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Gamma Ray Emissions from Binary Pulsar Systems Tony A Journal of the Arkansas Academy of Science Volume 48 Article 14 1994 Gamma Ray Emissions from Binary Pulsar Systems Tony A. Hall Arkansas State University Andrew T. Sustich Arkansas State University Follow this and additional works at: http://scholarworks.uark.edu/jaas Part of the Electromagnetics and Photonics Commons Recommended Citation Hall, Tony A. and Sustich, Andrew T. (1994) "Gamma Ray Emissions from Binary Pulsar Systems," Journal of the Arkansas Academy of Science: Vol. 48 , Article 14. Available at: http://scholarworks.uark.edu/jaas/vol48/iss1/14 This article is available for use under the Creative Commons license: Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0). Users are able to read, download, copy, print, distribute, search, link to the full texts of these articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the author. This Article is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Journal of the Arkansas Academy of Science by an authorized editor of ScholarWorks@UARK. For more information, please contact [email protected], [email protected]. Journal of the Arkansas Academy of Science, Vol. 48 [1994], Art. 14 Gamma Ray Emissions From Binary Pulsar Systems Tony A.Halland Andrew T.Sustich Arkansas State University Department ofPhysics State University, AR 72467 Abstract Amethod is developed for estimating the gamma ray flux impinging upon the earth from production inbinary pulsar systems. We calculate production of the 6.13 MeV gamma ray line characteristic of 16O. These are produced by protons emitted by the pulsar interacting with 16O atoms at the surface of the companion. We examine different types of compan- ion stars and estimate the gamma ray fluxat the earth as a function of proton emission from the pulsar and distance from the earth. Prospects for detection from earth are discussed. Introduction willexcite an 16O nucleus to the appropriate excitation level is given by A binary star system consists of two gravitationally stars, bound orbiting a common center of mass. A pulsar dP(x)-a(E' p)na(x)dx is a rapidly rotating neutron star, which, due to its intense magnetic field,emits a wide energy spectrum of charged where a (E'p) is the production cross section for the particles and electromagnetic waves into narrow cones gamma ray line inquestion and na (x) is the number den- about each of its magnetic poles. Inbinary pulsar systems sity of target nuclei (16O). in which at least one of the stars is a pulsar, protons emit- In most laboratory experiments, the target number ted from the pulsar can strike the surface of the compan- density na is constant, and the target is so thin that the ion star, where they interact to produce nuclear excita- proton does not lose any appreciable amount of energy tions (see Zeilik et al., 1992). Gamma rays are emitted in in traversing the target. In this case, an integration over the de-excitation process, and theses gamma rays travel the thickness / of the target yields the thin-target approxi- outward from the system until they may ultimately be mation for the probability of interaction (and production detected at the earth. of a gamma ray), In spectra from solar flare bursts, the most prominent 12 = gamma ray lines are the 4.43 MeV line from C followed P(E'p) G(E'p)na t. (3) by the 6.13 MeV line from 16O (Chupp et al., 1984). Since others have already focused on the 4.43 MeV line from In our situation, the protons continually lose energy as 12C inprevious solar flare work (Lang et al., 1987; Werntz they penetrate into the companion star and we must et al., 1990), we study the 6.13 MeV line from in this employ a thick-target approximation. The probability of article. interaction ina thickness dx at a distance x into the com- panion is = Model and Methods dP(x) <j(Ep(x,E'p))na(x)dx, (4) Gamma rays are produced when a proton scatters where E(p) is the energy of the proton of initial energy inelastically off a target 16O nucleus. The 16O nucleus is E'p after traversing the distance x. We change to an inte- left in an excited state and emits a gamma ray upon de- gration over initial proton energy excitation, 1 p+ 16(9 ¦*/>'+ 160* P^T (5) -> < 160* 160+ y(6.13 MeV). (1) where dE'p /dx 0 is the stopping power of the target material. The probability that a proton of energy E'p,in traversing As the gamma rays are produced at increasing depth a thickness dx of the target at distance x into the target, into the companion star, their