of an occultation by Pluto (e.g. Millis et al. 1993; Sicardy et al. 2003; Elliot et al. 2003; Young et al. 2008; Person et al. 2008; Gulbis et al. 2015; Olkin et al. 2015; Pasachoff et al. 2016, 2017). From these circumstances (coordinates of the observer, mid-time of the occultation, and impact parameter), it is possible to derive an offset between the observation deduced from these circumstances and a reference ephemeris. The procedure, based on the Bessel method used to predict stellar occultations, is described in Appendix A and the details of computation for each occultation are presented in Appendix B. The Pluto’s positions deduced from occultations published in other articles besides those of Meza et al. (2019) are presented in Table 3.

The positions derived from Pasachoff et al. (2016) involving single chord events and faint occulted stars, are not accurate enough to discriminate north and south solutions, i.e. to decide if Pluto’s centre as seen from the observing site passed north or south of the star. Finally, these positions were not used in the orbit determination.

3. NIMA ephemeris of Pluto

The NIMA code (Numerical Integration of the Motion of an Asteroid) was developed to refine the orbits of small bodies, in particular trans-Neptunian object (TNOs) and Centaurs studied using the technique of stellar occultations (Desmars et al. 2015). This technique consists of numerical integration of the equations of motion perturbed by gravitational accelerations of the planets (Mercury to Neptune). The Earth and Moon are considered at their barycentre and the masses and the positions of the planets are from JPL DE436.

The use of other masses and positions for planetary ephemeris produces insignificant changes; for example, the difference between the solution using DE436 and that using INPOP17a (Viswanathan et al. 2017) for Pluto, is less than 0.06 mas for the 1985−2025 period. Moreover, there is no need to take into account the gravitational perturbations of the biggest TNOs. For example, by adding the six biggest TNOs (Eris, Haumea, 2007 OR10, Makemake, Quaoar, and Sedna) in the model, the difference between the solutions with and without the biggest TNOs are about 0.04 mas in right ascension and declination for the 1985−2025 period, which is 100 times smaller than the milliarcsecond-level accuracy of the astrometric positions.

The state vector, i.e. the heliocentric vector of position and velocity of the body at a specific epoch, is refined by fitting to astrometric observations with the least-squares method. The main advantage of NIMA is allowing for the use of observations published in the Minor Planet Center² together with unpublished observations or astrometric positions of occultations. The quality of the observations is taken into account with a specific weighting scheme, in particular, it takes advantages of the high accuracy of occultations. Finally, after fitting to the observations, NIMA can provide an ephemeris through a bsp file format readable by the SPICE library³.

As NIMA is representing the motion of the centre of mass of an object, it allows us to compute the position of the Pluto’s system barycentre and not the position of Pluto’s centre itself. To deal with positions derived from occultations, we need an additional ephemeris representing the position of Pluto relative to its system barycentre. For that purpose, we use the most recent ephemeris PLU055 developed in 2015. The occultation-derived positions are then corrected from the offset between Pluto and the Pluto’s system barycentre (see Table 3) to derive the barycentric positions from the occultations, then used in the NIMA fitting procedure.

The precisions of the positions in right ascension and in declination derived from the occultations are provided in Table 1 for occultations presented in Meza et al. (2019) and in Appendix B for other publications. This precision is deduced from a specific model and reduction (for occultations in Meza et al. 2019) and from the precisions of timing and impact parameters (for other publications) without any estimation of systematic errors. For a realistic estimation of the orbit accuracy, the weighting scheme in the orbit fit needs to take into account the systematic errors (see Desmars et al. 2015 for details). The global accuracy for the positions used in the fitting depends on the accuracy of the stellar positions (from 0.1 to 2 mas), the precision of the derived position (from 0.1 mas to 11 mas), and the accuracy of the Pluto body-Pluto system barycentre ephemeris (estimated to 1−5 mas).

