Article On Mautner-Type Probability of Capture of Intergalactic Meteor Particles by Habitable Exoplanets Andjelka B. Kovaˇcevi´c Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia; [email protected] Received: 28 June 2019; Accepted: 10 July 2019; Published: 9 August 2019 First Version Published: 15 July 2019 (doi:10.3390/sci1020041) Second Version Published: 9 August 2019 (doi:10.3390/sci1020047) Abstract: Both macro and microprojectiles (e.g., interplanetary, interstellar and even intergalactic material) are seen as important vehicles for the exchange of potential (bio)material within our solar system as well as between stellar systems in our Galaxy. Accordingly, this requires estimates of the impact probabilities for different source populations of projectiles, including for intergalactic meteor particles which have received relatively little attention since considered as rare events (discrete occurrences that are statistically improbable due to their very infrequent appearance). We employ the simple but yet comprehensive model of intergalactic microprojectile capture by the gravity of exoplanets which enables us to estimate the map of collisional probabilities for an available sample of exoplanets in habitable zones around host stars. The model includes a dynamical description of the capture adopted from Mautner model of interstellar exchange of microparticles and changed for our purposes. We use statistical and information metrics to calculate probability map of intergalactic meteorite particle capture. Moreover, by calculating the entropy index map we measure the concentration of these rare events. We further adopted a model from immigration theory, to show that the transient distribution of birth/death/immigration of material for the simplest case has a high value. Keywords: intergalactic meteor particle; extrasolar planets; astrobiology 1. Introduction The Universe has been generating random events, which can be unpredictable and affect planetary environments in different ways. Probability distributions of such events are often observed to have power- law tails [1]. One of many examples include the natural transport of material within our Solar system. Molecules, excluding the most stable such as polycyclic aromatic hydrocarbons, are quickly (10–10,000 years) destroyed by e.g., the UV radiation of stars [2,3]. So, defensive vessels are required that would protect and transport them unaltered across space. Interestingly, recent observations accumulate evidence of interstellar, and even intergalactic transport of material. For example, observation of the first known Interstellar Object (ISO) 1I/2017 U1 Oumuamua by the Pan-STARRS telescope in October 2017 [4] has given a new impetus to a broad topic about the possibility of natural transport of solid material and complex molecules through interstellar space [5]. This object was the first macro–scale ISO observed. Almost two decades ago, Taylor et al. [6] discovered interstellar dust entering the Earth atmosphere. Ten years later, Afanasiev et al. [7] detected a hundreds of a micrometer size Intergalactic meteor particle (IMP). This IMP hit the Earth atmosphere with a hypervelocity 300 km s−1. However, only about 1% of meteors have velocities above 100 km s−1, and no previous meteor observations have confirmed velocities Sci 2019, 1, 47; doi:10.3390/sci1020047 www.mdpi.com/journal/sci Sci 2019, 1, 47 2 of 16 of several hundred km s−1 [8]. Afanasiev et al. [7] calculated that IMP was 0.01 cm in size and its mass was about 7 × 10−6 g. This IMP was two orders of magnitude larger than common interstellar dust grains in our Galaxy [9,10]. Additionally, its spectral features were a typical for the materials being exposed to the temperatures of 15,000–20,000 K. Its radiant appeared to coincide with the apex of the motion of the Solar system toward the centroid of the Local Group of galaxies. The authors calculated that average density of IMP population in the Earth’s vicinity could exceed 2.5 × 10−31 g cm−3. If the extragalactic dust is uniformly distributed over the entire volume of Local Group, with above density, Afanasiev et al. [7] claimed that the total mass of the dust is about of 1% of the total mass of the Local Group. Moreover, their followup observations identified a dozen IMP candidates consistent with velocity and radiant estimates of identified IMP, which is in disagreement with the lack of any evidence from other optical meteor observatories (see e.g., [11]). Nevertheless, Afanasiev et al. [7] study shows that the existence of meteors of galactic velocities cannot completely be ruled out. Linking estimates that our Milky Way galaxy is home to ~1010 exoplanets [12] and above mentioned possible influx of IMP on our planet, raises the question of the probability of material migration in our Local Group, including the delivery of chemicals potentially involved in the emergence of life. Although the trade of viable organisms between planets in our system is an open question [13], the exchange of molecular species is much more likely [14]. It is believed that material exchange between rocky planets could amplify the chemical space within the planetary system [15]. On the chemical space we assume the property space spanned by all possible molecules and chemical compounds under a given set of construction principles and boundary conditions. Meteoroids (particles from 1 µm up to 1 cm), meteorites (1 cm up to 10 m), comet’s nuclei and asteroids were suggested as potential transfer vehicles [16–20]. Moreover, ISO objects [21] and even planets can serve as transporters of complex molecules through space. This is supported by the recent discovery of an extragalactic planetary companion around HIP 13044 in our Galaxy [22]. HIP 13044, a very metal-poor star on the red Horizontal Branch and a member of the Helmi stream, was probably bounded to the Milky Way several Gyr ago from a satellite galaxy. Because of the long galactic relaxation timescale, it is most likely that its planet (HIP 13044 b with mass of 1.25 mass of Jupiter) was not captured by any Milky Way star. Interstellar and intergalactic meteoroids, able to transfer molecules, are very difficult to observe. Therefore, we do not have reliable information about their population density and dynamics. Unlike them, interstellar dust grains (.1 µm in size) have been intensively studied for a long time [23]. Dust grains mainly flow with interstellar gas. For example, due to uneven distribution of brighter star in the Galaxy, dust grains can have speed s of 2 to 10 km s−1 relative to the gas due to the radiation pressure [24]. Betatron mechanism (i.e., acceleration happens when the particle drift motion is in resonance with changes in the induction electric field caused by the variable magnetic field) can accelerate them up to 30 to 100 km s−1. Finally, dust grains and gas can be expelled into the intergalactic space [25,26], particularly in galactic regions of violent star formation and death. If such particles end up in a thick cluster of galaxies, they can be destroyed by hot intergalactic gas in the cluster with temperature in the order of ten million kelvin. In contrast, a particle can reach another galaxy and survive. In order to establish the importance of IMPs as material transporters, we ought to resolve their physical-dynamical characteristics, and impact probabilities. In this study we consider the exoplanets in habitable zones (HZEP) as targets and IMPs as a projectile on a trajectory crossing their orbits. We focus on the random probability that an IMP, during its cruise through our Galaxy, will collide with some of HZEP. Sci 2019, 1, 47 3 of 16 2. Materials and Methods The statistical impact probability of IMPs with HZEP, can be equivalently stated as calculating probability of cooccurrence of a planet being in the habitable zone and hit by an IMP. As the geophysical properties of potentially habitable exoplanets are currently unknown, it is not possible to determine exact HZEP probabilities. Instead, we calculated HZEP probabilities as a probability density function with respect to observationally constrained planet properties (distances and radii), assuming a very optimistic geometrical HZ boundaries. The probablity density function was estimated by machine learning implementation of 2D kernel density estimate (KDE) in Python. It is well known that the impact probabilities of projectiles (of negligible dimensions, moving on − Keplerian orbits around Sun) with terrestrial planets in our system are .10 8 per orbital revolution [27]. Estimating impact probability for each exoplanet by counting the number of hits onto the collisional sphere with a good statistical accuracy, would require sample size of (~1012) projectiles or even larger for each of them [27]. To circumvent the computational problems associated with such large number of projectiles, we instead applied a probabilistic approach inspired by previous work on directed panspermia [28,29]. We modify the approach by adopting that particle travel along linear trajectory at the orbital velocity of 10−3c, and the radius of an exoplanet to estimate the capture probability. An eccentricity of IMPs trajectory depends on its perihelion distance and velocity. The larger its perihelion distance (or larger its velocity relative to the Sun), its trajectory would be less modified by gravitational acceleration, while its eccentricity would increase. Thus, very distant IMPs will traverse almost straight lines (i.e., eccentricities converging to infinity) (see [30]). For simplicity, we will assume that an IMP follows a straight line when entering into our Galaxy from position of our solar system. Trajectory of an IMP is within ecliptic plane and perhaps further studies should make use of 3D probes. Calculated HZEP probabilities are small due to small sample of HZEP confined in very large parametric space. Also, hit probabilities are small as a ratio of exoplanet cross section area and IMP’s letal area.