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.

Ethics declarations

Competing interests

  This research received no external funding. The authors declare no
  competing interests.

Peer review

Peer review information

  Nature Communications thanks the anonymous reviewers for their
  contribution to the peer review of this work. A peer review file is
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  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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