Results of search for magnetized quark-nugget dark matter from radial impacts on Earth

Quark nuggets are theoretical objects composed of approximately equal numbers of up, down, and strange quarks. They are also called strangelets, nuclearites, AQNs, slets, Macros, SQNs, and MQNs. Quark nuggets are a candidate for dark matter, which has been a mystery for decades despite constituting ${\sim}85\%$ of mass in universe. Most models of quark nuggets assume no intrinsic magnetic field; however, Tatsumi found that a magnetar core may be a quark-nugget ferromagnetic liquid with a magnetic field B\textsubscript{S} between $10^{ 11}$ T and $10^{ 13}$ T. Applying that result to quark-nugget dark matter indicates magnetized quark nuggets $(MQNs)$ magnetically aggregated in the early universe before they could decay by the weak interaction and formed a broad and magnetically-stabilized mass distribution. These MQNs satisfy the requirements for dark-matter even though they are Standard Model baryons. They interact with normal matter through a magnetopause and can form non-meteorite impact craters, which are reported approximately annually. We report results from excavating such a crater. Hydrodynamic simulations indicate fractured granite below the crater and under 4.7 m of soft sediments is the first observational evidence of MQN dark matter. The results also constrain values of B\textsubscript{S} between $4x10^{ 11}$ T and $3x10^{ 12}$ T.

Most previous models of quark nuggets have assumed negligible self-magnetic field. However, Tatsumi [36] explored the internal state of quark-nugget cores in magnetars and found that quark nuggets may exist as a ferromagnetic liquid with a surface magnetic field BS= 10 12±1 T. Although his calculations used the MIT bag model with its well-known limitations [28], his results are testable by applying his ferromagnetic fluid theory for magnetar cores to quark-nugget dark matter [20,44,45]. These ferromagnetic quark-nuggets are called magnetized quark nuggets (MQNs). In this paper, we report the first positive observation of MQN dark matter.
Throughout this paper, we will use Bo as a key parameter. The value of Bo equals Tatsumi's surface magnetic field BS if the mass density of MQNs ρQN = 10 18 kg/m 3 and the density of dark matter was ρQN = 1 × 10 18 kg/m 3 when the temperature of the universe was 100 MeV. Witten [13] predicted ρQN is "somewhat greater than nuclear density". His approximate formula gives ~7.5 × 10 17 kg/m 3 , which is consistent with 6 × 10 17 to 7 × 10 17 kg/m 3 covering the range of uncertainty in the proton radius and corresponding mass density. Peng, et al.'s [38] more recent work covers a range of 1.7 × 10 17 to 3.3 × 10 18 kg/m 3 for quark matter in quark stars. We use ρQN = 1 × 10 18 kg/m 3 in the calculations below. In addition, Bo depends on the density of dark matter ρDM = 1.6 × 10 8 kg/m 3 at time t ≈ 65 μs, when the temperature T ≈ 100 MeV in accord [44] with the standard ΛCDM cosmology. If better values of ρQN and ρDM are found, then the corresponding values of BS can be calculated by multiplying the Bo from our results by (1 × 10 -18 ρQN) (6.25 × 10 -9 ρDM).
Previous and concurrent papers on MQNs showed 1) their self-magnetic field aggregates MQNs with baryon number A = 1 into MQNs with a broad mass distribution [44] with baryon number A between ~10 3 and 10 37 , which is strongly dependent on the surface magnetic field parameter Bo, 2) aggregation dominates decay by weak interaction [44], 3) interactions through the self-magnetic field still satisfy all criteria for dark matter [44], 4) the self-magnetic field forms a magnetopause that greatly increases the interaction cross section of a MQN with a surrounding plasma [20] and that causes MQNs to spin up and radiate at high frequency (kHz to GHz) during passage through matter [45], and 5) the lack of reported non-meteorite impacts in the last 2000 years that deposit > 30 Megatons of TNT equivalent energy per kilometer limits the value of Bo to 1.0 × 10 11 T ≤ Bo ≤ 3 × 10 12 T [44].
Theoretically, interaction with normal matter through the MQN magnetopause gives three measurable signatures of MQN dark matter: 1) hypervelocity (> 3 km/s) atmospheric transit without luminous streak and without breakup in an air shower [46] but with energetic (> 1 kJ/m) energy deposition and with multi-meter transit through solid-density matter; 2) electromagnetic emissions (kHz to GHz) from the rotating magnetic dipole after transit through matter [45], and 3) magnetic levitation of rotating magnetic dipole [45] by induced currents in adjacent conducting material or of static magnetic dipole above a superconductor.
We use the terms meteoroids and meteorites to refer to bodies composed of normal matter, i.e. with atoms held together by the electromagnetic force. Nuclear density quark nuggets are not meteoroids and meteorites.
For comparison, the effective area of Earth for MQN impacts is ~10 14 m 2 , so the corresponding event rate from 2π sr solid angle and for Bo = 1.0 × 10 11 T to 3 × 10 12 T, respectively varies from 10 9 to 3 per year for all MQN masses and from 18 to 0.01 for MQN masses >1 kg. Therefore, it is not surprising that testing the MQN hypothesis for dark matter is currently limited to geophysical observations. In this paper, we examine one crater produced by an impact None of these impacts was preceded by a luminous track in the sky. No meteorite material was found in or near any of the craters. Impact experts who reviewed the news reports concluded that these events were not meteorite impacts. Without a scientific basis for impacts that form craters without luminous tracks and without meteorite fragments, they attributed them to human-caused explosions by default. Our results provide evidence that magnetized quark nuggets can cause non-meteorite craters, not just human-caused explosions.
Each non-meteorite event provides a large-target opportunity to test the MQN dark-matter hypothesis. Since a multi-layer witness plate provides more information than a single-layer one, peat bogs on top of soft sediments and bedrock offer particularly useful opportunities.
We report results of hydrodynamic simulations of MQNs interacting with a three-layer witness plate of peat-bog, clay-sand mixture, and granite bedrock, and report semi-empirical fits to the radius of shattered rock around a line explosive to establish the signature of an MQN impact. The three-layer witness plate is typical of a ~3500 year-old peat bog in County Donegal, Ireland.
There are other peat bogs that could provide opportunities for investigating MQN impacts. However, County Donegal has the advantages of 1) maximum exposure to the directed flux of dark matter from the direction of the solar system's path about the galactic center and through the dark-matter halo, 2) a granite bedrock within excavation range of the surface, 3) a friendly and supportive population, and 4) a governing authority over peat bogs that can grant permits for exploration.
We report the results of excavation of a non-meteorite impact there in May of 1985 and find it to be consistent with a ~10 kg MQN [20]. That result and the event rate of non-meteorite impacts reduce the supported range of Bo from Tatsumi's 10 11 ≤ Bo ≤ 10 13 T to 4 × 10 11 ≤ Bo ≤ 3 × 10 12 T.

