IL NUOVO CIMENTO VOL. 9 C, N. 2 Marzo-Aprile 1986

High-Energy Neutrino Emission from Binary X-Ray Sources.

G. A V ~ I E ~ (*) Is t i tuto 5Vazionale di ~ i s i c a ~uv leare - Sezione dl ~ o m a

Dipart~f~ento di ~ i s i v a dell' Universl t~ (( ]Sa Sap ienza • . t~oma

H . B ~ O K O ~ a n d A . F . G m ~ L o

Is t i tuto ~Vazia~ale di ~ i s i e a ~ue leare - ~aborator~ ~ a z i o n a l i d~ ~rasea t i

(ricevuto 1'11 Set tembre 1985)

Summary.- Recently v-rays up to 1016 eV were observed from Cyg X3, Vela X1 and LMC X4. This is a strong indication tha t protons (or nuclei) are accelerated in the vicinity of the aecreting pulsar. We discuss in this paper the production of high-energy neutrinos associated with the v-ray production. We show tha t on the basis of observational parameters of the three b inary systems, the t ime average of the rat io of the neutr ino luminosi ty to the v-ray luninosi ty will be Lv /L v ~ 30. The neutr ino flux will be modulated with the orbi tal period of the system and the neutrino l ight curve will be determined by the densi ty profile of the companion star. In general some of the X-ray binaries can be both UHE v-ray and neutrino emit ters with a neutrino luminosi ty comparable to their X- ray luminosity. The brightest of these could be detected by future neutr ino telescopes such as DUMAND and MACRO at Gran Sasso.

PACS. 94.40. - Cosmic rays.

(*) On leave from Is t i tu to Astrofisiea Spaziale del C.N.R., Frascat i , I ta ly .

451

452 G. AUI~IEMMA, H. BILOKON and A. F. GRILLO

B i n a r y X - r a y st~rs were discovered abou t t en years ~go b y GIACCONI ~nd col labora tors (~,~). Since t h e n ~ 60 sys tems of this t y p e were observed and t h e y represent ~ 80 % of the known galact ic X - r a y sources wi th Zx>~ 10 $3 erg s -~. I n m a n y of these sys tems have been found X - r a y pulsars wi th per iods ranging f rom 69 ms to 835 s. The coherence of the pulsat ions, and the secular decrease in the i r period, establ ishes beyond doub t t h a t e~ch of these sys tems contains a magne t i zed neu t ron s ta r accre t ing mate r i~ l and ~ngular m o m e n t u m f rom a nondegenera te eompan io~ (s,4). ~ e a s u r e m e n t s of the o rb i t a l e lements of some sys tems require t h a t the mass of the puls~r be consis tent wi th t h a t expec ted for a neu t ron star. L ight curves f rom m a n y of the pulsars indicate t h a t the emission m u s t be b e a m e d (~). Such beaming and cyclo t ron fea tures in the X - r a y spect ra suggest a large magne t i c field ~ 10 ~ G a t the surface of the

pulsar . Recen t ly three of this sys tems were discovered to be s t rong emi t t e r s of

par t ic les which produce estensive ~ir showers in the a tmosphe re (~.9). The identif icat ion of these new sources wi th the b ina ry sys tems is s t rongly suggested b y the per iodic i ty of the U H E emission which is fa i r ly coincident wi th the b ina ry per iod of the X - r a y sources. Therefore we are forced to admi t t h a t the air showers are caused b y low-mass neu t ra l part icles which can t r ave l th rough the galact ic magne t ic field f rom distances of tens of kpe, conserving bo th direc- t iona l i ty and t i m e coherence. The mos t na tu ra l a s sumpt ion is t h a t the air showers are produced b y u l t rah igh-energy (Ut tE) y-rays .

