arXiv:1104.4572v4 [astro-ph.EP] 15 Mar 2013 nyafato ftekntceeg aaigtesolid the damaging to energy refer with kinetic therefore body, We the the surface. of exit fraction will a many and only body, target the enter ytmrcybde s“punctures”. as bodies rocky System surface- the the puncture: bodies, rocky the penetrating with in collisions difference their of observable outcome distinct the provides matter mti rs eto n h ihsraegaiy such gravity, surface high ge- the small and c in the resulting section and density cross high bodies ometric of System account Solar On with some Earth? collided Could have Universe? them the of in bodies asteroidlike and teor a lomd o irszdbakhls[0,ta work 12]. that [11, consideration [10], recently Similar holes extended black b) considerably microsized [9]; was for Moon made and also searched [8] was been distur- Earth have signatures on seismic seismic for subatomic such generating and 7], of size [6, tiny bances capable their and of account self-binding, on body rocky tde.a ysrneqakmte ncerts [6] “nuclearites” matter quark strange By of a) studies. [5]. Station AMS-spectrometer to Space International the efforts the with ongoing on flux mounted with strangelet [4] continues the the experiments search observe from production space soil laboratory the found in but nor been nu- [3], not Light Moon have 2]. matter, [1, strangelets density matter clearite nuclear ultrahigh strangeness-rich of as forms such novel as- of about presence insights the This recognizing to teroid impacts. path a meteorite provide bodies. matter should rocky ap- normal their solar from distinguish other which pearance and discussed are Moon features appli- the Simple as Mars, considerations the to extend cable and Earth, on cusing as r ue u 1,14]. [13, out ruled are mass) es asv opc aoojcs( objects halo mas- sur- compact for microlensing massive by limit provided mass is veys: upper objects An “invisible” wide. sive rather is periment etcass i omldniyojcssc splanets as such objects density normal (i) classes: ject M ynra atraelkl osrietastthrough transit survive to likely atmosphere. are Earth’s matter normal by ompact edsrb eetepyisof physics the here describe We Introduction. The hswr xed h asrneo ro puncture prior of range mass the extends work This M & . M CUDO CUDO 10 ⊕ u ltra 4 5 = m bu oe om fmte.W td h nryls nCD p 95.35.+d,14.80.-j,21.65.Qr,95.25.Pq CUDO numbers: PACS in impacts. loss CUDO energy and the Syste matter study Solar regular We the between matter. in differences of bodies forms rocky novel other about and Earth with density, nteUies,ada uhoe new offer such as and Universe, the in s proton d esuyitrcin fmtolk opc lrdneobj ultradense compact meteorlike of interactions study We asrneta sntecue yex- by excluded not is that range mass . ense 97 Wa fteeae“ak atrme- matter “dark” are there if —What × eercgie spsigars a across passing as recognized were CUDO o 10 jcs( bjects 24 CUDO g(..lre hnEarth’s than larger (i.e. kg ’hg est fgravitating of density high s’ MACHO oanRafelski Johann CUDO 1 CUDO eateto Physics, of Department h nvriyo rzn,Tco,Aioa 52 USA 85721 Arizona, Tucson, Arizona, of University The opc lrdneMte Impactors Matter Ultradense Compact ilpatclyalways practically will CUDO olsoswt Solar with collisions )“rse”o not or “dressed” s) opietoob- two comprise s MACHO ucuefo- puncture Dtd etme ,2012) 3, September (Dated: 1 ac Labun Lance , )with s) 2 rga nApidMathematics, Applied in Program vrl,b as h akmte saot4tmsas times 4 about is matter. matter visible is dark [20]. as the matter abundant visible mass, of by density local Overall, averaged the to equal efud h siae akmte est ntelocal is the Way in Milky density the matter of dark area to estimated is The matter observational dark found. indirect which be in gravitating or state direct the and constraining no evidence dynamical is There independent, component. an as matter present the to compared as system condition. solar the of domains within enhancement density periodic flux matter in resulting visible galaxy, high the of in enhanced that likely is of is type density It higher matter. comprising visible passes regions it arm particular, in spiral and, through times few circling Way, a Milky center the galactic of the domain large a samples System h xetdsotosrainpro cutcsignal acoustic period light observation of of short events than number numerous accumulated expected more much the the being bil- in