On the Ablation of Meteors and the Implications on Organic Delivery to Earth

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Graduate Theses and Dissertations Graduate School

October 2019

Christopher Alan Mehta University of South Florida

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On the Ablation of Meteors and the Implications on Organic Delivery to Earth

Christopher Alan Mehta

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy with a concentration in Cosmochemistry School of Geosciences College of Arts and Sciences University of South Florida

Major Professor: Matthew Pasek, Ph.D. Aurelie Germa, Ph.D. Jennifer Collins, Ph.D. Laurie Barge, Ph.D.

Date of Approval: October 17th, 2019

Keywords: Planetary Geology, Prebiotic Chemistry, Origin of Life.

DEDICATIONS

This dissertation is dedicated to my family. I would not be the person I am today without them.

ACKNOWLEDGEMENTS

I would like to thank my family Sunil Mehta, Janvi Mehta, Brian Mehta, and Andrea

Mehta for their love and support during my educational endeavors. I would especially like to thank my advisor Dr. Matthew Pasek for mentoring me through this process. A special thanks goes to Dr. Aurelie Germa, Dr. Jennifer Collins, Dr. Laurie Barge, and Dr. Maria Womack for helping me on my dissertation and for being on my committee. In addition, I would like to acknowledge Jennifer Lago, Dr. Maheen Gull, Dr. Arthur Omran Tian Feng, Josh Abbatiello,

Hanlei Zhang, Carylon Lang, Danny Lindsey, Quinton Vitelli-Hawkins, Kaylie Headings,

Anthony Perez, Lori Palaio, Mellyssa Green, Dr. John Dunbar, and Francisco Arreola.

I would also like to thank Paul Flaherty, Dr. Brian Belson, Mike Holmes, Jess Williams,

Rich Henning, Jack Parrish, Leonard Miller, Akshar Patel, RADM Nancy Hann, Joe Green,

Barry Damiano, Ian Sears, and others who worked with me at the National Oceanic and

Atmospheric Hurricane Hunters for helping me become a better leader and scientist.

Lastly, I would like to thank Monster Energy drink for providing me with the necessary amounts of caffeine to complete this dissertation. Unleash the Beast, indeed.

TABLE OF CONTENTS List of Tables ...... ii

List of Figures ...... iii

Abstract ...... vi

Chapter 1 ...... 1 1.1 Summary of different types of Meteorites ...... 2 1.2 Past Studies ...... 3 1.3 Radiometric Dation of Meteorites and Clues to the Early Solar System ...... 6 1.4 Organics in Meteoroids, Meteors, and Meteorites ...... 8 1.5 Meteor Ablation ...... 9 1.6 Log-Log and Meteor Fragmentation through Ablation ...... 9

Chapter 2. Caveats to Exogenous Organic Delivery from Ablation, Dilution, and Thermal Degradation ...... 13 2.1 Abstract ...... 13 2.2 Introduction ...... 15 Meteor Energy Loss Due to Ablation ...... 15 Thermal Diffusion and Meteor Ablation ...... 16 Meteoroid Source Region and Distribution on Impact ...... 17 2.3 Methodology ...... 19 Ablation Model ...... 19 Strewn Field Analysis ...... 22 Thermal Diffusion and Chemical Kinetics Model ...... 22 2.4 Results ...... 23 Strewn Field Analysis Results ...... 24 Radiation Model Results ...... 28 2.5 Discussion ...... 28 Calculation of Exogenous Material to The Early Earth ...... 32 2.6 Conclusion ...... 32

Chapter 3. The Power-Law and Mass Distributions of Meteoroids and Meteorites ...... 34 3.1 Abstract ...... 34 3.2 Introduction ...... 36 3.3 Methodology ...... 38 Meteorite Mass-Number Distribution ...... 38 Ablation Model ...... 40 Effect of Physical Variables on Ablation...... 41

i 3.4 Results ...... 42 Effects of Varying Angle of Entry, Initial Velocity, and Aspect Ratio ...... 43 Monte Carlo Simulation ...... 52 3.5 Discussion ...... 53 3.6 Conclusion ...... 56

Chapter 4. Ablation of Carbonaceous Asteroids and Organic Flux Delivery...... 57 4.1 Abstract ...... 57 4.2 Introduction ...... 58 4.3 Methods...... 58 4.4 Results ...... 61 4.5 Discussion ...... 63 4.6 Conclusion ...... 64

Chapter 5. Concluding Remarks ...... 66

References ...... 69

LIST OF TABLES Table 1.1. Rate of meteor impact of Earth ...... 5

Table 1.2. Summary of common organics found on the Murchison meteorite ...... 11-12

Table 2.1. Parameters used in ablation model ...... 21

Table 2.2. Minimum initial mass for impact to occur...... 26

Table 2.3. Percent of meteors that impact the surface with respect to atmosphere ...... 27

Table 3.1. Alpha values calculated using maximum likelihood ...... 44

Table 3.2. Slope values for finds and falls ...... 44

Table 4.1. Values used to calculate flux ...... 61

Table 4.2. Final mass as a function of initial velocity for 13,000 kg asteroid ...... 62

Table 4.3. Final mass as a function of initial velocity for a 20,000 kg asteroid ...... 66

iii

LIST OF FIGURES Figure 1.1. Family tree of meteorites ...... 4

Figure 2.1. Sketch of meteor ablating within Earth’s atmosphere ...... 21

Figure 2.2. Ablation values with respect to modern day atmospheric conditions ...... 25

Figure 2.3. Ablation values with respect to a thin, nitrogen, atmosphere ...... 25

Figure 2.4. Ablation values with respect to a carbon dioxide atmosphere ...... 26

Figure 2.5. Relationship between total mass recovered and the area over which fragments were recovered ...... 27

Figure 2.6. T-t-r profile ...... 28

Figure 2.7. Timescale it takes to degrade valine as a function of temperature ...... 29

Figure 2.8. T-t-r profile for 300mm radius ...... 33

Figure 3.1. Combined Antarctic ordinary chondrite finds ...... 45

Figure 3.2. Combined ordinary chondrite falls ...... 46

Figure 3.3. Mass distribution of a 100 kg spheroidal meteor entering atmosphere with varying angle of entry ...... 47

Figure 3.4. 100 kg object ablating at varying initial velocities ...... 48

Figure 3.5. 10,000 kg streamline meteor entering atmosphere at varying angle of entry ...... 49

Figure 3.6. 100 kg conical meteor entering atmosphere at varying angle of entry ...... 49

Figure 3.7. 100 kg conical meteor entering atmosphere at varying velocities ...... 50

Figure 3.8. Shape dependent final mass ...... 51

Figure 3.9. Shape dependent final velocity ...... 52

Figure 3.10. Final mass distribution of Monte Carlo simulation ...... 53

iv Figure 3.11. Log of the mass squared vs rank on the Antarctic ordinary chondrite finds ...... 55

Figure 4.1. Vaporization time of a 13,000 kg C-asteroid entering the atmosphere ...... 62

ABSTRACT

The synthesis of prebiotic organic compounds is a key step in the origin of life. Sources of these materials are divided into endogenous and exogenous sources. Endogenous synthesis— occurring potentially on the surface of the Earth—includes such historic experiments as the

Miller spark discharge and formose chemistry. However, one avenue for exogenous synthesis to occur is when meteors enters an atmosphere. Using principles of orbital mechanics, geology, physics, and chemistry, we study meteor ablation and the transport of organic matter to the surface of Earth. To do so, I create numerical models that simulates meteors traveling through the atmosphere of Earth to the surface. Then, I determine the key variables that dictate the rate of ablation of meteors to understand why meteorites follow a power-law mass distribution. Lastly, using data obtained from understanding the mass distribution relationship between meteoroids and meteorites, I calculate the minimum velocity needed for a carbonaceous asteroid that is 3

AU’s from the Sun to enter the atmosphere of Earth. The findings in this dissertation show that there are many conditions that need to be satisfied for meteors/asteroid to make it to the Earth’s surface with enough mass (and organics) to substantially aid in any prebiotic processes necessary for life. In general, I find that meteors only provided trace amounts of organic matter to the surface and other avenues such as hydrothermal vents and spark discharge provide most of the organic constitutes necessary for life on Earth.

CHAPTER ONE

INTRODUCTION

A hypothesis in prebiotic chemistry argues that organics were delivered to the early Earth

in abundance by meteoritic sources (Jenniskens et al., 2000). This study tests that hypothesis by

measuring how the transfer of organic matter from meteors to the surface of Earth is affected by

energy-dissipation processes such as ablation and airbursts. Exogenous delivery has been relied

upon as a source of primordial material, but it must stand to reason that other avenues (i.e.,

hydrothermal vents, electric discharge) played a bigger role in the formation of life as we know it

on Earth if exogenous material was unable to deliver significant quantities of organics (greater than 1015.5 kg for spark discharge over a billion year period per Chyba and Sagan, 1992). For this

dissertation, I look at various properties of meteors such as initial velocity and mass of the object,

and atmospheric composition to see how meteors with different initial velocities and masses ablate.

The synthesis of prebiotic organic compounds is a key step in the origin of life, and sources

of these materials are divided into endogenous and exogenous sources. Endogenous synthesis—

occurring potentially on the surface of the Earth—includes such historic experiments as the Miller

spark discharge (Miller, 1953) as well as formose chemistry (Gargaud et al., 2015). However,

environmental factors appear to be an important restraint for endogenous prebiotic synthesis. For

example, the lack of reduced gases such as H2 and CH4 could have greatly inhibited synthesis by

spark discharge and the presence of atmospheric ammonia is predicted to have been lost quickly

(Kuhn and Atreya, 1979; Furukawa et al., 2015; and Buchwald et al., 2016). To this end, exogenous

delivery of organics may have provided the key components of early prebiotic chemistry. Chyba

and Sagan (1992) outline the three ways exogenous material on meteoric sources may have

synthesized organic material on the early Earth: extraterrestrial origins are synthesized prior to

Earth entry through avenues such as radiation and delivered intact by meteorites, organic

compound synthesis from ablation when entering Earth, and lastly by impact shock on the surface

of Earth (Chyba and Sagan, 1992; Johnston et al., 2008). In this study, we examine how objects

ablate through Earth’s atmosphere to provide better constraints on the delivery of exogenous

organic matter.

To accurately understand the transport of exogenous organic matter, we must first understand how meteors ablate when traveling through the atmosphere of Earth and how much organics will survive the ablation process. Then, we must study the distribution of meteors in a

concentrated area to see how concentrated they are with fragments. Once this is fully understood,

the meteoroid/meteorite mass relationship is studied to see if there is a mathematical relationship

between the mass of meteoroids and meteorites. Lastly, using information collected from these studies, we then examine the total flux of carbon delivered to the Earth from a carbonaceous asteroid

1.1 Summary of different types of Meteorites

There are two groups of meteorites which are of interest to scientists studying transport of

prebiotically-relevant matter through extraterrestrial sources: chondrites (especially carbonaceous

chondrites) and iron meteorites (for phosphorus, see Pasek and Lauretta 2005). There are fifteen

types of meteorites that fall within the chondrite group (Pasek and Lauretta, 2008). Of the fifteen,

eight are classified as carbonaceous, three are classified as ordinary, and others fall within the

subcategories of enstatite chondrites, R chondrites, and K chondrites (Pasek and Lauretta, 2008). 2

Iron meteorites can be placed into fourteen major groups with about a remaining 110 objects

ungrouped (Weisberg et al., 2006).

