mirror matter in the solar system- new evidence for mirror matter from eros

8/14/2019 Mirror matter in the solar system- New evidence for mirror matter from Eros

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arXiv:ast

ro-ph/0211067v2

12Nov2002

November 2002astro-ph/0211067

Mirror matter in the Solar system:New evidence for mirror matter from Eros

R. Foota and S. Mitrab

a [email protected] of Physics

Research Centre for High Energy PhysicsThe University of Melbourne

Victoria 3010 Australiab [email protected]

Instituut voor Theoretische FysicaUniversiteit van Amsterdam

1018 XE AmsterdamThe Netherlands

Abstract

Mirror matter is an entirely new form of matter predicted to exist if mirror symmetry is afundamental symmetry of nature. Mirror matter has the right broad properties to explainthe inferred dark matter of the Universe and might also be responsible for a variety of otherpuzzles in particle physics, astrophysics, meteoritics and planetary science. It is knownthat mirror matter can interact with ordinary matter non-gravitationally via photon-mirrorphoton kinetic mixing. The strength of this possibly fundamental interaction depends onthe (theoretically) free parameter . We consider various proposed manifestations of mirrormatter in our solar system examining in particular how the physics changes for differentpossible values of . We find new evidence for mirror matter in the solar system comingfrom the observed sharp reduction in crater rates (for craters less than about 100 meters

in diameter) on the asteroid 433 Eros. We also re-examine various existing ideas includingthe mirror matter explanation for the anomalous meteorite events, anomalous slow-down ofPioneer spacecraft etc.
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I. INTRODUCTION

One of the most obvious candidates for a fundamental symmetry of nature is mirrorsymmetry. While it is an established experimental fact that mirror symmetry appearsbroken by the interactions of the known elementary particles (because of their left-handed

weak interactions), this however does not exclude the possible existence of exact unbrokenmirror symmetry in nature. This is because mirror symmetry (and also time reversal) canbe exactly conserved if a set of mirror particles exist [1,2]. The idea is that for each ordinaryparticle, such as the photon, electron, proton and neutron, there is a corresponding mirrorparticle, of exactly the same mass as the ordinary particle. Furthermore, the mirror particlesinteract with each other in exactly the same way that the ordinary particles do. The mirrorparticles are not produced (significantly) in laboratory experiments just because they couplevery weakly to the ordinary particles. In the modern language of gauge theories, the mirrorparticles are all singlets under the standard G SU(3)SU(2)LU(1)Y gauge interactions.Instead the mirror fermions interact with a set of mirror gauge particles, so that the gaugesymmetry of the theory is doubled, i.e. G

G (the ordinary particles are, of course, singlets

under the mirror gauge symmetry) [2]. Mirror symmetry is conserved because the mirrorfermions experience V+A (right-handed) mirror weak interactions and the ordinary fermionsexperience the usual VA (left-handed) weak interactions. Ordinary and mirror particlesinteract with each other predominately by gravity only.

At the present time there is an interesting range of experimental observations supportingthe existence of mirror matter, for a review see Ref. [3,4] (for a more detailed discussion ofthe case for mirror matter, accessible also to the non-specialist, see the recent book [5]).The evidence includes numerous observations suggesting the existence of invisible darkmatter in galaxies. Mirror matter is stable and dark and provides a natural candidate forthis inferred dark matter [6]. The MACHO observations [7], close-in extrasolar planets [8],

isolated planets [9], gamma ray bursts [10] and even the comets [3,5] may all be mirror worldmanifestations.While we know that ordinary and mirror matter do not interact with each other via

any of the known non-gravitational forces, it is possible that new interactions exist whichcouple the two sectors together. In Ref. [2,11], all such interactions consistent with gaugeinvariance, mirror symmetry and renormalizability were identified, namely, photon-mirrorphoton kinetic mixing, Higgs-mirror Higgs interactions and via ordinary neutrino-mirrorneutrino mass mixing (if neutrinos have mass). Of most importance though for this paperis the photon-mirror photon kinetic mixing interaction.

In quantum field theory, photon-mirror photon kinetic mixing is described by the inter-action

L = 2

FF, (1)

where F (F) is the field strength tensor for electromagnetism (mirror electromagnetism).This type of Lagrangian term is gauge invariant and renormalizable and can exist at treelevel [2,12] or may be induced radiatively in models without U(1) gauge symmetries (such asgrand unified theories) [1315]. One effect of ordinary photon-mirror photon kinetic mixingis to give the mirror charged particles a small electric charge [2,13,14]. That is, they coupleto ordinary photons with electric charge e.

