EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 654 (October 2021) A&A, 654 (2021) A87 Full HTML
Free Access
Issue
A&A
Volume 654, October 2021
Article Number A87
Number of page(s) 32
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/202140991
Published online 15 October 2021

© ESO 2021

1 Introduction

Physical parameters of asteroids, such as spin, shape, size, albedo, macroscopic roughness, and thermal inertia, form the basis for a significant number of Solar System studies. In particular, these parameters are of great interest for large asteroids as these are considered remnants of early phases of planetary formation (Morbidelli et al. 2009). Studying the way in which asteroid surfaces react to heating by the Sun (which, among others, depends on the spin axis inclination and spin rate), can reveal material properties of these layers (Murdoch et al. 2015; Keihm et al. 2012). Slowly rotating asteroids, with periods longer than 12 h, are especially interesting in this respect; they experience long periods of irradiation of the same surface parts, and the diurnal heat wave from solar irradiation can penetrate to larger thermal skin depths (Delbo’ et al. 2015; Čapek & Vokrouhlický 2010). Furthermore, the most recent results from the TESS mission (Transiting Exoplanet Survey Satellite; Ricker et al. 2015) reveal that slow rotators actually dominate the population of main-belt asteroids (see Fig. 7 in Pál et al. 2020). So far, however, they have been largely omitted by most ground-based studies mainly because of telescope time limitations and the small number of targeted campaigns (Warner & Harris 2011).

As a consequence of the scarcity of multi-apparition light curves which are needed for spin and shape reconstruction via light-curve inversion, the statistics of available spin- and shape-modelled asteroids are strongly biased towards faster rotators (Marciniak et al. 2015). This might have implications on our interpretation of the statistical properties of the asteroid population, such as for example the role of the YORP effect (Vokrouhlický et al. 2015) on the spatial distribution of spin axes (Hanuš et al. 2013), or the estimated contribution of tumblers and binaries in various asteroid populations (Ďurech et al. 2020).

Another hidden problem is that most of the well-studied asteroids, especially among slow rotators, are those with large-amplitude light curves (Warner & Harris 2011), caused by an elongated shape, high spin axis inclination, or both. In our survey, described in detail in Marciniak et al. (2015), we addressed two of these biases at the same time, focusing on slow rotators (P > 12 h) with maximum amplitudes no larger than 0.25 mag, at least at the target-selection stage. During our study, we found that several targets have somewhat larger amplitudes or shorter periods, but nevertheless we kept these in the final sample of this latter work.

The statistics of asteroids with reliably determined thermal inertia is even more biased. Recompiling data from previous works, as well as new values from Hanuš et al. (2018), Marciniak et al. (2018), and Marciniak et al. (2019), there are currently 36 main-belt slow rotators, compared to 120 fast rotators studied using detailed thermophysical modelling (TPM). This shows that, in terms of studying slow rotators in the infrared, we have only touched the tip of the iceberg.

Thermal inertia (Γ = κρc$\Gamma\,{=}\,\sqrt{\kappa \rho c}$) depends on the density of surface regolith ρ, thermal conductivity κ, and heat capacity c. Larger thermal inertia implies coarser regolith composed of grain sizes of the order of millimetres to centimetres, typical for young surfaces of small near-Earth asteroids (NEAs; Gundlach & Blum 2013), while much finer, lunar-like regolith with grain sizes of between 10 and 100 microns is expected at large (D > 100 km) main-belt asteroids (see e.g. Delbo’ & Tanga 2009, and references therein). This picture might however be complicated by various family formation ages, recent catastrophic events refreshing the surface, or by the presence of surface cohesion forces (Marchi et al. 2012; Rozitis et al. 2014). Also, as more asteroids become thermally characterised we can also understand how thermal processes like thermal cracking (Delbo’ et al. 2014; Ravaji et al. 2019) have shaped or are still shaping asteroid surfaces.

However, in light of recent results for two targets studied in situ, Ryugu and Bennu (Okada et al. 2020; Walsh et al. 2019), this standard interpretation of thermal inertia versus surface properties fails; there are boulders on the surface with relatively low thermal inertia, while one would expect regolith. Thermal conductivity, and thus thermal inertia dependance on temperature at various subsurface depths, is another factor to be considered (Hayne et al. 2017). It has been shown that submillimetre flux probes deeper layers, carrying information on the conditions in these layers (Keihm et al. 2012).

Harris & Drube (2016) estimated thermal inertias based on beaming parameters derived from WISE data (Masiero et al. 2011, and references therein) and found that thermal inertia increases with rotation period. This motivated us to add the thermophysical analysis to our study of slow rotators. At first, our results seemed to confirm this hypothesis (Marciniak et al. 2018), as we found large and medium thermal inertia values for the first sample of five targets. Later, with a sample of twice the size, we found a rather wide range of thermal inertia (Marciniak et al. 2019), from very small to medium, similarly to Hanuš et al. (2018), generally not showing any trend with the rotation period. Still, the size of the slow rotators sample with known thermal inertia remains small. In this work we continue our effort to expand this sample employing a different approach, namely the Convex Inversion Thermophysical Model (CITPM, see Sect. 3).

The light-curve inversion method (Kaasalainen et al. 2001) can robustly reproduce asteroid spin and shape, provided the visible data cover a wide range of viewing geometries. However, for targets orbiting close to the ecliptic plane (i.e. most of the main-belt asteroids), the result usually consists of two mirror pole solutions (Kaasalainen & Lamberg 2006; Kaasalainen & Ďurech 2020). These are similar in spin axis ecliptic latitude, but differ in ecliptic longitude: both solutions are roughly 180° apart, and have different associated shape models. One such mirror pole solution sometimes happens to fit thermal data better than the other (see e.g. Delbo’ & Tanga 2009). However, this can stem from the high sensitivity of thermal flux to small-scale shape details, and might not point to a truly better spin solution (Hanuš et al. 2015; Kaasalainen & Ďurech 2020). We therefore decided to switch from independent light curve inversion followed by thermophysical modelling of a fixed shape to simultaneous optimisation of both types of data. The method enabling this approach is the CITPM introduced in Ďurech et al. (2017). This method also enables the user to weight two types of data relative to each other to avoid the dominance of one data type over the other. Müller et al. (2017) applied this method for asteroid Ryugu and the derived size, albedo, and thermal inertia are very close to the in situ properties; however, the spin pole was not well determined by this method (probably because of the very low light-curve amplitude and the lack of high-quality measurements).

In Sect. 2, we describe the visible and infrared data used for modelling. Section 3 presents the main features of the method for combined optical and mid-infrared photometric inversion, which is followed in Sect. 4 by a description of the method used to scale the models by multi-chord stellar occultations. The resulting models, with their spin, shape, and thermal parameters with the occultation scaling are presented in Sect. 5. In Sect. 6 we summarise the results and discuss our ideas for future work. All the plots and figures asssociated with the models can be found in the appendix.

2 Visible and infrared data

Data for traditional, dense light curves in the visible range have been gathered in the framework of our long-term photometric campaign conducted since the year 2013, and are described in Marciniak et al. (2015), including target-selection criteria. In short, the aim of the project is to observe a few tens of slowly rotating main-belt asteroids with small brightness variation amplitudes. It involves over 20 observing stations with telescopes of up to 1 m in diameter, including for example TRAPPIST telescopes (Jehin et al. 2011). To compliment these data, we also use data from the Kepler Space Telescope in the extended K2 mission (Howell et al. 2014) downlinked within our proposals accepted by Kepler and K2 Science Center, as well as publicly available data from TESS (Pál et al. 2020)1, and Super WASP sky survey (Grice & et al. 2017)2. From the latter archive, we only used the best-quality subsets, choosing from targets with Super WASP datapoints already folded into light curves. Trimming those vast datasets was necessary because of their abundance and in order to avoid dominance of one apparition over others, but also because of their intrinsic noise. Noisy light curves can sometimes prevent the identification of a unique model solution over the whole dataset. The selection criteria for the best Super WASP light-curve fragments were the lowest photometric scatter and the widest possible range of observing dates.

The great majority of the dense light curve data from our photometric campaign were provided in the form of relative photometry, and the rest were treated as such to ascertain light-curve inversion convergence. Separate light-curve fragments obtained during our observing campaign in the R filter or unfiltered were combined to create composite light curves (Figs. E.1–E.66) using the criterion of minimum scatter between data points for initial period determinations. We present the light curves that cover most of the rotation period and show clear brightness variations. For modelling, however, we used all the data described in Table D.1. Determined synodic periods are in agreement in all apparitions, with differences of only a few thousandths due to changes in relative velocity of the observer and the source. The synodic period range from various apparitions, extended at least three times, is a range on which the precise, sidereal period is later searched for in the light-curve inversion procedure.

Composite light curves from various apparitions depict the general character of the asteroid shape (if regular and symmetric, or quite the opposite). Light-curve differences are due to phase-angle effects caused by shadowing on topographic features, and different viewing geometries (aspect angles). Apart from ensuring a full period coverage, sometimes tens of hours long, we paid special attention to covering the widest possible range of ecliptic longitudes and phase angles (see Table D.1), which is a necessary prerequisite for shape reconstruction (Kaasalainen & Ďurech 2020). The small point-to-point scatter of our light curves (see Appendix A), of the order of 0.01 mag down to a few millimagnitudes, captures brightness variations in great detail, even in those cases with very small amplitudes.

