New CCD astrometric observations of the five major uranian satellites using Gaia DR1 in 2014–2016

Accepted Manuscript New CCD astrometric observations of the five major uranian satellites using Gaia DR1 in 2014–2016 H.J. Xie, Q.Y. Peng, N. Wang, A. Vienne, C.W. Li, M.N. Xie, Z.W. Liu PII:

S0032-0633(18)30200-9

DOI:

https://doi.org/10.1016/j.pss.2018.11.007

Reference:

PSS 4613

To appear in:

Planetary and Space Science

Received Date: 24 May 2018 Revised Date:

11 July 2018

Accepted Date: 25 November 2018

Please cite this article as: Xie, H.J., Peng, Q.Y., Wang, N., Vienne, A., Li, C.W., Xie, M.N., Liu, Z.W., New CCD astrometric observations of the five major uranian satellites using Gaia DR1 in 2014–2016, Planetary and Space Science (2018), doi: https://doi.org/10.1016/j.pss.2018.11.007. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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New CCD astrometric observations of the five major Uranian satellites using Gaia DR1 in 2014 – 2016 H. J. Xiea,c , Q. Y. Penga,c,∗, N. Wanga,c , A. Vienneb,c , C. W. Lia,c , M. N. Xiea,c , Z. W. Liua,c a Department

of Computer Science, Jinan University, Guangzhou 510632, China de Lille, Observatoire de Lille, IMCCE, UMR 8028, 59000 Lille, France c Sino-French Joint Laboratory for Astrometry, Dynamics and Space Science, Jinan University, Guangzhou 510632, China

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b Universit´ e

Abstract

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710 CCD frames, observed by 1–m telescope at Yunnan Observatory over 15 nights, have been reduced to derive new precise positions of the five Uranian major satellites (Ariel, Umbriel, Titania, Oberon and Miranda). In the pixel positional measurement of the faint satellites near Uranus, a halo removal procedure similar to that of Veiga et al. (Veiga and Vieira Martins, 1995) was carried out. After that we adopted a two-dimensional symmetric Gaussian model with as high as a third order polynomial to deliver the pixel positions of the concerned satellites. Lastly, the positions of satellites were measured with reference stars from Gaia DR1. The theoretical positions of Uranian satellites were retrieved from the Jet Propulsion Laboratory (JPL) Horizons System that includes the satellite ephemeris ura111, while the position of Uranus was from DE431. We also compared our observations with different satellite ephemerides from the Institut de Mcanique Cleste et de Calcul des phmrides (IMCCE). When Gaia DR1 is used for the reference star catalogue and meanwhile satellites ephemeris is obtained from JPL, our results show that the absolute values of the mean (O-C) (observed minus computed) residuals are not greater than 0.020 arcsec in both right ascension and declination for the five satellites. The positional precision is better than 0.030 arcsec for the four greatest Uranian satellites and 0.050 arcsec for Miranda in each direction.

