Powering Starships with Compact CondensedQuark Matter

Marshall Eubanks

Asteroid Initiatives LLC, Clifton, Virginia(tme@asteroidinitiatives.com)

October 12, 2013

100 Year StarShip Symposium 2013Houston, Texas

1

Outline of Talk

• Introduction

• Quark Matter Nuggets

A Different Solution for Dark Matter

Basics of CCO theory

• Quark Matter and the Solar System

Capture of Dark Matter in the Proto-Solar Nebula

Can Quark Matter Simplify the Early Solar System?

• Evidence for “Strange Asteroids”

The Anomalous Rotation of Small Asteroids

• Extracting Energy From Strange Asteroids

Andreev Reflection in BCS Superconductivity

• Conclusions : Condensed Matter as a Source of Energy

2

Introduction

3

And Now For Something Completely Different

• This presentation is based on work on Compact Condensed Objects (CCOs), an alternativeexplanation for Dark Matter.

These would be nuggets of condensed quark matter (“Q-Balls”) left over from the earlyuniverse.

The CCO theory is from Zhitnitsky [2003a,b], which makes specific and testable predic-tions.

• What is the relevance of this for Starship Propulsion ?

If there is a significant density of primordial condensed quark matter, there will be somein the solar system (including literally below our feet).

If this material can be found, it can be used both as energy source and (through an analogto Andreev reflection) to produce antimatter.− It should be possible to do this in the near term, starting with existing technology.

• There is as yet no proof that CCOs exist, but there is some suggestive evidence from SolarSystem observations, and many opportunities to confront the new theory with observation.

It should be possible to confirm or deny this new theory within a few years.

• I thus feel that these ideas are important for the 100YSS effort.

4

An Introduction to Dark Matter

• Observations reveal a serious failure of physics at large astronomical scales (galactic disksand halos, clusters of galaxies and larger).

Apparent gravitational accelerations on these scales are consistently larger than can beexplained by the matter we can see (stars, gas, etc.).

This appears to be totally separate from the “dark energy” required to explain a relativelyrecent acceleration in the expansion of the universe.− Dark energy may be “just” the cosmological constant, which is simply a parameter in

General Relativity and need not indicate new physics.

• The galactic rotation and galactic cluster data definitely seem to indicate new physics.

The question is, where ?

• If these accelerations are attributed to some non-interacting (or “dark”) form of matter, thenroughly 85% of the matter in the universe is dark.

There have been many proposals to explain these discrepancies in terms of new particlesfrom new physics.− E.g., WIMPS (Weakly Interacting Massive Particles)

After decades of searching, there is no conclusive evidence that any such particles exist,which motivates a search for alternatives.

5

Quark Matter Nuggets

6

The QCD Era in the Early Universe

• CCOs are a new version of an old idea.

The idea that condensed quark matter could form in the early universe and persist untilthe present has a considerable history, dating back to the “quark nugget” proposal ofWitten [1984].

− Other names for similar proposals are stranglets, nuclearites, Q-Balls..

• CCOs would be relics of the “QCD epoch,” the period during the first 10 µseconds after theBig Bang when there were no baryons (protons, neutrons), but instead a quark-gluon plasma(QGP).

At that time the Hubble distance, RH , was ∼ 10 km.

The density was > 4 × 1017 kg m−3 (the nuclear density).

The temperature was ∼ 160 MeV (1.9 × 1012 K).

The redshift, z, was ∼ 1012.

• As the universe expanded and cooled, this represents the point where quarks became confinedand the QGP froze out into hadrons, forming protons and neutrons.

7

A (brief) review of Quantum ChromoDynamics (QCD)

• Recent work indicates that at low temperatures and high densities the lowest QCD energystate is Color-Flavor-Locked (CFL) superconducting quark matter [Alford, 1999, Madsen,2001, Zhitnitsky, 2003a, Kogut and Stephanov, 2004, Alford et al., 2008].

• In ordinary matter, quarks are confined. There are different “flavors” of quark (u,d and s arethe only ones of concern here) and each quark also has a “color” (r, g or b for normal matter).

Both flavor and color can be viewed as a charge, analogous to an electric charge, exceptthat

− Color and flavor charges are not just + / - , but are multi-valued.

− Color charges can be exchanged by gluons

− Any free particle has to be color-neutral.

