Asteroid impact, Schumann resonances and the end of dinosaurs
aa r X i v : . [ phy s i c s . c l a ss - ph ] J u l Asteroid impact, Schumann resonances and the end ofdinosaurs
Z. K. Silagadze
Budker Institute of Nuclear Physics and Novosibirsk State University, 630 090,Novosibirsk, Russia
Abstract
We estimate the expected magnitudes of the Schumann resonance fieldsimmediately after the Chicxulub impact and show that they exceed theirpresent-day values by about 5 × times. Long-term distortion of the Schu-mann resonance parameters is also expected due to the enviromental impactof the Chicxulub event. If Schumann resonances play a regulatory biologicalrole, as some studies indicate, it is possible that the excitation and distor-tion of Schumann resonances as a result of the asteroid/comet impact was apossible stress factor, which, among other stress factors associated with theimpact, contributed to the demise of dinosaurs. Keywords:
Schumann resonances, ELF electromagnetic fields, Chicxulubimpact, Dinosaur extinction
1. Introduction
Dinosaurs have been the dominant group of living organisms on the Earthfor over 160 million years (Myr). There were over 1000 specirs of dinisaursdistributed worldwide. The direct evolutionary descendants of non-aviandinosaurs, birds still make up one of the most proliferate and diverse group ofvertebrates. However, non-avian dinosaurs themselves suddenly disappearedabout 66 Myr ago [1].There are astounding number and variety of hypotheses about causes ofthe dinosaur extinction [1, 2]. However, the current research is concentratedaround three major ones: 1) an impact of a giant bolid (asteroid or comet) [3,
Email address: [email protected] ( Z. K. Silagadze) , 5]; 2) Volcanic activity in modern-day India’s Deccan Traps [6]; 3) Marineregression (drop in sea level) and the corresponding global environmentaldeterioration [7, 8].All three of the above stress factors occured at the end of the Cretaceous,which makes it difficult to disantangle their relative importance in the massextinction event that occured at the Cretaceous-Palogene (K-Pg) boundary(formely Cretaceous-Tertiary or K-T boundary). It is noteworthy that thereis little evidence that bolide impacts on the Earth correlate well with episodesof mass extinction other than K-Pg (there have been five mass extinctionsin the past 550 Myr), while both sea regression and massive volcanism docorrelate well with such episodes [2].Nevetheless, modern research [1, 9] found support for a bolide impactas the primary factor of the end-Cretaceous mass extinction. Evidence ofthe bolid impact, coinsiding in time with dinosaur extinction, is ubiquitous,including the huge 150 km wide Chicxulub crater in the Yucat´an Peninsulain Mexico, impact related iridium anomaly worldwide, sediments in variousareas of the world dominated by impact melt spherules and an unusuallylarge amount of shocked quartz.Yet another evidence of the enormous power of the Chicxulub impact hasbeen discovered recently [10]. After the impact, billions of tons of moltenand vaporized rock was thrown in all directions. After about ten minutes,these debris reached Tanis, a place at a distance of about 3 000 km fromthe impact. Bead-sized material, glassy tektites, fell from the sky, piercingeverything in its path. Fossil fish at Tanis, densely packed in the deposit,are found with the impact-induced spherules embedded in their gills.At about the same time, strong seismic waves, generated by the Chicxulubimpact, arrived at Tanis generating seiche inundation surge with about 10 mamplitude [10].Observations at Tanis expand our knowledge of the destructive effects ofthe Chicxulub impact, identifying the potential mechanism for sudden andextensive damage to the environment, delivered minutes after the impact towidely separated regions.Our goal in this short note is to show that the global extinction eventcould have had another very rapidly delivered global precursor, namely theexcitation of Schumann resonances with currently unknown but potentiallydangerous biological effects. 2 . Schumann resonances