This detect ion was v e r y surprising because t he b ina ry X - r a y sources show a t h e r m a l X - r a y spec t rum with no associated y - ray emission in the COS-B energy range (~0). The only possible except ion could be Cyg X3, which was detec ted in the SAS-2 su rvey (11), bu t not b y COS-B. I f the showering part icles are photons , the mos t plausible in te rp re ta t ion of the produc t ion of these photons require accelerat ion of pro tons or nuclei up to energy of the order of N (10 ~ -

(1) R. GIACCONI, H. GW~sKY, E. KELLOG, E. SCHREIER an(]. H. TANANBAU~: Astrophys. J. T~ett., 167, L67 (1971). (3) H. TANANBAUM, H. G~RSKY, E.M. KELLOG, 1~. LEVINSON, E. SCHREIER and R. GIACCO~-I: Astrophys. J..Lett., 174, L143 (1972). (8) K. DAWDSON and J .P . 0STRIKE~: Astrophys. J., 179, 585 (1973). (4) S. RAPFAPO~T and P.C. Joss: Nature (London), 266, 683 (1977). (~) M. IV[. BASXO and P. SVNYAEV: SOV. Astron. AJ. (Engl. Transl.), 26, 537 (1976). (~) M. SAMO~SKY ancl W. STAMM: Astrophys. J. Left., 268, L17 (1983). (~) J. LLOYI)-EvANS, R. N. CoY, A. LAMBE~T, J. LAPIK~NS, M. PATEL, R. J. 0. REID and A.A. WILSON: .Yatq~re (.London), 30S, 784 (1983). (s) R . J . P~OTHEnOE, R.W. CLAY and P .R . GERHARDY: Astrophys. J..Lett., 280, L47 (1984). (9) R . J . P~0TRE~OE and R.W. CLAY: s (T~ondon), 315, 205 (1985). (10) G.F. BIGNAMI and W. HEnMSES: Anna. :2ev. Astron. Astrophys., 21, 67 (1983). (11) R.C. LAME, C. E. FICHTEL, R.C. HARTmAN, D. A. KNIFFEN and D. J. THOMSON: Astrophys. J. Left., 212, L63 (1977).

ltlGII-ENERGY NEUTRINO E~ISSlON E~O~ BINAI~Y X-I~AY SOUI~CES 4~3

+ 1 0 ~) TeV. W])owczu and WOLFE~D~E (1~) have po in ted out t h a t ~ 3 0 sources of this s t reng th can feed to the Galaxy its ent i re con ten t in cosmic- r a y part icles. B u t even more puzzl ing was the detect ion of a modu la t ed flux of muons with energy E ~ > (0 .5_1) TeV f rom the direct ion of Cyg X3 claimed b y the SOUDAI~ group (~) and confirmed b y D'E~TO~E-P~hZZOL~ a t this conference (~). This new resul t canno t be in t e rp re t ed in t he f r amework of the known par t ic le physics (1~).

VES~A~D and ElCm~ER (~) h a v e proposed the s imple model , schemat ica l ly shown in fig. 1, which can expla in the produc t ion of U H E y- rays in b ina ry sys tem. I n this model protons (or nuclei) accelerated in the v ic in i ty of the pulsar ~re dr iven by the magne t i c field to hi t the surface of ~he companion. I n fac t H ~ A S (1~) has shown t h a t the p roduc t ion of U H E y-rays m u s t occur fa r f rom the pulsar~ otherwise the y- rays would be self-absorbed b y p~ir creat ion in i ts s t rong magne t i c field of the pulsar .

Accelerat ion of pro tons in the polar cups of the pulsar was originally advoca t ed b y EICRLER and VESTR~ND (~). Bu t this mechan i sm is inconsis tent wi th the slow spin ra tes of the pulsars in Vela X1 and LHC X4 systems. A more appeal ing mechan i sm was proposed b y C ~ u ~ A ~ and :BRECHER (1~).

to obsenven --v-- - - ~ X-ray - - ~ p u l s a p

cornpan/on ~ \ -,,4 /~///~ /

Fig. 1. - Model for UHE y-ray and neutrino production in X-ray binary systems (after V~STRAND and E:[CHLER (18)).