probability of escaping out Proceedings Arkansas Academy of Science, Vol.48, 1994 67 Published by Arkansas Academy of Science, 1994 67 Journal of the Arkansas Academy of Science, Vol. 48 [1994], Art. 14 of the companion material decreases exponentially. As a power data has been provided to us (Lang, 1993). The first approximation, we assume that all gammas produced cross section peaks in the 10-15 MeV range and falls slow- within one attenuation length of the companion surface ly with energy (See Fig. 1). The energy loss over one escape with 100% probability, and all those produced fur- attenuation length is obtained from the stopping power ther in than one attenuation length are completely absorbed before escaping. Hence, for a given proton energy we allow itto lose up to the energy loss at one (ID E'p, Uc_ attenuation length A(E'p). Beyond that point, the proton Jo cannot produce a gamma which willescape. Our gamma ray production probability is then where the attenuation length xy is obtained by assuming a purely hydrogen composition for the companion (Zombeck, 1990). (6) JE'p The dependence on target density na is really artificial here. We assume the target density to be given by the nuclear number density times a typical 16O stellar abun- dance. The stopping power dEp/dx is also proportional to the nuclear number density, so that our result is indepen- dent of the density of the companion. This production probability is then folded with the proton spectrum Np(E'p) from the pulsar which strikes the companion star to obtain the number of gamma rays per second pro- duced, + "' = e'p W'p> o(E ) , (7) NY f ~dE'pNp(E'p)f dEp p na = where Et 6.52 MeV is the threshold energy for produc- tion of the 6.13 MeV gamma ray. The proton spectrum is Fig. 1. Cross section for production of 6.13 MeV gamma assumed to obey a power law and is normalized toNp pro- rays by protons on 16O. tons per second, (8) Np(E'p)=NpNp(E'p)=Np K(E'p)">, Results and Discussion The resulting integral is integrated numerically to so that normalization constant Kis determined from obtain the number of gamma rays per second produced. We take the power factor for the proton spectrum to be a = 2. Aproton influx of A^= lO41/sec is taken as a baseline. j-iEr,fiw-i. (9) This is an upper limit estimate for the Crab Pulsar based on the luminosity of the surrounding nebula (Zombeck, 1990). Byinverting the order of integration and performing one The gamma ray production per unit energy of the integral analytically, we obtain incoming protons [the integrand ofequation (10)], = NffliEp^l^aiEl^'nEpr^iEp^E^r^ (10) Np(E'p)P(E'p) , (12) JEt '(EJl* Lrfx J I J dEp Data for the gamma production cross section are com- shows a peak behavior similar to the gamma ray produc- piled from the literature (Dyer et al., 1981; Lang et al., tion cross section and 90% of the gamma rays are due to 1987; Lesko et al., 1988). An analytic fit to stopping Proceedings Arkansas Academy of Science, Vol.48, 1994 68 http://scholarworks.uark.edu/jaas/vol48/iss1/14 68 Journal of the Arkansas Academy of Science, Vol. 48 [1994], Art. 14 < protons with energies E'p 50 MeV (See Fig. 2). Conclusions We have found the flux of 6.13 MeV gamma rays to be about two orders of magnitude smaller than an estimated background signal. This is probably an order of magni- tude below detection threshold. However, more effort needs to be devoted to investigating the proton flux and energy spectrum from pulsars and the calculation of the background signal before their detection is ruled out. Acknowledgements The authors are indebted to Dr. Carl Werntz and Dr. Fred Lang for introducting them to this problem and for much useful discussion regarding its solution. The hospi- tality of Dr. Carol Jo Crannell and the Solar Physics Branch of NASA-Goddard Space Flight Center during vis- its to NASA-Goddard is gratefully acknowledged. This Fig. 2. Production rate of 6.13 MeV gamma rays as a work has been supported by NASA grant NAG8-277, function of energy ofincoming protons from the pulsar. Arkansas Space Grant Consortium grant NL-3013S, SILO Undergraduate Research Fellowship, and NASA-Goddard Space Flight Center NSF-REU Program. The gamma ray flux at the Earth is obtained by divid- ing the gamma ray production rate by 47rrf2 where dis the distance to the pulsar. Using 1000 light-years as the dis- Literature Cited tance to the nearest pulsar we obtain Chupp, EX.,DJ. Forrest, P.R. Higbie, A.N.Suri, C. = 8 2 1 <))6.13y 2.4 x 10- (cm sec)- (13) Tsai and P.P.
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