A proton, for example, is a <u, u, d> triplet, and must have colors of <r, g, b>, but it isnot possible to assign a particular color to any one of these quarks.

8

CFL Quark Matter

• CFL quark matter is similar to BCS superconductors for electrons. A dense sea of cold quarksfill all available quantum states, allowing for quasiparticles, which can propagate freely.

Some differences :

− CFL is a color superconductor, but an electrical insulator.

− CFL forms a superfluid, with rotation and magnetic field confined to vortex lines

− Quasi particles are in color-flavor locked pairs, such as < dred, ugreen >

These differences will be important for power generation, to be dealt with later.

• CFL superfluids may be absolutely stable, in which case this, instead of the proton or 56Fe,is the fundamental state of matter.

• This state was the primary state of matter in the very early universe, and yet we exist. Howcan some, but not all, of the primordial CFL have survived to the present?

9

QCD Phase Diagram

The schematic phase diagram for quark matter, in terms of the temperature and chemical poten-tial. The Color-Flavor-Locked (CFL) superconducting phase has the highest density at near-zerotemperatures.

10

Why CCOs ?

• The “quark nugget” proposal of Witten [1984] envisioned quark matter being confined inbubbles in a violent first-order QCD phase transition.

Numerical results from lattice QCD modeling currently do not support a first-order QCDphase transition [Aoki et al., 2006], thus suggesting that this mechanism is not available.

• Zhitnitsky and his colleagues, however, hypothesize that the collapse of axion domain wallscreated CCOs [Forbes and Zhitnitsky, 2000, 2001, Son et al., 2001, Zhitnitsky, 2003a, Oakninand Zhitnitsky, 2005, Zhitnitsky, 2006].

• In this mechanism, the axion phase transition generates bubbles with sufficient pressure toform condensed quark superconductors.

Axions were hypothesized to explain the Charge-Parity conservation by the strong in-teraction, by turning a QCD constant, θ, into a field and thus a particle [Peccei, 2008,Srednicki, 2002].

11

Basics of CCO theory

• In the Zhitnitsky theory stable CCOs would be formed in a fairly narrow range of masses.

The lower mass limit is set by the stability of the CCO against decay and the upper masslimit by the requirement that the quark matter be compressed to greater than nucleardensity.

The stable CCO mass range is determined by fa, the axion decay constant. The currentuncertainty in fa [Lakic et al., 2012] constrains the stable CCO mass, MQ, to 105 kg .MQ . 4 × 1010 kg.

− I will show evidence that MQ is ∼ 1010 kg, implying a value for fa at the upper end ofthe allowed range.

− Note that a 10 megaton CCO would have a radius of only 1 mm.

• Zhitnitsky and his colleagues favor a small value for MQ, ∼ 1 gm, so that CCOs could ex-plain various anomalous radiation features in in the Galaxy [Forbes and Zhitnitsky, 2008a,b,Lawson and Zhitnitsky, 2013].

Such small CCOs would be inherently metastable, and would eventually decay. I preferto examine the case for stable CCOs.

12

What is the role for anti-matter in Primordial Quark Matter?

• An open question is the matter / antimatter ratio for CCOs. Oaknin and Zhitnitsky [2005]proposed a 3:2:1 mass ratio for (matter in CCOs, antimatter in CCOs and ordinary matter),in order to provide for the cosmological baryon asymmetry.

With the latest Planck data these ratios would not be exact integers, but more like 3.3:2.3:1

• These ratios are not mandated by the underlying theory. Other possibilities would include

5.6:0:1 : baryon asymmetry is from before the QCD era, as is commonly supposed.

2.8:2.8:1 : baryon asymmetry in ordinary matter is from after the QCD era, which seemsunlikely.

• I prefer to leave this as a parameter to be constrained by observations.

• In any case CFL CCOs would have a large superconducting gap energy, ∆, with ∆ ∼ 100MeV, so antimatter CCOs would not annihilate on contact with cold ordinary matter.

Temperatures in the center of the Sun are only a few MeV, so everywhere in the SolarSystem would be “cold” to CCOs.

13

Current Limits on CCO Dark Matter

• There are a variety of prior limits on CCOs as dark matter, which can be divided into threemass ranges.

• Low mass limits (MQ ¿ 1 gm) come from laboratory searches for dark matter.

