A&A 397, 635-643 (2003)
P. von Ballmoos1 - N. Guessoum 2 - P. Jean1 - J. Knödlseder 1
1 - Centre d'Étude Spatiale des Rayonnements, 9 Av. du Colonel Roche, 31028 Toulouse Cedex, France
2 - American University of Sharjah, College of Arts & Sciences, Physics Unit, Sharjah, UAE
Received 2 August 2002 / Accepted 10 October 2002
Galactic maps of e-e+ annihilation radiation based on CGRO-OSSE, SMM and TGRS data have indicated the existence of an extended component at positive Galactic latitudes ( , ), in addition to the emission from the galactic bulge and disk (Purcell et al. 1997; Cheng et al. 1997; Milne et al. 2000; Milne et al. 2001). This Positive Latitude Enhancement (PLE) was first attributed to an "annihilation fountain" in the Galactic center (Dermer & Skibo 1997) but has since been the object of several models.
After discussing the observational evidence for the PLE, we investigate various models for the PLE: besides the scenarios proposed in the literature, we have introduced a number of models requiring relatively modest positron rates due to a local origin of the e-e+ emission (local galactic-, solar system-, earth- and spacecraft-environment origins). The various scenarios for the PLE are constrained in the light of the latest OSSE-SMM-TGRS data analysis results: we have looked at the possible positron production mechanisms as well as the annihilation conditions in the different physical environments (temperature and dust grain content) proposed for the positive-latitude region. By constraining those parameters, based on the recent limits for the line width and the positronium fraction, we found that some of the models can essentially be discarded. A number of other scenarios will have to await further measurements and maps, such as will be possible with INTEGRAL's SPI and IBIS instruments. We present a table/checklist of model-falsification criteria.
Key words: elementary particles - ISM: bubbles - ISM: clouds - ISM: supernova remnants
The positron's signature is the gamma-ray line at 511 keV that is emitted when it annihilates with an electron. Upon encountering their nemeses, positrons can either annihilate directly or form a positronium (Ps) "atom." In the first process, which can occur with free electrons, bound electrons, or electrons in grains, two photons are produced at 511 keV (plus whatever kinetic energies are available). In the second process, depending on the spin state of the positronium, the annihilation (disintegration) produces either two photons of equal energies (in the "para", or anti-parallel state, which occurs 25% of the time) or three photons (in the "ortho", or parallel state, which occurs 75% of the time) with a continuous distribution of energies between 0 and 511 keV. Depending on the physical conditions of the environment (temperature, ionization state, dust content, etc.), the annihilation of the positrons will proceed via several possible routes: direct annihilation with free or bound electrons (including those in dust grains) or positronium formation with free electrons, charge exchange with atomic and molecular hydrogen, helium, etc. (see Guessoum et al. 1997a).
Line emission at 511 keV from the Galactic Center region has been observed since the early seventies in balloon and satellite experiments. In two balloon flights from Argentina, Haymes' group at Rice University first measured a gamma-ray line at 476 26 keV (Johnson et al. 1972). Later it was suggested that the detected line was actually the annihilation line, but that the shifted peak could have resulted from the convolution of the broad energy response of the NaI scintillators with the Galactic Center spectrum consisting of a narrow 511 keV line and the accompanying orthopositronium continuum. In 1977, high energy-resolution germanium (Ge) semiconductors were flown for the first time on balloons, enabling scientists to establish the narrowness of the annihilation line at 511 keV, with a width of only a few keV (Albernhe et al. 1981; Leventhal et al. 1978). The eighties were marked by ups and downs in the measured 511 keV flux through a series of observations performed by the balloon-borne germanium detectors (principally the telescopes of Bell-Sandia and GSFC). The fluctuating results were interpreted as the signature of a compact source of annihilation radiation at the Galactic Center (see e.g. Leventhal 1991). Additional evidence for this scenario came initially from HEAO-3 (Riegler et al. 1981) reporting variability in the period between fall 1979 and spring 1980. Yet, during the early nineties, this interpretation was more and more questioned, since neither eight years of SMM data (Share et al. 1990) nor the revisited data of the HEAO-3 Ge detectors (Mahoney et al. 1993) showed evidence for variability in the 511 keV flux.