Relative photometric data described above were supplemented with the calibrated V-band sparse data from the USNO (US Naval Observatory) archive3. These are necessary for size and albedo determination in the application of the full CITPM. We decided to exclusively use the USNO archive due to its relatively high quality among the available options. As has been shown by Hanuš et al. (2011) the median accuracy of USNO data is at the level of 0.15 mag.

Thermal infrared data were downloaded from the SBNAF Infrared Database4 (Szakáts et al. 2020). This database provides expert-reduced data products from major infrared space missions (Akari, Infrared Astronomical Satellite (IRAS), Wide-field Infrared Survey Explorer (WISE), Herschel, Midcourse Space Experiment (MSX), and Infrared Space Observatory (ISO)) as well as all the necessary auxiliary information, such as the observing geometry, colour correction, or overall measurement uncertainties. SBNAF Infrared Database was developed within the ‘Small Bodies: Near And Far’ Horizon 2020 project (Müller et al. 2018). This database stores calibrated flux densities obtained via careful consideration of instrument-specific calibration and processing procedures. All the measurement uncertainty values have been reanalysed for the sake of database consistency, and include contributions from in-band flux density uncertainty, absolute calibration errors, and colour correction uncertainties. The infrared data for our targets came mostly from three missions: WISE (Wright et al. 2010; Mainzer et al. 2011a) at 11.1 and 22.64 μm, Akari (Usui et al. 2011) at 9 and 18 μm, and IRAS (Neugebauer et al. 1984) at 12, 25, 60 and 100 μm, occasionallysupplemented with data from MSX (Egan et al. 2003) at 8.28, 12.13, 14.65, and 21.34 μm, where available. All the infrared datapoints were used, except in specific single cases where clear outliers were detected that were unable to be fitted by any of the models. Also, because of the large size of some targets resulting in large infrared flux, sometimes a subset or all WISE data at 11 μm were partially saturated, and could not be used in our analysis.

3 Convex inversion thermophysical model

To fit optical light curves and thermal infrared data, we used a combined inversion of both data types developed by Ďurech et al. (2017) called the convex inversion thermophysical model. The method combines convex inversion of light curves (Kaasalainen et al. 2001) with a thermophysical model (Lagerros 1996, 1997, 1998). The shape of an asteroid is parametrized by coefficients of spherical functions that describe a convex polyhedron of size D with typically hundreds of surface facets. For each facet, a 1D heat diffusion equation is solved to compute its temperature and infrared flux at the time of observation. The response of the surface to solar radiation is parametrized by the thermal inertia Γ, surface roughness (described by spherical craters of varying both the fraction of surface coverage f, and the opening angle γc), and light-scattering properties. For emissivity, a fixed value of 0.9 is used, following a standard approach (e.g. Lim et al. 2005). Instead of using absolute magnitude, Bond albedo, and geometric albedo – which are only unambiguously defined for a sphere – we use Hapke’s light-scattering model (Hapke 1981, 1984, 1986), from which any albedos can be directly computed. To tie the reflectance of the surface with the size of the asteroid, absolutely calibrated photometry is needed. Because most of the light curves we collected are provided as the relative photometry, we also use the calibrated V-band photometry from the USNO that covers a sufficiently wide range of solar phase angles. Parameters of Hapke’s model can be optimised to fit the phase curve. The merit function that we minimise is a sum χVIS2+wχIR2$\chi^2_{\mathrm{VIS}} + w \chi^2_{\mathrm{IR}}$ of χ2 values for optical and thermal data. The relative weight w is iteratively set such that (in an ideal case) the fit to light curves is as good as without thermal data, and the fit to thermal data is good, that is, the normalised χIR2$\chi^2_{\mathrm{IR}}$ is ~ 1. The advantage here is that the spin and shape model optimised against visible light curves only in most cases would not be optimal in the thermal radiation, as shown by Hanuš et al. (2015) and Hanuš et al. (2018); here it is optimised to fit both types of data.

The visual part of χ2 is computedas χVIS2 = ∑j = 1N−1∑i(Li,jobsL¯jobs−Li,jmodelL¯jmodel)2+0.2 ∑i(Li,Nobs−Li,NmodelL¯Nobs)2 ,\[ \chi^2_{\mathrm{VIS}} \,{=}\, \sum_{j\,{=}\,1}^{N-1} \sum_i \left( \frac{L_{i,j}^{\text{obs}}}{\bar{L}_j^{\text{obs}}} - \frac{L_{i,j}^{\text{model}}}{\bar{L}_j^{\text{model}}} \right)^2 + 0.2\, \sum_i \left( \frac{{L_{i,N}^{\text{obs}}} - L_{i,N}^{\text{model}}}{\bar{L}_N^{\text{obs}}} \right)^2 \,, \]

where N is the total number of light curves, and Li,j is the brightness (in arbitrary intensity units, not magnitudes) of the ith point of the jth light curve. The normalisation by the meanbrightness of the jth light curve L¯j$\bar{L}_j$ means that we treat all N − 1 light curves as relative and that we neglect differences in photometric accuracy between them. The only exception is calibrated photometry in V filter from USNO (the Nth light curve),for which we directly compare the observed flux with that predicted by our model without normalising by L¯jobs$\bar{L}_j^{\text{obs}}$ and L¯jmodel$\bar{L}_j^{\text{model}}$ separately. The empirical factor of 0.2 gives less weight to USNO data which is intentional because these have larger errors.

For thermal data, errors of individual measurements are known, and so the thermal part of the χ2 is computed classically as χIR2 = ∑i(Fiobs−Fimodelσi)2 ,\[ \chi^2_{\mathrm{IR}} \,{=}\, \sum_i \left(\frac{F_i^{\text{obs}} - F_i^{\text{model}}}{\sigma_i} \right)^2\,, \]

where Fi is observed or modelled flux and σi is the error of the measurement. By dividing χIR2$\chi^2_{\mathrm{IR}}$ by the number of degrees of freedom, we get reduced χred2$\chi^2_{\text{red}}$, which we use in Sect. 5 when presenting our results.

Table 1

Ancillary information on the data and physical properties of our targets.

4 Occultation fitting

For three targets of our current sample there were good quality, multi-chord stellar occultations available in the PDS archive5 (Herald et al. 2019, 2020). More recent occultation results were downloaded from the archive of the Occult programme6. We used them to independently scale the shape models obtained here, using the method described in Ďurech et al. (2011), in order to: compare obtained sizes with those from thermal fitting; confirm the shape silhouette; and if possible, identify the preferred pole solution (see Figs. C.1–C.3).

When scaling the models with occultations, we computed the orientation of the model for the time of occultation and projected the model on the fundamental plane (sky-plane projection). Because all models are convex, their silhouettes are also convex. We then iteratively searched for a scale of the silhouette that would provide the best match with chords. The mutual shift between thesilhouette and the chords was described by two free parameters that were also optimised. We used the χ2 minimisation, where the difference between the silhouette and the chords was measured as a distance in the fundamental plane between the ends of the chords and the silhouette (measured along the direction of the chord). We rejected the solutions in which a negative chord (no occultation was observed) intersected the silhouette.

5 Results

Table 1 provides the ancillary information on the visible and thermal datasets: number of apparitions and separate light curves, numbers of thermal measurements from separate missions, and WISE diameters from Mainzer et al. (2011b); Masiero et al. (2011) to be compared with diameters obtained in this work (see Table 2). We also cite taxonomic type following Bus & Binzel (2002a,b) and Tholen (1989), for a consistency check with our values for albedo (consistent in all cases).

Table 2 summarises all the rotational and thermophysical properties of the targets studied here. First the spin solution is presented, usually with its mirror counterpart. The quality of the fit to light curves in the visible range is given in Col. 5. The second part of the table presents the radiometric solution based on combined data from three infrared missions, the radiometric diameter, geometric albedo, thermal inertia, and the reduced χ2 of modelled versus observed fluxes. Lastly, the table contains the average heliocentric distance at which thermal measurements were taken, and thermal inertia reduced to one astronomical unit, using the formula (Rozitis et al. 2018): Γ1AU = Γ(r)rα,\begin{equation*} \Gamma_{\textrm{1AU}} \,{=}\, \Gamma(r)r^{\alpha} ,\end{equation*}(1)

where the α exponent is equal to 0.75, which takes into account a radiative conduction term in thermal conductivity. Different exponents are also possible (Rozitis et al. 2018), but here we opted for the most widely used value to facilitate comparison with previous works (see the discussion in Alí-Lagoa et al. 2020; Szakáts et al. 2020).