Hydrodynamic simulation of MQN impact in three-layer witness plate
Two-and three-dimensional simulations with the CTH hydrodynamics simulation software [46,47] were conducted to investigate MQN interactions with a three-layer witness plate of peatbog, clay-sand mixture, and granite bedrock. Two-dimensional simulations examined the impact of quark-nuggets as a function of deposited energy per unit length, which is related to MQN mass and the Bo parameter. Three-dimensional simulations investigated the circularity of the crater as a function of angle relative to vertical and guided the excavation of an impact site in County Donegal, Ireland.
In both cases, the initial energy/length would be deposited within the magnetopause [24] radius (e.g. ~1 mm radius for a 30 MJ/m energy deposition from a 1 kg MQN for Bo ≈ 10 12 T) and produce an initial temperature of ~2,100 eV. Radiation transport, high-temperature diffusion, and turbulent mixing with surrounding matter are assumed to dominate the early dynamics of the interaction and produce a channel of larger radius and lower temperature until the non-radiative hydrodynamics will dominate the evolution of the plasma. The pulse generated by this radiationdominated phase will have a duration on the order of ten microseconds, with high frequencies that will be strongly attenuated during propagation. Therefore, we assume the non-radiative hydrodynamics phase will dominate the pulse signature at the large distances of interest.
Therefore, we approximate the hydrodynamic phase of the plasma channel as a cylinder with full mass density of the peat, clay-sand, or granite. Temperature was varied from 0.5 to 1.55 eV; the results were essentially independent of temperature over that range and validated the assumption that energy/length is the dominant variable. For a given material and temperature, the initial radius of the channel was chosen to give the desired energy/length based on the SESAME4 [47] equation of state.
The fluid above the peat was atmosphere at standard temperature and pressure. The simulated depth of the peat was the actual 0.7 m of the Irish peat bog with initial density of 1.12 × 10 3 kg/m 3 and sound speed of 1.46 × 10 3 m/s. The 4.7 m-thick clay-sand layer was simulated with a 1.0 meter thick layer and with initial density of 2.02 × 10 3 kg/m 3 and sound speed of 2.2 × 10 3 m/s. The granite layer was simulated with a 0.3 m layer with initial density of 2.6 × 10 3 kg/m 3 and sound speed of 5.0 × 10 3 m/s. The bottom of each simulation was unmovable, and material could freely exit from the other boundaries.
Two-dimensional hydrodynamic simulations were conducted with 1, 3, 9, 27, 81, and 243 MJ/m energy deposition. They show that a shock wave reflects off the mass discontinuities and propagates radially outward in all three layers. Low-density and high-temperature material in the central channel is ejected into the atmosphere. Lower temperature material behind the shock wave moves radially and almost one-dimensionally outward. Finally, the peat distorts twodimensionally in response to the velocity field it has acquired and the shear planes that have developed within the peat.
Representative results of the density maps, when material velocities are well below their peak values, are shown in Fig. 1.  The central channel in the granite shown in Fig. 1 is caused by the compressive pulse, which decreases rapidly with increasing distance from the high-energy-density center. When the compressive pulse reflects at the boundary with lower-shock impedance, clay-sand material, it becomes a tensile pulse and breaks the rock in tension. Since the tensile strength of granite is only ~ 1.5% of the compressive strength [48], the diameter of fractured granite is much larger than the diameter of the compressed channel. [48] The geometry [49] and composition [48,49] of the explosive, the distance [48] to lower-shock-impedance material and the shock impedance of that material, all affect the fracture diameter to some extent. However, those effects are secondary to the main trend, as shown by the scatter in fracture data in Fig. 2. Over a wide range of parameters, the fracture diameter from the tensile strain is approximately a factor of 30 larger than the diameter of the channel caused by compressive strain.