There are three main types of meteorites: stony, stony-irons, and irons (Pasek, 2017). The stony group of meteorites consists of Chondrites and Achondrites (Pasek, 2017). Chondrites are one of the most common of the group and are defined by the presence of chondrules (spherical

amalgamations of silicate minerals) whereas Achondrites do not have chondrules. Achondrites are

among the oldest objects in the solar system (Pasek, 2017). In addition, there is also a class of chondrites, called the carbonaceous chondrites, which are composed of minerals such as serpentine and olivine. They also contain high amounts of elements such as aluminum and calcium (Pasek,

2017). Refer to Figure 1.1 for a family tree of meteorites.

A meteorite can be collected in two ways. It can be observed to fall through the atmosphere

(called a “fall”) or it can be obtained by finding it on the surface (meteorite finds). Most of the meteorites are found after they impact the surface (Ouknine et al., 2019). In addition, meteorite finds in the desert or Antarctic are easily spotted because the object in a white background are easier to spot with the human eye. On the other hand, meteorites in other environments can be more difficult to locate because they will be camouflaged with the surroundings (Ouknine et al.,

2019).

1.2 Past Studies

Broadly, we distinguish three size groups of extraterrestrial material: large impactors,

meteorites, and interplanetary dust particles/micrometeorites (Glavin and Bada, 2001). There is

necessarily a continuum between these divisions given that differentiating between large micrometeorites and small meteorites and between large meteorites and moderate-sized impactors

3 is not straight-forward. However, as a rule, the Earth is subjected to a high rate of impact (per year) from smaller meteors; the more massive the object, the less frequently it impacts Earth.

Nevertheless, when these massive objects do impact the surface, they do so with almost all their initial mass still intact. Table 1.1 shows the rate of impact of meteors with varying initial masses, the amount of matter transported per Earth year, and the average time between impacts.

Iron Stony-Iron Stone

Hexahedrite Octahedrite Ataxite Pallasite Mesosiderite Chondrite Achondrite

Ordinary Enstatite Carbonaceous Other Primitive Differentiated Planetary

Low-Low Metal EH CV R Ureilite Aubrite Lunar

Low Metal EL CO K Brachinite Angrite Martian

Howardite, Acapulcoite/Lo High Metal CM Eucrite, and dranite Diogenite

CK Winonaite

CB/CH

Figure 1. 1. Family tree of meteorites.

Intuitively, the delivery of organics to the surface of the early Earth requires that the organic compounds (see section 1.4) remain relatively unchanged from their synthesis in the interstellar medium or through aqueous alteration to reaching the surface of the Earth (Chyba and Sagan,

1992). Ablation proves to be an obstacle in this area (Goldstein et al., 2009). For an organic compound to reach the surface of Earth, it must survive thermal heating as it falls through the atmosphere. A meteor must also lose enough energy through both radiation and ablation during

the descent to reach the surface of the Earth while remaining relativity intact (Goldstein et al.,

2009).

Table 1.1. Rate of meteor impact on earth.

*Table adapted from Bland and Artemieva (2006) that shows the delivery by mass to the earth per year of meteors with specific initial masses, and the interval between falls of a given mass. For example, meteorites with an initial mass of 1 kg fall roughly four times every hour (0.00003 years), delivering a net 37,000 kg/year.

Past studies have developed computational models that calculate the amount of mass lost by

an object entering an atmosphere. For example, Bland and Artemieva (2006) modeled the ablation of meteors as they plummet through Earth’s atmosphere and as they impact the surface. This model is based on a series of equations that use physical characteristics of meteors that are crucial to solving for the ablation process. The authors also modeled meteor fragmentation that occurs during the ablation process. These models, coupled with statistical methods, provide estimates of the impacting frequency of these objects to the surface of Earth. Bland and Artemieva conclude that

5 chondrites that have an initial mass of greater than 50,000 kg impact the surface every fifty years.

Another significant study in ablation comes from Baldwin and Sheaffer (1971) who developed a model to predict ablation of objects as they enter the Martian atmosphere.

Hills and Goda (1993) discuss the importance of studying celestial objects traveling through our atmosphere and eventually impacting the surface of Earth. They focus on the consequences of the impact: the obvious of which is the loss of life and damage associated with the impact. By studying objects of varying composition (such as iron, stone, comets, and disaggregated material), they conclude that for massive objects, low levels of ablation and fragmentation occurs (Pizzarello and Shock, 2010). Lastly, Chyba, et al. (1993) discuss the well-known impact over Tunguska,

Siberia in 1908. In this study they employ a computational model of different atmospheric conditions to better understand the impact of this large object, coupled with actual observed data from people living in the region at the time. This dissertation utilizes methods from past studies to create an advance numerical model to simulate the ablation of meteors and gain understanding on how it potentially influences the transport of organics from meteoritic sources.

1.3 Radiometric Dating of Meteorites and Clues to the Early Solar System

Meteorites are one of the central tools we have in understanding the formation of our Solar

System. Calcium–Aluminum rich inclusions (CAIs) are the oldest objects in our Solar System

(approximately 4.6 billion years old) that formed by the condensation of matter left behind from the solar nebula of the Sun’s predecessor (Moynier et al., 2015). Coupled with basaltic angrites, they hold valuable information about the age of our Solar System and the formation of planets and moons.

Per Amelin (2008) some of the earliest sources of differential materials in our Solar System

are the basaltic angrites, which are a type of stony meteorite. Basaltic angrites, because of their

low degree of thermal metamorphism and shock effects, prove to be useful tools in understanding

the age and formation of our Solar System. Using Pb-Pb isochron dating methods, the authors were

able to better understand the age of our Solar System (McNeil et al., 1998). In addition, meteorites

have radiochronometers (26Al-26Mg and 182Hf-182W) that are used to understand timescales less than a million year in our Solar System (Amelin, 2008). Studying these radiochronometers helps

us determine differentiation and accretion events that led to how our Solar System became the way

it is today (Amelin, 2008; Bouvier et al., 2011). Furthermore, the formation of CAIs on meteoroids

can also give us information of the differentiation of celestial bodies (Kleine et al., 2009). Hf-W

are refractory elements that are abundant in chondrites, which tells us valuable information about

planetary formation (Kleine et al., 2009).. Kleine and others study this to augment our

understanding on the early evolution of our Solar System. Bouvier et al. (2011) study the NWA

2976 meteorite to make correlations to the age of the Solar System. They do so by utilizing U

isotopic analyses to conduct Pb-Pb dating techniques (Bouvier et al., 2011).

One of the rarest meteors found on Earth are those that originated from different planets.

Instinctively, it is apparent that they are rare because the object must have been ejected from the

surface of the parent planet via asteroid impact or some other avenue that releases high amounts

of energy to send objects at speeds higher than escape velocity for the parent planet. Furthermore,

the orbit of Earth must be in the right position for the meteoroid to enter the atmosphere and make

it to the surface. These objects hold valuable information about not only the formation of the Solar

System, but the formation and composition of the parent planet (or celestial object) it came from

(Koefoed et al., 2016). For example, Koefoed et al. (2016) studied the Northwest Africa (NWA)

7325 meteorite that is believed to originate from the planet Mercury. The Rare Earth Element

(REE) patterns and Mn/Mg ratio of olivine and high calcium pyroxene mineralogy show that the

object formed as a plagioclase rich cumulate from mafic, high magnesium and iron, magma

(Koefoed et al., 2016). There are more interpretations one can make based on the chemical makeup

of a meteorite which can provide clues to the formation of planetary bodies. For example, if the object has a highly reduced oxidation state, it must have been formed near the Sun in order to for this to occur (Koefoed et al., 2016). Lastly, the authors of the article gives the example that, due to the company of live 26Al in a number of achondrites, it must stand to reason that 26Al could have

been a heat source for planetesimal differential in the early stages of our Solar System (Koefoed

et al., 2016).

1.4 Organics in Meteoroids, Meteors, and Meteorites

Most of our current understanding of organic matter on meteorites comes from the

Murchison meteorite (Sephton, 2004; Aponte, et al., 2014; Hashiguchi and Naraoka, 2019;).

Furthermore, some of the organic matter takes the form of free molecules such as hydrocarbons,

amino acids, carboxylic acids, and aromatic networks which are all imbedded within the inorganic

meteorite matrix (proved by taking thin-section samples of various meteorites found on Earth). It is important to model the ablation of these objects because these organic, especially amino acids

(as they are central to making proteins), played a role to forming life as we know it one Earth

(Chyba et al., 1990; Chyba and Sagan, 1992; and Sephton, 2004). See Table 1.2 for list of common types of organic compounds found on the Murchison meteorite.

1.5 Meteor Ablation

When the aerodynamic pressure from the atmosphere exceeds the strength of the meteor, ablation occurs. This process generates heat from atmospheric entry and breaks up the meteor,

causing it to lose mass. Further, Zinn et al. (2004) state that when a meteor ablates, the material

ablated has a forward velocity that is equivalent to the velocity of the meteor as it makes the

transition from space to the surface. This is the predominant process in depositing the energy of

the meteor into the atmosphere of Earth and converting kinetic energy of the object into the air

(Zinn, et al., 2004). In addition, the ablated particles, along with the energy created by the ablation process, fall behind the meteor and in the tail (Zinn et al., 2004). Energy involved in the ablation

process also gets transferred into heating the meteor (which causes even more ablation) and also

into the surrounding atmosphere (Zinn et al., 2004). Most the energy that is transformed into the

surrounding atmosphere goes into air, breaking the ablated material (Zinn et al., 2004).

1.6 Log-Log and Meteor Fragmentation through Ablation

Generally, many things in nature follow a power-law distribution (Newman, 2004). For

example, the number and magnitude of earthquakes, and even the number of papers written by

fellow scientists (Newman, 2004). The ablation of meteors in terms of initial mass before ablation

and final mass (mass of meteorite) is no exception to this rule. When the masses are plotted against

each other utilizing a logarithmic scale, the trend is linear (see Chapter 3). This dissertation

explores the transport of organic matter by meteoric sources which can be accomplished by fully

understanding power-the law relationship between initial and final mass. The first subject of this

dissertation studies the influence ablation has on meteors entering the atmosphere of Earth and

how that affects prebiotic chemistry. The second subject of this study why meteors/meteorites

appear to follow a power law or a log-log distribution. Objects within the asteroid belt generally 9

follow this distribution, however, the sizes are limited to what is observable telescopically

(generally greater than 100 m diameter). Additionally, smaller asteroid and meteoroid debris

should also follow a similar power-law trend, with the best option for studying this smaller group

coming from the global collection of meteorites. However, due to atmospheric ablation, meteorites

may have been altered from their initial (meteoroid) size distribution. This dissertation also

explores the influence of various orbital mechanical and physical properties on the ablation of

meteors to understand how the mass distribution of meteoroids transforms to meteorites (focusing

specifically on ordinary chondrites and the extent to which they follow a power-law). To do so, I employed a Monte Carlo simulation that produces random angle of entry, initial mass and velocity, along with shape values, and compare the simulated values to empirical fall and find data. Lastly,

I see if any of these results rely on the structure mechanics of meteors and what it means for prebiotic chemistry.