In Fall 1990, the imaging SIGMA telescope showed a strong feature in the spectrum of 1E 1740.7-2942, a source located close to the Galactic center (Bouchet et al. 1991). This emission appeared and vanished within days in the energy interval 300-700 keV. Stimulated by this observation, Mirabel et al. (1992) performed several radio observations of 1E 1740.7-2942 with the Very Large Array (VLA), revealing two radio jets emanating from the central compact object. Since the discovery of that first galactic "microquasar", several similar Galactic sources were detected by SIGMA and CGRO-BATSE. The spectral and temporal behavior of 1E 1740.7-2942 earned this source the nickname "great annihilator"; the data could in fact be explained by a pair plasma in the vicinity of a compact object. Yet, no narrow annihilation line from any of the sources (compact or diffuse) in the Galactic center region was observed by SIGMA (Malet et al. 1995). A review of the pre-CGRO/GRANAT observations is found in Lingenfelter & Ramaty (1989), a summary of the 511 keV situation during the CGRO/GRANAT era is in Kurfess et al. (1999).
Throughout the nineties, CGRO's Oriented Scintillation Spectrometer Experiment (OSSE) measured steady fluxes from a galactic bulge and disk component, but in 1997 a third component, the "Positive Latitude (Annihilation) Enhancement" (PLE) feature was identified and has since provoked a flurry of models and press releases. Combining the data from CGRO-OSSE, the Transient Gamma-Ray Spectrometer (TGRS) and Solar Maximum Mission (SMM) instrument, Purcell et al. (1997) produced a first and rudimentary map of the 511 keV positron annihilation line radiation showing a positive-latitude e-e+ annihilation feature. Depending on the method for deriving the flux of this feature, values between (integrated flux within the PLE region) and are obtained (model fit of a PLE component).
With the enhanced exposure of the current datasets (more OSSE exposure and reanalyzed TGRS data) Milne et al. (2000) found lower fluxes for the PLE while confirming its existence. The most recent review by Milne et al. (2001) changed the situation again rather considerably: 1) the map still showed some positive latitude excess, but much less than the earlier maps showed, as the flux of the emission was found to be photons cm-2 s-1, much less than previous levels; 2) the positronium (Ps) continuum emission of the region shows no local enhancement; or equivalently, as Milne et al. (2001) put it, there is "a deficit for positronium continuum" in the positive-latitude annihilation. We will also adopt the line width as a mild constraint, even though there has been no measure of it directly from the PLE; however, TGRS measured the width of the annihilation line from the Galactic Center region and found it to be narrow ( keV) (Fig. 3 of Teegarden et al. 1996), consistent with previous measurements (e.g. the GRIS balloon measurements, Gehrels et al. 1991); moreover, the spatial distribution of the radiation inferred by TGRS is in broad agreement with the more recent maps of OSSE (Harris et al. 2000).
|Purcell 1997||Purcell 1997||Cheng 1997||Milne 2000|
|TGRS + SMM||TGRS + SMM||TGRS + SMM|
|Long. centroid [deg]||-4||-2|
|Lat. centroid [deg]||7||8|
|Size [deg FWHM]||not published||not published|
Table 1 shows the evolution of the PLE measured parameters (flux, location, and size) since 1997. It must be stressed that all the values shown are model-dependent (dependent on analysis methods, model components included, etc.) - e.g. the errors in Purcell et al. (1997) are derived assuming only a single parameter. A more complete error analysis would reduce the significance of these parameters. Yet, aside from indicating its existence and substantial flux, the present measurements do not clearly point to the nature and characteristics of the positive-latitude feature; indeed OSSE's angular resolution is limited by its wide field of view ( ), and its scintillator energy resolution (of 50 keV at 511 keV) does not allow the line width to be measured. Interestingly, however, Table 2 indicates that the flux - and the significance - of the feature have decreased as the analysis techniques were refined more and more. Moreover, the existence of the PLE feature is questioned by the fact that no evidence for such a phenomenon has been observed at other wavelengths - at least not on a galactic scale.