It is useful to introduce the following complex combination of the electricand magnetic fields, called Riemann-Silberstein vector in [11] : ~F = r ǫ ~D √ ǫ + ~B √ µ ! = ~E + ic ~B, (1)where ǫ is the dielectric constant, µ is the magnetic permeability, and c =1 / √ ǫµ is the light velocity in a homogeneous and static medium in which ~D = ǫ ~E and ~B = µ ~H .In terms of the Riemann-Silberstein vector, the Maxwell equations read i ∂ ~F∂t = c ∇ × ~F , ∇ · ~F = 0 . (2)It is well known that the process of solving the Maxwell equations can befacilicated by the use of potentials. The Riemann-Silberstein vector can beexpressed in terms of the Hertz vector (superpotential) as follows [11]: ~F = (cid:20) ic ∂∂t + ∇× (cid:21) (cid:16) ∇ × ~ Π (cid:17) . (3)It follows from the first Maxwell equation in (2) that the Hertz superpotential ~ Π must satisfy the equation (cid:18) c ∂ ∂t − ∆ (cid:19) (cid:16) ∇ × ~ Π (cid:17) = 0 . (4)The name ”superpotential” indicates that electric and magnetic fields are ex-pressed through the second derivatives of the superpotential, and not throughthe first derivatives, as in the case of standard potentials.Much like more familiar four-potential, Hertz vector is not determineduniquelly by (3). In fact the group of gauge transformations of the Hertz Maybe we have here an example of the zeroth theorem of the history of science: adiscovery (rule, regularity, insight), named after someone, almost always did not originatewith that person [12]. There are reasons to believe that this complex vector was firstintroduced by Heinrich Weber in his 1901 book on the partial differential equations ofmathematical physics based on Riemann’s lecture notes [13]. ~ Π( ~r, t ) = ~r Φ( ~r, t ) . (5)Then it follows from (4), since the operator ˆ ~L = ~r × ∇ commutes withthe Laplacian, that the complex function Φ( ~r, t ) = U ( ~r, t ) + iV ( ~r, t ) can beadjusted in such a way using the gauge freedom that it satisfies the waveequation [15, 16]: (cid:18) c ∂ ∂t − ∆ (cid:19) Φ = 0 . (6)Using well-known expressions of differential operators in spherical coordi-nates, we get from (3) and (5) F r = − r sin θ ∂∂θ (cid:18) sin θ ∂ ( r Φ) ∂θ (cid:19) − r sin θ ∂ ( r Φ) ∂ϕ , (7)which by using (6), and assuming harmonic dependance of fields on time ofthe form e ± iωt , can be transformed into F r = (cid:20) ∂ ∂r + ω c (cid:21) ( r Φ) . (8)The real and imaginary parts of Φ, U and V respectively, are called electricand magnetic Debye (super)potentials. They are scalars under the (proper)three-dimensional rotations, but have complicated transformation propertiesunder the Lorentz boosts [15].Schumann resonances are quasi-standing transverse magnetic modes inthe Earth-ionosphere cavity, in which the radial component of the magneticfield equals to zero and thus (8) implies V = 0. Then from (3) ~E = ∇ × ( ∇ × ~r ) U, ~B = 1 c ∂∂t ∇ × ~r U, (9)and for the harmonic (complex) fields with e iωt time dependance we get E r = (cid:20) ∂ ∂r + ω c (cid:21) ( rU ) , E θ = 1 r ∂ ( rU ) ∂r∂θ , E ϕ = 1 r sin θ ∂ ( rU ) ∂r∂ϕ ,B θ = iωc θ ∂U∂ϕ , B ϕ = − iωc ∂U∂θ . (10)4he wave equation (6) for U (with e iωt harmonic time dependance) can besolved by separation of variables in spherical coordinates. Namely, taking U ( ~r, t ) = ρ ( r ) Y lm ( θ, ϕ ) e iωt , where Y lm ( θ, ϕ ) are spherical functions, and us-ing ∆ = 1 r ∂∂r (cid:18) r ∂∂r (cid:19) + 1 r ∆ ⊥ , (11)where ∆ ⊥ is the angular part of the Laplacian with ∆ ⊥ Y lm = − l ( l + 1) Y lm ,we get the spherical Bessel differential equation for the radial function ρ ( r ): (cid:20) d dr + 2 r ddr + k − l ( l + 1) r (cid:21) ρ ( r ) = 0 , k = ωc . (12)Therefore, inside the Earth-ionosphere cavity the Fourier component of U has the form U ( ~r, ω ) = ∞ X l =0 l X m = − l h A lm h (1) l ( kr ) + B lm h (2) l ( kr ) i Y lm ( θ, ϕ ) , (13)where h (1) l ( kr ) and h (2) l ( kr ) are spherical Hankel functions of the first andsecond kinds, respectively. Since we have chosen e iωt for our time evolution, h (1) l ( kr ) corresponds to the spherical incoming wave, while h (2) l ( kr ) — to thespherical outgoing wave.A real Earth-ionosphere waveguide have a very complicated configuration.Here we assume a simplified model [17]. Earth is considered as a perfectlyconducting sphere of radius R . It is further assumed that the ionospherebegins with an inner radius of R + h and is an infinite, uniform and isotropicplasma with complex dielectric constant (the imaginary part of which isproportional to the plasma conductivity [18]).In the ionosphere we can have only outgoing spherical waves (Sommerfeldradiation condition [19]). Thus U ( ~r, ω ) = ∞ X l =0 l X m = − l C lm h (2) l ( kr ) Y lm ( θ, ϕ ) e iωt , r > R + h. (14)Schumann resonance frequencies are determined by boundary conditions at r = R and r = R + h [17] (for somewhat different approach, see [20]). namely,at