Abstract

   Earth’s atmosphere, whose ionization stability plays a fundamental role
   for the evolution and endurance of life, is exposed to the effect of
   cosmic explosions producing high energy Gamma-ray-bursts. Being able to
   abruptly increase the atmospheric ionization, they might deplete
   stratospheric ozone on a global scale. During the last decades, an
   average of more than one Gamma-ray-burst per day were recorded.
   Nevertheless, measurable effects on the ionosphere were rarely
   observed, in any case on its bottom-side (from about 60 km up to about
   350 km of altitude). Here, we report evidence of an intense top-side
   (about 500 km) ionospheric perturbation induced by significant sudden
   ionospheric disturbance, and a large variation of the ionospheric
   electric field at 500 km, which are both correlated with the October 9,
   2022 Gamma-ray-burst (GRB221009A).

Introduction

   Evidence of ionospheric disturbance induced by a gamma-ray burst (GRB)
   was first reported in 1988 by Fishman and Inan^[1]1 as due to the GRB
   occurred on 1st August 1983, the strongest ever observed at that time,
   with a total fluence exceeding 10^−3ergs/cm^2/s. The measured bulk
   effect on the ionosphere was the amplitude change of Very Low Frequency
   (VLF) radio signals, proof of the perturbation induced in the lower
   part of the ionosphere by that very energetic extrasolar event.

   During cosmic GRB (and solar flare too), the intense high energy photon
   flux can abnormally ionize the lower ionosphere^[2]2 by producing a
   large increase of free electron density^[3]3. As a consequence, the
   electron density grows giving rise to a variation of the ionospheric
   conductivity leading to a pronounced alteration in both VLF and ELF
   (Very Low and Extremely Low Frequency) electric field behaviour,
   respectively. Using ground VLF emitters, Inan et al.^[4]4 showed that,
   if the burst is sufficiently severe (total fluence exceeding
   10^−3ergs/cm^2) and long-lasting, the ionospheric perturbation caused
   by a GRB can be observed in the bottom-side ionosphere (from about 60
   km up to about 350 km of altitude). Although dedicated satellites
   recorded an average of more than one GRB per day in the last decade,
   intensive ionospheric reactions were seldom observed. In fact, only a
   handful of papers have reported the detection of ionospheric
   perturbations due to GRBs events^[5]3,[6]4,[7]5,[8]6,[9]7,[10]8, though
   always in the bottom-side ionosphere.

   In addition, both Sentman et al.^[11]9, and Price and Mushtak^[12]10
   have investigated GRB effects on Earth’s ionosphere finding no
   significant variation on the ELF electromagnetic wave data.
   Nonetheless, Tanaka et al.^[13]11 reported a clear detection of
   transient ELF signal caused by the December 27, 2004, event, a very
   intense cosmic gamma-ray flare, inducing a clear variation in the
   ionospheric Schumann resonance^[14]12 detected by electromagnetic
   ground stations.

   In this work we present the evidence of variation of the ionospheric
   electric field at about 500 km induced by the strong GRB occurred on
   October 9th, 2022. Using both satellite observations and a new ad hoc
   developed analytical model, we prove that the GRB221009A deeply
   impacted on the Earth’s ionospheric conductivity, causing a strong
   perturbation not only in the bottom-side ionosphere^[15]13,[16]14, but
   also in the top-side ionosphere (at around 500 km).

Results

   On October 9th, 2022, at 13:21 UT, a highly bright and long-lasting GRB
   (hereafter GRB221009A), triggered many of the X and Gamma-ray space
   observatories, in particular Swift^[17]15,[18]16, Fermi^[19]17,[20]18,
   MAXI^[21]19, AGILE^[22]20,[23]21 and INTEGRAL^[24]22,[25]23. The GRB
   follow-up was observed by most operative telescopes in space and
   on-ground. The INTEGRAL (see Integral satellite data section for more
   details) gamma-ray observatory^[26]24 detected the GRB both using the
   SPI spectrometer (SPectrometer of Integral) and the IBIS imager (Imager
   on-Board the INTEGRAL Satellite) as a complex, impulsive, very strong
   photon signal followed by a very intense gamma-ray afterglow^[27]25.
   The GRB221009A zenith was located over India and the GRB photon flux
   was illuminating Europe, Africa, Asia and part of Australia (Fig.
   [28]1).
   Fig. 1: Superposition of the GRB illumination area and CSES satellite
   orbit.
   [29]figure 1

   A map of the Earth with the CSES satellite orbit trace shown in blue.
   The green-colored part along the orbit marks the time of the electric
   field variation triggered by the GRB and detected by EFD. The gray
   shaded area shows the estimated illumination area of GRB221009A
   impinged at a latitude of 19.8^∘ and a longitude of 71^∘ (red circle).

