The Search for Celestial Positronium via the Recombination Spectrum
aa r X i v : . [ a s t r o - ph . H E ] O c t The Search for Celestial Positronium via the Recombination Spectrum
S. C. Ellis and J. Bland-Hawthorn
Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006,[email protected], [email protected]
ABSTRACT
Positronium is the short-lived atom consisting of a bound electron-positron pair. Inthe triplet state, when the spins of both particles are parallel, radiative recombinationlines will be emitted prior to annihilation. The existence of celestial positronium isrevealed through gamma-ray observations of its annihilation products. These observa-tions however have intrinsically low angular resolution. In this paper we examine theprospects for detecting the positronium recombination spectrum. Such observationshave the potential to reveal discrete sources of e + for the first time and will allow theacuity of optical telescopes and instrumentation to be applied to observations of highenergy phenomena.We review the theory of the positronium recombination spectrum and provide for-mulæ to calculate expected line strengths from the e + production rate and for differ-ent conditions in the interstellar medium. We estimate the positronium emission linestrengths for several classes of Galactic and extragalactic sources. These are comparedto current observational limits and to current and future sensitivities of optical andinfrared instrumentation. We find that observations of the Ps α line should soon bepossible due to recent advances in near-infrared spectroscopy. Subject headings: elementary particles – line: formation – line: identification
1. INTRODUCTION
Positronium (Ps) is the short-lived atom consisting of a bound electron-positron pair. Its exis-tence was predicted by Mohoroviˇci´c (1934) shortly after the discovery of the positron by Anderson(1933). Furthermore, Mohoroviˇci´c (1934) suggested that Ps should be observable by its recombina-tion spectrum and discussed its properties. Ps was first observed by Deutsch (1951) in a laboratoryexperiment designed to measure the lifetimes of positrons in gases.Ps is unstable and annihilates into two or more photons with a combined energy of 1022 keV,i.e. the rest mass of the atom (see § §
2, under certain conditions Psis stable for long enough that electronic transitions can occur between the quantum states of thesystem, giving rise to a recombination spectrum. Since the reduced mass of Ps is half that of H, 2 –the wavelengths are twice those of the corresponding H series. For example, Ps Lyman α (Ps Ly α )has a wavelength of 2431˚A and Ps Balmer α (Ps α ) has a wavelength of 1.313 µ m.Ps Ly α was first observed in laboratory experiments by Canter et al. (1975). So far, however,no detections have been made of recombination lines from celestial Ps. Nevertheless the existence ofcelestial Ps is inferred from observations of the 511keV annihilation line and continuum annihilationradiation seen both from the Sun (Chupp et al. 1973) and from the Galactic centre (Leventhal et al.1978), combined with the fact that in most astrophysical environments e + are expected to formPs before annihilation (cf. § ∼ ◦ ) of γ -ray satellites. The formation of Ps, however, providesa natural heterodyne process that converts the γ -ray energies associated with the production of e − - e + pairs, to the optical/ near-infrared energies of Ps recombination. Thus observation of Psrecombination lines would allow the superior spatial and spectral resolution of optical/ near-infraredtechnologies to be applied to high energy astrophysical phenomena.As a specific example, Ps observations could provide an important physical understanding ofjets. It is still uncertain whether high energy radio jets consist of an e − -p plasma or e − - e + orsome combination of both. Most attempts to answer this question have had to rely on indirectmethods of searching for the presence of e + , such as arguments based on the total energy budget ofthe jets (e.g. Celotti & Fabian 1993; Reynolds et al. 1996; Wardle et al. 1998; Hirotani 2005), withinconclusive results. Direct searches for the 511keV annihilation signature in jets (Marscher et al.2007) have likewise failed to provide conclusive results due to the poor point source sensitivity of γ -ray telescopes. If the positrons from the jet thermalise when the jet impacts the surroundingmedium allowing the formation of Ps, and if the acuity of optical observations can be brought to bearon this problem to allow a successful detection of Ps recombination lines, this would have significantimplications for our understanding of the physical processes responsible for the production of jets– processes which take place deep within the AGN (Blandford & Levinson 1995).The origin of the positrons responsible for the annihilation radiation observed from the Galacticcentre is uncertain. The current state-of-the-art observations are from the ESA’s INTEGRAL γ -ray observatory, which has detected extended Ps annihilation radiation centred on the Galacticcentre with a FWHM of ≈ ◦ (Kn¨odlseder et al. 2005; Weidenspointner et al. 2008a). The resultsare most consistent with a source of e + originating from old stellar populations such as type Iasupernovæ, classical novæ, and low mass X-ray binaries, although more exotic sources, such as darkmatter annihilation, cannot be ruled out. The angular resolution of INTEGRAL SPI is ∼ ◦ , andis therefore rather insensitive to the detection of point sources. The detection of Ps recombinationlines would allow discrete point sources of e + to be searched for on sub-arcsecond scales (see § e + production of specific sources for the first time. 3 –Despite the benefits of detecting Ps recombination lines there have been very few attempts todo so, and there has been little work on the expected astrophysical signatures. McClintock (1984)reviews the possibility of the optical detection of Ps, in particular the Ps Ly α line. The conclusionreached is that a visual extinction of 1 or 2 magnitudes is enough to make the Balmer and Paschenlines more intense than the intrinsically more luminous Lyman lines. Since most previous studieshave focussed on the Galactic centre as the most promising source of Ps recombination line emission(so far the only source other than the Sun in which Ps annihilation has been observed) and that atthe Galactic centre the visual extinction is very high, it is not surprising that this idea has remainedlargely forgotten. Burdyuzha & Kauts (1997) raised the possibility of optical/ IR detection of Psagain, and made predictions of the expected fluxes of the most important lines. However, theonly published attempt to detect Ps recombination lines was made by Puxley & Skinner (1996)who searched for Ps Paschen- β from the Galactic centre in the K band, and whose non-detectionprovides the only direct experimental constraints on the emission.Until recently, the prospect of a near-infrared (NIR) detection of the Balmer series of Ps wasrather bleak due to the relative insensitivity of NIR detectors and the strong foreground emissionfrom the atmosphere. However, we argue that the time is now right for a reappraisal of thisimportant window into the high energy universe. This renewed interest is motivated by severalrecent and imminent advances in technology. NIR detectors have improved remarkably and arenow capable of dark currents as low as 1 e − per 1000 s, and read noises of ≈ e − (Smith et al. 2006).Adaptive optics at NIR wavelengths can now deliver high Strehl ratios improving the signal tonoise for faint sources. The future generation of ELTs will deliver AO corrected images of fieldsof view of tens of arcminutes with huge gains in sensitivity from the vast collecting areas. TheJWST will provide unprecedented sensitivity at NIR wavelengths (Gardner et al. 2006). Recentbreakthroughs in photonic technologies promise superb background suppression in the NIR in thenear future (Bland-Hawthorn et al. 2004; Ellis & Bland-Hawthorn 2008).The purpose of this paper is to assess the probability of detecting Ps recombination spectra inlight of these advances and to identify the most fruitful strategies and targets for an observationalcampaign. We collect together sources from a broad literature published over many decades andcombine these to calculate the expected astrophysical signatures of Ps. The next section reviewsthe pertinent physical properties of Ps. We then discuss possible sources of Ps recombinationline emission, both Galactic and extragalactic, including predictions on the strengths of thesesources. Section 4 then assesses the prospects of detection and observational strategies. Finally wesummarise our findings in section 5. 4 –
2. PHYSICS OF THE POSITRONIUM RECOMBINATION SPECTRUM2.1. Formation of Ps
The fate of positrons in astrophysical environments depends on their energy and the ionisationfraction of the surrounding medium. Positrons are formed in highly energetic processes ( ≥ e − - e + pair), and initially may be highly relativistic. In order that Ps may beformed the e + must first lose energy. We consider two stages in the formation of Ps, the in-flightphase during which the positrons are losing energy, and the thermalised phase, during which the e + are in thermal equilibrium with the surrounding medium. Positrons can lose energy via collisions with electrons or by excitation and ionisation of atomsand molecules. During this energy loss phase, once the e + has an energy of less than a few tens of eV,Ps can be formed via charge transfer with H, H or He. Guessoum et al. (2005) and Bussard et al.(1979) show that the fraction of e + forming Ps in flight is a strong function of the ionisation fractionof the medium. In a completely neutral medium consisting of atomic H, approximately 95 per centof e + form Ps (via charge exchange). If the same medium were 50 per cent ionised, less than 10per cent of e + would form Ps (Guessoum et al. 2005). If the medium is collisionally ionised, thenthe ionisation fraction depends on the temperature and density of the gas. However, McClintock(1984) notes that in most cases of e + generation from an astrophysical source (e.g. supernovæ,microquasars, etc.), a radiative source capable of photoionising the surrounding medium will beinvolved. In this case the ionisation fraction of the medium close to the source is of order unityand independent of gas temperature. Consequently, almost all e + will survive the in-flight phaseand will eventually thermalise with the surrounding medium. Once thermalised, e + may form Ps via radiative recombination or via charge exchange. Therelative efficiencies of these processes are highly dependent on temperature (Bussard et al. 1979;McClintock 1984; Guessoum et al. 2005). For a collisionally ionised gas, Ps formation by radiativerecombination with free electrons dominates charge exchange at T ∼ < K (Guessoum et al. 2005).However, for a photoionised gas radiative recombination is dominant at all temperatures < K(McClintock 1984).It is possible for e + to annihilate directly with either free or bound e − without first formingPs. Direct annihilation with free e − has a cross section that is an order of magnitude lower thanradiative recombination for T < K (Guessoum et al. 2005). Direct annihilation with bound e − can only take place at low temperatures ( ∼ < K; Guessoum et al. 2005). Therefore for most 5 –astrophysical environments ( ∼ –10 K) Ps formation will be the dominant process leading toannihilation.
