(VLF) Radio Wave Signal Profile Due to Solar Flares Using

Home , Very Low Frequency

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S. Palit1, T. Basak2, S. K. Mondal1, S. Pal1, and S. K. Chakrabarti2,1 Open Access Open Access 1Indian Centre for Space Physics, 43-Chalantika, Garia Station Road, Kolkata-700084, India Climate 2S N Bose National Centre for Basic Sciences, JD Block, Salt Lake, Kolkata-700098, India Climate of the Past of the Past Correspondence to: S. K. Chakrabarti ([email protected]) Discussions

Received: 3 December 2012 – Published in Atmos. Chem. Phys. Discuss.: 7 March 2013 Open Access Open Access Revised: 25 July 2013 – Accepted: 25 July 2013 – Published: 16 September 2013 Earth System Earth System Dynamics Dynamics Abstract. X-ray photons emitted during solar flares cause the ion densities (Mitra, 1974), though the part of the photon Discussions ionization in the lower ionosphere (∼60 to 100 km) in ex- spectrum ranging from ∼2 to 12 keV is responsible for the cess of what is expected to occur due to a quiet sun. Very modulation at the reflection heights of very low frequency Open Access low frequency (VLF) radio wave signals reflected from the (VLF) radio waves. The VLFGeoscientific signal (3–30 kHz) reflected Geoscientific Open Access D-region of the ionosphere are affected by this excess ioniza- mainly from the D-regionInstrumentation ionosphere carries information of Instrumentation tion. In this paper, we reproduce the deviation in VLF signal such enhancements. By analysingMethods these and signals between a Methods and strength during solar flares by numerical modeling. We use transmitter and a receiver one could, for example, obtain en- GEANT4 Monte Carlo simulation code to compute the rate hancements in the electron-ionData densities Systems during such events Data Systems of ionization due to a M-class flare and a X-class flare. The (McRae et al., 2004). Discussions Open Access Open Access output of the simulation is then used in a simplified iono- In general, the entire radiation range of EUV, solar Lyman- Geoscientific spheric chemistry model to calculate the time variation of α, β, X-ray and γ -raysGeoscientific of solar origin (Madronich and electron density at different altitudes in the D-region of the Flocke, 1999) and from compact and transient cosmic ob- Model Development Model Development ionosphere. The resulting electron density variation profile jects as well as protons from cosmic rays and solar events act Discussions is then self-consistently used in the LWPC code to obtain as perturbative sources and lead to the evolution of the entire the time variation of the change in VLF signal. We did the atmospheric chemistry. The amount of energy deposited and Open Access Open Access modeling of the VLF signal along the NWC (Australia) to the altitudes of depositionHydrology depend on the and incoming radiation Hydrology and IERC/ICSP (India) propagation path and compared the re- energy. Thus the chemical changes in different layers vary. sults with observations. The agreement is found to be very Many workers have studiedEarth these System changes theoretically as Earth System satisfactory. well as using laboratory experiments.Sciences In F2 region, the chem- Sciences + + + + istry is simpler with N ,H and O with O as the domi- Discussions + Open Access nant ions (Mitra, 1974). Abundance of O dependsOpen Access on solar UV rays (Wayne, 2000). Similarly O+ and N + are dominant 1 Introduction in F1 region and their densities are governed by EUV of 10– Ocean Science Ocean Science 100 nm range (Mitra, 1974). E-region is mostly filled up by Discussions The most prominent causes of daytime lower ionospheric O2,N2 and NO molecules. During higher energetic X-ray + + modulation (other than the diurnal variation) are the solar emission (1–10 nm), O2 and N2 are produced. Here, the Open Access flares. The lowest part of the ionosphere, namely, the D- molecular NO and O are formed mainly throughOpen Access dissociative region, formed in the daytime due mainly to the solar UV recombination process. Mariska and Oran (1981) measured Solid Earth radiation, is significantly affected by these flares. The X- the evolution of E and F regionsSolid during Earth solar flares using ray and γ -ray from the solar flares penetrate down to the EUV data from the SOLRAD satellite system. The response Discussions lower ionosphere causing enhancements of the electron and Open Access Open Access Published by Copernicus Publications on behalf of the European Geosciences Union. The Cryosphere The Cryosphere Discussions 9160 S. Palit et al.: Modeling VLF signals due to Solar flares with GEANT4 simulation of the D-region is dominated by hard X-ray and γ Ray in- This program has been used by many workers and is quiet jection from flares and Gamma Ray Bursts (Mitra, 1974; successful for modeling of long-range propagation of VLF Wayne, 2000; Thomson et al., 2001; Holler¨ et al., 2009; Tri- signals even in presence of ionospheric anomalies (Grubor et pathi et al., 2011; Mondal et al., 2012). It has nearly similar al., 2008; Rodger et al., 1999; Chakrabarti et al., 2012; Pal et ion constituents as in the E-region along with hydrated ions al., 2012a, b). Instead of Wait’s model for the D-region iono- + + like O2 (H2O)n,H (H2O)n, etc. Several authors such as Mi- sphere, we used our own result for that part of the ionosphere, tra (1974), Mcrae (2004), Pal et al. (2012b), studied D-region by incorporating the results from the GEANT4 Monte Carlo electron density in detail. Beside these radiation events, reg- simulation and the GPI scheme in the LWPC program. ular solar proton events (SPE) having energies 1–500 MeV We compared the simulated VLF signal amplitude devia- affect the atmospheric chemistry drastically as one such pro- tions due to the effect of solar flares with those of the ob- ton can ionize millions of molecules. Joeckel et al. (2003) servational data detected by the ground based VLF receiver reported interesting observations on 14CO during SPE. Hol- of the Ionospheric and Earthquake Research Centre (IERC) loway and Wayne (2010), Jackman et al. (2001), Verronen et of Indian Centre for Space Physics (ICSP). To illustrate the al. (2005), etc. have reported the effects on the concentrations success of our method, we use one X2.2 type and one M3.5 14 of CO, NO, NO2 and O3 in mesospheric and stratospheric type solar flare data which occurred on 15 and 24 February regions. 2011, respectively, and compare with the predicted VLF out- Because the earth’s ionosphere (and atmosphere in gen- put from our model. Our interest is to reproduce the change eral) is a gigantic, noisy, yet free of cost detector of cosmic in the VLF signal during the solar event and examine the de- radiation, study of the evolution of its chemical composi- cay pattern of the signal due to the long recovery time. tion in presence of high energy phenomena (both photons The organization of the paper is as follows: in Sect. 2, we and charged particles) is of utmost importance not only to present the observational data. In Sect. 3, we present detailed interpret the results of VLF and other radio waves through procedures to model the data. This includes successive us- it, but also to understand long-term stability of this sensitive age of the GEANT4 simulation, GPI scheme and the LWPC system. In the present paper, we apply the GEANT4 simula- code. In Sect. 4, we present the results of our modeling which tion (applicable to any high energy radiation detector) only we compared with our observed data. Finally, in Sect. 5 we to understand the changes in the D-region electron density make concluding remarks. (Ne) during flares as the ion-chemistry leaves negligible im- pression on VLF propagation characteristics. For that reason knowledge of only the dominant chemical processes in the 2 Observational data D-region ionosphere would be enough to study the modula- The VLF receivers at the Indian Centre for Space Physics tion due to events like solar flares (Rowe et al., 1974; Mi- (ICSP) are continuously monitoring several worldwide tra, 1981; Chamberlain, 1987). One such simplified model, VLF transmitter signals including NWC (19.8 kHz), VTX namely, the Glukhov–Pasko–Inan (GPI) model (Glukhov et (18.2 kHz) and JJI (22.2 kHz). We use the VLF data for the al., 1992) can be applied for the events which cause excess NWC to IERC/ICSP propagation path (distance 5691 km) to ionization in the D-region. Inan et al. (2006) used this model compare with our simulation results. In Fig. 1a we present (though modified for lower altitudes) to find the effects of an example of variations of the NWC signal at 19.8 kHz for Gamma Ray Bursts on the state of ionization. The model has a typical solar active day (solid curve), with many flares and also been adopted successfully by Haldoupis (Haldoupis et a normal “quiet” day (dashed curve). There is a sudden rise al., 2009) for his work on the early VLF perturbations asso- of wave amplitude followed by a slow decay associated with ciated with transient luminous events. each of the flares. SoftPAL instrument was used in obtaining In the present paper, we model the VLF signal variation the data. In the present paper, we analyze stronger flares (one due to the D-region ionospheric modulation during solar X2.2 type and one M3.5 type) to begin with. In future, we flares by combining a Monte Carlo simulation (GEANT4) shall target weaker flares as they require more careful sub- for electron-ion production with the GPI model in the D- traction of the background. While analysing flares in ques- region to find the rate of free electron production at differ- tion, we use the GOES and RHESSI satellite data (Sui, et al., ent altitudes by X-rays and γ -rays emitted from flares. Fi- 2002) to obtain the light curve and spectrum of those flares. nally, the Long-Wave Propagation Capability (LWPC) code (Ferguson, 1998) has been used to simulate changes in VLF amplitude due to resulting variations of the electron num- 3 The Model ber density. The LWPC code computes the amplitude and phase of the VLF signal for any arbitrary propagation path 3.1 GEANT4 Monte Carlo simulation and ionospheric conditions along the path, including the effects of the earth’s magnetic field. It uses the exponential GEANT4 is a well-known object-oriented detector simu- D-region ionosphere defined by Wait and Spies (1964) and lation program (Agostinelli et al., 2003), used widely for wave guide mode formulations developed by Budden (1951). the study of the detector and instrument response to high

