Issue 
A&A
Volume 668, December 2022



Article Number  A141  
Number of page(s)  6  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/202243968  
Published online  15 December 2022 
An astrometric mass estimate for asteroid (223) Rosa
Instituto de Astrofísica de Andalucía, IAACSIC,
Glorieta de la Astronomía s/n,
18008
Granada, Spain
email: kretlow@iaa.es
Received:
6
May
2022
Accepted:
5
October
2022
Context. Outer main belt asteroid (223) Rosa is a possible flyby target of opportunity for the European Space Agency (ESA) JUpiter ICy moons Explorer (JUICE) mission when it passes the asteroid belt on the way to Jupiter. The very low albedo and the featureless red spectra indicate a Ptype asteroid in the Tholen taxonomy, though the yet known bulk density does not appear to match this classification.
Aims. The aim of this work is to derive new estimates for the mass and bulk density of (223) Rosa.
Methods. We derived the mass of Rosa by analyzing the gravitational deflection of small "test" asteroids that had a close encounter with Rosa in the past. To find such events suitable for the mass determination, we performed an encounter search with about 900 000 asteroids over the time span 1980–2030.
Results. Three encounters were identified from which two independent mass estimates for Rosa were derived: M = (5.32 ± 2.17) × 10^{17} kg and M = (3.15 ± 1.14) × 10^{17} kg, respectively. The weighted mean is M = (3.62 ± 1.25) × 10^{17} kg. This yields to a bulk density of ρ = 1.2 ± 0.5 g cm^{−3}, when adopting an effective diameter of D = 83 ± 8 km. This bulk density estimate is consistent with typical densities for Tholen taxonomy Ptype asteroids.
Key words: minor planets, asteroids: individual: (223) Rosa / astrometry / celestial mechanics / methods: numerical
© M. Kretlow 2022
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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1 Introduction
Asteroid (223) Rosa (hereafter also Rosa) was recently proposed as a potential ESA JUpiter ICy moons Explorer (JUICE) mission^{1} flyby target of opportunity on its way to Jupiter (Avdellidou et al. 2021; Agostini et al. 2022). Rosa is a very dark (p_{V} < 0.05) outer main belt asteroid (proper semimajor axis a_{p} = 3.09011 au)^{2}, with an effective diameter D of about 83 km (see Sect. 2), of which the composition (e.g., the taxonomic class) and evolution (e.g., the dynamical and collisional history) are still not fully understood.
Important physical parameters characterizing an asteroid are its size and mass, and therefore its bulk density. While diameter estimates do usually exist for an asteroid, provided by at least one of various wellknown methods such as radiometry, stellar occultations, and (occultation)scaled lightcurve inversion (3D models), mass estimates are much harder to derive and are known for only a small number (some 10^{2}) of the known asteroids. Compilations of asteroid masses are available in the literature (e.g., Hilton 2002; Carry 2012, and references therein), and are now also provided by webbased data archives (e.g., Kretlow 2020a).
One of the commonly applied methods in this domain (Hilton 2002) consists in gravitational deflection of a significantly smaller object ("test asteroid") by another asteroid ("perturber") in order to derive the mass of the latter during the mutual encounter. In addition to such investigations, which are used to study individual objects, asteroid masses are also derived as modelparameter fit results in major planetary ephemeris construction (simultaneously with other asteroid masses which are included in the dynamical model). Two mass estimates for Rosa were found in the literature, and both were derived in that way: Fienga et al. (2019) obtained a mass of M = (5.979 ± 2.971) × 10^{17} kg. Park et al. (2021) provide a value of M = 9.350 × 10^{17} kg.
As mentioned, diameter estimates are available for the majority of the known numbered asteroids, as they were observed by dedicated spacebased infrared surveys such as performed by the Infrared Astronomical Satellite (IRAS), the WideField Infrared Survey Explorer (WISE), and the Akari satellite, and/or were obtained using other methods, and therefore in many cases more than one size estimate is found in the literature. Using an uncertainty weighted average of D = 82.7 ± 8.4 km for the mean diameter and a mass of M = (5.979 ± 2.971) × 10^{17} kg from Fienga et al. (2019), Avdellidou et al. (2021) computed a bulk density of ρ = 1.79 g cm^{−3} with a relative uncertainty of about 50%^{3}.