Potential for liquefaction and flow of the clay-sand layer
Peat is ejected into the atmosphere and leaves a crater with smooth sides formed from the shear planes. The granite layer is fractured around the path of a MQN; however, the channel in the fully water-saturated clay-sand of the County Donegal peat-bog is very likely to undergo liquefaction and close the channel within tens of seconds after the passage of an MQN. According to Boulanger and Idriss [50], fine-grained soils (silts and clays for which the fines content (percent of dried soil passing through a No. 200 standard sieve) exceeds 50%) require careful testing and analysis to determine whether or not they will undergo liquefaction under an impulse or shaking. Conversely, soils with much less than 50% passing through a No. 200 sieve are much more likely to liquefy when they are saturated with water. We analyzed the clay-sand layer in the County Donegal peat-bog and found that it is composed of ~10% rock of ~1 cm diameter, ~20% soil that does not pass a 1 mm screen, and 11% soil passing through a No 200 sieve. Therefore, the fine-grained portion is only ~11% of total mass, or more conservatively, 19% of the sub-mm sized content and well within the < 50% criterion for susceptibility to liquefaction.
Owen and Moretti [51] have identified five conditions that contribute to liquefaction-induced soft-sediment deformation in sands under a transient increase in pore fluid pressure: 1) fine to medium-sized grains of sand, 2) high porosity, 3) high percent saturation with water, 4) low overburden pressure (<10 m of overburden), and 5) no previous liquefaction. The clay-sand layer between the peat and the granite satisfies all five conditions. In addition, Owen and Moretti cite impact by extra-terrestrial objects as a likely trigger for liquefaction. Therefore, we conclude the clay-sand layer is very likely to have undergone liquefaction and obscured the channel within tens of seconds after impact.

Simulations on circularity of MQN crater as a function of entrance angle
In addition to identifying the signature of MQN impacts, CTH simulations examined the circularity of the crater in the peat bog as a function of entrance angle relative to vertical. The information is helpful in identifying the likely path of the MQN through the liquefied intermediate layer to the bedrock.
Simulations modeled channels at 0°, 15°, 30°, 45°, and 60° to the vertical, extending from the surface to a depth of 1.0 m to an immovable solid, and instantaneously heated with 30 MJ/m energy density, as described above. Due to the low strength of the peat, the crater continues to grow for an extended period of time. In order to reasonably simulate the relative effects of the impact angle on the crater dynamics, each simulation was stopped at 10 ms. Figure 3 shows representative profiles. At y = -0.5 m, the ratio of major to minor axes is approximately cos -1 (θ), as expected for a cylinder intersecting a plane at angle θ. However, Fig. 3 shows the peat on the right-hand edges is forced against low-density air while the peat on the opposite side is forced against higherdensity peat. The less-impeded peat moves more. Therefore, the asymmetry is enhanced near the rim of the crater, and using the crater shape to estimate θ gives a maximum angle for the trajectory.

Non-meteorite crater in May 1985 near Glendowan, County Donegal, Ireland
Each of the recent non-meteorite impacts cited in the Introduction has an official investigation team dedicated to alleviate the public's concern over safety. Control of access to the impact site and information about the event make a scientific investigation by an outsider very difficult. The site is on Common Land with rights assigned to a group of nearby landowners, who kindly allowed our research. The National Parks and Wildlife Service has authority over the land and granted us a permit to excavate the site, which was done in three stages in 2017, 2018, and 2019.

Garda Mick Galligan and Glenveigh National Park Rangers David Dugan and Seamus
McGinty investigated it the day after the event. Garda Galligan took the photo with his daughter shown in Fig. 4 within a few days of the event. Garda Galligan had passed away before we began investigating the event. Park Rangers Dugan and McGinty were independently interviewed in May of 2006. Even though the interviews occurred twenty-one years after the event, the recollections were very consistent. Ranger Dugan recalled the inside sloped surface of the crater was very smooth; a few-centimeter diameter hole was present in the dirt at the center of the crater bottom; and there was a distinct, ~2 cm high lip on the peat edge of the crater. Ranger McGinty recalled the sides were smoothed, as if turned on a potter's wheel; pieces of the bog were scattered about 10 m away; there was a small "pointy" depression at the center in the underlying dirt; and no meteorite was ever found. Their eyewitness accounts were essential to understanding the impact in the peat and in the 4-meter thick layer of sand beneath the peat. The crater has a diameter of 3.984 ± 0.065 m. The yield strength of the peat was measured and found to be 530 ± 120 kN m -2 . Fig. 1c and Fig. 2 give an energy/meter of ~80 MJ/m for a 4.0 m diameter crater.
The shape of the crater was measured in 2006 before it was distorted by investigations. The best fit to an ellipse gives a 1.030 ± 0.005 ratio of major to minor axes and corresponds to θ ≤ 15°, as shown in Fig. 3a or Fig. 3b. The major axis aligned east-west. Therefore, the excavation was planned to explore the volume within 15° of vertical and optimized for east or west of center.