servational program was carried out at observatories near Beijing and Shanghai by Qiao et al. (2013). By using ASTROThe high-precision dynamics models of the major planets METRICA software Qiao et al. measured the positions of Uraand their satellites are necessary to study the formation and nian satellites. Camargo et al. (2015) carried out observations evolution of the Solar System (Emelyanov, 2010). Moreover, of Uranus and its five main satellites at the Pico dos Dias Obtheories of motion of natural satellites are important for a betservatory in Brazil, spanning from 1992 to 2011. Recently, ter understanding of their own internal structure (Lainey et al., Ershova et al. (2016) published 294 normal positions of the main 2009) and for more general studies of a specific planetary sys- 30 Uranian satellites observed from 2007 to 2016. With the further tem physics (Jacobson, 2014). In order to construct more accudevelopment of the theoretical research on the planetary satelrate orbital models of planets and satellites, a large amount of lites, the accuracy of positional measurements have been put continuous and high-precision observations are needed. forward higher requirements. It is well known that the precision At present, the astrometry of the main Uranian satellites of a reference star catalogue has a great impact on the meais routinely obtained by ground-based CCD observations (of surements of satellites. As Gaia DR1 star catalogue is availcourse, other techniques such as space observations and the able (Gaia Collaboration et al., 2016a, b), we believe that the observations of mutual events are also the important observamuch higher positional accuracy and precision of main sateltional sources). In the past, a few groups have conducted longlites of Uranus should be achieved. Meanwhile a quite great term regular observations of the five major Uranian satellites. CCD field of view allows us to calibrate its geometry accuVeiga et al. (2003) began their observations of the Uranus sys- 40 rately (Peng et al., 2012). In this paper, the measurement and tem in 1982, which belonged to the astrometric observation reduction process for Uranian satellites are all based on our own program initiated in Brazil. Another observations of Uranus software (Peng and Zhang, 2006; Peng et al., 2008). and its two satellites (Titania and Oberon) were made with the In order to derive a precise position of a Uranian satellite, Flagstaff Astrometric Scanning Transit Telescope by Stone (2001) its pixel positional measurement is fundamental. We performed during the period 1995-2000. And during 1998-2007, an oba procedure similar to that of Veiga and Vieira Martins(1995) to remove the halo light from its host planet. Furthermore, a two-dimensional symmetric Gaussian model with as high as a ∗ Corresponding author. third order polynomial was used to fit the image of satellite conEmail address: [email protected] (Q. Y. Peng)

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1. Introduction

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Keywords: techniques: image processing, astrometry, planets and satellites: individual: Uranus 2010 MSC: 00-01, 99-00

Preprint submitted to Elsevier

November 26, 2018

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Parameter

Value

Approximate focal length F-Ratio Diameter of primary mirror CCD field of view Size of pixel Size of CCD array Approximate angular extent per pixel

1330 cm 13 100 cm 7.1 arcmin × 7.1 arcmin 13.5 µm × 13.5 µm 2048 × 2048 0.209 arcsec/pixel

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Table 2 CCD observations of Uranian satellites. Column 1 lists observational dates. Column 2 shows the total number of observations. Column 3 to Column 7 list the numbers for the five major satellites of Uranus, respectively. Ariel No.

Umbriel No.

Titania No.

Oberon No.

Miranda No.

2014-01-01 2014-01-02 2014-01-03 2014-01-04 2015-11-03 2015-11-04 2016-09-25 2016-09-26 2016-10-22 2016-10-23 2016-10-24 2016-11-20 2016-11-21 2016-11-22 2016-11-23 Total

26 8 25 28 20 43 56 60 63 74 59 21 75 77 75 710

26 0 25 28 20 43 56 60 63 74 59 21 75 77 75 702

25 8 25 28 20 43 56 60 63 74 59 21 75 77 75 709

26 8 25 28 20 43 56 60 63 74 59 21 75 77 75 710

26 8 25 28 20 43 56 60 63 74 59 21 75 77 75 710

0 0 0 0 20 14 56 60 63 74 33 21 75 10 75 501

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cerned. The contents of this paper are arranged as follows. In Section 2, the CCD observations and the method of image processing as well as data reduction are described. Section 3 presents results and comparison with the ephemerides. Finally, in Section 4, conclusions are drawn.

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2. Observations, measurements, and reductions

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2.1. CCD observations All the observations during the period 2014–2016 were made with the 1–m telescope at Yunnan Observatory. The site (i.e. IAU code 286) is at longitude E102◦47′ 18′′ , latitude N25◦ 01′ 32′′ and height 2000 m above sea level. The exposure time for each CCD frame ranged from 18 to 120 seconds, depending on the meteorological conditions. For more instrumental details of the reflector and the CCD detector, see Table 1. A total of 710 CCD frames, with Johnson I-type filter, of Uranus and its satellites120 over 15 nights have been obtained. Owing to its nearness to the host planet and lower SNR (signal to noise ratio) caused by the planet’s halo light, the number of the measurable CCD images for each satellite is not the same. Distributions of the observations with respect to the observational date are listed in Table 2.