Table 1.2. Summary adapted from Sephton (2004) of common types of organic compounds found on the Murchison meteorite. Compounds Examples Structure

Amino acids L-alanine

Carboxylic Propionic acid

acids

Hydroxy Lactic acid

acids

Sugar Dihydroxyacetone

compounds

*Structures obtained by MolView (http://molview.org).

Table 1.2. Continued Compounds Examples Structure

Sugar Dihydroxyacetone

compounds

Amines Propylamine .

Amides Pyroglutamic acid

Aromatic 2-

hydrocarbons methylnapthalene

*Structures obtained by MolView (http://molview.org).

CHAPTER TWO

CAVEATS TO EXOGENOUS ORGANIC DELIVERY FROM ABLATION, DILUTION,

AND THERMAL DEGRADATION

Note to Reader: This chapter has been published: Mehta, C., Perez, A., Thompson, G., and Pasek, M.

(2018). “Caveats to Exogenous Organic Delivery from Ablation, Dilution, and Thermal

Degradation.” Life 8 (2): 13. https://doi.org/10.3390/life8020013.

2.1 Abstract

A hypothesis in prebiotic chemistry argues that organics were delivered to the early Earth

in abundance by meteoritic sources. This study tests that hypothesis by measuring how the

transfer of organic matter to the surface of Earth is affected by energy-dissipation processes such

as ablation and airbursts. Exogenous delivery has been relied upon as a source of primordial

material, but it must stand to reason that other avenues (i.e., hydrothermal vents, electric

discharge) played a bigger role in the formation of life as we know it on Earth if exogenous

material was unable to deliver significant quantities of organics. For this study, we look at

various properties of meteors such as initial velocity and mass of the object, and atmospheric

composition to see how ordinary chondrites with different initial velocities and masses ablate.

We find that large meteors do not slow down fast enough and thus impact the surface, vaporizing

their components; fast meteors with low masses are vaporized during entry; and meteors with

13 low velocities and high initial masses reach the surface. For those objects that survive to reach the surface, about 60-99% of the mass is lost by ablation. Large meteors that fragment (103-105 kgs) are also shown to spread out over increasingly larger areas with increasing mass, and small micrometeors (~1 mm) are subjected to intense thermal heating, potentially degrading intrinsic organics. These findings are generally true across most atmospheric compositions. These findings provide several caveats to extraterrestrial delivery models that—while a viable point source of organics—likely did not supply as much as an effective endogenous production route.

Key words: geology; cosmochemistry; astrobiology; ablation

2.2 Introduction

The synthesis of prebiotic organic compounds is a key step in the origin of life, and sources

of these materials are divided into endogenous and exogenous sources. Endogenous synthesis—

occurring potentially on the surface of the earth—includes such historic experiments as the

Miller spark discharge (Miller, 1953) as well as formose chemistry (Gargaud et al., 2015).

However, environmental factors appear to be an important restraint for endogenous prebiotic

synthesis. For example, the lack of reduced gases such as H2 and CH4 would have greatly

inhibited synthesis by spark discharge and the presence of atmospheric ammonia is predicted to

have been lost quickly (Buchwald, et al., 2016; Furukawa,et al., 2015; Kuhn and Atreya, 1979).

To this end, exogenous delivery of organics may have provided the key components of early

prebiotic chemistry. Chyba and Sagan (1992) outline the three ways exogenous material on

meteoric sources may have synthesized organic material on the early earth: extraterrestrial

origins are synthesized prior to Earth entry through avenues such as radiation and delivered

intact by meteorites; organic compound synthesis from ablation when entering Earth, and lastly

by impact shock on the surface of Earth (Chyba and Sagan, 1992; Johnston et al., 2008). In this study, we examine how objects ablate through Earth’s atmosphere to provide better constraints on the delivery of exogenous organic matter.

Meteor Energy Loss Due to Ablation

Depending on velocity, size, and composition a meteor entering the atmosphere could either explode (vaporize) before reaching the surface, or impact the surface (Cooper et al., 2001).

Understanding energy properties of the ablating meteor is cardinal towards understanding the fate of the meteor as it travels through the atmosphere of Earth. Interestingly, the energy required

to vaporize a meteor traveling at high speeds is much smaller than the initial kinetic energy of

the meteor (Nooner and Oró, 1967). In Zinn et al. (2004), the authors study the interactions of

Leonids meteors and Earth’s atmosphere. One of their findings was that the meteor vaporized

before it notably decelerated from the its entry velocity. In addition, the authors note that meteors

start out with a forward velocity identical to the initial velocity of the meteor. The major process

that is involved in the dissipation of meteor energy in the atmosphere is the transformation of the

kinetic energy to energy loss by ablation and heating of meteor mass. The energy of the ablated

meteor is dissipated with celerity and a good portion of the mass of the meteor is in its tail, where

the meteor breaks into finer particles (Cooper et al., 2001). Lastly, in our studies, we calculated

the maximum speed an object can hit the surface of Earth without vaporizing. This speed was

found to be greater than or equal to the escape velocity of Earth (see Discussion.). This is constant with a simple calculation utilizing the equation for kinetic energy (KE = ½ mv2) in

which we compare the final velocity at the surface and compare this to the enthalpy of

vaporization for rock (~10-15 MJ/kg per Pasek and Hurst 2016).

Thermal Diffusion and Meteor Ablation

Understanding the implications heating has in the ablation process of a meteor is still

somewhat new and there is still much work in this area that needs to be done to have a better

understanding on how the organics in a meteor may become altered by high temperatures during

ablation. It is obvious that the exterior of a meteor is heated to the melting point of rock based on

the presence of a glassy fusion crust, but the penetration of heat to the interior of a meteorite has

conflicting reports of hot and cold from actual observers (Nooner and Oró, 1967; Vinković,

2007). Vinkovic (2007) suggests that thermal diffusion process is at its most influential stage in

16 terms of ablation of meteors. During the ablation process, the meteor is interacting with atmosphere particles and if the conditions are right will be shielded by vapors and particles of the meteor. Vinkovic states that when the Knudsen number (Kn, which is defined as the dimensionless ratio of the atmosphere mean free path and the size of the entering body) is less than 100, the particles and vapors surrounding the meteor act as a barrier which protects the meteor from atmospheric influenced ablation and, when this happens, one of the ways the meteor augments energy loss is though radiation (Vinković, 2007).

Meteoroid Source Region and Distributions on Impact

Our knowledge of size distribution of asteroids and meteors—the parent source of meteorites—is still growing and there have been many attempts to understand the rate of Earth impacts for these objects (Cziczo et al., 2001; DeMeo and Carry, 2013; Zappala, et al.,1969;

Gladman et al., 2009). In our Solar System, the area of that is most densely populated with asteroids is located 1.8 to 4.0 Astronomical Units (AU) from Earth (Britt, Guy Consolmagno, S.

J., and Lebofsky, 2014). Other areas with debris include the Kuiper Belt and the Oort Cloud, which is further towards the edges of our Solar System (Britt et al., 2014). Lastly, there are objects close to Earth called Near-Earth Objects (Britt et al., 2014). Per Britt et al. (2014). 1036

Ganymed is the largest Near-Earth Object and has a diameter of about 38.5 km. Smaller objects greatly outnumber larger objects (Brown, 1960), but the larger objects may have more mass than all the smaller objects combined. In our study, we model meteors with initial masses ranging from 0.02 kg to 170,000 kg with varying initial velocities as they enter the atmosphere of Earth to determine how they ablate and if the organics in the meteor can survive the ablation process.

The initial velocities are varied from 10,000 m/s to 42,000 m/s. The former corresponds to Near-

Earth Objects that begin with a velocity equal to the escape velocity, or the velocity an object effectively has when captured by the gravitational pull of the earth. The higher velocities correspond to meteoroid source regions in the outer asteroid belt, which presumably is more likely to be carbonaceous. If the meteor can successfully survive the atmospheric entry process, then the main mass along with pieces that were fragmented off it while making the transition from being a meteor to meteorite provide organics over a confined region. Therefore, to study how concentrated an area is with meteorites, we examine the relationship of strewn field areas and meteorite masses. If an area can be highly concentrated with fragments of meteorites, then the amino acids and other organics present in the object could in fact interact with the surrounding environment to aid in prebiotic chemical processes present on the early Earth. We measured how the transfer of organic matter to the surface of the Earth is affected by ablation using the Riemann sum approximation. When a meteor ablates through Earth’s atmosphere the pieces are dispersed laterally and create an elliptical profile of fragments. Strewn fields are areas, often elliptical by nature, in which fragments of meteorites are found. Therefore, we also examine strewn fields and determine whether the total area of the field and the total recovered meteoric mass is enough to be a catalyst in prebiotic chemistry. The ablation model solves two equations describing velocity and change of mass (see equations 1 and 2). The atmospheric density is that of Earth and was set to 40.1 moles per meters cubed and decreases with height according to the scale height (eg. folding distance, or ~6-7 km). Bland and Artemieva (2006) describe a set of differential equations used to model ablation of meteors. Equation 1 describes the change in mass with respect to time and Equation 2 describes the change in velocity of the object with respect to time.

For the purposes of this study, and per Bland Artemieva (2003), we assume that the

estimated yearly flux of meteors that reach the surface all have masses greater than 0.02

kilograms. Therefore, only meteors that have a final mass of 0.02 kilograms were considered as

part of the mass flux. Given these values, the model calculated the time it takes the object to

impact Earth, the velocity along with the mass of the object at a given time, and the height-

dependent atmospheric density encountered by the object as it travels through the atmosphere to

the surface.

2.3 Methodology

We measured how the transfer of organic matter to the surface of the Earth is affected by ablation using a Riemann sum approximation. When a meteor ablates through Earth’s atmosphere the pieces are dispersed laterally and create an elliptical profile of fragments. Strewn

fields are areas, often elliptical by nature, in which fragments of meteorites are found. Therefore,

we also examine strewn fields and determine if there is a relationship between the total area of

the field and the total recovered meteoric mass, and the implications for exogenous sources in prebiotic chemistry.

Ablation Model

The ablation model solves two equations describing velocity and change of mass (1 and 2

below). The atmospheric density is that of Earth and was set to 40.1 moles per meters cubed,

and decreases with height according to the scale height (eg. e-folding distance, or ~6-7 km).

Bland and Artemieva (2006) describe a set of differential equations used to model ablation of

meteors.