In Appendix A we present the plots of χred2$\chi^2_{\text{red}}$ versus thermal inertia for various combinations of surface roughness and optimised size (Figs. A.1 – A.16). To transform various combinations of crater coverage and opening angle to rms of surface roughness, we used the formula no. 20 from Lagerros (1998). In these figures, f is the fraction of crater coverage, and the plots show the χred2$\chi^2_{\text{red}}$ of the crater opening angle that minimised the χred2$\chi^2_{\text{red}}$ for that value of f. The horizontal line is the acceptance threshold for χred2$\chi^2_{\text{red}}$ values, depending classically on the number of IR measurements and best χred2$\chi^2_{\text{red}}$ value: we accept all the solutions with χred2<(1+σ)$\chi^2_{\text{red}}<(1+\sigma)$, where σ = 2ν/ν$\sigma\,{=}\,\sqrt{2\nu}/\nu$, with ν being the number of degrees of freedom. For a few targets with a value of best χred2$\chi^2_{\text{red}}$ much below 1, probably due to unresolvable mutual parameter correlations, we used an empirical approach by Hanuš et al. (2015) to define that threshold: χred2<(χmin2+σ)$\chi^2_{\text{red}}<(\chi^2_{\text{min}}+\sigma)$.

For each target we also present the fit to WISE W3 and W4 thermal light curves, whenever available (Figs. B.1–B.25). Due to the scarce character of Akari and IRAS data (only 1–3 points per band on average), the model fits to them are not shown. The plots present the results for only one of two mirror pole solutions (the other pole gave very similar results, as indicated by χred2$\chi^2_{\text{red}}$ values from Table 2).

As a consistency check, we re-ran one of our previous targets, (478) Tergeste, now using the CITPM. In one of our earlier works (Marciniak et al. 2018), this target was spin- and shape-modelled, and then the resulting models that best fitted the light curves in the visible were applied in TPM procedures. In that work we obtained thermal inertia in the range of 30–120 J m−2 s−1∕2 K−1 (SI units), and reduced χ2 of models fit to infrared data of 2.18 and 1.53 for poles 1 and 2, respectively, revealing a strong preference for one of the spin and shape solutions, but also problems with fitting all the thermal data. New simultaneous optimisation on the same visible and infrared datasets performed here led to a somewhat different model. Most notably, the reduced χ2 decreased substantially to 0.94 for pole 1, and 0.88 for pole 2, and so some preference for one spin solution remained, and thermal inertia shifted to smaller values: 1–50 SI units. To further check, we modelled the IR data using the new shape models with the classical TPM approach (Lagerros 1996, 1997, 1998) and found a consistent solution.

The fit to visible light curves remained similarly good with both approaches, and the spin axis coordinates, size, and albedo agreed with the original ones within the error bars. In summary, the CITPM method enabled us to find a much better combination of spin, shape, and thermal parameters than the two-step approach used originally.

The CITPM method provides models for several targets for which previous analyses with the classical TPM method failed; for example a unique and stable solution was found for (487) Seppina. For (666) Desdemona, we constrained the size and albedo to a narrow range, while thermal inertia still remains uncertain. Furthermore, for two targets (667, 995), additional calibrated data used in the CITPM improved the solution of inertia tensors, which were previously erroneous (i.e. excessively stretched along the spin axis). Also, we were able to find more precisely constrained dimensions along the spin axis for the shape models for all the other targets, which is an area of frequent weakness in shape models based exclusively on relative photometry.

Independent confirmation of the robustness of our models also comes from fitting the models to stellar occultation chords. The results of occultation fitting are presented in Table 3, and in Figs. C.1–C.3, which show the instantaneous silhouette of the shape model on the η, ξ sky plane scaled in kilometres. Table D.2 lists the occultation observers and sites.

Spin and shape solutions had already been determined and published in the literature for some of our targets, while in some cases only some of the parameters were available. In Table 4 we cite their spin axis coordinates and sidereal periods, if available, together with their reference. Comparison with our results in Table 2 shows a general agreement, with the exception of (108) Hecuba modelled by Blanco & Riccioli (1998), (362) Havnia modelled by Wang et al. (2015), and (537) Pauly modelled by Blanco et al. (2000) based on different shape approximations. Parameters strongly differing from the solutions obtained in this work are marked in italics in Table 4. Within consistent solutions, the differences in sidereal periods are sometimes of the order of a few 10−4 h, which may appear small, but might be noticeable after a few apparitions. In the sections below, we focus on a few specific targets in more detail.

Table 2

Spin parameters and thermophysical characteristics of asteroid models obtained in this work.

Table 3

Diameters of equivalent volume spheres for CITPM shape models fitted to stellar occultations.

Table 4

Previously published spin parameters for targets studied here.

5.1 (362) Havnia

There were problems with some photometric data for this target. Firstly, data obtained by Harris & Young (1980) were published in the APC archive as a composite light curve, with an incorrect period of 18 h. As a consequence, only one out of three light curves couldbe used, the one with original timings. This is a general problem with some early asteroid light curves in the archives, and special attention must be paid when using them. Other problems were caused by Super WASP data. Although in many cases these serendipitously gathered data provided good light curves from desired geometries, in this case their intrinsic noise made it impossible to find a unique spin and shape solution. After removing most of the Super WASP light curves for Havnia and keeping only the five best ones (Fig. E.18), the uniqueness of the solution greatly improved. This demonstrates that the light curve inversion method is quite sensitive to noise in the data.

A spin and shape model of Havnia previously published by Wang et al. (2015) was based on a light-curve inversion using the Monte Carlo method on data from four apparitions (see Table 4), while our model was based on (visible) light curves from seven apparitions. The model by Wang et al. (2015) agrees with the model obtained here only in spin axis latitude (see Table 2), whereas the longitudes are substantially different. Sidereal periods might appear similar at first sight, but they would lead to a large divergence of extrema timings over just two apparitions.

Our model is characterised by a rather wide range of thermal inertia values due to a poor infrared dataset (only data from Akari and WISE W4 were available; see N values in Table 1), but Fig. A.5 shows a clear minimum around Γ = 100 SI units. Unfortunately, all WISE W3 data had to be removed because of partial saturation. Even keeping only their best subset led to divergence.

There is a four-chord stellar occultation from the year 2017 available in the PDS archive. Both of our spin and shape solutions fit this event very well, with all chords crossing close to the centre of the body (see Fig. C.1), resulting in volume-equivalent sizes a few percent smaller than the sizes provided by the CITPM method (compare D values in Tables 3 and 2). The small ± 1 km error in the occultation diameter is only a formal uncertainty determined via bootstrapping separate chords and repeating the fitting procedure multiple times. However, the real uncertainty must be larger because of the uncertainty on the shape model itself.

5.2 (537) Pauly

Spin and shape solutions for (537) Pauly have already been published by Blanco et al. (2000) and Hanuš et al. (2016). The results from the latter work are consistent with ours (see Tables 2 and 4), although our model of Pauly is made using many more dense light curves and also a richer set of thermal data (+9 Akari points), and via simultaneous optimisation of both data types. Later, (537) Pauly was also analysed with the TPM via the data bootstrapping method (Hanuš et al. 2018). Our size determinations (46 ± 2 km, and 47 ± 4 km) are somewhat larger than 40.7 ± 0.8 km by Hanuš et al. (2018), but the thermal inertia and albedo values agree. Our χred2$\chi^2_{\text{red}}$ IR residuals are smaller than in the previous model (0.7 vs. 1.1). The difference in size might stem from the elongated shape of this target, and the smaller set of infrared measurements in Hanuš et al. (2018), capturing the target within a limited range of rotation phases, which might have led to underestimation of the size in previous study.

5.3 (618) Elfriede

There were as many as four different stellar occultations by this target, each containing from two to four chords (Fig. C.2). However, these data did not help us reject any of our two models and we take pole 2 (λp = 341°, βp = +49°) as the preferred solution based simply on its slightly lower χ2.

In this case, the occultation size agrees exactly for pole 1 with the radiometric size, while for pole 2 it is a few percent larger (see Tables 3 and 2), but still within the radiometric error bars. Our results, though self-consistent, are in disagreement with most previous size determinations for 618 Elfriede. The occultation-determined size for pole 2 (155 ± 2 km) is almost 30% larger than Akari (121.54 km) and IRAS (120.29 km) determinations (Usui et al. 2011; Tedesco et al. 2004), and 18% larger than the diameter given by WISE (131.165 km Mainzer et al. 2011b). For pole 1, the size disagreement is less pronounced (20 and 11% respectively) and is even compatible with the WISE diameter within the error bars.

In summary, as the present study is the first to take a comprehensive and multi-technique approach to analysing this target (rich photometric set simultaneously combined with infrared data from three missions, plus independent occultation fitting), the size determined here (14–155 km) can probably be considered the most reliable.

5.4 (667) Denise

For asteroid (667) Denise there were three good stellar occultations – with one containing as many as ten positive chords – thanks to a very successful European campaign (observers are acknowledged in Table D.2). Although both pole solutions are formally acceptable from the thermophysical point of view (both present in Table 2), the occultation fitting clearly enabled us to reject the solution for pole 2 (see Fig. C.3), which is marked with italics in Table 2. The size determined from occultations (83 ± 2 km) is the same as the radiometric size (83−2+4$83^{+4}_{-2}$ km). The CITPM method proved to be robust and accurate, and provided the most accurate parameters in the case of dense stellar occultation chords.