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The most important experimental particle physics implication of photon-mirror photonkinetic mixing is that it modifies the properties of orthopositronium [13]. The current

experimental situation is summarized in Ref. [16], which shows that


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depleted after the comet enters the inner solar system for the first time. In this way thelong standing comet fading problem can be solved: Many comets lose their small ordinarymatter component after passing into the inner solar system leaving an almost invisible mirrormatter core. Furthermore, this idea is consistent with recent observations confirming theapparent absence of any visible cometary remnants [31].

Anyway, if small mirror matter bodies do exist and happen to collide with the Earth,what would be the consequences? If the only force connecting mirror matter with ordinarymatter is gravity, then the consequences would be minimal. The mirror matter space-bodywould simply pass through the Earth and nobody would know about it unless the bodywas so heavy as to gravitationally affect the motion of the Earth. However, it is possiblefor ordinary and mirror particles to interact with each other by new interactions. Of mostimportance (for macroscopic bodies) is the photon-mirror photon transition force, Eq.(1).The effect of this interaction is to make mirror charged particles (such as mirror electronand mirror proton) couple to the ordinary photon with effective electric charge e [2,13,14].

One effect of this interaction is that the mirror nuclei can interact with the ordinarynuclei, as illustrated below:

atom in the space-body

pp

pp

Proton from anair molecule

Mirror proton from a mirror

Figure 1: Rutherford elastic scattering of air molecules as they pass through the mirror matter

space-body. The X represents the photon-mirror photon kinetic mixing interaction.

In other words, the nuclei of the mirror atoms of the space-body will undergo Rutherfordscattering with the nuclei of the atmospheric nitrogen and oxygen atoms. In addition,

ionizing interactions can occur (where electrons are removed from the atoms) which canionize both the mirror atoms and also the (ordinary) atmospheric atoms. This would makethe mirror matter space-body effectively visible as it plummets to the surface of our planet.

The effect of the atmosphere upon the mirror SB depends on a number of factors, includ-ing, the strength of the photon-mirror photon transition force (), the chemical compositionof the space-body, its initial velocity and its size and shape. We could estimate the initialvelocity of the space-body by observing that the velocity of the Earth around the Sun isabout 30 km/s. The space-body should have a similar velocity so that depending on its di-

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rection, the relative velocity of the space-body when viewed from Earth would be expectedto be between about 11 and 70 km/s .

Previous work [21] has shown that for relatively large values of 106, a mirror matterSB impacting with the atmosphere will experience the standard drag force:

Fdrag

= Cd

air

Sv2/2 (2)

where air is the mass density of the air, v is the velocity of the SB relative to the Earth andS is the cross sectional area. The reason is that the nuclei of the air molecules Rutherfordscatter with the mirror nuclei of the mirror atoms which make up the mirror SB. Providedthat the scattering length is much less than the dimensions of the SB which happens tobe the case for large 106 the momentum transferred and hence the drag force onthe mirror SB will be roughly the same as the standard case of an ordinary matter SB. [InEq.(2), Cd is the drag coefficient, which incorporates the hydrodynamic properties of airflow around the body. It depends on the shape, velocity and other factors, but is typicallyof order 1].

Obviously if is small enough, the interactions of the air molecules with the SB willbecome weak enough so that the air molecules can pass through the SB without losingmuch of their momentum (in the rest frame of the SB). In this regime, the drag force isproportional to the total number of molecules within the SB rather than the bodies crosssectional surface area (S). Our purpose here is to study in detail the effect of the atmosphereon the SB as a function of the (fundamental) parameter , and the other variables such asvelocity, SB size etc. This section can be viewed as a generalization of the previous paper[21], which focussed mainly on the case of large 106.