The errors on Pluto’s centre determination have in fact various sources: the noise present in each occultation light curve and the spatial distribution of the occultation chords across the body. Assuming a normal noise, a formal error on the centre of the planet can then be derived, using a classical least-squares fitting and χ² estimation. However, other systematic errors may also be present, such as problems in the absolute timing registration and slow sky transparency variations that make the photometric noise non-Gaussian. Finally, the particular choice of the atmospheric model may also induce systematic biases in the centre determination. All those systematic errors are difficult to trace back. In that context, it is instructive to compare the reconstructions of the geometry of a given occultation by independent groups that used different chords and different Pluto’s atmospheric models. For example, occultations on 21 August 2002, 4 May 2013, and 29 June 2015 (see Table 4) indicate differences of few milliarcseconds, which is much higher than the respective internal precisions (order of 0.1 mas). Case by case studies should be undertaken to explain those inconsistencies. This remains out of the scope of this paper. Meanwhile, for the weighting scheme in the orbit fit, we adopt the estimated precision presented in Table 4 taking into account an estimation of systematic errors for each occultation.

Figure 1 shows the difference between NIMA⁴ and JPLDE436 ephemeris of Pluto’s barycentre in right ascension (weighted by cos δ) and declination. The blue bullets and error bars represent the positions and their estimated precision from our occultations. The red bullets represent the positions from occultations not listed in Meza et al. (2019) as follows: Millis et al. (1993), Sicardy et al. (2003), Elliot et al. (2003), Young et al. (2008), Person et al. (2008), Gulbis et al. (2015), Olkin et al. (2015), and Pasachoff et al. (2017). The grey area represents the one sigma uncertainty of the NIMAv8 ephemeris.

Fig. 1. Difference between NIMAv8 and JPL DE436 ephemeris of Pluto’s system barycentre (black line) in right ascension (weighted by cos δ) and in declination. Blue bullets and their estimated precision in error bar represent the positions coming from the occultations studied in this work and red bullets represent the positions deduced from other publications. The grey area represents the 1σ uncertainty of the NIMA orbit. Vertical grey lines indicate the date of the position for a better reading on the x-axis. The angular diameter of Pluto, as seen from Earth, is about 115 mas, while the atmosphere detectable using ground-based stellar occultations subtends about 150 mas on the sky.

Table 4 and Fig. 2 provide the residuals (O–C) of the positions derived from the occultations, compared with the NIMAv8 ephemeris, and the estimated precision of the positions used in the weighting scheme. After 2011, residuals are mostly below the milliarcsecond level, which is much better than any ground-based astrometric observation of Pluto. In that context, other classical observations of Pluto, such as CCD, appear to be less useful for ephemerides of Pluto during the period covered by the occultations 1988−2016.

Fig. 2. Residuals of Pluto’s system barycentre positions compared to NIMAv8. Circles indicate right ascension weighted by cos δ and bullets indicate declination. Blue represents the positions coming from the occultations studied in this work and red represents the positions deduced from other publications.

Figure 3 shows the difference in right ascension and declination between the most recent ephemerides of Pluto system barycentre: JPL DE436, INPOP17a (Viswanathan et al. 2017) and EPM2017 (Pitjeva & Pitjev 2014) compared to NIMAv8. These differences are mostly due to data and weights used for the orbit determination. They reveal periodic terms in the orbit of Pluto system barycentre that are estimated differently in orbit determination. As described in Desmars et al. (2015), the one-year period corresponds to the parallax induced by different geocentric distances given by the ephemerides. It is also another good indication of the improvement of the NIMAv8 ephemeris since the differences between these ephemerides reach 50−100 mas, whereas the estimated precision of NIMAv8 is 2−20 mas for the same period.

Fig. 3. Difference in right ascension weighted by cos δ (solid line) and declination (dotted line) between several ephemerides of Pluto system barycentre: JPL DE436, INPOP17, and EPM2017, compared to NIMAv8.

4. Discussion

The NIMA ephemeris allows very accurate predictions of stellar occultation by Pluto in the forthcoming years within a few millisecond levels. In particular, we predicted an occultation of a magnitude 13 star⁵ by Pluto on August 15, 2018, above North America to the precision of 2.5 mas, representing only 60 km on the shadow path and a precision of 4 s in time. As shown in Meza et al. (2019), the observation of a central flash allows us to probe the deepest layers of Pluto’s atmosphere. The central flash can be observed in an small band about 50 km around the centrality path. By reaching a precision of tens of km, we were able to gather observing stations along the centrality and to highly increase the probability of observing a central flash.