Ps can form when a e + is captured by a dust grain. Dust grains have a much larger cross-sectionthan the competing effects of recombination or charge-exchange and hence can play a significantrole in the formation of Ps. The effects of Ps formation in dust was first discussed by Zurek (1985)and the most recent treatment is given by Guessoum et al. (2005). We summarise the relevantfindings here.Guessoum et al. (2005) give four possible reactions between e + and dust grains, e + re-emission, e + backscattering, Ps formation in the grain, Ps ejection. Ps formed in the grain always annihilatesvia para-Ps (see § § e + capture. In the warm ionised ( ∼ ∼ K) phases of the ISM dust is thoughtto be negatively charged and e + capture can become significant. The reaction rate for radiativerecombination, direct annihilation and capture by dust grains are given by Guessoum et al. (2005)as 1 . × − , 1 . × − and 4 . × − cm s − respectively for the warm ionised medium,and 1 . × − , 1 . × − and 2 . × − cm s − for the hot medium. Thus in the warmphases recombination is dominant but in the hot phases dust process are the dominant form of Psformation.We also wish to know the relative rates of the reactions that will generate recombination lines,and this requires annihilation via ortho-Ps ( § ∼
10 per cent of Ps formed in dust will be ejected before annihilation. Taking this factor and the3:1 ortho:para ratio into account gives reaction rates in the hot phase of the ISM of 9 . × − and1 . × − cm s − for the formation of ortho-Ps via radiative recombination and dust capturerespectively. Ps is unstable and will eventually annihilate. The process of annihilation is governed bythe principle of invariance under charge conjugation (Yang 1950; Wolfenstein & Ravenhall 1952;Berko & Pendleton 1980) and the mechansim depends on the total spin of the atom (see e.g. 6 –Debenedetti & Corben 1954). Para-Ps annihilates into an even number of photons, with the mostlikely decay into two photons, whereas ortho-Ps annihilates into an odd number of photons with themost likely decay being into three photons. Furthermore conservation of energy and momentumrequires that para-Ps decays into two photons of equal energy, giving rise to the 511keV emissionline, whereas the energies of the three ortho-Ps annihilation photons can be any three energiesthat add to 1022keV, giving rise to a continuum of γ -ray photons < . × − s and ortho-Ps a lifetime of 1 . × − s (e.g. Berko & Pendleton 1980).The lifetimes of excited states are longer by a factor n (Wheeler 1946). Since para-Ps is a singletstate and ortho-Ps is a triplet state the relative weights of ortho-Ps to para-Ps are 3:1. Ps has a reduced mass of m e /
2, so the energy levels of Ps are almost exactly half those ofhydrogen, which has a reduced mass ≈ m e . Correspondingly, the wavelengths of the recombinationspectrum are twice those of hydrogen. This has been confirmed through laboratory observations ofthe Ps Ly α line at 2431˚A by Canter et al. (1975).Similarly, the radiative lifetimes are twice those of hydrogen. We have calculated the radiativelifetimes of Ps using the atomic hydrogen transition probabilities listed by Wiese et al. (1966). Weuse the ‘average’ values tables which are most applicable to astrophysical situations if it is assumedthat all atomic sub-states are occupied according their statistical weights. In Table 1 we showthe radiative and annihilation lifetimes for states n = 1–6 and l = 0 (the annihilation lifetimesare almost entirely independent of l ), and the ratios of these quantities. The ratio of annihilationlifetime to radiative lifetime ( T /τ ) gives the approximate number of photons that could be emittedfrom that state before decay. For triplet Ps all states could emit more than one photon (significantlymore for the lower energy states) before decay. Thus most triplet Ps annihilates from its groundstate. Singlet Ps would decay before any radiation is emitted. We note however that in mostcases Ps will form via case-A recombination and therefore after radiative recombination down tothe n = 1 level (perhaps via multiple transitions), we do not expect any re-excitation followedby further re-radiation, since this would require the presence of other Ps atoms nearby, which isunlikely in most cases. We also note that the probability of spin-flip before radiative transition isvery small ; the Einstein A coefficient for spontaneous spin-flip, A = 3 . × − s − . Collisionallyinduced spin-flip is highly unlikely as the lifetime of Ps is so short ( § see Burdyuzha, Durouchoux & Kauts 1999, http://jp.arxiv.org/abs/astro-ph/9912550 α emission resulting from electron capturethrough interaction of a positron with H or He.For a given source producing r positrons per second, the flux of Ps radiative emission in photonss − m − µ m − would be, f λ = rf Ps αβ × πD × . A × λ , (1)where f Ps is the fraction of e + which form Ps after thermalisation, the factor 3/4 is the fraction ofPs in the triplet state, α is the number of emitted Ps Ly α photons for each Ps atom, β is the ratioof the intensity of Ps Ly α to the line in question, D L is the luminosity distance of the source, thefactor 1 / . A accounts for an absorption coefficient of A , and ∆ λ is the line width in microns.We note an important point: γ -ray observations of the 511keV line are observing the anni-hilation of para-Ps, whereas observations of the radiative recombination spectrum are observingortho-Ps. Since the relative weights of para-Ps to ortho-Ps are 1:3 (singlet vs. triplet states), butthere are 2 × f λ ) can be related to the γ -ray line flux ( f photons s − m − ) by, f λ = f × × αβ × . A × λ , (2)The line width is given by Wallyn et al. (1996) as∆ λ = λ × . × − (cid:18) T K (cid:19) . , (3)which is somewhat narrower than the assumption of purely thermally broadened Ps emission, andresults from Monte-Carlo simulations of the combination process by Guessoum et al. (1991) whichshow that the electron-positron system is not in exact thermal equilibrium with the gas.Table 1: The radiative and annihilation lifetimes of Ps for various energy levels.Singlet Ps Triplet PsRadiative lifetime Annihilation lifetime Ratio Annihilation lifetime Ratio n τ /s T /s T /τ T /s T /τ . × − – 1 . × − –2 4 . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − . × − f Ps , α and β for different temperatures, which weinclude here for convenience in Table 2 along with the line widths of Ps Ly α and Ps α calculatedfrom equation 3. The positronium fraction, f Ps , is calculated from the reaction rates for radiativerecombination, charge exchange with H and He and direct annihilation given by Wallyn et al.(1996). The fraction of Ps which undergoes a Ly α transition, α , is given by Wallyn et al. (1996) intheir table 5. The ratio of the intensity of Ps Ly α to Ps α , β , is derived from the absolute intensitiesof the transitions listed in table 6 of Wallyn et al. (1996). Note that there are two values of f Ps given, one for a neutral medium which includes Ps formation via charge exchange, and one for anionised medium in which Ps only forms by radiative recombination.For Ps Ly α and Ps α we assume A = 1 . A V and A J = 0 . A V respectively (Rieke & Lebofsky1985).