Atmos. Chem. Phys., 13, 9159–9168, 2013 www.atmos-chem-phys.net/13/9159/2013/ signal at 19.8 kHz for a typical solar active day (solid curve), with many flares and a normal ‘quiet’ day (dashed curve). There is a sudden rise of wave amplitude followed by a slow decay associated with each of the flares. SoftPAL instrument was used in obtaining the data. In the present paper, we analyse stronger flares (one X2.2 type and one M3.5 type) to begin with. In future, we shall target weaker flares as they require more careful subtraction of the background. While analysing flares in question, we use the GOES and RHESSI satellite data (Sui, et al., 2002) to obtain the light curve and spectrum of those flares.

S. Palit et al.: Modeling VLF signals due to Solar ﬂares with GEANT4 simulation 9161

40 C8.57 M6.61 (a) C4.03 C7.67 C2.04 C4.26

30 A (dB)

20 (a)

0 20000 40000 60000 80000 t (sec)

Fig. 1. (a) The amplitude of VLF signal transmitted from the NWC (19.8 kHz) station, as a function of time (in IST = UT + 5.5 h) as recorded Fig. 1. (a) The amplitude of VLF signal transmitted from the NWC (19.8 kHz) station, as a function of time at IERC(ICSP), Sitapur, India, on the 18 February 2011. Six solar flares of different classes (C2.04 at 09:04 UT, C4.03 at 10:21 h, C8.57 at 12:03 h, C7.67 at 12:54(in IST=UT+5.5 h, C4.26 at hrs) 14:41 as recordedh and M6.61 at IERC(ICSP), at 15:42 h) Sitapur could be on seen. the 18th A solar-quietFeb 2011. daySix solardata isflares also of presented different (dotted line) for comparison whichclasses was recorded (C2.04 on at 09:04hrs,12 February C4.03 2011. at 10:21hrs,(b) The propagation C8.57 at 12:03hrs path from, C7.67 NWC/Australia at 12:54hrs, C4.26 to IERC(ICSP)/Sitapur, at 14:41hrs and India. M6.61 at 15:42hrs) could be seen. A solar-quiet day data is also presented (dotted line) for comparison which energy radiations.was The recorded earth’s on 12th ionosphere Feb 2011. is (b) a The giant propagation detec- pathThe from data NWC/Au is obtainedstralia to IERC(ICSP)/Sitapur, from NASA-MSISE-90 India. atmospheric tor and as such, the software used to analyze detectors in model (Hedin, 1991) of the atmosphere. high energy physics could be used here as well. Most of Initially, the Monte Carlo process is triggered by primary the ionizations occur in the ionosphere due to the collision particle generation class of GEANT4 with photons of energy 3 The Model of molecules with secondary electrons produced by initial ranging from 1–100 keV. We are not interested in higher en- photo-ionization. The program includes sufficiently adequate ergy gamma ray photons as their energy deposition height physical processes3.1 for GEANT4 the production Monte of Carlo electron simulation ion pairs in is much lower than that of the D-region ionosphere. First a the atmosphere by energetic photon interactions. uniform spectrum (equal number of photons per keV bin) GEANT4 (GEANTGEANT4 is the is a abbreviation well known ofobject-oriented Geometry and detectoris simulation chosen forprogram input (Agostinelliin primary etgeneration al., 2003), class, such that Tracking) is a openlyused widely available for the and study widely of the tested detector toolkit and instrumentthe incident response photons to high in energy a specific radiations. bin have The random ener- (freely availableearth’s from ionosphere the website is ahttp://geant4.cern.ch/ giant detector and as). such,gies the softw withinare the used range to analyse of the bin. detectors This givesin high a distribution of The Monte Carlo processes in this application deal with the electron-ion production rate in a matrix form, the ij th ele- transport and interactionenergy physics of particles could be with used matter hereas in well. a pre- Mostment of the of ionizat whichions gives occur the in electron the ionosphere production due rate (cm−3 s−1) defined geometryto and the store collision all the of molecules information with of secondary track, na- electronsin ith prodkmuced above by sea initial level photo-ionization. due to the incident The photons in the th ture and numberprogram of secondaries includes efficiently. sufficiently With adequate this physical appli- processesj keVfor bin. theWe production produce of suchelectron altitude ion pairs dependent in distribu- cation we can find accurately the ionization processes and tion by simulation with different incident angles of the pho- tracks without anythe prior atmosphere knowledge by energetic and assumption photon interactions. of chem- tons. The real altitude distributions of electron-ion produc- ical or physical modelGEANT4 of the (GEANT region. The is the included abbreviation electro- of Geometrytion rate and during Tracking) a flareis a are openly obtained available by multiplication and of the magnetic processes related with X-ray incidence are well matrix of corresponding time (hence angle of incidence) with developed and suitable for application in the context of the 4 the actual flux spectrum (see Fig. 2) at that time. For this ionosphere. For simulation with UV, the application at this we collect the back-ground subtracted solar spectra during stage is not quite suitable, but with some development in the the flares from RHESSI satellite data (http://hesperia.gsfc. toolkit area, it is possible to use it for Monte Carlo simulation nasa.gov/rhessi2/). This method helps us to save a significant with UV and EUV photons in the ionosphere. We simulated amount of computation time. only the rate of ionization at different altitudes due to solar In some previous work (e.g., Glukhov et al., 1992; Hal- X-ray photons during flares using GEANT4. For the chem- doupis et al., 2009) the rate of ionization was approximated istry part related to the interaction of the produced electron, from the total energy deposition by a photon, by dividing it ions and the neutrals in the D-region ionosphere, we adopt with a pre-assigned value of the average energy for produc- the GPI scheme. tion of an electron-ion pair. We did not require such an ap- The earth’s atmosphere, constructed in the detector con- proximation, instead, we follow the electron ionization inter- struction class consists of concentric spherical shells, so that actions down to the lowest possible level in the Monte Carlo the atmosphere is divided into several layers. The distribution process. For this, the lower energy threshold for electron and of layers is as follows, 100 layers above the earth surface, photon processes is extended down to 10 eV in the electro- 1 km each followed by 20 layer above this, 5 km each and magnetic processes in GEANT4 toolkit. From simulations, 12 more layers, 25 km each. They are formed with average we found the average energy required per electron-ion pair molecular densities and other parameters at those heights. production to be ∼ 31 eV. www.atmos-chem-phys.net/13/9159/2013/ Atmos. Chem. Phys., 13, 9159–9168, 2013 processes is extended down to 10 eV in the electromagnetic processes in GEANT4 toolkit. From simulations, we found the average energy required per electron-ion pair production to be ∼ 31 eV. processesIn Fig. 3 is we extended show the down altitude to 10 distribution eV in the ofelectromagnetic the rate of elec prtronocesses density in GEANT4produced by toolkit. the spectra From shownsimulations, in Fig. we 2(a-b) found at the the average peak flare energy time required assuming per the elect Sunron-ion to be at pair the productionzenith. to be ∼ 31 eV. In Fig. 3 we show the altitude distribution of the rate of electron density produced by the spectra 9162shown in Fig. 2(a-b) at the S. peak Palit flare et al.: time Modeling assuming VLF the Sun signals to be atdue the to zenith. Solar flares with GEANT4 simulation

Fig. 2. Spectra at three phases (dotted: ascent phase; solid: peak; dash-dotted: descent phase of the (a) M-class flare and the (b) X-class flare which are used in this paper. The spectra were obtained from the RHESSI satellite Fig. 2. Spectra at three phases (dotted: ascent phase; solid: peak; dash-dotted: descent phase) of the (a) M-class flare and the (b) X-class flare which are used indataFig. this and2. paper.Spectra the The OSPEX at spectra three software. phases were (dotted:obtained ascent from phase; the RHESSI solid: peak; satellite dash-d dataotted: and descentthe OSPEX phase software. of the (a) M-class flare and the (b) X-class flare which are used in this paper. The spectra were obtained from the RHESSI satellite data and the OSPEX software.

