Apophis source population and Earth encounter frequency of Apophis-like bodies

Abstract

We provide context for Apophis' 2029 Earth passage by analyzing its possible source populations, in particular, the Flora family, which has a similar composition, corresponding to LL chondrite meteorites. Out of ${\sim}3380$ NEOs larger or equal than Apophis (${\ge}420\,{\rm m}$), $610\pm 140$ are LL-like NEOs from Flora. Their mean encounter probability is $p = 86\times 10^{-18}\,{\rm km}^{-2}\,{\rm y}^{-1}$, corresponding to once per 13000 y frequency of encounters closer than 38000 km. However, this does not apply to Apophis alone, for which the specific encounter probability is higher, $p' = 1603\times 10^{-18}\,{\rm km}^{-2}\,{\rm y}^{-1}$, but the frequency is lower, only once per 430000 y, when we consider it as a single object. Our simulation of the Flora family over $\sim$1 billion years indicates that Apophis-like bodies have orbits that are particularly persistent in near-Earth space. The temporal distribution of encounter probabilities exhibits peaks (up to ${>}10^4$ in the same units) and the specific value for Apophis is not unusual (occurring ${\sim}70\%$ of time). In other words, there is always at least one Apophis-like body among NEOs. We find that such persistence also creates favorable opportunities for temporary capture as Earth coorbitals. Apophis-like bodies are ultimately removed from the inner solar system by approaching the Sun or by impact into one of the terrestrial planets, where the relative split between these outcomes is $(45\pm 2)\,\%$ and $(50\pm 2)\,\%$. While our current knowledge of Apophis' orbit guarantees no threat from Apophis in the next few centuries, we cannot predict any specific outcome for Apophis in the coming thousands or millions of years. Evaluating this statistically over the long term, we find that objects in Apophis-like orbits have a $(19\pm 2)\,\%$ chance of Earth impact over their lifetime of ${\sim}30\,{\rm My}$.

Figures (14)

• Figure 1: Binned distributions $M_j$ of semimajor axes $a$ and inclinations $i$ of synthetic NEO orbits, originating from individual asteroid families. Colours correspond to the number of test particles in bins; although the quantity $M_j(a, i)$ was eventually normalized. The bin sizes were $0.01\,{\rm au}$ and $1^\circ$, respectively. Apophis orbit is marked with a black cross, other LL-like NEOs from Binzel_2019Icar..324...41BMarsset_2022AJ....163..165M with gray crosses. Of the three, the highest density for producing Apophis-like objects is from the Flora family.
• Figure 2: Top: Osculating semimajor axis $a$ versus eccentricity $e$ showing long-term evolution of Apophis-like orbits, after 10 My. The curves correspond to the boundaries of the NEO space ($q < 1.3\,{\rm au}$, $Q > 0.983\,{\rm au}$) and of the adjacent Mars-crossing population. The dotted vertical lines correspond to locations of various mean-motion resonances, including the $\nu_6$ secular resonance. Majority of the 100 clones of Apophis remain in the NEO (or Mars-crossing) space; the respective orbit is relatively long-lived. Bottom: The number of Apophis clones $N$ versus time $t$. The corresponding e-folding time scale is ${\sim}30$ My, or $50$ My respectively, depending on whether or not planetary impacts were used as a criterion for removal of bodies.
• Figure 3: Lifetimes of LL-like NEOs originating from the Flora family according to our simulation. The $x$-axis is simulation time (spanning from 0, i.e., Flora disruption, to 1 Gy, the end of simulation), the $y$-axis is lifetime. One can see both short- (blue) and long-lived orbits (orange); their 'mix' determines the mean life time $\tau_{\rm neo}$.
• Figure 4: Top: Collisional probabilities of LL-like NEOs originating from the Flora family and their temporal distribution. Individual bodies (out of 1900) are distinguished by shades of gray. Vertical range shows both small and large probabilities. For comparison, horizontal lines indicate the mean probability $p$ of all NEOs (orange), short-term, initial probability $p'$ of Apophis (cyan), long-term probability $p"$ of Apophis (green). Bottom: The distribution of all $p$ values (gray) and of maximum $p$ value (black).
• Figure 5: Top: Collisions of Apophis clones with the Sun, Mercury, Venus, Earth, or Mars. Their positions in the ecliptic frame ($x$, $y$) are indicated (crosses), alongside the mean orbital distances of terrestrial planets (dotted circles). Bottom: Statistics of collisions. Specifically, $(45\pm 2)\,\%$ of the clones were eliminated due to low perihelion ($q < R_\odot$), while $(50\pm 2)\,\%$ due to planetary impacts. The respective uncertainties (error bars) are Poissonian (${\propto}\sqrt{N}$).