3. SOURCES OF POSITRONIUM
We now consider the expected Ps recombination line emission from various astrophysicalsources. We discuss both Galactic and extragalactic sources and calculate fluxes for Ps Ly α andPs α using the formulæ given in section 2.3. We quote our results in terms of line flux densities, i.e.the total line strength divided by the line width. This allows for a more meaningful comparisonto the source continuum spectrum and the atmospheric background, both of which are found todominate the Ps emission line fluxes. So far the only detections of Ps outside laboratory experiments are from the Sun (first ob-served by Chupp et al. 1973) and the Galactic centre (first identified by Leventhal et al. 1978). AllTable 2: A summary of the relevant parameters for calculating the recombination line fluxes fordifferent temperatures, extracted from Wallyn et al. (1996). The fraction of e + forming Ps inan ionised medium; a neutral medium; the Ps Ly α fraction, α ; the ratio of line intensities I(Ly- α )/I(Ps α ), β ; Ps Ly α and Ps α line widths. T / K f Ps ionised f Ps neutral α β ∆ λ (Ps Ly α )/ ˚A ∆ λ (Ps α )/ ˚A1 × × × × × × γ -ray observatory, which has de-tected extended Ps 511keV line emission and continuum emission centred on the Galactic centre(Weidenspointner et al. 2008a). Broadly, the distribution of 511keV radiation toward the Galac-tic centre is extended with a FWHM of ≈ ≈ + are long lived, and the reactionrates with the ISM are small (Guessoum et al. 2005) and positrons can diffuse long distances fromtheir sources before thermalisation (Jean et al. 2006; Gillard et al. 2007). Thus e + have a largemean free path before interaction and annihilation. Even allowing for the longevity of e + in theinterstellar medium, and the resulting diffuse nature of Ps annihilation radiation, it is likely thatsome fraction of the Ps annihilation radiation results from discrete sources. (i) It is expected thatindividual energetic sources will emit e + and therefore these should be brighter than any diffusebackground. (ii) The Sun is known to emit Ps 511keV radiation, and therefore more energeticsources of e + will also likely emit Ps 511keV radiation. (iii) There is a correlation between anasymmetry in the 511keV radiation originating from the inner Galactic disc and the distribution of γ -ray selected LMXBs (Weidenspointner et al. 2008b). (iv) The ISM is very inhomogeneous; therange of densities ranges from approximately 10 electrons m − in the hot diffuse gas ( ≈ K) to2 × atoms m − in cold gas ( ≈ ∼ ∼ f = 11 photons s − m − , or roughly 1 . − m − per source. Inaddition to this blind survey, Kn¨odlseder et al. (2005) also examine candidate sources includingSgr A*, microquasars, LMXBs, pulsars, SNRs, galaxies and AGN. No point sources are detecteddown to typical limits of ≈ . . − m − . The upper limit for Sgr A* is 1 photons s − m − . These results suggest that if point sources are responsible for the observed diffuse emission 10 –they are likely to be more than 8 and fainter than ≈ − m − . Assuming all sources tobe of equal strength we therefore empirically relate the 511keV flux of individual point sources tothe total number of sources, N , by, f ≈ . N photons s − m − . (4)Combining equation 4 with equations 2 and 3 and using the parameters listed in Table 2 wecan calculate the line flux per source as a function of the number of sources. This is plotted inFigure 1 for both Ps Ly α and Ps α for a range of temperatures. It was assumed that the extinctiontowards the Galactic centre was A V = 5 mag, although we note that there are several windows oflow extinction (Dutra et al. 2002), such as Baade’s window, which may be used to obtain deeperobservations of the Galactic centre. It is clear that Ps α emission is much brighter than Ps Ly α despite the fact that Ps Ly α is intrinsically brighter. For a temperature of 10 K the flux densityis higher for Ps α for any visual extinction A V > . α is brighter for A V > .
66 mag.We defer an assessment of the feasibility of observing such sources to section 4, but we note as aguide sources that with flux densities f λ ≫ − m − µ m − may be considered bright, whereasthose with f λ ≪ − m − µ m − may be considered faint, c.f § e + a) β + decay of radioactive nuclei; b) π + decay into µ + , which decays and gives off a positron; c) pair (electron-positron) productionthrough photon-photon interactions; d) pair production by the interaction of an electron with astrong magnetic field. All these processes are thought to occur naturally in the Universe. In theGalaxy, the main sources of e + are thought to be supernovæ, novæ, microquasars and pulsars,cosmic rays and γ -ray bursts, in that order (Guessoum et al. 2005). To this list we add the decayof Al, which is produced via nucleosynthesis in core-collapse supernovæ, novæ, asymptotic giantbranch stars and massive stars (Kn¨odlseder et al. 1999), and is expected to make a significantcontribution to the e + content of the Galactic disc (Kn¨odlseder et al. 2005). We also add decayingsuper-symmetric dark matter particles (Boehm et al. 2004; Beacom et al. 2005). We discuss eachof these in turn below, except for cosmic rays and dark matter decays. Both these processes areintrinsically diffuse, and thus while possibly significant in terms of the Galactic positron budgetthey are unlikely candidates for Ps emission line observations.Most of the sources listed above inject e + into the ISM, where they thermalise before formingPs and annihilating. Once in the ISM the e + will diffuse along magnetic field lines. The diffusiondepends primarily on the conditions in the ISM (assuming a restricted energy range for the injected e + ∼ e + , thus the average distance over which the e + will beessentially identical for all injecting sources. We therefore preface our discussion of the individualsources with a discussion of the diffusion of e + in the ISM. 11 –
10 20 50 100 200 500 100010 - f Λ (cid:144) ph s - m - Μ m - (a) Ps Ly α
10 20 50 100 200 500 10000.010.11101001000 N sources f Λ (cid:144) ph s - m - Μ m - (b) Ps α Fig. 1.— The line flux density of Ps Ly α and Ps α assuming that all the Galactic 511keV radiationis due to N equal point sources, and that the point sources are obscured with A V = 5mag at theGalactic centre. 12 – e + in the interstellar medium Before annihilation, e + diffuse through the ISM along magnetic field lines. Jean et al. (2006)have calculated the propagation distances of e + in the ISM based on the cross-sections of Guessoum et al.(2005). They consider three regimes of propagation, a quasi-linear regime in which e + are trans-ported in resonance with Alfv´en waves, a collisional in-flight phase in which the e + are losing energyand a collisional thermalised phase. Combining the propagation modes with the Ps formation andannihilation cross sections they calculate a maximum distance, d max , over which the e + can prop-agate before annihilation. It is found that in the warm phases of the ISM (8000 K) e + do notpropagate more than ≈
50 pc in a typical annihilation time of ∼ yrs. Even those e + whichsurvive longer than the typical annihilation time do not propagate much further since the diffusionconstant in the collisional regime is very small ( ∼ − pc yr − for a warm ionised ISM). Thusexcept in hot phases (10 K), escaping e + remain local to the e + source and we call this associatedvolume V source . Supernovæ (SNe) are thought to be a major, and possibly dominant, contributor to the originof the Galactic e + (Milne et al. 2002). SNe Ia produce e + from radioactive β + decay of Ni → Co → Fe, with a smaller contribution from Ti → Sc → Ca, and still a lesser contributionfrom Al → Mg (Chan & Lingenfelter 1993). The contribution from SNII is thought to be fewerby about an order of magnitude (Milne et al. 2002) and here we only consider SNIa.Milne et al. (1999) find the average positron yield from SNe Ia is ≈ × e + (see theirtable 4). Of these, after 2000 days, approximately 2–6 per cent escape the supernova, whilst lessthan 1 per cent of the trapped e + survive. We assume that all other e + annihilate. Thus we mayconsider the Ps recombination line emission from SNe Ia in two components: the initial emissionfrom the Ps formed in the supernova explosion, and the emission from the Ps formed from theescaping e + . In the following we assume an escape fraction of 5 per cent.We assume that 95 per cent of e + annihilate in the first 2000 days after a type Ia SN explosion.If we conservatively assume that this takes place evenly across the 2000 days we have a e + sourcerate of r ≈ . × e + s − . We make the further simplifying assumption that all e + whichannihilate in the ejecta thermalise before doing so, and we assume that the temperature of theejecta is ∼ K. Thus using equation 1 and the appropriate value from Table 2 we can calculatethe line flux density. The results are shown in Figure 2 for both Ps α and Ps Ly α , as a function ofdistance from Galactic SNe to the distance of the Virgo cluster assuming a high visual extinctionof A V = 5 mag, such as would be appropriate for the Galactic centre. The feasibility of detectionis deferred until section 4.We now consider the fate of the e + which survive and escape the ejecta. We assume these 13 – e + are thermalised in the interstellar medium, and consist of 5 per cent of original SN e + yield.Milne et al. (1999) show that the typical energy of an escaped e + is ≈ e + inthe ISM is determined by the energy of the e + , the density of the ISM, and the cross-sections for theprocesses of radiative, recombination, charge-exchange and direct annihilation, etc. These cross-sections have been calculated by Guessoum et al. (2005) for various phases of the ISM: molecular(10 K), cold (80 K), warm neutral (8000 K), warm ionised (8000 K), hot (10 K).Kn¨odlseder et al. (2005) discuss the SNIa rate and distribution in the Galaxy. Although theexact numbers are not known, estimates based on the 511keV line flux (Kn¨odlseder et al. 2005)and from extragalactic SNe rates (Tammann et al. 1994; Cappellaro et al. 1997; Mannucci et al.2005) suggest that there are 0.3–1.1 SNIa per century in the bulge, although Prantzos (2006)predict a much lower value of ≈ .