r = R the tangential components of the electric field must vanish. Thisleads to the condition ∂∂r ( rU ) (cid:12)(cid:12)(cid:12)(cid:12) r = R = 0 . (15)5t r = R + h , the tangential components of the electric field ~E , and thetangential components of the magnetic field ~H = ~B/µ must be continuous.If in the cavity ǫ ≈ ǫ , µ ≈ µ , while in the ionosphere ǫ = ˆ ǫ ǫ , µ ≈ µ , inlight of (10), the continuity conditions take the form ∂∂r ( rU ) (cid:12)(cid:12)(cid:12)(cid:12) r =( R + h ) − = ∂∂r ( rU ) (cid:12)(cid:12)(cid:12)(cid:12) r =( R + h ) + ,U ( r = ( R + h ) − ) = ˆ ǫ U ( r = ( R + h ) + ) . (16)If we substitute (13) and (14) into (15) and (16), we get a homogeneoussystem of linear equations u ′ l ( kR ) A lm + v ′ l ( kR ) B lm = 0 ,u ′ l ( k ( R + h )) A lm + v ′ l ( k ( R + h )) B lm − v ′ l ( √ ˆ ǫ k ( R + h )) C lm = 0 ,u l ( k ( R + h )) A lm + v l ( k ( R + h )) B lm − √ ˆ ǫ v l ( √ ˆ ǫ k ( R + h )) C lm = 0 . (17)Here we introduced the notations [17] u l ( x ) = xh (1) l ( x ) , v l ( x ) = xh (2) l ( x ) , u ′ l ( x ) = du l ( x ) dx , v ′ l ( x ) = dv l ( x ) dx . (18)The system (17) has a non-trivial solution for A lm , B lm , C lm , only when the3 × u ′ l ( kR ) v ′ l ( k ( R + h )) − u ′ l ( k ( R + h )) v ′ l ( kR ) =1 √ ˆ ǫ v ′ l (cid:16) √ ˆ ǫ k ( R + h ) (cid:17) v l (cid:16) √ ˆ ǫ k ( R + h ) (cid:17) [ u ′ l ( kR ) v l ( k ( R + h )) − u l ( k ( R + h )) v ′ l ( kR )] . (19)The solutions of this transcendental equation with respect to k determineeigenmodes ω = c k of the Earth-ionosphere resonator, which are calledSchumann resonances. Here c is the speed of light inside the resonator,which is the same as the light velocity in vacuum, c = 1 / √ ǫ µ , for theapproximations used. In general, ω is a complex number. Its real part givesthe eigenfrequency of the resonator, while the imaginary part determines theresonance width, since it corresponds to the damping factor of the eigenmode.The resonance width is characterized by the quality factor Q = ω/ ∆ ω , where∆ ω is the resonanse width at half maximum.6n the crude approximation of the infinite conductivity of the ionosphere,the right-hand-side of (19) vanishes and the equation for the eigenfrequenciessimplifies. Further simplification can be achieved by using h ≪ R , so thatwe can expand u ′ l ( k ( R + h )) ≈ u ′ l ( kR ) + u ′′ l ( kR ) kh , and v ′ l ( k ( R + h )) ≈ v ′ l ( kR ) + v ′′ l ( kR ) kh . Besides, it follows from the definitions of u l ( x ) and v l ( x ), that u ′ l ( x ) = h (1) l ( x ) + x dh (1) l ( x ) dx , u ′′ l ( x ) = 2 h (1) l ( x ) dx + x d h (1) l ( x ) dx ,v ′ l ( x ) = h (2) l ( x ) + x dh (2) l ( x ) dx , v ′′ l ( x ) = 2 h (2) l ( x ) dx + x d h (2) l ( x ) dx . (20)The second derivatives of the Hankel functions can be eliminated by using thefact that ρ ( r ) = h (1) l ( kr ) and ρ ( r ) = h (2) l ( kr ) satisfy the differential equation(12). This gives u ′′ l ( x ) = (cid:18) l ( l + 1) x − (cid:19) xh (1) l ( x ) , v ′′ l ( x ) = (cid:18) l ( l + 1) x − (cid:19) xh (2) l ( x ) . (21)Taking all this into account, in the case of perfectly conducting ionosphere,equation (19) simplifies to (cid:18) − l ( l + 1) k R (cid:19) " h (1) l ( x ) dh (2) l ( x ) dx − h (2) l ( x ) dh (1) l ( x ) dx x = kR = 0 . (22)The expression in the square brackets is the Wronskian of h (1) l ( x ) and h (2) l ( x ),and it is not zero, because these two solutions of the spherical Bessel equa-tions are independent. Therefore, from (22) we get ω l = c k l = c R p l ( l + 1),and in this crude approximation, the Schumann resonance frequencies are f l = ω l π = c πR p l ( l + 1) , l = 1 , , . . . (23)The observed frequencies of the first five Schumann resonances are 7.8, 14.1,20.3, 26.4 and 32.5 Hz, respectively [21], and they are about 25% lower thanit follows from (23).Winfried Otto Schumann, a professor at the Technische Hochschule M¨un-chen, rightfully gets most of the credit for predicting Schumann Resonances.However, Schumann resonance history is an interesting story [22]. The idea of7atural global electromagnetic resonances goes back to George F. Fitzgeraldin 1893 and Nikola Tesla in 1905 [22, 23]. The formula (23) for resonancefrequences of a spherical condenser was first obtained by Joseph Larmoralready in 1894 [22].Above we have outlined just some basics of Schumann resonances for thereader’s convenience. More detailed information about Schumann resonanceresearch can be found in books [17, 24, 25, 26, 27].