events of result puncture period will heavy a years over of flux lions integrated the of consideration sfamnsfo olso fnurnsa oe that cores (nearly star matter neutron quark of strange collision contain a from fragments as collisions. taglt erae ihterms ie1 like mass their with decreases strangelets nselreouineet sntrlysaladtheir and rare. very small be naturally would impacts is body events rocky evolution stellar in ucue ecoewt hr icsino h event on the deposition of discussion energy short of a discussion with signatures. close a We to puncture. turn then We eatn ev akmte particles. nonin- matter otherwise dark arise of heavy conglomerate would limit teracting loose as mass relatively such lower a The stability from gravitational here. in den- study higher originates we and which matter objects neutron (ii) sity and stars, dwarf and on ob tbeo omlgcltm cl [17]. scale time sufficiently cosmological nuclearite a be of flux on may expected stable the matter However, be quark to strange bound of macroscopic Such nuggets 16]. [15, matter) symmetric abundance n h u n ucuefeunyb massive by frequency puncture and flux the and 1 td fteBle lse 1]dmntae dark demonstrates [19] Cluster Bullet the of Study Solar the time “observation” puncture long this During vni h u fmassive of flux the if Even oeta ore of sources Potential ebgncnieigteptnilsucsof sources potential the considering begin We n eeihBirrell Jeremiah and , cs(UO,hvn ula rgreater or nuclear having (CUDO), ects sapsil oreo information of source possible a as m — CUDO ntr ftebd n discuss and body the of uncture CUDO ulaiemtoscnb produced be can meteors nuclearite s. ρ 2 d CUDO 5 = CUDO . CUDO 3 × and s 10 uha nuclearite as such s − bnac fany of abundance s 22 CUDO = kg CUDO / u m /M = 3 created s roughly , CUDO d aeof rate 6 18], [6, -quark CUDO CUDO s. 2

Considering that dark matter is the dominant form of impacts will be yet less damaging to the target body, but matter in our time, recent (on the scale of 100 millions of entail a much greater local force. years) impacts of dark matter CUDOs should be frequent: A conservative CUDO puncture rate is obtained by ig- The Sun and the large Solar System bodies comprise a noring the concentration of CUDOs in the proximity of vastly dominant fraction of the visible matter comoving the Solar system, i.e. spreading CUDO matter, taken as with Earth in the galaxy. Since by mass the abundance equal to the solar system visible matter, over the volume of visible and dark matter is similar, it follows that even cell in the Milky Way occupied by the solar system. For if a relatively small fraction e.g. 10−6 of dark matter is comoving CUDOs the gravity of the Sun focuses objects bound in meteor-sized objects, their flux would be similar passing nearby, increasing the flux of objects whose tra- to the number of normal matter meteorites, though the jectories enter the inner solar system (achieving a mini- distribution in space could be very different. mum radius smaller than Earth’s orbit Rorbit,E) and en- The above argument presumes that a tiny fraction of hancing in that way the effective cross section all dark matter is clumped. Clumping of the very heavy “cold” dark matter dust has so far received little atten- 2GM⊙ 2 σ = 1+ 2 4πR⊕. (1) tion and a study of this process is beyond the scope of vgalRorbit,E ! this work. However, large scale visible matter structure 2 in the Universe depends on the existence of gravitating (4πR⊕ is the planetary detector surface area.) dark matter density fluctuations formed in the early Uni- We do not know the CUDO mass distribution in the verse. Therefore the question is not if dark matter fluc- flux. Hence what follows is for an average mass compact tuations exist but if yet higher density gravitationally impactor. The CUDO number density n = ρd/M, leads bound dark matter objects can arise. to an expected annual event rate for puncture on the Earth, Beyond the first step described above there could be −18 km/s M⊕ −1 a continued mutual speed-up and reinforcement of visi- N⊕(v,M)= nσv 3 10 yr (2) ble matter and dark evolutionary dynamics: once enough ≃ v M visible matter converged together near the first dark mat- where M is the mass of a typical CUDO and v is the ve- ter fluctuations, and first stars form, these stars become locity attained by the object at Rorbit,E. We expect up −9 themselves gravitational attractors helping to aggregate to a dozen collisions