Radiodetection of cosmic neutrinos. A numerical, real time analysis

Volume 257, number 3,4

PHYSICS LETTERS B

28 March 1991

Radiodetection of cosmic neutrinos. A numerical, real time analysis F. H a l z e n , E. Z a s

Department of Physics, University of Wisconsin, Madison, W153706, USA and T. S t a n e v

Bartol Research Institute, University of Delaware, Newark, DE 19716, USA Received 13 December 1990

The coherent radiopulse generated by the excess charge in a high energy electron cascade in matter is numerically calculated. Particular attention is payed to the interplay between the physical dimensions of the shower and the features of the pulse. Interference effects between different particles in the shower front are responsible for the pulse spectrum and angular distribution. The calculation is relevant to the detection of neutrinos interacting with the Earth searching for GHz radiosignals. It is found that in the absence of radiowave absorption the radiosignal is above thermal background for distances linearly proportional to the primary electron energy confirming previous estimates. When the medium is ice r(m ) _~0.2E(TeV ).

Since p h o t o n s do not carry any i n f o r m a t i o n on cosmic sites and processes shielded from our view by m o r e than a few h u n d r e d grams o f intervening matter, the i m p o r t a n c e o f using weakly interacting neutrinos as a w i n d o w on the universe cannot be overstated. The goal o f high energy neutrino a s t r o n o m y is to build telescopes o f order 1 k m 2 area detecting neutrinos with characteristic energies o f order 1 TeV. The possibility has been raised to use large volumes o f polar ice as a low-noise particle detector sensing the Cerenkov emission from n e u t r i n o - i n d u c e d electromagnetic showers [ 1-4 ]. Although the most straightforward i m p l e m e n t a t i o n o f this idea would be to ins t r u m e n t the ice with p h o t o t u b e s detecting visible light [2], it was suggested almost 30 years ago that r a d i o a n t e n n a s might be able to detect microwave emission from neutrino-induced cascades in deep cold ice [5]. This idea has been held hostage to the fact that only rough estimates have been m a d e o f the power e m i t t e d [3,6]. We have p e r f o r m e d a numerical, real time c o m p u t a t i o n o f the power r a d i a t e d by T e V - P e V electromagnetic showers in the M H z - G H z frequency range. O u r calculations reveal a wealth of 432

insight and precise information about the signal. Unfortunately we will find that the energy threshold for the detection o f neutrinos is rather high thus confirming the low event rates for p r o p o s e d detectors calculated in refs. [ 1,2 ] on the basis o f the estimates o f Zeleznykh and collaborators [ 3,6 ]. That the signals are even close to observability is the result o f interesting physics. According to the F r a n k - T a m m formula the power r a d i a t e d by a particle with charge ze travelling a pathlength l in a med i u m o f refractive index n is given by [ 7 ]

dW-(4~2~h~)z2v(l-~l-~n2)

(1)

where v is the frequency and ~x= (137) -1. Naively one might expect the power generated in a shower o f N charged particles to be p r o p o r t i o n a l to N ( l ) . This is not correct. I f the e m i t t e d wavelength is large compared to the physical dimensions o f the shower, or equivalently, the electric pulse generated by the shower is short c o m p a r e d to the period o f the waves observed, then the emission by the shower particles

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Volume 257, number 3,4 is coherent and the power is of order [ 5,8 ]. Here Aq is the net charge Aq=

N(e-)-N(e + ) N(e-) +N(e + ) •

PHYSICS LETTERS B

(Aq.N)2(l) (2)