Fig. 3. Electron production rates per unit volume at peak times for the (a) M-class flare and the (b) X-class flare assuming the sun to be at zenith. Fig. 3. Electron production rates per unit volume at peak times for the (a) M-class flare and the (b) X-class flare assuming the Sun to be at zenith.

In Fig. 3 weFig. show 3. Electron the altitude production distribution rates per ofunit the volume rate at of peak timesdensity for the distribution (a) M-class profilesflare and thewith (b) the X-class light flare curves of the flares, From Fig. 3(a-b), it is evident that the ionization effect due to the solar X-rays is dominant in the electron densityassuming produced the bySun the to be spectra at zenith. shown in Fig. 2a taking into account the dependency of the electron density on and b at the peakD-region flare time (∼ 60-100 assuming km) only. the sun The to simulation be at the also showsthe angular that the positions. altitude of maximum ionization is zenith. We simulate the condition at the middle of the VLF prop- somewhatFrom Fig. lower 3(a-b), for X-class it is evident flare that (∼ 81 the km) ionization than that effect of (∼ du88e to km) the M-class. solar X-rays This is is dominantconsistent in with the From Fig. 3a and b, it is evident that the ionization effect agation path (Fig. 1b) and assume that the resulting electron due to the solarD-region X-rays is (∼ dominant60-100 km) in only. the D-region The simulation (∼60– also showsdensity that distribution the altitude applyof maximum for the wholeionization path. is Along the prop- 100 km) only. Thesomewhat simulation lower alsofor X-class shows flare that (∼ the81 altitude km) than6 thatagation of (∼ 88 path km) in M-class. question, This the is solar consistent zenith with angle variation is at of maximum ionization is somewhat lower for X-class flare the most ∼ 30◦. Figure 4 shows that the approximation is jus- (∼81 km) than that of (∼88 km) M-class. This is consistent tifiable, especially if the solar zenithal angle is close to 0 at with the fact that the relative abundance of high energy pho- 6 the mid-propagation path. tons is larger in X-class spectra. Using this method, we compute the free electron produc- The effects of the zenithal variation of the sun is included tion rates per unit volume for both of the flares we wish to in the simulation to account for the variation of the flux in model. Figure 5a and b show the GOES light curve of the M- long duration flares. Fig. 4 shows the simulated electron pro- class and the X-class flares respectively. The corresponding duction rate (cm−3 s−1) at various altitudes for the M-class free electron production rates per unit volume, at different al- spectrum (Fig. 2a) at the flare peak if it had occurred at dif- titudes as time proceeds during the flares, obtained from the ferent times of the day. In finding the rate of production of Monte Carlo simulation are shown in Fig. 5c and d. The latter electron density over the whole period of the flares, we con- curves generally follow the variation of X-rays. volve the normalized (by corresponding spectrum) electron

Atmos. Chem. Phys., 13, 9159–9168, 2013 www.atmos-chem-phys.net/13/9159/2013/ the fact that the relative abundance of high energy photons is larger in X-class spectra. The effects of the zenithal variation of the Sun is included in the simulation to account for the variation of the flux in long duration flares. Fig. 4 shows the simulated electron production rate (cm−3sec−1) at various altitudes for the M-class spectrum (Fig. 2a) at the flare peak if it had occurred at different times of the day. In finding the rate of production of electron density over the whole period of the flares, we convolve the normalized (by corresponding spectrum) electron density distribution profiles with the light curves of the flares, taking into account the dependency of the electron density on the angular positions. We simulate the condition at the middle of the VLF propagation path (Fig. 1b) and assume that the resulting electron density distribution apply for the whole path. Along the propagation path in question, the solar zenith angle variation is at the most ∼ 30◦. Figure 4 shows that the approximation S. Palit et al.: Modeling VLF signals due to Solar flares with GEANT4 simulation 9163 is justifiable, especially if the solar zenithal angle is close to 0 at the mid-propagation path.

dNe − + c + = I + γ N − βNe − α NeN − α NeN , (1) dt d d x dN − = βN − γ N − − α N −(N + + N +), (2) dt e i x dN + = I − BN + − α N N + − α N −N +, (3) dt d e i + dNx + c + − + = BN − α NeN − αiN N . (4) dt d x x The neutrality of the plasma requires,

− + + N + Ne = N + Nx . (5) Here, β is the electron attachment rate (Rowe et al., 1974), the value of which is given by,

