2. Concrete thin shells in Mexico: Félix Candela
2.6 Lost works
Both the NEATM and the spherical thermophysical model produced good fits to the SL1 spectrum for all values of bolometric emissivity () considered. With all other parameters held constant, a lower value of produces a relatively hotter subsolar point. Increasing thermal inertia (or beaming parameter, η, in the case of the NEATM) compensates for the increase in temperature associated with a lower value of . Allowing the diameter to vary compensates for the overall flux level in the modeled SED. Indeed, as we decrease in our model runs, both thermal inertia (or η for the NEATM) and effective diameter must be greater than in the =0.9 case to produce SEDs that fit our data.
There is a limit to this degeneracy. For the lowest value of considered ( = 0.5), there is a point at which increasing thermal inertia no longer changes the shape of the model SED because the model asteroid is essentially isothermal. This is apparent in our results for the spherical TPM fit to SL1, where the χ2 goodness-of-fit parameter asymptotes as a function of thermal inertia when = 0.5 because the SED is no longer changing significantly (Figure 4.9).
We constrain for the spherical models by comparing derived effective diameters for each case to results from studies of Psyche’s size. A radar shape model for Psyche produced by Shepard et al. (2017), and constrained by lightcurve inversion, occultation data, and adaptive optics imaging (Kaasalainen et al., 2002; Durech et al.ˇ , 2011; Hanuˇs et al., 2013a; Drummond et al., 2016), has dimensions of 279 km × 232 km × 189 km, with a spherical volume-equivalent diameter of 226 km (±10%). In the case of the NEATM, our results for the SL2 dataset show that for = 0.95 and 0.9, the derived effective diameters (158 ± 12 km and 163+13−14 km) are smaller than even the smallest radar-derived dimension (189 km). The derived diameters for the = 0.7 and 0.5 cases are consistent with the lower end of radar- constrained dimensions (and consistent with the fact that the SL2 observations were made while Spitzer was viewing a smaller surface area of Psyche). For SL1, effective diameters derived in the = 0.95 and 0.9 cases are most consistent with shape model constraints. The = 0.7 case requires an effective diameter on the larger end of the radar constraints, and the = 0.5 requires the effective diameter be greater than the greatest radar dimension plus its 10% uncertainty. Additionally, the geometric albedos derived for SL2 with = 0.5 and for SL1 with = 0.95 and = 0.9 (0.17 ± 0.03, 0.15 ± 0.03, and 0.14 ± 0.03, respectively) are the most consistent with Psyche’s previously reported geometric albedo of 0.15 ± 0.03 (e.g., Shepard et al.,2017). We find similar results for the spherical thermophysical models.
Figure 4.18: The reduced χ2 statistic as a function of effective radius for the NEATM. The
left frame (a) shows results for the SL2 spectrum, while the right frame (b) shows results for the SL1 spectrum. The red, green, purple, and blue curves represent emissivity values of 0.95, 0.90, 0.70, and 0.50, respectively. The colored, shaded region around each χ2 vs.
radius curve represents the spread due to uncertainties in the overall flux calibration. The grey shaded region in the background represents the ± 20% (2σ) range of effective radius values derived from radar studies by Shepard et al.(2017). The inset plots show the χ2 vs.
radius curves (colored, dashed lines) near the minima. The solid black line in each inset plot is the 1σ-cutoff value for χ2.
The highest fidelity results are those in which we include Psyche’s shape model in the TPM. For SL2, the TPM results using Psyche’s shape model are poorly constrained. For SL1, the = 0.9 (Γ =5–25 J m−2 K−1 s−1/2) models fit best when we consider only the nominal shape models (Figure 4.6). When we consider the ±10% uncertainty in its dimensions, the = 0.7 TPM also fits, with a relatively high thermal inertia of 80–95 J m−2 K−1 s−1/2. The = 0.5 models do not fit well even when we consider the reported uncertainties on the shape models. We argue that the = 0.9 case is the most likely. The = 0.9 case is also consistent with the emissivity spectra presented above, which suggest a fine-grained silicate regolith is present on Psyche’s surface. A surface covered in powdered silicate should have ≥0.9 and a low thermal inertia. The higher thermal inertia/lower emissivity case is possible if Psyche is on the larger end of its reported size range.
Matter et al. (2013) studied Psyche’s thermophysical properties using ground-based in- terferometric data. They report that Psyche is smooth, as we also conclude, but they find that Psyche has a higher thermal inertia of 114–133 ± 40 J m−2 K−1 s−1/2. Heliocentric distance affects the temperature distribution on an asteroid’s surface, and is related to ther- mal inertia as Γ ∝ r−3/4H (e.g., Delb´o et al., 2015). Matter et al. (2013) observed Psyche at a heliocentric distance of rH = 2.70 AU, and our SL1 observations took place when Psyche
had rH = 2.80 AU. Psyche’s thermal inertia should be measured as 1.03 times greater at
2.70 AU than at 2.80 AU, which is not sufficient to explain the differences in these results. Psyche’s orientation appears to correspond to that of our SL1 observations during at least one observing epoch included in theMatter et al. (2013) study, so it is not apparent if rota- tional variability is the source of the thermal inertia discrepancy, either. We note that these are two different datasets, obtained with different observational techniques, and modeled with different thermal models. Ideally, modeling this dataset with the Matter et al. (2013) model, and modeling the Matter et al.(2013) dataset with the model described here, would provide a test of the source(s) of the differences in thermal inertia.