It is thus of paramount importance that this feature be observed and measured precisely, as well as studied theoretically. If the feature is real, the background subtraction of older 511 keV measurements might have to be revisited since the PLE region is a privileged site for "off" pointings.
In this context, it might be (historically) noteworthy to point out a possible link between the PLE and the supposed variability of the 511 keV source at the Galactic Center as measured by balloon instrumentsin the early eighties.
Although the observations of these balloon spectrometers can already
be understood by their limited statistics, it is interesting to note
that a classical off-pointing for background subtraction - that is,
taking the same zenith angle as the target but an azimuth+180
will fall on the fountain region for GC pointings with high elevation
(low atmospheric absorption) for flights from Alice Springs. So if it
turns out that there really is 511 keV emission from the
fountain region, the azimuth+180
off-pointing strategy would
have resulted in a subtraction of the PLE flux from the GC signal.
This would have further weakened the already poor source statistics of
a balloon observation and could actually lead to the interpretation of
a source in an "off'' state. Table 2 summarizes the
history of the supposed "ON - OFF - ON'' state of the Galactic Center
511 keV source in relation to the off-pointing strategies of the
observations made with balloon-borne germanium spectrometers - note
the possible correlation between the background subtraction technique
and the "state" of the Galactic Center source.
There are two major constraints that may pose some difficulties for this model: 1) in such a hot environment (Dermer & Skibo 1997), the width of the 0.511 MeV line from the annihilation will be broader than that of the Galactic disk line emission (see Ramaty & Meszaros 1981; Guessoum et al. 1991), although this depends rather strongly on the dust content of the fountain; 2) it is quite difficult to prevent any continuum positronium emission (as now required by the latest PLE data analysis - see Milne et al. 2001) in such physical conditions, so the positronium (Ps) continuum fraction will not only be greater than zero, it will also be spatially varying across the whole region, from the disk to the top of the "fountain", an effect which INTEGRAL should be able to exhibit. We have run our program for positronium annihilation in a thermal environment (Guessoum et al. 1991, updated in Guessoum et al. 1997a) for a hot medium of various temperatures and grain fractions ( , as defined in Guessoum et al. 1991, where represents a total absence of grains, represents a density of dust equal to the average interstellar amount). We have found that if the dust is completely absent ( ), then the annihilation line produced is wide for T >a few times 105 K: ( keV when T > 106 K). If dust is present, with roughly normal amounts ( ), then the line is narrow enough ( keV), but the positronium fraction (which represents the fraction of positrons that annihilate via formation of positronium and indirectly gives a measure of the 3 continuum emission) is found to always be larger than 0.1. It is not clear from the Milne et al. (2001) paper what the PLE emission fraction is found to be (and with what uncertainties). Here we simply wish to point out that this quantity (which is inferred to be very low in the PLE but which can never be exactly zero, see Guessoum et al. 1991), can constrain the model and its physical parameters.
This model also predicts that the peak enhancement of the fountain's annihilation flux occurs >100 pc above the Galactic plane. Long-lived radioactivity is produced by supernovae and is convected upward with the gas flow. According to Dermer and Skibo, diffuse 1.809 MeV emission from 26Al should be observed at a flux level comparable to the INTEGRAL telescope's sensitivities.
It is difficult to falsify this model or compare it with present and/or future data, as its authors do not give any indication about the physical parameters of the medium where the positrons would annihilate, and this makes it impossible for us to constrain the model by calculating its predicted annihilation feature characteristics (line width and fraction). Moreover, no evidence for the transport of positrons in such environments exists from other observations or even for jets in other wavelengths.
In another variation on this burst scenario, Dermer & Boëttcher (2000) proposed a gamma-ray burst at positive latitude, which would cancel the need for positron transport. According to these authors the high-latitude annihilation could reveal a site of a past gamma-ray burst. If GRBs originate from (or are related to) the collapse of massive stars, then circumstellar clouds near burst sources will be illuminated by intense gamma radiation. If the energy intercepted by a single cloud is converted to pairs with a conservative 1% pair yield, past GRBs in the Milky Way would indeed be revealed by measurable annihilation radiation. Here again, the fraction constitutes a strong constraint (the width of the line can easily, and within various medium temperatures, ionization fractions, and dust content, be made to satisfy the constraint we have set, i.e. keV). A low value of in the PLE is best obtained, our simulations show, by making the medium as hot as possible, as fully ionized as possible, and as full of dust as possible, although a moderate (normal) abundance of grains is sufficient. In such a case (say K), the value of is found to be - still non-negligible.
