Nuclear emulsions from Nagoya University

Detector design

A nuclear emulsion is a special photographic film that is able to detect minimum ionizing particles such as cosmic-ray muons (Extended Data Fig. 1). The films used in this experiment were developed and produced at Nagoya University. In this design, silver bromide crystals with a diameter of 200 nm are dispersed in a 70-μm-thick sensitive emulsion layer, which is coated on both sides of a 175-μm-thick transparent polystyrene plastic base7,29 (Extended Data Fig. 1a and b). When a charged particle passes through this emulsion layer, its 3D trajectory (track) is recorded and can be revealed through the chemical development process (Extended Data Fig. 1c and e). Thanks to the precise grain size and structure, tracks can be reconstructed with sub-micrometre accuracy in 4π steradians by using an optical microscope (Extended Data Fig. 1d). The track reconstruction quality depends on the grain density per length along the line of a track. In this experiment, films with a grain density of 37 grains per 100 μm and a noise level of about 1 grain per 1,000 μm3 were used. These films can be used for long-term (2–3 months) measurement in an environment at 25 °C (temperature in the Queen’s chamber) by tuning the volume occupancy of silver bromide crystals (35%)30. Each 30 cm × 25 cm film was vacuum-packed in an aluminium laminated package for light shielding and humidity control (30% relative humidity, RH) (Extended Data Fig. 1f). An acrylic plate with 2 mm thickness was also packed together for the control of noise increase9. The packed film was fixed onto an aluminium honeycomb plate (Extended Data Fig. 1g and h) at Nagoya University, and then transported to Cairo by aeroplane. To avoid the elevated cosmic-ray flux during the flight, we transported the two emulsion layers of each detector separately and assembled them in Egypt. Since we reject the trajectories that are not crossing the two layers, the muons accumulated during the flight are rejected in the analysis and are considered as background tracks.

Data acquisition

The observation with nuclear emulsion films was launched in the Queen’s chamber in December 2015 and the films were periodically replaced. Each film was aligned with a reference line drawn with a laser marker and a spirit level, which led to an angular error of less than 10 mrad. After each exposure, we processed the films by photographic development in the dark room at the Grand Egyptian Museum Conservation Center. For the developing solution, we used the XAA developer (FUJI Film Co. Ltd) for 25 min at 20 °C. After development, we carried the films to Nagoya University, where they were read out by an automated nuclear emulsion scanning system developed since the early 1980s in Nagoya University31,32. In this experiment, tracks recorded in films were scanned by a Hyper Track Selector25 which can read out tracks at a speed of 4,700 cm2 h−1 with angular accuracy of 1.8 mrad for vertical tracks, and saved in a computer storage device as digital data (position, angle, pulse height). The angular acceptance is approximately |tanθ| ≤ 1.3, where θ is the zenith angle relative to the perpendicular of the emulsion surface.

Data analysis and statistics

The muon tracks are reconstructed by the coincidence between the two stacked films within the criteria of signal selection and then counted as detected muons26. In this analysis, a subset of the full data set was used to avoid decreasing the resolution because of the imaging parallax: 4.4 million tracks were accumulated for 98 days at position NE1 and 6.2 million tracks for 140 days at position NE2, with an effective area of 0.45 m2. Subsequently, detected muons were integrated into 2D angular space (tanθ x –tanθ y ) with a bin size of a specified size (for example, 0.025 × 0.025) and angular acceptance of |tanθ| ≤ 1.0, and converted to muon flux (muons per square centimetre per day per steradian) in each bin (Fig. 2a and b).

We used the Monte Carlo simulator Geant4 Version 10.2 (ref. 28) to compute the expected muon flux at the detector position. In these simulations, the physical processes of electromagnetic interactions and decays of muons were included, Miyake’s formula33 for the integrated intensity of cosmic-ray muons was used as a flux model, and only muons were generated as primary particles. To reduce the processing time, only muons were propagated and the range of incident muon energy was limited to 20–1,000 GeV in the zenith angular range 0°–70° (−2.75 < tanθ < 2.75). For the pyramid simulation, we modelled the shape and the location of the known structures (the Grand Gallery, the King’s chamber, the corridor that connects them, and the Queen’s chamber) using the survey of ref. 34. We defined that any void would be filled with air and that the stones are limestone (2.2 g cm−3) except around the King’s chamber, where they are granite (2.75 g cm−3). The exposure period in the simulation is compatible with 1,000 days, which is approximately ten times longer than that of the analysed data. We estimated the 2D rock thickness distribution from the detector position: the minimum thickness is 65 m and the maximum thickness is 115 m. If we assume that the scale of the fluctuation of the surface structure is 1 m (stone size), the effect of the relative fluctuation is less than 2%.