(1)

(2)

Where V is the initial velocity of the meteor, m is the mass of the meteor, cd is the Drag Transfer

Coefficient, ch is the heat transfer coefficient, gis the density of Earth’s Atmosphere, A is the

Cross-Sectional Area of the meteor, g is gravity on Earth, Q is the heat of ablation, is the

Stephan-Boltzmann constant, T is temperature, and is the angle the meteor enters Earth’s

atmosphere. The initial distances for all meteors are set to 200 km and the angle of entry for all

the simulations was set to 45 degrees. The distance is calculated by the following calculation:

D = (3)

where, DN-1 is the previous value of D, VN-1 is the velocity of the meteor at the previous distance,

tN is the current time step and tN-1 is the previous time step. Initial mass of the meteors varied and all successive masses were calculated by formula 2 where MN-1 is the calculated value of the

mass preceding time steps.

M = (4)

For the purposes of this study and per Bland and Artemieva (2003), we consider only the flux of

meteors that reach the surface that have masses greater than 0.02 kilograms. Therefore, only

meteors that have a final mass of 0.02 kilograms were considered as part of the mass flux. Given

these values, the model calculated the time it takes the object to impact Earth, the velocity along

with the mass of the object at a given time, and the height-dependent atmospheric density encountered by the object as it travels through the atmosphere to the surface. The parameters used in this study are summarized in Table 2.1.

Table 2.1. Parameters used in ablation model.

Figure 2.1. Sketch of meteor ablating within Earth’s atmosphere.

Strewn Field Analysis

A second consideration of meteoritic delivery is the actual concentration of meteoritic

material over a geographic area. Since many meteorites fragment on entry, meteoritic masses are

often spread over a region called a strewn field, confined to an ellipse where the masses are

ultimately located. To determine if the surviving organic matter can be distributed in a large

enough area to aid in prebiotic chemistry, strewn fields are also studied because of their role in

the transport of organic matter through meteoritic sources. For the intents of this study, a strewn

field is defined as an area, often elliptical, in which fragments of meteorites are found. 1MetBase, a meteorite information database software that catalogs the fall and the 1impact site meteorites, is

used to study the disbursement of fragments and organic matter from meteors.

Thermal Diffusion and Chemical Kinetics Model

One potential deleterious avenue that may affect semi-stable organic compounds within

meteors is degradation through thermal diffusion of a meteor as it heats up and sheds mass, as it

makes it transition from space to the surface of Earth (Suttle et al., 2017). We examine this by

creating a computational model that calculates the heating profile occurring when a meteor is

heated up by the atmospheric entry. This is achieved by solving a differential equation (Equation

5), which considers factors such as thermal conductivity, temperature, radius of a spherical

meteor, and time between the iterations of calculations performed. Equation 5 solves for the

1 MetBase: Meteorite Information Database, http://www.metbase.org, 1994-2017, GeoPlatform UG, Germany.

change in temperature with respect to radius where r is the radius in mm, T is the temperature in

K, and α is the diffusion coefficient (set to 1 mm2/s. e.g. Pasek et al. 2012).

(5)

To this temperature-time (Tt) profile we add the kinetics of the decay of amino acid from

Yaboklov et al. (2013) wherein the stability of valine and other amino acids were investigated to

determine the rate of their decomposition as a function of time. The decomposition rates were

found to be 1st order with respect to amino acid quantity in the solid phase, and hence are likely

related well to the phases found in chondrites. These data provide Arrhenius equations such as:

ln = 1.78 × 10 −160 (6) 11 𝑅𝑅𝑅𝑅 𝑘𝑘 𝑒𝑒 where R is 0.008314 kJ/mol K and T is the temperature in Kelvin. Using this data, we

approximate the thermal stability of organics in meteors ranging in size from 0.1 mm to 10 mm

heated for 0.1 to 10 seconds and with thermal diffusivity constants of 0.1 mm2/s to 10 mm2/s with an outside edge heated to 1000 K, an estimate of the melting point of chondritic material.

2.4 Results

On average, objects traveling at initial speeds of 10,000 m/s all reach the surface with 50

to 60% of their mass so long as they are at least 0.05kg before entering the atmosphere. Objects

traveling at speeds of 14,000 m/s impact the surface with 26-36% of their initial mass intact

(Figure 2.2). Meteors with initial velocities of 18,000 m/s reach the surface with only 11-17% of

their initial mass. If the initial velocity is 22,000 m/s, objects are subjected to more heating, thus

more readily ablate and reach the surface with 3-5% of their initial mass. However, as the initial velocity increases, a meteor is subjected to even more ablation. For example, meteors with initial velocities between 26,000 to 38,000 m/s reach the surface with only 0.9 to 0.0001% of their starting mass. Table 2.2 summarizes the minimum initial mass, in kilograms, that is needed for a meteor to reach the surface with sufficient mass to aid in reach the surface of the earth. Using the data obtained from this portion of our study, we consider the size distribution and location of meteor objects to understand where objects that make it to the surface, and those who do not, originate from.

Strewn Field Analysis Results

Over one hundred strewn fields ranging from small to large (radial area of 1000 km2 and greater) were studied. We considered the amount of mass in kilograms that were recovered in these fields. When we analyze the different strewn fields found on Earth along compared to the total recovered meteorite mass, we can see that there is a relationship between strewn field radial area and total mass recovered. For example, we see objects within 1-9 kg are most likely to be found in strewn fields with areas in between 1- 10 km2, and 10-99 kg objects are most likely to

be found in 10-99 km2 strewn fields. When the strewn field sizes reach 100-1000 km2, the size of

the objects found reaches sizes <1000 kg. Figure 2.5 shows the relationship between the total

mass of a single meteorite recovered, and the area over which all the fragments were recovered

(the strewn field). The regression line has a slope of log A = 1.25 log M − 0.23 (R2 = 0.47)

where A is the radial area and M is the mass. This is not to say that the mass is the direct control

on strewn field area, as other factors (angle of entry, meteoroid structural integrity prior to entry)

likely play as large of roles in strewn field sizes. Some of this information is not known for these

strewn fields as many are meteorite finds. However, that there is a relationship between mass and

24 area is suggestive that the mass controls a portion of the area over which a meteorite is distributed.

Figure 2. 2. Ablation values with respect to modern day atmospheric conditions.

Figure 2. 3. Ablation values with respect to a thin, nitrogen, atmospheric conditions.

Figure 2. 4. Ablation values obtained from simulating a thick, carbon dioxide atmosphere assumed to be similar to that of the Heavy Bombardment period.

Table 2. 2. The minimum initial mass for a meteoroid before atmospheric entry for impact to occur for Earth’s modern day atmosphere.

Initial Velocity Minimum Initial (m/s) Mass (kg) 10000 0.05 14000 0.1 18000 0.2 22000 0.72 26000 2.64 30000 13.5 34000 132 38000 13,000

Table 2. 3. Percent of meteors that impacted the surface using a thin nitrogen and thick carbon dioxide based atmosphere.

Initial Velocity

(m/s) 10000 14000 18000 22000 26000 30000 34000

Thin Nitrogen 96% 92% 86% 80% 70% 58% 36% Thick Carbon Dioxide 96% 92% 86% 80% 70% 40% 48%

*Note that in the case of a thick carbon dioxide atmosphere, more meteors reached the surface when traveling at high speeds. This is because the atmosphere acted as an insulator to the meteor and shielded the object from some of the ablation process.

Figure 2. 5. Relationship between the total mass of a single meteorite recovered, and the area over which all the fragments were recovered (the strewn field).

Radiation Model Results

The thermal profile of a 1 mm radius meteor with an exterior heated to 1000 K for one second is shown as Figure 2.6. It is apparent from this calculation that the meteor is completely heated to 1000 K to its core over this short timescale (we arrive at 1 second from the timescale of peak mass loss for most meteors). In contrast, the kinetic stability of amino acids is extremely short at 1000 K. At this temperature, 99% of amino acids degrade completely in about 10-4 seconds, implying little survival of amino acids during this heating event.

Figure 2.6. T-t-r (Temperature, time, and radius) profile predicted for meteors in contact with a 1000 K surface *This model assumes a total meteor radius of 1 mm, and the dashed lines provide the temperature from the center (0 mm) to the exterior (1 mm) as a function of time.

2.5 Discussion

We find the assumption that organics originated from exogenous delivery needs to be approached cautiously. First, most of the mass of meteoroids is lost upon atmospheric entry.

For large objects, the effects of ablation are not as prominent as they are for small to medium 28

objects. For small objects (having an initial mass of 0.02 kg), ablation is an evaporative process,

completely disintegrating the object. Intuitively, this makes sense; the smaller the meteor, the

more it abates. Larger meteors have enough strength the withstand the ablation process and

impact the Earth with significant mass. Some meteors exploding while transitioning through the

atmosphere. When explosion occurs, all the organics that were on the meteor can be assumed to

be destroyed.

The following are conditions in which meteors explode during atmospheric entry: objects

that enter the atmosphere with an initial mass of 7,000 to 170,000 kg with an initial velocity of

10,000-14,000 m/s; 17,000-170,000 kg with an initial velocity of 18,000 m/s; 24,000-170,000 kg

with an initial velocity of 22,000 m/s; 65,000-170,000 kg with an entry velocity of 26,000 m/s;

and meteors that have an initial mass of 170,000 kg explode entering Earth at 30,000 m/s.

Figure 2.7. The timescale it takes to degrade valine as a function of temperature. *The black line is the time required to degrade 50% of the material (a chemical half-life), and the red line corresponds to the time required to degrade 99% of the valine.

In contrast to the ablation and effective evaporation of small meteors going at high speeds, large meteors do not ablate significantly. Correspondingly, they also do not decelerate significantly. As a result, our second caveat is that these objects impact the earth’s surface at high velocity, often a velocity high enough to have more than the internal energy necessary to vaporize rock ( 10 MJ/kg, Pasek and Hurst 2016). If a large object strikes the earth’s surface at greater than 4000≳ m/s, then it is highly likely that the object will completely vaporize on impact, and all minerals and organics contained within are reduced to gases. Both fast and large

(massive) meteors would vaporize on impact. The effect of various atmospheres on mass loss through ablation is not as huge as might be expected. A thin nitrogen atmosphere would have resulted in ablation similar to the modern atmosphere. A thick CO2 atmosphere results in greater deceleration of larger meteors but somewhat higher total ablation of meteors as they travel through the atmosphere. The benefit of a thicker atmosphere on meteor survival is hence contingent on the mass distribution of the incoming bodies.

A potential route around the vaporization of meteors on impact is through fragmentation.

Large meteors that fragment as they enter the atmosphere should ablate and decelerate if they do so 20000-50000 m above the surface. Fragmentation effectively allows ablation to act over a much larger surface area, enabling the deceleration and survival of the meteor on impact.

However, our analysis of strewn fields suggests a third caveat: the size of strewn fields increases at a greater proportion than the increase in total mass. This implies that more massive meteors spread out over a larger area (thus providing less mass/area) than an equivalent smaller meteor.

As a result, large objects are less effective as organic sources than smaller meteors: a net dilution effect (e.g., Pearce, et al., 2017.)