   The light curves from the SPI detector and the IBIS imager (Fig. [30]2)
   show a multi-peaked structure with a moderately intense precursor,
   starting at 13:16:58 UTC, followed by a very strong prompt GRB
   emission, peaking at 13:21 UTC and, a long-lasting, sustained, soft
   gamma afterglow detected by both instruments in the energy range
   75–1000 keV (SPI) and 0.250–2.6 MeV (IBIS), respectively. Optical
   follow-up with the OSIRIS (Optical System for Imaging and
   low-Intermediate-Resolution Integrated Spectroscopy) at the 10.4m GTC
   (Gran Telescopio CANARIAS) telescope confirmed the presence of a strong
   optical afterglow in the range 3700-10000Å with features suggesting a
   supernova progenitor^[31]26.
   Fig. 2: Light curves from INTEGRAL satellite observations.
   [32]figure 2

   Time profile of GRB221009A detected by INTEGRAL, scaled for background.
   The red curve shows the SPI/ACS count rate on 1s time-bin plotted in
   erg/cm^2/s in the energy range 75-1000 keV; the black curve shows the
   IBIS/PICsIT data in the energy range 0.25–2.60 MeV. The differences
   between the two light curves are due to: i) difference in computing the
   two energy bands, ii) statistical fluctuations (IBIS/PICSiT is less
   sensitive in this case because of the partial shield absorption to low
   energy photons), iii) instrument saturation and/or telemetry loss due
   to the exceptionally strong photon flux from GRB221009A.

   The fluence of the prompt emission (i.e. the total time-integrated
   energy per unit area), lasting about 800s, was 0.013 erg/cm^2 in the
   75–1000 keV energy range^[33]23. This value is a lower limit estimate,
   due to the partial saturation and pile-up caused by the intense GRB
   photon flux. As far as we know, this GRB is among the largest ever
   detected. Assuming both a measured distance corresponding to a
   red-shift z=0.151^[34]27 and an isotropic emission (E-Iso) only in the
   high energy band, the energy emitted during the prompt GRB was about
   8 ⋅ 10^53 ergs. It should be noted that both fluence and E-Iso values
   are lower limits, due to the partial saturation of instruments (SPI)
   and telemetry data transmission (IBIS). The prompt emission was
   followed by an unusual strong soft gamma-ray long tail^[35]25 decaying
   with a power index around -2, and lasting at least 40 minutes before
   crossing the detection threshold of both SPI and IBIS detectors (Fig.
   [36]2).

   GRB221009A strongly perturbed the D-region^[37]13 (about 60−100 km of
   altitude) and, for the first time, its effect was observed also in the
   top-side ionosphere (507 km) by the Electric Field Detector
   (EFD)^[38]28 onboard the Low Earth Orbit (LEO) Chinese Seismo
   Electromagnetic Satellite (CSES - see CSES satellite electric field
   data section for more details)^[39]29, which was orbiting from North to
   South over the European sector (blue line in Fig. [40]1). Figure [41]3
   shows the comparison between the SPI/ACS gamma-ray flux (panel a) and
   the ionospheric electric field measured by EFD (panel b). At 13:17:01
   UT, EFD was switched on just before entering the Auroral Oval (AO). In
   this region (blue-shaded region), the electric field variations are
   strongly dominated by the auroral electrojet (a large horizontal
   current flowing mainly in the E region of the ionosphere, located at an
   altitude of about 100 − 150 km), generated by complex solar
   wind-magnetosphere interaction processes^[42]30,[43]31,[44]32. This
   effect results in the impossibility to correlate the evolution of
   GRB221009A peaks from 13:17:07 to 13:20:44 UT. The position of the AO
   boundaries were determined by using Ding et al. algorithm^[45]33. At
   13:25:03, about 1.5 min (Δt[GI]) after the beginning of the third and
   final peak of GRB221009A, the EFD observed a strong peak in the
   ionospheric electric value of about 54mV/m. We hypothesize that such an
   electric field variation in the top-side ionosphere can be driven by
   the GRB221009A occurrence.
   Fig. 3: Comparison of INTEGRAL gamma-ray and CSES electric field
   measurements.
   [46]figure 3

   Comparison between the SPI gamma-ray flux (panel a) and the ionospheric
   electric field observed by the CSES satellite (panel b), after the
   subtraction of the v[s] × B induced electric field (v[s] and B are the
   spacecraft speed and the local magnetic field, respectively). The
   blue-shaded region corresponds to the CSES flight over the Auroral
   Region. The CSES electric field observations were measured at an
   altitude of 507 km.

