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Nathan P. Myhrvold DPS48 in the Presence of Reflected Sunlight EPSC11

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Nathan P. Myhrvold DPS48 in the Presence of Reflected Sunlight EPSC11 Asteroid Thermal Modeling Nathan P. Myhrvold DPS48 in the Presence of Reflected Sunlight EPSC11 Abstract Many Studies Violate Kirchhoff’s Law Impact on Estimates of D and pIR pace telescopes that use mal Model (NEATM) that incorpo- It has been common practice in A more correct method solves for Incorporating Kirchhoff’s law into the a synthetic data set of asteroid obser- short-wavelength infrared (IR) rates Kirchhoff’s law and correctly many previous asteroid studies, in- emissivity in the short-wave IR bands NEATM could have significant ef- vations, using models that enforced or bands observe light from as- accounts for the presence of reflected cluding the NEOWISE studies1–10, to (W1 and W2) and then uses Kirch- fects on the best estimates of asteroid violated Kirchhoff’s law. Resulting es- Steroids that is a mixture of reflected sunlight. Monte Carlo simulations set the emissivity ϵ to a constant val- hoff’s law to estimate the albedo. In diameters and IR albedos from ob- timates of diameter D and short-wave sunlight and thermal emission. Kirch- were run on a synthetic data set of ue and to solve for the IR albedo pIR. long-wave IR bands (W3 and W4), servational data. To explore the mag- emissivity ϵ1,2 show that enforcing hoff’s law of thermal radiation applies 33,000 asteroids having properties This approach is incorrect, however, the emissivity can be set to a constant nitude and direction of these effects, Kirchhoff’s law reduces error in these and has important implications. Pre- identical to those in NEOWISE ob- because it violates Kirchhoff’s law of value of 0.9, which implies an albedo Monte Carlo trials were performed on estimates by a factor of 10 or more. vious asteroid studies, including the servations. The results show that the thermal radiation. at those wavelengths of 0.1. Fit extended Estimated NEOWISE studies, do not correctly conventional NEATM, which violates 11 choices of ϵ1,2 NEATM with diameter Kirchhoff's law D account for Kirchhoff’s law. Kirchhoff’s law, produces less accurate 33,000 synthetic Generate 100 est INCORRECT asteroids observations in This study presents a new exten- estimates of diameter and near-IR al- (3,000 per ) Property Short-wave IR (W1, W2) Long-wave IR (W3, W4) ϵ1,2 W1, W2, W3, W4 Asteroid statistical Fit extended Estimated short- sion of the Near Earth Asteroid Ther- bedo than the corrected model does. properties from NEATM without wave emissivity p(λ) solve for p 0.0 NEOWISE IR Kirchhoff's law ϵ1,2est ϵ(λ) 0.9 0.9 Estimated IR albedo pIR with Kirchho ’s law 14 1.0 0.8 0.6 0.4 0.2 0.0 Thermal Emission + Reflected Sunlight w 1.0 w With Kirchho’s law s la ’ s la 95% Confidence interval: ±1.9% ’ CORRECT 12 0.8 0.2 chho y s law Property Short-wave IR (W1, W2) Long-wave IR (W3, W4) 10 ’ chho chho 0.6 0.4 Thermal emission: p(λ) 1 − ϵ(λ) 0.1 8 without Kir 2 without Kir 1, IR ( ) F (T, ) ϵ ϵ λ neatm λ 6 p ϵ(λ) solve for ϵ1,2 0.9 0.4 0.6 Probability Densit Without Kirchho’s law 4 Reflected sunlight: 95% CI: –2.5 % / +132% Emissivity and albedo unaected by Kir 0.2 0.8 2 p(λ) Fsun(λ) NEATM Extended to Reflected Sunlight 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Estimated IR albedo 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Estimated emissivity Dest /D Estimated emissivity ϵ1,2 with Kirchho ’s law The NEATM was extended to account Telescope F Asteroid Incoming sunlight: D /D o rao a est for reflected sunlight. The total ob- α Kirchhoff's Law Bands Median 68.27% (1 ) Confidence Interval Relative Width of 1 CI 95% Confidence Interval Relative Width of 95% CI Fsun(λ) σ σ with W1, W2, W3, W4 1.000 0.990 – 1.009 1.00 0.981 – 1.019 1.00 served fluxF obs at wavelength λ and dis- ros without W1, W2, W3, W4 1.009 0.988 – 1.107 6.26 0.975 – 2.324 35.50 γ ras with W1, W2 1.014 0.818 – 1.461 33.84 0.539 – 3.381 