The prediction of the August 15, 2018 Pluto occultation was used to assess the accuracy of our predictions using the NIMA approach. Figure 4 represents the prediction of the occultation by Pluto on August 15, 2018 using two different ephemerides: JPL DE436/PLU055 and NIMAv8/PLU055. The prediction using JPL ephemerides is shifted by 36.8 s and 8 mas south (representing about 190 km) compared to the prediction with NIMAv8 ephemeris. Several stations detected the occultation, some of which reveal a central flash. For instance, observers at George Observatory (Texas, USA) reported a central flash of typical amplitude 20%, compared to the unocculted stellar flux (Blank & Maley, priv. comm.).

Fig. 4. Prediction of the occultation by Pluto on 15 August 2018, using JPL DE436/PLU055 (top) and NIMAv8/PLU055 (bottom) ephemerides. The red dashed lines represent the 1σ uncertainty on the path, taking into account the uncertainties of NIMAv8 ephemeris and of the star position. The bullets on the shadow central line are plotted every minute. The dark and light blue thinner lines are the shadow limits corresponding the stellar half-light level and 1% stellar drop level (the practical detection limit), respectively.

As the amplitude of the flash roughly scales as the inverse of the closest approach (C/A) distance of the station to the shadow centre, the amplitude may serve to estimate the C/A distance. A central flash reported by Sicardy et al. (2016) was observed at a station in New Zealand during the June 29, 2015 occultation. It had an amplitude of 13% and a C/A distance of 42 km. Thus, the flash observed at George Observatory provides an estimated C/A distance of 25 km for that station. This agrees with the value predicted by the NIMAv8/PLU055 ephemeris, to within 3 km, corresponding to 0.12 mas. This is fully consistent with, but smaller than our 2.5 mas error bar quoted above, possibly indicating an overestimation of our prediction errors.

The precision of our predictions remains at few milliseconds up to 2025 (in particular in declination) and it is even more important since the apparent position of Pluto as seen from Earth is moving away from the Galactic centre, making occultations by Pluto more rare.

Another point of interest is to look at past occultations. In particular, for the occultation of August 19, 1985, Brosch & Mendelson (1985) reported a single chord occultation of a magnitude 11.1 star⁶ by Pluto, showing a gradual shape possibly due to Pluto’s atmosphere. The observation was performed at Wise observatory in Israel under poor conditions (low elevation, flares from passing planes, close to twilight). Thanks to Gaia DR2 providing the proper motion of the star and to NIMAv8, we make a postdiction of the occultation of August 19, 1985 (Fig. 5). The nominal time for the occultation, i.e. the time of the closest approach between the geocentre and centre of the shadow, is 17:58:57.1 (UTC), leading to a predicted mid-time of 17:59:49.8 (UTC) at Wise observatory. Brosch (1995) gave an approximate observed mid-time of the occultation for Wise observatory at 17:59:54 (about 4 s later than the prediction). The predicted shadow of Pluto at the same time is presented in the figure and the location of the observatory is represented as a green bullet. Taking into account the uncertainties of the NIMAv8 ephemeris and of the star position, the uncertainty in time for this occultation is about 20 s, whereas the crosstrack uncertainty on the path is about 10 mas (representing 220 km). This is fully consistent with the fact that the occultation was indeed observed at Wise observatory.

Fig. 5. Postdiction of the Pluto’s occultation of 19 August 1985, using NIMAv8/PLU055 ephemerides. The shadow of Pluto at 17:59:54 (the mid-time of the occultation provided in Brosch 1995) is represented. The green bullet represents the WISE observatory. The red dashed lines represent the 1σ uncertainty on the path. Areas in dark grey correspond to full night (Sun elevation below −18°) and areas in light grey correspond to twilight (Sun elevation between −18° and 0°), while daytime regions are in white. The dark and light blue thinner lines are the shadow limits corresponding the stellar half-light level and 1% stellar drop level (the practical detection limit), respectively.

