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Risks for Life on Proxima B from Sterilizing Impacts

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Risks for Life on Proxima B from Sterilizing Impacts Draft version October 30, 2020 Typeset using LATEX twocolumn style in AASTeX62 Risks for Life on Proxima b from Sterilizing Impacts Amir Siraj1 and Abraham Loeb1 1Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA ABSTRACT We consider the implications that a debris belt located between Proxima b and Proxima c would pose for the rate of large asteroid impacts that could sterilize Proxima b from life. Future observations by ALMA or JWST could constrain the existence of an asteroid belt in the life-threatening regime. We generalize our rate calculation of sterilizing impacts for habitable planets in systems with an asteroid belt and an outer planet. Keywords: M dwarf stars { Habitable planets { Debris disks { Asteroid belt { Impact phenomena 1. INTRODUCTION devastate prospects for both the development and sur- Proxima b is an Earth-mass planet in the habitable vival of life (Maher & Stevenson 1988; Sleep et al. 1989; Abramov & Mojzsis 2009; Sloan et al. 2017). zone of the nearest star, Proxima Centauri (M? = Our discussion is structured as follows. In Section 0:12 M ), at a separation of ∼ 0:05 AU (Anglada- Escud´eet al. 2016). Proxima b is thought to possibly 2, we consider the rate of sterilizing impacts on Earth hold potential for life (Ribas et al. 2016; Turbet et al. from the asteroid belt owing to Saturn. In Section3, 2016). Proxima c, an outer planet orbiting at a distance we apply a similar calculation to Proxima b, given the existence of Proxima c. In Section4, we investigate the of ∼ 1:5 AU with a mass of ∼ 10 M⊕, was recently dis- covered (Damasso et al. 2020; Kervella et al. 2020). A generalized sterilizing impact rate for habitable worlds −3 in multiplanetary systems. In Section5, we evaluate warm dust belt with a total mass of ∼ 10 M⊕ at a distance of ∼ 0:4 AU from Proxima Centauri was re- the detectability of an asteroid belt between Proxima b ported (Anglada et al. 2017), but later disputed as a and c with JWST and ALMA. Finally, in Section6 we possible stellar flare (MacGregor et al. 2018). A pos- explore key predictions and implications of our model. sible connection between flare activity and planitesimal accretion has also been considered (Beech 2011). 2. EARTH IMPACT RATE In the Solar system, Saturn sets the ν6 secular reso- For an asteroid impact on Earth, the final crater di- nance (Ito & Malhotra 2006; Minton & Malhotra 2011), ameter Dcr is related to the impactor diameter Dimp as which controls the inner edge of the asteroid belt and follows (Collins et al. 2005), therefore the rate of impacts from near-Earth asteroids (Morbidelli et al. 1994; Bottke et al. 2000). The rela- D D 0:78 v 0:44 tion between Saturn's location relative to the asteroid cr ∼ 29 imp imp belt and mass and the impact rate have been explored km km 20 km s−1 (1) through numerical simulation (Smallwood et al. 2018). 1=3 ρimp 1=3 arXiv:2006.12503v3 [astro-ph.EP] 29 Oct 2020 If an asteroid belt exists between Proxima b and Prox- (sin θ) ; ρ⊕ ima c, Proxima c could control the rate of asteroid im- pacts on Proxima b. Here, we consider the risks that an −3 where vimp is the impact speed, ρimp ∼ 2 g cm is the asteroid belt located between Proxima b and Proxima c −3 impactor density, ρ⊕ ∼ 3:5 g cm is the density of the would pose for life on Proxima b. While asteroid impacts Earth's mantle, and θ is the angle of the impact with can help foster conditions for life (see Livio 2018 for a re- respect to the surface of the Earth. view), sufficiently large impacts can boil off oceans and The observed cratering rate on Earth is (Hergarten & Kenkmann 2015), [email protected], [email protected] D −2:557 Γ ≈ 6:64 × 104 Gyr−1 cr ; (2) ⊕ km 2 Siraj & Loeb trial asteroid impact rate on the location of Saturn, in ] terms of a dimensionless coefficient κ, for distances of 1 1 r 10 ∼ 3Ra; − 4:5Ra; , where Ra; ≈ 2:7 AU is the loca- y G [ tion of the asteroid belt in the Solar system, normalized 2 e 10 t to Saturn at a distance of 9:537 AU (thereby spanning a r t 3 c 10 the range κ ∼ 0:26 − 1:25). We adopt the appropri- a p ate scaling for the dimensionless coefficient δ, for the m i 10 4 h effect of a ∼ 0:1 Saturn-mass planet on the terrestrial t r a impact rate (δ ∼ 0:2), since that is the mass of Proxima E 5 10 c, where δ is normalized to a Saturn-mass planet given 18 19 20 21 22 23 24 25 10 10 10 10 10 10 10 10 the results in Table 2 of Smallwood et al.