Section 2 gives an overview of the available size measurements and we aim to provide a (current) best value. In Sect. 3, this work provides a new mass estimate derived from mutual encounters with other small asteroids. Section 4 summarizes the proposed best values for the size and mass of (223) Rosa, provides the resulting bulk density, and discusses these values with respect to the taxonomic class of the asteroid.
2 Diameter estimates
The value (and uncertainty) of the diameter D is crucial for the resulting bulk density due to ρ ∝ D^{−3}. As mentioned in the introduction, mostly thermal diameters have been published so far. Table 1 presents the values published up to now. It is out of the scope and beyond the capability of this study to discuss and to evaluate every diameter estimate given in Table 1 in order to identify and argue in favor of a best value. The effective diameter used in this work for Rosa is therefore derived by averaging all these literature values. Because in weighted arithmetic means the error σ is used as weight w = 1/σ^{2}, outliers with small formal uncertainties will bias the result. An alternative form of averaging is the expected value method (EVM; Birch & Singh 2014), which is more robust against outliers. Table 1 provides both the traditional weighted average (D = 82.6 ± 8.2km) and the EVM average (D = 83.3 ± 8.1 km) for the published diameter estimates.
As shown in Fig. 1, Rosa was observed photometrically in different viewing aspects, with Phase Angle Bisector (PAB) longitudes of between 75° and 352°, phase angles α of between 0.9° and 17.1° and aspect angles θ of between 37.6° and 153.8° for pol solution 1 (respectively between 29.3° and 140.5° for pol solution 2) derived by Marciniak et al. (2021). The highest lightcurv amplitude in the set of light curves (Fig. 2) archived at the Centre de Données Stellaires (CDS^{4}) is Amax = 0.16 mag for a nearly equatorial view, which corresponds to an axis ratio a/c = 1.16 for an aspect angle θ = 90°. The Asteroid Lightcurve Database (LCDB^{5}) provides values Amin = 0.06 mag and Amax = 0.13 mag. Putting this together we can expect that Rosa is neither very elongated nor irregular and the assumption of a spherical body made in simple thermal models such as the standard thermal model (STM) or nearEarth asteroid thermal model (NEATM) is appropriate for this asteroid. Averaging all available size estimates derived from STM, NEATM, and also the thermophysical model (TPM) as described above seems reasonable in order to derive a reliable value for the effective diameter.
The observation of stellar occultations by asteroids provides the shape and size of the apparent profile on the sky plane with accuracy to the nearest kilometer. Up to now, three stellar occultations by (223) Rosa were successful observed (Herald et al. 2019): 2004 Sep. 29 (single visual observation with two subsequent occultation events and corresponding chord lengths of 34 km and 78 km, but inconsistent with adjacent negative observations), 2008 May 27 (two chords), and 2014 Apr. 13 (one chord: length = 46.4 km). The 2008 May 27 stellar occultation was recorded by three stations operated by the same observer (i.e., two unattended stations), yielding two positive detections (chord lengths of 54.5 km and 66.7 km) and one negative observation (no occultation detected).
The observation of further stellar (multichord) occultations by Rosa will help to refine its volume, especially in combination with lightcurve data. Therefore, stellar occultation predictions were performed until the year 2025, considering Gaia EDR3 (Early Data Release 3, Brown et al. 2021) stars down to G = 16 mag. These predictions will be available on the website^{6} of the author. Two upcoming events crossing over Europe (2022 Oct. 7) and the USA (2023 Feb. 24), regions potentially well covered by occultation observers, are presented in Fig. 3.
Compilation of literature values for the effective diameter reproduced from Avdellidou et al. (2021) and completed with recent publications.
3 Mass estimates
There are only two mass estimates published in the literature from the construction of planetary ephemerides; just one of these includes error bars (see Sect. 1). The aim of this work is to derive a new estimate for the mass of Rosa by means of a gravitational deflection analysis.
In a first step, a search for suitable test asteroids was performed essentially by integrating (223) Rosa and about 900 000 known asteroids^{7} backwards until the year 1980 (and also into the future until the year 2030 in order to identify upcoming events). If the euclidean distance between Rosa and another (test) asteroid became smaller than 0.05 au during this ephemeris interval, the mutual encounter was stored together with additional information such as the time span of available observations of the test asteroid, the relative encounter velocity, and the parameter ; with D_{1} the diameter of the perturber (set to D_{1} = 83 ± 8 km; see Sect. 2), r the encounter distance between both objects in km, and v their relative encounter velocity in km s^{−1}. P is a proxy for the change in the mean motion ∆n of the perturbed body (Galád 2001). This resulting list of encounters was finally used to select candidates for the asteroid mass determination. For (223) Rosa, three close encounters were identified to be potentially suitable for the mass determination (Table 2).