   In fact, Δt[GI] might be related to a characteristic feature of the
   ionosphere in response to ionizing flux^[47]34,[48]35, which in
   general, depends on the balance between the electron production rate
   (dominated by photo-ionization) and the electron losses (resulting from
   recombination)^[49]34,[50]36,[51]37. The physical effect caused by the
   electron loss process is to delay the response of the changes in
   electron density ρ[e] to changes induced by the photo-ionization
   process. As a consequence Δt[GI] should represents the time taken for
   the ionospheric photo-ionization recombination processes to recover the
   equilibrium after an increase of irradiance. The higher is the
   ionospheric density, the larger is the delay time^[52]35,[53]37,[54]38.

   Figure [55]4 shows the CSES electric field observations during the
   GRB221009A occurrence for the three geographical components E[x] (panel
   a), E[y] (panel b) and E[z] (panel c), where x is directed northward, y
   westward, and z along the (negative) radial direction. It can be easily
   seen that the EFD variation (black curve) is superimposed to a
   low-frequency modulation induced by v[s] × B effect^[56]28.
   Fig. 4: Ionospheric Electric field observations from CSES satellite.
   [57]figure 4

   CSES electric field waveform as function of time during the GRB221009A
   occurrence for the three components E[x] (panel a), E[y] (panel b) and
   E[z] (panel c) with (black curve) and without (blue curve) the v[s] × B
   induced electric field component. The blue-shaded region corresponds to
   the CSES flight over the Auroral Region. The CSES electric field
   observations were measured at an altitude of 507 km.

   At 13:25:03 UT a large peak in the ionospheric electric field is
   visible along the three components, whose amplitudes are:
   ΔE[x] = 32.6mV/m; ΔE[y] = − 39.5mV/m; ΔE[z] = 27.9mV/m.

Discussion

   These observations are consistent with an anomalous high ionization in
   the ionosphere. In general, such a ionospheric perturbations are caused
   by solar flares and/or solar particle events leading to sudden radio
   wave absorption (in both the medium frequency - MF - and high frequency
   - HF - ranges)^[58]39. These effects are detected in the D-region and
   are called Sudden Ionospheric Disturbances (SID)^[59]40. In the present
   case, the very strong and long-lasting photon flux due to GRB221009A
   triggered an unprecedented level of ionization in the ionosphere
   producing both a significant SID in the bottom-side ionosphere and a
   strong electric field variation in the top-side ionosphere.

   We hypothesize that the strong variations of the ionospheric electric
   field measured by CSES at an altitude of 507 km can only originate from
   a strong variation in the ionospheric parallel conductivity
   (σ[0])^[60]41,[61]42, which is directly dependent on the plasma density
   (see equation ([62]5) in Analytical model for top-side Ionospheric
   Electric field variation induced by a GRB section). To confirm such a
   scenario, on the one hand we investigated the distribution of the
   ionospheric Total Electron Content (TEC) over Europe, as measured by
   Global Navigation Satellite System (GNSS) receivers (see GNSS Total
   Electron Content Data section). As from Fig. [63]5, GNSS receivers
   located in the Mediterranean area recorded a significant TEC increase
   on October 9th (panel b) between 13:00 and 14:00 UT compared to the day
   before (panel a) and after (panel c) at the same time, thus confirming
   the ionizing effect of the intense GRB^[64]1,[65]13,[66]43.
   Fig. 5: TEC map over Europe during the GRB occurrence.
   [67]figure 5

   Map of the vertical total electron content (TEC) around the CSES
   satellite position one day before (panel a), at the moment of (panel b)
   and one day after (panel c) the GRB occurrence. All the maps have been
   averaged over 1 hour, between 13:00 UT and 14:00 UT. Colors are
   representative of the TEC value.

   On the other hand, we developed an analytical model (see Analytical
   model for top-side Ionospheric Electric field variation induced by a
   GRB for more details) able to give a first rough quantitative
   evaluation of the top-side ionospheric electric field variation driven
   by an impulsive photon flux (e.g., the impinging of a GRB). As can be
   seen from Fig. [68]6, an impulsive photon source can generate a
   variation in the top-side ionospheric electric field of about 30mV/m
   only if the ratio R[αβ] between ion production (α) and absorption (β)
   rates are greater than 5. In addition, if R[αβ] is lower than 2, the
   effect of the ionization seems not to be able to produce significant
   variation in the electric field. Such a result is in agreement with the
   previous experimental observations related to GRBs impinging the
   ionosphere^[69]1,[70]4,[71]43,[72]44.
   Fig. 6: Modelling of ionospheric electric field variation induced by a
   GRB.
   [73]figure 6

   Model results of top-side ionospheric electric field time variation
   induced by a impulsive photon source. Colours are representative of
   different photon production/absorption rate ratio.

   In addition, our model predicts a time delay (Δt[th]) between the peak
   of the GRB and the peak of the ionospheric electric field variation of
   1.22 minutes for R[αβ] = 5. This Δt[th] is in agreement with the Δt[GI]
   observed.