Normalization was performed to compare real and simulated data in the region without the analysing target (the Grand Gallery, the King’s chamber, and the anomaly region). The region of excess muon flux was clearly apparent in the images (Fig. 2a–d). Two histograms (Fig. 2e and f) show the muon flux extracted from the slice in 0.4 ≤ tanθ y < 0.7. From the comparison between data and the simulation, the significances of each anomaly region were evaluated to be 13.7σ (statistical) for position NE1 and 12.7σ for position NE2.

To locate the anomalous structure, we performed triangulation from the two positions. The centre of the detector positioned at NE1 was located 5.8 m east of the axis of the Grand Gallery and 4.5 m west for position NE2. The distance between position NE1 and NE2 is 1.1 m north–south. To determine the direction towards the anomaly region, we fitted the excess muon region to a Gaussian function by dividing the region (0 ≤ tanθ y < 1) into four regions with a segment of 0.25 in tanθ y , because the new structure seems to align along the tanθ y axis direction (Extended Data Fig. 2). The fitted centre value was used for triangulation and the errors of the estimated positions were defined from the errors on the sight lines coming from half of the bin width, that is, 0.0125 in tanθ x and 0.125 in tanθ y (Fig. 2g–i).

Scintillator hodoscopes from KEK

Detector design

The detector consists of two units of double layers, the x and y layers, of plastic scintillator arrays (Extended Data Fig. 3a–c). A single scintillator element is 10 mm × 10 mm in cross-section and 1,200 mm long. Each layer has 120 elements tightly packed, and hence its active area is 1,200 mm × 1,200 mm (Extended Data Fig. 3d). The element has a central hole along its length, through which a wave-shifter optical fibre is inserted to transfer the scintillation light efficiently to a multi-pixel photon counter sensor (Hamamatsu). The bias voltage of this counter sensor was selected according to the temperature of the Queen’s chamber, which is constant regardless of the weather outside. Each layer has its own data acquisition box, which digitizes the information of sensor signals and sends them to a common personal computer inside the detector frame. The total power consumption of the detector system is 300 W. The vertical distance between the two units is 1,500 mm at position H1 and 1,000 mm at position H2, and gives an angular resolution around 7 mrad and 10 mrad, respectively. The tangent acceptance ranges from 0 (vertical) to 0.8 rad and 1.2 rad, respectively.

The detector introduces a dark cross-shaped artefact visible on the 2D histograms (Fig. 3a–d), which adds a small systematic error of 3% to the analysis. According to our analyses, the error is likely to be caused by the very narrow gap between neighbouring scintillator elements, but this effect has not been fully understood yet. This systematic error is not relevant in the present analysis, which examines only the existence of the new void.

Data acquisition

Raw data—time and position of all hit channels—are first stored in a personal computer and regularly retrieved with USB memory to be sent to KEK through the Internet. In the off-line analysis, a muon event is defined by the coincidence of the four layers, with at most two neighbouring hits in each of them. Events are accumulated in 2D bins (Δx, Δy) given by the channel number differences between the upper and lower layers along the x and y axes. The bin number hence ranges from −120 to 120 and provides the tangent of the incident angle when divided by 150 for position H1 and by 100 for position H2. We installed the detector at position H1 in August 2016, and continued the data acquisition for five months until January 2017. During this period, we accumulated 4.8 million events. We then moved the detector 2.9 m west to investigate the newly observed void better. The data acquisition will continue for more than eight months and 12.9 million events were accumulated at position H2 at the end of September 2017, with overall smooth acquisition for more than a year.

