Magnetised quark nuggets in the atmosphere

A search for magnetised quark nuggets (MQN) is reported using acoustic signals from hydrophones placed in the Great Salt Lake (GSL) in the USA. No events satisfying the expected signature were seen. This observation allows limits to be set on the flux of MQNs penetrating the Earth’s atmosphere and depositing energy in the GSL. The expected signature of the events was derived from pressure pulses caused by high-explosive cords between the lake surface and bottom at various locations in the GSL. The limits obtained from this search are compared with those obtained from previous searches and are compared to models for the formation of MQNs.

GSL contains a concentrated brine, not seawater. Sound speed was found to vary with depth and location, as the salinity and corresponding mass density of the brine varies as a function of depth. The sound speed was measured with a factory calibrated time of flight sensor. All measurements were in the water column, not the sediment. The resulting sound speed and standard deviation of the mean of the measurements versus depth are shown in Fig. S1 for Latitudes < 40⁰ 55.22′. The gradient in the sound speed cs in Fig. S1 is Δcs/Δz ~ 0.5 s -1 . From Snell's law of refraction, a constant gradient curves a sound wave into a circle with radius Rs given by For a vertical explosion or MQN impact in water 5 m deep, sound waves originating at depth 0 to 5 m respectively reflect from the surface at radial distances of 0 to 180 m. Therefore, propagation has to consider refraction and attenuation in the realistic environment of the Great Salt Lake.

Supplemental Information on Methods: Explosive calibrations emulating MQN impacts
Explosive calibrations were conducted with 130-kJ or 260-kJ line explosives placed vertically in the ~5-m deep water column along lines to the north and east of the sensors. Depth versus distance for the two sets of calibrations is shown in Fig. S2.

Figure S2.
Depth versus distance is shown for the calibrations to the north (blue) and east (red) of the sensor.
PETN explosive cords of radius 2mm and mass 21.6 gm/m were used for the calibration shots. Single cords gave a deposited energy of 130 kJ/m and 2 cord shots 260 kJ/m. The high ~750 m/s detonation velocity of the PETN explosive gave a top-to-bottom asynchrony of only 0.7 ms, which is much less than the ~ 60-ms evolution of explosively produced channel, so PETN explosions are a reasonable emulation of an MQN impact.  Fig. S3 show samples of the calibration shots. These produced ~ 100 ms duration pulses with a distinct structure. The absolute value of the pressure has a precursor of frequency ~ 250 Hz with duration varying with distance from the hydrophone array, followed by ~ 20 ms burst with higher frequencies and higher amplitudes decaying to ambient conditions in another ~ 20 ms. The variation of the duration of the precursor burst with distance showed that it had group velocity 2.7% greater than that of the high frequency burst. The corresponding data from the explosive calibrations along a line to the north of the sensor with depth increasing with distance from the sensor are given in Fig. S5.

Modelling using the ORCA Simulation in the Pekeris waveguide of the GSL.
The ORCA simulation proved to be very sensitive to the different assumptions made about the geology under the floor of the GSL, which is not well known and is described in the main text. The simulation for an ideal constant 5 m depth lake of brine produced conditions which matched observations when the sub-floor was assumed to have a hard top of thickness 0.75m over a 3m thick layer of mud with a mirabilite layer sitting on 5 m of bedrock. Fig. S6 shows the ratio of the resonant group velocity at 250 Hz to that at high frequency as a of mirabilite thickness. The arrow at mirabilite thickness 1.8 m shows the group velocity ratio of 1.03, the value obtained from the calibration shots. The attenuation at this point was 30 db/km in reasonable agreement with the values obtained from the calibration shot data. Figure S6. The variation with mirabilite thickness of the ratio of the group velocities of the resonant signal at 250 Hz to that at higher frequencies of 500 Hz (blue) and 1000 Hz (red). The arrow shows the mirabilite thickness that best fits the data.

Supplemental Information on Methods: Variation in trigger level from weather effects
The ambient background was surveyed every hour and the trigger level was adjusted accordingly, as discussed in the main text and is summarized in Table S1.