Mid-IR Observations of IRAS, AKARI, WISE/NEOWISE, and Subaru for Large Icy Asteroid (704) Interamnia: A New Perspective of Regolith Properties and Water Ice Fraction

In this study, we conducted observations on Interamnia with the 8.2 m Subaru telescope at Maunakea on 2014 January 18 at 11:00 UTC, at a solar phase angle of 8399 and central wavelengths of 7.8, 8.7, 9.8, 10.3, 11.6, 12.5, 18.7, and 24.5 μm, using the Cooled MIR Camera and Spectrometer (COMICS; Kataza et al. 2000). In addition, we further collected the mid-IR data of this asteroid from IRAS, AKARI, and WISE, which are acquired from the NASA/IPAC Infrared Science Archive (IRSA) ⁸ with a search cone radius of 1''. IRAS observations contain four wave bands centered at 12, 25, 60, and 100 μm, with solar phase angle ranging from −17° to −15°. The AKARI observations were obtained from the AKARI Asteroid Flux Catalog. ⁹ AKARI observed this asteroid at 9.0 and 18.0 μm in two separate epochs, with a solar phase angle of 21°–22°. WISE surveyed the sky at four wave bands, i.e., W1 (3.4 μm), W2 (4.6 μm), W3 (12.0 μm), and W4 (22.0 μm). The mission continued to survey the sky known as NEOWISE after the depletion of the cryogen. Thus, we query the WISE/NEOWISE mid-IR data from two catalogs, the WISE All-Sky Single Exposure (L1b) Source Table and the NEOWISE-R Single Exposure (L1b) Source Table, ¹⁰ by using the Moving Object Search. For Interamnia, the WISE/NEOWISE measurements account for the largest proportion of all mid-infrared observations and are given the largest weight in the procedure of fitting thermophysical parameters.

Note that, according to the Explanatory Supplement to the WISE data products, ¹¹ WISE observations of large asteroids, such as Interamnia, tend to be saturated in W3 and W4, whose magnitudes of W3 and W4 bands range from −0.076 to 0.328 and from −2.022 to −1.670, respectively. The characteristic magnitudes at which sources begin to saturate are 8.0, 6.7, 3.8, and −0.4 mag for W1–W4, respectively. WISE can extract useful measurements of saturated sources through fitting of the point-spread function (PSF) wings, until too few nonsaturated pixels are available in the measurement area. A linear correction was applied to the saturated W3 and W4 data, and we have set the error bars to 0.2 mag right at these limits in order to account for the changes in the PSF (Mainzer et al. 2011a). Moreover, as described in Wright et al. (2010), a correction to the red and blue calibrator discrepancy in W3 and W4 filters is required, which yields a −8% and +4% adjustment to the zero magnitudes for the two bands. To resolve the flux differences, we adjust the effective wavelength of W3 3%–5% blueward and that of W4 2%–3% redward.

Wright et al. (2010) presented the method to convert the WISE magnitude to thermal fluxes in units of Jy. Here we have optimized the method as follows.

For an asteroid, the flux density conversion is given by

$$\begin{eqnarray}&&{F}_{\nu }=\frac{{F}_{\nu 0}^{* }}{{f}_{c}}\times {10}^{-{m}_{\mathrm{vega}}/2.5}(\mathrm{Jy})\end{eqnarray} \tag{ 1 }$$

where ${F}_{\nu 0}^{* }$ is the zero magnitude flux density derived for sources with power-law spectra F_ν ∝ ν⁻², which is 306.682, 170.663, 31.368, and 7.953 Jy (Wright et al. 2010) for W1, W2, W3, and W4 bands, respectively. We emphasize that the changes in ${F}_{\nu 0}^{* }$ at W3 and W4 are due to the adjustment of the central wavelengths of two bands to λ(W3) = 11.0984 μm and λ(W4) = 22.6405 μm to correct the discrepancy of red and blue sources (Wright et al. 2010). Here f _c is the color correction.