The current best such limits are from the MACRO Collaboration [2002], which disallowCCOs smaller than ∼ 10 milligrams.

• Mid-range (kg to ton) limits come from seismology [Herrin et al., 2006].

• Finally, at the upper end of the mass range (planetary masses) there are limits from gravita-tional µlensing [Alcock et al., 1998], and (for primordial CCOs) from the requirement thatCCOs could not be larger than the horizon at the QCD era [Madsen, 2006]

• All of these constraints are consistent with the CCO mass range allowed by the Zhitnitskyaxion domain wall theory.

14

Limits on CCO Dark Matter

1e-22

1e-21

1e+20 1e+25 1e+30 1e+35 1e+40 1e+45 1e+50

1e-05 1 100000 1e+10 1e+15 1e+20ρ Q

(kg

m-3

)

Baryon Number(B)

Mass (kg)

MACRO

Halo CDM Density

Apollo ALSEP

Horizon Mass

µLensing

Axion

Domain

Wall

Model

Mass

Range

VFR Asteroids

USGS

This figure assumes a monochromatic CCO mass spectrum. The Halo CDM Density is from localstellar kinematics [Bovy and Tremaine, 2012]. Note that the experimental “asteroid constraints”and the theoretical “axion domain wall mass range” are consistent with each other and with allthe other experimental constraints.

15

Quark Matter and the Solar System

16

Why should there be Dark Matter in the Solar System?

• Dark matter (whether microscopic or macroscopic) would be included in the Solar Systemprimordially (from its formation).

• Planetary systems such as the Solar System appear to form in the collapse of molecular cloudsas they cool.

The formation of molecules reduces the gas pressure, disrupting the balance betweenpressure and gravitational attraction.

• Dark matter would not be subject to gas pressure, but would respond to subsequent changesin the gravitational potential.

• Most dark matter would have a large relative velocity (∼ 300 km sec−1) and would passrapidly through the collapsing cloud (vcollapse . 5 km sec−1) before the potential could changemuch.

• However, a small portion would have (by chance) relative velocities < 5 km sec−1, and wouldbe subject to capture.

This is especially true for matter in the so called “dark disk” [Purcell et al., 2009], withtypical relative velocities ∼ 50 km sec−1.

17

Primordial Dark Matter in the Solar System

• Assuming the Sun formed under conditions similar to its location in the Galaxy today :

Primordial capture probabilities are ∼ 2 × 10−4 and 3 × 10−6 for dark disk and Halodark matter, respectively.

The total amount of primordially captured dark matter would be ∼ 10−6 M¯ or ∼ 3 ×1024 kg), with ∼ 98% of the captured material coming from the dark disk.

That corresponds to ∼ 3 × 1014 (1010 kg/ MQ) CCOs.

• With their large superconducting gap energies, there is nothing to stop these CCOs frombeginning to accrete normal matter mantles, forming “strange planetesimals.”

Bodies with radii . 100 meters would have most of their mass coming from their strangematter cores and would be truly “strange asteroids.”

• CCOs could thus serve as planetesimal nucleation centers, and could help to resolve boththe “meter-barrier” to planetesimal growth [Brauer et al., 2008, Mordasini et al., 2010], andthe complicated history of heating and high energy irradiation in the early Solar System, asrevealed by meteorite samples.

18

Evidence for “Strange Asteroids”

19

How to find CCOs in the Solar System

• Much of the primordial CCO dark matter should be currently located in the center of the Sunand planets, where it would be hard to detect, and even harder to reach.

The Earth, for example, would be expected to have about 3 × 10−5 of its total massresiding in an ∼ 4 meter radius strange matter sphere at its center.− This could be detected by aiming a neutrino beam from a terrestrial accelerator [Kopp,

2007] directly down at the core and placing a neutrino telescope in the∼ 10 m neutrinoshadow of the CCO core at the beam antipode.

− Although feasible, this is not going be done in the immediate future.

• Small (∼ 100 meter radius) strange asteroids are both more likely to both reveal their CCOcores and (if detected) could be suitable for direct exploration by spacecraft.

• Asteroids in that size range are strongly perturbed by radiation pressure, which can be dividedinto

The Yarkovsky effect [Vokrouhlicky et al., 2000], effectively a proton rocket effect fromIR emission, which changes orbits, sweeping small asteroids into and then out of NearEarth Object (NEO) orbits.

