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Defining the Flora Family: Orbital Properties, Reflectance Properties and Age

The Flora family resides in the densely populated inner main belt, bounded in semimajor axis by the $ν_6$ secular resonance and the Jupiter 3:1 mean motion resonance. The presence of several large families that overlap dynamically with the Floras (e.g., the Vesta, Baptistina, and Nysa-Polana families), and the removal of a significant fraction of Floras via the nearby $ν_6$ resonance complicates the Flora family's distinction in both proper orbital elements and reflectance properties. Here we use orbital information from the Asteroids Dynamic Site, color information from the Sloan Digital Sky Survey, and albedo information from the Wide-field Infrared Survey Explorer to obtain the median orbital and reflectance properties of the Floras by sampling the core of the family in multidimensional phase space. We find the median Flora SDSS colors to be $a^*$ = 0.126 $\pm$ 0.007 and $i-z = -0.037 \pm 0.007$; the median Flora albedo is $p_V$ = 0.291 $\pm$ 0.012. These properties allow us to define ranges for the Flora family in orbital and reflectance properties, as required for a detailed dynamical study. We use the young Karin family, for which we have an age determined via direct backward integration of members' orbits, to calibrate the Yarkovsky drift rates for the Flora family without having to estimate the Floras' material properties. The size-dependent dispersion of the Flora members in semimajor axis (the "V" plot) then yields an age for the family of $910^{+160}_{-120}$ My, with the uncertainty dominated by the uncertainty in the material properties of the family members (e.g., density and surface thermal properties). We discuss the effects on our age estimate of two independent processes that both introduce obliquity variations among the family members on short (My) timescales: 1) the capture of Flora members in spin-orbit resonance, and 2) YORP-driven obliquity variation.