Data analysis and statistics

The first step of the analysis is the normalization of the data by a Monte Carlo simulation that takes into account the cosmic ray muon flux and muon interactions35,36 (energy loss and multiple scattering) in the pyramid. We assume a constant energy loss4 of 1.7 MeV per (g cm−2), a mean density of 2.2 g cm−3, and a radiation length of 26.5 g cm−2 for the stones. Muons are propagated in steps of 0.1 m. Because the known structures of the pyramid are simulated, their effects are removed after the normalization of the data and the remaining muon excess shows the existence of an unknown corridor-like new structure. The successful elimination of the known structures suggests the reliability of our simulation. Slices of the images along Δx are presented in Extended Data Fig. 4a and b. The vertical scale is the relative yield to the simulation result. The new structure can clearly be seen in each slice. The significance of the muon excess was obtained by a Gaussian fit: at position H1 the excess heights in the slices range from 5.2% to 8.9% and are higher than 10σ except for the outermost slice, in which the height is still greater than 5σ. At position H2 the height ranges from 8.9% to 11% and is again above 10σ except for the outermost slice, in which the excess is above 7σ. From these slices, we found that the structure starts almost at the centre of the pyramid and ends at an angle whose tangent is 0.8 to the north. As a result, the length of the main part of the new structure is approximately 30 m. Results from both positions H1 and H2 show that the new void is above the Grand Gallery, which is consistent with Nagoya’s result.

Gas detectors from CEA

Detector design

A telescope (Extended Data Fig. 5a) is composed of 4 Micromegas (Extended Data Fig. 5b), a Micro-Pattern Gaseous Detector invented at CEA-Saclay37 (Extended Data Fig. 5c). All the detectors are identical, with an active area12 of 50 × 50 cm2. They are built using bulk technology38 with a screen-printing resistive film on top of the readout strips to allow for stable operation and higher gain39. Each detector provides x and y coordinates through a 2D readout inserted onto the printed circuit board (Extended Data Fig. 5d). The 1,037 readout strips (482 μm pitch) of each coordinate are multiplexed according to a patented scheme40. An argon–iC 4 H 10 –CF 4 , non-flammable gas mixture (95–2–3) is flushed in series through all the detectors of a telescope, with a flow limited to below 0.5 litres per hour by a tight seal (measured gas leakage of less than 5 ml per hour per detector).

Each telescope is operated with a Hummingboard nano-computer running GNU/Linux, which controls all the electronics12: a dedicated high-voltage power supply card with five miniaturized modules (CAEN), which provide up to 2 kV with 12-V inputs, and the front-end unit readout electronics based on the DREAM ASIC41. A particularly important feature of DREAM is its self-triggering option to generate the trigger from the detectors themselves. A dedicated software package was developed to interface all these electronic components to the Hummingboard, which performs the data acquisition with the front-end unit. It also monitors and sets the high voltages through the high-voltage power supply and a patented amplitude feedback to keep the gain constant in spite of the extreme environmental conditions of the Giza plateau (Extended Data Fig. 5e–g). The overall consumption of a telescope is only 35 W.

A trigger is formed by the front-end unit when at least five coordinates out of eight observe a signal above a programmable threshold. The sampled signals (50 samples at a frequency of 100/6 MHz, Extended Data Fig. 5h) of all the electronic channels (64 × 8) are then directly converted to a ROOT file42, a format commonly used in particle physics. The nano-computer performs the online reconstruction of muon trajectories, and the muon track parameters are sent to CEA in France with some environmental data (temperature, pressure, humidity in the gas) through a 3G connection.

Data acquisition

The data were collected from 4 May to 3 July 2017. Two telescopes were installed in front of the chevrons (north face), at a distance of 17 m and 23 m, respectively (Fig. 1b and c). The axis of both telescopes deviated slightly from the north–south axis, towards the east, to prevent the Grand Gallery from being at the centre of the image, where some correlated noise can show up. During acquisition time the two telescopes (called Alhazen and Brahic, at positions G1 and G2, see Fig. 1b and c) recorded 15.0 and 14.5 million triggers, respectively, from which 10.6 and 10.4 million track candidates were identified. After the χ2 quality cut, 6.9 and 6.0 million good tracks were reconstructed, and form the images shown in Fig. 4a and d.

Data analysis and statistics

From the acquired tracks, we searched for anomalies by extracting slices in tanϕ, that is, horizontal slices. To get more statistics, the thickness of the slices is larger than the binning shown in the 2D images. We chose a slice thickness of 0.10 for the Alhazen telescope, and we increased it to 0.11 for the Brahic telescope to keep roughly the same statistics. Extended Data Fig. 6 illustrates all the slices made with Alhazen from 0.21 to −0.19. From one histogram to another, the slice position is shifted by 0.02, which means the data of consecutive histograms largely overlap. The goal is to scan the pyramid and detect any deviation from statistics, whether fluctuations or not.