Assume that the mirror matter SB is composed of atoms of mass MA and the air iscomposed of molecules of mass MA. The (mirror) electric charge in units ofe of the (mirror)nuclei, will be denoted as Z (Z). Let us assume that the trajectory of the SB is a straight

line along the z axis of our co-ordinate system. In the rest frame of the SB, the change inforward momentum of each of the on-coming atmospheric molecules is then

dPzdt

= collMA(v cos scatt v) = 2collMAv sin2 scatt2

(3)

where scatt is the scattering angle in the rest frame of the SB and coll is the collision rateof the atmospheric molecules with the mirror atoms of the SB. The collisions also generatetransverse momentum, which we can approximately neglect for the moment since it averagesout to zero (which means that we can replace v by vz below).

The collision rate, coll can be related to the cross section in the usual way, coll =vzSB /MA, and thus Eq.(3) becomes

dPzdt

= 2

MAMA

d

dSBv

2

z sin2

scatt2

d (4)

The minimum velocity of a space-body as viewed from Earth is not zero because of the effect

of the local gravity of the Earth. The minimum velocity of a space-body is the Earths escape

velocity, about 11 km/s.

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There are two main processes which can contribute to the scattering cross section. For thevelocities of interest, v

1) and weak

coupling regime (DSB/z 1, that is,DSB160Z

2Z2SB 2e4

v4M2AMA

DSB5 metres

2 1082 30 km/s

v

4

> 1.[Strong coupling regime]. (9)

Note that because v can only decrease, a SB initially in the strong coupling regime willalways remain in the strong coupling regime.

In this strong coupling regime the drag force has the (standard) form Eq.(2), which caneasily be shown to lead to an exponentially decaying SB velocity:

vSB = viSBe

( xL),

= viSBe(h

H ) (10)

where h = x cos , H = L cos ( is the zenith angle of the SB, as illustrated in Figure 2)and

H =x cos x atmSCddx

2MSB

. (11)

Figure 2: Trajectory of a SB entering the Earths atmosphere, taken to be approximately a straight

path.

For the special case of constant air density (and Cd 1), H = 2 cosDSBSB/atm, whereDSB V /S is a measure of the size of the SB. Of course, the air density is exponentially

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decreasing with a scale height of h0 8 km [i.e. atm = 0atmeh/h0, 0atm 1.2103 g/cm3is the air density at sea-level]. Thus, we see that there is a critical SB size [

DSB ()] givenapproximately by

DSB ()

h0

0atm

2cos SB 5 metres

cos

. (12)

Space-bodies smaller than about

DSB lose their initial velocity in the atmosphere, while

space-bodies larger than

DSB retain most of their velocity. In other words, in the strongcoupling regime there are two limiting cases of interest:

(a) DSB DSB 5 metres

cos vfSB viSB (13)

Note that the above conclusion applies also to an ordinary matter SB. Of course, in practice

there are complications due to surface melting (ablation) and potential break up of the body(which we will return to in the following section).

Before we investigate what happens in the weak coupling regime, let us first introducethe following quantity:

DSB ( = 0)

z=

160Z2Z2SB 2e4

DSB ( = 0)

M2AMAv4

=80Z2Z20atmh0

2e4

M2AMAv4

2 1082

30 km/sv

4

. (14)

With this definition, the strong coupling regime corresponds to

>

DSB ( = 0)

DSB 5 metres

DSB[Strong coupling regime] (15)

B. The weak coupling regime

In the weak coupling regime, the air molecules will pass through the SB without losing

much of their momentum. In this case the atmospheric drag force will have quite a differentform to Eq.(2) (and we will calculate it in a moment). The weak coupling regime occurs

when DSB/z


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or in terms of ,


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where 0atm MAn0 1.2 103 g/cm3 is the air mass density at sea-level, and h0 8km is the scale height. Eq.(21), which can be derived from hydrostatic equilibrium, is

approximately valid for h


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Finally, observe that the experimental limit 11 km/s together imply that 10

5

Excluded

(from < 10-6

Retains

velocity

Retainsvelocity

STRO

NGCOUPLINGRE

GIME

WEAK

COUPLIN

GRE

GIME

Loses

velocity

105

5 metres

42~~

and v > 11 km/s)

Figure 3: Pictorial summary of the results of this section.

III. OBSERVATIONS OF ANOMALOUS IMPACT EVENTS

There are many reported examples of atmospheric phenomena resembling fireballs, whichcannot be due to the penetration of an ordinary meteoroid into the atmosphere (for a review

of bolides, including discussion of these anomalous events, see Ref. [32]). Below we discussseveral examples of this strange class of phenomena.

(i) The Spanish event January 18, 1994.