It should be noted that f _c is temperature dependent, and Wright et al. (2010) provided f _c values for a variety of temperatures for blackbody spectra B_ν (T), e.g., 100, 141, 200, and 283 K. In that work, near-Earth asteroids are usually in association with B_ν (283 K), where the f _c values for W1–W4 are 1.3917, 1.1124, 0.8791, and 0.9865, respectively. However, the main-belt asteroids have B_ν (200 K) with f _c values for the four wave bands of 2.0577, 1.3448, 1.0005, and 0.9833, respectively. This approximation can be achieved when only W3 and W4 data are used. But the f _c values of W1 and W2 bands are very sensitive to temperature. We fit the f _c values provided by Wright et al. (2010) with respect to the four WISE wave bands to four curves that vary with temperature in Figure 1. As can be seen, when T < 200 K, f _c at W1 and W2 decreases rapidly. If we adopt the W1 and W2 data in our radiometric process, f _c values under separate temperatures could have significant influence on the results. For example, supposing that the effective temperature of an asteroid at a certain epoch is 170 K, according to the fitted curve f _c (W1) = 2.7069 can be obtained. However, from Wright et al. (2010) we can obtain f _c (W1, 141 K) = 4.0882 and f _c (W1, 200 K) = 2.0577; in such a case, using f _c at 141 K or 200 K will cause a 30%–50% deviation in the observational flux. Thus, it is necessary to evaluate the effective temperature of the target asteroid at the observed epochs to derive more reliable color correction values. The flux density for an asteroid at heliocentric distance d can be expressed as

$$\begin{eqnarray}&&{F}_{a}=\frac{{L}_{\odot }}{4\pi {d}^{2}},\end{eqnarray} \tag{ 2 }$$

where L_⊙ is the luminosity of the Sun, which is given by the Stefan–Boltzmann law ${L}_{\odot }=4\pi {R}_{\odot }^{2}\sigma {T}_{\odot }^{4}$, where R_⊙ is the radius of the Sun, σ is the Stefan–Boltzmann constant, and T_⊙ is the temperature of the Sun. Considering an asteroid of radius R _a , the radiant flux absorbed by the asteroid is

$$\begin{eqnarray}&&{{\rm{\Phi }}}_{a}=\pi {R}_{a}^{2}{F}_{a},\end{eqnarray} \tag{ 3 }$$

while the emitted flux from the asteroid is

$$\begin{eqnarray}&&{P}_{a}=4\pi {R}_{a}^{2}\sigma {T}_{\mathrm{eff}}^{4}.\end{eqnarray} \tag{ 4 }$$

For an asteroid in the thermodynamical equilibrium state, the rate at which it radiates energy is equal to the rate at which it absorbs energy; thus, we have Φ_a = P _a . Combining Equations (2)–(4), the effective temperature can be deduced as

$$\begin{eqnarray}&&{T}_{\mathrm{eff}}={T}_{\odot }\sqrt{\displaystyle \frac{{R}_{\odot }}{2d}}.\end{eqnarray} \tag{ 5 }$$

We denote the effective temperature of Interamnia at the epochs for WISE with asterisks in Figure 1. The derived T_eff at the observations ranges from 151 to 177 K. As observed, the flux corrections at W1 and W2 bands change significantly at the observed epochs for Intermania. Hence, it is very necessary to deal with temperature-varied color corrections.

Zoom In Zoom Out Reset image size

Clearly, the observed fluxes contain thermal radiation from the asteroid and solar reflection. The reflected sunlight should be corrected for the IR observations at short wavelength, along with those when the asteroids are far away from the Sun. Here we adopted the method described in Yu & Ip (2021) to evaluate the proportion of the reflected sunlight in each wave band, which combines the Lambert–Lommel–Seeliger law that introduces a coefficient C_L to Lambertian reflection (Yu & Ip 2021). The ratios of reflected part and observation for each wave band are shown in the top panel of Figure 2. It is clear that the reflected part is negligible at WISE W3 and W4 bands, AKARI, Subaru, and IRAS. In Table 1, we list F_reflect/F_obs and T_eff for W1 and W2 at each epoch. By contrast, the portion of reflected sunlight can occupy nearly 85%–99% of the total observed flux for W1, whereas it can occupy 7%–30% for W2. In addition, since f _c is temperature dependent, the observed flux relates to temperature. Figure 2 displays the relation of F_reflect/F_obs versus the effective temperature T_eff at W1 and W2, which is suggestive of a linear decreasing trend.

Zoom In Zoom Out Reset image size

Table A1 in the Appendix summarizes the observational fluxes and the observational geometries (the heliocentric distance r_helio, the distance from the observer Δ_obs, and the solar phase angle α). The Subaru telescope provides the observations at small solar phase angles of 8399. WISE/NEOWISE values are the bandwidth flux (i.e., without color correction).