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and is greatly affected by the halo light of the planet. According to Veiga and Vieira Martins(1995), the center of Miranda’s image would be shifted towards the main body center if the background gradient were not removed. As such, with reference to their practice, we chose an axis (horizontal axis or vertical axis, depending on the position of Miranda), which passed through the planet center determined by the circle fitting. Then the pixel value of Miranda was subtracted with the value of its axisymmetric pixel. Even after the halo-removal mentioned above, the background of a faint satellite near to the host planet is not perfectly flat. A polynomial is usually added to model. For instance, Pascu et al. (1987) and Veiga et al. (2003) modeled the inclined background of Miranda using a second order polynomial. Theoretically, a background very near to the host planet should have high order variation in its pixel intensities, a higher order polynomial may be eligible to model it. By contrast, a background far from the planet should approach to a flat, i.e., a constant background. As such, we try to find the highest order polynomial to model our nearest background to the host planet. An experiment was conducted. After the background gradient was removed, we used a two-dimensional symmetric Gaussian model with a zeroth, first, second and third order polynomial to determine the center of a total of 181 Miranda’s images, respectively. These observatons were made on the successive four nights (see Table 2) in November, 2016. The effect of halo removal was showed in Fig. 1. It demonstrated a typical CCD frame before and after halo removal, and the corresponding slice image of Miranda that links through the centers of Uranus and Miranda. Table 3 listed the statistics of (O-C) residuals on these successive four nights. It can be seen that the difference between residuals of the 1 st , 2nd and 3rd order polynomial fitting was very small. But the residuals of the constant background case (i.e. the 0th ) were quite different. Due to the quite difference , only the 1 st , 2nd and 3rd order polynomial background cases were shown in Fig. 2. As we see from Table 3, our results in the case of the 0th order showed a quite bias from the other cases for the mean (O-C)s in right ascension and declination though similar standard deviations in each direction. Furthermore, the standard deviations in both directions when using 3- order polynomial fitting was slightly better than those of the 1- or the 2- order polynomial. Thus in subsequent measurment of Miranda, we preferred to choose a Gaussian model with a 3- order polynomial to fit its images after our halo removal. In order to obtain the precise positions of the five Uranian satellites, Gaia DR1 was used as the reference catalogue. Then we matched the stars with those in the reference star catalogue Gaia DR1 due to its wide coverage of available stars. Our observations were made in the period of 2014-2016, near the epoch of Gaia DR1 (J2015.0), the effect brought by proper motions for faint stars (no proper motions as usual) could be neglected.

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Table 1 Specifications of the 1-m telescope and CCD detector.

2.2. Image processing 2.3. Data reduction All CCD frames were processed to obtain the centers for After obtaining the measured pixel positions of satellites the five major Uranian satellites as well as the reference stars. and reference stars, a data reduction procedure was performed. In many cases, the image of Miranda is quite close to Uranus130 The correction of CCD frames affected by geometric distortions 2

ACCEPTED MANUSCRIPT Table 4 Statistics of (O–C) residuals for the five satellites of Uranus using different star catalogues. Column 1 represents the different objects. The second column shows the star catalogues. The following columns list the mean (O–C) and its standard deviation (SD) in right ascension and declination, respectively. All units are in arcsec. The ephemeris used is JPL ura111/DE431.

Ariel Umbriel Titania Oberon Miranda

800 700 1099

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1113

900 800 700

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Fig. 1. Typical CCD image of Uranus and its main satellites, as obtained on 21 November, 2016. Upper left (right) panel: CCD frame before (after) halo removal. Lower left (right)140 panel: a slice of the Mirandas image that links through the centers of Uranus and Miranda and the same slice after halo removal.