− 300 − 600 Fig. 4. Variation of electron production rates with the angular posi- = 31 + × 29 ( T ) 2 β 10 NO2 NN2 1.4 10 ( )e NO . (6) Fig. 4. Variation of electrontion of production the sun at different rates with heights the angular assuming position an M-class of the spectrum. Sun at different heights assuming T 2 an M-class spectrum. NO2 and NN2 represent the number densities of molecular Oxygen and Nitrogen respectively, and T is the electron temperature. The neutral atom concentrations at different alti- Using this method,3.2 we The compute GPI modelthe free electron production rates per unit volume for both of the tudes, required for the calculations of the coefficients, were flares we wish to model.Our next Figs. goal 5a and is to5b compute show the the GOES changes light in curv atmospherice of the M-classobtained and the from X-class the NASA-MSISE atmospheric model. The flares respectively. Thechemistry corresponding due to the free flare. electron These producouldction be obtained rates per using unit volume,detachment at different coefficient, i.e., the coefficient of detachment a simplified model, such as the GPI model (Glukhov et al., of electrons from negative ions has contributions from both altitudes as time proceeds1992). during In this the model, flares, the obtained number densityfrom the evolution Monte Carlo of four simulationphotodetachment are shown in (at daytime) and also processes other than Figs. 5c and 5d respectively.types of ion The species latter are curves taken generally into account follow for the the estimationvariation of X-rays.photodetachment. The coefficient for the photodetachment of the ion density changes in the D-region. These are: elec- process is ∼ 10−2 to 5 × 10−1 and for the other process it is trons, positive ions, negative ions and positive cluster ions. ∼ 10−1 to 10−2 at 80 km (Bragin, 1973). According to Lehti- 3.2 The GPI model + + + The positive ions N comprise of mainly O2 and NO2 . The nen and Inan (2007) and Pasko and Inan (1994), the value of − − − − − the detachment coefficient γ varies widely from 10−23N s−1 negative ions N include O2 , CO3 , NO2 , NO3 etc. The + + −16 −1 Our next goal is to computepositive cluster the changes ions N inare atmospheric usually of chemis the formtry H due(H to2O) then. flare.to 10TheseN coulds . Following be Glukhov et al. (1992) the value of x − − The GPI model is meant for the nighttime lower ionosphere. γ is taken to be 3×10 18N s 1, where N is the total number obtained using a simplified model, such as the GPI model (Glukhov et al., 1992). In this model, the Modified set of equations exists (Lehtinen and Inan, 2007), density of neutrals. In our calculations the value of γ comes − − number density evolutionwhich of are four applicable types of at ion even species lower areheights taken (∼ into50 km), account where for theout estimation to be 2.4 × of10 the2 at 75 km to 6.6 × 10 3 at 84 km, which the inclusion of negative ion clusters N − is important and the is reasonable. ion density changes in the D-region. These are: electrons,x positive ions, negative ions and positive scheme has been used for the daytime lower ionosphere also Previous studies (Lehtinen and Inan, 2007; Rowe et (Inan et al., 2007). However, for the altitudes (above 60 km) al., 1974) predict that the effective coefficient of dissocia- −7 of our interest, where the VLF7 wave is reflected, the simpli- tive recombination αd may have values from 10 to 3 × −7 −3 −1 −7 −3 −1 fied GPI model is sufficient. While considering the solar pho- 10 cm s . We have used 3 × 10 cm s for αd. tons, we concentrate only on the ionization produced by the The effective recombination coefficient of electrons c ∼ −6 X-rays from solar flares, not from the regular UV and Lyman with positive cluster ions αd has the value 10 – alpha lines etc. Though it is a simplification, this will produce 10−5 cm−3 s−1. Here the value of 10−5 cm−3 s−1 is adopted good results as long as the electron-ion production rates due as suggested by Glukhov et al. (1992). The value of the ef- to X-ray dominates over the regular production rates. The fective coefficient of ion–ion recombination processes for model is suitable for the strong flares (at least higher C-class all types of positive ions with negative ions is taken to be and above) and is valid up to the time of recovery when the 10−7 cm−3 s−1 (Mitra, 1968; Rowe et al., 1974). B is the ef- above approximation holds. fective rate of conversion from the positive ion (N +) to the + −30 2 −1 According to the model, the time evolution of the ion den- positive cluster ions (Nx ) and has the value 10 N s sities follow ordinary differential equations, the right hand (Rowe et al., 1974; Mitra, 1968), in agreement with Glukhov sides of which are the production (+ve) and loss (-ve) terms. et al. (1992). The term I, which corresponds to the electron-ion production rate, can be written as I = I0 + Ix. Here I0 is from the constant source of ionization which are responsible for the

www.atmos-chem-phys.net/13/9159/2013/ Atmos. Chem. Phys., 13, 9159–9168, 2013 9164 S. Palit et al.: Modeling VLF signals due to Solar ﬂares with GEANT4 simulation

-2 -4 10 -5 10

-5 10

-6 10 (a) (b) -6 10 X-ray flux (Watt m ) 30000 36000 10000 20000 30000

2 10 3 80 km 80 km 10 76 km 76 km

-3 -1 72 km 72 km 1 2 10 68 km 10 68 km 64 km 64 km

0 1 10 (c) 10 (d)

Elec. prod. (cm s ) -1 0 10 10 30000 36000 10000 20000 30000 t (s) [started from 06:56:40 UT] t (s) [started from 01:23:20]

Fig. 5. Light curves of the flares from GOES satellite of an (a) M-class and (b) X-class flare. The time variation of the electron production Fig. 5. Light curves of the flares from GOES satellite of an (a) M-class and (b) X-class flare. The time rates at different heights as obtained from GEANT4 simulation for these flare respectively are shown in (c) and (d). variation of the electron production rates at different heights as obtained from GEANT4 simulation for these flare respectively are shown in (c) and (d).