WISE bands span bandwidths on the order of 2–10 μm, while the observed flux calculated from Equation (1) is the monochromatic flux at a single wavelength, which is color corrected by using temperature-varied f _c as mentioned above. However, the usage of f _c can only be suitable for the thermal emission part, while the light that is being reflected from the Sun will have a solar-like spectrum; thus color corrections of blackbody and G2V stars are required to be taken into account in combination, especially for W1 and W2 data, which contain nonnegligible solar reflection. As a matter of fact, the ratio of the reflected sunlight to the observed fluxes is not yet entirely clear. Therefore, we then employ the bandwidth flux rather than monochromatic flux to perform fitting of observations. In the fitting, we first convert the WISE magnitude into thermal emission without using the color corrections to determine the bandwidth flux measured by the observer, i.e., ${F}_{\nu ,\mathrm{obs}}={F}_{\nu 0}^{* }\times {10}^{-{m}_{\mathrm{vega}}/2.5}(\mathrm{Jy})$. Then, the total theoretical flux is expressed as follows:

$$\begin{eqnarray}&&{F}_{\mathrm{total}}={F}_{\mathrm{th}}* {f}_{c}(T)+{F}_{\mathrm{reflect}}* {f}_{c,{\rm{G}}2{\rm{V}}},\end{eqnarray} \tag{ 6 }$$

where F_th denotes the theoretical single-wavelength thermal emission multiplied by blackbody color correction f _{c ,blackbody} (temperature varied), whereas F_reflect is the theoretical reflected sunlight that is multiplied by G2V color correction f _{c ,G2V}. Hence, F_total is adopted to conduct fitting of total observed flux F_ν,obs.

Thermal inertia is a key parameter that dominates the surface heat conduction process of the asteroidal surface, which controls the cyclic temperature variation as the asteroid rotates (Delbo et al. 2015). In the classical Thermophysical Model (TPM; Lagerros 1996) or the Advanced Thermophysical Model (ATPM; Rozitis & Green 2011), thermal inertia is treated as a free parameter in the fitting process. However, according to the definition of thermal inertia, ${\rm{\Gamma }}=\sqrt{\rho C(T)\kappa (T)}$, where κ and C are thermal conductivity and specific heat capacity, respectively, both of which strongly correlate to surface temperature. If an asteroid has a large orbital eccentricity or a high obliquity close to 90°, it would show significant variations in temperature at the orbital distances, which could lead to various thermal inertias at each epoch. Consequently, a mean thermal inertia may not well describe thermal characteristics of an asteroid, relating to its surface environment. For an asteroid that is covered by a dust mantle, the thermal conductivity relates to grain size r by

$$\begin{eqnarray}&&\kappa (r,T,\phi )={\kappa }_{\mathrm{solid}}(T)H(r,T,\phi )+8\sigma \epsilon {T}^{3}{\rm{\Lambda }}(r,\phi ),\end{eqnarray} \tag{ 7 }$$

where ϕ is the volume filling factor, which is set to be 0.5 in this work, and κ_solid is the heat conductivity of solid material, which equals 1.19 + 2.1 × 10⁻³ × T Wm⁻¹ K⁻¹. Λ(r, ϕ) is the mean free path of photons and can be expressed by $1.3\tfrac{(1-\phi )}{\phi }r$. H(r, T, ϕ) is the Hertz factor, which can be expressed as

$$\begin{eqnarray}&&H(r,T,\phi )={\left[\displaystyle \frac{9\pi }{4}\displaystyle \frac{1\,{\mu }^{2}}{E}\displaystyle \frac{\gamma (T)}{r}\right]}^{1/3}\cdot {f}_{1}\exp ({f}_{2}\phi )\cdot \chi ,\end{eqnarray} \tag{ 8 }$$

where the first term of Equation (8) describes heat transfer reduction due to van der Waals force, and here μ, E, and γ(T) are Poisson's ratio, Young's modulus, and the specific surface energy of the material, respectively. f₁ = (5.18 ± 3.45) × 10⁻² and f₂ = 5.26 ± 0.94 are empirical constants. The last factor χ describes the reduction of the heat conductivity that is induced by the distinction between monodisperse spherical particles (model assumption) and irregular polydisperse grains of a real regolith. Hence, we adopted RSTPM in which the mean dust grain size rather than the mean thermal inertia is used as a free parameter to derive the asteroid's thermal parameters because it would be nearly unchanged at each orbital position.

