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IN SEARCH OF ANTIMATTER IN THE UNIVERSE BY CHRIS HERRON It is believed that when the universe was forged during the Big Bang, equal amounts of matter, and its intrinsic opposite, antimatter, should have formed. But look around today. Matter surrounds us almost everywhere we could think to look. The whereabouts of this ‘missing’ antimatter is one of the great physical mysteries of modern science, demanding new and innovative methods of detection. The Standard Model of Particles What is Antimatter? In 1928, Paul Dirac predicted the existence of an ‘anti-electron’, a particle that had the same mass as an electron, but opposite charge; an antiparticle1. Today, under the Standard Model of particles (Figure 1), every particle has a corresponding antiparticle; protons have antiprotons, neutrons have antineutrons, and so on. Each antiparticle has the same mass, but opposite charge of the ‘normal’ particle. Perhaps the most mystifying feature of this relationship is the complete annihilation that occurs whenever a particle and its corresponding antiparticle collide. Figure 1: All fundamental particles have a corresponding antiparticle. In particular, the electron has the positron as its antiparticle. Particles known as baryons, such as protons and neutrons, are composed of quarks, and their antiparticles are composed of the corresponding anti-quarks. From: http://theta13.lbl.gov/neutrinos_universe/neutrinos _11.html (accessed 10/10/10) Credit: The Diablo Canyon Neutrino project. When annihilation occurs, no mass from either particle remains. This is to say, that the mass of both particles is converted to energy in the form of photons, and the amount of energy released can be determined by Einstein’s famous equation, E = mc2. Positronium and Hydrogen Positronium: Exotic Atom One form in which antimatter can be found is the short-lived atom known as Positronium. Similar to the Hydrogen atom, Positronium involves an electron orbiting a positively charged core; however in Positronium, Hydrogen’s proton has been replaced by a positron, the anti-electron2,3. (Figure 2) Because the electron and positron are so close together in Positronium, it is only a (very short) matter of time before they annihilate4. When para-Positronium annihilates, it releases two gamma ray photons that have a characteristic energy of 511 keV. One method of detecting Positronium is by detecting this emission, using Gamma ray telescopes such as INTEGRAL. Experiments observing this emission have shown that Positronium is forming and annihilating near the Sun, and at the centre of our own Milky Way galaxy.5,6 However, one limitation of Gamma ray telescopes is that they have poor resolution. This means that using this emission to search for Positronium only gives a rough idea of where it is; we can’t pinpoint its location. Figure 2: On the left is the Hydrogen atom, consisting of an electron and a proton, and on the right, is Positronium, consisting of an electron, and its antiparticle, the positron. Positronium comes in two forms, para- and ortho-Positronium, depending on the spin of the electron and positron. Para-Positronium has both spins anti-parallel (singlet state), whereas ortho-Positronium has both spins parallel (triplet state). Because of the number of ways these states can occur, the ortho- state outnumbers the para- state by 3:1. Ortho-Positronium is more stable than para-Positronium, generally living for 1.41 x 10-7s, whereas para-Positronium generally lives for 1.26 x 10-10s.4 http://www.stolaf.edu/academics/positron/intro. htm (accessed 2/10/10), property of the Positron Research Group at St Olaf College, Northfield, MN. One way of overcoming this barrier is to apply a form of emission that occurs in the Hydrogen atom, based on the Bohr model of the atom. In this model, when the electron transits between certain quantised energy levels, a photon is emitted with energy equal to the energy difference between the levels (Figure 3). This causes Hydrogen to have a characteristic series of emission lines at optical wavelengths, known as the Balmer series. Positronium has a similar series of unique emission lines, which lie near visible wavelengths of light. By detecting the Ps-alpha emission at 1.3µm, we can take advantage of the higher resolution of optical telescopes, and detect point sources of Positronium for the first time. Birthplaces of Positronium We aim to determine where Positronium is likely to form in the universe, and test whether its emission is bright enough to be detectable from Earth. Balmer Emission of Hydrogen As mentioned previously, Positronium has been detected near the Sun, and at the centre of the Milky Way, implying that Positronium forms in high energy environments. Other high energy environments where Positronium may form in our galaxy include supernovae, pulsars, Low Mass X-Ray binaries and micro-quasars, the weird and wonderful extremes of the universe. An extragalactic source of Positronium may include the jets of