On the early morning of 1994 January 18, a very bright luminous object crossed the skyof Santiago de Compostela, Spain. This event has been investigated in detail in Ref. [24].The eye witnesses observed the object to be low in altitude and velocity (1 to 3 km/s). Yet,an ordinary body penetrating deep into the atmosphere should have been quite large andluminous when it first entered the atmosphere at high altitudes with large cosmic velocity(between 11 and 70 km/s). A large ordinary body entering the Earths atmosphere atthese velocities always undergoes significant ablation as the surface of the body melts and

vapourises, leading to a rapid diminishing of the bodies size and also high luminosity asthe ablated material is heated to high temperature as it dumps its kinetic energy into thesurrounding atmosphere. Such a large luminous object would have an estimated brightnesswhich would supersede the brightness of the Sun, observable at distances of at least 500 km.Sound phenomena consisting of sonic booms should also have occurred. Remarkably neitherof these two expected phenomena were observed for this event. The authors of Ref. [24]concluded that the object could not be a meteoric fireball.

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In addition, within a kilometre of the projected end point of the objects trajectorya crater was later discovered. The crater had dimensions 29 m 13 m and 1.5 mdeep. At the crater site, full-grown pine trees were thrown downhill over a nearby road.Unfortunately, due to a faulty telephone line on the 17th and 18th of January (the fireballwas seen on the 18th) the seismic sensor at the nearby geophysical observatory of Santiago

de Compostela was inoperative at the crucial time. After a careful investigation, the authorsof Ref. [24] concluded that the crater was most likely associated with the fireball event, butcould not definitely exclude the possibility of a landslide. No meteorite fragments or anyother unusual material was discovered at the crater site.

(ii) The Jordan event April 18, 2001.

On Wednesday 18th April 2001, more than 100 people attending a funeral processionsaw a low altitude and low velocity fireball. In fact, the object was observed to break upinto two pieces and each piece was observed to hit the ground. The two impact sites werelater examined by members of the Jordan Astronomical Society. The impact sites showedevidence of energy release (broken tree, half burnt tree, sheared rocks and burnt ground) but

no ordinary crater. [This may have been due, in part, to the hardness of the ground at theimpact sites]. No meteorite fragments were recovered despite the highly localized nature ofthe impact sites and low velocity of impact. For more of the remarkable pictures and moredetails, see the Jordan Astronomical Societys report [25]. As with the 1994 Spanish event(i), the body was apparently not observed by anyone when it was at high altitudes whereit should have been very bright. Overall, this event seems to be broadly similar to the 1994spanish event (i). For the same reasons discussed in (i) (above) it could not be due to anordinary meteoric fireball. Of course the energy release evident at the Jordan site is anothercompelling reason against an ordinary meteorite interpretation.

There are many other reports of such anomalous events. For an anomalous meteoritecatalogue see Ref. [34].

Can these anomalous meteorite events be due to the penetration into the atmosphere of amirror SB? Clearly, the low impact velocity suggests that the body has lost its cosmic velocityin the atmosphere. From our analysis in the previous section, we see that a small (DSB

cos .This suggests a rough upper bound on of about

> 109, which is certainly possible sincethe current experimental limit is

5 km/s) whichmeans that a small body (DSB


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h> 20 km). At low altitudes a small ordinary body is very dim, and its surface has already

cooled by the time it reaches the Earths surface. For this reason observations of meteoritefalls are quite rare. To summarize, an ordinary small body starts off very bright and becomesdimmer which is the exact opposite of what was observed for the anomalous meteorite events.

In the case of a mirror matter SB, things are quite different. Because the air molecules

penetrate the SB, the energy of the impacting air molecules on the SB is distributed through-out the whole volume of the SB, not just at its surface (much like the distinction between aconventional oven and microwave oven!). A mirror body would therefore heat up internallyfrom the interactions of the atmospheric atoms which would penetrate within the space-body. Thus, initially, the rate of ablation of a mirror matter SB can be very low, whichmeans that the mirror SB can be quite dim at high altitudes where it first enters the atmo-sphere. Evidently, the non-observation of the Spanish and Jordan events at large distances(> 50 km) is explained if they are caused by a small mirror matter SB. Furthermore, be-

cause the mirror SB heats up internally, it can act as a heat reservoir. If there happens tobe any ordinary fragments embedded within the SB, such fragments will be heated to hightemperature and may thereby be a source of light. This may allow the body to appear brightto nearby observers, perhaps consistent with the observations. Of course, one must checkthat the mirror SB does not heat up enough so that the whole body melts. In Ref. [22], therelevant calculations were done and it was shown that small mirror SB can remain intact if itis made of highly non-volatile material and have initial velocities near the minimum allowedvalue 11 km/s. For volatile material such as ices and/or impacts at higher velocities,mirror SB typically heats up so much that the whole body melts, leading to a rapid releaseof the SB kinetic energy into the atmosphere an air burst.