In our fitting process, we adopt the shape model obtained from Hanuš et al. (2020), with a pole orientation of (87°, 63°) in an ecliptic coordinate system. Like other thermophysical models, we obtain the temperature distribution of each facet by solving the 1D heat conduction equation and calculate the theoretical flux by using the Planck function to fit with observations. We scan mean grain radius $\widetilde{r}$ ranging from 1 to 1000 μm and roughness fraction f _r ranging from 0 to 1. For each pair of $\widetilde{r}$ and f _r , a corresponding geometric albedo p _v and effective diameter D_eff are utilized to compute a reduced χ². In addition, we use a fractional coverage of a macroscopic bowl-shaped crater with a depth-to-diameter ratio of 0.5 to describe the surface roughness.

Figure 3 shows the best-fitting outcomes of mean dust grain radius, geometric albedo, and effective diameter (with optimized color corrections). From Figure 3(a), the minimum value of χ² (0.348) is related to $\widetilde{r}={190}_{-180}^{+460}$ μm and ${f}_{r}={0.30}_{-0.17}^{+0.35}$ in 3σ error uncertainties. The rms slope can then be evaluated to be ${27}_{-9}^{+13}$ deg (Spencer 1990). The geometric albedo of Interamnia is constrained to be ${p}_{{\rm{v}}}={0.0472}_{-0.0031}^{+0.0033}$ (Figure 3(b)), which agrees with the typical values of C-type or B-type asteroids, and the effective diameter is calculated to be ${D}_{\mathrm{eff}}={339}_{-11}^{+12}$ km with an absolute magnitude of 6.28 from the Minor Planet Center (MPC; Figure 3(c)). The derived diameter D_eff is consistent with the disk-resolved diameter of 332 ± 6 km from VLT-SPHERE observations (Hanuš et al. 2020) and that of 343 ± 5 km (Drummond et al. 2009) from the 10 m Keck telescope, but it is larger than D_WISE and D_AKARI, which are 312 and 316 km, respectively (Mainzer et al. 2011b; Usui et al. 2011). We also presented a scattering weight factor w_L of 0.40, which represents the Lambertian term in the scattering law. Our derived thermal parameters are listed in Table 2. To compare with those of temperature-varied color corrections for WISE/NEOWISE, we further present the corresponding results at 141 and 200 K for constant color corrections in Table 2. Note that a smaller reduced χ² is given by using optimized color corrections.

Zoom In Zoom Out Reset image size

Table 2. Radiometric Results of (704) Interamnia

f c	Grain Size (μm)	Deff (km)	p v	f r	θRMS (deg)	wf	${\chi }_{\min }^{2}$
Temperature-varied	${190}_{-180}^{+460}$	${339}_{-11}^{+12}$	${0.0472}_{-0.0031}^{+0.0033}$	${0.30}_{-0.17}^{+0.35}$	${27}_{-9}^{+13}$	0.40	0.348
Bν (141 K)	${160}_{-145}^{+370}$	${350.2}_{-8.4}^{+7.8}$	${0.0443}_{-0.0019}^{+0.0022}$	${0.30}_{-0.15}^{+0.31}$	${27}_{-8}^{+12}$	0.20	0.848
Bν (200 K)	${160}_{-133}^{+150}$	${337.8}_{-1.4}^{+7.3}$	${0.0476}_{-0.0020}^{+0.0004}$	${1.00}_{-0.16}^{+0.00}$	${50}_{-4}^{+0}$	0.50	1.595

Download table as:  ASCIITypeset image

To ensure the reliability of our results, we show the ratio of observed flux and theoretical flux in Figure 4. The left panel shows the ratio of each wavelength and has no obvious characteristics with λ, which indicates that the emissivity and albedo of Interamnia are not significantly dependent on wavelengths. Although theoretical flux at 3.4 μm (W1 band) appears to underestimate the observed value, in general, the ratios of various λ are uniformly distributed about 1. The right panel of Figure 4 shows that F_obs/F_model is plotted against solar phase angle. The ratio seems independent of the phase angle, indicating that the thermal infrared beaming effect is well resolved by the RSTPM model. Thus, the derived thermal parameters are reliable in the fitting procedure.

Zoom In Zoom Out Reset image size

Interamnia bears quite small regolith grain size, which is indicative of a fine and mature regolith layer. In such a case, the efficiency of heat conduction between different grains is significantly lower than that in a monolith, causing the fine regolith to be a poor heat conductor and have low thermal inertia (Delbo et al. 2015). As mentioned above, Γ strongly depends on temperature. With the derived mean regolith grain size and the temperature distribution calculated by RSTPM, the seasonal variation of Γ can be evaluated.