Active Galactic Nuclei (AGN) (See title, Figure 4,5) These colossal jets originate from the central super-massive black hole of the galaxy, flying through the galaxy around them at speeds close to the speed of light. It is possible that these jets contain electrons and positrons, meaning it is likely that Positronium will form somewhere along the jet. Figure 3: When an electron transits from a higher energy state to a lower energy state, as in the Bohr atom, a photon with the same energy as this difference is emitted. Positronium can undergo similar transitions. However, as its reduced mass is half that of the hydrogen atom, the wavelengths of the same transitions are double that of Hydrogen. This means that the H-alpha line (red in the picture) occurs at 1.3 µm for Positronium, and this is known as the Ps-alpha line. http://outreach.atnf.csiro.au/education/senior/as trophysics/spectroscopyhow.html, (accessed 3/10/10). Credit: HyperPhysics, and CSIRO Australia Figure 4: The jet of M87 is shown at visible wavelengths to stretch into the Active Galactic Nucleus at the centre of the galaxy. http://fermi.gsfc.nasa.gov/public/science/agn. jpg (accessed 12/10/10). Credit: NASA, HST The high velocity of the jet means that the constituent particles are at high energies, higher than the ionisation energy (energy required to remove an electron) of Positronium. This means that even if a positron and electron are close enough to form Positronium, they will not bind together4. On the other hand, if a jet were to collide with a star, the remnant of a star (such as a Planetary nebula or a supernova remnant), or a molecular cloud, then the particles in the jet would collide with the particles of the body, and slow down. Once a particle has undergone enough collisions, and has less energy than the ionisation energy, then it can combine to form Positronium. As the time required for thermalisation is relatively small, we can assume that thermalisation occurs instantaneously.4,7 Spiral galaxies do not often feature AGN, and so instead, we consider elliptical galaxies, which have stars evenly distributed throughout the volume of an ellipse. One such galaxy is Centaurus A, which is the closest galaxy to us with an AGN jet, at 3.7 Mega parsecs (1 parsec is 3.1x1016 m). This means its jet can be studied in greater detail than is possible in more remote sources. (Figure 5). This has allowed ‘knots’ in the jet to be resolved in x-ray and radio wavelengths (Figure 6). The cause of these knots has remained unknown for many years, although recent evidence suggests that they may be caused by collisions of the jet with stars, or other large gaseous objects, and thus they may be sites of Positronium formation.8,9 Figure 5: This is a composite image of Centaurus A, using visible, x-ray and submillimetre wavelengths. The streamer of gas coming out of the centre is the jet of the galaxy, which remains well structured until eventually dispersing into a plume of gas. The jets of these Active Galactic Nuclei can erupt into enormous lobes of gas larger than the galaxy itself! http://chandra.harvard.edu/photo/2009/cena/ , accessed 1/10/10 Credit: X-ray: NASA/CXC/CfA/R.Kraft et al.; Submillimeter: MPIfR/ESO/APEX/A.Weiss et al.; Optical: ESO/WFI. Probability of Collision To determine the chance that a jet does hit a star, we need to know how the stars are distributed throughout the galaxy. By observing galaxies, we can see that the intensity of light emitted by the galaxy decreases with radius, and as we would expect, the brighter a region is, the more stars are in that region, and hence more mass. This fact can be used to determine an expression for how the mass density of the galaxy varies with radius. (See Equation 1, Figure 7) 10 In order to convert this mass density to a stellar density (number of stars per unit volume), we need to divide the mass density by the average mass of a star. This can be calculated to be 0.35 times the mass of the sun,11,12 allowing us to graph how the stellar density changes across an elliptical galaxy, and hence how the number of stars varies. As seen in the graphs (Figures 8,9), stellar density decreases with radius, and the number of stars reaches a maximum relatively close to the centre of the galaxy. The total number of stars calculated from the graph is 8.4 x 1011, similar to that observed in most galaxies, so our model of the galaxy is realistic. It is also important to consider what the average size of a star is. By looking at what percentage of main sequence stars have a certain mass, and weighting this by the radius of a star of that mass, we can determine the average cross-sectional area of a star. To make this more comprehensive, we also include the size of Planetary Nebulae, supernova remnants and Asymptotic Giant Branch stars, weighted by how common these are in a galaxy, and what length of time they remain in a condensed form. This gives an average area of 6 x 10-6 square parsecs. The final quantity to consider is the area of the jet itself. If we assume