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Table 3 Statistics of (O-C) residuals for Miranda when using a Guassian model of different orders polynomial. The first column represents different orders of polynomial. The next few columns list the mean (O-C) and standard deviation (SD) in right ascension and declination, respectively. All units are in arcsec. Orders

¡O-C¿

SD

¡O-C¿

RA

0-order 1-order 2-order 3-order

0.049 0.018 0.023 0.021

0.031 0.031 0.030 0.030

UCAC4 Gaia UCAC4 Gaia UCAC4 Gaia UCAC4 Gaia UCAC4 Gaia

0.032 0.020 0.031 0.019 0.030 0.019 0.027 0.020 0.774 0.010

SD

¡O-C¿

RA

SD DE

0.110 0.021 0.106 0.020 0.116 0.016 0.106 0.017 0.418 0.046

-0.056 -0.008 -0.055 -0.006 -0.058 -0.007 -0.055 -0.012 -0.011 -0.010

0.061 0.027 0.063 0.029 0.050 0.029 0.057 0.025 0.066 0.037

was also taken into account. The detailed steps will be specified as follows. Firstly, the pixel positions of the five major Uranian satellites and the reference stars were corrected for their geometric distortions according to the method of Peng et al. (2012). Secondly, we used a four parameter model to calculate the observed positions of Uranian satellites. And the model was obtained beforehand by comparing the pixel positions of reference stars with their standard coordinates using least square fitting. The theoretical positions of satellites were retrieved from Jet Propulsion Laboratory (JPL) Horizons ephemeris service ( http://ssd.jpl.nasa.gov/), which includes the satellite ephemeris ura111 and planetary ephemeris DE431. Finally, the residual of (O-C) (observed minus computed) for each satellite was derived.

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-0.015 0.004 -0.000 0.001

0.025 0.024 0.023 0.022

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3. Results

In order to analyze the effects of different reference star catalogues on the positional precision, the UCAC4 (Zacharias et al., 2013) was also adopted as a reference catalogue. Table 4 listed the statistics of (O–C) residuals for each satellite using both catalogues. The same ephemeris retrieved from JPL was used. It can be seen that when Gaia DR1 was used, the five satellites have better agreements and much smaller dispersions in each direction. Then the absolute mean (O–C) was not bigger than 0.020 arcsec in each direction and the precision was better than 0.030 arcsec in each direction (except for Miranda). As mentioned in the Section 2, Miranda is pretty close to the primary planet and is greatly influenced by the halo light. The standard deviations of Miranda in both directions were worse than those of the other four satellites by a factor of two. Fig. 3 showed a scatter plot of the (O–C) residuals for each satellite in right ascension and declination with respect to different catalogues. It can be seen that when Gaia DR1 was referred to, the dispersion of each satellite was significantly smaller than that when UCAC4 was referred to. We also compared our observed positions with those from two different satellite ephemerides retrieved using the ephemerides of planets and natural satellites server MULTI-SAT (Emel’yanov and Arlo 2008) on the website http://nsdb.imcce.fr/multisat/.

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(O-C)(arcsec) in RA

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Fig. 2. (O-C) residuals of Miranda when fitted by using a Gaussian function with one, two and three order polynomial. The left and right figures show the residuals in right ascension and in declination. The residuals when using 1, 2 and 3 order polynomial are represented by black, red, and blue dots, respectively.

Table 5 Statistics of (O–C) residuals for the five satellites of Uranus by using different satellite ephemerides. Column 1 shows the different objects and column 2 shows the satellite ephemerides. The following columns list the mean (O–C) and its standard deviation (SD) in right ascension and in declination, respectively. All units are in arcsec. ¡O-C¿