with CUDOs of M < 10 M⊕ over dark matter, assisting in the formation of dark gravita- the course of Earth’s history. If the CUDO mass spectrum tionally self bound objects, which can be freed at the end parallels the normal matter impactor mass spectrum [23], of some stellar evolution cycles. The lighter CUDOs with lower mass punctures will be significantly more frequent −15 a mass significantly below that of the Earth are those and collisions with M < 10 M⊕ (i.e. objects of mass that would be of interest in the puncture process we ad- below 6 million tons) occurring as often as every few hun- dress here. dred years. Like in the study of neutron stars, dark matter CUDO punctures.—A CUDO comoving at low rel- CUDO properties are obtained solving Oppenheimer- ative velocity outside the solar system achieves v Volkov equations for a heavy gravitating dust [21, 22]. 20 60 km/s relative to Earth. As a result, the CUDO∼ The higher the mass of the cold dark particles, the penetrating− the crust will be supersonic in the mantle smaller the Oppenheimer-Volkov upper mass stability (cs 8 km/s). Understanding the dynamics of a super- limit, and the fewer particles that are needed to form sonic∼ compact gravitating body passing through a dense self-bound body. Should the upper stability mass limit planetary medium is the key physics challenge. We gen- be exceeded, a dark black hole is formed in a gravitational eralize and expand on preceding considerations of punc- collapse [12]. Aside from this upper mass limit there is tures by micro black holes [10, 11]. a minimum mass required for the presence of sufficiently We propose estimates of magnitudes based on linear high self gravity to provide stability in during the Uni- response and two mechanisms of energy exchange with verse’s evolution to the current epoch. planetary matter: (i) pulverization and entrainment of We consider punctures by a member of the cloud of ob- rock nearest the trajectory of the object, and (ii) cre- jects comoving with the solar system. Any such accompa- ation of a supersonic shock. We expect the assumption nying CUDOs have isotropic velocities vgal a few km/s of linear response breaks down for masses greater than ∼ relative to the solar system. Given that the two classes some Ms(v), resulting in a more inelastic nonlinear re- of collisions (normal and CUDO) with rocky bodies were sponse. The following scaling considerations can be con- not distinguished before, we consider the velocity distri- sidered valid only for M

101 In an ideal fluid model, capture efficiency is 100% and 2 2 Ak = 2 1 b /R⊕. The numerical coefficient is ob- 100 − tained withq the density of mantle ρ 4000 kg/m2 and ≃ -1 Rc Rc Rc Rc considering Ak = 1. However, there is also the kinetic 10 energy and the drag of uncaptured material which we

c expect to be of similar magnitude. 10-2 L/R Comparison to the kinetic energy before collision, 4 -3 10-9M 10-7M 10-5M 10-3M 10 ⊕ ⊕ ⊕ ⊕ ∆E ρ 2 40 km/s M = Ak R⊕πRc 0.013 (7) E M ≃ v M⊕ 10-4   −4 suggests that objects M < 10 M⊕ pass completely 10-5 through Earth without being stopped and the energy 10-5 10-4 10-3 10-2 10-1 100 101 102 103 transferred to the entrained matter is at and below r [m] 1/1000. While the total energy deposited in the target body is a small fraction of the total kinetic energy, the FIG. 1: The tidal fracture length scale L from Eq. (4) normal- energy deposited by the CUDO at the surface is still much ized to the capture radius Rc Eq. (5) as a function distance from the trajectory. The velocity of the compact object is smaller. A normal matter meteorite is stopped soon after fixed at v = 40km/s and cs = 8km/s used for the speed of impacting the surface, which requires that it dissipates sound in the mantle; a higher v only reduces L/Rc. all of its kinetic energy in a relatively small target area. Therefore the CUDO puncture is much less destructive than normal matter meteorite. expect a fracture to open within the length L. We com- We note features specific to the case of strangelet pare the differential gravitational pressure, which is the CUDOs which originate in the electrical charge of the product of the tidal acceleration and mass per unit area, strange quark matter core. Strangelet CUDOs are ex- pected to acquire a dressing of normal matter, forming 2GML P (r L/2) P (r + L/2) = ρL, (3) a “crust” [25] . For the mass range of interest, the ki- − − r3 netic energy will suffice to press additional matter across the electric potential into the quark matter core. Con- to the material’s bulk modulus K = ρc2, which is a func- s sequently, additional matter can be captured. The re- tion of the density ρ and the sound speed c . L then s sulting change in strangelet mass will depend primarily scales with the distance r from the trajectory as on the amount of matter encountered during the punc- 3/2 ture: we find the fractional mass change corresponding L r −3 = A . (4) to Eq.