which enters in the coherent case because the electric fields from opposite charges cancel for the same { l). As we will see further on Aq is positive mainly because o f C o m p t o n scattering of shower photons on atomic electrons creates an excess of negative charges in the shower. Coherence thus implies an enhancement (Aq)ZNwhich can compensate the loss in power associated with the u dependence ofeq. ( 1 ). Roughly, from visible light to G H z radiowaves the suppression associated with the factor v in the F r a n k - T a m m relation is a factor 106 which can be compensated by coherence as N is of order 106 for PeV showers. There is no doubt that this argument is qualitatively correct. The technique has been successfully tested in experiments measuring radio emission by air showers observed in coincidence with particle arrays [ 9 ]. Whereas atmospheric fluctuations make the systematics of the radioemission difficult to handle, this is not a problem in ice. The density is high and the physical dimension of the shower reduced, as the radiation length is only 39 cm. The coherence is retained to shorter wavelengths, i.e., higher frequencies, where more energy is available. Determination of the precise threshold for observation in a medium like ice depends on the details o f the cascade and we therefore performed a real time numerical simulation of electromagnetic cascades in ice. Our calculations show that to a very good precision the enhancement factor from coherence (Aq)2N is proportional to the primary energy and therefore the power of the radioemission is proportional to the square of the cascade energy. This, combined with the fact that absorption of the signal in ice is not significant below a few GHz, makes ice a natural medium for this technique. We will however conclude that antennas sample ice only to a depth in kilometers given by 0.2E(PeV), neglecting absorption in the ice. Therefore only neutrinos with energies in excess of 5 PeV are detected in a volume of 1 km 3. We have used a detailed electromagnetic Monte Carlo cascade generator which follows the cascade particles from PeV to MeV energies covering nine orders of magnitude in energy. This program follows

28 March 1991

the tracks of all particles in three dimensions as well as their time delay associated with geometrical effects and non-relativistic velocities. This arduous task is necessitated by the fact that the dominant contribution to the negative charge excess Aq and the total tracklength I is associated with MeV electrons ~. We evaluate the radio emission from the electromagnetic shower by full simulation. However, in order to allow qualitative checks as well as comparison with related work we also compiled (i) the negative charge excess, (ii) the tracklength (projected along the shower axis) associated with particles contributing to the charge excess, and (iii) the total tracklength for all charges, which is the relevant quantity when the emission becomes incoherent. In decreasing order of importance the following processes contribute to the tracklength associated with the charge excess: (i) C o m p t o n scattering 7 + atomic e-~y+e(53%); (ii) Bhabha scattering e + + atomic e - ~ e + + e - (36%); (iii) positron annihilation in flight (18%), and finally (iv) M611er scattering e - + atomic e - - ~ e - + e - which decreases the excess tracklength ( - 7%) as it degrades e - energy. The numbers in brackets are for a 1 TeV shower but the relative contributions depend weakly on energy. C o m p t o n scattering is the dominant effect as the number of MeV photons in the electromagnetic cascade is much larger than the combined number o f electrons and positrons. The projected tracklength associated with the excess charge rises to 15% of the total tracklength for particles with energy above 100 keV; see fig. 1. The corresponding value of Aq rises to 20% near shower m a x i m u m and slowly increases at greater depth. The necessity to follow the particles to low energy can be underscored by noting that more than 50% o f the tracklength associated with excess electrons is due to particles with energy below 3.5 MeV. Although the tracklengths still increase as the Monte Carlo threshold is further decreased, the rise associated with particles below 100 keV, which happens to be close to the threshold for Cerenkov radiation in ice, is negligible. Below this energy the photoelectric effect rapidly terminates the shower. Before discussing the associated radioemission we One might expect the LPM effect to play a role in a medium like ice. Its effect on the radio power is however negligible [ 10] as it only affects the first few interactions. 433

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PHYSICS LETTERS B 10000

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~\

I00 TeV

~\\ x

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Fig. 1. Sum of tracklengths for all charged particles in 1, 10, and 100 TeV electron showers as a function of the calculational cutoff. The three sets of curves correspond to (i) the sum of the absolute tracklengths; (ii) the sum of the tracklengths projected onto the shower axis, and (iii) the difference of electron and positron tracklengths. Several showers are shown for 1 and 10 TeV primaries indicating the effect of fluctuations.

want to emphasize that the computed tracklengths are proportional to energy and fluctuate negligibly. The number of particles is so large that a single shower represents excellent statistics. Unlike in air, the shower is short and completely sampled and fluctuations in shower size, reflecting the first interaction depth as well as other effects, are irrelevant. We are now ready to calculate the features of the radiopulse in a detector antenna positioned at a distance r. Following Feynman we define a celestial sphere around the observation point where the electric field E(t) generated by a particle with apparent or celestial angle O(t) is given by [9,11 ] E(t)=

e

47~eoC2

O'(t)