The mass M of the perturbing body (Rosa) was determined by means of a leastsquares fit of the solvefor parameters to the astrometric observations^{8} of the test asteroid by solving the system of linear equations: (1)
where P = ∂(α, δ)/∂E is the matrix of partial derivatives of the observed coordinates (α, δ) with respect to the six initial values E_{1}, …, E_{6} (position and velocity) of the test asteroid. Q = ∂(α,δ)/∂M is the matrix of partial derivatives of the observed coordinates of the test asteroid with respect to the perturbing mass M, and R is the matrix depending on the (O–C) residuals in coordinates of the test asteroid. ΔE = (ΔE_{1}, …, ΔE_{6}) are the corrections to the six initial values of the test asteroid and AM is the correction to the mass of the perturbing body. The partial derivatives P, Q were not computed by numerical variation, but rather by integrating a set of seven differential equations together with the equations of motion of the test asteroid (Sitarski 1971).
The numerical integration was carried out using a multistep, variableorder, predictorcorrector (PECE) method with selfadjusting step size (Shampine & Gordon 1975). The masses of the planets and their state vector during the integration were read from an external file (JPL DE440). The perturbing asteroids of the dynamical model were handled in a similar way, as was the perturber Rosa. The ephemerides of all of these objects are precomputed and stored as Chebyshev polynomials in external files, to be used in the program on demand. The perturbing asteroids are summarized in Table 3. If applicable, those astrometric observations of the test asteroid which were reduced with nonGaia star catalogs, were debiased (Eggl et al. 2020). For the weights of the observations during the differential orbit correction of the test asteroid, the error estimates given by Veres et al. (2017) were used.
Fig. 1 Aspect data for the light curves given in Fig. 2. The left panel shows the PAB longitude distribution. In the middle and right panel the phase and aspect angle α, θ are given as a function of PAB longitude (middle) and MJD (right). The phase angle α is marked with dots. The aspect angle θ is computed for both solutions derived by Marciniak et al. (2021). Solution λ_{p}, β_{p} = (22°, 18°) is marked by triangles (▲), the mirror solution λ_{p}, β_{p} = (203°, 26°) by upsidedown triangles (▼). 
Fig. 2 Overview of all 58 currently available optical light curves archived at the CDS (http://cdsarc.ustrasbg.fr/vizbin/cat/J/A+A/654/A87, Marciniak et al. 2021). Given is the relative brightness (in intensity units) normalized to the mean brightness vs time (MJD) for the time span 20072020. The maximum amplitude Amax for the epoch around MJD 55950 is 0.16 mag and corresponds to a nearly equatorial view; see Fig. 1 (right panel). The LCDB (https://www.minorplanet.info/PHP/lcdb.php) provides the values Amin = 0.06 mag and Amax = 0.13 mag. 
Fig. 3 Two stellar occultation predictions for (223) Rosa. The red line marks the 1 − σ crosstrack uncertainty (about 24 km for both events). Minute time ticks are marked with yellow dots. The time of geocentric closest approach (c.a.) is marked by the red dot. Lefthand side: occultation of the star Gaia EDR3 0664382207483343488 on 2022 Oct. 7 at 05:27:31 UT (c.a.), visible in Portugal and Spain (though twilight will interfere in the eastern part of Spain). The star has G = 13.5 mag, the expected magnitude drop will be 2.0 mag, the maximum duration about 2.9 s. Righthand side: occultation of the star Gaia EDR3 0661647103588763776 on 2023 Feb. 24 at 01:54:39 UT (c.a.), visible in the U.S. and northern Africa (Morocco, Algeria, etc.) The star has G = 13.9 mag, the expected magnitude drop will be 0.8 mag, and the maximum duration about 9.6 s. 
Test asteroids and their mutual encounter events used for the mass determination of (223) Rosa, ordered by encounter date.
List of perturbing asteroids included in the dynamical model.