The lack of ordinary fragments is also explained if the mirror SB is made of (or predom-inately of) mirror matter. Yet, mirror matter fragments should be stopped in the ground(and potentially extracted!) because the small electromagnetic force implied by the photon-

mirror photon kinetic mixing is strong enough to oppose the force of gravity (provided that

> 1010) [22]. After the mirror matter body strikes the ground its properties dependimportantly on the sign of (for a detailed discussion, see Ref. [22]). For > 0, mirroratoms repel ordinary atoms (at close range) while for < 0, mirror atoms attract ordinaryatoms. Hence, for positive one might expect some fragments of mirror matter to exist righton the ground, depending perhaps on the composition of the ground and SB and also onthe velocity of impact etc. On the other hand, for negative epsilon mirror matter could becompletely embedded within ordinary matter, releasing energy in the process. Perhaps thisrelease of energy was responsible for the burning of the ground (and tree!) at the Jordanimpact site.

Another source of energy release from an impacting mirror body might come from thebuild-up of ordinary electric charge within the body [35]. Electric charge can accumulatedue to the effect of ionizing collisions. Air molecules (initially) strike the SB with velocityv 30 km/s, which implies a kinetic energy of:

E =1

2MAv

2 140

v

30 km/s

2eV (26)

Clearly, the energy of the impacting air molecules is great enough for ionizing collision to

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occur. Furthermore, ionized air molecules can be trapped within the SB due to the effects ofRutherford scattering, while the much faster moving electrons can escape the body, leadingto a build up of ordinary electric charge within the mirror SB.

Thus, it seems that the small anomalous meteorite events are only anomalous if they aredue to an ordinary matter SB. If they are instead composed of mirror matter, then they

apparently fit the observations. Clearly this is good reason to take this possible explanationseriously. Another reason is that there is no other known mechanism which can explain theirexistence!

On larger scales, we have the famous Tunguska event [26]. The Tunguska event is theonly recorded example of a large SB (DSB 100 metres) impact. This event is characterizedby a huge release of energy at a height of about 8 km. Recall that an ordinary or mirror SBof size DSB 100 metres does not lose much of its initial velocity in the atmosphere (pro-vided that it remains intact). Presumably the Tunguska space-body rapidly disintegratedat low altitudes causing a large increase in effective surface area of the body allowing it toquickly dump its kinetic energy into the atmosphere. Remarkably no significant fragmentsor chemical traces were found at the Tunguska site. Furthermore there was evidence for

smaller subsequent explosions at even lower altitudes and some evidence that part of theSB continued its journey after the initial explosion [26]. While the huge explosion may havevaporized most of the SB material the lack of even chemical traces (such as iridium excessin the soil), small fragments, and the evidence for smaller subsequent explosions make theTunguska event quite puzzling.

If the Tunguska event is due to the penetration of a mirror SB, then it seems to besomewhat less puzzling. In this case the lack of ordinary fragments and chemical tracesare automatically explained. The atmospheric explosion is expected as the body heats upinternally and melts. Previous calculations [22] have shown that the typical height for thisto occur is of order 5 10 km for a mirror icy body moving at 11 km/s. In this caseit is quite possible for small pieces of the body to survive especially if the body is not ofhomogeneous (mirror) chemical composition, which can lead to secondary explosions.