(3)

where t is the retarded time, i.e. the time measured by the observer. The origin of the Cerenkov pulse is related to the fact that the field E(t) is determined by the particle's position at a time t' < t. The use of the apparent angle correctly takes into account the retardation. Similarly, light was emitted by a star in an earlier position along its track with respect to its location in the sky at observation. The formula is ob434

vious for dipole radiation, but is true in general and can therefore describe the transition from coherent to incoherent radiation. Using (3) we calculate the electric field associated with every particle track in the shower. We subsequently compute its Fourier transform

E(v) = ; E(t)

exp(iox) dt,

(4)

with ~o=2z~u. For a particle created at time t and stopped (absorbed by the ice) at t + At [ 9 ] /~(v) =

e 27~o C2

× {exp(-i~ot)-exp[-ko(t+At)l}O.

(5)

The contributed power is given by d2W

dvd.Q - 2

tnceo[r~(u) ]2

(6)

The program adds coherently the fields contributed by all particles. The definition of when a particle stops is somewhat arbitrary. We choose the cutoff near the Cerenkov threshold of 107 keV kinetic energy and

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have checked that the results are not sensitive to the precise choice. The numerical simulations correctly reproduce the expected coherent ( i n c o h e r e n t ) b e h a v i o r for low (high) frequency. At 10 M H z ( 2 -~ 17 m ) the radiation is coherent a n d we observe constructive interference in all directions. There is no Cerenkov peak. Instead the angular d i s t r i b u t i o n o f the signal follows an a p p r o x i m a t e sin 0 b e h a v i o r reflecting the projection o f the particle tracks on the celestial sphere o f the observer; see fig. 2. At higher frequencies the destructive interference gradually sets in and is m i r r o r e d by the a p p e a r a n c e o f a peak a r o u n d the Cerenkov angle o f 56 °. A useful way o f visualizing this is to think o f the longitudinal depth o f the shower as a slit which forms a diffraction pattern a r o u n d the Cerenkov angle. The pattern is clearly visible in fig. 2. The app r o x i m a t e half-widths o f the Cerenkov peak is 4.5 ° for 300 M H z or 2_~57 cm, 1.5 ° for 1 G H z o r 2 - ~ 17 cm and 0.5 ° for 3 G H z o r 2 - ~ 6 cm. We now look at the frequency d e p e n d e n c e o f the signal. F o r a one d i m e n s i o n a l shower, i.e. no transverse spread, the Cerenkov angle d e t e r m i n e s the direction o f constructive interference. The electric field is coherent and rises linearly with energy; see fig. 3. D e p a r t u r e s from this b e h a v i o r a p p e a r a r o u n d 300 MHz. The variations are again a result o f diffraction

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Fig. 2. Angular distribution of the electric field generated by a 10 TeV electron. The observation angle is the polar angle of the radiation with respect to the shower axis. The quantity rff~(u), distance times electric field, is related to power by eq. (6).

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28 March 1991

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Fig. 3. Frequency spectrum of the electromagnetic pulse generated by a 10 TeV electron for two observation angles relative to the shower axis; Oc is the Cerenkov angle. through a slit formed by the transverse spread o f the shower. The signal at 1 G H z is 50% o f the expected signal for full coherence. Notice in fig. 3 the peak ( d i p ) at 2 (20) GHz. As these variations reflect the transverse shower size, they are fairly i n d e p e n d e n t o f energy as expected. F o r practical purposes it should be kept in m i n d that absorption in the ice increases swiftly above ~ 1 GHz. This is not reflected in fig. 3. We now briefly discuss the implications o f our results for future experiments. As previously mentioned the critical p a r a m e t e r is the energy threshold for detection which not only depends on the power generated but also on the absorption in the ice and the background noise from the apparatus and its environment. A b s o r p t i o n at 1 G H z depends critically on t e m p e r a t u r e and therefore on the location o f the experiment. D e t e r m i n a t i o n o f in situ background noise is a complex problem. Experiments indicate that thermal noise o f t e m p e r a t u r e 300 K represents an adequate guess o f the background [ 12]. F o r this ass u m p t i o n the a m p l i t u d e o f the noise spectrum rises linearly with frequency, i.e. it exhibits the same dependence as the signal below ~ 1 G H z [ 9 ]; see fig. 3. In a detector o f b a n d w i d t h Av the noise varies as A u t/2, and therefore the b a n d w i d t h enhances the signal to noise ratio by the square root o f the bandwidth. Neglecting absorption and assuming A u = 1 GHz, a signal to noise ratio o f unity is achieved for a 435

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d e t e c t i o n t h r e s h o l d linearly p r o p o r t i o n a l to the dist a n c e r f r o m the s h o w e r Eth(TeV) - 5r(m) .