07 SNIa per century based on extrapolations from SNIa ratesin early type galaxies. We assume a value of 0.5 SNIa per century in the bulge or a timescale of T SNB = 200 yr. Thus in a volume V source (see § T SN = T SNB V bulge V source . For typical values in the bulge of T ann ≈ yr and d max ≈
50 pc at10 K (Jean et al. 2006), T SN ≫ T ann therefore we may consider each SN event individually sincethe probability of multiple SNe in the same volume V source within a few e -folding timescales is verysmall.The number of e + in a volume V source following a SN is governed by the differential equationd N d t = − N ( t ) T ann , (5)hence, N ( t ) = N e − tT ann , (6)where t is the time since the SNe and N is the initial number of surviving e + per SN, andthe annihilation timescales, T ann are given by Jean et al. (2006). Since we are interested in theformation of Ps we need to distinguish between the timescale for annihilation by any means, T ann ,which includes Ps formation and direct annihilation, and the timescale for Ps formation alone .The former will govern the depletion of Ps in the ISM, and the latter will govern the formationrate of Ps. So the number of Ps formed as a function of time is therefore N Ps = f Ps N (cid:16) − e − tT ann (cid:17) , (7)where as before f Ps = T ann /T Ps is the fraction of e + which form Ps. Thus the Ps formation rate isd N Ps d t = f Ps N T ann e − tT ann . (8)This expression can be substituted for r × f Ps in equation 1 to give the total line flux for e + originating from SNIa. This is the timescale for annihilation of free e + in the ISM, and includes the timescale for the formation of Ps.This should not be confused with the timescale for Ps annihilation, T Ps
14 –Using values of T ann and d max from Jean et al. (2006) (for 1Mev e + ), values of f Ps fromGuessoum et al. (2005), α and β from Wallyn et al. (1996) (and assuming the 8000K values fromJean et al. 2006 are appropriate for the 10 K values of Wallyn et al. 1996), we have calculatedthe surface brightness of Ps Ly α and Ps α from SNIa as a function of time for both a neutral andionised ISM at 10 K. We assume the SN is located at the Galactic centre with a distance 8kpc and A V = 5 mag. The results are shown in Figure 3, and are exceedingly faint — orders of magnitudebelow the detection limit for any planned space or ground based mission.These fluxes correspond to a total e + annihilation rate over the entire bulge of ≈ × e + s − , assuming one SN every 200 yrs, which is in good agreement with the values Milne et al. (2002)of ≈ × e + s − for the entire Galaxy with bulge/disc ratios of 0.2–3.3. This annihilationrate corresponds to a total flux of 511 keV photons of ≈
40 photons s − m − , which is in order ofmagnitude agreement with the value of 11.2 photons s − m − reported by Kn¨odlseder et al. (2005). Novæ are potentially significant sources of positrons. Novæ are caused by a runaway ther-monuclear reaction due to the accretion of hydrogen rich material onto the surface of a whitedwarf. Positrons are expected to be produced by β + decay of radioactive nuclei produced dur-ing the runaway, and carried to the surface of the nova by rapid convection (Clayton & Hoyle1974). Detailed calculations of the expected e + annihilation signatures were first calculated byLeising & Clayton (1987). These show an early peak in emission due to decay from N followedby decay from F, with lesser contributions from O, O and m Cl. This early peak lasts ∼ < Na. This is particularlyrelevant for ONe novæ which have a larger abundance of Na than CO novæ. The longer durationemission is pertinent since the bright early peak occurs before the maximum in visual luminosity,i.e. before discovery (Hernanz et al. 2002).Hernanz et al. (1999) provide updated light curves of the expected 511 keV radiation fromboth CO and ONe novæ. We use their table 2 of the fluxes at various epochs along with equation 2to calculate the expected Ps Ly α and Ps α line strengths. Leising & Clayton (1987) assume thatthe e + thermalise before forming Ps, and have a temperature of < K, such that Ps formationdominates over direct annihilation. Following this prescription we assume a temperature of 10 Kand an ionised medium and use the appropriate values from Table 2. Novæ are thought to residemainly in the bulge of the Galaxy, therefore we assume a distance of 8kpc and a conservativeextinction of A V = 5 mag. Figure 4 shows the resulting Ps α and Ps Ly α fluxes for the CO andONe novæ. The flatter light curve of the ONe novæ is due to the higher abundance of Na. Wedefer a discussion of the feasibility of detection to §
4. 15 – Distance (cid:144) kpc f Λ (cid:144) ph s - m - Μ m - Ps Α Ps Ly Α Fig. 2.— The line flux density of Ps Ly α and Ps α as a function of distance for Ps formed in theejecta of SNe Ia in the first 2000 days, i.e. for those e + which do not escape. See the text for details. - - - - time (cid:144) yr S u rf ace b r i gh t n e ss (cid:144) ph s - m - Μ m - a r c s ec - Fig. 3.— The surface brightness of Ps α (thick lines) and Ps Ly α (thin lines) emission from the e + released in a SN Ia located near the Galactic centre. The continuous lines are for an ionisedmedium at 8000K and the dashed lines for a neutral medium at 8000K. 16 – Microquasars are a promising source of e + in the Galaxy (Guessoum et al. 2006). The accretiondisc of a low mass X-ray binary will produce e − - e + pairs, which in a microquasar are ejected intothe ISM via a relativistic jet in a manner analogous to AGN (see § >
100 MeV γ -rays (Tavani et al. 2009), which are also potentially promising point sources of e + .There is good evidence that even those LMXBs which do not produce a jet are an importantsource of e + in the Galaxy; there is an asymmetric distribution of 511keV radiation from the innerGalactic disc, which coincides with the asymmetric distribution of LMXBs (Weidenspointner et al.2008b). For LMXBs without a jet, the e + can escape in a stellar wind. Since the origin of the e + is the same as for microquasars, and since the annihilation timescale is long compared to thediffusion timescale, the diffuse annihilation radiation is expected to be identical for LMXBs andmicroquasars. However, as discussed below microquasars have the important distinction that insome cases the jet can collide with the secondary star, producing a point source of emission.From consideration of energetics, and from an empirical analysis of the INTEGRAL SPI data,Guessoum et al. (2006) calculate a typical e + flux of ≈ e + s − from a microquasar. Theannihilation in the jet is expected to be small (see the discussion for AGN in § § e + will diffuse along the magnetic field of the ISM as described in § § e + frommicroquasars and LMXBs will form an extended emission region ∼ d max given by Jean et al. (2006) we havecalculated the surface brightness of a cloud using the same assumptions for f Ps , α , β and as in § e + from microquasars is very faint, and arelisted in Table 3.Table 3: The surface brightness of Ps α and Ps Ly α emission resulting from e + escaping into theISM from the jets of microquasars or winds of LMXBs, see the text for details.Surface brightness/ ph s − m − arcsec − µ m − T/ K Ps Ly α Ps α
10 3 × − × −
80 1 × − × − × − × − × − × − × − × −
17 –Guessoum et al. (2006) also consider misaligned microquasars, in which the jet from the ac-cretion disc impinges on the secondary star, as a possible class of point sources of annihilationradiation. Their model accounts for deformation of the stellar surface due to the jet, and the frac-tion of annihilation photons which escape the atmosphere of the star and the jet induced cavityin the direction of the observer. Thus they calculate expected 511keV fluxes for several confirmedand candidate misaligned microquasars.We have converted these fluxes into the equivalent recombination line fluxes using the assump-tions implicit in equation 2 with the further assumption that recombination line photons emittedin a upward direction escape the surface of the star. This assumption is reasonable since the inter-action depth at which relativistic e + from the jet are slowed down enough to form Ps via chargeexchange is λ form ∼ . − (Guessoum et al. 2006), whereas the mean free path of visible pho-tons in a typical stellar photosphere is λ ∼ . − , and assuming this value is valid for thewavelengths of both Ps Ly α and Ps α upward photons should escape the star. The resulting fluxesare given in Table 4 for a 10 K and a 10 K gas. We assume the visual extinction corrections, A V ,from Schlegel et al. (1998), but note these may not be accurate for sources close to the Galacticplane. Pulsars produce e + via pair-production due to the interaction of an e − with the strong magneticfield. We will mainly consider the Ps formation rates for e + escaping the pulsar, but first we brieflyconsider e + forming Ps in the atmosphere of the pulsar.Usov & Melrose (1996) describe a model in which Ps is formed from the decay of synchroton γ -ray radiation produced in the strong magnetic fields of pulsars. It is argued that the Ps escapefrom the polar gap with Lorentz factors of Γ ∼ , and thereafter quickly dissociate. The Lorentzfactors for the Ps in the pulsar are thus so high that the emission lines will be very highly redshiftedfor any orientation of the beam, even toward or tangential to the observer, due to time dilation.Baring & Harding (2001) argue that Ps will be short lived in the atmosphere of pulsars except inthe case of very high Lorentz factors or for a narrow range of magnetic field strengths. Thus wewill not consider direct observation of Ps in the atmospheres of pulsars further.We now turn our attention to Ps formed from e + escaping the pulsar. Sturrock & Baker (1979)estimate the e + production rate from the Crab pulsar to be ≈ × e + s − . Wang et al. (2006)examine pair-production from three separate catogories of pulsars: normal pulsars (e.g. the Crabpulsar), magnetars in gamma-ray burst (GRB) progenitors, and milli-second pulsars. They estimate e + - e − injection rates of 10 e + s − and 10 e + s − for the Crab and Vela pulsars respectively.For millisecond pulsars they estimate an injection rate of 5 × e + s − . We do not consider themagnetar GRB progenitors here, since although they may contribute to the diffuse e + annihilationradiation they are too infrequent in the Galaxy ( ≈ × − yr − ; Piran 2004) to be a tenable 18 –Table 4: The Ps Ly α and Ps α fluxes for the microquasars of Guessoum et al. (2006) as describedin § − m − µ m − .10 K 10 KSource Ps Ly α Ps α Ps Ly α Ps α GRO J1655-40 249 73.8 9.25 2.70V4641 Sgr 62.7 8.74 2.33 0.320XTE J1550-564 51.3 24.7 1.90 0.903XTE J1118+480 3810 299 141 11.0LSI+61 ◦