IV. OTHER APPLICATIONS

A. Impact craters on asteroids

The proportion of mirror SB to ordinary ones in the solar system is theoretically un-certain. However there are some reasons to think that mirror SB could actually dominateover the ordinary ones. First, if comets really are the mirror SB, then estimates [31] of

the number of such bodies in the inner solar system inferred from the rate at which newcomets are seen is large and dwarfs the visible (ordinary body) population. Second, if theanomalous meteorite events (including Tunguska) are due to mirror SB this hints at a largemirror SB population. Indeed, recent estimates of small visible bodies (presumably made ofordinary matter since mirror SB would appear to be quite dark, potentially unobservable) issurprisingly low, giving a Tunguska-like impact rate of one per thousand years [37]. So, theexistence of a Tunguska sized event within the last 100 years does suggest that the mirrorSB impact rate may exceed the ordinary body rate. Finally, there is one more indication of

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a large population of mirror SB coming from observations of crater rates on asteroids, as wewill now explain.

Impacts of mirror SB on small ordinary bodies such as asteroids or moons is of particularinterest because of the absence of atmospheric effects. In this case the mirror SB will lose itsenergy at or below the surface. The stopping distance (L) of a mirror SB can be calculated

from Eq.(8) with the replacement SB asteroid and MA MA , which is

L v4M2AMA

160asteroidZ2Z22e4

v

30km/s

4 109

2km, (27)

This formula only makes sense in the region of parameter space where L> DSB . In the

case where L DSB and

> 108 then the SB will (typically) completely melt and breakup before releasing all of itsenergy within the target object (moon/asteroid). Roughly, the energy will be released overa significant (cone shaped) volume. This will cause heating of the target object which may

also melt, but will subsequently reform.Clearly, the impact of a mirror SB will be quite different to an ordinary impact, even

when L DSB . This is because the energy is released not as quickly as an ordinary impact,which may well be expected to reduce the size of the crater, if indeed one is formed. Ofcourse, detailed numerical simulation work needs to be done. Nevertheless, qualitatively,we can at least observe that it might be possible to infer the size of by looking for acharacteristic crater size below which there is a significant reduction in crater rates. Thepoint is that small mirror SB with sizes DSB/L 1 will not form impact craters because theenergy is released too slowly and over too large a volume. Of course, to have an observableeffect assumes that there is a significant proportion of mirror SB in the solar system, which

is certainly quite possible (as discussed above).Taking a vmax of 30 km/s, then the condition that L DcritSB implies that:

108

v30km/s

2

DcritSB /10metres(28)

This equation relates the value of to the minimum size of the SB (DcritSB ) for which a cratercan form. We now need to relate the crater size (Dcrater) to the size of the impacting SB(DSB). [Roughly, we would expect Dcrater (10 100)DSB ]. We also need to see if there isany evidence of a crater hiatus at a critical crater size.

Actually, there is interesting evidence for such a crater hiatus coming from observationsof the NEAR-Shoemaker spacecraft. This spacecraft studied the asteroid 433 Eros in greatdetail, orbiting it and eventually landing on its surface in February 2001. Analysis of the

Observations on asteroids are particularly clean because of the absence of secondary impacts

(i.e. impacts caused by ejected material falling back on the body after the primary impact) which

inevitably occur for impacts on large bodies such as the moon.

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size of craters on Eros surface shows [38] a sharp decrease in the crater rate for craters lessthan about 70 metres in diameter. The number of craters below 30 metres in diameter isseveral orders of magnitude less than expected [38]. Interpreting this reduction as the onsetof the predicted crater hiatus for mirror SB impacts suggests an of order 107 109. [Amore precise estimate would require a detailed simulation of mirror SB impacts to determine

a) more precisely DcritSB [i.e. improve on our rough estimate, Eq.(28)] and b) more precisely

how Dcrater is related to DcritSB ].

Taking a closer look at Eros, we can find one more tantalizing hint supporting the mirrorSB hypothesis. Crater ponds were unexpectedly observed on Eros [39,38]. These are flatsurfaces at the bottoms of craters (for a picture of one of these, see Ref. [39,40]). In fact,they are found to be extremely flat (relative to local gravity), as if they were formed by afluid-like motion. Yet, the ponds are currently no longer fluid-like, since their surfaces havesteep-walled grooves, small craters and support boulders [39]. In other words, the materialcomprising the ponds was fluid-like when the ponds were formed, but then became solid-like. These puzzling observations may have a simple explanation within the mirror SBhypothesis. The impact of a large mirror SB, large enough to form a crater, would melt

not only the mirror SB, but also a part of the asteroid. The melted rock of the asteroidand/or the remnants of the mirror SB may have left a smooth flat surface, depending on theviscosity of the material, rate of cooling etc. Indeed, the pictures of the ponds [39,40] lookso much like real ponds that it is tempting to speculate that they are made of mirror ice,with perhaps a surface covering of ordinary dust. This might be possible if the mirror SBwere predominately made of mirror ices (mirror H2O, mirror NH3 etc). After the impact,a large part of the mirror SB vaporized, and some condensed remnants were left on theasteroid surface which eventually froze .