3. Excitation of Schumann resonances by an asteroid impact
Schumann resonances are excited primarily by lightning discharges. Onthe other hand, it is known that explosions and hypervelocity impacts areaccompanied by macroscopic charge separation [28, 29, 30]. Upon a hyper-velocity impact, a partially ionized plasma is formed, which rapidly expands.In addition to plasma, the impact will result in the formation of molten andfragmented debris of the target material, which are expected to become neg-atively charged when in contact with the plasma, since electrons are muchmore mobile than ions. The subsequent inertial separation of the positivelycharged plasma and the negatively charged debris will lead to the separationof charge over macroscopic distances [30].One can also imagine some other mechanisms of charge separation, forexample, those that act during the dust storms [31] and volcanic eruptions[32]. Therefore, we assume that an asteroid impact is immediately accompa-nied by a thunderstorm with a large number of lightning discharges. Namely,let dN ( t ) = N e − t/T dtT be the number of lightning discharges during a timeperiod dt at the time t after the impact. Here T ≈
100 s is the transientcrater formation time for the Chicxulub event [33], and N is the total numberof lightning strikes in the impact thunderstorm. If the current in an averageindividual lightning strike is I e − t/τ , with τ ≈ µ s and I ≈ · A [34],the total current will be I ( t ) = t Z e − t − sτ dN ( s ) = N I T e − tτ t Z e ( τ − T ) s ds ≈ N I τT e − tT , (24)where at the last step we have taken into account that T ≫ τ (in fact,this condition is not sufficient do discard the second exponent e − t/τ , whichoccurs after the integration in (24), since short signals with ω n τ ∼ ω n T ≫ ω n τ ≪
1, which is satisfied bythe first few Schumann resonances).Accordingly, as the current density, which we will consider having only aradial component, we take j r ( ~r, t ) = I ( t )∆ l πr sin θ δ ( θ ) δ ( r − R )Θ( t ) , (25)where Θ( t ) is the Heaviside step function introduced to indicate that thereis no current for t <
0, and ∆ l ≈ m [34] is the length of an averagelightning channel. The current density (25), when integrated over the wholespace, gives the total current moment: R j r ( ~r, t ) dV = I ( t )∆ l .Now we will consider how the Schumann resonanses are excited by thevertical electric dipole with current density (25). We will closely follow [24],for other approaches see [26] and [17, 34].Maxwell equations ∇ × ~E = − µ ∂ ~H∂t , ∇ × ~H = ǫ ∂ ~E∂t + ~j ( ~r, t ) , (26)for Fourier components with e iωt time dependance take the form ∇ × ~E ( ~r, ω ) = − iωµ ~H ( ~r, ω ) , ∇ × ~H ( ~r, ω ) = iωǫ ~E ( ~r, ω ) + ~j ( ~r, ω ) , (27)where ~j ( ~r, ω ) has only the radial component j r ( ~r, ω ) = ∞ Z −∞ e − iωt j r ( ~r, t ) dt = N I ∆ l τ iωT δ ( θ ) δ ( r − R )2 πr sin θ . (28)A vertical electric dipole source at θ = 0 can excite only fields that do nothave a ϕ -dependance. This follows from the azimuthal symmetry of theproblem. Then it can be checked in spherical coordinates that the fieldsgiven by equations (10) still satisfy the Maxwell equations (27) if the Debyesuperpotential U ( r, θ ) satisfies the equation r (∆ + k ) U = (cid:18) ∂ ∂r + k (cid:19) ( rU ) + 1 r sin θ ∂∂θ (cid:18) sin θ ∂U∂θ (cid:19) = − j r ( ~r, ω ) iωǫ . (29)Since j r ( ~r, ω ) is proportional to δ ( r − R ), it vanishes in the Earth-ionospherecavity. Thus, in the cavity U ( ~r, ω ) is still given by (13) with the difference9hat only m = 0 modes are excited due to azimuthal symmetry, and, there-fore Y lm spherical functions can be replaced simply by Legendre polynomials P l (cos θ ): U ( ~r, ω ) = ∞ X n =0 (cid:2) A n h (1) n ( kr ) + B n h (2) n ( kr ) (cid:3) P n (cos θ ) . (30)The boundary condition at r = R + h is ∂∂r ( rU ) (cid:12)(cid:12)(cid:12)(cid:12) r = R + h = 0 , (31)if the ideally conducting ionosphere is assumed. To get the boundary condi-tion at r = R , we integrate (29) over r from R − ε to R + ε , take into accountthat inside the ideally conducting Earth there is no tangential electric fieldand hence ∂∂r ( rU ) (cid:12)(cid:12) r = R − ε = 0, and finally take the limit ε →