6 Conclusions and future work

We fully characterised spin, shape, and thermal properties of 16 main-belt asteroids from the group that until recently has been neglected because of observing selection effects. The multi-apparition targeted observing campaign together with good-quality infrared data, especially from the WISE spacecraft, led to consistent spin and shape models accompanied by precise size and albedo determinations, and thermal inertia being determined for most of the targets for the first time. Thanks to simultaneous use of both visible and infrared data, our shape models are optimal in terms of reproducing both types of data well. Also, the CITPM gained additional evidence for its robustness, providing an optimal solution in one of the cases, as confirmed by an independent method. The set contains two updated models (478 Tergeste, and 537 Pauly), and a few targets with partial solutions due to the scarcity of infrared data.

With this work we increase the number of slow rotators with thermal inertia determined from detailed thermophysical modelling by 40%. It is necessary to enlarge the pool of such well-studied targets so that we can gain more insight into different asteroid groups and families separately and explore links between thermal properties, surface material properties, and family formation ages (Harris & Drube 2020). Most targets presented here do not belong to any collisional family (with the exception of 923 Herluga and 995 Sternberga, both from the Eunomia family, and also 618 Elfriede and 780 Armenia, each having their own small, compact family), and so their low thermal inertia was expected.

Our target sizes span the range from a few tens of kilometres to over 100 km, with most of the determinations being within 10% of previous determinations based on WISE data only, and the NEATM thermal model (Harris 1998). Sizes determined for a few targets (223, 552, 618) differ by more, although our approach (including infrared data combined with spin and shape models) has been shown to be robust. We therefore consider our results to be most reliable. Furthermore, obtained albedo values agree with previously published taxonomic classifications.

The thermal inertia values determined here are <100 SI units for most targets, indicating the presence of a thick layer of insulating regolith on most of these bodies. These values of thermal inertia reduced to 1 AU display no trend with size, because our current targets are well within the size range where largely different thermal inertias have been found in previous works (see Fig. 7 in Hanuš et al. 2018). The correlation between thermal inertia and size found by Delbo’ et al. (2007) could only be evident if our sample also contained asteroids smaller than 10 km, these being too faint for our photometric campaign on small telescopes.

We also found no evidence to support the hypothesis that thermal inertia increases with rotation period (e.g. Harris & Drube 2016). Our results are in agreement with those of (Marciniak et al. 2019) and Hanuš et al. (2018). Biele et al. (2019) showed that a fine-grained, highly porous surface layer of just a few millimetres thick can hide thermal signatures of denser, more thermally conductive layers due to its relatively small thermal skin depth (ds) of a few millimetres, while to see signatures of the denser layers would require probing a centimetre range. However, despite their longer rotation periods (11–59 h) compared to the typical light-curve inversion and TPM targets found in theliterature, the thermal skin depths of our targets calculated according to the formula given by Spencer et al. (1989) still lie in the range of a few millimetres. The cases with large thermal inertia error bars could still be compatible with ds up to 3.5 cm, however all the values below it are equally possible, and so this cannot be used for drawing firm conclusions.

Furthermore, we did not find any correlation between thermal inertia and spin axis inclination, or any specific problems with fitting more inclined targets, which must experience seasonal cycles of heating and cooling. However, our thermal inertia determinations, as is often the case, are burdened with large uncertainties. It is possible that the trend linking thermal inertia and rotation period simply eludes us in our investigations, as precise thermal inertia determinations might be hampered by slow rotation, decreasing the thermal lag. For future studies, it will be beneficial to focus on targets with thermal measurements from WISE spacecraft obtained at epochs separated in time by as much as possible (longer than ~100 days). This should help to constrain thermal inertia better thanks to more varied viewing geometries, enabling comparison of thermal flux from for example pre- and post-opposition geometries.

Our scaled spin and shape models and their thermal parameters are available in the new versionof DAMIT (Database for Asteroid Models from Inversion Techniques; Ďurech et al. 2010)7, and data tables with photometry in the visible are available via the CDS.

Acknowledgements

This work was was initiated with the support from the National Science Centre, Poland, through grant no. 2014/13/D/ST9/01818; and from the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement no 687378 (SBNAF). The work of J.D. was supported by the grant 20-08218S of the Czech Science Foundation. A.P. and R.S. have been supported by the K-125015 grant of the National Research, Development and Innovation Office (NKFIH), Hungary. This project has been supported by the Lendület grant LP2012-31 of the Hungarian Academy of Sciences. This project has been supported by the GINOP-2.3.2-15-2016-00003 grant of the Hungarian National Research, Development and Innovation Office (NKFIH). L.M. was supported by the Premium Postdoctoral Research Program of the Hungarian Academy of Sciences. The research leading to these results has received funding from the LP2018-7/2020 Lendület grant of the Hungarian Academy of Sciences. The work of T.S.-R. was carried out through grant APOSTD/2019/046 by Generalitat Valenciana (Spain). This work was supported by the MINECO (Spanish Ministry of Economy) through grant RTI2018-095076-B-C21 (MINECO/FEDER, UE). E. P. acknowledges the Europlanet 2024 RI project funded by the European Union’s Horizon 2020 Research and Innovation Programme (Grant agreement No. 871149). This article is based on observations obtained at the Observatório Astronômico do Sertão de Itaparica (OASI, Itacuruba) of the Observatório Nacional, Brazil. F.M. would like to thank the financial support given by FAPERJ (Process E-26/201.877/2020). E.R., P.A., H.M., M.E. and J.M. would like to thank CNPq and CAPES (Brazilian agencies) for their support through diverse fellowships. Support by CNPq (Process 305409/2016-6) and FAPERJ (Process E-26/202.841/2017) is acknowledged by D.L. The Joan Oró Telescope (TJO) of the Montsec Astronomical Observatory (OAdM) is owned by the Catalan Government and operated by the Institute for Space Studies of Catalonia (IEEC). This article is based on observations made in the Observatorios de Canarias del IAC with the 0.82 m IAC80 telescope operated on the island of Tenerife by the Instituto de Astrofísica de Canarias (IAC) in the Observatorio del Teide. This article is based on observations made with the SARA telescopes (Southeastern Association for Research in Astronomy), whose nodes are located at the Observatorios de Canarias del IAC on the island of La Palma in the Observatorio del Roque de los Muchachos; Kitt Peak, AZ under the auspices of the National Optical Astronomy Observatory (NOAO); and Cerro Tololo Inter-American Observatory (CTIO) in La Serena, Chile. This project uses data from the SuperWASP archive. The WASP project is currently funded and operated by Warwick University and Keele University, and was originally set up by Queen’s University Belfast, the Universities of Keele, St. Andrews, and Leicester, the Open University, the Isaac Newton Group, the Instituto de Astrofisica de Canarias, the South African Astronomical Observatory, and by STFC. TRAPPIST-South is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant PDR T.0120.21. TRAPPIST-North is a project funded by the University of Liège, in collaboration with the Cadi Ayyad University of Marrakech (Morocco). E. Jehin is FNRS Senior Research Associate. Funding for the Kepler and K2 missions are provided by the NASA Science Mission Directorate. The data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. Data from Pic du Midi Observatory have been obtained with the 0.6-m telescope, a facility operated by Observatoíre Midi Pyrénées and Association T60, an amateur association. We acknowledge the contributions of the occultation observers who have provided the observations in the dataset. Most of those observers are affiliated with one or more of: European Asteroidal Occultation Network (EAON), International Occultation Timing Association (IOTA), International Occultation Timing Association European Section (IOTA/ES), Japanese Occultation Information Network (JOIN), and Trans Tasman Occultation Alliance (TTOA).

Appendix A Chi-squared plots vs. thermal inertia

This section contains plots of χred2$\chi^2_{\text{red}}$ versus thermal inertia for various combinations of surface roughness and optimised size (Figures A.1 - A.16).

thumbnail Fig. A.1

Reduced χ2 values vs. thermal inertia for various combinations of surface roughness (symbol coded) and optimised diameters (colour coded) for asteroid (108) Hecuba.
thumbnail Fig. A.2

Reduced χ2 values vs. thermal inertia for (202) Chryseis
thumbnail Fig. A.3

Reduced χ2 values vs. thermal inertia for (219) Thusnelda
thumbnail Fig. A.4

Reduced χ2 values vs. thermal inertia for (223) Rosa
thumbnail Fig. A.5

Reduced χ2 values vs. thermal inertia for (362) Havnia
thumbnail Fig. A.6

Reduced χ2 values vs. thermal inertia for (478) Tergeste
thumbnail Fig. A.7

Reduced χ2 values vs. thermal inertia for (483) Seppina
thumbnail Fig. A.8

Reduced χ2 values vs. thermal inertia for (501) Urhixidur
thumbnail Fig. A.9

Reduced χ2 values vs. thermal inertia for (537) Pauly
thumbnail Fig. A.10

Reduced χ2 values vs. thermal inertia for (552) Sigelinde
thumbnail Fig. A.11

Reduced χ2 values vs. thermal inertia for (618) Elfriede
thumbnail Fig. A.12

Reduced χ2 values vs. thermal inertia for (666) Desdemona
thumbnail Fig. A.13

Reduced χ2 values vs. thermal inertia for (667) Denise
thumbnail Fig. A.14

Reduced χ2 values vs. thermal inertia for (780) Armenia
thumbnail Fig. A.15

Reduced χ2 values vs. thermal inertia for (923) Herluga
thumbnail Fig. A.16

Reduced χ2 values vs. thermal inertia for (995) Sternberga

Appendix B Thermal light curves

Model fits to WISE thermal light curves (Figures B.1 - B.25).