Excavations of the 1985 non-meteorite crater in County Donegal, Ireland.
Field work a third of the way around the world and in a protected wilderness area is challenging at best. However, it is the least expensive way to test the MQN dark-matter hypothesis. The additional information in Supplementary Methods: Excavations should assist independent groups in learning from our experiences and re-excavating the site.
The site was excavated in three stages as shown in Fig. 5. The 2017 expedition excavated the volume bounded by the black line in Fig. 5, cleared out debris and plant growth by hand, and found the bottom at depth 0.6 ± 0.1 m was a compacted clay-sand mixture. The compacted, post-liquefaction material was too hard to continue excavating by hand.
In 2018, a 6-ton excavator was used in an attempt to reach the bedrock. The volume bounded by the red line in Fig. 5 was excavated, with the sides sloping an average of 0.5:1, i.e. 0.5 m horizontal for every 1.0 m vertical, or ~27° from vertical, in accord with local experience in this soil. At 4.7 ± 0.1 m depth, a grouping of fractured rock was discovered just east of the center line. After an hour of observing the stability of the sides, the principal investigator was cleared by the civil engineer safety officer to enter the pit. He scooped accumulated water into a bucket and found the rock was closely packed shards of granite with dimensions varying between 0.02 m and 0.1 m.
The excavation had to be quickly abandoned because the sides of the water-saturated clay-sand mixture showed signs of fracture and sliding at various points down the slope. Since we did not have time to do a careful and well-documented investigation, no samples were removed. The dimension of the rocky bottom was at least the ~0.5 m of the cleared bottom but the horizontal dimension of the rocky area could not be determined; it could be an extensive layer of fractured rock, fractured bedrock, or a localized deposit.
The 2019 expedition used two 14-ton excavators to dig the hole bounded by the blue line in Fig.  5. The slope of the sides averaged 1.5:1, i.e. 1.5 m horizontal for every 1.0 m vertical, or ~55° from vertical, to assure they would not collapse. Ten boulders were found throughout the excavation. Two of these are shown in Fig. 6. Since the material above the rocky grouping of interest had been back-filled after the 2018 excavation, the precise positions of the boulders was not relevant to the 1985 event and were not recorded by the excavator operators.
The operators were to excavate to the rocky layer at -4.7 ± 0.1 meters, stop, and alert the team. They did so; however, by the time they stopped and measured the depth, they had removed the volume of fractured rock in just one bucket load, demonstrating that it was a localized deposit, and discharged it through the relocation process to a pile where it spread out. Although they showed us where that load lay, its relational context was lost. We encourage another group to reexcavate the site and look for fractured granite in the bedrock below our excavation; extreme care is recommended to preserve the context of fractured rock.
Water was pumped from the excavation. The muddy bottom was explored by hand. Rocks shown in Fig. 7 were found. They are similar to the shards found in the 2018 excavation and may have been from that grouping. These granite rocks were examined with Energy Dispersive Spectroscopy for evidence of large pressure gradients having altered the quartz in the granite. Streaks of darkened mineral was determined by to be natural feldspar. No damage attributable to extreme pressures was found.
The excavation continued to a depth of 5.7 m, illustrated by the rectangle outlined in blue in Fig.  5. The west face of the crater, just west of the grouping of shards found in 2018, was washed with a pressure washer to better reveal its composition. A photo of the washed face is shown in Fig. 8.  Figure 8 shows no evidence of a horizontal layer of shards or bedrock, demonstrating that the ensemble of fractured granite was an isolated one, approximately the size of a shattered boulder. These shards were in the projected path of the impactor and was the only such grouping found in the excavation. Since boulders closer to the surface but outside the projected path were not shattered, we conclude that the ensemble of fractured granite was not shattered by pressure waves originating from energy deposited near the surface.
Since the shattered granite was well within the trajectory of a hypervelocity object that produced the crater in the peat, we infer the hypervelocity object shattered the granite boulder after passing through 0.7 m of density 1120 kg/m 3 peat and 3.9 m of density 2020 kg/m 3 water-saturated claysand.
At ~6.3 m depth, we found irregular boulders and large flat slabs of granite, with the vector normal to a slab inclined at ~60° to the vertical on the north and ~30° to the vertical on the south. We did not find a uniform slab of bedrock that would have been a perfect witness plate of a quark-nugget passage by showing a cylinder of fractured granite extending into the earth.
We could not determine if the mixture of rocks and slabs at different angles to the horizontal were characteristic of the site before the 1985 event or were caused by that event. Additional excavation directly beneath the grouping of fractured rock at ~4.7 m depth was blocked by two large boulders or displaced slabs to either side of that volume. These obstacles were too large to move with available equipment. In addition, the excavation from 4.8 m to 6.3 m had nearly vertical walls, which introduced a safety risk and precluded more excavation within the limitations of the project.