SD

¡O-C¿

Ariel

JPL LA15 EM13

0.020 0.021 0.012

0.021 0.027 0.024

-0.008 -0.009 -0.010

Umbriel

JPL LA15 EM13

0.019 0.017 0.014

0.020 0.021 0.022

-0.006 -0.005 0.016

Titania

JPL LA15 EM13

0.019 0.016 0.019

0.016 0.016 0.021

-0.007 -0.008 0.013

Oberon

JPL LA15 EM13

0.020 0.019 0.026

0.017 0.017 0.016

-0.012 -0.009 -0.002

Miranda

JPL LA15 EM13

0.010 0.008 0.014

0.046 0.043 0.056

-0.010 -0.014 -0.010

DE

Ariel Umbriel Titania Miranda

0.027 0.029 0.028

0.029 0.029 0.029 0.029 0.024 0.023

0.025 0.024 0.023 0.037 0.047 0.038

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The (O–C) residuals were listed from Table 5 by using different ephemerides. On the whole, our observations were in good agreement with all the three ephemerides. The differences between any two ephemerides were very small. Except for the mean values of Umbriel and Titania in declination (less than 20 mas), the offsets of different ephemerides were not bigger than 10 mas. LA15 is a short form of Lainey’s theory (Lainey, 2008; Arlot et al., 2016) and EM13 is a short form of Emelyanov and Nikonchuk (2013). However, for the five satellites, almost all the absolute mean values of (O–C) in right ascension were larger than those in declination. The differences might be mainly from the contribution of the theoretical210 error of Uranus rather than that from satellites’ ephemerides. Table 6 listed the mean values and standard deviations of the other satellites when measured with respect to Oberon and the JPL ephemerides were referred to. It appeared that corresponding mean (O–C) in right ascension for inter-satellites became much smaller. And the dispersion of the inter-satellite was also improved. To compare our observations with others, some major observational statistics of the five Uranian satellites were listed in Table 7. And as for our observations, the theoretical positions220

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Table 6 Overall residuals with respect to Oberon. Column 1 lists the different objects. The following columns show mean (O–C) and standard deviation of the other four satellites referred to Oberon in right ascension and in declination, respectively. All units are in arcsec.

4

0.000 -0.000 -0.001 -0.007

SD DE

0.017 0.019 0.013 0.044

0.003 0.005 0.005 -0.001

0.022 0.021 0.020 0.036

were obtained from JPL ephemeris. It can be seen that our observations had a smaller dispersion and the positional precision had been significantly improved. Table 8 listed an extract of our observed topocentric astrometric positions of the five main satellites of Uranus. The data were presented in the following form: The first column represented different satellites. JD denoted the exposure middle time of each CCD frame in the form of Julian Date (UTC). RA, expressed in hours, minutes and seconds, were the positions of corresponding satellites in right ascension. DE, expressed in degrees, arcminutes and arcseconds, were the positions of corresponding satellites in declination. As we computed the atmospheric refraction during data reduction, positions given here were not affected by atmospheric refraction. The complete data can be obtained from our site https://astrometry.jnu.edu.cn/do 4. Conclusions 710 new CCD positions of the five Uranian satellites taken at Yunnan Observatory with the 1–m telescope in 2014-2016 were presented in this paper. During the reduction, Gaia DR1 and UCAC4 were both used for the reference star catalogues. The reduction was really better with Gaia DR1. Since there was no regional error in Gaia DR1 catalogue, the absolute positions of the five Uranian satellites when Gaia DR1 was referred to will be valuable in improving the Uranus planetary ephemeris. Comparisons have been made between different ephemerides of Uranian satellites. When Gaia DR1 was referred to and JPL ephemeris was adopted, the absolute values of the mean (O-C) (observed minus computed) residuals were not greater than 20 mas in right ascension and in declination for all the five satel-

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Fig. 3. (O–C) residuals of the major Uranian satellites. The dark points represent the (O–C) residuals using UCAC4 star catalogue and the red ones represent the (O–C) residuals using Gaia DR1 star catalogue.

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Objects

No.