303 302 166 11.2 6.06Cyg X-1 134 99.4 4.99 3.64Sco X-1 997 114 36.9 4.19LS5039 2.27 39.8 0.0843 1.46SS433 11.5 22.8 0.425 0.835GRS 1758-258 0.114 4.10 0.00423 0.150Cyg X-3 0.386 4.41 0.0143 0.161CirX-1 × − × − × − × − × − × − IGR J17091-3624 109 12.7 4.05 0.464IGR J17303-0601 71.2 11.8 2.64 0.433IGR J17464-3213 0.934 5.80 0.0346 0.212IGR J18406-0539 9.83 × − × − e + leaving the pulsar thermalise before forming Ps, thus they will firstdiffuse through the ISM according to § V source (see § N ( t ) = n e + te − tT ann , (9)where n e + is the positron injection rate and T ann is the annihilation timescale, and we have madethe simplifying assumption that e + thermalise instantly on injection into the ISM. Thus the numberof Ps atoms formed as a function of time is N Ps = f Ps n e + t (1 − e − tT ann ) (10)where as before f Ps is the fraction of e + which form Ps before annihilation. Therefore the Psformation rate in the volume V source around a pulsar isd N Ps d t = n e + f Ps − e − tT ann + e − tT ann tT ! , (11)which in the limit t >> T ann becomes d N Ps d t ≈ n e + f Ps . (12)Thus assuming a positron injection rate of 10 e + s − for the Crab pulsar and following thesame assumptions as in § α and Ps Ly α around pulsars. The results are given in Table 5; the surface brightnesses for escaped e + frompulsars are extremely faint.Table 5: The surface brightness of the diffuse Ps α and Ps Ly α emission arising from e + escapingfrom pulsars as a function of temperature. For details see § − m − µ m − arcsec − Ps Ly α Ps α
10 6 × − × −
80 2 × − × − × − × − × − × − × − × −
20 –
The only detected sources of Ps annihilation radiation are from our own Galaxy and the Sun.However the production processes responsible for the generation of e + within the Galaxy will alsobe active in other galaxies, and hence in principle they too should be sources of Ps recombinationline emission. This is discussed in § § § α emission, which lies in the infrared region is not coincident withbright atmospheric emission lines. Powerful relativistic jets are a property of many AGN. These jets emit strongly at radiowavelengths with a power-law spectrum which is interpreted as being due to synchrotron emissionfrom e − carried at relativistic energies along the magnetic field lines emanating from the poles ofthe AGN. These jets must be electrically neutral otherwise the potential difference induced by thejet would impede and eventually halt the jet.It is an unsolved issue whether the positive component of jets consists of protons, positronsor a mixture of both. From a theoretical viewpoint it is expected that AGN jets should containsome e − - e + pairs; a pair plasma has the advantage of explaining γ -ray jets (Blandford & Levinson1995) and the very high Lorentz factors (Γ ∼ >
5) required to account for superluminal bulk velocitiesof jets (Begelman et al. 1984). From an observational view point the situation is unclear as mostattempts to answer this question have had to rely on indirect methods of searching for the presenceof e + . For example estimates on the bulk kinetic energy contained in jets on a variety of scaleshave been used to argue for both e − -p plasma (Celotti & Fabian 1993) and e − - e + plasma (e.g.Reynolds et al. 1996; Wardle et al. 1998; Hirotani 2005).Marscher et al. (2007) searched for the 511 keV annihilation signature in 3C 120, and theirnon-detection places upper limits on the e + content of jets (albeit not significantly constraining).In doing so they have also developed theoretical arguments for the e + content of jets which we willuse here to estimate the Ps formation rate due to jets. Marscher et al. (2007) show that the flux 21 –of e + in a jet is given by F ( e + ) = πR cf Γ N s E − s min (13)where R is the cross-sectional radius of the jet, f is the fraction of the jet which consists of a pairplasma (i.e. 0 . × f is the e + fraction of the jet), Γ is the Lorentz factor for the bulk velocity ofthe jet, E min is the minimum energy of the power-law distribution of relativistic e − - e + , s is thespectral index of the synchrotron radiation from the jet ( F ν ∝ ν − s ) and N is the normalisation ofthe e − - e + number density per unit energy such that N ( E ) = N E − s − . (14)The parameters N , R , E min , s and possibly f should be determined independently for indi-vidual AGN (e.g. as in Marscher et al. 2007 for 3C 120). Marscher (1983) gives formulæ to relate N to observational parameters, viz. the angular size of the source, θ ; the frequency of synchrotronself-absorption turnover, ν m ; the flux density at ν m , F ν ( ν m ); the spectral index s ; the redshift z ;the luminosity distance D L ; and the Doppler beaming factor δ = Γ(1 − β cos φ ) − ( φ is the angleof the velocity vector away from the line of sight and β is the velocity divided by c ).Ghisellini et al. (1993) provide measurements of the above observable parameters for differentclasses of AGN, viz. BL Lacs, core-dominated quasars (low and high polarisation), lobe dominatedquasars and radio galaxies. We have followed the formulæ of Marscher (1983) to calculate N assuming a spectral index s = 0 .
75 and median values of Γ, since these measurements are notavailable for all the sources. With the further assumption that E min = mc (i.e. γ min = 1) and f = 0 .
5, and setting R = 7 . × m (as calculated for 3C 120 by Marscher et al. 2007), we cancalculate the positron flux for all the AGN in Ghisellini et al. (1993). We report the mean, medianand standard deviation of the fluxes calculated for each class of source in Table 6. For the sourcesof Ghisellini et al. (1993) the blazars are the most powerful e + emitters. Blazars also have theadvantage that the jet is aligned along the line of sight of observations, and is thus not obscuredby the dusty torus which surrounds the AGN. Therefore we focus our attention on blazars as themost promising AGN candidate for a successful Ps detection and we assume the mean value of10 e + s − as the default flux. We note that the assumption of a uniform jet implicit in thesecalculations may result in the e + flux being too small by a factor ∼
10 (cf. Marscher et al. 2007;see also a similar discussion for uniform/ non-uniform wind Marscher 1977). Furthermore thereare significant uncertainties in the parameters taken from Ghisellini et al. (1993), particularly theself-absorption frequency and consequently the flux at the self-absorption frequency for which itwas assumed that the frequency of the VLBI observation is equal to the self-absorption frequency.Bearing these caveats in mind, the values in Table 6 should be treated as approximate.Having calculated the e + flux from AGN jets we are now in a position to estimate the Ps flux.We assume that the Ps formation rate in the jet is insignificant since the e + have energies above 22 – - (cid:144) hrs f Λ (cid:144) ph s - m - Μ m - CO Ps Α ONe Ps Α CO Ps Ly Α ONe Ps Ly Α Fig. 4.— The Ps α and Ps Ly α flux densities of CO and ONe novæ at a distance of 8 kpc as afunction of time.Table 6: Average positron fluxes calculated from the AGN observations of Ghisellini et al. 1993.Class No. of sources Mean/ e + / s Median/ e + /s σ / e + /sBL Lac objects 22 10 Core-dominated high-polarisation quasars 24 10 Core-dominated low-polarisation quasars 24 10 Lobe-dominated quasars 11 10 Radio galaxies 8 10
23 –the ionisation energy of Ps. Furthermore Furlanetto & Loeb (2002) show that annihilation beforethermalisation occurs for only ∼ e + produced in jets. When the jet interacts with agas cloud, the positrons will thermalise on a timescale, T therm = 4 . × (cid:18) k B T (cid:19) (cid:18) − cm − n e (cid:19) yr (15)(Furlanetto & Loeb 2002), which for T = 10 K and n e = 10 cm − is 0.12 yr. Thus we assumethat e + thermalise instantly on interaction with a cloud.After thermalisation the e + diffusion distance will be very small (cf. § f = 10 e + s − and A V = 1 mag we have calculated the Ps flux for Ps Ly α and Ps α as a functionof redshift, and the results are plotted in Figure 5. The total 511keV emission from the Galactic bulge and disc is 10 . ± . ± − m − respectively (Kn¨odlseder et al. 2005). Using equation 2 and assuming a temperature of 10 K anda visual extinction of A V = 2 mag this translates into a line flux density of f λ ≈ − m − µ m − for Ps α and Ps Ly α respectively. We assume that this value holds for all other largespiral galaxies. Thus for local galaxies we can compute the expected line flux density by scalingthe above numbers by (8 /d ) , where d is the distance to the galaxy in kpc; we show results out toa distance of the Virgo cluster ( ∼
18 Mpc) in Figure 6.We note that the assumption of the similarity of other galaxies to the Milky Way in terms of e + production and annihilation can only be considered an approximate estimate; different classesof galaxies could produce different amounts of e + than the Milky Way. In particular starburstsand ULIRGs could be copious emitters due to the SNe and other high energy processes associatedwith star-formation regions. Supernovæ and gamma ray bursts are both expected to produce copious amounts of positrons(see § Galactic
Ps, and their remnants are toodiffuse, but they could be very promising candidates for observation in other galaxies.. Figure 2shows the estimated line flux density for SNIa as a function of distance.The results are expected to be similar for GRBs. Furlanetto & Loeb (2002) estimate ≈ × e + to be released in a GRB, with only a “small fraction” annihilating in the early stages duringwhich the ejecta expands (cf. 5 per cent for SNeIa in § ∼ e + to be produced by a GRB. 24 – - F l ux (cid:144) ph s - m - Μ m - (a) Ps Ly α - F l ux (cid:144) ph s - m - Μ m - (b) Ps α Fig. 5.— The line flux density of Ps Ly α and Ps α for typical AGN jets as a function of redshift fordifferent temperatures in an ionised ISM. The assumptions in calculating the fluxes are describedin the text. 25 –
4. PROSPECTS FOR DETECTION
Having examined potential sources of Ps recombination lines, and estimated the strength ofthe sources we now assess the feasibility of observation. We begin with a summary of the expectedPs fluxes with a comparison to current upper limits based on the non-detections of Ps Paschen- β byPuxley & Skinner (1996), the non-detection of Galactic 511keV point sources by Kn¨odlseder et al.(2005) and the non-detection of 511keV annihilation in the jets of 3C 120 by Marscher et al. (2007).We then examine the sensitivity of current and upcoming instruments to Ps Ly α and Ps α emission.We finish by simulating observations of Ps α in AGN. The most direct observational constraint on Ps recombination emission line strengths comesfrom the non-detection by Puxley & Skinner (1996) who searched for Ps Paschen- β from the Galac-tic centre. They found an upper-limit to the line strength of 3 × − W m − . If we assume atemperature of the ISM of 10 K and an extinction of A V = 5 mag, we can use the relative linestrengths predicted by Wallyn et al. (1996) to convert this to a line strength of Ps Ly α =19 andPs α =6200 ph s − m − µ m − , where we have also divided by the line width as given by equation 3.These upper-limits are not constraining compared to the expected fluxes calculated in § We have discussed the limits on the Ps recombination emission line strength provided by current511keV observations as given by Kn¨odlseder et al. (2005) in § (cid:144) Mpc f Λ (cid:144) ph s - m - Μ m - Ps Α Ps Ly Α Fig. 6.— The line flux density of Ps α and Ps Ly α in spiral galaxies as a function of distance. 26 –there are 100 sources of equal strength responsible for the total Galactic 511keV radiation then thisequates to line strengths of Ps Ly α =0 .