Unique signature of quark nuggets and first evidence of quark-nugget dark matter
The 80 MJ/m deposited in the 1985 event requires the impactor to have been a hypervelocity body, which generally refers to velocities > 3,000 m/s and impacts in which material strength is much less than internal stresses. Hydrodynamic simulations [52] of a meteoroid passing through a planetary atmosphere at cosmic velocity have recently been advanced after the Shoemaker-Levy 9 (formally designated D/1993 F2) comet provided the first direct observation of an extraterrestrial collision of Solar System objects. The aerodynamic force, proportional to atmospheric density times the square of the velocity, causes it to decelerate and produces a strong shock wave directly in front of it. At the apex of the bow shock, the atmosphere is compressed, heated, and ionized. Plasma temperatures can reach 25,000-30,000 K. The hot, opaque cap of plasma emits an enormous flux of thermal radiation that is absorbed by the leading surface of the impactor, causing rapid vaporization and ablation. If the body is small it completely ablates, leaving only a trail of ionized air and meteoritic vapor. If it is sufficiently large and sufficiently aerodynamic, it reaches the ground intact before a significant fraction of its mass can ablate and is still moving at hypervelocity. It forms an impact crater preceded by a luminous track and accompanied by meteorite material at the impact site.
A meteoroid with size between these two bounding cases, descends through the atmosphere and encounters an exponentially increasing density gradient before it slows significantly. Dynamic pressure (proportional to the local atmospheric density times the velocity squared) increases rapidly until it exceeds the material strength of the body, causing it to deform and fragment. Both of these processes cause the area-to-volume ratio to increase, which increases the stopping force, deceleration, and ablation rate, eventually reaching a threshold in which it is better described as a multiphase, turbulent fluid consisting of fragments in a high-temperature plasma bath. Under these conditions, the radiative transfer of energy from the plasma to the fragments is on a timescale that is much faster than the resulting vapor can expand. The internal pressure rises abruptly and possibly produces a nonchemical detonation that reduces the meteoroid to small pieces. The resulting and much larger area/mass ratio causes the material to quickly decelerate to a velocity insufficient to cause a crater.
The dynamics associated with passage through atmosphere with density less than or equal to 1 kg/m 3 assures only a small fraction of meteoroids with < 20 m diameter survive and maintain hypervelocity speeds. [52] Transit through solid or liquid density matter requires survival of dynamic forces more than 1000 times those of transit through the atmosphere. The probability of an approximately spherical body (not a long rod penetrator) doing so for distances much greater than their diameter is vanishingly small for normal matter held together by electromagnetic forces.
However, the material strength of quark nuggets is determined by the strong nuclear force. They are indestructible in interactions at even 250 km/s. The corresponding mass density is the nuclear density, which is > 7 × 10 17 kg/m 3 and assures their momentum lets them penetrate many meters or even kilometers into Earth, depending on their mass. Consequently, large energy deposition after passage through many meters of soil is a unique signature of quark-nugget dark matter.
The impactor in the 1985 event delivered 80 MJ/m to the 0.7 m of peat, penetrated 4.0 m of water-saturated soft sediments, and still had enough momentum to shatter the granite boulder with an observed diameter ≥0.6 m. As shown in Ref. 24, any MQN that deposits in the peat 80 MJ/m will deposit in the granite 156 MJ/m, which is well in excess of the 1 MJ/m required to shatter the boulder, as shown in Fig. 2. Since the associated dynamic force in penetrating 2000 kg/m 3 clay-sand is 2000 times the dynamic force in the 1 kg/m 3 atmosphere, the shattered granite at a depth of 4.7 meters confirms that the impactor has material strength consistent with the strong force and the corresponding nuclear density. Within the Standard Model of Particle Physics, only quark nuggets have nuclear density and sufficient mass to deliver that much energy per unit length. Therefore, hypervelocity penetration of the atmosphere and multiple meters of sediment and subsequent fracture of granite provides a unique signature of quark nugget impact.
The 1985 event has that unique signature and provides the first evidence for quark-nugget dark matter.

Potential for independent validation of the 1985 event
The force equation for a high-velocity body with instantaneous radius rm, mass m, and velocity v, moving through a fluid of density ρp with a drag coefficient K ≈ 1 is (1) MQNs have a velocity-dependent interaction radius [20] equal to the radius of their magnetopause in which rQN is the radius of the MQN of mass m and mass density ρQN: ( The interaction radius of a MQN varies as velocity v -1/3 in equation (2). Including that velocity dependence in the calculation with initial velocity vo gives velocity as a function of depth x yields in which xmax is the stopping distance for a MQN: The ~10 kg MQN inferred for the 1985 crater penetrates to xmax = 3572 m for ρp = 2020 kg/m 3 . Since we only explored the 1985 event to a depth of 6.5 m, it is possible for an independent team to re-excavate the site of the 1985 event to the bedrock and look for an extended volume of fractured granite. We marked the site to facilitate such an independent examination.

New limit on Bo to >4 × 10 11 T
The ~10-kg MQN mass depends on the Bo parameter and varies between 67 kg for Bo = 10 11 T and 2.7 kg for Bo = 3 × 10 12 T. However, the MQN mass distribution also depends on Bo [44]. Distributions with a maximum mass insufficient to deposit 80 MJ/m in peat are excluded by the 1985 impact. As shown in Fig. 5 of Ref. 44, that constraint excludes Bo < 4 × 10 13 T.

Axion Quark Nuggets (AQNs)
Zhitnitsky, et al. [16] proposed that axions will form AQNs with a mass [32] between ~10 -2 to 1 kg. Sixty percent of them are composed of anti-matter. He also proposed that annihilation of normal matter intersecting the geometric cross section of the antimatter AQN will deposit between ~40 to 200 MJ/m along its path for AQN mass 10 -2 to 1 kg, respectively [32]. Therefore, the results from the 1985 event appear to support both MQNs and AQNs.

Annual reports of non-meteorite cratering events and duplicative constraint on Bo
The three press reports of non-meteorite impacts cited in the Introduction show the reported event rate is approximately once per year. None of these craters have been examined for the unique signature of a quark-nugget impact. If they are caused by quark nuggets, then we can compare that annual event rate with expectations from the simulated crater size as a function of deposited energy/length in Fig. 2

Death and serious injury by dark matter
Sidhua, et al. [53] noted that the apparent lack of reports of death or serious injury of people in North America and Western Europe by > 100 J of deposited energy without an apparent energy source from 2010 to 2019 excludes dark matter candidates with interaction cross section σX >10 −8 to 10 −7 cm 2 and mass mX <50 kg, assuming all dark matter has a single mass. However, a nonmeteorite impact reported in the press and cited in the Introduction killed one man and injured three others in India in 2016 and another injured one woman in Rhode Island in 2015. The injuries required hospitalization. Our examination of the 1985 non-meteorite impact in Ireland indicates these non-meteorite impacts were compatible with MQN dark matter and suggest the excluded values should be reconsidered for a distribution of masses and for a broader population sample. -18-Observations from the three witness-plate layers combine to support crater formation by quarknugget impact and, consequently, provide the first, of many needed, observational evidence of MQN dark matter.