Finally, it is worth noting that the high-latitude annihilation feature - and other localized hot spots of annihilation radiation that will be mapped in detail with INTEGRAL's instruments, could reveal sites of past GRB explosions.
The possibility that these sources may contribute to the 511 keV emission of the PLE should still be considered. Furthermore, the Gould belt is rich in molecular clouds which are potential sources of annihilation radiation by means of cosmic rays irradiating the cloud and reacting with ambient nuclei, thereby producing positron-emitting nuclei. Guessoum et al. (2001) have considered the 511 keV radiation from nearby giant molecular clouds and have determined the expected flux as a function of the cloud's mass and distance, as well as of the composition of the bombarding cosmic rays. Applying the results of that work to the Gould belt, one can conclude that unless the molecular clouds contributing to the annihilation radiation have a total mass of more than , or unless the cosmic rays are made predominantly of metals, in which case one needs clouds smaller by an order of magnitude, unless these conditions are fulfilled the Gould belt is unlikely to explain the enhanced annihilation.
Observations performed by de Geus (1992), de Geus & Burton (1991), and de Geus et al. (1989) show an interaction of the slow expanding shell of the Upper-Scorpius association with the Ophiuchus clouds. This shell is driven by stellar winds and, as suggested by de Geus (1992), by a supernova explosion of a star that would have occurred 1 to 1.5 Myr ago.
A 40 should produce about of 56Ni, 2.3 10 of 44Ti (Woosley & Weaver 1995) and of 26Al (Woosley et al. 1995). Even if only a small fraction of the positrons from 56Ni survive (0 to 10%), we estimate the rate of positrons penetrating the Oph clouds ranging between to s-1. This estimate takes into account the uncertainties in the age of the SN, it assumes that the positrons released by the above isotopes are diluted in the 10-15 km s-1expanding 1-4 pc thick shell (radius 40 pc). The amount of 26Al, considering the SN age (between 1 to 1.5 Myr) and its dilution in the 30 diameter shell would have made its 1.8 MeV emission undetectable for GRO-COMPTEL.
Annihilation in a molecular cloud has been treated by Guessoum et al. (1997b) who considered the Orion cloud and produced calculated annihilation line shapes; and as referred to previously Guessoum et al. (2001) considered the annihilation of positrons in giant molecular clouds such as Ophiuchus, and indeed considered this cloud (and others) specifically, but only in the context of cosmic-ray bombardment. It was found that the line width does remain within the constraints set by the TGRS measurements ( keV), although the line sometimes displays a wide ( keV) base surmounted by a narrower (2 keV) line. The positronium fraction, however, we find to be very difficult to reduce below about 0.4 (averaged over the cloud phases, although the filling factors are not always known to a good accuracy), even with strong dust content ( ).
In a future treatment, we plan to consider this scenario of wind-driven positron annihilation in nearby molecular clouds like Ophiuchus in greater detail, taking into account the propagation/diffusion of the positrons (by the supernova bubble) through the SN shell and into the cloud, and obtain predictions for 511 keV line fluxes and spectra.
Knowing all too well the difficulties of observational gamma-ray astronomy, particularly in the 511 keV band where a multitude of instrumental effects make background subtraction an extremely sensitive task, we have decided not to a priori exclude the possibility that the PLE could be an artifact. Even in this astrophysically uninteresting case, it is important to understand the local or instrumental origins of such an effect. Beyond the astrophysical implications, INTEGRAL's observational strategies and future gamma-ray instrumentation would largely benefit from such a lesson.