(12) j . WDOWCZYK and A.W. WOLFE~DALE: Nat~'e (London), 305, 609 (1983). (1S) 1~. L. ~VIA~RSI:IAK, J. BARTELT, H. COURANT, K. HELLER, T. JOYCE, ~E. A, PETERSON, K. RUDmCK, M. StIU~E, D. S. AYRES, J. DAWSON, T. FIELDS, E. N. MAY, L. E. P~ICE and K. SIVArnASAD: Phys. Rev. Lett., 54, 2079 (1985). (la) G. BATTXS~ONI, E. B~LLOTTI, C. BLOISE, G. BOLOGNA, P. CA~rANA, C. CASTAGNOLI, A. CASTELLINA, V. CmAa~ELLA, A. ClOClO, D. CUNDY, B. D'ETTo~nE-PIAZZOLI, E. ~IO- RINI, P. GALEOTTI, E. I~noccI, C. LIGVORI, G. MAN~ocem, G. M~TAS, P. NEGnI, G. NICOLETTI, P. Plcc~tI, M. PRICE, A. PULLIA, S. RAGAZZI, M. ]{OLLIER, 0 . SAAYEDtCA, L. SATTA, P. SERI~I, S. VERN~TTO and L. ZANOTTI: Phys. Lett. B, ~o be published. (1~) M.V. BARNtlILL I I I , T .K . GAISSE~, T. S~ANEV and F. HALZEN: preprint MAD- PH-243 (April 1985). (~8) W.T . VEST,AND and D. EICHLER: Astrophys. J., 26], 251 (1982). (1~) A. ~ . HILLAS: ~ature (London), 312, 50 (1984). (is) D. EIC~L]~R an4 W. T. VES~RA~D: .STature (JSondon), 307, 613 (1984). (1~) G. C~IANMUGA~ and K. B~EeHER: ~ature (London), 313, 767 (1985).

~ G. AURI:Ei~CI~C[A, It . ]BILOKO:N ~ l l d A. l~. GRILLO

They suggest tha t the large electrostatic potential required for the particle acceleration is induced by dynamo effect of the pulsar magnetic field, in the highly ionized plasma forming the X-ray emitting accretion disk around the pulsar itself. In this ease the particle luminosity of the object is related to the accretion rate and to the mass M x of the collapsed object, being Z x < Lp < Z~, where J5 E ~ 1.38.103S(Mx/Mo) erg/s is the Eddington luminosity, and L x is the X-ray luminosity. I t is worth to notice that the UHE T-ray luminosity is, iu fact, proportional to the X-ray luminosity ill the three sources detected up to now, as predicted by the acceleration model.

Neutrino production by hadronie cascade in cosmic sources was computed by BEICETZINSKY and VOLI~SKY (2o), STE~GER (~1) and more recently by LEE and BLUDMAN (22) and GA/SSER and STANEV (23). All these computations are based on extremely idealized models of the matter distribution in the source. Therefore, their results cannot be applied to predict the emissivity of complex systems such as the X-ray binaries.

First of all the matter distribution in the model depicted in fig. 1 is extre- mely anisotropic. Therefore, whereas the T-rays are emitted only when the beam of particles hits the limb of the star, the neutrino are emitted mainly during the occultation of the pulsar. Hence the duration of the T-ray flashes will be approximately

Ho (1) ~, ~- P x - ~ ,

where P is the orbital period, H the scale height of the star's atmosphere and Ro its radius. Neutrino emission per orbit will last

P/i~o (2) v~ ,~ - - - ,

ae

where ao is the separation of the system. We can expect, therefore, that

(3) L~<< L~<s .'gy

assuming e> ~ e, ~ ~ as obtained from ref. (~1). Another important point is that the density of the external layers of the

companion star in the system is far from being uniform. In fact a high-energy

(2o) V.S. BERETZlNSKY and V.V. VOLINSKY: Proceedings o] the X V I International Cosmic Ray Con]erence, MN 6-5 (Kyoto, 1979), p. 326. (21) V . J . STENGER: Astrophys. J., 284, 810 (1984). (22) H. LEE and S.A. BLUDMAN: Ast~ophys. J., 290, 28 (1985). (23) T .K . GAISSER and T. STANEV: Phys. Rev. /~ett., 54, 2265 (1985).