(35525) 1998 FV64
This encounter between 1998 FV64 and Rosa at the end of the year 2010 has the smallest perturbation parameter value of all three events presented here. The preencounter as well as postencounter observation coverage is extensive and homogeneous. A mass estimate M = (5.32 ± 2.17) × 10^{17} kg was derived for Rosa.
(315162) 2007 FL24
2007 FL24 had a long and slow encounter with Rosa in 2016 (showing the largest perturbation parameter P of all three cases), and also good astrometric coverage both preencounter and postencounter. The orbit solution for this encounter yields a mass estimate M = (3.15 ± 1.14) × 10^{17} kg.
Because the osculating orbital elements of Rosa and 2007 FL24 appear very similar, the possibility of being an asteroid pair was investigated. First, the distance between them in the threeparameter space was calculated using their proper elements^{9} and the formula (Zappala et al. 1990): (2)
with a the mean of both semimajor axes, n the corresponding mean motion, and the standard metric weighting factors k_{a} = 5/4, k_{e} = k_{i} = 2. Though the high value of d = 51 m s^{−1} made it unlikely that these two bodies are an asteroid pair, a 500 kyr backward integration was made using the mercury6 software (Chambers 2012) regarding all major planets (MN) plus the dwarf planet or asteroids Ceres, Pallas, and Vesta, but without applying any nongravitational forces. No close encounter or coincidence point was found in this time span, and therefore the orbital similarity seems to be a random coincidence.
(78824) 2003 QS13
Though this encounter in 2001 has a perturbation parameter P = 8.1 ± 2.3 km s, which is even larger than that of the interaction with 1998 FV64, the orbit solution did not yield a physically reasonable mass solution for Rosa. A likely explanation is that only four preencounter nights of observation are available, one night in September 1960 (Palomar Mountain, 675), one single observation in 1994 (Tautenburg, 033), and two sequential nights in December 1996 (Prescott, 684). A rereduction of these preencounter observations (if available) using the Gaia star catalog could be helpful. A search in image archives^{10} to retrieve additional and precise positions was not successful, because the object was usually too faint to be detected on older survey images such as NEAT (NearEarth Asteroid Tracking) GEODSS/Maui. Table 4 lists the images that were examined for this asteroid. It is also conceivable that a different numerical approach, such as a Monte Carlo parameter estimation (Siltala & Granvik 2020), might be able to use this encounter for a mass determination with the existing astrometry. A summary of all three encounter circumstances and the derived mass results is given in Table 2.
Archived survey images on which the asteroid (78824) 2003 QS13 would have potentially been observed.
Fig. 4 Bulk density as a function of the diameters given in Table 1 for the final mass estimate M = (3.62 ± 1.25) × 10^{17} kg. The horizontal dashed line marks the typical density ρ ≈ 1.3 g cm^{−3} for Tholen taxonomy Ptype asteroids. 
4 Results and discussion
From two individual close encounters with small asteroids, we estimated the mass of Rosa to be M = (5.32 ± 2.17) × 10^{17} kg and M = (3.15 ± 1.14) × 10^{17} kg, respectively. The weighted mean value is M = (3.62 ± 1.25) × 10^{17} kg. Figure 4 shows the bulk density as a function of the diameters given in Table 1. By adopting D = 83.3 ± 8.1 km as the (currently) best value for the diameter, the corresponding bulk densities are ρ = 1.8 ± 0.9 g cm^{−3} and ρ = 1.0 ± 0.5 g cm^{−3}. The weighted mean is ρ = 1.2 ± 0.5 g cm^{−3}. The EVM mean of the visual albedo is p_{V} = 0.033 ± 0.006.
The mass values derived in this work are smaller than the values M = (5.979 ± 2.971) × 10^{17} kg and M = 9.350 × 10^{17} kg (Fienga et al. 2019; Park et al. 2021), which yield bulk densities of ρ = 2.0 ± 1.1 g cm^{−3} and ρ = 3.1 g cm^{−3}, respectively.
From the reassessment of the existing spectra and spectrophotometric data, supplemented with their own nearinfrared and visible spectra taken in 2021 and the very low albedo, Avdellidou et al. (2021) concluded that Rosa is probably a Tholen taxonomy Ptype asteroid, though the previously mentioned densities of 2.0 ± 1.1 g cm^{−3} and 3.1 g cm^{−3} would be somewhat too large for this taxonomic class.