+ + + − cluster ions. The positive ions N comprise of mainly O2 and NO2 . The negative ions N include − − − − + + O2 , CO3 , NO2 , NO3 etc. The positive cluster ions Nx are usually of the form H (H2O)n. The GPI model is meant for the night time lower ionosphere. Modified set of equations exists (Lehtinen and Inan, 2007), that are applicable at even lower heights (∼ 50 km), where the inclusion of negative − ion clusters Nx is important and the scheme has been used for the day time lower ionosphere also (Inan et al., 2007). However, for the altitudes (above 60 km) of our interest, where the VLF wave is reflected, the simplified GPI model is sufficient. While considering the solar photons, we concentrate only on the ionization produced by the X-rays from solar flares, not from the regular UV and Lyman Fig. 6. Electron densityalpha at lines different etc. layersThough during it is a the simplification,(a) M-class and this(b) willX-class produce flares. good results as long as the electron- Fig. 6. Electron density at different layers during the (a) M-class and (b) X-class flares. ion production rates due to X-ray dominates over the regular production rates. The model is suitable for the strong flares (at least higher C-class and above) and is valid up to the time of recovery when ambient distributions80 of ions. In our case, I0 corresponds 80the ion density terms with their ambient values, I by I0 and grossly to the partthe produced(a) above approximation by the background holds. ultraviolet equating(b) the rates to zero (Glukhov et al., 1992). ray, Lyman alpha lines,According etc. from to the the model, sun, the producing time evolution the D of the ionUsing densiti thees follow conditions ordinary of equilibrium differential equa- and the above replace- region. The term Ix is the modulated component of the ion- ments in Eqs. (1–4), we get the following set of equations 75tions, the right hand sides of which are the production75 (+ve) and loss (-ve) terms. ization rate. Here Ix is generated by the X-ray photons (in the energy range from 2 to 12 keV, important for the D-region) dNe − + + + h (km) = Ix + γ N − βNe − αd(N0eN + NeN + NeN ) h (km) 0 dNe − dt + c + coming from the solar coronal region during solar= I + flaresγN only.−βNe −αdNeN −α NeN , (1) 70 dt 70− c d+ + x + + + To account for the time variation of the number density of αd(N0eNx NeN0x NeNx ), (7) the ion species, we divide each term into a constant and a dN − 8 = βN − γ N −− time dependent parts, i.e., Ne is replaced with N0e + Ne(t), dt e + + 65+ − − − + 65 N with N + N (t), N with N + N (t) and Nx with − + + − + + + + 0 1000 1000 αi100[N (N + N 1000) + N (N 10000+ N + N + N )], (8) + + -3 0 x -3 0 0x x + electron density Ne (cm ) electron density N e (cm ) N0x Nx (t). A set of equations governing the equilibrium conditions can be obtained from Eqs. (1–4), by replacing Fig. 7. Altitude profiles of electron density as obtained from GPI model at three different times for an (a) M-class and (b) X-class flare. Solid line shows the ambient profile before the beginning of the flare while the dashed and the dot-dashed lines represent the profile during the peak and at a time during recovery. Atmos. Chem. Phys., 13, 9159–9168, 2013 www.atmos-chem-phys.net/13/9159/2013/

from the GPI scheme. We show this for the X-class ﬂares only. It is to be noted that they are the outcome of simpliﬁed chemical model devoid of physical processes such as the transport of ions through the layers of Ionosphere etc. These processes are being studied and would be reported elsewhere.

3.3 Modeling VLF response with LWPC

Now that we have the electron densities (Ne) at various altitudes, we can use them to obtain the time variation of the deviation of the VLF signal amplitude during a flare event. We use the Long Wave Propagation Capability (LWPC) code (Ferguson, J.A., 1998) to accomplish this. LWPC is a very versatile and well-known code and the current LWPC version has the scope to include arbitrary ionospheric variations as the input parameters for the upper waveguide. The electron density profiles (Fig. 6) represent the modulated D-region ionosphere due to the solar flares and can be used as

11 Fig. 6. Electron density at different layers during the (a) M-class and (b) X-class ﬂares. S. Palit et al.: Modeling VLF signals due to Solar ﬂares with GEANT4 simulation 9165

80 80

(a) (b)

75 75 h (km) h (km)

70 70

65 65

100 1000 100 1000 10000 -3 -3 electron density Ne (cm ) electron density N e (cm )

Fig. 7. Altitude profiles of electron density as obtained from GPI model at three different times for an (a) M-class and (b) X-class flare. Solid Fig. 7. Altitude profiles of electron density as obtained from GPI model at three different times for an (a) line shows the ambient profile before the beginning of the flare while the dashed and the dot-dashed lines represent the profile during the peak and at a timeM-class during recovery. and (b) X-class flare. Solid line shows the ambient profile before the beginning of the flare while the dashed and the dot-dashed lines represent the profile during the peak and at a time during recovery. dN + is to be noted that they are the outcome of simplified chemi- = I − BNfrom+ − theα (N GPIN scheme.+ + N N We+ show+ N N this+) for the X-classcal flares model only. devoid It is of to physical be noted processes that they are such the as the transport dt x d 0e e 0 e outcome of simplified chemical model devoid of physicalof ions through processes the such layers as ofthe Ionosphere transport of etc. ions These processes − − + + − + + − + αi(N0 N N N0 N N ), (9) through the layers of Ionosphere etc. These processesare being are bestudieding studied and would and would be reported be reported elsewhere. dN + x = BN + − αc(N N + + N N + + N N +) dt elsewhere.d 0e x e 0x e x 3.3 Modeling VLF response with LWPC − − + + − + + − + αi(N0 Nx N N0x N Nx ). (10) 3.3 Modeling VLF response with LWPC Now that we have the electron densities (Ne) at various al- The ambient values of the electron and ion densities are ob- titudes, we can use them to obtain the time variation of the tained from the IRINow model thatwe (Rawer have et the al., electron 1978). densities Unperturbed (Ne) at variousdeviation altitudes, of the we VLF can signal use them amplitude to obtain during the a flare event. − We use the Long-Wave Propagation Capability (LWPC) code negative ion densitytimeN variation0 is obtained of the deviation from the of relationship the VLF signal amplitude during a flare event. We use the Long N − = λN , where λ is the relative composition of the neg- (Ferguson, 1998) to accomplish this. LWPC is a very versa- 0 0e Wave Propagation Capability (LWPC) code (Ferguson, J.A., 1998) to accomplish this. LWPC is a ative ions. The values of positive ion densities are calculated tile and well-known code and the current LWPC version has from the charge neutralityvery versatile condition, and well-known i.e., code and the currentthe LWPC scope versi toon include has the arbitraryscope to include ionospheric arbitrary variations as the ionospheric variations as the input parameters for theinput uppe parametersr waveguide. for The the electron upper waveguide. density profiles The electron den- + − = + + + sity profiles (Fig. 6) represent the modulated D-region iono- N0e N0 N0x N0 . (11) (Fig. 6) represent the modulated D-region ionospheresphere due due to tothe the solar solar flares flares and and can can be used be used as as the inputs Using the ionization rate per unit volume (Ix) obtained from of the LWPC code to simulate the VLF signal behavior. The the GEANT4 simulation and the coefficients of the ODEs 11electron-neutral collision frequency in the lower ionosphere calculated from MSIS data, we solve the ODEs (Eqs. 7–10) plays an important role for the propagation of VLF signals. by Runge–Kutta method to find the residual electron density We used the collision frequency profiles between electrons at various altitudes during the course of the flare. and neutrals as described by Kelley (2009). This is given by −10 1/2 Figure 6a and b show the electron density variations at the following equation, νe(h) = 5.4 × 10 nnT , where different altitudes throughout the flares. The enhancement in nn and T are the neutral density (in cc) and electron tem- electron density from ambient values can be clearly seen. perature (in K), respectively. Assuming the temperature of Figure 7a and b shows the altitude variations of the elec- the electrons and the ions are same and using the ideal gas tron densities as obtained from the GPI model. These are equation, the above equation can be expressed as (Schmitter, 12 −1/2 plotted at three different times including the peak time. The 2011), νe(h) = 3.95 × 10 T exp(−0.145h). times are shown by arrows in Fig. 6a and b, The ambient electron density during the X-class flare was higher than that of the M-class flare. This is because the background X-ray 4 Results flux during the X-class flare was stronger. Though we do not expect drastic changes in the VLF ra- So far, we used various ways to obtain altitude variations of dio signal due to the changes in the chemical composition at the electron densities before and during flares. We use the the altitudes of our interests, for the sake of completeness, LWPC model to compute the resulting VLF amplitude. To we show in Fig. 8, the altitude profile of three types of ion find the observational deviation in the VLF signal due to densities at three different times evaluated numerically from flares, we subtract the flare day data from the VLF data of the the GPI scheme. We show this for the X-class flares only. It nearest quiet day. For the signal generated by the LWPC code www.atmos-chem-phys.net/13/9159/2013/ Atmos. Chem. Phys., 13, 9159–9168, 2013 9166 S. Palit et al.: Modeling VLF signals due to Solar flares with GEANT4 simulation