a conical expansion of the jet, then it is possible to relate the cross-sectional area of the jet to the angle formed at the base of the jet. (Equation 2). Combining these quantities allows us to determine the number of stars that the jet will collide with at a given radius. This is simply calculated by finding the volume of the jet at this radius, and multiplying by the density of stars. (Equation 3) Summing the values for the probability of hitting a star at a given radius gives a total probability of 1.6 x 1011%, corresponding to 1.6x109 stars being hit. (Figure 10) So we expect the AGN jet to collide with very many stars as it moves through the galaxy. Impacting Positrons and the Formation of Positronium In order to determine how many Positrons are colliding with a star per second, we first consider the positron flux (number of positrons passing a given area per second) of an AGN jet. If we assume that all of the positrons that are initially injected into the jet remain in the jet along its length (a reasonable assumption as the annihilation of positrons and electrons in the jet is quite small)4,7 then the positron flux in the jet is approximately constant. (Equation 4) When the jet hits a star, the ratio of the area of the star to the area of the jet shows what fraction of the positrons in the jet will thermalise by collision. This allows us to calculate the positron flux that would occur if the jet hits a star at a certain radius, and thus the rate of Positronium formation. The number of Positronium atoms that are formed on collision is proportional to the number of positrons incident on the surface of the star. It turns out that the proportionality constant depends on the temperature of the medium in which the positrons thermalise, and if we take T = 106 K (a high enough temperature to allow thermal X-ray emission), then this proportionality constant is 41%. This allows us to plot the rate of Positronium formation if the jet hits a star at a certain distance (Figure 11). As expected, this decreases with distance, as the incident flux of positrons decreases with distance. 4 Figure 6: A 0.8 – 3 keV unsmoothed image of the Centaurus A jet at X-ray wavelengths using the Chandra X-ray observatory. Each bright spot represents a ‘knot’. From Worrall et al 2008, ApJ, 673, L135. Equations and Results Equation 1: This equation is for the mass density in solar masses, derived from the brightness profile of a galaxy.10 Here, r is the distance from the centre of the galaxy, Re is the effective radius of the galaxy (both in parsecs), b and p are parameters that depend on the Sersic index, n, of the galaxy, M/L is the mass to luminosity ratio of the galaxy in terms of the solar M/L, and I0 is the central intensity in solar L pc-2. Figure 7: Mass density (solar masses per cubic parsec) of a theoretical elliptical galaxy as a function of distance from the galactic centre. The total mass is 3x1011 solar masses. Figure 8: Stellar density (stars per cubic parsec) as a function of distance from the galactic centre. The average density is 0.002 stars per cubic parsec. Figure 9: Number of stars in the galaxy as a function of distance from the galactic centre. There is a clear maximum at about 500 parsecs. The total number of stars is 8.4x1011, close to the expected number for Centaurus A. This graph is formed by calculating the number of stars in a shell of width 5 parsecs, in 5 parsec intervals from the centre of the galaxy. A = πr2 = π(rb + R tanθ)2 Equation 2: Cross-sectional area of the jet at distance R parsecs from the centre of the galaxy. rb is the radius of the base of the jet in parsecs, and θ is the half angle of the jet, in degrees. N = A η ΔR Equation 3: Number of stars hit at a certain radius from the galactic centre. A is the crosssectional area of the jet in square parsecs, η is the star density in stars per cubic parsec, and ΔR is the increment in radius, taken to be 5 parsecs. Figure 10: Number of stars hit by the jet as a function of distance from the galactic centre. There is a clear maximum at 500 parsecs, where most of the stars are. The total number of stars hit is 1.6x109. F(e+) = π R02 ρ v f Equation 4: Formula for the positron flux of the jet. R0 is the initial radius of the jet, ρ is the particle density of the jet (particles per cubic parsec), v is the velocity of the jet (parsecs per second) and f is the fraction of particles that are positrons.13 Figure 11: The rate of Positronium formation as a function of distance from the galactic centre if the jet hits an average sized star, and thermalises at 106 K. Equation 5: Formula for the flux of observed photons emitted by Positronium. r is the positron flux, fPs is the fraction of positrons that form Positronium, α, β are parameters regarding the emission line observed, DL is the distance to the source in metres, A is the absorption coefficient, Δλ is the width of the emission line. 4 Figure 12: The observed brightness of the Positronium Ps-alpha line if the jet collided with the gas shell left by a