In order to obtain the seasonal temperature variation of various local latitudes of the asteroid, we generated the position vector of Interamnia in the heliocentric ecliptic coordinate system from JPL Horizons, ¹² with time specification from 2020 January 1 to 2025 May 6, to cover a whole orbital period. The global temperature distributions at these orbital positions are computed by solving the 1D heat conduction equation. As shown in the left panel of Figure 5, the x-axis represents the mean anomaly, where zero means the perihelion, while the y-axis stands for local latitude, where zero means the equator. The temperature changes periodically as the asteroid orbits the Sun and varies from 67 K (at aphelion) to 242 K (at perihelion) for the subsolar point. The temperature differs a lot between the northern and southern hemispheres. The subsolar point is located at the north region when the mean anomaly reaches about 240° and moves toward the south pole when the asteroid is near the perihelion. Additionally, considering the argument of perihelion 9480, the pole orientation (87°, 63°) ± 5°, and the orbital inclination ∼17°, when Interamnia is near perihelion, the Sun will radiate directly on a local latitude of −40° to −50°. The sunlight illuminates on the southern hemisphere steadily, causing polar daylight within a large fraction of the southern hemisphere. Therefore, heat can penetrate deeper than other regions, resulting in higher temperature (with a subsolar temperature of 242 K). Similarly, while the asteroid moves after the aphelion, the sunlight illuminates on the northern hemisphere steadily, but the temperature is lower than at perihelion owing to larger heliocentric distances (as shown in the left panel of Figure 5).

Zoom In Zoom Out Reset image size

Since ${\rm{\Gamma }}=\sqrt{\rho C(T)\kappa (T)}$, the relation between specific heat capacity and temperature can be approximately represented by Debye's formula:

$$\begin{eqnarray}&&C(T)=\displaystyle \frac{3{k}_{{\rm{B}}}}{{m}_{{\rm{a}}}}\left[\displaystyle \frac{a{\hat{T}}^{3}\left(a{\hat{T}}^{3}+2b{\hat{T}}^{2}+3c\hat{T}+4\right)}{{\left(a{\hat{T}}^{3}+b{\hat{T}}^{2}+\hat{T}+1\right)}^{2}}\right],\end{eqnarray} \tag{ 9 }$$

where $\hat{T}=T/{T}_{{\rm{D}}}$, T_D ≈ 700 K, a ≈ 39.09, b ≈ 14.46, c ≈ 3.304, and m _a ≈ 22 (Yu & Ip 2021). The correlation between thermal conductivity and temperature can be expressed via Equation (7). Considering a density of 1.98 g cm⁻³ (Hanuš et al. 2020), the variation of thermal inertia due to seasonal temperature change can then be given as shown in the right panel of Figure 5. If considering the 3σ uncertainty of mean regolith grain size $\widetilde{r}$, the surface thermal inertia of Interamnia ranges from 9 to 92 Jm⁻² s^−1/2 K⁻¹. The diurnal temperature also changes obviously within a rotation period. Since thermal inertia increases monotonically with temperature (Figure 5), the thermal inertia distribution at a certain orbital position is in relation to seasonal temperature distribution, which may result in the variation of distribution of thermal inertia on the asteroid's surface as it spins. As shown in Figure 6, we plot the thermal inertia distribution of Interamnia at the perihelion and aphelion, where its shape model is adopted from Hanuš et al. (2020). The maximum thermal inertia emerges at the southern hemisphere when the asteroid is near perihelion, whereas it occurs at the northern hemisphere after aphelion. However, due to the daylight phenomenon on Interamnia, the higher or lower thermal inertia can be retained for a relatively long time (about a quarter of an orbital period), and the thermal inertia of the diurnal effect seems to be less remarkable than that of the seasonal effect. Moreover, the thermal inertia of the southern and northern hemispheres greatly differs over an entire orbital period, thereby giving rise to diverse thermal characteristics in the southern and northern regions.