All the above seem to point to small meteors as being preferred sources of organics for exogenous delivery. Indeed, small meteors can lose energy through radiation in addition to ablation, thus they may reach the surface of the earth more readily. Our fourth caveat concerns small meteorites: we find the diffusion of heat to be rapid, and in the case of micrometeorites, is sufficient to promote the complete degradation of organic molecules such as amino acids. A spherical meteor about 1 mm in radius will be completely heated to the exterior temperature

(estimated here as 1000 K- see Greshake et al. 1998), at which temperature it only takes 10-4 s to lose 99% of its amino acids. The interior of objects larger than 1 mm in radius may be more protected from this aggressive heating, and hence the organics in such objects should survive.

Although we present here a somewhat negative outlook on exogenous delivery, we acknowledge that there are several caveats to our own cautions. For one, a thick atmosphere results in more meteors reaching the surface of the earth intact. Secondly, the entry angle of meteors under consideration was assumed to be 45° (the average of 0 and 90°). Meteors with a more acute angle of entry suffer from less ablative effects as their vertical velocity is less.

Finally, these models assume spherical objects. For micrometeorites, this appears to be reasonable, but for most other objects, other shapes can alter the extent of ablation and of thermal heating. For instance, interplanetary dust particles are rarely spherical, hence the thermal diffusion model presented here for those objects would be less applicable. Additionally, larger objects are susceptible to less thermal degradation in the core of the object. Thus, organics in the core of meteors can still theoretically survive the atmospheric entry process (Figure 2.8).

However, many of the concerns raised here should be considered carefully in any putative prebiotic model that relies extensively on exogenous delivery for its key components.

Calculation of Exogenous Material to The Early Earth

The above caveats provide some constraints on the actual delivery of organic compounds to

the surface of the earth. Using an assumed 1022 kg of meteoritic material accreting to the earth

based on highly siderophilic elements (following Marchi et al., 2014), we assume that the mass is

distributed according to the following equation:

Log N = -0.8 Log M + 17.1 (7)

where N is the number of meteorites with mass greater than M, and the -0.8 comes from Brown

(1960) and Huss (1991). In such a case, the largest meteor to impact the earth would have by

~2.5×1021 kg, with masses decreasing by the log-log relationship from this largest mass as a

starting point, and totaling 1022 kg. To this data, we apply the ablation survival calculations, assuming an average velocity of 18000 m/s, and find that meteors of about 50000 kg will survive without complete vaporization on landing (10% or 5000 kg reaches the surface of the earth).

2.6 Conclusion

We find a total mass of about 5×1017 kg delivered in this size range reaching the

surface of the Earth over the billion-year bombardment period spread across the entire surface.

To calculate the organic flux, this mass of meteorites is assumed to be 5% carbonaceous

chondrites, with 2.2 wt.% carbon, of which 10% are soluble organic compounds (Pasek and

Lauretta 2008), giving a total organic delivery of about 5×1013 kg, or about 1014 kg in the thick

CO2 atmosphere. Spread across the surface of the earth this would correspond to about

105kg/km2 of total organics delivered over this bombardment period, or about 100g/m2.

Figure 2. 8. T-t-r (Temperature, time and radius) profile predicted for meteors in contact with a 1000 K surface. *This model assumes a total meteor radius of 1 mm, and the dashed lines provide the temperature from the center (0 mm) to the exterior (300 mm) as a function of time.

This high number would suggest that exogenous delivery may still be significant even with all the caveats we outlined above, but it must be noted that this is the total flux, integrated over the several hundred million years assumed for delivery by Marchi et al. (2014). This number is also the total soluble organics, and not of individual molecular functional groups (e.g., not just amino acids, but including carboxylic acids and others). In contrast, over the same amount of time electric discharge is expected to form ~1015.5-1017.5 kg of organics (Chyba and

Sagan, 1992). Nonetheless, this data does hint that the exogenous delivery, even with several cautionary caveats, may act as a significant organic source.

CHAPTER THREE

A POWER-LAW MASS DISTRIBUTION FOR METEORITES: A RELATIONSHIP TO

METEOROIDS

Note to Reader: This chapter has submitted for publication: Mehta, C., Thompson, G., and Pasek, M. (2019). “A power-law mass distribution for meteorites: a relationship to meteoroids”.

3.1 Abstract

Objects within the asteroid belt generally follow a power-law size distribution, though the

sizes are limited to what is observable telescopically (generally greater than 100 m diameter).

Smaller asteroid and meteoroid debris should also follow a similar power-law trend, with the

best option for studying this smaller group coming from the global collection of meteorites.

However, meteorites may have been altered from their initial (meteoroid) size distribution by the

process of ablation. Here we study the influence of various orbital mechanical and physical

properties on the ablation of meteors to understand how the mass distribution of meteoroids

transforms to meteorites, focusing specifically on ordinary chondrites and the extent to which

they follow a power-law. To do so, we employ a Monte Carlo simulation that produces random

angle of entry, initial mass and velocity, along with shape values, and compare the simulated

values to empirical fall and find data. We find that the initial velocity of the meteor is the main

determining factor that influences the effect of ablation on meteors, with shape following in

34 importance, and angle of entry being least important. The mass distribution of meteorites does in fact appear to reflect the mass distribution of meteoroids, providing clues to the size-frequency distribution of smaller objects.

Key words: meteorites; asteroids; ablation; frequency distributions

3.2 Introduction

Power-law distributions are commonly found in nature. Some examples include the magnitude of earthquakes, the intensity of solar flares, and the diameter of moon craters

(Newman, 2004). A distribution can be defined as being a power-law if the number (n) of

independent variable m is related linearly in log-log coordinate space such that log(n) log(m).

Understanding power-law distributions and slope values can yield valuable information∝ about

masses of meteoroids and meteorites. The slopes of the power-law vary and are dependent of

physical properties such as the diameter of the object.

The size distribution of asteroids has been widely studied by using a variety of methods

ranging from crater sizes, to numerical modeling, and to radar systems (Huss 1991; Hawkes et

al., 2002; Mathews, et al., 2002; Zolensky et al., 2006; Pasek and Lauretta 2008; Badyukov and

Dudorov 2013; Włodarczyk and Leliwa-Kopystyński 2014; Vinnikov et al., 2016; Ryabova 2017

Schult et al., 2018; and Rubincam 2018). Asteroids follow a power-law distribution that is

independent of population index (Bottke et al., 2005). For example, when studying asteroids,

Davis et al. (2002) showed that the slope of the power-law is directly dependent of the asteroid’s

diameter. Trojan asteroids with a diameter of 10 to 20 km show a slope of nearly 0, whereas

asteroids that have a dimeter of 20 to 250 km have slopes around -5 (Davis et al., 2002) in log-

log coordinates. The near 0 slope for small bodies is due to the fact that they are harder to

telescopically observe (see Ryan et al., 2012), hence their distribution cuts off at ~2 km. Ryan et

al. (2012) demonstrate that small main belt asteroids are typically more diverse than larger main

belt asteroids. Cellino et al. (1991) conclude that non-family asteroids (with diameters of around

150 km) have a size distribution with a strong change in slope. Furthermore, the size distribution

within the Flora region (located within the inner region of the asteroid belt) suggests that large

36 asteroids have not been substantially affected by collisional events with other objects. However, these asteroids are fragments as a result of collisional events (Cellino et al., 1991). These collisional events are thought to harvest the parent bodies of iron meteorites and produce most small sized asteroids (Davis et al., 2002 and Bottke et al., 2005)

Meteorites may serve as proxies for the smaller material that is difficult to observe telescopically. This may be true especially if meteorites follow Zipf’s law and tantamount Pareto distributions (Newman, 2004, He et al., 2014). Both relationships are used to understand the frequency distributions of objects (James et al., 2018 and Tria et al., 2018). Below we employ

Zipf’s law along with the fundamental knowledge of Pareto distribution (see He et al., 2014) to understand how ablation of meteors as they interact with the atmosphere of Earth might influence their mass-number distribution upon collection at the Earth’s surface.

Aside from ablation, a possible factor that may affect mass distribution of meteorites is the fact that objects within a specific mass range will temporarily get caught into the Sun-Earth (or

Earth-Moon) orbit, which will cause the meteoroid to reach close proximity to Earth (Hasnain, et al., 2012; Gong and Li, 2015; Fedorets et al., 2017; Murtazov, 2018; and Sokolova et al., 2018).

The majority of meteorites appear to come from the Main-Belt asteroid region, which not only houses asteroids (and parent meteoroids) but also comets (Di Carlo et al., 2018 and Snodgrass et al., 2018), with the latter shedding meteoroids during their dust-ejection process (Williams,

1999).

Although the size distribution of asteroids has been widely studied by many scientists using a variety of methods ranging from numerical modeling to radar systems (Huss 1991; Hawkes et al., 2002; Mathews et al., 2002; Zolensky et al., 2006; Pasek and Lauretta, 2008; Badyukov and

Dudorov 2013; Włodarczyk and Leliwa-Kopystyński, 2014; Vinnikov et al., 2016; Ryabova

2017; Rubincam 2018; and Schult et al., 2018), in this study, we employ a numerical model

along with a large sample pool of observed meteor fall data to understand the mass distribution

of chondritic meteorites. Prior studies have focused on just the amount of mass ablated by

meteors, and here, we focus on how they follow a power-law distribution. This is accomplished by constructing rank/frequency plots and coupling them with the maximum likelihood estimates of the power-law coefficient (corresponding to the alpha value). The rank/frequency plot, as the name implies, ranks the masses of meteorites and plots them as a function of the frequency. The maximum likelihood estimation calculates the most likely value of alpha by increasing the probability that the alpha value best fits the power-law distribution being studied (Newman

2004). Using an alpha analysis, we compare the values of falls, finds, and computational models to understand the relationship between meteoroids and meteorites.

3.3 Methodology

We investigate the power-law distributions of meteorites by combining meteorite fall

data with simulated ablation models. The hypothesis tested in this study is if the meteorite mass

vs. number relationship can reflect that of the meteoroid mass vs. number relationship. To test

this, a series of numerical analysis were conducted for ablation in conditions that match present

day Earth’s atmosphere.

Meteorite Mass-Number Distributions

The meteorite distribution data was obtained from MetBase1, which is a meteoritic data

retrieval software. We use both falls and Antarctic finds to assemble mass vs. number

relationships. In terms of sample size, ordinary chondrites provide us with a larger sample size of

rocks with similar material strength (as opposed to the rarer iron meteorites or more friable

carbonaceous chondrites) and hence provide a more precise calculation of size distributions.

These distributions were then used to simulate the effect of ablation on meteoroid to meteorite

size distributions.