At the present time, Eros is the only small (i.e. asteroid-sized) body which has beenmapped in detail on small scales. Clearly, we would expect a similar dearth of small craters

to occur on other small bodies such as other asteroids and the moons of Mars. Ponds couldalso be expected to occur, but they might be obscured by dust and debris, depending onthe strength of the bodies gravity.

We now turn to another indication for mirror matter in our solar system, coming fromquite a different direction.

Of course, this explanation would only be viable if there were some mechanism to keep the

mirror matter on the surface. Mirror matter in the solid state can potentially exist on the surface

because the small photon-mirror photon interaction can oppose the feeble gravity on a solid mirror

fragment(c.f. Ref. [22]). However, while the mirror matter is in the liquid form one might expect

it to seep into the asteroid, thereby preventing a mirror ice pond from forming on the surface.

However, it might b e possible for the mirror water to freeze at some depth below the surface,

which could then act as an impermeable barrier to keep the mirror liquid from seeping further into

the asteroid, at least long enough for a frozen pond to form on the surface.

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B. Pioneer Spacecraft anomaly

Another interesting indication for mirror matter in our solar system comes from thePioneer 10 and 11 spacecraft anomalies. These spacecraft, which are identical in design,were launched in the early 1970s with Pioneer 10 going to Jupiter and Pioneer 11 going

to Saturn. After these planetary rendezvous, the two spacecraft followed orbits to oppositeends of the solar system with roughly the same speed, which is now about 12 km/s. Thetrajectories of these spacecraft were carefully monitored by a team of scientists from the JetPropulsion Laboratory and other institutions [27]. The dominant force on the spacecraft is,of course, the gravitational force, but there is also another much smaller force coming fromthe solar radiation pressure that is, a force arising from the light striking the surface ofthe spacecraft. However, the radiation pressure decreases quickly with distance from thesun, and for distances greater than 20 AU it is low enough to allow for a sensitive test foranomalous forces in the solar system. The Pioneer 11 radio system failed in 1990 when itwas about 30 AU away from the Sun, while Pioneer 10 is in better shape and is about 70AU away from the Sun (and still transmitting!).

The Pioneer 10/11 spacecrafts are very sensitive probes of mirror gas and dust in our solarsystem if the photon-mirror photon transition force exists [23]. Collisions of the spacecraftwith mirror particles will lead to a drag force which will slow the spacecraft down. Thissituation of an ordinary matter body (the spacecraft) propagating through a gas of mirrorparticles is a sort of mirror image of a mirror matter space-body propagating through theatmosphere which was considered in the section II.

Interestingly, careful and detailed studies [27] of the motion of Pioneer 10 and 11 have re-vealed that the accelerations ofboth spacecrafts are anomalous and directed roughly towardsthe Sun, with magnitude, ap = (8.7 1.3) 108 cm/s2 . In other words, the spacecraftsare inexplicably slowing down! Many explanations have been proposed, but all have been

found wanting so far. For example, ordinary gas and dust cannot explain it because thereare rather stringent constraints on the density of ordinary matter in our solar system com-ing from its interactions with the suns light. However, the constraints on mirror matter inour solar system are much weaker because of its invisibility as far as its interactions withordinary light is concerned.

If the interactions of the mirror particles are strong enough so that the mirror particleslose their relative momentum within the spacecraft, then the drag force on the spacecraftis proportional to the bodies cross sectional area, Eq.(2) [with air replaced by the massdensity of mirror matter encountered by the spacecraft]. The condition that the mirrorparticles lose their relative momentum within the spacecraft can be obtained from Eq.(9):

> 107

v

12 km/s

2centimetre

DSB(29)

This is the case considered in Ref. [23]. In this case setting ap = Fdrag/MPioneer implies thatthe density of mirror matter in our solar system is about 4 1019 g/cm3. It correspondsto about 200,000 mirror hydrogen atoms (or equivalent) per cubic centimetre [23]. If themirror gas/dust is spherically distributed with a radius of order 100 AU, then the totalmass of mirror matter would be about that of a small planet ( 106Msun) with only about

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108Msun within the orbit of Uranus, which is about two orders of magnitude within presentlimits. If the configuration is disk-like rather than spherical, then the total mass of mirrormatter would obviously be even less.