HIGH-ENEItGY N ] g U T R I N O EI~IISSION FI~OM BINARY X - R A Y SOURCES ~

pro ton penetra tes deep inside the photosphere of the star. Hence the hadronie cascade develops in a medium with near ly exponent ia l densi ty distribution. This s i tuat ion is similar to the development of showers in the Ear th ' s atmos- phere.

Analyt ical solutions of the cascade equat ion in an exponent ia l a tmosphere are repor ted by DA~ (~4) for an input spectrum of protons

(4) tv, = K~ • E~ v

in the form

where E k is the cri t ical energy for pion re- interact ion before decay:

m,~eHo (6) Ek --

where m= and T= are the muss and l ifet ime of the charged pions, v the light veloci ty and Ho is the scale height of the stellar photosphere.

The scale height pa ramete r which enters in eq. (6) regulates the neutr ino emission at high energies. Therefore at high energies the spectral index of the neutr ino spectrum approaches ~ @ 1. The extension of the stellar atmos- phere is determined by the effective t empera tu re of the star and its surface gravi ty . Both this quanti t ies according to the stellar evolut ion theory (~5) are funct ion of the muss os the star. Hence we can predict t h a t the neutr ino spectrum to be expected from b inary system will depend on the mass of the companion star. B~AD~ and McCLIN~0C~ (~e) divide the b inary X- ray systems into two classes: i) the massive systems, which have a large-mass ear ly- type companion; ii) the low-mass systems including a la te- type companion. This classification is ex t remely re levant also from the point of view of the neutr ino spectrum. According to the above-referred considerations we aspect t h a t massive systems~ like Vcla X1 and L!VIC X4, will have a harder neutr ino spectrum t h a n a low-mass system like Cyg X3 (~7).

In thei r recent paper G~SSE~ and STONY (~8) have pointed out also t h a t high-energy neutr inos are adsorbed in the body of star, during the occultation. This effect introduces a t ime-modula ted high-energy cut-off in the neutr ino

(24) A. DA~: Phys. l~ev. Lett., 51, 227 (1983). (25) D.D. CLAYTON: Principles o/ Stellar Evolution and ~gueleosynthesis (l~IcGraw-Hfll, New York, N.Y., 1968). (36) H.V.D. BI~ADT an(1 J. E. ~CCLINTOCK: Anna. l~ev. Astron. Astrophys., 21, 13 (1983). (~) Very similar results are obtained by F.W. ST~CKER, A.K. HARmNG and J . J . B~tn~a~D: preprint GSFC (1985).

~ G. AURIEFI1RA, tI . B ILOKON and A. F. Gl t lLLO

spect rmn. Very roughly the cut-off energy in the t ime-ave raged neutr ino spec t rum will be

(7) Eo ~ lo M-~'

where R e and M are respec t ive ly the radius and the mass of the companion s ta r in solar uni ts .

I n conclusion we find t ha t the neut r ino spec t rum emi t t ed b y a b inary sy s t em is similar to the one ske tched in fig. 2. I n this spec t rum are present a b r eak due to the pion re in terac t ions and a cut-off due to the self-absorpt ion of neutr inos in the stellar interiors. The posi t ion of th is two spect ra l features depends on the mass of the companion star . In genera l we will expect t h a t the neut r ino spec t rum of a low-mass sys t em will be softer t h a n the one of a mas- sive system.

NNN~E~ I~(R21M)(T e V) Log E

Fig. 2. - Spectral distribution of neutrinos from binaries. The dashed line is the asso- ciated y-ray emission from G ~ decay.