02 and Ps α =6 ph s − m − µ m − , see Figure 1.Kn¨odlseder et al. (2005) also provide 511keV 3 σ flux limits for individual sources (see theirtable 4). We convert these to Ps Ly α and Ps α flux limits again assuming T = 10 K and usingthe appropriate extinction values from Schlegel et al. (1998) or A V = 5 mag for sources closethe Galactic plane for which the extinction models are inaccurate. We use the most constrainingobservations for each class of source and compare these to our predictions in Table 7. From ourpredictions it is not expected that any of the sources would have been observed. Marscher et al. (2007) searched for annihilation radiation in the jet of 3C 120 and find a 2 σ upper limit of 0 .
33 ph s − m − . We again convert to Ps emission line strengths assuming T = 10 K with A V = 1 mag, and find Ps Ly α =0 .
89 and Ps α =1 . − m − µ m − . We summarise the results of § § µ m − ), which takes into account the width of the line and makes a comparison tothe background more meaningful. From our estimates of the fluxes of the sources it is not expectedthat any of the sources should have been detected in the 511keV observations.Table 7: A comparison of the predicted fluxes for different classes of sources in § § − m − µ m − Ps Ly α Ps α Ps Ly α Ps α Kepler SNR 1.6 7.9 12 a a LMXB GX 5-1 0.065 3.7 0.65 a a Crab Pulsar 130 110 190 a a
3C 120 8.9 1.5 170 b b
27 –
We now examine the sensitivity of current and future instruments to Ps emission line radiation.The signal to noise ratio is given by
SN R = f λ tǫ p f λ tǫ + Btǫ + Dt + R (16)where t is the exposure time, ǫ is a factor which takes into account the efficiency of the instrumentand collecting area of the telescope, B is the background, D is the detector dark current and R isdetector read out noise. Since the expected Ps recombination line emission is faint in all cases itis likely that the background will also include continuum emission from the source in question aswell as the usual night sky background etc.We first address the issue of whether it is more efficient to observe Ps Ly α or Ps α . Ps Ly α isalways intrinsically brighter than Ps α . It does not follow however, that it is more efficient to observePs Ly α than Ps α . This is because the interstellar extinction, the line width, the background andthe seeing all very with wavelength.Interstellar extinction is greater for Ps Ly α than for Ps α . This means that the integratedline strength for Ps α is greater than that for Ps Ly α for visual extinctions A V ∼ > .
65 mag, wherethe exact value depends on the temperature of the ISM in which the Ps is forming, see Figure 7.However, the line width is also greater for Ps α compared to Ps Ly α so the line flux density, f λ ,which is more meaningful to compare to the background is greater for Ps α for visual extinctions A V ∼ > . α and Ps α , and then determine the expected sensitivity ofobservations compared to the expected brightnesses of example objects.The U band background at a typical good observing site is U = 21 . − , whichis equivalent to a background of B U = 140 ph s − m − µ m − arcsec − , which we assume is alsoappropriate for observations at 2430˚A.The background in the near-infrared is dominated by atmospheric hydroxyl emission lines.Thus the background depends sensitively on the wavelength and the resolution of the observa-tions. Figure 9 shows the logged background around the Ps α line, taken from the model ofEllis & Bland-Hawthorn (2008). There is a very bright OH emission line very close to the Ps α line. Note that Figure 9 is at the intrinsic resolution of the night sky, i.e. the width of the lines isthe natural width due Doppler and pressure broadening; when observed with a spectrograph, theresolution and scattering of the spectrograph will cause the OH line to severely contaminate thePs α line. Subtracting the OH line results in a high Poisson and systematic noise (see Davies 2007;Ellis & Bland-Hawthorn 2008). Indeed, we postulate that this is the reason that Ps α has neverbeen observed serendipitously. 28 – A V (cid:144) mag I n t e g r a t e d li n e s t r e ng t h P s Α (cid:144) P s L y Α Fig. 7.— The ratio of Ps α /Ps Ly α for integrated line strengths as a function of visual extinctionfor different temperatures in the ISM. The horizontal dot-dashed line marks the point at which theintegrate line strength of both lines are equal. Above the dashed line Ps α is brighter than Ps Ly α . A V (cid:144) mag L i n e f l uxd e n s it y P s Α (cid:144) P s L y Α Fig. 8.— The ratio of Ps α /Ps Ly α for line flux densities as a function of visual extinction fordifferent temperatures in the ISM. The horizontal dot-dashed line marks the point at which theintegrate line strength of both lines are equal. Above the dashed line Ps α is brighter than Ps Ly α . 29 –Fig. 9.— The background around the Ps α line is shown by the thin grey line. The flux is loggedto emphasise the fainter lines and the interline continuum. The dashed line marks the position ofthe Ps α line. The thick black line shows the background spectrum after OH suppression. 30 –The brightness of the near-infrared sky is problematic for many areas of observational astron-omy, as exemplified by the particular science case of detecting Ps α . For this reason there havebeen significant technological developments aimed at tackling this problem. The implementationof several of these projects is now imminent, promising much darker near-infrared skies in the nearfuture. These technological developments are the motivation behind our renewed interest in thelong standing observational challenge of detecting Ps recombination emission lines.There are two technologies in particular which should be very beneficial for the detection ofPs α . These are the James Webb Space Telescope (see e.g. Gardner et al. 2006) and OH suppressingfibre Bragg gratings (Bland-Hawthorn et al. 2004; Bland-Hawthorn et al. 2008). The James WebbTelescope mission is designed specifically to achieve very low infrared backgrounds, both for imagingand moderate resolution spectroscopy ( R ≈ ≈ α line after suppression with FBGtechnology based on current performance. We note that at NIR wavelengths the background canbe further reduced with adaptive optics which permits the use of a smaller aperture to collect thesame object flux. After OH suppression the background flux density at the wavelength of Ps α isless than that of Ps Ly α , assuming the interline continuum in the model of Ellis & Bland-Hawthorn(2008) is correct.The calculation of the difference in backgrounds is complicated by the fact that the line widthof Ps α is greater than that of Ps Ly α and so the background must be integrated over a largerwavelength range for Ps α . Conversely the seeing is smaller at longer wavelengths, and so the Ps α background can be measured from a smaller aperture than for Ps Ly α ; this effect is even morepronounced with adaptive optics which can further reduce the necessary aperture in the infrared,but not in the ultraviolet.In order to take into account all these various effects we have calculated the Ps Ly α and Ps α flux limits to obtain a signal-to-noise of 10 as a function of time for backgrounds correspondingto Ps Ly α in natural seeing and Ps α in natural seeing and adaptive optics corrected and withand without OH suppression. The results are shown in Figure 10. (Note that here we quote theresults as total line strengths since the signal to noise calculation requires integrating the emission
31 –line and the background over the line width.) We assume that the Ps lines are resolved, and thebackgrounds integrated over the line width are 0.0272, 13.05 and 0.197 ph s − m − arcsec − for PsLy α , Ps α and OH suppressed Ps α respectively. We assume that natural seeing is 1 arcsec in theUV and 0.5 arcsec in the NIR and that AO delivers a PSF of 0.1 arcsec FWHM. We assumed a 8mtelescope and a total system efficiency of 0.2.The limiting fluxes are compared to the average expected flux for microquasars (specificallywe compare to GROJ1655-40 the brightest confirmed mis-aligned microquasar, cf. Table 3) ascalculated above in § α and the Ps α lines should easily be detectable. Wealso compare to the fluxes for 3C 120, assuming the same backgrounds as for Ps at z = 0 (notethat the NIR background is a strong function of wavelength so this assumption is approximate inthe case of no OH suppression). In this case the Ps emission lines are too faint to be detected innatural seeing and natural backgrounds for both Ps Ly α and Ps α . However with OH suppressionand or AO correction Ps α should be detectable. We have estimated the Ps recombination emission line strengths for a wide variety of sources;the expected fluxes are fainter than current observational limits for Ps Ly α and marginal for Ps α .However with the development of OH suppressing technologies and the future launch of the JWST(Gardner et al. 2006) we are on the threshold of a new era in NIR spectroscopy with much lowerbackgrounds and consequently much more sensitivity. The improved sensitivity will make thedetection