(7) is of order 10 (M/M⊕), and only 150 times R f R c  c  larger when considering the Sun as a target. However, a charged strangelet CUDO [26] would lose additional en- with A = √2(c /v). R is the capture radius [24] f s c ergy during the puncture due to electrical ionization and 2 polarization effects, which may be particularly impor- 4GM 6 40 km/s M Rc := 2 = 10 m (5) tant in strangelet collisions with the Sun. Solar impacts v v M⊕   as well as strangelet-strangelet collisions depend further within which material can be entrained with the object on strange quark matter bulk properties. These are the subject of present day interest in view of nontrivial color- and acquires its velocity v. Figure 1 shows that L/Rc < superconducting and color-flavor locked cold quark mat- 0.1 for radii less than Rc. All capture-eligible material is broken into pieces small enough to be pulled along with ter phases [27]. the object, thus forming a slug of fine particulate matter To establish that material in and around the slug is carried with the CUDO even as it exits the target body. indeed molten, we look at temperature in the bow shock The velocity of the CUDO is reduced by the capture 2 kBT = AT v (8) of material, because the slug of entrained material must acquire the comoving kinetic energy, the average gain in with AT depending on the atomic composition of the potential gravitational energy being small in comparison material. Taking an ideal gas model [28] in view of the −27 high temperatures expected gives AT =3 10 kg and 2 2 2 5 × 2 v 31 40 km/s M T 10 K. Estimating based on the continental secular ∆E = AkρR⊕πRc 6.4 10 J ≃ 2 2 ≃ × v M⊕ cooling rate of Earth 80 mW/m , the conduit formed    (6) by the puncture could∼ remain a significant local source Ak contains factors for capture efficiency (which may dif- of thermal energy, recognized by transient deep-origin fer from unity due to drag between captured and neigh- volcanism not related to plate boundaries. boring material) and impact parameter b (which deter- Supersonic shock wave.—At ranges larger than Rc tidal mines total volume of tube radius Rc around trajectory). stresses generate an intense seismic wave. Since the ve- 4 locity of the CUDO is greater than the speed of sound and relatively small in particle number CUDOs could be in the mantle or crust, the wave is compressed into a formed primordially by density fluctuations [32], poten- shock. Energy deposition via coherent acoustic emission tially absorbing a large fraction of dark matter particles has been given as Eq. (13) in [11] as used in flux estimate Eq. (2). Strangelet CUDOscan be 2 2 formed in more recent times, e.g. in collapsing stars [16]. dE 2 2 26 M 40 km/s J = AsπRc ρv 1.9 10 Discussion and outlook.—The salient observable dx ≃ × M⊕ v m shock     feature of CUDOs is their capability to create puncture in (9) 2 2 rocky bodies. On account of the relatively small energy where As = (1/8) ln(cs/4πGρa ), a being typical inter loss distributed across the puncture conduit, even rel- atomic spacing. This estimate finds a large amount en- atively massive CUDO punctures preserve the integrity ergy in the compression wave, 40 times the captured mat- of the target and inflict in such event a relatively small ter kinetic energy Eq. (6). shotlike damage. CUDO stability on impact.