   As previously said, being the observations in the bottom-side
   ionosphere analogous to the effects induced by solar flares (Solar
   Flare Effect - SFE)^[74]45,[75]46, we investigated the possibility of a
   sudden intensification of the Solar quiet (Sq) ionospheric current
   system^[76]47,[77]48 and of the ionospheric Equatorial Electrojet
   (EEJ)^[78]49,[79]50 induced by the GRB221009A^[80]51. The Sq
   ionospheric electric currents are located in the E-region and are
   responsible of the diurnal variation in the geomagnetic field observed
   at ground^[81]52. Figure [82]7b shows the comparison between the
   equatorial electrojet, estimated in terms of the variation of the
   North-South component of the geomagnetic field (H - see Equatorial
   electrojet evaluation section for more details), calculated for a solar
   quiet day (October 12^th, 2022, black line) and for the day of the GRB
   occurrence (October 9^th, 2022, red line). It can be seen that the
   occurrence of the GRB221009A (vertical black dashed line) generated a
   perturbation of the EEJ. Indeed, superimposed to the long-term
   variation, featured in both days and characterized by a minimum around
   both dawn and dusk, and by a maximum around the noon, at about 13:21 UT
   a low frequency (0.35 mHz) fluctuation appears. Such a variation is
   more clear in the original magnetometer data used for the EEJ
   evaluation (panels a, b, c and d) in Fig. [83]7). In fact, looking at
   Tatuoka data (panels b and d) which is located inside the EEJ, we can
   see that during quiet conditions (panel b) the geomagnetic field
   reaches its maximum values around the local noon remaining almost
   stable for about 2.5 hours before decreasing down as the station
   approaches the local dusk^[84]49. Differently, on October 9th (panel
   d), before the GRB occurrence, as expected the H field reaches its
   maximum value, but, around 13:21 UT, in coincidence with the occurrence
   of the first peak of the GRB (vertical black dashed line), instead of
   remaining stable, starts to fluctuate with a low frequency of 0.35 mHz.
   Interestingly, such alteration lasted up to 19:00 UT, possibly
   sustained by the hard GRB221009A long tail (Fig. [85]2), containing
   more than 10% of the total energy of the prompt emission.
   Fig. 7: Comparison between Equatorial Electrojet during quiet period
   and GRB occurrence.
   [86]figure 7

   Estimation of the Equatorial Electrojet for the a solar quiet day of
   October 2022 (black line) and for the day of the GRB occurrence (red
   line): panel a) and c) show original observations of the H component of
   the geomagnetic field from San Juan magnetometer station during quiet
   and GRB day, respectively; panel b) and d) show original observations
   of the H component of the geomagnetic field from Tatuoka magnetometer
   station during quiet and GRB day, respectively; panel e) shows the EEJ
   results in terms of ΔH. Black dashed lines represent the time
   occurrence of the first peak of the GRB.

   In conclusion, the unprecedented photon-flux associated to the
   GRB221009A deeply impacted on the Earth’s ionospheric conductivity,
   causing a strong perturbation not only in the bottom side
   ionosphere^[87]13,[88]14, where it is typically observed using ground
   VLF antennas^[89]53, but also in the top-side ionosphere (at around 500
   km). In fact, a huge variation of the ionospheric electric field,
   induced by the strong ionospheric conductivity change was detected in
   the top side ionosphere (507 km) as a consequence of a GRB impact,
   which increased the ionospheric plasma density by the huge
   photo-ionization (even in the dayside), as depicted in Fig. [90]5. The
   analytical model described in this work supports the observations and
   confirms the hypothesis that the interaction between GRB and top-side
   ionosphere is a threshold process^[91]1,[92]4,[93]44. Our model
   suggests that such a threshold strictly depends on both the
   production-to-loss-rate ratio of ions and the time duration of the
   ionization process.

   As a closing remark, we want to highlight that, differently to previous
   similar studies^[94]13 focused on the impact of GRB on both D- and F-
   regions by using TEC data^[95]6,[96]43 and/or VLF ground
   electromagnetic transmitters^[97]1,[98]4,[99]14, our work represents,
   at our knowledge, the first-ever top-side ionospheric (507km)
   measurement of electric field variation triggered by impulsive cosmic
   photons.

Methods

   This section contains the description of the datasets used in this
   study and the analytical description of the model developed for the
   explanation of the experimental results.