1) Water-saturated peat
• The 4 m crater diameter, the smoothness of the sides, and the location of ejecta at ≥10 m from the crater, as reported by the park rangers, are consistent with the shear planes and detaching ejecta in the hydrodynamic simulations with 80 MJ/m energy deposition in a small-diameter channel, as shown in Fig. 1c.
• The 80 MJ/m energy deposition is consistent with a ~10 kg MQN interacting through its magnetopause cross section and impacting at 2.5 × 10 5 m/s, which is the velocity of the solar system moving through the dark-matter halo.
• The 80 MJ/m energy deposition is also consistent with a ~1 kg antimatter AQN and interacting by matter-antimatter annihilation within the geometric cross section.
2) Water-saturated clay-sand • CTH hydrodynamic simulations indicate the 80 MJ/m channel will open a 1 m diameter crater in the soft-sediment layer. However, the rangers saw only a "fewcentimeter diameter hole" or a "pointy depression" at the center of the crater bottom.
• The 4.0 m thick, soft-sediment layer between the peat and the granite meets all the requirements for liquefaction [50]. The liquefied material will flow closed at the bottom first, where the pressure from the overburden is greatest, and proceed upwards. When the overburden pressure is too small to overcome viscosity, a "pointy" depression should remain, as reported by the park rangers.
• Since the clay-sand layer meets all the indicators for liquefaction, the observed state of the clay-sand layer is also consistent with ~80 MJ/m energy deposition from passage of ~10 kg quark nugget.

3) Granite
• The measured 1.030 ± 0.005 ratio of major-to-minor crater axes is consistent with a hypervelocity body impacting at a trajectory within 15° of vertical.
• A volume of shattered granite was found only at 4.7 m depth and within the projected impact trajectory at 15° from vertical. All 10 boulders found outside the trajectory were intact. The uniqueness of the shattered granite and its location indicates the hypervelocity body that caused the crater in the peat layer also shattered the granite boulder at 4.7 m depth.
• Passage through the 0.7 m peat layer and 4.0 m soft-sediment layer with sufficient residual velocity to shatter the granite requires the hypervelocity body to have had material strength much greater than that afforded by the electromagnetic force, which precludes its being normal matter. The material strength of the strong -19-nuclear force, the corresponding nuclear mass density, and energy deposition in the MJ/m range in solid density matter is a unique to quark nugget dark matter. Therefore, hypervelocity penetration through many meters or kilometers of solid or liquid density normal matter and energy deposition in the MJ/m range are a unique signature of quark nugget dark matter.
Quark nuggets, neutronium, and black holes have mass densities greater than the required value. However, neutronium is not stable outside of neutron stars and black holes small enough to provide the local density of dark matter and provide at least one impact per year reported in the press, i.e. ~10 kg mass, would have evaporated in about 150 y, which is much shorter than the time over which the effects of dark matter have been stable. Therefore, crater formation by quark-nugget impact is the only explanation that fits the data.
Other incidences of crater formation without meteorites should be investigated as quark-nugget events. The three events cited in the Introduction show the event rate for potential non-meteorite craters is sufficient to continue testing the MQN dark-matter hypothesis. The estimated energy/meter deposited from Fig. 2 above and the MQN mass from Fig. 2 of Ref. 44 for the 2016 event in Tamil, India that killed a man was ~80 MJ/m, which is comparable to the County Donegal event. If this event was caused by a quark nugget, it is consistent with a ~10 kg MQN or a ~1 kg antimatter AQN [32].
The 2015 event in Rhode Island, USA, is consistent with ~1 kJ/m energy deposition and a ~50 mg MQN or a 2 x 10 -9 kg AQN. If this event was caused by a quark nugget, it is consistent with MQNs' broad mass distribution but is not consistent with the 10 -2 kg minimum theoretical mass of AQNs [32].
If the 2014 event in Managua, Nicaragua, was caused by a quark nugget, it is consistent with ~30 GJ/m deposited in soft-sediment and a ~1000 kg MQN or a 350 kg antimatter AQN. If this event was caused by a quark nugget, it is consistent with MQNs' broad mass distribution but is not consistent with the ~ 1 kg maximum theoretical mass of AQNs [32].
All four are consistent with the MQN mass distributions [44] with just Standard Model physics, assuming all dark matter is composed of MQNs, and with the non-excluded and most likely range of 4 × 10 11 T ≤ Bo ≤ 3 × 10 12 T. Two of the four are consistent with the currently estimated mass distributions in antimatter-AQN theory [32].
Candidates for investigating additional events are listed in Supplementary Results: Additional candidate sites for MQN impacts in County Donegal. However, the dates of these potential events are unknown, and there may be competing processes for producing crater-like holes in otherwise flat terrain.
Additional and independent excavation of the 1985 event in County Donegal is lower risk and could independently confirm or invalidate our result by determining if the bedrock shows the expected cylindrical hole of fractured granite with radius of fracture decreasing with increasing depth. In addition, the expedition could determine if the tilted granite slabs and granite rocks at 6.3 meters depth are a universal feature of the bedrock in the area or were caused by the 1985 event. The latter case would provide additional evidence of large and local energy deposition at -20-depth. The information in Supplementary Methods: Excavations should be helpful to such an expedition.

