SCATTERING LAW FITS FOR DUAL POLARIZATION RADAR ECHOES OF USING ARECIBO OBSERVATORY PLANETARY RADAR DATA L. F. Zambrano-Marin1,2, A. K. Virkki2 , E. G. Rivera-Valentín2,3, P. A. Taylor2 ; 1Escuela Internacional de Posgrado, Universidad de Granada, Spain ([email protected]), 2Arecibo Observatory, Universities Space Research Association (USRA), Arecibo, PR, 3Lunar and Planetary Institute, USRA, Houston,TX.

INTRODUCTION: following the work by Virkki et. al. [1], Thompson et al. SCATTERING FUNCTIONS: We fit the following scattering functions to the observed scaled radar reflectivity [2], and Wye et. al. [3], we test models of radar scattering using as a function of the angles of incidence, to study their suitability to model the radar reflectivity of dual-polarization radar observations to elucidate the near-surface near-surfaces: physical properties of asteroids. Here we test radar scattering models Cosine: R is related to the Fresnel reflection coefficient on near-Earth asteroids (441987) 2010 NY65, 2014 JO25, 2007 LE, at a normal incidence ( = 0), and C is a (285263) 1998 QE2, 3122 Florence, and , all observed Hagfors: roughness parameter ( , with the planetary radar system at the Arecibo Observatory. where λ is the wavelength of the incident Gaussian: signal (12.6 cm), L is the correlation length and METHODS: Analysis of the backscattering function was done by h is the root-mean-square height). In Bragg, rms k is the wave number denoted by: k = 2/λ . plotting the backscattered power as a function of angle of incidence Exponential: for both senses of polarization (OC: opposite circular, SC: same circular), selecting primarily targets where a roughly spheroidal Bragg: shape can be assumed based on radar images. Selected targets had continuous wave (CW; frequency only) spectra as well as radar images with sufficient resolution to obtain high backscatter signal per pixel at a range of incidence angles.

Table 1. Best fit values for each function by color underlined. Target R (C, H, G, E, B) C (C, H, G, E, B) ϵ (C, H, G, E, B) 0.01, 0.013, 0.007, 0.018, 1.222, 1.03, 1.485, 1.591, 1.413, Phaethon 0.009, 0.005 0.577, 0.067 1.46, 1.46 0.057, 0.081, 0.048, 0.358, 1.845, 2.644, 3.235, 2.429, Florence 0.055, 0.009 1.187, 0.753, 0.008 2.597, 2.597 0.04, 0.053, 0.029, -0.159,1.022, 2.261, 2.558, 1.997, 1998 QE2 0.035, 0.001 0.885, 0.474, 0 2.139, 2.139 D(m) Tax Class D(m) Tax Class D(m) Tax Class [5] [6] 0.096, 0.142, 0.088, 1.383, 3.726, 3.613, 4.894, 3.392, 6000 F[4], B[4] 4350 S 2200 Ch 2007 LE 0.1, 0.12 2.135, 1.478, 0.822 3.71, 3.71 0.17, 0.252, 0.151, 1.188, 3.519, 5.78, 9.083, 5.167, 2014 JO25 0.178, 0.03 1.916, 1.377, 0.016 6.043, 6.043 0.108, 0.153, 0.084, 0.309, 1.645, 1.336 3.914, 5.215, 3.298, 2010 NY65 0.106, 0 0.81, 904.824 3.868, 3.868

Figs 1-6: Radar vs. backscatter angle for selected targets. The OC component of the signal is shown by ★, the fit to each scattering law with solid line by color. Table 1 shows the fitted values for R (related to reflection D(m) Tax Class D(m) Tax Class D(m) Tax Class coefficient), C(related to surface [9] [7] [8] 230 S Complex 560 S? roughness) and ϵ (electric 870 S permittivity) with the best fit values underlined. Color coding represents scattering law result.

Discussion of Results As we can see in this small sample of targets, one formulation does not fit all. There is no clear correlation between taxonomic class and preference of scattering law. The 2 preferred fit was determined by selecting the least value from all functions; smallest values are underlined in Table 1. For (441987) 2010 NY65 the Exponential law is the best fit, whereas for 2014 JO25 and for 2007 LE Hagfors showed higher accuracy. For (285263)1998 QE2 and (3200) Phaethon the best fit was with the Bragg approximation, with Phaethon having the smallest density; and for (3122) Florence the Cosine function gave the best result. Traditionally, C has been considered to depend only on the surface undulations so that the r.m.s slope of an average surface facet is s = 1/√C, which does not take into account the diffuse scattering effects of boulders at wavelength-scale. The goal of this research is to analyze the R and C parameters in terms of physical properties of the surface. This will help us to understand how to consider the diffuse scattering by surface features at wavelength-scale using radar scattering laws as opposed to using only the rms slope.

REFERENCES: [1] A. Virkki et. al (2017) EPSC, abstract id. 750. [2] T. W. Thompson (2011) J. Of ACKNOWLEDGEMENTS: This material is based upon work supported by the National Aeronautics Geophysical Research, Vol. 116, E01006 [3] L. C. Wye (2011), Stanford University, Dept. of and Space Administration under grants NNX12AF24G and NNX13AQ46G issued through the Electrical Engineering [4] J. de León et. al (2010) A&A, EDP Science [5]L. A. Benner (2017) Near-Earth Object Observations program to Universities Space Research Association (USRA) for Observation Planning-Florence, http://echo.jpl.nasa.gov [6]M. Hicks et. al (2013)ATel #5121 [7] the Arecibo Planetary Radar Program. The Arecibo Observatory is operated by SRI International S. K. Fieber-Beyer (2015) Icarus, Volume 250, p. 430-437 [8]Center for NEO Studies (CNEOS) under a cooperative agreement with the National Science Foundation (NSF; AST-1100968) in (2017) [9]NEOShield-2, (2016)Intermediate observations and analysis progress report. alliance with Ana G. Méndez-Universidad Metropolitana and USRA.