0. As a result,we get [24] ∂∂r ( rU ) (cid:12)(cid:12)(cid:12)(cid:12) r = R = − N I ∆ l τ iωT δ ( θ )2 πiǫ ωR sin θ = − ∞ X n =0 a n P n (cos θ ) . (32)where a n = N I ∆ l τ iωT πiǫ ωR (cid:18) n + 12 (cid:19) , (33)and at the last step, we have expanded δ ( θ ) / sin θ into a series of Legendrepolynomials: δ ( θ )sin θ = ∞ X n =0 (cid:18) n + 12 (cid:19) P n (cos θ ) . (34)Substituting (30) into (31) and (32), we get the following system of linearequations for unknown coefficients A n and B n : A n u ′ n ( k ( R + h )) + B n v ′ n ( k ( R + h )) = 0 ,A n u ′ n ( kR ) + B n v ′ n ( kR ) = − a n . (35)This system is easily solved, and if the results are substituded in (30), weobtain U = ∞ X n =0 a n v ′ n ( k ( R + h )) h (1) n ( kr ) − u ′ n ( k ( R + h )) h (2) n ( kr ) u ′ n ( k ( R + h )) v ′ n ( kR ) − v ′ n ( k ( R + h )) u ′ n ( kR ) P n (cos θ ) . (36)10rom (12) It follows that the Hankel functions satisfy the relation (cid:18) d dr + k (cid:19) (cid:0) rh (1 , n ( kr ) (cid:1) = n ( n + 1) r h (1 , n ( kr ) . (37)Then from (10) and (36) we obtain the following expression for the Fouriercomponent E r ( ~r, ω ) of the electric field on the ground (at r = R ): E r ( ~r, ω ) = ∞ X n =0 a n n ( n + 1) R c n P n (cos θ ) , (38)where c n = v ′ n ( k ( R + h )) h (1) n ( kR ) − u ′ n ( k ( R + h )) h (2) n ( kR ) u ′ n ( k ( R + h )) v ′ n ( kR ) − v ′ n ( k ( R + h )) u ′ n ( kR ) . (39)Now we use, as in the previous section, smallness of the ratio h/R and expandboth the numerator and denominator of c n in terms of this small quantity.To first order, we have u ′ n ( k ( R + h )) v ′ n ( kR ) − v ′ n ( k ( R + h )) u ′ n ( kR ) ≈ kh (cid:0) n ( n + 1) − k R (cid:1) W,v ′ n ( k ( R + h )) h (1) n ( kR ) − u ′ n ( k ( R + h )) h (2) n ( kR ) ≈ kR W, (40)where W is the Wronskian of h (1) l ( x ) and h (2) l ( x ) at x = kR . Replacing n ( n + 1) by R c ω n , and k by ω c , we get E r ( ~r, ω ) = ∞ P n =0 a n ω n P n (cos θ ) h ( ω n − ω ) = NI ∆ l τ πiǫ ωR h (1+ iωT ) ∞ P n =0 ω n ( n + ) P n (cos θ ) ω n − ω . (41)But ω n ω n − ω = 1+ ω ω n − ω , and the first term according to (34) will lead to a δ ( θ )proportional contribution that is equal to zero outside the source. Therefore,finally we can write E r ( ~r, ω ) = N I ∆ l τ πiǫ R h (1 + iωT ) ∞ X n =0 ωω n − ω (2 n + 1) P n (cos θ ) . (42)To find the electric field in the time domain, we perform the inverse Fouriertransform of the frequency domain field E r ( ~r, ω ) (since it is assumed thatthe Earth is perfectly conductive, the electric field on the ground is radial,so we omit the lower index indicating the radial component in E ( ~r, t )): E ( ~r, t ) = 12 π ∞ Z −∞ e iωt E r ( ~r, ω ) dω. (43)11owever, for the integral (43) to have a well-defined meaning, it is necessaryto indicate how to handle the singularities of the integrand: as is clear from(42), we have three simple poles at ± ω n and iT , and the first two of them lieon the integration contour of (43).This problem is solved by noting that in reality the Earth and ionosphereare not ideal conductors and as a result the Schumann eigenfrequences be-come complex with small imaginary parts γ n = ω n Q n ≪ ω n [17] (the qual-ity factors for the first Schumann resonanses are Q ≈ . Q ≈ . Q ≈ . Q ≈ . Q ≈ .