INTEGRAL satellite data

   INTEGRAL, an ESA lead space observatory for observations in the energy
   range from a few keV up to 10 MeV, was launched in 2002 and is still
   fully operative. In this study data from the Imager IBIS^[100]54 and
   the SPectrometer SPI^[101]55 have been used. In particular, IBIS
   observes from 25 keV to 10 MeV, with an angular resolution of 12
   arcmin, enabling a bright source to be located to better than 1 arcmin.
   SPI observes radiation between 20 keV and 8 MeV with an high energy
   resolution of 2 keV at 1 MeV, capable to resolve candidate gamma-ray
   lines^[102]56. The INTEGRAL instruments were pointed to a sky direction
   at about 60 degree offset respect to the GRB arrival direction and the
   signal were detected by the omni-directional SPI/ACS shield and by the
   IBIS/PICsIT detector through the telescope shield (see annex material
   for detailed telescope response^[103]57). The INTEGRAL data are
   transmitted continuously in real-time to ground, and distributed in
   almost real-time via GCN web network and also through the
   Interplanetary Network (IPN).

CSES satellite electric field data

   CSES-01 (Chinese Seismo-Electromagnetic Satellite) is a LEO satellite
   orbiting sun-synchronously at about 507 km since February
   2018^[104]29,[105]58. CSES-01 has nine instruments on board for the
   electromagnetic field, waves and charged particle observations in the
   upper ionosphere. For this analysis we used electric field data from
   the Electric Field Detector (EFD)^[106]59. EFD is able to measure the
   electric field in four frequency bands: ULF (DC -16 Hz) with a sampling
   frequency of 125 Hz; ELF (6 Hz–2.2 kHz) with a sampling frequency of 5
   kHz; VLF (1.8 kHz–20 kHz) with a sampling frequency of 50 kHz; and HF
   (High-frequency, 18 kHz–3.5 MHz) with a sampling frequency of 50 kHz.
   Due to the limitation of telemetry capability, the waveform data are
   only available for both the ULF and ELF bands, and for a few minutes,
   over the global seismic belts, for both VLF and HF bands. During the
   remaining part of the orbit the VLF and HF data are transmitted as Fast
   Fourier Transform (FFT)^[107]28.

   To eliminate the v[s] × B effect (v[s] and B are the spacecraft speed
   and the local magnetic field, respectively), induced by the motion of
   the satellite inside the geomagnetic field, from the E field
   components, we applied the technique described in Diego et al.^[108]28.

GNSS total electron content data

   To investigate the ionospheric scenario leading to the observed
   impulsive variation of the current generated in the ionosphere, we
   collected and processed standard daily RINEX files provided by the
   permanent stations, located in Europe, of the University NAVSTAR
   Consortium and of the Rete Integrata Nazionale GNSS^[109]60 managed by
   the Istituto Nazionale di Geofisica e Vulcanologia (INGV). In
   particular, to calibrate vertical total electron content (vTEC) data,
   we processed GNSS measurements as described in D’Angelo et al.^[110]61
   by using the technique by Ciraolo et al.^[111]62 and Cesaroni et
   al.^[112]63. Specifically, to generate maps over a specific world zone,
   we performed an average of one hour vTEC observations over 1^∘ × 1^∘ of
   geographic latitude and longitude bin using data recorded by all
   satellites in view of each selected GNSS ground receiver.

Equatorial electrojet evaluation

   The equatorial electrojet (EEJ) was obtained using the method described
   in Soares et al.^[113]64. We considered the H (North-South) component
   the geomagnetic field at ground alone, being directly related to the
   east-west flow of the EEJ^[114]49. We used two pairs of ground stations
   consisting of one magnetometer close to the magnetic equator and one
   out at almost the same meridian. This assumption allows to have only
   one observatory under the influence of the EEJ. To estimate the EEJ, we
   evaluated the difference between the H component measured by the two
   pair stations after the subtraction of the nighttime baseline. Finally
   the EEJ signal at the longitude of the equatorial stations is obtained
   referred to as ΔH. The ground stations information used for the EEJ
   estimation are reported in Table [115]1.
   Table 1 Magnetometer Ground Station Location: Information about the
   location of the ground magnetometer stations used for the EEJ
   estimation

   Magnetometer data were obtained from INTERMAGNET magnetometer array
   network. INTERMAGNET is a consortium of observatories and operating
   institutes that guarantees a common standard of data released to the
   scientific community, allowing the possibility to compare the
   measurements carried out at different observation points.

Analytical model for top-side Ionospheric Electric field variation induced by
a GRB

   In order to develop a model able to represent the effect of GRB
   impinging the top-side ionosphere, we started from the ionospheric
   Ohm’s law^[116]65:

   $${{{{{{{\bf{J}}}}}}}}={{{{{{{\boldsymbol{\sigma }}}}}}}}\cdot
   {{{{{{{\bf{E}}}}}}}}={\sigma }_{0}{{{{{{{{\bf{E}}}}}}}}}_{| | }+{\sigma
   }_{p}{{{{{{{{\bf{E}}}}}}}}}_{{{{{{{{\boldsymbol{\perp }}}}}}}}}+{\sigma
   }_{H}\frac{{{{{{{{\bf{B}}}}}}}}\times
   {{{{{{{\bf{E}}}}}}}}}{{{{{{{{\bf{B}}}}}}}}},$$