Data Availability
All final analyzed data generated during this study are included in this published article except the movies of pressure, density, and temperature from the 81 MJ/m CTH simulation, whichare available at https://datadryad.org/stash/share/Lt7dMvxEAUWNnkfKt2xPg2l5TuWz7Bbec67iY4Kvazg (Date of access: 17/03/2020)]. Witten [13] showed quark-nuggets are in the theoretically predicted, ultra-dense, color-flavorlocked (CFL) phase [25] of quark matter. Steiner, et al. [26] showed that the ground state of the CFL phase is color neutral and that color neutrality forces electric charge neutrality, which minimizes electromagnetic emissions. However, Xia, et al. [17] found that quark depletion causes the ratio Q/A of electric charge Q to baryon number A to be non-zero and varying at Q/A ~ 0.32 A -1/3 for 3 < A < 10 5 . In addition to this core charge, they find that there is a large surface charge and a neutralizing cloud of charge to give a net zero electric charge for sufficiently large A. So quark nuggets with A ≫ 1 are both dark and very difficult to detect with astrophysical observations.

Results of search for magnetized quark-nugget dark matter from radial impacts on Earth
Witten and Xia, et al. also showed their density should be somewhat larger than the density of nuclei, and their mass very large, even the mass of a star. Large quark nuggets are predicted to be stable [13,14,25,27] with mass between 10 -8 kg and 10 20 kg within a plausible but uncertain range of assumed parameters of quantum chromodynamics (QCD) and the MIT bag model with its inherent limitations [28].
Although Witten assumed a first-order phase transition formed quark nuggets, Aoki, et al. [29] showed that the finite-temperature QCD transition that formed quark nuggets in the hot early universe was very likely an analytic crossover, involving a rapid change as the temperature varied, but not a real phase transition. Recent simulations by T. Bhattacharya, et al. [30] support the crossover process.
A combination of quark nuggets and anti-quark nuggets have also been proposed within constraints imposed by observations of neutrino flux [31]. Zhitnitsky [16] proposed that Axion Quark Nuggets (AQN) that forms quark and anti-quark nuggets were generated by the collapse of the axion domain wall network. Although the model relies on the hypothetical particle that is a proposed extension of the Standard Model to explain CP violation, it appears to explain a wide variety of long-standing problems and leads to quark and anti-quark nuggets with a narrow mass distribution form ~10 -2 to ~1 kg [32]. Atreya, et al. [33] also found that CP-violating quark and anti-quark scatterings from moving Z(3) domain walls should form quark and anti-quark nuggets, regardless of the order of the quark-hadron phase transition.
Experiments by A. Bazavov, et al. [34] at the Relativistic Heavy Ion Collider (RHIC) have provided the first indirect evidence of strange baryonic matter. Additional experiments at RHIC may determine whether the process is a first order phase transition or the crossover process. In either case, quark nuggets could have theoretically formed in the early universe.
In 2001, Wandelt, et al. [20] showed that quark nuggets meet all the theoretical requirements for dark matter and are not excluded by observations when the stopping power for quark nuggets in the materials covering a detector is properly considered and when the average mass is >10 5 GeV -25-(~2 × 10 -22 kg). In 2014, Tulin [22] surveyed additional simulations of increasing sophistication and updated the results of Wandelt, et al. The combined results help establish the allowed range and velocity dependence of the strength parameter and strengthen the case for quark nuggets. In 2015, Burdin, et al. [35] examined all non-accelerator candidates for stable dark matter and also concluded that quark nuggets meet the requirements for dark matter and have not been excluded experimentally. Jacobs, Starkman, and Lynn [18] found that combined Earth-based, astrophysical, and cosmological observations still allow quark nuggets of mass 0.055 to 10 14 kg and 2 × 10 17 to 4 × 10 21 kg to contribute substantially to dark matter. The large mass means the number per unit volume of space is small, so detecting them requires a very large-area detector.
These studies did not consider an intrinsic magnetic field within quark nuggets. However, Tatsumi [23] has shown that the lowest-energy configuration of a quark nugget depends on the QCD coupling constant and can be a ferromagnetic liquid that can account for magnetars. He calculates the value of the magnetic field at the surface of a quark-nugget core inside a magnetar to be 10 12±1 T, which is large compared to expected values for the magnetic field at the surface of a magnetar star with a quark-nugget core. For a quark nugget of radius rQN and a magnetar of radius rs, the magnetic field scales as (rQN/rs) 3 . Therefore, the surface magnetic field of a magnetar is smaller than 10 12 T because rs > rQN. Since quark-nugget dark matter is bare, the surface magnetic field of what we wish to detect is 10 12±1 T.
Although the cross section for interacting with dense matter is greatly enhanced [24] by the magnetic field which falls off as radius rQN -3 , the collision cross section is still many orders of magnitude too small to violate the collision requirements [18,20,22,35] for dark matter and will be discussed below.
Chakrabarty [36] showed that the stability of quark nuggets increases with increasing external magnetic field ≤ 10 16 T, so the large self-field described by Tatsumi should enhance their stability. Ping, et al. [37] showed that magnetized quark nuggets should be absolutely stable with the newly-developed equivparticle model, so the large self-field described by Tatsumi should ensure that quark nuggets with sufficiently large baryon number will not decay by the weak interaction.
The large magnetic field also alters MQN interaction with ordinary matter through the greatlyenhanced stopping power of the magnetopause around high-velocity MQNs moving through a plasma [24]. Searches [38] for quark nuggets with underground detectors would not be sensitive to highly magnetized quark nuggets, which cannot penetrate the material above the detector. For example, the paper by Gorham and Rotter [31] about constraints on anti-quark nugget dark matter (which do not constrain quark-nuggets unless the ratio of anti-quark nuggets to quark nuggets is shown to be large) assumes that limits on the flux of magnetic monopoles from analysis by Price, et al. [39] of geologic mica buried under 3 km of rock are also applicable to quark nuggets. Gorham and Rotter also cite work by Porter, et al. [40][41] as constraining quarknugget (nuclearite) contributions to dark matter by the absence of meteor-like objects in the lower atmosphere that are fast enough to be quark nuggets. Bassan, et al. [42] looked for quark nuggets (nuclearites) with gravitational wave detectors and found signals much less than expected for the flux of dark matter. However, all of these analyses assumed quark nuggets can reach the detector volume because the cross section for momentum transfer is the geometric cross section. In contrast, the MQN magnetopause cross section [24] is many orders of magnitude larger and prevents all but the most massive MQNs from being detected.