I n tab le I we have repor ted the re levan t physica l p a r a m e t e r s for the three U H E binaries so fa r detected. We have indicated also the b r eak and cut-off energy es t imated f rom eqs. (6) and (7). F r o m the point of view of the to ta l neutr ino luminosi ty the effect of dens i ty is not re levant , bu t f rom the point of view of the detectabi l i ty , the effect of softening due to the densi ty of the eompaion s ta r could be catas t rophic . I n fact S~E~GER (2s) and GAISS]~ and STANEV (29) have shown t h a t undersea or underground detectors are sensit ive only to the ex t r eme end of the neut r ino spect rum, well above 10 TeV.

(2s) V.J . S'r]~NG]~R: preprint HD0-4-85 (April 1985). (2~) T .K. G x i s s ~ and T. STArChY: Phys. _Rev. D, 31, 2770 (1985).

HIGH-ENERGY Na~VT~INO ]~MlSSlOI~ FROM BINARY X-I~AY SOITRCIES

TABL~ I . - Physica~ parameter o/ U H E binaries.

457

Cyg X3 Vela X1 LMC X4

Distance 12 kpc 1.4 kpc 55 kpc Lx((2_~10) keV) ~ 10 as erg/s 6 X 10 s6 erg/s 4 X l0 ss erg/s Period 4.8 h 8.97 d 1.4 d spectral type ? B05 Ib 07 I I I -- V Mo 4 - - 10M e 20M e 17M o /~ 2R e 30R o 8.9R e a~/Ro 1.05 1.46 1.3 ~ r c ~ 107 cm 2 • l0 s cm 3 • l0 s cm ET~ 1.8 TeV 35 TeV 50 TeV E~ 5.6 TeV 450 TeV ~ 50 TeV ~/Ty (*) ~ 30 ~ 27 ~ 30

(*) T h e z'v/z" Y v a l u e i s d e d u c e d f r o m m e a s u r e d y p u l s e s h a p e a n d h a s t o b e c o n s i d e r e d a n u p p e r l i m i t .

G e n e r a l l y speaking , if t h e s a m e a c c e l e r a t i o n m e c h a n i s m is a t w o r k in a n y

X - r a y e m i t t i n g b i n a r y sys t em, we can e x p e c t ~ s t rong U H E y- rays a n d n e u t r i n o

emiss ion f r o m e x t r e m e l y close sy s t em, w i t h r a t i o Ro/ao close to u n i t y . A m o n g

t h e s e sy s t ems t h e m a s s i v e ones wh ich inc lude an e a r l y - t y p e c o m p a n i o n s t a r

h ~ v e a h ~ r d e r IneuCrino s p e c t r u m , b e i n g t h e cut-off e n e r g y p r o p o r t i o n a l t o

t h e r a t i o R ~ / M .

W e are g r a t e f u l t o V. CASTELLA~I, L. R0SSI, T. GAISSER und T. STA~-~V

for e x t r e m e l y he lp fu l discussion a n d sugges t ion .

@ R I A S S U N T 0

Recentemente ~ stata r ivelata emissione di raggi gamma con energia siao a 1018 eV da Cyg X3, Vela X1 ed LMC X4. Questa osservazione indica ehe protoni (o nuclei) sono aceelerati nella vieinanza della pulsar contenuta in questi tre sistemi binaxi. In questo lavoro si calcola la produzione di neutrini di alta energia, associata alla produzione di raggi gamma. I1 risultato ottenuto ~ che, tenendo conto dei parametri dedotti dalle osservazioni spettroscopiche dei tre sistemi considerati, il rapporto i ra la luminosita in neutrini e la luminosita gamma b L, /L v ~ 30. Inoltre il flusso di neu- trini sara modulato con il periodo binario del sistema e la curva di luce dei neutrini sara determinata dalla distribuzione di densita della stella compagna. In generale alcune delle binarie X possono essere sorgenti sin di gamma di altissima energia che di neu- trini, con una luminosita in neutrini paragonabile alla luminosita in raggi X. Le pifi intense i ra queste potranno essere osservate da futuri telescopi per neutrini come DUMAND o MACRO.

~ G. ALTI~I]~MMA, It. BILOKO~ ~tnd A. F. GI~ILLO

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(*) HepeeeOeno peOatcttueit.