   (1)

   where E is the electric field, B is the ambient magnetic field, σ is
   the conductivity tensor with σ[p], σ[H], and σ[0] being respectively
   the Pedersen, Hall, and parallel conductivity. The formation of the
   electric current in the ionized layer is caused by the difference
   between the velocities of ions (typically NO^+, O\({}_{2}^{+}\), O^+,
   H^+, H\({}_{e}^{+}\) and N^+) and electrons. In ionosphere, the
   temporal variability of the electrodynamics processes is slow enough
   that one can ignore the displacement current in Maxwell’s equations
   (i.e., the term ∂E/∂t)^[117]41, therefore Ampère-Maxwell law reduces to

   $${\mu }_{0}{{{{{{{\boldsymbol{\nabla }}}}}}}}\cdot
   {{{{{{{\bf{J}}}}}}}}={{{{{{{\boldsymbol{\nabla }}}}}}}}\cdot
   ({{{{{{{\boldsymbol{\nabla }}}}}}}}\times {{{{{{{\bf{B}}}}}}}})=0,$$

   (2)

   where μ[0] is vacuum magnetic permeability. By combining equations
   ([118]1) and ([119]2), we obtain:

   $${{{{{{{\boldsymbol{\nabla }}}}}}}}\cdot ({{{{{{{\boldsymbol{\sigma
   }}}}}}}}\cdot {{{{{{{\bf{E}}}}}}}})=0.$$

   (3)

   At about 500 km (i.e. CSES orbiting altitude) both σ[H] and σ[p] are
   negligible with respect to σ[0] (see Fig. [120]7 in Denisenko et
   al.^[121]66). As a consequence, equation ([122]3) simplifies to

   $${{{{{{{\boldsymbol{\nabla }}}}}}}}\cdot ({{{{{{{{\boldsymbol{\sigma
   }}}}}}}}}_{{{{{{{{\bf{O}}}}}}}}}\cdot {{{{{{{{\bf{E}}}}}}}}}_{| |
   })=0.$$

   (4)

   Once σ[0] is known, equation ([123]4) can be numerically solved to
   obtain the E field behaviour. Equation for the parallel conductivity in
   the ionosphere as given by Maeda^[124]42 reads

   $${\sigma }_{0}=\frac{{n}_{e}{q}_{e}^{2}}{{m}_{e}{\nu }_{e}}$$

   (5)

   $${\nu }_{e}={\nu }_{e,i}+{\nu }_{e,n},$$

   (6)

   where n[e] is the electron density, ν[e,n] is electron-neutral
   collision frequency, ν[e,i] electron-ion collision frequency, q[e] is
   the unsigned electric charge (i.e. 1.602 ⋅ 10^−19C), and m[e] is the
   electron mass (i.e. 9.109 ⋅ 10^−31kg). Following the results of
   Aggarwal et al.^[125]67, we can estimate the electron collision
   frequency at about 500 km as ν[e] = 10^2sec^−1.

   Being σ[0] directly dependent on the electron density, it is
   straightforward that any variation of n[e] causes a changes in E. In
   general, the rate of change of the electron density is expressed by a
   continuity equation^[126]68:

   $$\frac{d{n}_{e}}{dt}=A-L,$$

   (7)

   where A is the production coefficient and L the loss coefficient by
   recombination/losses. Naturally, the recombination coefficient depends
   of what ion species are present, and hence on the ionospheric altitude.
   At high altitudes (>200km, i.e. top-side ionosphere) where O^+ is the
   dominant ion species, L becomes proportional to the electron
   density^[127]68. So, equation ([128]7) becomes:

   $$\frac{d{n}_{e}}{dt}=A-\beta {n}_{e},$$

   (8)

   where β is the loss rate. Equation ([129]8) is valid only at altitudes
   higher than 200 km (and hence at the altitude of our electric field
   observations), being L, at lower altitudes (bottom-side ionosphere),
   proportional to the square of the electron density^[130]68. To simulate
   the production rate induced by a GRB, we used a Gaussian impulsive
   function of the form \(\alpha
   {e}^{-{(\frac{t-{t}_{0}}{{s}_{0}})}^{2}}\), so that equation ([131]8)
   can be written as:

   $$\frac{d{n}_{e}}{dt}=\alpha
   {e}^{-{\left(\frac{t-{t}_{0}}{{s}_{0}}\right)}^{2}}-\beta {n}_{e},$$

   (9)

   where α is the production rate induced by the GRB that depends on its
   photon flux, t[0] is the time of the maximum production rate, and s[0]
   is the width of the pulse.