95 [17]). For a dissipative ionosphere,the imaginary part γ n of the positive pole at ω = ω n is positive. Theimaginary part of the negative pole at ω = − ω n is fixed by the condition E ∗ r ( ~r, ω ) = E r ( ~r, − ω ) (the reality condition for the time domain field E r ( ~r, t ))and turns out to be also γ n . Therefore, we replace ( ω − ω n ) − in the integral(43) by [( ω − ω n − iγ n )( ω + ω n − iγ n )] − , close the integration contour in theupper half-plane where the integrand decreases exponentially, and evaluatethe integral according to the Cauchy residue theorem as a sum of residues atthree simple poles. As a result, we obtain E ( ~r, t ) = NI ∆ l τ πǫ R h ∞ P n =0 (2 n +1) P n (cos θ )1+ ω n T h e − tT − e − γ n t (cos ω n t + ω n T sin ω n t ) i . (44)The first e − t/T term in square braces expresses the direct, non-resonant con-tribution to the electric field from the source, while the remaining termscorrespond to to the excitation of resonant modes of the cavity [34]. Since ω n T ≫
1, the resonant part of the electric field takes the form E res ( ~r, t ) = − N I ∆ l τ πǫ R h X n =0 (2 n + 1) e − γ n t ω n T sin ω n t P n (cos θ ) . (45)To estimate an avarage amplitude of the excitation, we replace e − γ n t by itsavarage value T T R e − γ n t dt ≈ γ n T [34]. In this way, we get for the amplitudeof the first Schumann resonance A ≈ N I ∆ l τ πǫ R hω γ T = 3∆ Q ∆ l πǫ R hω γ T , (46)where ∆ Q = N I τ is the total amount of electric charge separated by amacroscopic distance. In [30] the following empirical relation was obtained12or ∆ Q in laboratory scale hypervelocity impacts (all quantities are in the SIunits) ∆ Q ≈ − m (cid:18) V (cid:19) . ± . , (47)where m is the impactor mass, and V is its velocity. It was argued [35]that the Chicxulub impactor was a fast asteroid or a long-period comet withenergy between 1 . × J and 5 . × J, and mass between 1 . × kgand 4 . × kg. Taking the lowerest numbers m = 1 . × kg and E kin = 1 . × J, for the velocity we obtain V = q E kin m ≈
50 km / s.Then an interpolation of empirical relation (47) to this enormous scale givesa huge number ∆ Q ≈ . × C. However, a recent simulation resulted inthe Chicxulub scale impact-generated magnetic field that was three ordersof magnitude smaller than expected from the relation (47). Therefore, asa more realistic estimate, we will take ∆ Q ≈ . × C. As for otherparameters in (46), we will assume R = 6400 km, h = 75 km, ω = 49 and γ = 5 .
3. Then we get from (46) the following amplitudes for the electricand magnetic fields of the first Schumann resonance: A ≈
50 V / m , B = A V ph ≈
230 nT , (48)where V ph ≈ . c is the phase veocity of the electromagnetic waves in theearth-ionosphere cavity. For comparision, the measured Schumann resonancebackground fields are very small, of the order of mV / m for the electric field,and severel pT for the magnetic field [23]. As we see, estimated magnitudesof the Chicxulub impact induced Schumann resonance fields exceed to theirpresent-day values about 5 × times.