We note here a few caveats to this approach. For example, the largest ordinary chondrite

found in Antarctica is not as massive as what has been recovered as an ordinary chondrite fall

(Jilin at 4000 kg). Indeed, for larger chondrites, if craters were to have formed in the ice/snow

they could have been covered with recharging snow or ice (Corti et al., 2008). However,

meteorite recovery from the white, icy surface of Antarctica is much easier and smaller objects

are easier to spot compared to those that fall in other areas-such as grassy areas or meteorites in

rocky deserts (Harvey 2003; Pasek and Lauretta, 2008). These variables in finding the meteorites are the cause of the primary reason in the discrepancy in slope values of meteorites found on

Earth for low-mass meteorites (a left-hand truncation, see Pickering et al., 1995).

The masses of all fall and Antarctic meteorites were ranked from most to least massive. This data was used to arrive at the following relationship:

log = log + (1)

𝑛𝑛 𝛼𝛼 𝑚𝑚 𝑏𝑏 Where n is the number of samples with mass m or greater, is the power-law coefficient, and b

is the y intercept (the n where m = 1 kg). Per Newman (2004𝛼𝛼 ), the power-law coefficient can also

be calculated by the equation:

= 1 + [ ]-1 (2) 𝑛𝑛 𝑚𝑚𝑖𝑖 𝛼𝛼 𝑛𝑛 ∑𝑖𝑖=1 𝑙𝑙𝑙𝑙 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 where mi is the mass and mmin is the minimum mass in the sample pool. Lastly, code for the analysis of maximum likelihood of the power-law coefficient was obtained from GISMO – a

seismic data analysis toolbox that is capable of calculating power-law coefficients (as described by Thompson and Reyes, 2018) for MATLAB (software package).

Ablation Model

The ablation model created for this study was adapted from Pasek and Lauretta (2008) and

Mehta et al. (2018). We consider physical properties of a meteor and atmospheric properties to

simulate the effect ablation has on a meteor transiting through the atmosphere. Atmospheric

ablation occurs when the material strength exceeds the surrounding atmospheric pressure. The

effect of ablation on a meteor is enough to generate significant mass loss (Mehta et al., 2018).

When a meteor enters the atmosphere, it can either impact the surface at terminal velocity and be

collected as a meteorite, it can form crater if the object impacts the surface at velocities greater a

few km/s, it can explode in the atmosphere, or the ablation process can cause total mass loss of

the meteor (Mehta et al., 2018). To simulate this, we create an ablation model that solves two

equations that describes velocity and change of mass. Mehta et al. (2018) adapted a set of

differential equations utilized by Bland and Artemieva (2006) to simulate meteor ablation. Those

equations are:

= + ( ) 2 (3) 𝑑𝑑𝑑𝑑 𝜌𝜌𝑔𝑔𝐴𝐴𝑉𝑉 𝑑𝑑𝑑𝑑 −𝐶𝐶𝑑𝑑 𝑚𝑚 𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝜃𝜃

= 3 (4) 𝑑𝑑𝑑𝑑 𝑐𝑐ℎ𝜌𝜌𝑔𝑔𝑉𝑉 𝑑𝑑𝑑𝑑 −𝐴𝐴 2𝑄𝑄

where V is the initial velocity of the meteor, m is the mass of the meteor, cd is the drag

coefficient, ch is the heat transfer coefficient, ρg is the density of Earth’s atmosphere at a given

height (defined by the scale height, ~7 km), A is the cross-sectional area of the meteor, g is

gravity on Earth, Q is the heat of ablation, and Θ is the angle the meteor enters Earth’s

atmosphere. Refer to Figure 2.1 and Table 2.1 for summary of variables used in the ablation model.

Effect of Physical Variables on Ablation

Four different computer simulations were conducted in order to understand the factors that influence meteor ablation. These simulations varied initial (entry) velocity, angle of entry, and “shape”. The first test was conducted to see how angle of entry affected ablation. The numerical model was set up such that we simulated a 100 kg object traveling at escape velocity at angles ranging from 1° to 90° to see how the angle of entry influences the ablation process.

Although, this could be done in one dimension, to accurately understand entry, we needed to calculate the radial and traverse velocities of the object and consider the trajectory of the object as it enters through the atmosphere due to the curvature of Earth. The second test sought to understand how velocity affected the rate of meteor ablation. The entering meteor had an initial mass (m) of 100 kg entering the atmosphere of Earth at a 45°, traveling with initial velocity (v) ranging from 11,600 to 18,000 to meters per second.

It is imperative to note that Bland and Artemieva, (2006) and Mehta et al., (2018) model meteor ablation assuming the meteor is solid, nondeformable, and spheroidal in shape. So thirdly, we investigated how varying shape from spherical affects ablation. This is accomplished by calculating the aspect ratio with respect to drag coefficient to mimic different meteor shapes.

The aspect ratio (k-value) is a direct relationship of the ratio of depth to the diameter/width of the initial object. Shape also determines the drag coefficient, which may also vary from close to zero

to greater than 1. For this test, we conducted the velocity and angle of entry test with the same initial parameters used as stated above but with a streamline and conical shape.

For our fourth test, we utilized a Monte Carlo simulation to investigate how the final masses of meteorites reflects the initial masses of meteors when the above variables (velocities, angles of entry, and shapes) are varied randomly initial masses and to see if the resulting final masses resemble the final masses of real-world fall and find meteorite data. The initial meteor mass is evenly distributed with respect to the power-law (log n = -0.86 log m, with the largest m being 5500 kg (selected by Monte Carlo method), velocity is distributed around an average initial velocity of 16,000 m/s with a minimum of escape velocity and a standard deviation of

6000 m/s. The angle of entry was selected between 1-90° with a mean of 45° with a standard deviation of 10°. The drag coefficient was selected between 0.09-1.15 with a mean reflecting that of a sphere (0.47). Lastly, the aspect ratio was selected from 0.50-25.6 with an average also reflecting the aspect ratio of a sphere (1). The drag coefficient and aspect ratio both have a log- normal standard deviation of 0.2 (a times/divided by factor around the mean). The Monte Carlo simulation was used to implement equal likelihood of variables being selected within a given range of values. Lastly, we take into consideration in our calculations a flux by Bland et al.,

(1996) who state that, due to weathering and other environmental factors that affect the sizes of meteorites, the accumulation rate of meteorite falls is approximately 0.02 kg per 106 km2 per year.

3.4 Results

Combining ordinary chondrite fall and Antarctica ordinary chondrite finds yields a power-law relationship with an alpha value of 0.65 +/- 0.03 and 0.63 +/- 0.01 (Table 3.1). The

difference in alpha values between the two is a direct result of the number of samples used in this

study, and for all intents and purposes, the similarity between the two data sets demonstrates that

meteorites obey a power-law distribution for masses greater than ~10g. Below this mass we

presume the small meteorites are not collected as frequently due to their size, and hence the

power-law behavior is not evident. Figures 3.1 and 3.2 shows the power-law relationship of LL,

L, and H Antarctic ordinary chondrite finds and ordinary chondrite falls that were used as

controls in this study. Lastly, we see that the slopes for Antarctic ordinary chondrite finds and

ordinary chondrite falls to be -0.83 and -0.78, respectively (Table 3.2). We can imply, since the

slope is greater than -2.00, that the larger meteorites are more important to the mass flux to the

surface of Earth (Newman 2004).

Effects of Varying Angle of Entry, Initial Velocity, and Aspect Ratio

The influence the angle of entry has on the ablation process of a spheroidal meteor was found

to be minimal such that regardless of angle of entry, the meteor ablated roughly 60% of its initial

mass (Figure 3.3). An object—independent of initial angle of entry—impacted the surface retaining a consistent amount of mass (for instance, 39kg at 11.6 km/s for a spherical body).

However, the initial velocity has a more prominent role in the rate of ablation (Figure 3.4). As the initial velocity increases, the amount of mass lost increases as well. For example, a 100 kg object entering the Earth’s atmosphere at 11,600 m/s is expected to impact the surface with a final mass of 39 kilograms. At 15,600 m/s the same object impacts the surface with a final mass of 19 kilograms. At speeds greater than or equal to 35,600 m/s, the object effectively totally ablates and has no mass upon reaching the surface. Generally, we see that a 100 kg meteor entering the atmosphere at speeds close to escape velocity tended to shed more than half of its initial mass and, as the initial velocities increased, shed almost all its mass.

Table 3. 1. Alpha values calculated using maximum likelihood approximation from GISMO.

Alpha Value Error (+/-)

Antarctic Finds 0.63 0.01

Ordinary Chondrite Falls 0.65 0.03

Monte Carlo Simulation Initial 0.78 0.01

Mass (Meteor/Meteoroid)

Monte Carlo Simulation Final 0.75 0.01

Mass (Meteorite)

Table 3. 2. Slope values for Antarctic ordinary chondrite finds and ordinary chondrite falls.

Ordinary Chondrites Slope Value

Antarctic Finds -0.83

Falls -0.78

Monte Carlo Simulation Initial Mass -0.86

(Meteor/Meteoroid)

Monte Carlo Simulation Final Mass -0.84

(Meteorite)

Figure 3. 1. Combined Antarctic ordinary chondrite finds.

Figure 3. 2. Combined Ordinary Chondrite Fall data.

Figure 3. 3. Mass distribution of a 100 kg spheroidal meteor entering the atmosphere at an initial velocity of 11,600 m/s with varying angle of entry (from 1-90 degrees).

Furthermore, as the velocity increased, objected were more prone to exploding in the

atmosphere. This is due to the extreme stress caused by the interactions of high velocities with

the air particles.

The effect of shape was modeled by varying both drag coefficient and the aspect ratio (k-

value). A 100 kg streamlined shape (drag coefficient = 0.04) entering the atmosphere at 18,000 m/s with angle of entry varying from 1-90° completely ablates regardless of the angle it enters

the atmosphere. However, when the initial mass is changed to 100,000 kg, small amounts do

make it to the surface. On one hand, from 1-46°, a 100,000 kg-object traveling at 18,000 m/s will vaporize within 16 seconds. On the other hand, when entering at angles 47-90°, the streamline meteor will impact the surface. The streamline shape, unlike a sphere and cone, tends to show an increase in final mass with respect to higher angles. Objects traveling at high angles will hit the

surface faster than objects traveling at lower angles (i.e. a 100,000 kg object will impact the surface at 15 seconds traveling with an angle of entry of 46° whereas the same object entering the atmosphere at a 60° angle will impact the surface within 12 seconds, see Figure 3.5). In addition, the impact velocity of a 100,000 kg streamline shaped meteor with an initial velocity of

18,000 m/s, entering the atmosphere at 46° will impact the surface with velocities exceeding

14,000 m/s within 15 seconds of atmospheric entry. As the angle of entry increases, the streamline meteor was calculated to impact at higher velocities.

Figure 3. 4. Mass distribution of a 100 kg spheroidal meteor entering the atmosphere at a 45- degree angle traveling at varying initial velocities. Note, the minimum starting velocity is 11,600 m/s (escape velocity).

Simulating ablation of a 100 kg streamline object entering the atmosphere with varying initial velocities entering the atmosphere at 45°, show the object being vaporized within 20 seconds when traveling at speeds greater than or equal to 14,500 m/s. The model does record final masses for objects traveling at lower speeds, however, they do not reach the surface with a final mass greater than or equal to 0.02 kg (the minimum meteorite mass calculated by Bland et 48

al., 1996 for the flux of 50,000 reaching the earth’s surface). For example, at speeds of 14,500 m/s, the object vaporizes with a final velocity of 3000 m/s. However, when the same object is going 14,400 m/s, the model records fine dust particles reaching the surface with a velocity of 14 m/s at 740 seconds after atmospheric entry.