Fig. 6. Reconstruction of Pluto’s shadow trajectories on Earth for occultations observed from 2002 to 2016; see details in Meza et al. (2019). The bullets on the shadow central line are plotted every minute, and the black arrow represents the shadow motion direction (see arrow at lower right corner). The dark and light blue thinner lines are the shadow limits corresponding the stellar half-light level and 1% stellar drop level (the practical detection limit), respectively. The green bullets correspond to the sites with positive detection used in the fit. Areas in dark grey correspond to full night (Sun elevation below −18°) and areas in light grey correspond to astronomical twilight (Sun elevation between −18° and 0°), while daytime regions are in white.

Fig. 6. continued.

5. Conclusions

Stellar occultations by Pluto provide accurate astrometric positions thanks to Gaia catalogues, in particular Gaia DR2. We determine 18 astrometric positions of Pluto from 1988 to 2016 with an estimated precision of 2−10 mas.

These positions are used to compute an ephemeris of the barycentre of Pluto system thanks to the NIMA procedure with an unprecedented precision on the 1985−2015 period. This ephemeris NIMAv8 was also used to study the possible occultation of Pluto observed in 1985 to predict the recent occultation by Pluto on August 15, 2018 or the forthcoming occultations⁷ with a precision of 2 mas, a result that is impossible to reach with classical astrometry and previous stellar catalogues. In fact, the presence of the usually unresolved Charon in classical images causes significant displacements of the photocentre of the system with respect to its barycentre. As a consequence, and even modelling the effect of Charon, as in Benedetti-Rossi et al. (2014), accuracies below the 50 mas level are difficult to reach.

This method can be extended, for instance for Chariklo, with an even better accuracy of the order of 1 mas (Desmars et al. 2017) and illustrates the power of stellar occultations not only for better studying those bodies, but also for improving their orbital elements.

Acknowledgments

Part of the research leading to these results has received funding from the European Research Council under the European Community’s H2020 (2014−2020/ERC Grant Agreement No. 669416 “LUCKY STAR”). This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. J.I.B.C. acknowledges CNPq grant 308150/2016-3. M.A. thanks CNPq (Grants 427700/2018-3, 310683/2017-3 and 473002/2013-2) and FAPERJ (Grant E-26/111.488/2013). G.B.R. is thankful for the support of the CAPES (203.173/2016) and FAPERJ/PAPDRJ (E26/200.464/2015-227833) grants. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. F.B.R.acknowledges CNPq grant 309578/2017-5. A.R.G-J thanks FAPESP proc. 2018/11239-8. R.V-M thanks grants: CNPq-304544/2017-5, 401903/2016-8, Faperj: PAPDRJ-45/2013 and E-26/203.026/2015 P.S.-S. acknowledges financial support by the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement no 687378, as part of the project “Small Bodies Near and Far” (SBNAF).

References

Appendix A: Method to derive astrometric positions from occultation’s circumstances

We present in this section a method to derive an astrometric position from an occultation’s observation, knowing the occultation’s circumstances. The determination of an occultation’s circumstances consists in computing the Besselian elements. The Bessel method makes use of the fundamental plane that passes through the centre of the Earth and perpendicular to the line joining the star and the centre of the object (i.e. the axis of the shadow). The method is for example described in Urban & Seidelmann (2013). The Besselian elements are usually given for the time of conjunction of the star and the object in right ascension but in this paper the reference time is the time of closest angular approach between the star and the object.

The Besselian elements are T₀ the UTC time of the closest approach, H the Greenwich Hour Angle of the star at T₀, x₀ and y₀ the coordinates of the shadow axis at T₀ in the fundamental plane, x′ and y′ the rates of changes in x and y at T₀, and α_s, δ_s the right ascension and the declination of the star. Their computation are fully described in Urban & Seidelmann (2013).

The quantities x₀, y₀, x′, and y′ depend on the ephemeris of the body and allow us to represent the linear motion of the shadow at the time of the occultation. In this paper, x₀, y₀ are expressed in Earth radius unit and x′,y′ are in Earth radius per day.

From T₀, α_s, δ_s, and H, the coordinates⁸ of the shadow centre (λ_c, ϕ_c) at T₀ can be derived.