As can be seen in Extended Data Fig. 6, the slices show smooth distributions, except around histograms 5, 6 and 15. Histograms 6 and 15 correspond to Fig. 4b and c, respectively. These distributions were fitted with different functions, in particular polynomials. Though such functions are essentially empirical, a CRY/Geant4 simulation was performed to validate this choice further, leading to a good agreement using a second-order polynomial with a reduced χ2 of 1.4. The same function reproduces data distributions fairly well—with a reduced χ2 value of 1.6 and 2.0, respectively, for histograms 6 and 15—except in a region where an excess is clearly observed on both slices, with single-bin excesses of 4.2σ and 5.3σ respectively. Re-fitting with a second-order polynomial and a Gaussian significantly reduces the χ2 to 1.2 and 1.4, with a Gaussian integral of 141.3 ± 28.3 (5.0σ, histogram 6) and 141.8 ± 24.7 (5.7σ, histogram 15). Similarly, Brahic data show two significant excesses, corresponding to Fig. 4e and f. A second-order polynomial alone results in a reduced χ2 value of 1.8 and 2.4, respectively, while adding a Gaussian reduces them to 1.5 and 1.6. The Gaussian integral is 167.1 ± 44.6 (3.7σ, Fig. 4e) and 163 ± 26.5 (6.1σ, Fig. 4f).

The 3D model confirms that the (compatible) excesses from Fig. 4c (Alhazen) and 4f (Brahic) point to the same region of the pyramid and overlap very well with the Grand Gallery (Fig. 4h). The quasi-full overlap of the cones (owing to the purposeful proximity of the telescopes) justifies adding the two excesses, leading to 304.8 ± 36.2 (that is, 8.4σ). This fully validates the ability of the telescopes to unambiguously detect large structures in the core of the pyramid.

The 3D model also confirms that the excesses from Fig. 4b and e point to the same region. As before, the quasi-full overlap of the cones justifies adding the two excesses, leading to 308.4 ± 52.8 (5.8σ). A 3D comparison with the triangulation made by Nagoya University further confirms a large overlap of these regions. The other slices show no other anomaly exceeding 5σ.

It is worth mentioning that this analysis relies directly on raw data without model subtraction, which means the systematics are much smaller, and can only originate from the fitting function. As an exercise, a third-order polynomial fit was used for the histograms showing the new void, resulting in excesses of 5.2σ and 3.6σ for Alhazen and Brahic, and a combined excess of 303.5 ± 52.1 (5.8σ).

3D model of the pyramid

We designed an accurate 3D model of the pyramid by combining existing architectural drawings34,43 photogrammetry44, and laser scanner measurements44, both inside and outside the pyramid. After merging these data, the model contains about 500,000 triangles (Extended Data Fig. 7b–d). This model was mainly used in the RTMS (see below) and as reference for the simplified models used in the other simulators. The full model has a precision of approximately 30 cm for the internal structures and approximately 1 m for the external casing.

Real-Time Muography Simulator

The RTMS (Extended Data Fig. 7a) is a fast, interactive simulator that was mainly used for preliminary analyses, to aid in positioning the gas sensors (telescopes), and for confirming the results obtained from the other simulators. It allows the user to place a sensor in the detailed 3D model of the pyramid and to simulate the observed muon rate in real time. Muon scattering is not simulated. For each pixel of the sensor, which represents a direction relative to the sensor, the simulator computes the opacity (integral of the density along the path) from the sensor to the outside of the pyramid, along this direction. We used a density of 2.2 g cm−3 for the limestone, and 2.6 g cm−3 for the granite. We consider that muons lose energy at a constant rate4 of 1.69 MeV per (g cm−2), which allows us to compute the minimal energy E min to cross the pyramid given the value of the opacity. Finally, we use Miyake’s formula33 to calculate the distribution of muons that have greater energy than E min coming in at a zenith angle θ. This value is computed for each pixel of the image, leading to a 2D histogram similar to those obtained with the detectors.

Data availability

The data that support the findings in this study are available from the corresponding authors on reasonable request.