However, the bulk density ρ = 1.2 ± 0.5 g cm^{−3} that we obtain for Rosaagrees well with typical densities of Ptype asteroids, such as (87) Sylvia and (107) Camilla (ρ ≈ 1.3 g cm^{−3}; see e.g., Carry et al. 2021; Vernazza et al. 2021).
Acknowledgements
The occultation observations made by Roger Venable (USA), provided by the International Occultation Timing Association (IOTA) and by Herald et al. (2019) are acknowledged. Also appreciated are the services and data provided by the Asteroids Dynamic Site (AstDys), JPL Horizon and the Minor Planet Center (MPC). 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). The author thanks the referee for the helpful comments and constructive review of the paper. I also like to thank Anna Marciniak (A. Mickiewicz University, Poznan, Poland) for her comments on theirwork and results on (223) Rosa and José Luis Ortiz (IAA, Granada, Spain) for reading and commenting the original manuscript. Finally I like to acknowledge opensource software and tools, like Linux, Julia + Packages, Jupyter, Python + Packages, Gnuplot, GNU Fortran, SQLite, GSHHG (shorelines DB), etc.
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Proper elements taken from AstDyS, https://newton.spacedys.com/astdys/.
Orbital elements taken from MPC's MPCORB.DAT (https://www.minorplanetcenter.net/iau/MPCORB.html).
Provided by the Minor Planet Center (MPC, https://www.minorplanetcenter.net/).
Provided by AstDyS (https://newton.spacedys.com/astdys/).
Using the CADC Solar System Object Image Search (SSOIS, https://www.cadcccda.hiaiha.nrccnrc.gc.ca/en/ssois/index.html).
All Tables
Compilation of literature values for the effective diameter reproduced from Avdellidou et al. (2021) and completed with recent publications.
Test asteroids and their mutual encounter events used for the mass determination of (223) Rosa, ordered by encounter date.
Archived survey images on which the asteroid (78824) 2003 QS13 would have potentially been observed.
All Figures
Fig. 1 Aspect data for the light curves given in Fig. 2. The left panel shows the PAB longitude distribution. In the middle and right panel the phase and aspect angle α, θ are given as a function of PAB longitude (middle) and MJD (right). The phase angle α is marked with dots. The aspect angle θ is computed for both solutions derived by Marciniak et al. (2021). Solution λ_{p}, β_{p} = (22°, 18°) is marked by triangles (▲), the mirror solution λ_{p}, β_{p} = (203°, 26°) by upsidedown triangles (▼). 

In the text 
Fig. 2 Overview of all 58 currently available optical light curves archived at the CDS (http://cdsarc.ustrasbg.fr/vizbin/cat/J/A+A/654/A87, Marciniak et al. 2021). Given is the relative brightness (in intensity units) normalized to the mean brightness vs time (MJD) for the time span 20072020. The maximum amplitude Amax for the epoch around MJD 55950 is 0.16 mag and corresponds to a nearly equatorial view; see Fig. 1 (right panel). The LCDB (https://www.minorplanet.info/PHP/lcdb.php) provides the values Amin = 0.06 mag and Amax = 0.13 mag. 

In the text 
Fig. 3 Two stellar occultation predictions for (223) Rosa. The red line marks the 1 − σ crosstrack uncertainty (about 24 km for both events). Minute time ticks are marked with yellow dots. The time of geocentric closest approach (c.a.) is marked by the red dot. Lefthand side: occultation of the star Gaia EDR3 0664382207483343488 on 2022 Oct. 7 at 05:27:31 UT (c.a.), visible in Portugal and Spain (though twilight will interfere in the eastern part of Spain). The star has G = 13.5 mag, the expected magnitude drop will be 2.0 mag, the maximum duration about 2.9 s. Righthand side: occultation of the star Gaia EDR3 0661647103588763776 on 2023 Feb. 24 at 01:54:39 UT (c.a.), visible in the U.S. and northern Africa (Morocco, Algeria, etc.) The star has G = 13.9 mag, the expected magnitude drop will be 0.8 mag, and the maximum duration about 9.6 s. 

In the text 
Fig. 4 Bulk density as a function of the diameters given in Table 1 for the final mass estimate M = (3.62 ± 1.25) × 10^{17} kg. The horizontal dashed line marks the typical density ρ ≈ 1.3 g cm^{−3} for Tholen taxonomy Ptype asteroids. 

In the text 
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