For an observing site, the method requires the local circumstances which are the mid-time of the occultation and the impact parameter ρ, the distance of closest approach between the site, and the centre of the shadow in the fundamental plane. Usually, the impact parameter is given in kilometres and when the occultation has only one chord, two solutions (North and South) can be associated.

The first step is to add a shift to x₀ and y₀ to take into account the impact parameter, i.e. the fact that the observing site is not right on the centrality of the occultation, as follows:

(A.1)

(A.2)

where s is the ratio of ρ to Earth radius.

Given the longitude λ and the latitude⁸ϕ of the observing site, the coordinates in the fundamental plane are given by

(A.3)

(A.4)

(A.5)

The time of the closest approach for the observer is given by the relation

(A.6)

In fact, t_m, u, v, w are calculated iteratively by replacing λ_c by λ_c − Ω(t_m − T₀), where Ω is the rate of Earth’s rotation, to take into account the Earth’s rotation during t_m − T₀.

If Δt is the difference between the observed time of the occultation for the observer and the nominal time of the occultation T₀, the correction to apply to the Besselian elements x₀, y₀ are

(A.7)

(A.8)

The quantities Δx, Δy are determined iteratively and finally transformed into an offset in right ascension and in declination between the observed occultation and the predicted occultation (from the ephemeris).

For single chord occultation, there are two solutions (north and south), meaning that we do not know whether Pluto’s centre went north or south of the star as seen from the observing site. Conversely, for multi-chord occultation there is a unique solution. In that case, the astrometric position deduced from the occultation is the reference ephemeris plus the average offset deduced from all the observing sites.

This is a powerful method to derive astrometric positions from occultations. It only requires local circumstances of the occultation for the observing sites such as the mid-time of the occultation and the impact parameter. If the impact parameter is not provided, we can deduce it from the timing of immersion and emmersion knowing the size of the object and assuming it is spherical. Thus, the method can be used for any object.

Appendix B: Astrometric positions from other occultations

In this section, we derive astrometric positions from occultations published in various articles using the method previously presented. The Besselian elements corresponding to the occultations are presented in Table B.7 and the reconstructed shadow trajectories of occultation are presented in Fig. B.1.

Fig. B.1. Reconstruction of Pluto’s shadow trajectories on Earth for occultations presented in other publications from 1988 to 2015. The legend is similar to Fig. 6.

Fig. B.1. continued.

B.1. Occultation of June 9, 1988

Millis et al. (1993) presented the June 9, 1988 Pluto occultation. They derived an astrometric solution by giving the impact parameter for the eight stations that recorded the event.

According to the mid-time of the occultation derived from the paper, we determine the following offsets:

For Black Birch, there is only the immersion timing so the mid-time of the occultation cannot be derived. The average offset of this occultation was determined using the same set of the preferred astrometric solution of Millis et al. (1993), i.e. data from Charters Towers, Hobart, Kuiper Airbone Observatory (KAO), and Mont John (see Table B.1).

Finally, we derive the average offset of Δα cos δ = +19.9 ± 0.5 mas and Δδ = −33.5 ± 0.3 mas.

B.2. Occultation of July 20, 2002

Sicardy et al. (2003) obtained a light curve of the occultation by Pluto near Arica, north of Chile. They derived an astrometric solution of the occultation by giving distance of closest approach to the centre of Pluto’s shadow for Arica (975 ± 250 km).

In Arica, the mid-time of the occultation occurs at 01:44:03 (UTC), giving Δt = 23.2 s. There are two possible solutions but the occultation was also observed at Mamiña⁹ in Chile (Buie, priv. comm.) so the only possible solution is that of the south. Finally, we derive the offset of Δα cos δ = +7.7 ± 1.9 mas and Δδ = −4.4 ± 11.2 mas, assuming a precision of 2 s for the mid-time.

B.3. Occultation of August 21, 2002

Elliot et al. (2003) derived an astrometric solution of the occultation by giving distance of closest approach to the centre of Pluto’s shadow for Mauna Kea Observatory (597 ± 32 km) and Lick Observatory (600 ± 32 km). They observed a positive occultation with three telescopes (two in Hawaii and one at Lick Observatory).