4. On biological effects of ELF electromagnetic fields
Schortly after Schumann and his graduate student K¨onig made their firstattempts to detect Schumann resonances, K¨onig and Ankerm¨uller noted astriking similarity between these signals and human brain electroencephalo-grams (EEG) [37].The classical EEG rhythms are delta (1-3 Hz), theta (4-7 Hz), alpha (8-13Hz), beta (14-29 Hz) and gamma (30-80+ Hz) [38], and we can try to roughlyestimate these fundamental brain frequences as follows [39].13uman neocortex, which form most of the white matter, contains about10 interconnected neurons. Imagine that the wrinkled surface of each hemi-sphere, where these neurons are situated, is inflated so that to create a spher-ical shell with effective radius a = p S/ π , where S = 1000 − is thesurface area of the hemisphere. Characteristic corticocortical axon excitationpropagation speed is V = 600 −
900 cm / s. Therefore we can write the waveequation for the propagation of these excitation waves on the surface of thesphere as follows: ∆Φ( θ, ϕ, t ) = 1 V ∂ Φ( θ, ϕ, t ) ∂t , (49)where Φ is some quantity characterizing the excitation. Because of sphericalsymmetry, we seek the solution of (49) in the formΦ( θ, ϕ, t ) = ∞ X l =0 l X m = − l A lm F l ( t ) Y lm ( θ, ϕ ) . (50)Recalling (11) and taking into account that r = a = const and ∆ ⊥ Y lm = − l ( l + 1) Y lm , we get the following differential equation for F l ( t ) after sepa-rating the variables: 1 V d F l ( t ) dt = − l ( l + 1) a F l ( t ) . (51)This is the equation of harmonic oscillations with the cyclic frequency ω l = Va p l ( l + 1) . (52)In particular, for the first fundamental frequency we get f = ω π = 8 −
18 Hz,which is close to the frequency of alpha rhythm [39].From how we obtained Schumann resonances and brain waves, it shouldbe clear that the similarities between them are the result of spherical sym-metry and the small height of the ionosphere compared to the radius ofthe Earth. The existence of standing waves requires only that the materialmedium supports traveling waves that do not decay too quickly. Then thecorresponding resonant frequencies are determined from the geometry of theproblem and from the boundary conditions. Therefore any similarity be-tween brain waves and Schumann resonances may well be just a coincidence,and for their interconnection a wild stretch of our imagination will be re-quired [40]. Nevertheless, some arguments can be envisaged that these twodesperately different phenomena are actually interrelated.14LF electromagnetic fields and Schumann resonances have been presenton Earth since the formation of the ionosphere. Therefore, they accompaniedlife from the very beginning, and it does not seem too wild to assume that inthe course of evolution living organisms have found some useful applicationto these ubiquitous electromagnetic fields. One can even imagine that theELF electromagnetic fields and related electric activity in the PrecambrianEarth’s atmosphere played the crucial role in the emergence of life accordingto the following scenario [41, 42].In the Precambrian era, the atmosphere of the Earth was much largerand more similar to what Jupiter has today. In addition, the ionosphere wasalso much farther than today, about 10 km far from the Earth’s surface, inthe immediate vicinity of the Van Allen belts. As a result, fluctuations ofcurrent in the Van Allen belts were capably of generating huge currents in thenearby ionosphere and the coupling of these currents to the Earth’s metalliccore would lead to an enormous and constant electrical activity. It is believed[41], these electrical discharges were essential for production of amino acidesand peptides from which the first living organisms were formed. This processwas accompanied by an intense background of the ELF electromagnetic field,which could affect the formation and functionality of the first living cells andorganisms.It has been suggested that these atmospheric ELF background fieldsplayed a major role in the evolution of biological systems, especially in theearly stages of evolution [43]. In particular, the dominant brain wave fre-quencies may be the evolutionary result of the presence and effect of thisELF electromagnetic background [44]. This idea is to some extent supportedby the amazing fact that many species exhibit, irrespective of the size andcomplexity of their brain, essentially similar low-frequency electrical activity[43].Various remote sensing systems of living organisms, such as visual systemor the infrared sensors of snakes, have been developed due to the presence ofelectromagnetic energy in the corresponding parts of the spectrum. On earlyEarth, there was a significant amount of electromagnetic energy in the ELFportion of the spectrum. Thus, we can expect that organisms could adapt andsomehow use this part of the electromagnetic spectrum too, in particular theSchumann peaks of the Earth’s ELF electromagnetic field [44]. The followingobservation provides some support for this idea.Heat shock genes are responsible for adapting organisms to harsh environ-mental conditions. They are ubiquitous, present in various organisms from15acteria to humans and represent the most conservative and ancient groupof genes. The proteins encoded by these genes (heat shock proteins, HSPs)serve as molecular chaperones, which help in the repair, folding and assemblyof nascent proteins during stress and prevent the accumulation of