We have estimated the annihilation rate and flux from these "primary
positrons". For this we needed the flux of primary CR positrons
entering the solar system. Measurements of such particles are usually
made for energies higher than about 1 GeV, and the spectrum of these
particles is a power law (of index
see for example
Longair 1994) for high energies but flattens out around 1 GeV due to
solar wind modulation. CR protons have an integrated flux of about
1800 protons/m2/str/sec; electrons are fewer by about 2 orders of
magnitude, and positrons are less abundant than electrons by a factor
of 10 (for recent, accurate measurements of energy spectra of
electrons and positrons, primary plus secondary, at
see Boezio et al. 2000). For the ambient matter, we need the
density and the temperature in the disk for the various types of
particles (free electrons, neutral atoms, dust). For free electrons,
Petelski et al. (1980) give measurement data for ,
(and other quantities) at 1 AU, 10 AU, and 100 AU, which we
interpolate to obtain the following approximate expressions:
The cross section for e+-e- direct annihilation is cm-2, which combined with the above information gives a flux of emission of 511 keV photons of photons cm-2 s-1, which is several orders of magnitude lower than the PLE emission.
For neutral atoms in the disk, again by interpolating from the data of Petelski et al. (1980) we write the following approximate relation: cm-3. The cross section in this case is that of the "charge exchange" process ( ): cm-2. Integrating these quantities over the extent of the ecliptic ( AU), we obtain a rate of 511 keV of photons cm-2 s-1, which must be regarded as an upper limit, since this figure assumes a density of hydrogen that rises linearly with distance (and a constant ecliptic matter scale height).
Thirdly, we need to consider the annihilation of positrons on the dust. Observations indicate a total dust mass of g (Grün et al. 1997). Assuming typical dust grains (of radius , density , normal metallicity), one obtains a total number of dust grains of . This translates into an average dust grain density of cm-3, which implies a totally negligible contribution to any annihilation emission from the disk, especially since the positron-grain cross section is also very low: cm2, for the typical grain parameters we have adopted (see Guessoum et al. 1991; Zurek 1985).
There remains one possibility: that the thousand-fold more abundant primary CR protons would produce, through nuclear reactions with the ambient nuclei, enough secondary positrons to produce substantial annihilation from the disk. Using the above free-electron density as a measure of ambient proton density, a cross section of proton-proton production of positrons of 30 mb, multiplied by the yield in pions/positrons for each CR proton, and a positron mean free path of (at most) cm, we obtain a fraction of secondary positrons (to primary protons) of , which is many orders of magnitude lower than the primary positron abundance. This is indeed confirmed by the data of Boezio et al. (2000), which show the data for primary plus secondary positrons to be almost exactly equal to the ratio of primary positrons to primary protons, i.e. the negligibility of secondary positrons produced by the ecliptic disk.
We have concluded that in all of the above variations on the "ecliptic plane annihilation" scenario, although some 511 keV photons will be produced, the flux of such an emission seems to be largely insufficient to explain the observed PLE flux.
Artificial injection of positrons into that region of space was discovered in the eighties by SMM when radiation at 511 keV was detected from unshielded satellite-borne reactors (Rieger et al. 1989; Share et al. 1989). This "nuclear noise" cannot explain the PLE radiation simply because the latter is not a series of regular, short timescale events that could be linked to specific injections. Indeed, the positrons in that region (height km) would not survive more than a few hundreds or thousands of seconds, and would therefore need to be continuously resupplied.
On the other hand, natural injection of positrons into "plasma sheets" (in shells of inner and outer radii that depend on the positrons' kinetic energies) is known to occur, mainly by albedos of pairs produced by high-energy cosmic rays hitting the dense layers of the atmosphere (at a height of km). Indeed, the recent Alpha Magnetic Spectrometer (AMS) experiment aboard the International Space Station measured fluxes of positrons (along with electrons, protons, helium nuclei, etc.) and found surprising levels of energetic ( GeV) positrons at altitudes of 400 km or more (Alcaraz et al. 2000; Lipari 2002). It was thus tempting to investigate whether the annihilation of such positrons would produce an emission that would appear to come from a specific direction ofspace, namely the ecliptic, especially if the solar wind does rearrange the plasma sheets in such a way as to produce a symmetry with respect to the ecliptic plane.
It appears that the solar wind has too small an effect at such altitudes for it to significantly reshape the plasma sheets and give them a preferred direction of annihilation along the ecliptic. The spacecraft (CGRO in this case), being at about the same altitudes as the plasma sheets, would practically bathe in them and therefore not only see no preferred direction but moreover find no difference between the "on" and "off" directions of observations.