thumbnail Fig. B.1

Infrared model fluxes (red circles) compared to measured fluxes in W3 band of WISE spacecraft (black circles) for asteroid (108) Hecuba.
thumbnail Fig. B.2

(108) Hecuba, thermal light curve in W4 band.
thumbnail Fig. B.3

(202) Chryseis
thumbnail Fig. B.4

(219) Thusnelda
thumbnail Fig. B.5

(223) Rosa
thumbnail Fig. B.6

(362) Havnia
thumbnail Fig. B.7

(478) Tergeste
thumbnail Fig. B.8

(478) Tergeste
thumbnail Fig. B.9

(483) Seppina
thumbnail Fig. B.10

(483) Seppina
thumbnail Fig. B.11

(501) Urhixidur
thumbnail Fig. B.12

(501) Urhixidur
thumbnail Fig. B.13

(537) Pauly
thumbnail Fig. B.14

(537) Pauly
thumbnail Fig. B.15

(552) Sigelinde
thumbnail Fig. B.16

(618) Elfriede
thumbnail Fig. B.17

(666) Desdemona
thumbnail Fig. B.18

(666) Desdemona
thumbnail Fig. B.19

(667) Denise
thumbnail Fig. B.20

(667) Denise
thumbnail Fig. B.21

(780) Armenia
thumbnail Fig. B.22

(923) Herluga
thumbnail Fig. B.23

(923) Herluga
thumbnail Fig. B.24

(995) Sternberga
thumbnail Fig. B.25

(995) Sternberga

Appendix C Occultation fits

Instantaneous silhouettes of shape models from this work fitted to occultation timing chords.

thumbnail Fig. C.1

CITPM shape models of asteroid (362) Havnia fitted to a stellar occultation from 7. January 2017. In all the figures, north is up and west is right. The blue solid contour and the magenta dashed contour represent the model for pole 1 and pole 2, respectively. Black lines in those figures mark occultation shadow chords calculated from occultation timings, with timing uncertainties shown at the extremities of each chord. The scale in seconds is given for reference as a red line. Negative (no occultation) chords are marked with dotted lines, while visual observations (as opposed to video or photoelectric) are marked with dashed lines. See Table 3 for diameters of equivalent volume spheres.
thumbnail Fig. C.2

CITPM shape models of (618) Elfriede fitted to stellar occultations from 26 May 2008, 13 April 2013, 30 December 2015, and 10 May 2018. The visual, southernmost chord in the first event probably has an underestimated duration. See Table 3 for diameters of equivalent volume spheres. See caption of Fig. C.1 for description of the figure.
thumbnail Fig. C.3

CITPM shape models of (667) Denise fitted to stellar occultations from 8 April 2008, 11 April 2020, and 10 May 2020. The pole 1 solution (blue contour) is clearly preferred over pole 2 (dashed magenta contour). See Table 3 for equivalent volume sphere diameter for the preferred pole solution. See caption of Fig. C.1 for description of the figure.

Appendix D Observational details

Details of all light curve observations used for the modelling (Table D.1), and the list of stellar occultation observers and sites (Table D.2).

Table D.1

Details of all visible photometric observations: observing dates, number of light curves, ecliptic longitude of the target, sun-target-observer phase angle, observer’s name (or paper citation in case of published data), and the observing site. Some data come from robotic telescopes, and so they have no observer specified. For data from the TESS spacecraft, the number of light curves denotes the number of days of continuous observations. CSSS stands for Center for Solar System Studies, PTF - Palomar Transient Factory, GMARS - Goat Mountain Astronomical Research Station, ESO - European Southern Observatory, SOAO - Sobaeksan Optical Astronomy Observatory, BOAO - Bohyunsan Optical Astronomy Observatory, LOAO - Lemonsan Optical Astronomy Observatory, OASI - Observatório Astronômico do Sertão de Itaparica, CTIO - Cerro Tololo Interamerican Observatory, ORM - Roque de los Muchachos Observatory.

Table D.2

List of stellar occultation observers and locations of the observing sites.

Appendix E Visible light curves

Composite light curves in the visible, with the new data of target asteroids (Figures E.1 - E.66).

thumbnail Fig. E.1

Composite light curve of (108) Hecuba from the year 2015.
thumbnail Fig. E.2

Composite light curve of (108) Hecuba from the years 2016-2017.
thumbnail Fig. E.3

Composite light curve of (108) Hecuba from the years 2017-2018.
thumbnail Fig. E.4

Composite light curve of (108) Hecuba from the year 2019.
thumbnail Fig. E.5

Composite light curve of (202) Chryseis from the year 2014.
thumbnail Fig. E.6

Composite light curve of (202) Chryseis from the years 2015-2016.
thumbnail Fig. E.7

Composite light curve of (202) Chryseis from the year 2017.
thumbnail Fig. E.8

Composite light curve of (202) Chryseis from the year 2019.
thumbnail Fig. E.9

Composite light curve of (219) Thusnelda from the year 2013.
thumbnail Fig. E.10

Composite light curve of (219) Thusnelda from the year 2016.
thumbnail Fig. E.11

Composite light curve of (219) Thusnelda from the year 2017.
thumbnail Fig. E.12

Composite light curve of (219) Thusnelda from the years 2018-2019.
thumbnail Fig. E.13

Composite light curve of (223) Rosa from the year 2015.
thumbnail Fig. E.14

Composite light curve of (223) Rosa from the year 2016.
thumbnail Fig. E.15

Composite light curve of (223) Rosa from the year 2018.
thumbnail Fig. E.16

Composite light curve of (223) Rosa from the year 2019.
thumbnail Fig. E.17

Composite light curve of (223) Rosa from the year 2020.
thumbnail Fig. E.18

Composite light curve of (362) Havnia from the year 2006.
thumbnail Fig. E.19

Composite light curve of (362) Havnia from the year 2015.
thumbnail Fig. E.20

Composite light curve of (362) Havnia from the years 2016-2017.
thumbnail Fig. E.21

Composite light curve of (362) Havnia from the years 2019-2020.
thumbnail Fig. E.22

Composite light curve of (483) Seppina from the year 2005.
thumbnail Fig. E.23

Composite light curve of (483) Seppina from the year 2013.
thumbnail Fig. E.24

Composite light curve of (483) Seppina from the year 2015.
thumbnail Fig. E.25

Composite light curve of (483) Seppina from the year 2016.
thumbnail Fig. E.26

Composite light curve of (483) Seppina from the year 2017.
thumbnail Fig. E.27

Composite light curve of (483) Seppina from the year 2018.
thumbnail Fig. E.28

Composite light curve of (501) Urhixidur from the year 2013.
thumbnail Fig. E.29

Composite light curve of (501) Urhixidur from the years 2014-2015.
thumbnail Fig. E.30

Composite light curve of (501) Urhixidur from the year 2016.
thumbnail Fig. E.31

Composite light curve of (501) Urhixidur from the year 2017.
thumbnail Fig. E.32

Composite light curve of (501) Urhixidur from the year 2018.
thumbnail Fig. E.33

Composite light curve of (501) Urhixidur from the year 2019.
thumbnail Fig. E.34

Composite light curve of (537) Pauly from the year 2016.
thumbnail Fig. E.35

Composite light curve of (537) Pauly from the years 2017.
thumbnail Fig. E.36

Composite light curve of (537) Pauly from the year 2018.
thumbnail Fig. E.37

Composite light curve of (537) Pauly from the years 2019-2020.
thumbnail Fig. E.38

Composite light curve of (552) Sigelinde from the year 2015.
thumbnail Fig. E.39

Composite light curve of (552) Sigelinde from the years 2016-2017.
thumbnail Fig. E.40

Composite light curve of (552) Sigelinde from the year 2018.
thumbnail Fig. E.41

Composite light curve of (552) Sigelinde from the year 2019.
thumbnail Fig. E.42

Composite light curve of (618) Elfriede from the year 2014.
thumbnail Fig. E.43

Composite light curve of (618) Elfriede from the years 2015-2016.
thumbnail Fig. E.44

Composite light curve of (618) Elfriede from the year 2017.
thumbnail Fig. E.45

Composite light curve of (618) Elfriede from the year 2018.
thumbnail Fig. E.46

Composite light curve of (618) Elfriede from the year 2019.
thumbnail Fig. E.47

Composite light curve of (666) Desdemona from the year 2015.
thumbnail Fig. E.48

Composite light curve of (666) Desdemona from the year 2016.
thumbnail Fig. E.49

Composite light curve of (666) Desdemona from the years 2017-2018.
thumbnail Fig. E.50

Composite light curve of (666) Desdemona from the year 2019.
thumbnail Fig. E.51

Composite light curve of (667) Denise from the year 2014.
thumbnail Fig. E.52

Composite light curve of (667) Denise from the year 2015.
thumbnail Fig. E.53

Composite light curve of (667) Denise from the year 2016.
thumbnail Fig. E.54

Composite light curve of (667) Denise from the year 2017.
thumbnail Fig. E.55

Composite light curve of (667) Denise from the years 2018-2019.
thumbnail Fig. E.56

Composite light curve of (780) Armenia from the year 2014.
thumbnail Fig. E.57

Composite light curve of (780) Armenia from the year 2015.
thumbnail Fig. E.58

Composite light curve of (780) Armenia from the year 2016.
thumbnail Fig. E.59

Composite light curve of (780) Armenia from the years 2017-2018.
thumbnail Fig. E.60

Composite light curve of (780) Armenia from the years 2018-2019.
thumbnail Fig. E.61

Composite light curve of (923) Herluga from the year 2014.
thumbnail Fig. E.62

Composite light curve of (923) Herluga from the year 2015.
thumbnail Fig. E.63

Composite light curve of (923) Herluga from the year 2019.
thumbnail Fig. E.64

Composite light curve of (995) Sternberga from the years 2013-2014.
thumbnail Fig. E.65

Composite light curve of (995) Sternberga from the year 2015.
thumbnail Fig. E.66

Composite light curve of (995) Sternberga from the years 2017-2018.