¡O-C¿ RA -0.096 -0.030 -0.030 0.043 0.020

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Table 7 Compared with other observations. Column 1 lists the different satellites. Column 2 lists the authors and Column 3 lists the number of observations. The following columns list the mean (O–C) and its standard deviation (SD) in right ascension and in declination, respectively. All units are in arcsec. V+03, Q+13, C+15 and E+16 are the short forms of Veiga et al. (2003), Qiao et al. (2013)(the best precision results from their Table 5), Camargo et al. (2015) and Ershova et al. (2016), respectively. All units are in arcsec. SD

¡O-C¿ DE

SD

0.140 0.090 0.065 0.110 0.021

-0.006 0.000 -0.021 -0.074 -0.008

0.153 0.130 0.040 0.110 0.027

-0.090 -0.020 -0.028 0.025 0.019

0.146 0.090 0.062 0.090 0.020

-0.011 0.040 -0.027 -0.069 -0.006

0.145 0.120 0.048 0.110 0.029

V+03 Q+13 C+15 E+16 This work

1754 269 1710 80 702

Umbriel

V+03 Q+13 C+15 E+16 This work

1746 389 1987 255 709

Titania

V+03 Q+13 C+15 E+16 This work

1726 673 2588 523 710

-0.088 -0.010 -0.025 -0.009 0.019

0.151 0.080 0.059 0.030 0.016

-0.008 0.000 -0.035 -0.014 -0.007

0.153 0.090 0.048 0.030 0.029

Oberon

V+03 Q+13 C+15 E+16 This work

1714 835 2928 578 710

-0.088 -0.020 -0.035 -0.001 0.020

0.164 0.080 0.056 0.030 0.017

-0.030 0.020 -0.026 -0.019 -0.012

0.150 0.090 0.042 0.040 0.025

Miranda

V+03 Q+13 C+15 E+16 This work

1452 15 584 501

-0.080 -0.080 -0.022 0.010

0.156 0.100 0.096 0.046

0.006 0.310 -0.008 -0.010

0.161 0.090 0.060 0.037

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Table 8 Extract of the observations. Gaia DR1 was used as the reference catalogue for measuring the positions of satellites. The first column shows the different satellites. 1-5 represent Ariel, Umbriel, Titania, Oberon and Miranda, respectively. Column 2 lists the exposure middle time of each CCD frame in form of Julian Date (UTC). RA and DE are the observed topocentric astrometric positions of the five major Uranian satellites in right ascension and declination, respectively. The whole table is available on the website https://astrometry.jnu.edu.cn/download/main.htm Satellites 1 2 3 4 ... 1 2 3 4 5

Date (JD)

RA (h m s)

2456658.9712037 2456658.9712037 2456658.9712037 2456658.9712037 ... 2457716.1331019 2457716.1331019 2457716.1331019 2457716.1331019 2457716.1331019

0 32 15.0959 0 32 15.3850 0 32 15.1178 0 32 16.2712 ... 1 17 58.7194 1 17 58.6549 1 17 57.7225 1 17 56.9235 1 17 58.4143

DE (◦

′ ′′

)

2 43 58.595 2 43 47.701 2 44 31.520 2 43 29.616 ... 7 33 26.310 7 33 5.649 7 33 0.635 7 33 55.606 7 33 14.635

lites. For the four greatest Uranian satellites, the standard deviations of the (O-C) residuals were less than 30 mas in each direction. While the corresponding values were less than 50 mas for Miranda. The differences of any residuals for each satellite between our observed position and theoretical one from any ephemeris available at the JPL and IMCCE for the five Uranian satellites, were usually not more than 10 mas. Acknowledgments

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This research work is financially supported by the National Natural Science Foundation of China (grant nos. U1431227, 11273014 and 11703008) and partly by the Fundamental Research Funds for the Central Universities. We acknowledge the

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support of the staff of the 1 m telescope at Yunnan Observatories. 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. Lastly, the authors are very grateful to the valuable suggestions from the referee Dr Emelyanov and another anonymous one. References

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1113

D(Pixels)

1120

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TE D

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ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT 710 CCD frames are reduced for the positions of the five major Uranian satellites These positions are compared with the present ephemerides available Miranda can be precisely and conveniently detected by removal technique

AC C

EP

TE D

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The positions can be used for the dynamics of Uranus itself and its satellites