supernova remnant, of cross-sectional area 20 square parsecs. This requires a slightly wider jet, and a large increase in the density of positrons at the gas-jet interface due to shock formation as the jet ploughs into the gas, compared to the jet hitting an ‘average star’. The emission should just be visible out to 600 pc for a galaxy at 3.7 Mpc, if these requirements are met. Positronium Emission Once the rate at which Positronium forms has been determined, we can finally determine how bright the Ps-alpha emission would appear from Earth, using Equation 5. If we consider a galaxy as far away from us as Centaurus A, then we obtain a graph similar to Figure 12 for our theoretical galaxy. The brightness of the emission line decreases with distance, as we would expect, based on the decrease in positron flux. Unfortunately, we see that the peak brightness is 3x10-10 photons s-1 m-2 µm-1. This means that if we had a telescope with an area of 1 m2, then it would collect 1 photon every 100 years. Obviously, this will not be visible. But this is the brightness we would expect if the jet hits the ‘average star’. If we instead consider a much larger object, such as the gas shell of a supernova, then we obtain Figure 12. In this case, the emission line is just visible up to 600 parsecs, after which the brightness drops below 0.1 photons s-1m-2, and the emission line will be hard to distinguish from background noise. Considering future optical telescopes that may be 25m in diameter, this corresponds to 150 photons s-1. Conclusion We have found that the jets of Active Galactic Nuclei will collide with very many stars in elliptical galaxies, and thus are a potential source of Positronium formation. Centaurus A, being the closest galaxy with an AGN, is likely the best galaxy in which to search for the Ps-alpha emission of Positronium, as the brightness of the emission decreases strongly with distance. Furthermore, if the knots in the Centaurus A jet (Figure 6) are due to jet-gas collisions, then these may provide a bright source of Ps-alpha emission, particularly as they are estimated to have a radius of 0.5-2.5 pc.8 On calculating the number of stars in the Centaurus A jet, the number of planetary nebulae and supernovae should be about 15, comparable to the number of knots in the jet. As we have also found that objects with radii close to 2.5 pc may be bright enough sources of Positronium alpha emission to be visible from Earth, we conclude that likely visible sources of Ps-alpha emission are the larger knots in the Centaurus A jet, found closer to the centre of the galaxy. If this emission is detected from these knots, then it will be the first time antimatter has been detected outside our own galaxy, and it will provide strong evidence for the mechanism responsible for the formation of knots in AGN jets. Acknowledgements Thank you to Dr Simon Ellis and Prof Joss Bland-Hawthorn for their guidance and thorough help in this project. Thanks also to Prof Dick Hunstead and Dr Michael Biercuk for directing and managing the Physics TSP, and insightful feedback. Title picture from http://www.dailygalaxy.com/photos/uncategori zed/2007/07/30/supermassive_black_holejpg_ 1_2.jpg (accessed 10/10/10). Credit: The Daily Galaxy and Casey Kazan. References 1. http://en.wikipedia.org/wiki/Antimatter (Accessed 2/10/10) 2. http://en.wikipedia.org/wiki/Positronium (Accessed 2/10/10) 3. http://www.stolaf.edu/academics/positron/ intro.htm (Accessed 2/10/10, Positron Research Group, St Olaf College) 4. Ellis. S. C., Bland-Hawthorn. J. 2009, The Astrophysical Journal, Vol 707, Issue 1, pg 457 5. Bandyopadhyay. R.M., Silk. J., Taylor. J.E., Maccarone. T.J., 2009, Monthly Notices of the Royal Astronomical Society, 392, pg 1115 6. Weidenspointner. G., Skinner. G., Jean. P., Knodlseder. J., von Ballmoos. P., Bignami. G., Diehl. R., Strong. A.W., Cordier. B., Schanne. S. Winkler. C., 2008, Nature, Vol 451, pg 159 7. Furlanetto. S.R., Loeb. A, 2002, The Astrophysical Journal, 572, pg 796 8. Goodger. J.L., Hardcastle. M.J., Croston. J.H., Kraft. R.P., Birkinshaw. M., Evans. D.A., Jordan. A., Nulsen. P.E.J., Sivakoff. G.R., Worrall. D.M., Brassington. N.J., Forman. W.R., Gilfanov. M., Jones. C., Murray. S.S., Raychaudhury. S., Sarazin. C.L., Voss. R., Woodley. K.A., 2010, The Astrophysical Journal, Volume 708, Issue 1, pg 675. 9. Kraft. R. P., Forman. W. R., Hardcastle. M. J., Birkinshaw. M., Croston. J. H., Jones. C., Nulsen. P. E., Worrall. D. M., Murray. S. S., 2009, The Astrophysical Journal, Volume 698, Issue 2, pg 2036. 10. Terzic. B., Graham. A.W., 2005, Monthly Notices of the Royal Astronomical Society, Volume 362, Issue 2, pg 197 11. Bland-Hawthorn. J., Karlsson. T., Sharma. S., Krumholz. M., Silk. J., 2010, The Astrophysical Journal, Volume 721, Issue 1, pg 582. 12. Chabrier. G., 2005, Astrophysics and Space Science Library, Volume 327, Springer/Dordrecht, pg 41 13. Marscher. A.P., Jorstad. S.G., Gomez. J.L., McHardy. I.M., Krichbaum. T.P., Agudo.I., 2007, The Astrophysical Journal, 665, pg 232