References

  1. Alí-Lagoa, V., Müller, T. G., Kiss, C., et al. 2020, A&A, 638, A84 [EDP Sciences] [Google Scholar]
  2. Barucci, M. A., di Martino, M., & Fulchignoni, M. 1992, AJ, 103, 1679 [NASA ADS] [CrossRef] [Google Scholar]
  3. Benishek, V., & Pilcher, F. 2009, Minor Planet Bull., 36, 167 [NASA ADS] [Google Scholar]
  4. Biele, J., Kührt, E., Senshu, H., et al. 2019, Prog. Earth Planet. Sci., 6, 48 [CrossRef] [Google Scholar]
  5. Blanco, C., & Riccioli, D. 1998, A&AS, 131, 385 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  6. Blanco, C., Cigna, M., & Riccioli, D. 2000, Planet. Space Sci., 48, 973 [CrossRef] [Google Scholar]
  7. Brinsfield, J. W. 2009, Minor Planet Bull., 36, 64 [NASA ADS] [Google Scholar]
  8. Bus, S. J., & Binzel, R. P. 2002a, Icarus, 158, 146 [NASA ADS] [CrossRef] [Google Scholar]
  9. Bus, S. J., & Binzel, R. P. 2002b, Icarus, 158, 106 [CrossRef] [Google Scholar]
  10. Čapek, D., & Vokrouhlický, D. 2010, A&A, 519, A75 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  11. Delbo’, M., & Tanga, P. 2009, Planet. Space Sci., 57, 259 [CrossRef] [Google Scholar]
  12. Delbo’, M., dell’Oro, A., Harris, A. W., Mottola, S., & Mueller, M. 2007, Icarus, 190, 236 [CrossRef] [Google Scholar]
  13. Delbo’, M., Libourel, G., Wilkerson, J., et al. 2014, Nature, 508, 233 [CrossRef] [Google Scholar]
  14. Delbo’, M., Mueller, M., Emery, J. P., Rozitis, B., & Capria, M. T. 2015, Asteroid V, Asteroid Thermophysical Modeling (Tucson: University of Arizona Press), 107 [Google Scholar]
  15. Ďurech, J., Sidorin, V., & Kaasalainen, M. 2010, A&A, 513, A46 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  16. Ďurech, J., Kaasalainen, M., Herald, D., et al. 2011, Icarus, 214, 652 [NASA ADS] [CrossRef] [Google Scholar]
  17. Ďurech, J., Delbo’, M., Carry, B., Hanuš, J., & Alí-Lagoa, V. 2017, A&A, 604, A27 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  18. Ďurech, J., Tonry, J., Erasmus, N., et al. 2020, A&A, 643, A59 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  19. Egan, M. P., Price, S. D., & Kraemer, K. E. 2003, AAS Meeting Abs., 203, Abstracts, 57.08 [NASA ADS] [Google Scholar]
  20. Grice, J., Snodgrass C., Green S., Parley N., & Carry, B. 2017, in Asteroids, Comets, meteors (USA: HarperCollins) [Google Scholar]
  21. Gundlach, B., & Blum, J. 2013, Icarus, 223, 479 [NASA ADS] [CrossRef] [Google Scholar]
  22. Hanuš, J., Ďurech, J., Brož, M., et al. 2011, A&A, 530, A134 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Hanuš, J., Ďurech, J., Brož, M., et al. 2013, A&A, 551, A67 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  24. Hanuš, J., Delbo’, M., Ďurech, J., & Alí-Lagoa, V. 2015, Icarus, 256, 101 [CrossRef] [Google Scholar]
  25. Hanuš, J., Ďurech, J., Oszkiewicz, D. A., et al. 2016, A&A, 586, A108 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  26. Hanuš, J., Delbo’, M., Ďurech, J., & Alí-Lagoa, V. 2018, Icarus, 309, 297 [CrossRef] [Google Scholar]
  27. Hapke, B. 1981, J. Geophys. Res., 86, 3039 [NASA ADS] [CrossRef] [Google Scholar]
  28. Hapke, B. 1984, Icarus, 59, 41 [Google Scholar]
  29. Hapke, B. 1986, Icarus, 67, 264 [Google Scholar]
  30. Harris, A. W. 1998, Icarus, 131, 291 [Google Scholar]
  31. Harris, A. W., & Drube, L. 2016, ApJ, 832, 127 [NASA ADS] [CrossRef] [Google Scholar]
  32. Harris, A. W., & Drube, L. 2020, ApJ, 901, 140 [NASA ADS] [CrossRef] [Google Scholar]
  33. Harris, A. W., & Young, J. W. 1980, Icarus, 43, 20 [NASA ADS] [CrossRef] [Google Scholar]
  34. Harris, A. W., Young, J. W., Dockweiler, T., et al. 1992, Icarus, 95, 115 [NASA ADS] [CrossRef] [Google Scholar]
  35. Hayne, P. O., Bandfield, J. L., Siegler, M. A., et al. 2017, J. Geophys. Res. Planets, 122, 2371 [Google Scholar]
  36. Herald, D., Frappa, E., Gault, D., et al. 2019, Asteroid Occultations V3.0, NASA Planetary Data System [Google Scholar]
  37. Herald, D., Gault, D., Anderson, R., et al. 2020, MNRAS, 499, 4570 [Google Scholar]
  38. Howell, S. B., Sobeck, C., Haas, M., et al. 2014, PASP, 126, 398 [NASA ADS] [CrossRef] [Google Scholar]
  39. Jehin, E., Gillon, M., Queloz, D., et al. 2011, The Messenger, 145, 2 [NASA ADS] [Google Scholar]
  40. Kaasalainen, M., & Lamberg, L. 2006, Inverse Prob., 22, 749 [NASA ADS] [CrossRef] [Google Scholar]
  41. Kaasalainen, M., & Ďurech J. 2020, ArXiv e-prints [arXiv:2005.09947] [Google Scholar]
  42. Kaasalainen, M., Torppa, J., & Muinonen, K. 2001, Icarus, 153, 37 [NASA ADS] [CrossRef] [Google Scholar]
  43. Keihm, S., Tosi, F., Kamp, L., et al. 2012, Icarus, 221, 395 [CrossRef] [Google Scholar]
  44. Klinglesmith, Daniel A., I., Hendrickx, S., Kimber, C., & Madden, K. 2017, Minor Planet Bull., 44, 244 [Google Scholar]
  45. Lagerkvist, C. I., & Kamel, L. 1982, Moon Planets, 27, 463 [NASA ADS] [CrossRef] [Google Scholar]
  46. Lagerkvist, C. I., Magnusson, P., Debehogne, H., et al. 1992, A&AS, 95, 461 [NASA ADS] [Google Scholar]
  47. Lagerros, J. S. V. 1996, A&A, 310, 1011 [Google Scholar]
  48. Lagerros, J. S. V. 1997, A&A, 325, 1226 [NASA ADS] [Google Scholar]
  49. Lagerros, J. S. V. 1998, A&A, 332, 1123 [Google Scholar]
  50. Lim, L. F., McConnochie, T. H., Bell, J. F., & Hayward, T. L. 2005, Icarus, 173, 385 [NASA ADS] [CrossRef] [Google Scholar]
  51. Mainzer, A., Bauer, J., Grav, T., et al. 2011a, ApJ, 731, 53 [NASA ADS] [CrossRef] [Google Scholar]
  52. Mainzer, A., Grav, T., Masiero, J., et al. 2011b, ApJ, 741, 90 [NASA ADS] [CrossRef] [Google Scholar]
  53. Marchi, S., Paolicchi, P., & Richardson, D. C. 2012, MNRAS, 421, 2 [NASA ADS] [Google Scholar]
  54. Marciniak, A., Pilcher, F., Oszkiewicz, D., et al. 2015, Planet. Space Sci., 118, 256 [NASA ADS] [CrossRef] [Google Scholar]
  55. Marciniak, A., Bartczak, P., Müller, T., et al. 2018, A&A, 610, A7 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  56. Marciniak, A., Alí-Lagoa, V., Müller, T. G., et al. 2019, A&A, 625, A139 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  57. Masiero, J. R., Mainzer, A. K., Grav, T., et al. 2011, ApJ, 741, 68 [NASA ADS] [CrossRef] [Google Scholar]
  58. Morbidelli, A., Bottke, W. F., Nesvorný, D., & Levison, H. F. 2009, Icarus, 204, 558 [Google Scholar]
  59. Müller, T. G., Ďurech, J., Ishiguro, M., et al. 2017, A&A, 599, A103 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Müller, T. G., Marciniak, A., Kiss, C., et al. 2018, Adv. Space Res., 62, 2326 [Google Scholar]
  61. Murdoch, N., Sánchez, P., Schwartz, S. R., & Miyamoto, H. 2015, Asteroids IV, Asteroid Surface Geophysics (Tucson: University of Arizona Press), 767 [Google Scholar]
  62. Neugebauer, G., Habing, H. J., van Duinen, R., et al. 1984, ApJ, 278, L1 [NASA ADS] [CrossRef] [Google Scholar]
  63. Oey, J. 2009, Minor Planet Bull., 36, 4 [NASA ADS] [Google Scholar]
  64. Okada, T., Fukuhara, T., Tanaka, S., et al. 2020, Nature, 579, 518 [NASA ADS] [CrossRef] [Google Scholar]
  65. Pál, A., Szakáts, R., Kiss, C., et al. 2020, ApJS, 247, 26 [CrossRef] [Google Scholar]
  66. Pilcher, F. 2012, Minor Planet Bull., 39, 171 [NASA ADS] [Google Scholar]
  67. Pilcher, F. 2013, Minor Planet Bull., 40, 158 [NASA ADS] [Google Scholar]
  68. Pilcher, F. 2014, Minor Planet Bull., 41, 250 [NASA ADS] [Google Scholar]
  69. Ravaji, B., Alí-Lagoa, V., Delbo’, M., & Wilkerson, J. W. 2019, J. Geophys. Res. Planets, 124, 3304 [CrossRef] [Google Scholar]
  70. Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, J. Astron. Teles. Instrum. Syst., 1, 014003 [Google Scholar]
  71. Rozitis, B., Maclennan, E., & Emery, J. P. 2014, Nature, 512, 174 [CrossRef] [Google Scholar]
  72. Rozitis, B., Green, S. F., MacLennan, E., & Emery, J. P. 2018, MNRAS, 477, 1782 [CrossRef] [Google Scholar]
  73. Spencer, J. R., Lebofsky, L. A., & Sykes, M. V. 1989, Icarus, 78, 337 [Google Scholar]
  74. Stephens, R. D. 2009, Minor Planet Bull., 36, 157 [NASA ADS] [Google Scholar]
  75. Stephens, R. D. 2013, Minor Planet Bull., 40, 34 [NASA ADS] [EDP Sciences] [Google Scholar]
  76. Stephens, R. D., Pilcher, F., Hamanowa, H., Hamanowa, H., & Ferrero, A. 2011, Minor Planet Bull., 38, 208 [NASA ADS] [Google Scholar]
  77. Szakáts, R., Müller, T., Alí-Lagoa, V., et al. 2020, A&A, 635, A54 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  78. Tedesco, E. F., Noah, P. V., Noah, M., & Price, S. D. 2004, NASA Planetary Data System, IRAS [Google Scholar]
  79. Tholen, D. J. 1989, in Asteroids II, eds. R. P. Binzel, T. Gehrels, & M. S. Matthews (Tucson: University of Arizona Press), 1139 [Google Scholar]
  80. Usui, F., Kuroda, D., Müller, T. G., et al. 2011, PASJ, 63, 1117 [Google Scholar]
  81. Vokrouhlický, D., Bottke, W. F., Chesley, S. R., Scheeres, D. J., & Statler, T. S. 2015, Asteroids IV, eds. P. Michel, F. E. DeMeo, & W. F. Bottke (Tucson: University of Arizona Press), 509 [Google Scholar]
  82. Walsh, K. J., Jawin, E. R., Ballouz, R. L., et al. 2019, Nat. Geosci., 12, 242 [NASA ADS] [CrossRef] [Google Scholar]
  83. Wang, X., Muinonen, K., & Wang, Y. 2015, Planet. Space Sci., 118, 242 [NASA ADS] [CrossRef] [Google Scholar]
  84. Warner, B. D. 2006, Minor Planet Bull., 33, 85 [NASA ADS] [Google Scholar]
  85. Warner, B. D. 2007a, Minor Planet Bull., 34, 72 [NASA ADS] [Google Scholar]
  86. Warner, B. D. 2007b, Minor Planet Bull., 34, 104 [NASA ADS] [Google Scholar]
  87. Warner, B. D., & Harris, A. W. 2011, Icarus, 216, 610 [CrossRef] [Google Scholar]
  88. Waszczak, A., Chang, C.-K., Ofek, E. O., et al. 2015, AJ, 150, 75 [NASA ADS] [CrossRef] [Google Scholar]
  89. Weidenschilling, S. J., Chapman, C. R., Davis, D. R., et al. 1990, Icarus, 86, 402 [NASA ADS] [CrossRef] [Google Scholar]
  90. Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868 [Google Scholar]
  91. Zappalà, V., Di Martino, M., Cellino, A., et al. 1989, Icarus, 82, 354 [CrossRef] [Google Scholar]