Figure 3. 5. Ablation of a streamline shape meteor entering the atmosphere of Earth at varying angle of entry.

Figure 3. 6. Ablation rate of a conical meteor entering the atmosphere of Earth at varying angle of entry. 49

When running the model using a 100 kg conical shape (drag coefficient = 0.50) entering the atmosphere at 18,000 m/s with angle of entry varying from 1-90°, every object simulated impacted the surface with a final mass of about 12 kg at 88 m/s. However, when simulating ablation of a 100 kg conical object entering the atmosphere with varying initial velocities entering the atmosphere at 45°, we see that objects traveling at lower speeds will impact the surface with retaining more mass than those traveling at faster speeds. The final velocity decreased with higher initial velocities and the time to impact will increase with increasing initial velocities. Based on these tests, the streamline shape does not withstand the ablation process as well as a meteoroid that has a shape closer to a cone (Figure 3.7).

Figure 3. 7. Ablation of a conical meteor entering the atmosphere of Earth at varying initial velocities.

The influence of aspect ratio with respect to drag coefficient (Figures 3.8 and 3.9), objects with a drag coefficient of 0.01 to 0.05 all vaporize within seconds of atmospheric entry regardless of their aspect ratio. When the drag coefficient increases to 0.09, objects do start to reach the surface of Earth, however, they are fine particles with masses less than 0.02 kg (Figure

3.8). Generally, meteors that had high aspect ratios coupled with low drag coefficient reached high speeds that caused the object to explode or vaporize on impact.

Figure 3. 8. Shape dependent final mass. Meteors simulated with low drag coefficients vaporize within seconds of atmospheric entry. *The initial mass, initial velocity, and angle of entry was fixed to 100 kg, 11,600 m/s (escape velocity,) and 45°, respectfully.

Figure 3. 9. The final velocity of objects simulated using varying aspect ratios (k-Value) and drag coefficient. *Note that objects with relatively high k-Values and low drag coefficients explode while traveling through the atmosphere of Earth.

Monte Carlo Simulation We simulate ablation of meteors as they enter the atmosphere of Earth using numerical

modeling. Initial meteor parameters were selected using a Monte Carlo approximation that

randomly assigned values for initial mass, initial velocity, angle of entry, and drag coefficient.

Our model selected masses greater than 1 kg, velocities greater than 11,600 m/s and angle of

entry between 1-90°. For the purposes of this test, we assumed that the initial shape of the meteor

was spheroidal in shape. Performing 10,000 iterations, we see that the cumulative number greater

than mass vs. initial mass and final mass follow a power-law relationship (Figure 3.10). In

addition, the slope of the cumulative number greater than mass vs. initial mass was found to be -

0.84, similar to the initial value of -0.86 for cumulative number greater than mass vs. final mass.

Figure 3.10. Final Mass distribution of Monte Carlo Simulation. *Out of the 10,000 meteors simulated, 1,300 reached the surface with masses below 0.02 kg.

3.5 Discussion

Meteorites are shown to follow a power-law relationship between mass and frequency, as shown by both meteorite falls (which occur globally) and Antarctic finds (which are collected more systematically). We use ordinary chondrite falls specifically because of the large sample pool available (as a fraction of falls), and because meteorite falls can be much more massive than

Antarctic finds: the largest ordinary chondrite found in Antarctica is 407 kilograms, compared to

Jilin (a fall) with a mass of 4000 kilograms. However, for smaller meteorites the white, icy

surface of Antarctica allows for a higher probability of being spotted and collected than for

objects that fall in other areas such as eolian environments (Harvey 2003; Pasek and Lauretta,

2008). Therefore, human error and the ability to effective collect meteorites proves to be a

stymie.

Using the maximum likelihood approximation, the alpha values calculated by GISMO for

Antarctica ordinary chondrites finds, ordinary chondrites falls, Monte Carlo initial mass, and

Monte Carlo final mass simulations was found to be 0.63, 0.65, 0.78, and 0.75 respectfully

(Table 3.1). In addition, the initial mass of the meteors is strongly reflected in the final mass of

the meteorites using the Monte Carlo simulation. In other words, stochastic effects are not severe

enough to alter the fundamental distribution of meteorites from meteoroids with the large body

of meteorites in the modern collection. The slope of the initial mass was calculated to be -0.86

and the slope of the final mass was found to be -0.84. Comparing the final mass of the meteorites

on Earth with the simulated values, yield a similar slope and final mass values. The individual

slopes of Antarctic LL, L and H ordinary chondrites were found to be -0.84, -0.96, and -0.80, respectively. These values are close to the slope values that were calculated from the Monte

Carlo simulation, however, we see that the data demonstrate a left-hand truncation. Typically, left-hand truncation (LHT) is for small scale objects and is due to that limiting resolution in our

sample (Pickering et al., 1995). Nominally, the results of maximum likelihood approximation

(Table 3.1) and the slopes calculated (Table 3.2) should be identical and hence these results

suggest an error in the value of the alpha exponent averaging about +/- 0.1.

As a check, we see that the power law may not in fact be linear but instead may follow a

parabolic power-law (e.g., log n [log m]2). The parabolic power law gives a much stronger

linear relationship for ordinary chondrite∝ fall and Antarctica ordinary chondrite finds,

respectively (Figure 3.11). We are uncertain at present why this might be, but the parabolic log- log relationship hints at an underlying physical process forming the size distribution of meteoroids and meteorites. This finding may merit future study.

Figure 3. 11. Log of the mass squared vs rank of the Antarctic ordinary chondrite finds.

In addition, out of the variables that were modeled, angle of entry, which was originally thought to have a substantial influence in ablating objects, turned out to only have a marginal influence when the object is spherical. However, the initial velocity and initial shape of the meteor was found to have a major role in ablating objects and are key variables in determining if an object will impact the surface of Earth or vaporize in the atmosphere, and angle of entry matters more for non-spherical objects with varying speeds.

3.6 Conclusion

Our results are consistent with Huss (1991), Newman (2004), and Pasek and Lauretta

(2008) because the calculated alpha value is less than two, and hence the observed masses are divergent. In other words, the observed total meteorite masses on Earth are strongly dependent on the largest meteorites. Additionally, our slopes are constant with Harvey and Cassidy (1989), who found the slopes of the fitted power-law fell within the ranges of -0.698 to-0.856. According to Harvey and Cassidy (1989), these values were also reported in Brown (1960), Hartmann and

Hartmann (1968), and Dohnanyi (1972).

Furthermore, the Monte Carlo approximation demonstrates that a log-log relationship among meteors is preserved even through the process of ablation. Random variations in angle of entry and velocity do not greatly affect the total net ablation. We find that shape and velocity are more important (in general) than angle of entry in determining the effect of ablation.

CHAPTER FOUR

ABLATION OF CARBONACEOUS ASTEROIDS AND ORGANIC FLUX DELIVERY

4.1 Abstract

A common type of asteroid in our Solar System is the carbonaceous asteroid, or C-Type asteroids, which are said to be the parent body of carbonaceous chondrites. The purpose of this chapter is to explore how much potential organic matter can be delivered to Earth from a C-Type asteroids impacting the surface and its implications for prebiotic chemistry. I utilize an ablation model that simulates the breakup of meteors/asteroids and analyze the percent of mass loss from a carbonaceous meteoroid. Additionally, we employ basic principles in orbital mechanics and meteor ablation to calculate the minimum velocity of an asteroid (located in the outer edges of the Asteroid Belt) and investigate the influence of the Earth’s atmosphere. We find that the total average mass of carbonaceous chondrites delivered in 1 year to be 1100 kg/yr, the fraction of soluble carbon to be roughly 1.22 kg/yr, and the fraction of insoluble carbon to be 11 kg/yr.

Key words: cosmochemistry; astrobiology; ablation

4.2 Introduction

Recall from previous chapters, atmospheric ablation occurs when an object (meteoroid or asteroid) travels through the atmosphere and the aerodynamic pressure of the surrounding atmosphere surpasses the material strength of the object. This generates heat from atmospheric entry and breaks up the object, causing it to lose mass (Bland et al., 1996; Bland and Artemieva,

2006; Mehta et al., 2018). In Chapter 2, we saw that depending on the size, initial velocity, composition of object, and angle of entry, an asteroid or meteor entering the atmosphere of Earth is subjected to partial or total ablation. Additionally, it was found that the deciding factor in how much an object ablates is a function of the velocity and shape in which it initially enters the atmosphere (Mehta et al., 2019, chapter 3). The purpose of this chapter is to combine Kepler’s

Laws of planetary motion and basic orbital mechanics, to calculate the minimum velocity of a simulated asteroid that is on an orbital trajectory to Earth and see if distance influences rate of ablation of asteroids. In addition to calculating mass loss, a calculation of potential flux from carbonaceous asteroids is done to understand how much soluble carbon is obtained by these objects. Although previous studies have focused on the transport of organics through meteoroids, we now shift the focus to asteroids because of the high amount of potential organic matter that could be delivered to Earth.

4.3 Methods

The hypothesis tested in this study was to see how an asteroid that originates 3 AU from the

Sun would be affected by the ablation process if it enters Earth’s atmosphere. To test this, I calculate ablation of an asteroid entering the atmosphere at a range of initial velocities to gain a

rough understanding on how distance effects the final mass of an asteroid ablating in the

atmosphere.

To determine the rate of ablation of an asteroid, the same ablation calculations were used as

discussed in chapters 2 and 3. I calculated the initial velocity of an asteroid before it enters the

atmosphere. Coupled with a series of differential equations that account for ablation. The

asteroid is subjected to mass loss while entering the atmosphere. Steel (1998) states that the average minimum and maximum impact speeds of asteroids with Earth is approximate 12,000 m/s and 40,000 m/s, respectfully. Here, I arrived at similar velocities by calculations of orbital velocities of asteroids by using basic orbital mechanics coupled with elementary Newtonian physics and Kepler’s Laws. Assumptions were made while solving the equation. For example, it was assumed that the Sun, Earth, and Asteroid Belt are all on one orbital plane and that the asteroid has a free path to the Earth (no collision or transfer of energy with another moving body that will influence its trajectory). In other words, the object does not speed up or slow down due to any impact with other celestial bodies in the Solar System. Therefore, we arrive at Equation 1 which was obtained from Kurzweg (2019).