damagedcellular proteins.It has been experimentally demonstrated that the ELF electromagneticfields can induce various heat shock proteins and, in particular, HSP70, likea real heat shock. The most surprising fact was that the electromagneticfields caused the synthesis of HSP70 at an energy density of fourteen ordersof magnitude lower than in heat shock [45].Such extraordinary sensitivity to the ELF magnetic fields (unlike ELFelectric fields, magnetic fields easily penetrate biological tissues) should havea good evolutionary basis. Astrophysical simulations show that shortly afterthe formation of the solar system, giant planets Jupiter and Saturn beginto migrate inward or outward. This planetary migration destabilizes theorbits of Neptune and Uranus into eccentric ellipses. As a result of this, theice giants begin to cross the planetesimal disk beyond the orbit of Neptuneand gravitationally scatter these planetesimals, forcing many of them to goalong the Earth-crossing trajectories. The resulting so-called Late HeavyBombardment (LHB) could have both positive and negative consequencesfor the emergence of life [46]. In any case, the first living cells are expectedto face grave dangers of powerful bombardment by meteorites (LHB tail).Thus, it can be assumed that the cells could use ELF magnetic pulses as akind of early warning system that gives them time to prepare for other reallydangerous stressors such as the heat pulse and the blast wave, which oftenfollow the electromagnetic pulse [47].However, a very detailed analysis in [48] indicates that, from the point ofview of the conventional classical physics, it remains a mystery that very weakELF electromagnetic fields can cause any biological effect at all. The problemis the thermal noise. If we assume that random electric fields in biologicaltissues generated by thermal fluctuations of charge densities are correctlydescribed by the Johnson-Nyquist formula, as in ordinary conductors, thenthe inevitable conclusion is that, for external ELF electric fields weaker than300 V / m, and for external ELF magnetic fields weaker than 50 µ T, it seemsimpossible to influence biological processes, since any effects generated bysuch fields in the body will be masked by thermal noise [48]. This objectionis known as the kT problem.Despite of these categorical conclusions, biologists continued the exper-16mental attempts to detect biological effects of ELF electromagnetic fields,remembering the words of Szent-Gyorgyi that ”the biologist depends on thejudgement of the physicist, but must be rather cautious when told that thisor that is improbable” [49].As a result of these attempts, a diverse and incontrovertible evidencehad been accumulated indicating that ELF radiation has important effectson the functioning of cells [50]. We cite only a few reviews of the subject[51, 52, 53, 54, 55, 56], where further references can be found.The usual formulation of the kT problem is based on several implicit as-sumptions that are not always justified [57, 58]. For example, the Johnson-Nyquist formula assumes that the system is in a thermal equilibrium. Evenso, although a living organism as a whole is very far from thermal equilibrium,the nature of this non-equilibrium is such that the concept of a well-definedtemperature nevertheless exists [59]. In fact, the physical nature of the bio-logical effects of ELF fields still remains an enigma, and more work is neededto elucidate the comprehensive mechanisms behind these effects [56, 59].
5. Concluding remarks
As we have seen, the magnitudes of the Schumann resonance fields areexpected to increase tremendously after the Chicxulub impact. Nevertheless,this effect will be rather short-lived, since Schumann resonance fields decayrapidly due to low Q-factors of resonances.In the long run, the impact of this magnitude will cause a very seriousenviromental demage. As a result, stratospheric dust, sulfates released asa result of impact, and soot from extensive worldwide forest fires causedby exposure to the impact related thermal radiation, can lead to significantclimate changes over decades (impact winter) [61] and hence modify lightningactivity, which is the main source of energy for Schumann resonances.In addition, blast wave for some time distorts the ionosphere and changesthe frequencies of Schumann resonances (after high altitude ”Starfish” nu-clear test explosion, all resonance frequencies abruptly dropped by about0.5 Hz [27]).It has been suggested that ELF background atmospheric fields playeda major role in the evolution of biological systems, and in particular thatSchumann resonances are used for synchronization by living organisms [43,61]. If so, then the change in the Schumann resonance parameters after the17hicxulub impact could have a stressful effect, contributing to a devastatingload on the global biosphere, including dinosaurs.A somewhat similar idea can be found in [62], where it was suggestedthat the influence of the ELF and ultra-law frequency (ULF) electromagneticfields produced by widespread earthquakes and volcanism in the dinosaur erastimulated their growth in size, and when these phenomena were no longerso common dinosaurs became extinct for a number of reasons, including theloss of intensity of the ULF/ELF electromagnetic fields.
Acknowledgments
The work is supported by the Ministry of Education and Science of theRussian Federation.
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