80 80 (a) (b)

75 75 h (km) h (km)

70 70

65 65

1000 10000 1 100 10000 Negative ion density N - (cm - 3 ) Positive ion density N+ (cm - 3 )

80 4 Results (c)

So far, we used various ways to obtain75 altitude variations of the electron densities before and during flares. We use the LWPC model to compute the resulting VLF amplitude. To find the observational h (km) deviation in the VLF signal due to70 flares, we subtract the flare day data from the VLF data of the nearest quiet day. For the signal generated by the LWPC code also the subtraction is made, but with

a ﬂat VLF proﬁle obtained from the65 ambient electron density shown in Fig. 6(a-b). The variation of

1000 10000 + - 3 ambient ion densities during the course of thePositive day affectscluster ion density the N xrecombination (cm ) process of the modulated

Fig. 8. AltitudeD-region profiles ionosphere of three types when of ion the densities flare duration as obtained is long. from the This GPI is scheme: evident(a) fromnegative Eqs. ions, (7-10)(b) positive that the ions, rate and (c) positive Fig. 8. Altitude profiles of three types of ion densities as obtained from the GPI scheme: (a)Negative ions, (b) cluster ions.of The change solid, of dashed the electron and dot-dashed density lines depends represent on respectively the ambient the ambientconcentration. profile, the If profile it was at not the thepeak case, and the the profile at a time during recovery ofPositive the X-type ions, flares and as (c) discussed Positive in Cluster the text. ions. The solid, dashed and dot-dashed lines represent respectively the subtraction would have made no difference. ambient profile, the profile at the peak and the profile at a time during recovery of the X-type flares as discussed in the text.

the inputs of the LWPC code to simulate the VLF signal behaviour. The electron-neutral collision frequency in the lower ionosphere plays an important role for the propagation of VLF signals. We used the collision frequency proﬁles between electrons and neutrals as described by Kelley (2009). This is given by the following equation,

−10 1/2 νe(h) = 5.4×10 nnT ,

Fig. 9. Simulation resultswhere, ofn VLFn and amplitudeT are the modulations neutral density(dotted line) (in andcc) corresponding and electron observed temperature VLF data(in K) (solid respectively. line) are plotted As- with UT for an (a) Fig.M-class 9. Simulation flare and an results(b) X-class of VLF flare, amplitude respectively. modulations (dotted line) and corresponding observed VLF data suming the temperature of the electrons and the ions are same and using the ideal gas equation, the (solid line) are plotted with UT for an (a) M-class flare and an (b) X-class flare respectively. above equation can be expressed as (Schmitter, 2011), also the subtraction is made, but with a flat VLF profile ob- The response of the VLF signal to this electron distribution The response of the VLF signal to this electron distribution as obtained from the LWPC code tained from the ambient electron density shown in Fig. 6a and 12as obtained−1/2 from the LWPC code after appropriate subtrac- νe(h) = 3.95×10 T exp(−0.145h). b. The variationafter appropriate of ambient subtraction ion densities of during the background the course of is showntion in ofFig. the 9(a-b). background We see is shownthat the in variation Fig. 9a, in b. We see that the day affects the recombination process of the modulated the variation in VLF signal strengths resemble with those D-regionVLF ionosphere signal strengthswhen the flareresemble duration with is those long. recorded This is forrecorded NWC to for IERC/ICSP NWC to propagation IERC/ICSP propagationpath by the path by the evident fromIERC Eqs. monitors. (7)–(10) Forthat the rate M-class of change flare, of the the resulting elec- VLFIERC signa monitors.ls from For the the model M-class matches flare, the with resulting the VLF sig- tron density depends on the ambient concentration. If it was nals from the model matches with the observation up to a observation up to a certain time beyond which modelled slope becomes gradually lower than that not the case, the subtraction would have made no difference. certain12 time beyond which modelled slope becomes gradu- of the observation. For the X-class flare, the modelledally slope lowerbecomes than that gradually of the observation. higher than For that the of X-class flare, the observation. The M-class flare occurred at the local afternoon when the diurnal ambient electron