of Ps α lines feasible.The most promising targets for observation are mis-aligned microquasars and active galacticnuclei. Emission from other candidates is generally too diffuse. Mis-aligned microquasars shouldhave a spot of Ps emission where the jet impacts the secondary star. AGN should have similarspots of emission where the jet impacts gas clouds surrounding the nucleus. In the case of AGNthere will be bright emission from the nucleus itself, which must be subtracted off to reveal thefaint Ps emission.We have simulated observations of Ps α from an AGN. We use the observations of NGC 4151by Storchi-Bergmann et al. (2009) as our template for the the AGN emission. Specifically we modelthe spectrum of the region 0.7 arcsec E of the nuclues (see their figure 2, panel B), taking emissionline fluxes from their table 1 and using a continuum value of 6 × − erg s − cm − ˚A − . Wemodel the Ps α line by taking the flux for 3C120 based on the calculations of Marscher et al. (2007)(see Table 7) and scaling it to the redshift of NGC 4151. The background spectrum is takenfrom Ellis & Bland-Hawthorn (2008). The simulated components of the spectrum are shown inFigure 11.The simulations assume OH suppressed observations on an 8m telescope with a 1 arcsec diam-eter fibre bundle as described in Ellis & Bland-Hawthorn (2008), with adaptive optics correction 32 – (cid:144) hrs f Λ (cid:144) ph s - m - Ps Α , natural seeingPs Α , AO correctedPs Α , natural seeing, OH suppressedPs Ly Α , natural seeingPs Α , AO corrected, OH suppressed f Λ Μ QSO Ps Α f Λ Μ QSO Ps Ly Α f Λ
3C 120 Ps Α f Λ
3C 120 Ps Ly Α Fig. 10.— The flux limits to obtain a signal to noise of 10 as a function of time for Ps Ly α andPs α under various assumptions of the background (see text for details). 33 –delivering a Strehl ratio of 0.3. The spectral resolution was assumed to be R = 3000. The sim-ulations assume a varying night-sky background and systematic errors in wavelength calibrationsbetween reads. For further details see Ellis & Bland-Hawthorn (2008).Since the AGN continuum is much brighter than the Ps α it must be treated as background,and observations will be required of the AGN plus Ps α and of the AGN alone. For this reason weanticipate that integral field spectroscopy will allow the greatest chance of a successful detection,since fluxes from many regions of the AGN can be differenced, nullifying the requirement to know a priori in which region Ps might be forming.For the purposes of the simulation we assume that the AGN continuum can be precisely scaledbetween these two locations (i.e. in the simulations we assume the AGN emission does not change).The simulation assumes a 6hr observation (composed of 12 ×
30 min individual exposures) of bothregions. The resulting background and continuum subtracted spectrum is shown in Figure 12. ThePs α line is clearly visible. Without OH suppression the Ps α is much fainter than the noise fromthe residual sky lines, and any detections would be marginal.
5. SUMMARY AND DISCUSSION
The existence of astrophysical sources of Ps is revealed through observations of Ps annihilationradiation emanating from the Galactic bulge, with a weaker component originating in the disc (e.g.Weidenspointner et al. 2008a). It is expected that those Ps atoms in the triplet state will emitrecombination emission lines prior to annihilation (McClintock 1984). The wavelengths of therecombination spectral lines will be twice those of the corresponding hydrogen lines (Mohoroviˇci´c1934). In this paper we have assessed the possibility of observing the Ps recombination spectrum.In § e + are in thermal equilibrium with the ISM. The reason is that e + are produced in highenergy processes, and they are initially relativistic. They must therefore lose energy before theycan radiatively recombine with a free electron or undergo charge exchange with a H atom to formPs. We note that for photoionised astrophysical environments with temperatures in the range 10 – 10 K, Ps formation by radiative recombination dominates both charge exchange and the directannihilation of e + with bound or free electrons. This will be this case in close proximity to mostastrophysical sources of Ps, which will also emit strong ultraviolet radiation which will ionise thesurrounding medium. We emphasise that this is not the case for most e + , which will travel farfrom their origin ( § ∼ < K (McClintock 1984). However, in the case of point sourcesof Ps recombination emission lines, we are interested in the regime in which the Ps is formed in closeproximity to the source and therefore assume that radiative recombination dominates. Followingthese arguments, we gave formulæ to calculate the Ps emission line strengths for sources of known 34 – e + production rate under different conditions in the ISM. We also developed a formula to convert511keV fluxes to Ps recombination line fluxes.In § e + , both Galactic and extragalactic, and estimated e + production rates from the literature. The e + production rates were used to calculate Ps emissionline strengths. Taking into account e + diffusion in the ISM (cf. § e + are ejected isotropically into the ISM the resulting Ps emission linehas very low surface brightness. Thus whilst sources such as SNe, novæ and pulsars may produce apotentially significant fraction of the total Galactic e + budget, they are not promising candidatesfor Ps recombination line observations.On the other hand sources such as microquasars, LMXBs and AGN jets are potentially promis-ing candidates in which to observe Ps recombination lines. The reason being that the e + areanisotropic and may therefore produce a point source of emission if the jet collides with a densecloud in the ISM. For example in mis-aligned microquasars the jet impacts the secondary star,in LMXBs the jet may collide with stellar winds, and in AGN the jet will impact the gas cloudssurrounding the galactic nucleus.In § α are rather sensitive to the extinction, sources withlow extinction will be brighter at Ps Ly α than Ps α (cf. Figures 7 and 8). Thus deep observationswith careful continuum subtraction may yield Ps Ly α detections.The current handicap to observations of Ps α is the brightness of the background; this situationwill not last for much longer. Several imminent advances in near-infrared spectroscopy will allowmuch deeper observations than currently possible. In particular the long standing problem of thenight-sky is very close to being solved both by the launch of the JWST, and through photonic OHsuppression from the ground (Bland-Hawthorn et al. 2004; Bland-Hawthorn et al. 2008). Combinedwith advances in adaptive optics and NIR detector technology the prospect of detecting Ps α in thenear future is propitious, cf. Figure 10.The successful detection of Ps recombination lines has the potential to yield immediate ad-vances in our knowledge of several topics of interest. Observations of Ps recombination lines at thelocation of AGN jet-cloud interactions would provide direct confirmation that jets are composedof a pair plasma – a long standing problem which is still controversial (e.g. Celotti & Fabian 1993;Reynolds et al. 1996; Wardle et al. 1998; Hirotani 2005). We suggest an observing campaign of 35 –several classes of AGN, e.g. targeting the regions around the jets of blazars, offering a potentiallyunobscured view of the most energetic region of the AGN, and the possibility of Ps formation in theregions adjacent to the jet. Similarly observations of the radio lobes of AGN offer the possibilityof detecting the location at which the e + surviving the jet thermalise with the ISM.An immediate and direct advance in our knowledge of the origin Galactic e + would result froma detection of Ps emission from a class of Galactic sources such as microquasars. This would placedirect constraints on the significance of such sources the Galactic e + budget, and indirect constraintson the significance of other sources through comparison with the total e + budget from 511keVobservations. Similarly, such detections would place constraints on the astrophysical processesresponsible for the production of e + in the sources.Looking further into the future, one can envisage more ambitious experiments. For example,many models of dark matter invoke a super-symmetric dark matter particle. In this case thedark matter particle will annihilate (albeit with a small cross section), resulting in the eventualproduction of an e − - e + pair (see e.g. Boehm et al. 2004). Such a mechanism has been proposed toaccount for the Galactic 511keV radiation described above. If significant constraints can be placedon the astrophysical origin of Galactic e + this may have implications on the masses or existenceof super-symmetric dark matter particles. If dark matter were found to be a significant sourceof Galactic e + then one could in principle use observations of Ps recombination lines to infer themasses and density profiles of dark matter haloes. Such experiments are not feasible with anyenvisaged telescopes, but are a theoretically interesting possibility.