(2018). As a Impactor mass [g] caveat, we imagine an architecture similar to the Solar system with a gas giant at location that would allow for Figure 1. Asteroid impact rate on Earth (solid line) in a secular resonance near Proxima b. Gyr−1 as a function of impactor mass in g, with the dotted The impact rate is also linearly dependent on the mass line indicating an impact with enough energy to boil off all of the asteroid belt Ma, assuming the size distribution of the oceans on Earth, in which 100% of the kinetic energy is similar to that of the Solar system (motivated by the is converted into thermal energy. fact that the Solar system's small body size distribu- tion is the only one measured, in addition to the sim- which is thought to be complete for the largest crater ilarity of the observed size distribution of interstellar sizes considered. The time-dependence is unimportant objects (Siraj & Loeb 2019) to the Dohnanyi(1969) col- for the purposes of this analysis as the timescales con- lisional model), and inversely dependent on the asteroid sidered here are & 1 Gyr. belt's orbital period Ta. Furthermore, the impact rate 1=3 Substituting Dimp ∼ (6Mimp/πρimp) into Eq. (1) is proportional to the cross-section of Proxima b's or- 2 and subsequently into Eq. (2) yields, bit relative to that of the asteroid belt (Rb=Ra) , and inversely proportional to the square of the orbital dis- tance of Proxima b, R , to account for the effect of or- M −2=3 ρ 0:38 b −4 −1 imp imp bital distance on the one-dimensional cross-section of Γ⊕ ≈ 8 × 10 Gyr 22 −3 1:7 × 10 g 2 g cm an Earth-like planet at a fixed planetary radius. The v −0:38 imp (sin θ)−0:28 : factors enumerated above result in the following de- 20 km s−1 pendencies for the asteroid impact rate at Proxima b, (3) Γ / κδM T −1(R =R )2R−2. There is no dependence The infinitesimal element of solid angle is d[sin(θ)] and b a a b a b on R since the relative orbital cross-section scales as so the cumulative probability of encounter up to a given b R2 while the relative impact cross-section scales as R−2. value of theta converges at small angles, and the assump- b b When normalized to solar system values, the rate is ex- tion that most objects impact the surface on normal tra- pressed as, jectories is justified, since the average value of sin(θ) over the range of impact angles is 2/π, resulting in a correc- tion of order unity in Equation (3) which is disregarded 1=2 −7=2 2 Ma;P MP Ra;P rb 22 here. An impactor with mass Mimp ∼ 1:7 × 10 g is Γb ∼ Γ⊕κδ ; Ma; M Ra; r⊕ capable of boiling off all of the oceans on Earth if 100% (4) of the kinetic energy is converted into thermal energy where rb and r⊕ are the radii of Proxima b and of the (Sloan et al. 2017), since the overcoming the vaporiza- Earth, respectively. The sterilizing impact rate at Prox- tion enthalpy of water to vaporize the oceans requires ima b as a function of asteroid belt mass and asteroid 34 33 ∼ 3×10 erg of energy in addition to the ∼ 3×10 erg belt location is shown in Figure2. An asteroid belt necessary to heat the water to 100 C. Figure1 shows −4 with a mass of & 10 M⊕ could imply as significant the Earth impact rate as a function of impactor mass. likelihood that Proxima b was sterilized in the past. As The chance that life on Earth was sterilized during its discussed in Section5, the upcoming James Webb Space lifetime (∼ 4:5 Gyr) is ∼ 1%. Telescope1 (JWST) will able to determine the existence of an asteroid belt at the distances of interest, which 3. PROXIMA b STERILIZATION RATE We interpolate the results in Table 2 of Smallwood et al.(2018) to find the dependence of the terres- 1 https://www.jwst.nasa.gov/ Risks for Life on Proxima b 3 Figure 2. Logarithm of impact rate at Proxima b in units of −1 (10 Gyr) as a function of asteroid belt mass in in M⊕ and radius in AU. Proxima c is considered to be a ∼ 0:1 Saturn- mass outer planet, and the asteroid belt mass is scaled based −4 on that of the solar system, ∼ 4 × 10 M⊕ (Pitjeva & Pit- jev 2018). The dotted line indicates an impact with enough energy to boil off all of the oceans on an Earth-like planet, in which 100% of the kinetic energy is converted into thermal energy.
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