—Micro black holes are While the exit “wounds” must be fewer than puncture stable and puncture through the target. Nuclearite entries, on account of possible CUDO instability after en- CUDOs are bound by nuclear scale forces and if stable try, their appearance should be more characteristic con- on cosmological time scale, atomic scale forces cannot sidering that there is little else in the Universe that can pull them apart. On account of the much larger dark generate an exit conduit from a body and, considering matter particle mass, the dark matter CUDO has a very Earth puncture, can transport material into the upper high density, and its Roche limit (2ρ <ρ for CUDO at t c atmosphere. A puncture event may be thus recognized target surface) is not relevant in stability consideration. by coincidental presence of impact and ultrastrong “vol- In fact our evaluation of the effect of a CUDO on the tar- canic” eruption. The AD 536 event [33–35] which has get body is like an “inverse” Roche process in that the lead to a major historical climate excursion invites reex- target structure is locally broken by the tidal forces of amination as a possible full CUDO puncture, i.e. impact the high density CUDO. and exit accompanied by material transport into the up- Conversely, for a gravitationally self-bound CUDO of per atmosphere. sufficiently small mass, the potential energy at the sur- face will be small enough to allow the target induced Most recent and present epoch CUDOs are possibly polarization force to shear and attract particles from the dressed in normal matter and thus many punctures are CUDO. The qualitative condition for transfer of matter also “normal” meteorite impacts. Depending on the ratio is that the presence of the target body opens a potential of normal to CUDO mass and the composition of normal valley from the binding potential of the CUDO at its sur- matter component, there are characteristic CUDO fea- tures in comparison to impacts by solely normal meteors: face Rc towards the potential of the target body ‘t’. The minimal stable mass condition arises from the require- (a) Preceding the impact, in transit through atmosphere, ment that transfer of CUDO particles to target begins the CUDO core binds and stabilizes even the heated me- after surface penetration, teorite material, making the normal matter impactor ap- pear exceptionally stable. (b) At impact on the surface, Rc the normal matter material will largely evaporate, if not Mc >Mt . (10) Rt entrained with the CUDO into the mantle and beyond. A We find a large domain between this lower, and the up- possible signature of CUDO surface impacts is then the per gravitational collapse limit, wherein one can consider absence of both CUDO and normal impactor material. CUDO collisions with Earth and other rocky bodies [29]. (c) At exit, the kinetic energy of the moving CUDO may CUDOs in Particle Physics.—The features of create an exit “hump” and/or appearance of lava flow in CUDO impacts discussed here arise from their compact- environments where none should be present. While rapid ness, and the mass-radius scale, for beyond-standard- terrestrial surface evolution would mask some exit fea- model (BSM) CUDOs set by the energy-mass scale of tures, they should be well preserved on Mars, the Moon, the dark matter particles [21, 22]. Strangelet CUDOs and other rocky bodies. and BSM CUDOs are distinguished by the large split- Present day models of meteor impacts do not introduce ting between their respective energy scales, 1 GeV and the possibility of a high density impactor and the result- & 250 GeV. Terrestrial impacts should allow∼ differentia- ing surface puncture. It is the absence of the CUDO type tion on the corresponding scale of impacting CUDOs mass option in detailed impactor models that in our opinion and size. Considering the upper and lower mass limits leads to ongoing intense discussions within diverse geo- originating in the constituent particle properties [29], a logical and planetary communities regarding the prior- constraint on the dark matter energy-mass scale could ity of impacts versus eruptions, raising further questions arise. We expect to at least be able to differentiate heavy about the mechanism of major unexplained phenomena BSM particle CUDO from e.g. color-flavor-locked quark (e.g., “Volcanism, impact and mass extinctions: incredi- matter [27, 30]. Such quark matter CUDO impacts are ble or credible coincidences?” [36]). These topics are well believed to have several distinctive features [31]. beyond the current context, yet the wide ranging debates Another aspect controlled by the BSM-dark matter are indicating the need for a novel event type, and punc- energy scale is CUDO formation scenario. Compact, ture seems to fit the need. 5

Research supported in part by the U.S. Department fense Science & Engineering Graduate Fellowship (ND- of Energy, Grant No. DE-FG02-04ER41318 and by the SEG) Program. Department of Defense (DOD) through the National De-

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