6. ACKNOWLEDGMENTS
We thank the referee for useful comments which have improved this manuscript. We thankAlan Marscher for advice on the calculation of the e + flux in AGN jets. JBH is supported by aFederation Fellowship from the Australian Research Council. REFERENCES
Anderson, C. D. 1933, Phys. Rev., 43, 491Baring, M. G., Harding, A. K. 2001, ApJ, 547, 929Beacom, J. F., Bell, N. F., Bertone, G. 2005, Physical Review Letters, 94, 171301Begelman, M. C., Blandford, R. D., Rees, M. J. 1984, Reviews of Modern Physics, 56, 255Berko, S., Pendleton, H. N. 1980, Annual Review of Nuclear and Particle Science, 30, 543Bland-Hawthorn, J., Buryak, A., Kolossovski, K. 2008, Journal of the Optical Society of AmericaA, 25, 153 36 –Bland-Hawthorn, J., Ellis, S., Haynes, R., Horton, A. 2009, Anglo-Australian Observatory Newslet-ter, 115, 15Bland-Hawthorn, J., Englund, M., Edvell, G. 2004, Optics Express, 12, 5902Blandford, R. D., Levinson, A. 1995, ApJ, 441, 79Boehm, C., Hooper, D., Silk, J., Casse, M., Paul, J. 2004, Physical Review Letters, 92, 101301Burdyuzha, V. V., Kauts, V. L. 1997, Ap&SS, 258, 329Bussard, R. W., Ramaty, R., Drachman, R. J. 1979, ApJ, 228, 928Canter, K. F., Mills, Jr., A. P., Berko, S. 1975, Physical Review Letters, 34, 177Cappellaro, E., Turatto, M., Tsvetkov, D. Y., Bartunov, O. S., Pollas, C., Evans, R., Hamuy, M.1997, A&A, 322, 431Cass´e, M., Cordier, B., Paul, J., Schanne, S. 2004, ApJ, 602, L17Celotti, A., Fabian, A. C. 1993, MNRAS, 264, 228Chan, K.-W., Lingenfelter, R. E. 1993, ApJ, 405, 614Chupp, E. L., Forrest, D. J., Higbie, P. R., Suri, A. N., Tsai, C., Dunphy, P. P. 1973, Nature, 241,333Clayton, D. D., Hoyle, F. 1974, ApJ, 187, L101Davies, R. I. 2007, MNRAS, 375, 1099Debenedetti, S., Corben, H. C. 1954, Annual Review of Nuclear Science, 4, 191Deutsch, M. 1951, Phys. Rev., 83, 866Dirac, P. 1933, Camb. Phil. Soc. Proc., 30, 150Dolgov, A. D. 2002, Nuclear Physics B Proceedings Supplements, 113, 40Dutra, C. M., Santiago, B. X., Bica, E. 2002, A&A, 381, 219Eisberg, R., Resnick, R. 1985, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles,2nd Edition (Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2ndEdition, by Robert Eisberg, Robert Resnick, pp. 864. ISBN 0-471-87373-X. Wiley-VCH ,January 1985.)Ellis, S. C., Bland-Hawthorn, J. 2008, MNRAS, 386, 47Furlanetto, S. R., Loeb, A. 2002, ApJ, 572, 796 37 –Furlanetto, S. R., Loeb, A. 2002, ApJ, 569, L91Gardner, J. P., et al. 2006, Space Science Reviews, 123, 485Ghisellini, G., Padovani, P., Celotti, A., Maraschi, L. 1993, ApJ, 407, 65Gillard, W., Jean, P., Marcowith, A., Ferri`ere, K. 2007, in ESA Special Publication, Vol. 622, ESASpecial Publication, 65–+Guessoum, N., Jean, P., Gillard, W. 2005, A&A, 436, 171Guessoum, N., Jean, P., Prantzos, N. 2006, A&A, 457, 753Guessoum, N., Ramaty, R., Lingenfelter, R. 1991, ApJ, 378, 170Hauser, M. G., Dwek, E. 2001, ARA&A, 39, 249Hernanz, M., G´omez-Gomar, J., Jos´e, J. 2002, New Astronomy Review, 46, 559Hernanz, M., Jos´e, J., Coc, A., G´omez-Gomar, J., Isern, J. 1999, ApJ, 526, L97Hirotani, K. 2005, ApJ, 619, 73Jean, P., Kn¨odlseder, J., Gillard, W., Guessoum, N., Ferri`ere, K., Marcowith, A., Lonjou, V.,Roques, J. P. 2006, A&A, 445, 579Kn¨odlseder, J., et al. 1999, A&A, 344, 68Kn¨odlseder, J., et al. 2005, A&A, 441, 513Leising, M. D., Clayton, D. D. 1987, ApJ, 323, 159Leventhal, M., MacCallum, C. J., Stang, P. D. 1978, ApJ, 225, L11Mannucci, F., Della Valle, M., Panagia, N., Cappellaro, E., Cresci, G., Maiolino, R., Petrosian, A.,Turatto, M. 2005, A&A, 433, 807Marscher, A. P. 1977, ApJ, 216, 244Marscher, A. P. 1983, ApJ, 264, 296Marscher, A. P., Jorstad, S. G., G´omez, J. L., McHardy, I. M., Krichbaum, T. P., Agudo, I. 2007,ApJ, 665, 232McClintock, J. E. 1984, ApJ, 282, 291Milne, P. A., Kurfess, J. D., Kinzer, R. L., Leising, M. D. 2002, New Astronomy Review, 46, 553Milne, P. A., The, L.-S., Leising, M. D. 1999, ApJS, 124, 503 38 –Mohoroviˇci´c, S. 1934, Astron. Nachr., 253, 93Murphy, R. J., Share, G. H., Skibo, J. G., Kozlovsky, B. 2005, ApJS, 161, 495Ore, A., Powell, J. L. 1949, Phys. Rev., 75, 1696Piran, T. 2004, Rev. Mod. Phys., 76, 1143Prantzos, N. 2006, aanda, 449, 869Puxley, P. J., Skinner, C. K. 1996, in Astronomical Society of the Pacific Conference Series, Vol.102, The Galactic Center, ed. R. Gredel, 439Reynolds, C. S., Fabian, A. C., Celotti, A., Rees, M. J. 1996, MNRAS, 283, 873Rieke, G. H., Lebofsky, M. J. 1985, ApJ, 288, 618Sakharov, A. D. 1967, Soviet Journal of Experimental and Theoretical Physics Letters, 5, 24Schlegel, D. J., Finkbeiner, D. P., Davis, M. 1998, ApJ, 500, 525Shanks, T., Georgantopoulos, I., Stewart, G. C., Pounds, K. A., Boyle, B. J., Griffiths, R. E. 1991,Nature, 353, 315Smith, R., et al. 2006, in Presented at the Society of Photo-Optical Instrumentation Engineers(SPIE) Conference, Vol. 6276, High Energy, Optical, and Infrared Detectors for AstronomyII. Edited by Dorn, David A.; Holland, Andrew D.. Proceedings of the SPIE, Volume 6276,pp. 62760R (2006).Steigman, G. 1976, ARA&A, 14, 339Storchi-Bergmann, T., McGregor, P. J., Riffel, R. A., Sim˜oes Lopes, R., Beck, T., Dopita, M. 2009,MNRAS, 394, 1148Sturrock, P. A., Baker, K. B. 1979, ApJ, 234, 612Tammann, G. A., Loeffler, W., Schroeder, A. 1994, ApJS, 92, 487Tavani, M., et al. 2009, ArXiv e-printsUsov, V. V., Melrose, D. B. 1996, ApJ, 464, 306Wallyn, P., Mahoney, W. A., Durouchoux, P., Chapuis, C. 1996, ApJ, 465, 473Wang, W., Pun, C. S. J., Cheng, K. S. 2006, A&A, 446, 943Wardle, J. F. C., Homan, D. C., Ojha, R., Roberts, D. H. 1998, Nature, 395, 457Weidenspointner, G., et al. 2008a, New Astronomy Review, 52, 454 39 –Weidenspointner, G., et al. 2006, A&A, 450, 1013Weidenspointner, G., et al. 2008b, Nature, 451, 159Wheeler, J. A. 1946, Ann. N. Y. Acad. Sci., 48, 219Wiese, W. L., Smith, M. W., Glennon, B. M. 1966, Atomic transition probabilities. Vol.: Hy-drogen through Neon. A critical data compilation (NSRDS-NBS 4, Washington, D.C.: USDepartment of Commerce, National Buereau of Standards, 1966)Wolfenstein, L., Ravenhall, D. G. 1952, Physical Review, 88, 279Yang, C. N. 1950, Physical Review, 77, 242Zurek, W. H. 1985, ApJ, 289, 603
This preprint was prepared with the AAS L A TEX macros v5.2.
40 – Λ (cid:144) Μ m f Λ (cid:144) ph s - m - Μ m - Fig. 11.— Comparison of the components of the simulated spectrum of Ps α emission from anAGN. The emission from the AGN is shownby the thick black line, and is based on observa-tions of NGC 4151 by Storchi-Bergmann et al. (2009). The Ps α emission line is shown by thedashed black line and is based on calculations of the e + production of 3C120 by Marscher et al.(2007). The near-infrared background is shown by the thin black line and is based on the modelsof Ellis & Bland-Hawthorn (2008). 41 –Fig. 12.— A background and continuum subtracted simulated observation of Ps α from an AGN.The simulations are shown with OH suppression by the thick black line, and without by the thingrey line. The dashed line shows the expected location of the Ps αα