Zoom In Zoom Out Reset image size

Hanuš et al. (2020) estimated the mass of Interamnia to be (3.79 ± 1.28) × 10¹⁹ kg and measured the mean diameter to be 332 ± 6 km, which presents a bulk density of 1.98 ± 0.68 g cm⁻³. The density is indicative of a moderate proportion of water inside the asteroid. In this work, the mean diameter is derived to be ${339}_{-11}^{+12}\,\mathrm{km}$, and if we adopt the same mass as Hanuš et al. (2020), a bulk density of 1.86 ± 0.63 g cm⁻³ can be estimated, indicating that much more water ice may exist on Interamnia. Hence, with the bulk density, we may make a rough estimation of porosity, which can be described as

$$\begin{eqnarray}&&p=1-\frac{{\rho }_{b}}{{\rho }_{g}},\end{eqnarray} \tag{ 10 }$$

where ρ _b and ρ _g are bulk density and grain density of the material, respectively. First, we assume that there is no water ice inside the asteroid, and since Interamnia is a B/F-type asteroid, we consider the density and porosity of carbonaceous chondrites. Macke et al. (2011) measured the average grain density of 63 different carbonaceous chondrites to be 3.44 g cm⁻³; by substituting this into Equation (10), we can obtain p = 48%. The porosity (assuming no water ice) is relatively high as compared to the measured carbonaceous chondrites, which varies from 0% to 41% (Macke et al. 2011). The derived porosity is also close to that of Bennu for the OSIRIS-REx mission, whose porosity is predicted to be 40% ± 10% (Lauretta et al. 2019). However, the selection effect of Earth's atmosphere can remove high-porosity materials, so the meteorites may not be the best analog for understanding the asteroid's porosity. In addition, Bennu is a near-Earth object with a mean diameter of 490 m; thus, it might not be suitable to simply compare the porosity of two bodies. In fact, the macroporosity tends to decrease with increasing size (Vernazza et al. 2021), and large asteroids with mass ≥10¹⁹ kg appear to have minimal macroporosity (≤5%–10%). Thus, although Britt et al. (2002) estimated the average porosity of C-type asteroids to be 17%, and several C-type asteroids even have porosities larger than 50%, we still infer that (704) Interamnia is a coherent asteroid that may possess a low porosity, resembling other large objects in the main belt, like (1) Ceres, (2) Pallas, and (4) Vesta, presumably due to remarkable gravitational compression (Britt et al. 2002). Based on this assumption, we safely suggest that Interamnia would be likely to contain a certain amount of water ice.

To evaluate the volume fraction of water ice (denoted as f _w ), we suppose that Interamnia only consists of water ice and grains of uniform density for simplicity. The bulk density can then be expressed as

$$\begin{eqnarray}\begin{array}{rcl}{\rho }_{b} & = & \frac{{M}_{\mathrm{total}}}{V}=\frac{{M}_{w}+{M}_{g}}{V}=\frac{{\rho }_{w}{V}_{w}+{\rho }_{g}{V}_{g}}{V}\\ & = & {\rho }_{w}{f}_{w}+{\rho }_{g}(1-{f}_{w}-p),\end{array}\end{eqnarray} \tag{ 11 }$$

where M _w and M _g are the mass of water ice and grains, V _w and V _g are the volume of water ice and grains, ρ _w and ρ _g are the water ice density and grain density, and p is the mean porosity. Thus, the volume fraction f _w can be deduced as

$$\begin{eqnarray}&&{f}_{w}=\frac{{\rho }_{g}(1-p)-{\rho }_{b}}{{\rho }_{g}-{\rho }_{w}}\times 100 \% .\end{eqnarray} \tag{ 12 }$$

Considering that the real mean grain density and porosity of Interamnia are yet unknown, we can estimate f _w from the grain density of meteorites and other large asteroids. A previous study showed that grain densities of carbonaceous chondrites span from 2.42 g cm⁻³ (CI1 Orgueil) to 5.66 g cm⁻³ (CB Bencubbin; Macke et al. 2011); we exclude those extremely high grain densities and the limit density estimate to 2.5–3.5 g cm⁻³. As aforementioned, Interamnia is more likely to be a coherent asteroid than a loosely consolidated object. According to Britt et al. (2002), we then assume that the porosity of Interamnia is no more than 20%. Substituting ρ = 2.42–3.78 g cm⁻³ and p = 0%–20% into Equation (12), we can obtain the variation of f _w with porosity and density, as seen in Figure 7. Note that the bulk density is set to be 1.86 g cm⁻³ and the negative f _w is treated as zero. The volume fraction of water ice lies in the range of 9%–66%, implying that high grain density and low porosity are related to larger f _w .

Zoom In Zoom Out Reset image size