The Yarkovsky-OKeefe-Radzievskii-Paddack, or YORP, effect [Bottke et al., 2006], whichspeeds up (or slows down) asteroidal rotation.

20

Anomalous Rotation of Small Asteroids

• A small (. 200 meter radius) strange asteroid would respond differently to the Yarkovskyand the YORP effects.

The mass could be greatly increased over an ordinary matter body of the same size,which would greatly decrease Yarkovsky accelerations; such objects would have a longerresidence time in NEO orbits.

The moment of inertia change would be negligible, so there would be nothing to stopYORP spin-up of rotation period.

However, a small strange asteroid would have a higher than expected surface gravity, andthus would be more resistant to rotational disruption, and thus could be spun up very fast.

• I actually thought that this would be a good way to disprove the massive CCO theory. How-ever

Fast rotating small asteroids are very common, with the shortest known period being 25seconds.

This tendency for fast rotation could be explained by CCO masses in the stable rangepredicted by the Zhitnitsky theory, which of course is completely independent of anyasteroidal data.

• It is fair to say that this surprised me.

21

Asteroid “Rubble Pile” rotation limits

• It is hard to directly determine asteroid masses (unless there is a satellite or spacecraftpresent), but rotation rates are available for (at present) 5077 bodies, and it is simple todetermine the disruption rotation period, at least for so-called rubble piles with no internalstrength (cohesion).

• Suppose that you have a spherical asteroid, with a bulk density ρA, mass MA and radius RA,being spun up by YORP. At what point will it be rotationally disrupted?

• Disruption could come from internal fractures, but it is simple to consider the point at whichsurface mass is lost, when the gravitational and rotational accelerations are equal on thesurface at the equator.

• This is the so called “Rubble Pile” limit (RPL), which occurs at a rotational frequency, ΩRPL,with

Ω2RPL =

GMA

R3A

=4πGρA

3(1)

• Note that the RPL depends only on the bulk density.

For ρA = 2300 kg m3 the RPL rotation limit (PRP ) is ∼ 2.2 hours.

For an asteroid of solid Osmium, PRP ∼ 0.7 hours.

I call asteroids with P < 0.6 hours “Very Fast Rotators” (VFR).

22

The asteroid rotation period-radius relation

0.01

0.1

1

10

100

1000

10000

0.001 0.01 0.1 1 10 100 1000

Rot

atio

n P

erio

d (H

ours

)

Asteroid Radius (km)

(2981) Chagall

(66391) 1999 KW4

2008 TC3

(216) Kleopatra

NEOMain BeltTrans-Neptune ObjectsComet-Like OrbitsRPL (2.2 hr)Very Fast Rotator Limit (0.6 hr)

The change in the character of asteroid rotation rates at R ∼ 200 m is obvious to the eye, withmost asteroids with R < 200 m having rotation periods < 1 hour while almost all asteroids withR > 200 m have periods & 2 hours. The horizontal solid line is the Rubble Pile limit of Equation1 for a uniform density of 2300 kg m−3, and the horizontal dashed line is the 0.6 hour VFR limit.

23

Estimating Core Masses from the Rubble Pile Model

• The Rubble Pile limit of Equation 1 can be inverted :

Assuming a lack of internal cohesion it is straightforward to take the observed radiusand rotation frequency and estimate the mass of the CCO core, MQ, (assuming a defaultdensity, ρO, for the ordinary matter mantle, and a spherical body).

• This indirect mass estimate is not as firm as a direct mass estimate (say, from an orbitingspacecraft), but it can be done for numerous bodies.

• When this is done the centroid of the MQ distribution is ∼ 2.0 and 2.2 × 1010 kg, for allbodies and the VFR respectively, towards the upper end but still within the range predictedby the axion domain wall model for CCO formation.

The CCO theory can thus constrain the axion decay constant, fa, to near the upper end ofits predicted range (i.e., fa ∼ 2.8 × 1011 GeV).