= + (1) 2 2 2 16𝜋𝜋 𝑅𝑅 2 𝑉𝑉 �𝑉𝑉2 3𝑡𝑡 where V is the entry velocity of the carbonaceous asteroid in meters per second, V2 is the orbital

velocity of the asteroid in meters per second (found by using ), R is the radius of Earth 2 3 in kilometers, and t is the number of seconds in a year. The orbital𝑇𝑇 ∝ 𝑅𝑅velocity of the object was calculated using the following relationship, and velocity is equal to distance over time, 2 3 one can calculate the velocity of an asteroid 𝑇𝑇approximately∝ 𝑅𝑅 3.5 AU. Employing Kepler’s Laws to

calculate the initial velocity of the asteroid, an orbital velocity of 16,000 m/s for an asteroid

located on the outskirts of the asteroid belt (home to most C-Type asteroids) is obtained. Thus,

one can arrive at the conclusion that an asteroid traveling to Earth from the asteroid belt would

have an approximate entry velocity of 38,000 m/s. Recall from Chapter 2, the minimum mass for an object with an initial velocity of 38,000 m/s must be at least 13,000 kilograms for the meteor to impact the surface. For the purposes of this study, and per Bland Artemieva (2006), I assumed that the estimated yearly flux of meteors that reach the surface have masses greater than 0.02 kilograms. Thus, asteroids are only considered to impact the surface if they retain a mass of 0.02 kg or greater. Therefore, a constant mass of 13,000 kg was used in this model with velocities ranging from 38,000 m/s to 50,000 m/s. The angle of entry was fixed to 45 degrees and the object shape was spheroidal to augment the final mass of the object which is enable us to provide a maximum value for final mass of the asteroid. Lastly, the velocity of asteroids entering Earth from distances greater than 3.5 AU’s was done using the impact velocity of a Main Belt Asteroid

entering Earth as a minimum value. The maximum value was set to 5.9 x 105 m/s, which is the

velocity of the fastest known object in our Solar System that had an aphelion of 170 AU’s as observed by telescopes.

We calculate the flux of exogenous material to the surface by using real-world Antarctic ordinary chondrite finds as a control. Table 3.2 of Chapter 3 lists the slopes calculated for ordinary chondrite falls, Antarctic finds, and the Monte Carlo simulation. Pasek and Lauretta

(2008) state that there are roughly 50,000 chondrite falls per year with 5% being carbonaceous chondrites. Taking this information, Antarctic finds were ranked from most to least massive.

This data was then used to arrive at the following relationship used in Chapter 3, log(n) = slope * log(m) + b, where m is the mass, n is the rank, and b is the y-intercept. We then solve for m to arrive at the mass of carbonaceous chondrites delivered to the surface, with respect to the slope

value calculated after one year. The mass flux over one year was calculated using the following

equation from Pasek and Lauretta (2008) which state that:

= (3)

𝐹𝐹𝑋𝑋 𝑀𝑀𝐹𝐹 ∗ 𝑋𝑋𝐸𝐸 ∗ 𝑋𝑋 Where, is the total mass flux in one year, is the total mass of carbonaceous chondrites

𝑋𝑋 𝐹𝐹 delivered to𝐹𝐹 the Earth, and X is the soluble carbon𝑀𝑀 fraction. Table 4.1 shows data utilized to calculate prebiotic flux of soluble carbon.

Table 4. 1. Values used to calculate prebiotic flux of carbon.

Value Carbon, wt.% 2.20% Soluble Carbon 10% Slope -0.83

*Note, the value for the weighted percent and amount of soluble carbon was obtained from Pasek and Lauretta (2008). Slope value was calculated in Chapter 3.

4.4 Results

When calculating the rate of ablation for a 13,000 kg asteroid entering the atmosphere at 45

degrees, the object reaches the surface (has a mass of greater than or equal to 0.02 kilograms)

when the initial velocity is within 38,000 to 41,400 m/s (Table 4.1). The impact time for the

object increases with increased initial velocity (which is constant with past ablation models).

Velocities greater than or equal to 42,000 m/s will result in total ablation of the 13,000 kg

asteroid.

Table 4.2. Final mass as a function of initial velocity of a 13, 000 kg asteroid entering Earth.

Entry Velocity (m/s) Final Mass (kg)

38000 0.40

39000 0.19

40000 0.08

41000 0.03

42000 + Vaporizes

Figure 4.1. Vaporization time of a 13,000 kg C-asteroid entering the atmosphere.

Using velocity to understand how distance affects rate of ablation, I modeled a 20,000

kg asteroid entering the atmosphere of Earth at a range of velocities from the minimum impact

velocity of a Main Belt Asteroid to the velocity of the fastest known sungrazing object in our

Solar System (aphelion of 170 AU’s which was determined by telescopic observations2). It is found that asteroids traveling over 42,000 m/s vaporize before the asteroid could impact the surface of Earth. However, if the asteroid enters the atmosphere at roughly 38,000 m/s, the asteroid impacts the surface with a final mass of 0.61 kg. At roughly 39,000 m/s, the asteroid impacts the surface with a final mass of 0.30 kg. For asteroids entering Earth at velocities greater than 42,000 m/s, it will be traveling at extreme velocities and vaporizes in the atmosphere

(Figure 4.3). See Table 4.2 and 4.3 for a summary of final mass with respect to the velocity of the simulated asteroid entering Earth.

Table 4. 3. Final mass of a 20,000 kg asteroid entering the Earth at velocities ranging from 38,000 m/s to 42,000 m/s.

Entry Velocity (m/s) Final Mass (kg) 38000 0.61 39000 0.30 40000 0.13

41000 0.05 42000 + Vaporizes

*Velocities greater than 42,000 m/s result in vaporization.

4.5 Discussion

Through the utilization of a numerical model that simulates ablation of Main Belt

Asteroids the mass loss of a carbonaceous asteroid (calculated entry velocity of 38,000 m/s) was

2 The Sungrazer Project. https://sungrazer.nrl.navy.mil 63

determined. At this velocity Mehta et al., 2018 showed that the object must be at least 13,000 kg

for the asteroid to impact the surface. However, at 38,000 m/s, the asteroid lost nearly 99% of the

initial mass. In addition, 13,000 kg asteroids heading towards Earth at velocities greater than

42,000 m/s are not expected to impact the surface of Earth and vaporize within seconds of

atmospheric entry.

To understand how much mass is lost from a massive 20,000 kg asteroid entering

Earth, the same ablation model was performed, but with higher velocities that can potentially

provide insight on how distance affects ablation. At velocities over 42,000 m/s, a 20,000 kg

asteroid vaporizes while in the atmosphere of Earth. Distant objects, such as Kreutz comets, that

enter Earth’s atmosphere are not expected to impact the surface and vaporize in the atmosphere.

Using log(n) = slope * log(m) + b, where m is the mass, n is the Cumulative Number >

Final Mass (kg), and b is the y-intercept. I solved for the mass of carbonaceous chondrites delivered to the surface over one year by using equation 3 and data obtained from Table 4.1. In

the previous chapter, we discovered that the mass distribution relation of meteorites strongly

reflects the mass distributions of meteoroids (asteroids). These calculations showed the power-

law slope for all Antarctic finds is -0.83. In addition, if it is assumed that there are roughly

50,000 chondritic falls per year, with 5% being carbonaceous chondrites (Pasek and Lauretta

2008), the total mass of carbonaceous chondrite delivered in one year is 1100 kg/yr spread

throughout the entire Earth. The fraction of soluble carbon approximal equals 1.22 kg/yr.

4.6 Conclusion

Our results are consistent with Pasek and Lauretta (2008) and Mehta et. al., 2018 such

that a Main Belt Asteroid is subjected to 99% mass loss traveling at high velocities. 20,000 kg

asteroids entering the Earth at velocities of 42,000 m/s and greater are not expected to survive the ablation process and vaporize in the atmosphere. Kreutz objects that are 20,000 kg are also expected vaporize upon atmospheric entry. Lastly, using Antarctic ordinary chondrite finds as a control, the calculated fraction of soluble carbon obtained from Main Belt carbonaceous asteroids per year is a value that is effectively insignificant and not enough to drastically aid in any prebiotic processes on the early Earth.

CHAPTER FIVE

CONCLUDING REMARKS

In this dissertation, several cautionary points are addressed when assuming that meteorites were the principal source of organics to the prebiotic Earth. This series of studies show that the atmosphere acts as an effective filter for most meteors, vaporizing fast meteors and many small meteors upon atmosphere entry and descent towards the surface. In addition, these meteors are subjected to intense heating due to the atmospheric entry process and organics could alter their initial, prebiotically-relevant form. When studying the meteorites that do in fact reach the surface, we saw that initial velocity and shape are the determining agents in the rate of ablation of a meteor. On average, for a modern, a thinner nitrogen, and a thick carbon dioxide atmosphere, objects traveling at initial speeds of 10,000 m/s all reach the surface with 50 to 60% of their mass so long as they are at least 0.05kg before entering the atmosphere. Objects traveling at speeds of 14,000 m/s impact the surface with 26-36% of their initial mass intact. Additionally, meteors with initial velocities of 18,000 m/s reach the surface with only 11-17% of their initial mass. If the initial velocity is 22,000 m/s, objects are subjected to more heating, thus more readily ablate and reach the surface with 3-5% of their initial mass. However, as the initial velocity increases, a meteor is subjected to even more ablation. For example, meteors with initial velocities between 26,000 to 38,000 m/s reach the surface with only 0.9 to 0.0001% of their starting mass.

Furthermore, the mathematical methods used to calculate ablation were used to

understand size distributions of meteoroids and meteorites. The general power-law and mass distributions of meteorites strongly reflect that of meteoroids (and asteroids) found in space.

Using this data, and basic laws in physics and orbital mechanics, it was shown that an asteroid located 3 AU’s from the Sun, a region that houses many C-type asteroids, has many caveats to reaching the surface. Mainly, it exceeds the minimum velocity needed to reach the surface without either ablating or vaporizing on impact.

To calculate the organic flux, this mass of meteorites is assumed to be 5% carbonaceous chondrites, with 2.2 wt.% carbon, of which 10% are soluble organic compounds

(Pasek and Lauretta 2008), giving a total organic delivery of about 5×1013 kg. During the Heavy

Bombardment, this number increases slightly to 1014 kg. Spread across the surface of the Earth

this number implies that 105kg per km2 of total organics delivered over this bombardment period, or about 100g/m2. This high number would suggest that exogenous delivery may still be

significant even with all the caveats we outlined above, but it must be noted that this is the total

flux, integrated over the several hundred million years assumed for delivery by Marchi et al.

(2014). This number is also the total soluble organics, and not of individual molecular functional

groups (e.g., not just amino acids, but including carboxylic acids and others). In contrast, over

the same amount of time electric discharge is expected to form ~1015.5-1017.5 kg of organics during the Heavy Bombardment period (Chyba and Sagan, 1992).

Future work will be to understand the transport of organics from meteors to other

celestial objects and exoplanets. For example, one can use the numerical model developed for

this study to understand how meteors ablate on the planet Mars and use that data to calculate the

amount of potential organics delivered to the surface. Here, we focus specifically on chondrites

as a control, however, future works will aim to understand the transport of organics from iron

meteorites. In addition, the computational model can also be translated to aid in planetary defense programs in understanding the effects of asteroids impacting Earth and augment our current knowledge of objects in space that could potentially be a threat to the Earth.

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