All Tables

Table 1

Ancillary information on the data and physical properties of our targets.

In the text
Table 2

Spin parameters and thermophysical characteristics of asteroid models obtained in this work.

In the text
Table 3

Diameters of equivalent volume spheres for CITPM shape models fitted to stellar occultations.

In the text
Table 4

Previously published spin parameters for targets studied here.

In the text
Table D.1

Details of all visible photometric observations: observing dates, number of light curves, ecliptic longitude of the target, sun-target-observer phase angle, observer’s name (or paper citation in case of published data), and the observing site. Some data come from robotic telescopes, and so they have no observer specified. For data from the TESS spacecraft, the number of light curves denotes the number of days of continuous observations. CSSS stands for Center for Solar System Studies, PTF - Palomar Transient Factory, GMARS - Goat Mountain Astronomical Research Station, ESO - European Southern Observatory, SOAO - Sobaeksan Optical Astronomy Observatory, BOAO - Bohyunsan Optical Astronomy Observatory, LOAO - Lemonsan Optical Astronomy Observatory, OASI - Observatório Astronômico do Sertão de Itaparica, CTIO - Cerro Tololo Interamerican Observatory, ORM - Roque de los Muchachos Observatory.

In the text
Table D.2

List of stellar occultation observers and locations of the observing sites.

In the text

All Figures

thumbnail Fig. A.1

Reduced χ2 values vs. thermal inertia for various combinations of surface roughness (symbol coded) and optimised diameters (colour coded) for asteroid (108) Hecuba.
In the text
thumbnail Fig. A.2

Reduced χ2 values vs. thermal inertia for (202) Chryseis
In the text
thumbnail Fig. A.3

Reduced χ2 values vs. thermal inertia for (219) Thusnelda
In the text
thumbnail Fig. A.4

Reduced χ2 values vs. thermal inertia for (223) Rosa
In the text
thumbnail Fig. A.5

Reduced χ2 values vs. thermal inertia for (362) Havnia
In the text
thumbnail Fig. A.6

Reduced χ2 values vs. thermal inertia for (478) Tergeste
In the text
thumbnail Fig. A.7

Reduced χ2 values vs. thermal inertia for (483) Seppina
In the text
thumbnail Fig. A.8

Reduced χ2 values vs. thermal inertia for (501) Urhixidur
In the text
thumbnail Fig. A.9

Reduced χ2 values vs. thermal inertia for (537) Pauly
In the text
thumbnail Fig. A.10

Reduced χ2 values vs. thermal inertia for (552) Sigelinde
In the text
thumbnail Fig. A.11

Reduced χ2 values vs. thermal inertia for (618) Elfriede
In the text
thumbnail Fig. A.12

Reduced χ2 values vs. thermal inertia for (666) Desdemona
In the text
thumbnail Fig. A.13

Reduced χ2 values vs. thermal inertia for (667) Denise
In the text
thumbnail Fig. A.14

Reduced χ2 values vs. thermal inertia for (780) Armenia
In the text
thumbnail Fig. A.15

Reduced χ2 values vs. thermal inertia for (923) Herluga
In the text
thumbnail Fig. A.16

Reduced χ2 values vs. thermal inertia for (995) Sternberga
In the text
thumbnail Fig. B.1

Infrared model fluxes (red circles) compared to measured fluxes in W3 band of WISE spacecraft (black circles) for asteroid (108) Hecuba.
In the text
thumbnail Fig. B.2