74.79 tances (in AU, see figure at right) from F Kirchhoff’s Law of Thermal Radiation sun without W1, W2 1.009 0.689 – 1.545 45.05 0.017 – 3.565 93.37 an asteroid of diameter D (in meters) is: s Sun with W3, W4 1.000 0.974 – 1.026 2.74 0.950 – 1.051 2.66 p(λ) + ϵ(λ) = 1 Enforcing Kirchhoff’s law dramatically affects estimates of both asteroid diameters( above left) and albedo/emissivity (above right, below left and right). The effect on diameters is illustrated by histograms and confidence intervals of Dest/D, the ratio of estimated to known diameters for the synthetic asteroid data. With Kirchhoff’s law (red distribution), errors in diame- ter estimates are symmetric and low. In contrast, errors are >10× as large and skewed toward overestimation by a conventional • Maxwell’s equations are time-invariant $ % model that violates Kirchhoff’s law (blue distribution), especially when observations are limited to the W1 and W2 bands (table). ! # " For albedo and emissivity, estimates unaffected by Kirchhoff’s law would fall along a diagonal in the chart at above right. • Emission & reflection:same physics The absence of that pattern indicates the importance of the law. As with diameters, ignoring Kirchhoff’s law causes pronounced skew and increases in errors in the estimates of ϵ (below left). The expanded model corrects that problem (below right). 1,2 • Kirchhoff’s law isrequired for the where q is the empirically derived by using the HG phase function, pa- Without Kirchhoff's Law With Kirchhoff's Law Planck distribution of thermal radiation 50 visible-band phase integral, obtained rameterized by the slope parameter G. 10 40 8 y Reflected Sunlight for IR Asteroids y 30 6 ◂Solar light energy incident FUV UV Vis Near IR Medium IR Thermal emission on an asteroid can be modeled -2 0 10 Reflected sunlight 10 20 1.0% 15.6% 25.4% 54.3% 3.8% as a Planck distribution for a 4 Probability Densit temperature of 5778 K. Only Probability Densit about a quarter of the total W1 W2 2 10 incident energy falls within the = 0.1 B(5778 K, ) ϵ1,2 λ Johnson-V band visible band, and just 11.3% is y) (J 11.3% = 0.5 y in the Johnson-V band, which ϵ1,2 AU more realistically reflects the 10-3 10-1 –0.8 –0.6 –0.4 –0.2 0.0 0.2 0.4 0.6 –0.10 –0.05 –0.00 0.05 0.10 AU = Estimated − Model = Estimated − Model = 1 Δ 1,2 1,2 1,2 Δ 1,2 1,2 1,2 ao range of wavelengths passed r by astronomical filters. = as r In the W1 and W2 infrared ▸ ϵ1,2= 0.9 bands, the flux from reflect- References and Acknowledgments Solar Flux at 1 ed sunlight (dashed lines) al Flux at W1, W2 Band Sensitivit 1. Mainzer, A., Bauer, J.M., Grav, T., et al. Astrophys. J. 784, 110. doi:10.1088/0004-637X/791/2/121 can exceed flux from thermal 10-4 10-2 doi:10.1088/0004-637X/784/2/110 8. Mainzer, A., Grav, T., Masiero, J., et al. Astrophys. J. Lett. 760, L12. emission (solid curves) when Spectr 2. Grav, T., Mainzer, A.K., Bauer, J., et al. Astrophys. J. 742, 40. doi:10.1088/2041-8205/760/1/L12 doi:10.1088/0004-637X/742/1/40 9. Masiero, J.R., Mainzer, A., Grav, T., et al. Astrophys. J. 759, L8. ϵ1,2 emissivities at these wave- 3. Grav, T., Mainzer, A.K., Bauer, J., et al. Astrophys. J. 744, 197. doi:10.1088/2041-8205/759/1/L8 lengths (indicated by colored doi:10.1088/0004-637X/744/2/197 10. Grav, T., Mainzer, A., Bauer, J.M., et al. Astrophys. J. 759, 49. 4. Mainzer, A., Grav, T., Masiero, J., et al. Astrophys. J. 736, 100. doi:10.1088/0004-637X/759/1/49 labels) are low. doi:10.1088/0004-637X/736/2/100 5. Mainzer, A., Grav, T., Bauer, J.M., et al. Astrophys. J. 743, 156. Wayt Gibbs, Andrei Modoran, and Dhileep Sivam doi:10.1088/0004-637X/743/2/156 assisted in the creation of this poster. No funding 10-5 10-3 6. Masiero, J.R., Mainzer, A., Grav, T., et al. Astrophys. J. 741, 68. was sought for this research. 0.2 0.5 1 2 5 3 4 5 doi:10.1088/0004-637X/741/2/68 Nathan Myhrvold: [email protected] λ (μm) λ (μm) 7. Masiero, J.R., Grav, T., Mainzer, A., et al. Astrophys. J. 791, 121. Intellectual Ventures LLC, Bellevue, WA 98005.
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