Atmos. Chem.densities Phys., at various 13, 9159– altitudes9168, are 2013 decreasing. During the decay of the flare www.atmos-chem-phys.net/13/9159/2013/ when the effect of ambient ion densities start to dominate, observed slope of decay become higher in value (than that predicted from the model, where this effect is ignored) while still following the trend of variation of observed VLF amplitude at that time. The X-class flare, on the other hand, occurred in the morning when ambient electron densities are increasing with time due to the diurnal variation. In this case, the slope of observed decay is a lower. It can also be seen (comparing Fig. 9 with Fig. 6) that the differences in slopes of decay between the models and the observations start to occur when the electron densities fall below a certain level for both the flares (∼ 2000 cm−1 at 80 km). Furthermore, since the M-class flare spectrum is

13 S. Palit et al.: Modeling VLF signals due to Solar flares with GEANT4 simulation 9167 the modelled slope becomes gradually higher than that of the ionospheric dynamics during flares and adoption of more re- observation. The M-class flare occurred at the local afternoon alistic values of ionospheric parameters will lead to results in when the diurnal ambient electron densities at various alti- better agreement with observations. In future, these modifi- tudes are decreasing. During the decay of the flare when the cations will be made in the time analysis of the flare decay effect of ambient ion densities start to dominate, observed and the sluggishness of ionosphere. slope of decay become higher in value (than that predicted from the model, where this effect is ignored) while still following the trend of variation of observed VLF amplitude at Acknowledgements. Sourav Palit and Sujay Pal acknowledge that time. The X-class flare, on the other hand, occurred in MOES for financial support. Sushanta K. Mondal and Tamal Basak the morning when ambient electron densities are increasing acknowledge CSIR fellowship. with time due to the diurnal variation. In this case, the slope of observed decay is a lower. Edited by: F.-J. Lubken¨ It can also be seen (comparing Fig. 9 with Fig. 6) that the differences in slopes of decay between the models and the observations start to occur when the electron densities fall be- References low a certain level for both the flares (∼2000 cm−3 at 80 km). Agostinelli, S., Allison, J., Amako, K., Apostolakis, J., Araujo, H., Furthermore, since the M-class flare spectrum is relatively Arce, P., Asai, M., Axen, D., Banerjee, S., Barrand, G., Behner, softer than that of the X-class one, the ambient electron den- F., Bellagamba, L., Boudreau, J., Broglia, L., Brunengo, A., sity starts to dominate the VLF amplitude a bit earlier during Burkhardt, H., Chauvie, S., Chuma, J., Chytracek, R., Coop- decay of the M-class flare. We can see that the deviation of erman, G., Cosmo, G., Degtyarenko, P., Dell Acqua, A., De- the modelled slope from the observed one starts earlier for paola, G., Dietrich, D., Enami, R., Feliciello, A., Ferguson, M-class flare than the other. C., Fesefeldt, H., Folger, G., Foppiano, F., Forti, A., Garelli, S., Giani, S., Giannitrapani, R., Gibin, D., Gomez Cadenas, J. J., Gonzalez, I., Gracia Abril, G., Greeniaus, G., Greiner, 5 Concluding remarks W., Grichine, V., Grossheim, A., Guatelli, S., Gumplinger, P., Hamatsu, R., Hashimoto, K., Hasui, H., Heikkinen, A., Howard, In this paper, we have used a three step approach to com- A., Ivanchenko, V., Johnson, A., Jones, F. W., Kallenbach, J., Kanaya, N., Kawabata, M., Kawabata, Y., Kawaguti, M., Kelner, pute the deviation of the VLF signal amplitude during a so- S., Kent, P., Kimura, A., Kodama, T., Kokoulin, R., Kossov, M., lar flare. The steps are (i) GEANT4 Monte Carlo simulation Kurashige, H., Lamanna, E., Lamp, T., Lara, V., Lefebure, V., for ionization rate estimation, (ii) GPI-scheme of ionospheric Lei, F., Liendl, M., Lockman, W., Longo, F., Magni, S., Maire, chemistry analysis and finally (iii) LWPC modeling of sub- M., Medernach, E., Minamimoto, K., MoradeFreitas, P., Morita, ionospheric VLF signal propagation. This combined model Y., Murakami, K., Nagamatu, M., Nartallo, R., Nieminen, P., is self-consistent, realistic and uses a few justifiable assump- Nishimura, T., Ohtsubo, K., Okamura, M., O’Neale, S., Oohata, tions. Our method is capable of estimating the VLF signal Y., Paech, K., Perl, J., Pfeiffer, A., Pia, M. G., Ranjard, F., Rybin, behavior directly using the corresponding incident solar flux A., Sadilov, S., DiSalvo, E., Santin, G., Sasaki, T., Savvas, N., variation on D-region ionosphere during a solar flare. Sawada, Y., Scherer, S., Sei, S., Sirotenko, V., Smith, D., Starkov, In our model computation, we have ignored the effects N., Stoecker, H., Sulkimo, J., Takahata, M., Tanaka, S., Tcherni- of the variation of ambient concentrations, i.e., the diurnal aev, E., SafaiTehrani, E., Tropeano, M., Truscott, P., Uno, H., Urban, L., Urban, P., Verderi, M., Walkden, A., Wander, W., We- variations (ambient) of N , N +, etc. are not taken into ac- 0e 0 ber, H., Wellisch, J. 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