(108) Hecuba, thermal light curve in W4 band.
In the text
thumbnail Fig. B.3

(202) Chryseis
In the text
thumbnail Fig. B.4

(219) Thusnelda
In the text
thumbnail Fig. B.5

(223) Rosa
In the text
thumbnail Fig. B.6

(362) Havnia
In the text
thumbnail Fig. B.7

(478) Tergeste
In the text
thumbnail Fig. B.8

(478) Tergeste
In the text
thumbnail Fig. B.9

(483) Seppina
In the text
thumbnail Fig. B.10

(483) Seppina
In the text
thumbnail Fig. B.11

(501) Urhixidur
In the text
thumbnail Fig. B.12

(501) Urhixidur
In the text
thumbnail Fig. B.13

(537) Pauly
In the text
thumbnail Fig. B.14

(537) Pauly
In the text
thumbnail Fig. B.15

(552) Sigelinde
In the text
thumbnail Fig. B.16

(618) Elfriede
In the text
thumbnail Fig. B.17

(666) Desdemona
In the text
thumbnail Fig. B.18

(666) Desdemona
In the text
thumbnail Fig. B.19

(667) Denise
In the text
thumbnail Fig. B.20

(667) Denise
In the text
thumbnail Fig. B.21

(780) Armenia
In the text
thumbnail Fig. B.22

(923) Herluga
In the text
thumbnail Fig. B.23

(923) Herluga
In the text
thumbnail Fig. B.24

(995) Sternberga
In the text
thumbnail Fig. B.25

(995) Sternberga
In the text
thumbnail Fig. C.1

CITPM shape models of asteroid (362) Havnia fitted to a stellar occultation from 7. January 2017. In all the figures, north is up and west is right. The blue solid contour and the magenta dashed contour represent the model for pole 1 and pole 2, respectively. Black lines in those figures mark occultation shadow chords calculated from occultation timings, with timing uncertainties shown at the extremities of each chord. The scale in seconds is given for reference as a red line. Negative (no occultation) chords are marked with dotted lines, while visual observations (as opposed to video or photoelectric) are marked with dashed lines. See Table 3 for diameters of equivalent volume spheres.
In the text
thumbnail Fig. C.2

CITPM shape models of (618) Elfriede fitted to stellar occultations from 26 May 2008, 13 April 2013, 30 December 2015, and 10 May 2018. The visual, southernmost chord in the first event probably has an underestimated duration. See Table 3 for diameters of equivalent volume spheres. See caption of Fig. C.1 for description of the figure.
In the text
thumbnail Fig. C.3

CITPM shape models of (667) Denise fitted to stellar occultations from 8 April 2008, 11 April 2020, and 10 May 2020. The pole 1 solution (blue contour) is clearly preferred over pole 2 (dashed magenta contour). See Table 3 for equivalent volume sphere diameter for the preferred pole solution. See caption of Fig. C.1 for description of the figure.
In the text
thumbnail Fig. E.1

Composite light curve of (108) Hecuba from the year 2015.
In the text
thumbnail Fig. E.2

Composite light curve of (108) Hecuba from the years 2016-2017.
In the text
thumbnail Fig. E.3

Composite light curve of (108) Hecuba from the years 2017-2018.
In the text
thumbnail Fig. E.4

Composite light curve of (108) Hecuba from the year 2019.
In the text
thumbnail Fig. E.5

Composite light curve of (202) Chryseis from the year 2014.
In the text
thumbnail Fig. E.6

Composite light curve of (202) Chryseis from the years 2015-2016.
In the text
thumbnail Fig. E.7

Composite light curve of (202) Chryseis from the year 2017.
In the text
thumbnail Fig. E.8

Composite light curve of (202) Chryseis from the year 2019.
In the text
thumbnail Fig. E.9

Composite light curve of (219) Thusnelda from the year 2013.
In the text
thumbnail Fig. E.10

Composite light curve of (219) Thusnelda from the year 2016.
In the text
thumbnail Fig. E.11

Composite light curve of (219) Thusnelda from the year 2017.
In the text
thumbnail Fig. E.12

Composite light curve of (219) Thusnelda from the years 2018-2019.
In the text
thumbnail Fig. E.13

Composite light curve of (223) Rosa from the year 2015.
In the text
thumbnail Fig. E.14

Composite light curve of (223) Rosa from the year 2016.
In the text
thumbnail Fig. E.15

Composite light curve of (223) Rosa from the year 2018.
In the text
thumbnail Fig. E.16

Composite light curve of (223) Rosa from the year 2019.
In the text
thumbnail Fig. E.17

Composite light curve of (223) Rosa from the year 2020.
In the text
thumbnail Fig. E.18

Composite light curve of (362) Havnia from the year 2006.
In the text
thumbnail Fig. E.19

Composite light curve of (362) Havnia from the year 2015.
In the text
thumbnail Fig. E.20

Composite light curve of (362) Havnia from the years 2016-2017.
In the text
thumbnail Fig. E.21

Composite light curve of (362) Havnia from the years 2019-2020.
In the text
thumbnail Fig. E.22

Composite light curve of (483) Seppina from the year 2005.
In the text
thumbnail Fig. E.23

Composite light curve of (483) Seppina from the year 2013.
In the text
thumbnail Fig. E.24

Composite light curve of (483) Seppina from the year 2015.
In the text
thumbnail Fig. E.25

Composite light curve of (483) Seppina from the year 2016.
In the text
thumbnail Fig. E.26

Composite light curve of (483) Seppina from the year 2017.
In the text
thumbnail Fig. E.27

Composite light curve of (483) Seppina from the year 2018.
In the text
thumbnail Fig. E.28

Composite light curve of (501) Urhixidur from the year 2013.
In the text
thumbnail Fig. E.29

Composite light curve of (501) Urhixidur from the years 2014-2015.
In the text
thumbnail Fig. E.30

Composite light curve of (501) Urhixidur from the year 2016.
In the text
thumbnail Fig. E.31

Composite light curve of (501) Urhixidur from the year 2017.
In the text
thumbnail Fig. E.32

Composite light curve of (501) Urhixidur from the year 2018.
In the text
thumbnail Fig. E.33

Composite light curve of (501) Urhixidur from the year 2019.
In the text
thumbnail Fig. E.34

Composite light curve of (537) Pauly from the year 2016.
In the text
thumbnail Fig. E.35

Composite light curve of (537) Pauly from the years 2017.
In the text
thumbnail Fig. E.36

Composite light curve of (537) Pauly from the year 2018.
In the text
thumbnail Fig. E.37

Composite light curve of (537) Pauly from the years 2019-2020.
In the text
thumbnail Fig. E.38

Composite light curve of (552) Sigelinde from the year 2015.
In the text
thumbnail Fig. E.39

Composite light curve of (552) Sigelinde from the years 2016-2017.
In the text
thumbnail Fig. E.40

Composite light curve of (552) Sigelinde from the year 2018.
In the text
thumbnail Fig. E.41

Composite light curve of (552) Sigelinde from the year 2019.
In the text
thumbnail Fig. E.42

Composite light curve of (618) Elfriede from the year 2014.
In the text
thumbnail Fig. E.43

Composite light curve of (618) Elfriede from the years 2015-2016.
In the text
thumbnail Fig. E.44

Composite light curve of (618) Elfriede from the year 2017.
In the text
thumbnail Fig. E.45

Composite light curve of (618) Elfriede from the year 2018.
In the text
thumbnail Fig. E.46

Composite light curve of (618) Elfriede from the year 2019.
In the text
thumbnail Fig. E.47

Composite light curve of (666) Desdemona from the year 2015.
In the text
thumbnail Fig. E.48

Composite light curve of (666) Desdemona from the year 2016.
In the text
thumbnail Fig. E.49

Composite light curve of (666) Desdemona from the years 2017-2018.
In the text
thumbnail Fig. E.50

Composite light curve of (666) Desdemona from the year 2019.
In the text
thumbnail Fig. E.51

Composite light curve of (667) Denise from the year 2014.
In the text
thumbnail Fig. E.52

Composite light curve of (667) Denise from the year 2015.
In the text
thumbnail Fig. E.53

Composite light curve of (667) Denise from the year 2016.
In the text
thumbnail Fig. E.54

Composite light curve of (667) Denise from the year 2017.
In the text
thumbnail Fig. E.55

Composite light curve of (667) Denise from the years 2018-2019.
In the text
thumbnail Fig. E.56

Composite light curve of (780) Armenia from the year 2014.
In the text
thumbnail Fig. E.57

Composite light curve of (780) Armenia from the year 2015.
In the text
thumbnail Fig. E.58

Composite light curve of (780) Armenia from the year 2016.
In the text
thumbnail Fig. E.59

Composite light curve of (780) Armenia from the years 2017-2018.
In the text
thumbnail Fig. E.60

Composite light curve of (780) Armenia from the years 2018-2019.
In the text
thumbnail Fig. E.61

Composite light curve of (923) Herluga from the year 2014.
In the text
thumbnail Fig. E.62

Composite light curve of (923) Herluga from the year 2015.
In the text
thumbnail Fig. E.63

Composite light curve of (923) Herluga from the year 2019.
In the text
thumbnail Fig. E.64

Composite light curve of (995) Sternberga from the years 2013-2014.
In the text
thumbnail Fig. E.65

Composite light curve of (995) Sternberga from the year 2015.
In the text
thumbnail Fig. E.66

Composite light curve of (995) Sternberga from the years 2017-2018.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.