Finally, we should should point out that this scenario is one of the easiest to check with INTEGRAL, since the latter conducts 90% or more of its observations above the radiation belts. No PLE feature would then be observed with INTEGRAL.
CGRO's solar panels (and other observational constraints) did not allow OSSE observations of any region of the sky at any given time. Over many observations, the ecliptic plane is necessarily introduced as an "averaged" symmetry. We know that the earth's space environment is the principal source of background, although the net effect for a single observation might often be marginal (depending on CGRO's orientation). Over time, such symmetries might add up to a positive excess in what seems to be the ecliptic plane. The reported positronium continuum deficit in the PLE (Milne et al. 2001) is readily explained in this scenario: as the positrons are quickly slowed down by the dense spacecraft material, they will lack the necessary energy to induce charge exchange (Ps formation) with atoms - as a result, the annihilation produces mainly 511 keV photons.
Again in this scenario, INTEGRAL should not see any 511 keV PLE feature. In addition to being more sensitive, INTEGRAL's instruments have a different architecture and observation scheme, so that if artifacts appear at the sensitivity limit, they are unlikely to coincide with the PLE's "location".
|Figure 1: The "+'' data points refer to values of the parameters that produce satisfactory results for the constraints on and ; the "o'' points refer to parameters that violate one or both of the constraints. The shaded region is that where the parameter-space produces unsatisfactory results for and in the PLE.|
|Open with DEXTER|
|Model||Falsification Criterion||Falsification Possibility|
|Galactic Fountain||SPI: narrow 511 keV line; IBIS/SPI: constant over PLE||Yes|
|Pair Jet||Unfalsifiable Hypothesis (only non detection by SPI/IBIS)||No|
|Gamma-Ray Burst||in SPI/IBIS (no other features)||Yes|
|EGRET Sources||IBIS: non-detection of point sources + SPI: detection of the PLE||Yes|
|Modest starburst||SPI: emission not coincident with association/starburst regions||Yes|
|Ophiuchus Cloud||IBIS/SPI: PLE not coincident with position of Oph. cloud||Yes|
|Ecliptic Plane||SPI: non detection of the PLE out of the ecliptic plane||Yes|
|Space Environment||SPI: detection of a PLE||Yes|
|Sun-CGRO Symmetry||SPI: detection of a PLE||Yes|
A relatively simple way to, physically but not quite astronomically, achieve this is to make the medium fully ionized, in order to destroy the neutral hydrogen, which has the highest cross section for positronium formation. The hotter the medium, the fewer hydrogen atoms there will be; however, increases in the temperatures lead to a widening of the emission line, which is supposed to be "narrow", as we discussed previously. This latter constraint is dealt with best by increasing the dust content of the environment, assuming as usual that the line from grains has a fixed width of 1.8 keV for direct annihilation and 2.5 keV for annihilation via positronium, independent of the temperature (an assumption that is not quite experimentally confirmed either). We have thus run our program for various values of the temperature and the grain factor (the ratio of dust abundance in the medium compared to the normal ISM abundance) and determined the values of and in each case. Table 4 shows our results, and Fig. 1 shows the regions of the parameter space that would be consistent with the constraints from and .
The results show that a parameter space of roughly high temperatures ( K) and high dust abundances ( ) would satisfy the constraints on and . It is not clear, of course, whether such conditions could exist in the PLE region ( kpc above the galactic plane).
The combined analysis of IBIS and SPI data will enable us to discriminate between all the presently existing models, with an uncertainty only regarding one hardly falsifiable model (pair jet).
Table 5 lists the models of the previous sections, showing the criteria for their testing/falsification by INTEGRAL. Aside from the discrimination between the existing PLE models, we do not exclude that the high quality of INTEGRAL data will result in a new and probably totally unexpected view of the e+e- annihilation in the inner Galaxy.
N. Guessoum would like to acknowledge financial support from the American University of Sharjah (UAE) as well as the Centre d'Etude Spatiale des Rayonnements (Toulouse, France), where much of this work was conducted.