(7)

E.g. only n e u t r i n o s o f 5 P e V a n d a b o v e can be samp l e d in 1 k m o f ice. T h i s is a v e r y high t h r e s h o l d . Existing e x p e r i m e n t s already set l i m i t s o n high n e u t r i n o fluxes w h i c h i m p l y e x t r e m e l y low e v e n t rates a b o v e 5 P e V [ 2 ]. T h i s t h r e s h o l d e s t i m a t e is b a s e d on a signal to n o i s e a r g u m e n t . T h e p o w e r in the signal, w h i c h we o b t a i n f r o m fig. 3 a n d eq. ( 6 ) , is a b o u t an o r d e r o f m a g n i t u d e s m a l l e r t h a n the result q u o t e d by Zelezn y k h a n d c o l l a b o r a t o r s [ 3 ] . T h e y use the F r a n k T a m m f o r m u l a w h i c h o v e r e s t i m a t e s the power, as d i f f r a c t i v e effects are n o t t a k e n into a c c o u n t . T h e f o r m u l a o n l y d e s c r i b e s c o h e r e n t (2erenkov r a d i a t i o n p r o v i d e d the w a v e l e n g t h is small c o m p a r e d to the typical t r a c k l e n g t h o f a s h o w e r p a r t i c l e c o n t r i b u t i n g to the charge excess and large c o m p a r e d to the s h o w e r lateral d i s t r i b u t i o n . D e t a i l s o f the c a l c u l a t i o n s a n d its i m p l i c a t i o n s will be p u b l i s h e d elsewhere. We t h a n k C h a r l e s G o e b e l for a careful r e a d i n g o f the m a n u s c r i p t .

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References [1] For a review see S. Barwick and F. Halzen, Proc. 1990 Summer Study on High energy physics - research directions for the decade (Snowmass, CO), to be published. [2] F. Halzen, J. Learned and T. Stanev, Proc. AIP Conf., eds. D.J. Mullan, M.A. Pomerantz and T. Stanev, Vol. 198 (American Institute of Physics, New York, 1989) p. 39. [ 3 ] M.A. Markov and I.M. Zeleznykh, Nucl. Instrum. Methods A248 (1986) 242. [4]J.P. Ralston and D.M. McKay, Proc. Astrophysics in Antarctica Conf., eds. D.J. Mullan, M.A. Pomerantz and T. Stanev, Vol. 198 (American Institute of Physics, New York, 1989) p. 24; G. Smoot, private communication. [5] G.A. Askar'yan, Sov. Phys. JETP 14 (1962) 441; 48 (1965) 988. [6] I.M. Zeleznykh, Proc. XXIth Intern. Cosmic ray Conf. (Adelaide, 1989), Vol. 6, pp. 528-533. [7] I. Frank and I. Tamm, Proc. Acad. Sci. USSR 14 (1937) 109. [8] M. Fujii and J. Nishimura, Proc. Xlth Intern. Cosmic ray Conf. (Budapest, 1969)pp. 709-715. [ 9 ] For a review see H.R. Allan, Progress in elementary particles and cosmic ray physics, Vol. 10 (North-Holland, Amsterdam, 1971) p. 171. [10] D.M. McKay, private communication. [ 11 ] J.A. Wheeler and R.P. Feynman, Rev. Mod. Phys. 21 (1949) 425. [ 12] I.N. Boldyrev, G.A. Gusev, M.A. Markov, A.L. Provorov and I.M. Zeleznykh, Proc. XXth Intern. Cosmic ray Conf. (Moscow, 1987), Vol. 6, p. 472.