Supplementary Methods: Excavations
In hopes that another team will extend the excavation into the bedrock to independently test and extend our findings, the three excavations are described in this section. Please check the Acknowledgements for the names of essential team members from County Donegal.
The 2017 expedition cleared out debris and plant growth by hand. The bottom, at depth -0.6 ± 0.1 m, was compacted clay-sand mixture.
The 2018 expedition employed a single Hitachi EX-60, 6-ton excavator shown in Fig. S1 with the 4 m diameter crater drained by the channel on the right edge. The site was excavated with the sides sloping at 27° to the vertical, in accord with local experience in this soil. However, the excavation had to be quickly abandoned because the sides of the water-saturated clay-sand mixture showed signs of fracture and sliding at various points down the 27° slope. The 2019 expedition employed two Doosan 140LC, 14-ton excavators. One was on a ramp inside the excavation and moving material to the surface. The second excavator relocated each scoop of material to a safe distance from the hole to avoid increasing pressure on the soil -27-adjacent to the hole and provide a flat surface for the second excavator to traverse. The slope of the sides was approximately 55° from vertical as shown in Figure S2. That slope held. An additional 1.5 m of material, plus a water-collecting hole for the submersible pump, was excavated to look for bedrock. From 4.8 m to 6.3 m depth, we found irregular boulders, smaller rocks, and large flat slabs of granite with their normal vector inclined at 30° to the vertical on the south side, and 60° to the vertical on the north, as shown in Fig. S3. We did not find a uniform slab of bedrock and could not determine if the mixture of rocks and slabs at different angles to the horizontal were characteristic of the site before the 1985 event or were caused by that event. Additional excavation directly beneath the grouping of fractured rock at ~4.5 m to ~4.8 m depth was blocked by two large boulders or displaced slabs to either side of that volume. These obstacles were too large to move with available equipment. In addition, the excavation from 4.8 m to 6.3 m had nearly vertical walls, which introduced a safety risk that precluded more excavation within the limitations of the project.
If another group re-excavates the site to examine the bedrock and search for the signature of MQN passage, i.e. a cylinder of fractured granite extending well into the earth, extreme care is recommended below the 6.3 m depth to preserve the context of fractured rock.
In accord with our permit, the site was first filled with the rock and clay-sand mixture and topped with the peat layer. A wooden pole was driven into the peat to mark the center of the original 1985 impact crater. Three orange plastic stakes are located on elevated mounds at 1) 21.9 m to the south, 2) 26.76 m to the west, and 3) at 40.12 m at 61.5° north of west. Surveyor's lines from each stake connect the stake to the center post in hopes that another expedition could easily find and re-excavate the site. Since no one reported witnessing their being formed, we could not confirm that they were associated with impacts.
Since the aerial search in 2006, the resolution in the Google maps covering the western portion of the peat bog has been improved to the point that the maps are useful for a survey. Water flowing below the peat can create multiple holes aligned along the flow in peat bogs. Other mechanisms may also produce holes. Therefore, a survey of isolated round holes, like the 1985 event but without eye witnesses, will only give an upper limit to the event rate. A survey that was informed by the examination of the two holes found in 2006 was conducted in 2014. The survey consisted of 200 randomly selected areas in a square defined by the GPS coordinates of the -30-opposing corners (54.918855, -8.222008) and (54.977614, -8.421822). The chosen area had adequate resolution and did not include any human structures. It was a peat bog with reeds growing on top of the older peat. The total area surveyed in the 200 samples was 3 km 2 . The survey identified 33 circular depressions like the two we qualified in the ground-based survey. The 33 positions are shown in Table S1. Poisson statistics gives a 95% confidence for an upper limit of 11 ± 3.7 events per km 2 . Their diameters ranged from 2 ± 1 m to 9 ± 2 m. The crater from the 1985 event has changed little in 33 years and should last at least 100 years under the same environmental stresses. The extrema of 100 and 200 years for the time period give an estimated event rate of 0.1 to 0.05 events/km 2 /yr. Since the area of the earth is ~5 × 10 8 km 2 , the corresponding global event rate is between 30 × 10 6 and 60 × 10 6 events per year. Such a large number of potential events illustrates the likelihood of other phenomena forming holes in peat bogs and the importance of eyewitnesses to impacts.