   Putting together equations ([132]4), ([133]5), and ([134]9), and
   assuming at 500 km both an average electron density of
   1.2 ⋅ 10^11cm^−3 ^[135]69 and an average loss rate coefficient of
   0.6 ⋅ 10^−6sec^−1 ^[136]70,[137]71,[138]72, we can model the electric
   field variation induced by a GRB as a function of the ionospheric
   plasma density variation at 500 km of altitude. Figure [139]6 shows the
   results of our model for different ratios between production (α) and
   loss (β) rate. It can be easily seen that the effect of a GRB is
   negligible if α/β < 3. To obtain results similar to what was observed
   on October 9th, 2022, our model requires a production-to-loss ratio
   greater than 5.

   The usage of a formalism directly related to the ratio between α and β
   allows the model to being independent (for the present analysis) of the
   calculation of a realistic photon production rate caused by a GRB,
   whose evaluation needs a Montecarlo approach and the estimation of the
   real top-side ionospheric ion cross-section, which is out of the scope
   of the present work but a more accurate modelling of the effect of a
   GRB on the top-side ionospheric electric field is in progress.

   Anyway, despite being very simplified, our model can be used to give a
   first quantitative explanation of the effect induced in the top-side
   ionosphere by GRB221009.

Data availability

   We cannot supply our source data in any public depository since they
   are property of: European Space Agency (INTEGRAL satellite data);
   Italian Space Agency (CSES satellite data); International Real-time
   Magnetic Observatory Network (ground magnetometer data); University
   NAVSTAR Consortium (GNSS satellite data). Anyway all of them can be
   freely downloaded from the relative website after registration. CSES
   satellite data are freely available at the LEOS repository
   ([140]www.leos.ac.cn/#/home, accessed on 08/09/2023) after
   registration; GNSS data are freely available at University NAVSTAR
   Consortium ([141]https://www.unavco.org/accessedon08/09/2023) after
   registrtion. INTEGRAL SPI data are freely available at the ISDC
   ([142]https://www.isdc.unige.ch/integral/, accessed on 08/09/2023)
   repository. INTEGRAL PiCsIt/IBIS data are proprietary data of authors
   of the paper without any restriction. Ground magnetometer data are
   freely available at INTERMAGNET website
   ([143]https://imag-data.bgs.ac.uk/GIN_V1/GINForms2, accessed on
   08/09/2023). The datasets generated during and/or analysed during the
   current study are available from the corresponding author on request.

Code availability

   Codes used to produce results and figures were obtained using Matlab
   software package. They are not public but can be made available upon
   request to the corresponding author.

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Acknowledgements

   The authors thank the Italian Space Agency for the financial support
   under the contract ASI “LIMADOU Scienza+” n^∘ 2020-31-HH.0, and the
   financial support under the “ INTEGRAL ASI-INAF” agreement n^∘
   2019-35-HH.0. M.P., and G.d.A. thank the ISSI-BJ project “The
   electromagnetic data validation and scientific application research
   based on CSES satellite” and Dragon 5 cooperation 2020-2024 (ID.
   59236). Part of the research leading to the result has receiving
   founding support from the EuropeanUnion’s Horizon 2020 Programme under
   the AHEAD2020 project (grant agreement n. 871158). This material is
   based on services provided by the GAGE Facility, operated by EarthScope
   Consortium, with support from the National Science Foundation, the
   National Aeronautics and Space Administration, and the U.S. Geological
   Survey under NSF Cooperative Agreement EAR-1724794. The authors thank
   the INGV group for providing the RING data. We thank the national
   institutes that support INTERMAGNET for promoting high standards of the
   magnetic observatory practice ([298]www.intermagnet.org) used in this
   paper.

Author information

   Author notes
    1. These authors contributed equally: Mirko Piersanti, Pietro
       Ubertini, Roberto Battiston, Angela Bazzano, Giulia D’Angelo, James
       G. Rodi, Piero Diego.