24

CCO Core Mass Histograms from Asteroid Rotation

0

5

10

15

20

25

30

35

40

45

32 34 36 38 40 42 44 46

1e+06 1e+08 1e+10 1e+12 1e+14 1e+16 1e+18

# A

ster

oids

/ B

in

Log 10 Baryon Number

Mass (kg)

Axion ModelRange

Consistent withMaximum fa

All Rotation DataVFR (P < 0.6 hr)

Gaussian Fit : All DataGaussian Fit : VFR Data

Histogram of the CCO core mass required to prevent rotational disruption, assuming gravitationalbinding only. Estimates are referenced to a rubble pile model with a default ρ = 2300 kg m−3.Note that the centroids of these distributions are within the mass region predicted (completelyindependently) by the axion domain wall theory.

25

What About Cohesion?

• Real small asteroids are likely to have some cohesion, which will violate the Rubble Pilelimit of Equation 1.

For example, a rotation estimate of 97 seconds is available for the 2 meter body 2008TC3, which impacted the Earth over the Sudan, with no sign of a CCO core. This bodywas presumably held together

• This is a complicated topic, but note that some of the VFR have large surface accelerations(up to 1 m sec−2); it is hard to see how cohesion could be maintained over time (i.e., the firstmeteorite strike would disrupt the object).

This argument is more persuasive for the larger objects.

26

Positive outward equatorial accelerations(rotational minus gravitational)

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0.001 0.01 0.1 1 10 100

Out

war

d A

ccel

erat

ion

at th

e E

quat

or (

m s

ec-2

)

Asteroid Radius (km)

(2981) Chagall

2008 TC3

Near Earth AsteroidsMain Belt

P = 0.6 hr (VFR Limit)P = 1.3 hrP = 2.0 hr

Positive outward equatorial accelerations (rotational minus gravitational), assuming sphericalbodies with a density of 2300 kg m−3. (Positive outward accelerations of course imply that anyloose material at the equator would be lost to space.) A set of asteroids with a common densityrotating at their rubble pile limit would form a diagonally sloping cluster of points. Two suchclusters are visible and are marked by a diagonal dashed lines.

27

Extracting Energy From Strange Asteroids

28

Andreev reflection and Extracting Energy from a CCO

• Suppose that CCOs are indeed found in the NEO. Can energy be extracted from them?

This would be most straightforward from an antimatter CCO, but suppose that all CCOsare normal matter.

• The answer is that material added to a CCO would release a substantial amount of its totalenergy as they compress to the lower energy of the CFL condensate. This depends on theaxion decay constant and the mass of the CCO, but would be in the 10% to 20% range.Further, there is the possibility of Andreev reflection [Sadzikowski and Tachibana, 2002]

In Andreev reflection, quarks impacting on the CCO surface at or above the supercon-ducting gap energy, ∆, can pass inside the CCO, creating a new Cooper pair inside thesuperconductor through the creation of particle-antiparticle pairs, yielding one or moreantiparticles leaving the CCO boundary.

In other words, as seen from the outside, Andreev reflection consists of the reflection ofan incoming particle as an antiparticle.

• Andreev reflection offers the possibility of creating antimatter by exposing a normal matterCCO to a beam of 200 MeV protons.

29

Conclusions

30

Conclusions

• Thank you for your patience for a long review touching on a wide variety of subjects.

• There is a theoretical justification for assigning the dark matter to condensed quark matter,and observational justification to conclude that such matter is present in the Solar System.

• If such matter is available, it can be found and used for scientific research and resource(energy) extraction.

The NASA Asteroid Rendezvous and Retrieval Mission (ARRM), and the various com-mercial efforts in the same direction, would thus assume even greater importance.

• How much energy is potentially available? A 1010 kg CCO could potentially produce ∼ 4 ×1025 Joules worth of high energy and antimatter.

• While there would certainly be capture losses, it is worth pointing out that

this is ∼ 85,000 years worth of current human energy consumption, based on the 2013Statistical Review of World Energy [BP, 2013], and

this would suffice to accelerate a megaton mass spacecraft to close to the speed of lightand

there should be substantially more than 1 CCO available for NEO utilization.

31

Supporting Information

32

The “Bullet” Cluster(Chandra X-ray image with gravitational lensing mass

estimates overlaid)

The Bullet Cluster is the best current test of the non-gravitational physics of dark matter. Twoclusters have slammed into each other; the stars and dark matter continue on while the gas isstopped by fluid drag. This sets a strong constraint on the mass-cross section ratio of dark matter[Clowe et al., 2006].

33

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