For values of much less than 107 we are in the weak coupling regime and the drag forceis proportional to the mass of the spacecraft (assuming it is of uniform chemical composition).

In this case, the anomalous acceleration is given by [using Eq.(20) and adrag = vdv/dx]:

adrag =Z2Z22e440S

MAM2Av2

(30)

To explain the measured anomalous acceleration requires

S 1017

3 109

2g/cm3 (31)

Constraints on the presence of invisible matter from the orbit of Uranus [36] suggest anupper bound on S of 1017 g/cm3 assuming that the invisible matter is sphericallydistributed, while, if the mirror matter is predominately distributed on the ecliptic (ratherthan spherical), then the limits on S from the gravitational perturbations of the outerplanets are very much weaker.

C. Earth through going events

Hitherto we have discussed SB coming from our solar system. For such SB, their velocity(relative to the Earth) is limited to about 70 km/s. SB coming from outside the solar systemwould have a much larger velocity. A mirror SB from the galactic halo would have a typicalvelocity of about 300 km/s, while an intergalactic SB would have an even higher velocity.

Such high velocity bodies would penetrate the atmosphere without losing significant velocityand penetrate a significant distance underground. Of course, such events should be very rare,but nevertheless should occur from time to time. Such events could cause Earthquakes,perhaps distinguishable from ordinary Earthquakes by the location of the epicenter (farfrom fault lines etc).

As well as causing Earthquakes, it might also be possible to have a through going SB,that is, one that enters and exits the Earth. From Eq.(27), we have

L v4M2AMA

160EarthZ2Z22e4

v

300km/s

4 109

2104 km. (32)

Interestingly, a recent study [41] has found evidence for two such events (both with L 104

km), which might be consistent with such a high velocity SB if 108 1010. Clearly,more work (and more data!) is needed.

This concludes our exploration of the solar system implications of mirror matter.

The requirement that the mirror gas/dust be denser than its ordinary counterpart at these

distances could be due to the ordinary material having been expelled by the solar wind.

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V. CONCLUDING REMARKS

We have explored further the implications of mirror matter in the solar system. These im-plications depend importantly on the fundamental parameter which describes the strengthof the photon-mirror photon interaction. We have decided to ignore interesting, but as

yet unconfirmed hints suggesting 106

[16] coming from the 1990 vacuum cavity or-thopositronium experiment [17] and study how the physics changes as we vary (i.e. with

0 < 109. In addition, a similar bound also arises from the mirror matter explanation for

the Pioneer spacecraft anomaly (assuming that the mirror matter is spherically distributed).We have argued that there are some hints that small mirror space-body actually dominate

over ordinary matter bodies in the solar system. In fact, under this assumption, we havefound some interesting new evidence for mirror matter in the solar system. This arises fromthe observation that mirror space-bodies colliding with asteroids should not leave any craterif the space-bodies are below a certain size, the precise value depending on . Thus, weexpect a crater hiatus for craters smaller than some characteristic size. Interestingly, sucha sharp crater reduction is in fact observed, suggesting that is in the range 107 109.This range is consistent with the mirror matter interpretation of the anomalous meteoriteobservations (including the Tunguska and Jordan events) and Pioneer spacecraft anomaly.

The results of this paper have important implications for future orthopositronium exper-iments (such as the ETH-Moscow experiment [28]). These experiments may be able to covermuch of the interesting parameter range, especially if happens to be larger than about108. However, if we are unlucky and happens to be below about 108 then it may notbe possible to reach the required sensitivity with orthopositronium for a while. In any case,direct detection of mirror matter is possible at the impact sites such as the one in Jordan[25], which only requires that the mirror matter is stopped in the ground (i.e.

> 1010

[22]) and could be the best way of really proving the existence of mirror matter.

Acknowledgements

R.F wishes to thank S. Blinnikov and J. Learned for learned correspondence regardingthe through going space-bodies and R. Volkas and T.L. Yoon for general discussions. R.F.would also like to thank G. Filewood, for some viscous discussions.

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