As there are at least two stations observing this occultation, there is a unique solution. According to the mid-time of the occultation in the two stations (see Table B.2), we derived the following offsets:

Finally, for this occultation, we used an average offset of Δα cos δ = +15.4 ± 1.0 mas and Δδ = −9.1 ± 1.7 mas.

B.4. Occultation of June 12, 2006

Young et al. (2008) presented the analysis of an occultation by Pluto on June 12, 2006. They published the half light time (ingress and egress) and the impact parameter (closest distance to the centre of the shadow) for five stations:

• REE = Reedy Creek Observatory, QLD, AUS (0.5 m aperture).

• AAT = Anglo-Australian Observatory, NSW, AUS (4 m).

• STO = Stockport Observatory, SA, AUS (0.5 m).

• HHT = Hawkesbury Heights, NSW, AUS (0.2 m).

• CAR = Carter Observatory, Wellington, NZ (0.6 m)

These parameters allow us to compute the mid-time of the occultation and to finally derive an offset for each station (see Table B.3).

Finally, for this occultation, we used an average offset of Δα cos δ = +9.8 ± 0.8 mas and Δδ = −0.4 ± 0.1 mas.

B.5. Occultation of March 18, 2007

Person et al. (2008) presented an analysis of an occultation by Pluto observed in several places in USA on March 18, 2007. From five stations, they derived the geometry of the event by providing the mid-time (UTC) of the event at 10:53:49 ± 00:01 (giving Δt = −344.1 s) and an impact parameter of 1319 ± 4 km for the Multiple Mirror Telescope Observatory (MMTO).

According to the geometry of the event, the south solution ( ρ = −1319 km) has to be adopted, giving the offset related to JPL DE436/PLU055 ephemeris of Δα cos δ = 10.7 ± 0.3 mas and Δδ = 0.8 ± 0.2 mas.

B.6. Occultation of June 23, 2011

Gulbis et al. (2015) presented a grazing occultation by Pluto observed in IRTF (Mauna Kea Observatory) on June 23, 2011. They derived an impact parameter of 1138 ± 3 km and a mid-time (UTC) of the event at 11:23:03.07 (±0.10 s).

The single chord leads to two possible solutions providing the following offset related to JPL DE436/PLU055 ephemeris (see Table B.4).

According to Gulbis et al. (2015), the north solution has to be adopted. Finally, the offset is Δα cos δ = 16.1 ± 0.1 mas and Δδ = 5.5 ± 0.1 mas, assuming the estimated precision of the timing and the impact parameter.

B.7. Occultation of May 4, 2013

Olkin et al. (2015) presented the occultation by Pluto on May 4, 2013 observed in South America. They derived the mid-time (UTC) of the event at 08:23:21.60 ± 0.05 s (giving Δt = 99.8 s) and an impact parameter of 370 ± 5 km for the LCOGT at Cerro Tololo. From these circumstances, we derived an offset related to JPL DE436/PLU055 ephemeris of Δα cos δ = 18.7 ± 0.1 mas and Δδ = 8.4 ± 0.2 mas.

B.8. Occultation of July 23, 2014

Pasachoff et al. (2016) published the observation of two single-chord occultations at Mont John (New Zealand) on June 2014. They provided the timing and impact parameter for the two occultations.

The fitted impact parameter for July 23 is ρ = 480 ± 120 km, providing two possible solutions and the mid-time (UTC) of the occultation 14:24:31 ± 4 s is derived from the ingress and egress times at 50% and corresponds to Δt = −88.1 s.

Each solution provides the following offset related to JPL DE436/PLU055 ephemeris (see Table B.5).

According to the precisions of the mid-time and of the impact parameter, the estimated precision of the offset is 4.0 mas for Δα cos δ and 5.2 mas for Δδ.

B.9. Occultation of July 24, 2014

Pasachoff et al. (2016) also provided circumstances of the occultation on July 24, 2014 at Mont John Observatory.