Authors and Affiliations

    1. Department of Physical and Chemical Sciences, University of
       L’Aquila, 67100, L’Aquila, Italy
       Mirko Piersanti
    2. National Institute of Astrophysics, IAPS, Rome, 00133, Italy
       Mirko Piersanti, Pietro Ubertini, Angela Bazzano, Giulia D’Angelo,
       James G. Rodi, Piero Diego, Igor Bertello, Antonio Cicone, Fabrizio
       De Angelis, Emiliano Fiorenza, Bruno Martino, Alfredo Morbidini,
       Fabrizio Nuccilli, Emanuele Papini, Alexandra Parmentier, Dario
       Recchiuti, Andrea Russi, Silvia Tofani, Nello Vertolli & Ugo
       Zannoni
    3. Department of Physics, University of Trento, Povo, Italy
       Roberto Battiston, Andrea Di Luca, Francesco Maria Follega,
       Giuseppe Gebbia, Roberto Iuppa, Alessandro Lega, Alessio Perinelli,
       Dario Recchiuti, Ester Ricci, Veronica Vilona & Paolo Zuccon
    4. TIFPA-INFN, Povo, 38123, Trento, Italy
       Roberto Battiston, William J. Burger, Marco Cristoforetti, Andrea
       Di Luca, Francesco Maria Follega, Giuseppe Gebbia, Roberto Iuppa,
       Alessandro Lega, Coralie Neubüser, Francesco Nozzoli, Alessio
       Perinelli, Ester Ricci & Paolo Zuccon
    5. National Institute of Natural Hazards, Ministry of Emergency
       Management of China, Beijing, 100085, People’s Republic of China
       Zhima Zeren
    6. INFN, University of Rome Tor Vergata, Rome, 00133, Italy
       Roberto Ammendola, Davide Badoni, Simona Bartocci, Piero Cipollone,
       Livio Conti, Cinzia De Donato, Cristian De Santis, Matteo Martucci,
       Giuseppe Masciantonio, Matteo Mergè, Francesco Palma, Alexandra
       Parmentier, Piergiorgio Picozza, Gianmaria Rebustini, Alessandro
       Sotgiu, Roberta Sparvoli & Vincenzo Vitale
    7. INFN - Sezione di Torino, 10125, Torino, Italy
       Stefania Beolè, Silvia Coli, Stefania Perciballi & Umberto Savino
    8. INFN-Sezione di Napoli, Naples, 80126, Italy
       Donatella Campana, Marco Mese, Giuseppe Osteria, Beatrice Panico,
       Francesco Perfetto & Valentina Scotti
    9. Dipartimento di Ingegneria e Scienze dell’Informazione e
       Matematica, University of L’Aquila, 67100, L’Aquila, Italy
       Antonio Cicone
   10. Uninettuno University, 00186, Rome, Italy
       Livio Conti
   11. University of Bologna, Bologna, 40127, Italy
       Andrea Contin, Alberto Oliva & Federico Palmonari
   12. INFN - Sezione di Bologna, 40127, Bologna, Italy
       Andrea Contin, Marco Lolli, Alberto Oliva, Federico Palmonari,
       Michele Pozzato & Zuleika Sahnoun
   13. Fondazione Bruno Kessler, 38123, Povo, TN, Italy
       Marco Cristoforetti
   14. CNR, V. Fosso del Cavaliere 100, 00133, Rome, Italy
       Bruno Martino
   15. Agenzia Spaziale Italia, Rome, 00133, Italy
       Matteo Mergè & Simona Zoffoli
   16. Università degli Studi di Napoli Federico II, 80126, Naples, Italy
       Marco Mese, Beatrice Panico & Valentina Scotti
   17. Department of Physics, University of Rome Tor Vergata, Rome, 00133,
       Italy
       Piergiorgio Picozza & Roberta Sparvoli
   18. INFN-LNF, Frascati, Rome, 00100, Italy
       Marco Ricci
   19. IFAC-CNR, Sesto Fiorentino, Florence, 50019, Italy
       Sergio B. Ricciarini
   20. National Space Science Center, Chinese Academy of Sciences,
       Beijing, 100190, People’s Republic of China
       Xuhui Shen

Contributions

   M.P. writing–original draft, formal analysis, methodology and
   supervision; P.U. writing–revision, editing and methodology; R.B.
   writing–revision, formal analysis and validation; A.B.
   writing–revision; G.d.A. writing–revision, formal analysis; J.C.R.
   writing–revision, formal analysis; P.D. data validation, funding, Z.Z
   data validation. R.A., D.B., S.B., S.Be., I.B., W.J.B., D.C., A.C.,
   P.C., S.C., L.C., A.Co., M.C., F.d.A., C.d.D., C.d.S., A.d.L., E.F.,
   F.M.F., G.G., R.I., A.L., M.L., B.M., G.M., M.M., M.Me., M.Mes, A.M.,
   C.N, F.N., F.Nu, A.O., G.O., F.P., F.Pa., B.P., E.P., A.P., S.P., F.P.,
   A.Pe., P.P., M.Po., G.R., D.R., E.R., M.R., S.B.R., A.R., X.S., Z.S.,
   U.S., V.S., A.S., R.S., S.T., N.V., V.V., V.Vi, U.Z., S.Z., P.Z., are
   part of the CSES-Limadou Collaboration whose significant contribution
   made satellite observations possible.

Corresponding author

   Correspondence to [299]Mirko Piersanti.

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Cite this article

   Piersanti, M., Ubertini, P., Battiston, R. et al. Evidence of an upper
   ionospheric electric field perturbation correlated with a gamma ray
   burst. Nat Commun 14, 7013 (2023).
   https://doi.org/10.1038/s41467-023-42551-5

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     * Received: 04 February 2023
     * Accepted: 13 October 2023
     * Published: 14 November 2023
     * DOI: https://doi.org/10.1038/s41467-023-42551-5

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