The fitted impact parameter is ρ = 510 ± 140 km providing two possible solutions and the mid-time (UTC) of the occultation 11:42:29 ± 8 s is derived from the ingress and egress times at 50% and corresponds to Δt = 9.1 s.

Each solution provides the following offset related to JPL DE436/PLU055 ephemeris (see Table B.6).

According to the precisions of the mid-time and impact parameter, the estimated precision of the offset is 7.7 mas for Δα cos δ and 6.1 mas for Δδ.

B.10. Occultation of June 29, 2015

Pasachoff et al. (2017) presented the occultation by Pluto on June 29, 2015. They derived the mid-time (UTC) of the event at 16:52:50 (giving Δt = −111.4 s) and an impact parameter of −53.1 km for the Mont John Observatory in New Zealand.

From these circumstances, we derived an offset of Δα cos δ = 22.1 mas and Δδ = 12.7 mas related to JPL DE436/PLU055 ephemeris. The precision of the offset cannot be determined since the precision in mid-time and in the impact parameter are not indicated.

All Tables

All Figures

Fig. 1. Difference between NIMAv8 and JPL DE436 ephemeris of Pluto’s system barycentre (black line) in right ascension (weighted by cos δ) and in declination. Blue bullets and their estimated precision in error bar represent the positions coming from the occultations studied in this work and red bullets represent the positions deduced from other publications. The grey area represents the 1σ uncertainty of the NIMA orbit. Vertical grey lines indicate the date of the position for a better reading on the x-axis. The angular diameter of Pluto, as seen from Earth, is about 115 mas, while the atmosphere detectable using ground-based stellar occultations subtends about 150 mas on the sky.

In the text

	Fig. 2. Residuals of Pluto’s system barycentre positions compared to NIMAv8. Circles indicate right ascension weighted by cos δ and bullets indicate declination. Blue represents the positions coming from the occultations studied in this work and red represents the positions deduced from other publications.
In the text

	Fig. 3. Difference in right ascension weighted by cos δ (solid line) and declination (dotted line) between several ephemerides of Pluto system barycentre: JPL DE436, INPOP17, and EPM2017, compared to NIMAv8.
In the text

Fig. 4. Prediction of the occultation by Pluto on 15 August 2018, using JPL DE436/PLU055 (top) and NIMAv8/PLU055 (bottom) ephemerides. The red dashed lines represent the 1σ uncertainty on the path, taking into account the uncertainties of NIMAv8 ephemeris and of the star position. The bullets on the shadow central line are plotted every minute. The dark and light blue thinner lines are the shadow limits corresponding the stellar half-light level and 1% stellar drop level (the practical detection limit), respectively.

In the text

Fig. 5. Postdiction of the Pluto’s occultation of 19 August 1985, using NIMAv8/PLU055 ephemerides. The shadow of Pluto at 17:59:54 (the mid-time of the occultation provided in Brosch 1995) is represented. The green bullet represents the WISE observatory. The red dashed lines represent the 1σ uncertainty on the path. Areas in dark grey correspond to full night (Sun elevation below −18°) and areas in light grey correspond to twilight (Sun elevation between −18° and 0°), while daytime regions are in white. The dark and light blue thinner lines are the shadow limits corresponding the stellar half-light level and 1% stellar drop level (the practical detection limit), respectively.

In the text

Fig. 6. Reconstruction of Pluto’s shadow trajectories on Earth for occultations observed from 2002 to 2016; see details in Meza et al. (2019). The bullets on the shadow central line are plotted every minute, and the black arrow represents the shadow motion direction (see arrow at lower right corner). The dark and light blue thinner lines are the shadow limits corresponding the stellar half-light level and 1% stellar drop level (the practical detection limit), respectively. The green bullets correspond to the sites with positive detection used in the fit. Areas in dark grey correspond to full night (Sun elevation below −18°) and areas in light grey correspond to astronomical twilight (Sun elevation between −18° and 0°), while daytime regions are in white.

In the text

	Fig. 6. continued.
In the text

	Fig. B.1. Reconstruction of Pluto’s shadow trajectories on Earth for occultations presented in other publications from 1988 to 2015. The legend is similar to Fig. 6.
In the text

	Fig. B.1. continued.
In the text